ASD TECHNICAL REPORT 61-566 THE UN I V E R S I T Y OF M I C H I G A N COLLEGE OF ENGINEERING Department of Engineering Mechanics V Final Report WIDE-TEMPERATURE-RANGE SPRINGSH. Gascoigne J. ^. Enns P. Kessel J. Ormondroyd, Project Supervisor ORA Project 02879 under contract with: DEPARTMENT OF THE AIR FORCE AERONAUTICAL SYSTEMS DIVISION CONTRACT NO. AF 33(616)-6284 WRIGHT-PATTERSON AIR FORCE BASE, OHIO administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR September 1961

:^t/i.~~~ "FOREWORD This report was prepared by The University of Michigan under USAF Contract No. AF 33(616)-6284. The contract was initiated under Project No. 9(8-7360), "Study of Materials Criteria for Precision High Temperature Springs," Task No. 73605. The work was administered under the direction of the Directorate of Materials and Processes, Deputy for Technology, Aeronautical Systems Division, with Mr. Richard R. Rowland acting as Project Engineer. This report covers work conducted from 1 February 1959 to 30 September 1961.

ABSTRACT Bimetallic spring systems of 40% nickel-60% iron alloy combined with Inconel X and type 304 stainless steel exhibit characteristics suitable for applications from -65F to 600~F. In this range the spring constant is held within +0.250. The general theory of bimetallic, temperature independent helical coil and Belleville type springs is presented. The bimetallic systems tested show that a temperature independent spring is feasible although working stresses must be maintained at relatively low levels. PUBLICATION REVIEW This report has been reviewed and is approved. FOR THE COMMANDER: RICHARD R. ROWLAND Chief, Applied Mechanics Section Metals and Ceramics Laboratory Directorate of Materials and Processes iii

TABLE OF CONTENTS Page I. INTRODUCTION 1 IIo THERMOELASTIC PROPERTIES OF SPRING-TYPE MATERIALS 3 Ao Glass and Ceramic Springs 3 B. Ferromagnetic Alloy Springs 4 III. HELICAL COIL COMPRESSION SPRINGS 7 Ao Introductory Discussion 7 B. Dynamic Shear Modulus of Selected Materials 8 C. Analysis of Temperature-Compensated Bimetallic Coil Spring Systems 10 1. General considerations. 10 2o Bimetallic series system. 11 3. Bimetallic parallel system. 13 Do Experimental Procedures and Results 14 1o Selection of test springs'. 14 2. Method of testing and determination of spring constants. 15 30 Results of individual springs. 16 4. Results for bimetallic spring systems. 17 5 Time effects. 18 E. Experimental Apparatus Used for Testing 18 F. Conclusions 19 G. Recommendations 19 IV. ANALYSIS OF BELLEVILLE SPRING WASHERS AS A MEANS OF PRODUCING A SPRING HAVING A CONSTANT SPRING-RATE VERSUS TEMPERATURE 21 A. Introduction 21 B. Theoretical Considerations 21 C. Elastic Moduli 24 Do Dimensionless Ratios k/ko versus temperature for 304 and 430 Stainless Steels and 31%, 42%, 50% Nickel-Balance Iron Alloys 25 E. Individual Washer Data 25 F. Combinations of Washers 25 1. Stacking by use of spacer plates. 26 2. Stacking by welding washers together. 26 Go Test Apparatus 27 iv

TABLE OF CONTENTS (Concluded) Page APPENDIX I. ANALYSIS OF BIMETALLIC TUBE-CORE SYSTEM 29 APPENDIX II. SAMPLE CALCULATIONS FOR BIMETAL COIL SPRING SYSTEMS 31 APPENDIX III. ANALYSIS AND EXPERIMENTAL PROCEDURES FOR DETERMINATION OF DYNAMIC SHEAR MODULUS 35 REFERENCES 39 v

LIST OF ILLUSTRATIONS Table Page I CHEMICAL COMPOSITION OF MATERIALS USED IN DYNAMIC SHEARMODULUS TESTS - Figure 1 Young's modulus versus temperature for iron-nickel family between 30% and 60% nickel. 40 2 Dynamic shear modulus versus temperature. 41 3 Dynamic shear modulus versus temperature, 42 4 40% nickel alloy compression spring. Wire diameter 0o125 in., outside diameter 0098 in. 43 5 40% nickel alloy coils. Wire diameter 3/32 ino, c = 9.0, n = 9-1/2, p = 9/64 in. (on left); wire diameter 3/32 in,, c = 9,0, n = 4-2/3, p = 9/64 in (on right). Note surface scaling. 44 6 40% nickel alloy coils. Wire diameter 3/32 in., c = 7,0, n = 15, p = 9/64 in. (on left); wire diameter 3/32 in,, c = 6.95, n = 10, p = 9/64 in.(on right). 44 7 Inconel X spring temper coils. Wire diamter 3/32 in., c = 9,0, n = 15, p = 9/64 in. (on left); wire diameter 3/32 ino. c = 9.0, n = 9-1/29 p = 9/64 in. (middle); wire diamter 3/32 ino, c = 9.09 n = 5, p = 9/64 in. (on right)O 45 8 Inconel X spring temper coils. Wire diameter 3/32 in, c = 7.0, n = 15, p = 9/64 in, (on left); wire diameter 3/32 in,, c = 7.09 n = 10 p = 9/64 in. (middle); wire diameter 3/32 in., c = 7.09 n = 5, p = 9/64 in. (on right), 45 9 Load versus deformation for Instron testing machines with test fixtures. 46 10 Stress-strain diagrams for 40% nickel-60% iron alloy at 70 and 700~F. Material annealed before tests at 1200"F for 2 hours. 47 vi

LIST OF ILLUSTRATIONS (Continued) Figure Page 11 Load-deflection output of coil spring as traced by recorder. 40% nickel alloy at 4400~F 48 12 Load-deflection output of coil spring as traced by recordero 40% nickel alloy at 695~F. 49 13 Spring constant-temperature diagram for 40% nickel alloy coil springs. 50 14 Spring constant-temperature diagram for 40% nickel alloy coil spring 51 15 Nondimensional spring constant versus temperature for 40% nickel alloy, Inconel X spring temper and 304 stainlesssteel coil springs. 52 16 Nondimensional spring constant versus temperature for 40% nickel alloy, Inconel X spring temper and 304 stainlesssteel coil springs. Lines indicate average of data shown in Fig. 15. 53 17 Plot of spring constant and nondimensional spring constant versus temperature for 49% nickel-balance iron coil spring. 54 18 Nondimensional spring constant versus temperature for bimetal coil spring systems tested, 5 19 40% nickel alloy c = 6.95, n = 10, d = 3/32 in., p = 9/64 in. paralleled with Inconel X spring temper c = 9,18, n = 9, d = 0.112 in o, p = 0.16 in. 56 20 40% nickel alloy c = 7.65, n = 8, d = 3/32 in., p = 9/64 in. paralleled with 304 stainless steel c = 11.17, n = 8, d = 3/32 in., p = 9/64 in. 56 21 Stress relaxation diagram. 57 22 Spring constant "relaxation" diagram. 57 23 Instron testing machine type TTCLM1. 58 vii

LIST OF ILLUSTRATIONS (Continued) Figure Page 24 Instron testing machine table model Type TM with associated furnace and control equipment. 58 25 Instron testing machine TTCLM1 with furnace and test fixtures in place, 59 26 Spring-loading apparatus. 60 27 Lower test fixtures showing spring. 61 28 Schematic diagram of testing apparatus. 62 29 Schematic diagram of furnace control. 63 30 Parallel and series stacking of Belleville spring washers. 64 31 Geometrical notation of Belleville spring washers. 64 32 Dimensionless ratios k/ko and E/Eo versus temperature for 50% nickel-balance iron alloy where ko and Eo are values of spring constant and elastic modulus at 70~F. 65 33 Elastic modulus versus temperature for 430 stainless steel. 304 stainless steel and 50% nickel-balance iron alloy. 66 34 Dimensionless ratio k/ko versus temperature for 430 stainless steel, 304 stainless steel and 50% nickelbalance iron alloy. 67 35 Dimensionless ratio k/ko versus temperature for 42% nickel-balance iron and 30% nickel-balance iron alloys. 68 36 Dimensionless ratios k/ko and E/Eo versus temperature for 430 stainless steel where ko and Eo are values at 700F. 69 37 Biaxial state of stress, 70 38 Load versus deflection for 42% nickel-balance iron alloy washers, 71 viii

LIST OF ILLUSTRATIONS (Continued) Figure Page 39 Load versus deflection for 42% nickel-balance iron alloy washers. 72 40 Test load versus test fixture deflection for 5/16-inodiameter pull rod, load cell "C." 73 41 Load versus deflection for 430 stainless steel washers at 70~Fo 74 42 Load versus deflection for 50% nickel-balance iron alloy washers at 700Fo 75 43 Load versus deflection for 304 stainless steel washers at 70TFo 76 44 Load versus deflection for 31% nickel-balance iron alloy washers at 70TFo 77 45 Load versus deflection for 42% nickel-balance iron alloy washers at 70(Fo 78 46 Load versus deflection for 50% nickel-balance iron alloy washers at 70~Fo 79 47 Load versus deflection for 304 stainless steel washers at 70 Fo 80 48 Load versus deflection for 304 stainless steel washers at 70oFo 81 49 Load versus deflection for 430 stainless steel washers at 700Fo 82 50 Load versus deflection for 430 stainless steel washers at 700Fo 83 51 Belleville spring washers stacked using spacer plates. 84 52 k/ko versus temperature for washer combinations using spacer plates 85 53 k/ko versus temperature for washer combinations using spacer plates~ 86 ix

LIST OF ILLUSTRATIONS (Concluded) Figure Page 54 Belleville spring washers stacked by means of welding. 87 55 Belleville spring washers stacked by means of welding. 87 56 k/ko versus temperature for washer combinations stacked by means of welding. 88 57 k/ko versus temperature for washer combinations stacked by means of welding. 89 58 k/ko versus temperature for washer combinations stacked by means of welding. 90 59 k/ko versus temperature for washer combinations stacked by means of welding. 91 60 Coefficients of thermal expansion versus temperature for 430 stainless steel and 42% nickel-balance iron alloy, 92 61 Bimetal system composed of Inconel X thin-walled tubing 0.09375 in. ID, 0.119 in. OD with core 40% nickel-balance iron alloy 0.09375 in, diameter. Outside diameter lo0 in,, n = 9-1/2. View before test. 93 62 End detail of Inconel X-40% nickel-balance iron alloy bimetal tube-core configuration. Note core and jacket. 93 63 Spring constant versus temperature for Inconel X-40% nickel-balance iron alloy tube-core configuration coil spring. Initial heat treatment at 1200F for 2 hours. 94 64 Coil spring definition sketch, 95 65 Schematic diagram of torsion pendulum apparatus. 96 66 Shear modulus testing at -11O0Fo 96 x

LIST OF SYMBOLS AND DEFINITIONS k spring constant or spring rate usually expressed in pounds per inch. of deflection (lb/in.) ko reference spring constant taken at 700F,unless otherwise stated, lb/ino ke equivalent spring constant (lb/in.) G shear modulus of material, lb/in.2 Go reference shear modulus taken at 70~F, unless otherwise stated, lb/ino T temperature, ~F mG thermoelastic coefficient based on shear modulus defined as 1 AG o1 Go AT' mk thermoelastic coefficient based on spring constant of individual spring defined as 1 Ak mk = ko AT coefficient of linear thermal expansion defined as A 1 Al FC^ = ~, OF 1o AT where 1o is a reference length, dimensionless length ratio. a normal stress, lb/in.2 Poisson's ratio T shear stress, lb/in.2 normal strain, in./ino d coil spring wire diameter, in., derivative n number of active coils in helical coil spring xi

P force exerted on spring, lb. 5 over-all spring compression, ino D mean coil diameter of spring R mean coil radius of spring = D/2, c spring index defined as c = D/d t time, linear dimension E Young's modulus of elasticity e 1 TE thermoelastic coefficient of Young's modulus, OFl E AT xii

I. INTRODUCTION The problem of the wide-temperature-range spring, of prime importance to the aircraft industry in fuel-control systems, has been a subject of research for many years. One of the early studies, supported by the National Advisory Committee for Aeronautics, by Keulegan and Houseman at the National Bureau of Standards (NBC Research Paper No. 531, 1933), was on thermoelastic coefficients of spring-type alloys. The temperature range that they covered was -60~ to +120~F. The temperature range proposed by the Aircraft Control Industry for this project was -65~ to +1000~F, with an upper limit of +450~F as a first objective. These limits have been primary guides to this program, along with the understanding that, whatever the system, it must be simple and of a physical size within the realm of the usual coiled type of spring. Also, because elastic strain in general tends to change to plastic strain at elevated temperatures, the relaxation properties of the system must remain realistic. Three main ideas were considered at the beginning of this study, all intended to counter the loss in material stiffness with temperature riseo (a) a change in the geometry of cross section of an elliptic tube due to thermal pressures created by the fluid within; (b) a bimetallic system utilizing differences in linear thermal expansion; and (c) a multi-material system utilizing positive and negative thermoelastic materials. The geometric approach, (a), was considered analytically and turned out to be quite difficulto No satisfactory solution was derived which related the internal fluid pressure to dimension changes in the principal axes of tubular cross section, All experimental evidence indicated that the wall thickness required to give an effective change in cross section with the stipulated thermal pressure changes were too thin to support any appreciable load. Therefore this phase of the program was discontinued, For (b), a simple, bimetallic-thermal expansion device in the form of a cantilever beam was analyzed. Such a system cannot result in a temperatureindependent spring rate unless one of the two materials has a positive thermoelastic coefficient, because the thermoelastic coefficients for ordinary springtype alloys are about ten times larger than their thermal expansion coefficients, The stiffening effect derived from thermal expansion is thus not sufficient to compensate for the loss in stiffness due to two materials with negative thermoelastic coefficients. For (c), while for many years it has been known that certain iron-nickel alloys in the ferromagnetic state have a positive thermoelastic coefficient, nothing in the literature indicated that such alloys have been applied to the Manuscript released by authors 30 September 1961 for publication as an ASD Technical Report

problem of the wide-temperature-range spring. Certain alloys of this family, such as Ni-Span C, have been developed with a thermoelastic coefficient of zero over the temperature range -60~ to +120~F. No spring-type alloy seems to be available whose isoelastic behavior goes past 200~F. However, in the above iron-nickel series, alloys with positive thermoelastic coefficients of a much wider temperature range are known. Thus the combination of plus and minus materials to achieve a constant spring rate over a wider temperature range seemed logical. The investigation of such systems in coiled and Belleville spring form became the major effort of this project. Nonmetallic materials with anomalous thermoelastic properties, such as graphite, glasses, and ceramics were investigated as discussed in the next section. It was concluded that, while their thermoelastic behavior might be very promising, their structural properties are insufficient. 2

II. THERMOELASTIC PROPERTIES OF SPRING-TYPE MATERIALS The elastic stiffness constants of solids vary inversely with atomic spacing, and almost all solid metals expand on heating; thus, roughly speaking, thermal expansion results because it is easier to increase interatomic spacing than to decrease it. The observed decrease in the elastic moduli with increasing temperature is hence to be expected for all such metals. These properties appear so basic that it is hard to conceive what could account for a vanishing or even negative expansion coefficient of some solid materials. Materials known to vary from the above basic behavior of differing degrees are pure graphite, certain glasses, and the ferromagnetic alloys. The negative thermal expansion coefficients of graphite goes well beyond 1000~F, and from this standpoint graphite would be a most promising material. However, the maximum permissible stresses for pure graphite are far below thoseof the usual springtype metals. Since the energy-storage capacity of springs is an important practical parameter, and the energy stored is proportional to the square of the stress springs made from any known graphite material would be prohibitive in size. Future study of materials among which graphite is an important component may result in a practical spring material. This aspect was not considered further. A. GLASS AND CERAMIC SPRINGS The feasibility of glass or ceramic springs was investigated for this project by Dr. E. B. Shand, of Corning, New York. Dr. Shand is a technical consultant and author on this subject. The following is a short summary of his investigation. The silica network in the glass structure tends to produce a modulus of elasticity which increases with temperature. As modifying ions are introduced into the composition, the modulus increasingly tends to droop with rising temperature. By suitable choice of composition, an aluminosilicate glass-Corning Noo 1723-has been produced whose Young's modulus increases linearly from about 11.8 x 106 psi at 75~F to 11.9 x 106 psi at 1150~F. Over the same temperature range the rigidity modulus increases from about 4,7 x 10 to 4.8 x 106 psi. Poisson's ratio for this glass is given as 0.234 to 0.242. The elastic moduli of ceramic materials tend to decrease with temperature. A particular ceramic called Mullite is the most stable. Its Young's modulus decreases from about 20. 106 t x 1 to 20 x 106 psi over the same 1000~F temperature rise, From the structural standpoint, both materials are brittle and hence ex3

tremely notch-sensitive. Ordinarily reported working stresses are of little value since the flow level is so important, and this differs widely for different specimens. Also, these materials are very sensitive to impact loading because they are so brittle. The over-all effect results in a fairly low permissible working stress compared to the metal alloys. Analysis shows that energy stored in a unit volume of spring is the product of the specific resilience of the material and the efficiency of loading. Specific torsional resilience is given by T2/2G, and is the criterion of the material for torsion-spring applications. T is taken to be the permissible working shear stress and G, the rigidity modulus. An approximate computation shows that a coil spring, 1 in. OD and 3 in. long, made from a material of specific resilience of 10 in.-lb/in3, can store roughly 4.5 in.-lb of energy. For a spring rate of 40 lb per in. deflection, the maximum spring load will be slightly under 20 lb, For the above-mentioned aluminosilicate glass, a specific torsional resilience of 20 in.-lb/in. is considered reasonable up to about 750~F. At 1000~F (probably because of relaxation behavior), this value would have to be greatly reduced. For ceramics, available data on breaking stresses for the conditions here considered are entirely inadequate, according to Dr. Shand. He estimates that the specific resilience may range from 12 to 20 in.-lb/ins At room temperature the specific resilience of good metal springs is about 160 in.-lb/in? However, this too has to be decreased according to the maximum operating temperature, and so the 8:1 unfavorable volume ratio of metal to glass quoted by Dr. Shand would actually become much less. A basic materials study of glasses and ceramics with the intent of gaining in springlike properties should be considered in any new program on wide-temperaturerange springs. B. FERROMAGNETIC ALLOY SPRINGS The thermoelastic properties of the Ni-Fe system has been reported by W. Koster (1) from 100% Ni down to 28% Ni, with the remainder as Fe. A number of Young's modulus E vs. temperature T curves from his paper are shown in 1 dE Fig. 1. The range of positive thermoelastic coefficient (e = E dT) below the Curie temperature (the temperature at which a ferromagnetic material becomes paramagnetic, indicated by arrow) is to be noted. The Ni-Fe alloys whose spring data are reported on below were selected with Fig. 1 as a guide. The region of positive slope in these curves is generally explained as due to the fact that here ferromagnetic contraction exceeds thermal expansion. The known isoelastic alloys derived from the Ni-Fe system by the addition of minor constituents fails to meet the isoelastic temperature range of present interest. An example of this is Ni-Span C, of composition 42% Ni, 2.5% Ti, 4

5-5% Cr, 003% C and the rest FeO The manufacturer of this material considers its isoelastic range only between -58~F and +1220F. By comparison the 40% Ni60% Fe curve of Fig. 1 shows a region of positive slope extending over about 4500F. Achieving an effective isoelastic range of 450~F from this material combined with an ordinary spring-type alloy with negative thermoelastic properties seems to be a direct possibility. Nothing in the literature indicates that this approach has been investigated, Bimetallic spring systems of this type, both in helical and Belleville form, were studied in this program and the results are reported in IIT-D and IV-F. 5

IIIo HELICAL COIL COMPRESSION SPRINGS Ao INTRODUCTORY DISCUSSION To use the positive thermoelastic coefficient of the ferromagnetic alloys previously mentioned, the type of mechanical spring best suited to experimental studies had to be selected. Although torsion-bar springs are easy to test using a torsion pendulum with an associated furnace for elevatedtemperature and a cold chamber for low-temperature testing, we wanted to use a more common type of spring: either or both helical coil and Bellevilletype springso The BGR Division of the Associated Spring Corporation, located in Plymouth, Michigan, agreed to fabricate any springs which might be required, and to give technical assistance during the duration of the projecto We found the existing literature insufficient, and in some cases contradictory, regarding thermoelastic data (modulus variation with temperature), and therefore decided to determine experimentally the variation in shear modulus with temperature of materials possibly suited to spring applications. Since the spring constant of coil springs with relatively low coil pitch angle is proportional to the shear modulus, such data are necessary for proper analysis of a bimetallic spring system. The dynamic shear modulus-temperature variation of 15 materials was determined using a torsion pendulum, with the results reported in this section. As a result of the torsion-pendulum tests, 4o0 nickel-60% iron alloy, Inconel X and 304 stainless steel were the materials selected for detailed evaluation. Next, several coil springs were fabricated and tested statically to see if the results agreed with those previously obtained by a dynamic testo The general trend of modulus variation was the same with the exception that the thermoelastic coefficients were substantially different. This result has been found in previous work (2), and although not at first considered critically important, came to be regarded very seriously as the work progressed. To determine the thermoelastic coefficient required in coil-spring calculations, several sets of springs were tested, in which the spring index and number of active coils were varied to see if there was a dependence on the geometry of the spring. One possible reason for such a dependence is that the stress distribution in the cross section of the wire varies with the spring indexo This dependence was substantiated only in the 40% nickel alloy and it is relatively slighto Finally, on the basis of the results of tests on individual springs, coaxial (parallel) spring systems were designed, fabricated, and tested. Each spring combination tested resulted in a system in which the spring con7

stant remained essentially constant over a temperature range far greater than any single-alloy spring presently commercially availableo The limited amount of relaxation testing indicated no serious problems below 5000F, but considerably more relaxation testing should be doneo Bo DYNAMIC SHEAR MODULUS OF SELECTED MATERIALS The dynamic shear moduli of the materials proposed for use in a bimetallic system were measured in a conventional manner using a torsion pendulum. The results of this work are shown in FigSo 2 and 3o The nominal chemical composition and heat treatment for these materials is given in Table Io The materials that show an increase in shear modulus with increasing temperature are 36% nickel alloy, 39% nickel alloy, and 40% nickel alloy. The 49o nickel alloy tested exhibited nearly constant modulus until about 600~F, rising until approximately 750~F, and then decreasing Of these materials in the iron-nickel family, 40 nickel was considered to show the most promise of utility in a bimetal system, due to the somewhat higher temperature possible until a decrease in shear modulus results. This material was selected for detailed investigation, but another member of the iron-nickel family could have been selected just as well. For example, 39% nickel alloy appears to have a greater temperature range in which the slope is constant and hence a constant thermoelastic coefficient over a wider rangeo Also, the so-called "Iso-Elastic" material has constant modulus to slightly over 200OFo This material exhibited the most constant modulus of the materials tested but had a very limited range of temperature independence. Note also in FigSo 2 and 3 that all the conventional spring materials have shear moduli which decrease with increasing temperature The increasing shear modulus of one material coupled with the decreasing shear modulus of another will possibly result in a system in which the spring constant is insensitive to temperature over a relatively wide temperature range. Several comments are in order regarding Figso 2 and 3~ The absolute values of the moduli as calculated by Eq. (25) (see Appendix III) agreed with most of those in the literature with the exception of 304 stainless steelo As a result of testing and subsequent calculation by Eq. (25), a shear modulus of 9080 x 106 lb/ino2 was found at room temperatureo Most of the published data give a room-temperature shear modulus of between 11 x 106 and 11.5 x 106 lb/ino 2 The data and calculations were rechecked with no indication of error. Apparently some mistake had been made in experiment (probably in period measurement of the oscillations), resulting in an erroneous valueo In all the calculations that follow the room-temperature shear modulus for 304 stainless steel was taken as 115o x 106 lb/ino2o The 40% nickel alloy tested, also resulted in a room-temperature modulus somewhat lower than that published by the International Nickel Companyo However, an independent check was made since tension test stress-strain data were available (see Figo 10)o Using the equation G = 2( — and assuming 8

TABLE I CHEMICAL COMPOSITION OF MATERIALS USED IN DYNAMIC SHEAR-MODULUS TESTS Material Composition Condition 1. 430 stainless steel Cr 18 — _ 2. Hy Mu 80 Ni 79, Mo 4 Annealed at 1200~F Fe 18 _+ Si Mn, etc. __ 35 Iso Elastic Special Ni 3537,. Cr 7, C o05- 15 Mo o.35-75, Mn.45o75 4. 49% Nickel (Simonds) 49 Ni, 50 Fe Annealed at 1200~F _+ Si, Mn, etco 5o "Hy Per 49" 48 Ni, 50 Fe Annealed at 1200~F 49% Nickel (Hy Per) + Si, Mn, etc. 6. 40%o Ni Alloy 40 Ni, 60 Fe Unaged nominal 7. 39% Ni Alloy 39% Ni, 61 Fe Unaged nominal. 8o S-816 Co 40-44, Cr 19-21 Annealed National Standard Co. Ni 1921., Fe 5 Mo 305-4.5, Cb 3-45 w. -. -___ 9~ NS-25 Co 50, Cr 1.9-21 Annealed National Standard Co Ni 9i-1 W 14=16 Fe 3 10 Inconel X Co 1, Cr 14-17 Annealed National Standard Co. Ti 2-2.5 Ni 69...::...... Fe 5,9 11. Haynes 25 Ni 10, Cr 20, W 14-15 Mn 1.4, Si.0,5 Ti 0.15 ___Bal Co___ 12 Tantaloy Ta 92.5 W 7.5 20% cold-drawn 13o NS-A-286 Cr 13o5 1.6, Ni 24-27 Annealed National Standard Coo Mo 11.,o759 Ti 1.75-2.25 V.1=-5, Al.35, Bal Fe 14. 304 stainless steel Cr.l9, Ni 9 ___ 9

p = 0.28, the room-temperature value of the shear modulus was calculated to be 6,93 x 106 lb/ino2 which agreed with the torsion-pendulum result. C. ANALYSIS OF TEMPERATURE-COMPENSATED BIMETALLIC COIL-SPRING SYSTEMS lo General Considerations. —Since spring elements may be combined in two basic ways, series and parallel arrangements (with the possibility of further combinations of these basic schemes), it is of interest to discuss the utilization of such systems. For a multi-spring system the series combination is one in which the same force is exerted on each componentO When more springs are added in series to an existing system the over-all stiffness, or force per unit deflection, is reducedo Excluding problems of mechanical stability when the system, or some part of the system, is under a compressive force, any stiffness, or spring constant, is possible simply by the addition of more springs in series, Of course, the more springs added, the softer is the resultant system, In a parallel arrangement the over-all deformation of each spring element is the same and adding more springs in parallel to an original system increases the system stiffness. Here mechanical stability is usually not a consideration so that in some ways the parallel arrangement may be more satisfactory, The stability mentioned here is in the sense of mechanical buckling as a result of some slenderness index (perhaps the ratio of length to over-all transverse dimension) being too large. But there are other stability problems having to do with nonlinear softening springs that are acting as part of an oscillating system. Here one can get unstable motions in which the amplitude of motion. grows prohibitively large due to nonlinear spring characteristics, Fortunately, conventional coil springs do not show this softening character and hence this oscillatory stability is not an issue, When some form of internal or external guide is provided to prevent buckling or when the external dimension perpendicular to the axis of the spring is limited due to space restrictions, the series arrangement may be quite usefulo If these conditions do not prevail or if quite a stiff spring is required, a parallel arrangement may prove most beneficial. When conditions limit the volume occupied by the spring, a parallel coaxial system may be considered, as one spring sits inside another, having common axial center lines, For example, see Figs. 19 and 20, Several types of problems involve the effect of temperature, First, there is the elevated-constant-temperature spring problem. Whatever the temperature may be, the spring must function properly, depending on the applicationo Usually a high-temperature spring must be free of "load loss" or relaxation at a relatively high stress, have good fatigue properties if cycling is incurred, and have a prescribed spring constant at the elevated temperature in question, Further, in many high-temperature spring applica10

tions the spring constant should be the same over quite a wide range in temperatureo The initial objective of this project was to develop a constantstiffness spring to operate from -65~F to 450~F with 10000F as a prospective goal. As previously pointed out, the shear moduli of all the common hightemperature spring materials, Inconel X, A-286, S-816, Haynes 25, and NS-25, decreasing as temperature increases. There is thus no hope that these materials alone can compose a system of constant stiffness for variable temperatures. Combining a material which has a stiffening characteristic with increasing temperature with one which decreases in stiffness is one solution to this problem. Of course, the ideal situation would be to have both materials increasing or decreasing linearly in stiffness over a temperature range sufficient to cover the desired temperature range. Looking at Figs, 2 and 3, it will be noted that most of the materials decreasing in stiffness do so in a relatively linear fashion. The 36%, 39%, and 40% nickel ferromagnetic alloys increasein stiffness linearly over a temperature sufficient to be of considerable interest. One would probably select the ferromagnetic alloy that has the greatest linear modulus-temperature characteristic so that, when combined with a material that decreased linearly in stiffness, the result could be a temperature-independent system, 2, Bimetallic Series System.-Let a system composed of two, smallpitch-angle, helical coil springs arranged in series (placed end to end) be subjected to an axial compressive forceo The ratio of the applied force to the corresponding deflection of the individual springs is commonly called the spring constanto For the series arrangement consisting of two springs, the equivalent spring constant can be written as 1 1 1 or k kk2 (1) ke kl k2 kl + k2 where kl and k2 are the spring constants of the individual springs, and ke is the equivalent spring constant. The temperature characteristic slope is found by taking the first derivative with respect to temperature, which is, after some reduction, 2 dk2 2 dki dke k dT + k2 dT dT (k1 + k2)2 From elementary spring theory (3), Gd k = 8nc3 11

where G = shear modulus of material, d = spring wire diameter, n = number of active coils, and c = spring index; ratio of mean coil diameter to wire diameter. dk _ 1 dG dd d — _ d + G dT 8nc3 dT dT dk = Godo- r dG +1 dd dT 8nc _Go dT do dT When n = number of actual turns (assumed constant) c = - (assumed constant) d But 1 dG d = mG = thermoelastic coefficient of G Go dT 1 dd =1 d = =coefficient of expansiono do dT Therefore dk = o + mG (3a) For a spring constant, ke independent of temperature - k 2ok2o r2 + + k2k + o 1 + mG1 =0 dT Therefore 1ko0 2+m + m k20 i0al + m = 0 If dlo = d20 Dlo = D20 C1 = 02 12

G10 + m - 1 + m7i ~andu ~n n2 and n2 = _o (o+mG) (4) nj G1o ( a2+mG2) This equation relates the material properties to system geometryo Note in Eq. (4) that if both materials have positive coefficients of linear expansion, and if the thermoelastic coefficients are larger in magnitude than the expansion coefficients (which are assumed positive), then one material must have a positive thermoelastic coefficient and one a negative thermoelastic coefficiento Also, if the thermoelastic coefficients mG, and mG2 are constant as well as the thermal expansion coefficients cl and a2, the ratio n2/ni is constant, This is highly desirable as it would be very difficult to vary the number of active coils as a function of temperatureo Some experimental work was done with series bimetallic springso But most of the results were not encouraging because, during the early stages of the work, accurate information on the thermoelastic coefficients was not available. There was no time for experimental work to validate the theory presented above; more work in this area is definitely neededo 30 Bimetallic Parallel Systemo —Instead of placing two coils end to end, let one be nested inside the other to form a parallel arrangement where both springs are of the same free lengths Making the springs coaxial decreases the volume required for the bimetallic system and is done here for that purpose. The springs could be placed side by side. For this arrangement, the equivalent spring constarnt is ke =- + k (5) Again taking the derivative with respect to temperature, dke dkl.,d dk2 d Gd + d G2dg (6) dT dT *dT dT T 8nicl dT n8n2c After considerable reduction, one can show that for a temperature-independent spring, with the same approximations as in the series analysis, (2 = _(d2 o (a2+mG2) 2/Go ( DW dlo (a9+mG) n2/ni where D2o and Dio refer to the mean coil diameters of the two springso Equation (7), while more involved than Eqo (4) has the same structure, one re13

lating material properties to geometry. Once the particular materials are selected, one can vary the number of active coils, wire diameter, and mean coil diameters for the combination until the equation is satisfied. There is no theoretical restriction on the number of different combinations that can satisfy Eq. (7)~ Physically, certain combinations satisfying Eq. (7) will not be possible due to interference of the two coils if a coaxial arrangement is used. Figures 19 and 20 show two combinations tested. An interesting parallel combination is one shown in Figs. 61 and 62. Here a coil spring is fabricated from a material with negative thermoelastic coefficient in very-thin-walled tube form with the inside filled with a material with positive thermoelastic coefficient. The analysis for this system appears in Appendix I. This scheme has the advantage of stressing the tube to a higher level (usually the negative thermoelastic materials have much higher stress capacity than the ferromagnetic materials) than the central core, providing a protective jacket for the temperaturecorrosion-sensitive nickel alloy as well as a convenient spring package. The results of the tests for this spring are given in Appendix Io D. EXPERIMENTAL PROCEDURE AND RESULTS 1. Selection, of'- Test Springs - The''Qst. promising materials appeared to be 40% nickel alloy, Inconel X, and AISI type 304 stainless steel. The former is of the ferromagnetic class with positive thermoelastic coefficient, and the latter two materials have negative thermoelastic coefficients. The thermoelastic coefficients of Inconel X and 304 stainless steel were different enough so that, when combined with the 40% nickel, most sizing problems could be solved by either a series or parallel combinationo Several sets of springs were fabricated and preliminary tests were conductedo Here the coil springs were tested essentially statically using the test apparatus described in Section E. The shear moduli of the materials tested were calculated using Eq. (3) and the coil-spring static shear modulus versus temperature was plotted. Calculations of the thermoelastic coefficients were made from these data; comparison showed that the thermoelastic coefficient based upon the coil spring data was consistently less, in an algebraic sense, than that calculated on the basis of the dynamic shear modulus tests. One of the first 40%0 nickel alloy springs tested is shown in Fig. 4. At this point it was decided to fabricate a set of springs of each material to be investigated with the spring index and the number of active coils as parameters By this it could be determined if the thermoelastic data were dependent on a spring-size parametero Here the 40% nickel alloy springs had nominal spring indices of 7, 9, and 11 with several different numbers of active coils. The Inconel X springs had nominal indices of 7 and 9 and different numbers of active coils, Some of these springs are shown in Figs. 58. Since the 304 stainless steel was considered to be an alternate neg14

ative thermoelastic material, no new springs of this material were fabricated in this phase of the program. With few exceptions, the springs fabricated were made with two solid turns on each end so as to eliminate end effects (see definition sketch in Fig. 64) o The 40% nickel alloy was secured in bar stock and drawn into wire form by the Hoskins Manufacturing Co., Detroit, Michigan. The Inconel X spring temper wire was obtained from National Standard Co., Niles, Michigan. This material has good strength and relaxation properties up to a maximum of 650~F to 7500F. See Ref. 4 for information about this material, 2. Method of Testing and Determination of Spring Constants.-Since heat treatment has a pronounced effect on the behavior of springs, a standard heat treatment was given to each of the test springs before testing. All coil springs tested, unless otherwise stated, were heated to 1000~F and held at that temperature for a period of two hours and slowly cooled in air. As can be seen from Figs.26 and 28, the load-carrying components of the testing apparatus, namely, the load cell, pull rod, and holding fixtures, act as a spring in series with the test spring. It was therefore necessary to consider several problems associated with the determination of the spring constant of the test spring. First, since one has essentially two springs in series, the testing apparatus and the test spring, the load-deformation output shown on the recorder (see Fig. 28) is a measure of the over-all response of the two mentioned components. It is therefore necessary, if one is concerned with the absolute value of the spring constant of the test spring, to know the response of the testing apparatus individually so that this can be taken into account. Secondly, if the apparatus response varies with the test temperature, the variations should also be known. If the test apparatus response does not significantly vary with temperature, then one may display the data in dimensionless form, for example, comparing the gross output elevated- or reduced-temperature data to that at room temperature. But if there is a significant variation in test apparatus behavior with temperature, then the nondimensional scheme will not be convenient. Figure 9 shows the room temperature load-deformation response of the two machines used for both 5- and 10-lb full chart scale. Next, several tests were made to see if temperature had an effect on these data. No significant variation in the testing apparatus response with temperature was determined. Two individual checks were made where load-deformation data were taken in increments of 1000F to a maximum of approximately 800~F in the test furnace. Since no temperature dependence was noted, one could make a nondimensional display of the gross output of the recorder to reflect the behavior of the test spring accurately. This procedure was used in displaying the data obtained, 15

A stress calculation was made on each spring to determine the maximum permissible load so as not to exceed the proportional limit of the material, The 40% nickel alloy was most critical in this respect, as the proportional limit in tension at 700'F was approximately 25,000 lb/in,2 as determined by a simple tension testo Figure 10 shows stress-strain diagrams at 70~F and 700~F for this material. Taking one-half this value for the proportional limit in shear as a basis for calculation, the maximum load for each spring was determined. The Inconel X and 304 stainless steel maximum spring loads were calculated similarly, See Appendix II for stress calculations. The test spring in question was gradually loaded from free height with the deformation being linear with time to a peak value below the calculated maximum value, and then unloaded. For any given temperature, several loadingunloading cycles were produced to obtain an average condition, With each loading-unloading cycle, an associated load-deflection curve was traced out on the recorder chart, shown in Figs. 11 and 12, The spring constant for the spring in question was calculated by taking two convenient, well-spaced points on the loading curve and calculating the slope of a chord line formed by these two points. In almost every spring tested, the load-deflection curve was very nearly linear. The test temperature was varied in convenient increments and the above procedure repeated until enough data were obtained to plot a spring constant-temperature curve Typical spring constant-temperature curves are shown in Figso 13 and 14. To consolidate the data into a convenient display, a dimensionless plot was made by forming the ratio of the spring constant at a particular temperature to the room temperature value and plotting versus temperature. In most cases, at least two complete temperature cycles of an individual spring were run to determine if the behavior was reproducible, Variations between the results were very small,.3o Results for Individual Springs —The results for the individual springs tested are shown in Fig. 15, plotted in nondimensional form versus temperature, Figure 16 shows the same plot with fitted lines through the average of the data of Fig, 15. Note that Fig. 16 shows a dependence on spring index of the 40% nickel-60% iron alloy, The thermoelastic coefficient based on the coil-spring data is very easily calculated from these nondimensional plots by the equation A k 1 ak k mk k o (8) ko AT AT where the A refers to a difference between two points on the curve, The values of mk calculated in this manner are given below and were constant over the temperature range indicated,'16

Material mk Tempo Range 40% nickel alloy, spring index < 9 +155 x 10-6/OF -1100F to +550~F 40% nickel alloy, spring index > 9 +135 x 10-6/~F -110F to +550"F Inconel X, spring temper -165 x 10-6/~F -1100F to +700"F 304 stainless steel -275 x 10-6/"F 70~F to +700~F For the purpose of this investigation, testing was restricted to the range of from -110 F to approximately 7000Fo Since the 40% nickel alloy thermoelastic coefficient becomes less positive after approximately 550F and becomes negative at about 625~F to 650~F, higher temperatures were thought unnecessary. The 40o nickel alloy springs exhibited moderate scaling as a result of the elevated-temperature environment as shown in FigSo 5 and 6o As shown by Fig. 2, the 49% nickel alloy seemed to have possibilities because of the relatively constant dynamic shear moduluso The results for a 49% nickel (Hy-Per 49) spring are shown in Figo 17o As can be seen the spring constant decreased until about 600~F, with indications of a rise starting at 7000Fo Since the 40% nickel alloy is not suitable past about 600700~F, a 40%-49% nickel bimetallic system did not appear suitable for further study. 4. Results for Bimetallic Spring Systemso-On the basis of the thermoelastic data obtained from the coil-spring tests, it was concluded that Eq. (7) should be modified by replacing m b k, so as to reflect the actual coil-spring behavioro With this change, Eq. (7) becomes 3 4 20) d20 (c2+mk2) o.G20o/Gio (9) \Bio'\d1o (Cle+mkl) n2/nlJ Using this equation, calculations were made for several parallel spring combinations designed to be temperature-independent relative to the spring constant, Appendix II gives several sample calculations that were the basis for spring fabrication. Figure 18 shows a dimensionless display of the spring constant versus temperature for these combinations. Of the five bimetal combinations reported in Fig. 18, none varied more than 1.5% in spring constant over the temperature range of from-110~F to 525 Fo The second and third combinations shown in Fig. 18 (see also Figo 19) had less than 0.5% variation in spring constant in the range of from -65~F to 6000Fo Figure 18 shows one combination which was slightly stiffening with increasing temperature. All the bimetal spring systems resulted in spring constants in the range of from 34-43 lb/in. 17

5. Time Effects. —It should be recalled that all the work mentioned has been done for nonrelaxation conditions. Relaxation is generally regarded as the inability of a spring to remain at a fixed height under a specified load at a specified temperature for relatively long periods of time. The conventional relaxation test involves loading the spring to a fixed height, resulting in a maximum wire stress (to be predetermined), subjecting the spring to an elevated temperature, and at a specified elapsed time releasing the spring to free length and measuring the resulting free length. Knowing the starting free length, one can calculate the "loss in stress" resulting from the reduced free height after exposure to the elevated temperature for the period of time in question, Making a plot of maximum wire stress versus time at constant temperature with stress as a parameter is the normal way to display data of this nature (see Fig. 21). For "fixed distance" applications where a mechanical spring must hold a constant distance between two components, the above method of test and representation appears to be adequate. But sometimes the force per unit deflection is to be held constant, with absolute distances not being a critical consideration. Then a representation as shown in Fig.o 22 could be used to judge the time-temperature characteristic of a particular spring or spring system. The spring is stressed to a particular level and held. At convenient intervals of time, the spring is loaded and unloaded and the spring constant is determined, An indication of the ability of the particular spring or spring system to maintain its spring constant would be determined. We planned to obtain considerable time effects, but the intial aspects of the coil-spring program took more time than we anticipated. Only an indication of time effects is given here, along with the results from very limited time-temperature testing. The method described above, resulting in the representation shown in Fig. 22, was followed in testing the bimetallic spring system composed of 40% nickel alloy c = 6.95 and Inconel X c = 9,18 parallel combination. The results for a 12-hour test at 500~F with a maximum wire stress of approximately 10,000 lb/ino2 for the 40% nickel alloy indicated no reduction of spring constant. Further work in this area should be considered for any future program. E, EXPERIMENTAL APPARATUS USED FOR TESTING Figures 23 and 24 show the testing machines used for the experimental work done. Figure 23 shows the Instron textile testing machine type TTCLMl; Fig. 24 shows the table model type TM machine. Figure 23 shows the larger unit with furnace in place. The esential features of both test set-ups are as follows: starting at the top (see Figs. 23 and 26) is a heavy steel extension tube with associated cooling fans, the purpose of which was to keep the load cells at a constant temperature. Since the load cell is an electrical strain gauge, it is quite important that the temperature remain 18

constant throughout testingo Next comes a 1/2-ino-diameter round rod, which extends through the machine crosshead, and a fixture assembly consisting of a stainless-steel pipe' The rod runs through the inside diameter of the test spring and is accommodated with a thread end for the purpose of a spring holding plug (see Figo 27)o All components of test fixtures were made of stainless steel to reduce corrosion problems as well as heat conduction, The Instron machine is commonly-used in industrial research. Its basic functioning is shown in Figo 28, The advantage here over the normal testing machine or a dead weight system is one of extreme force-measuring accuracy as well as continuous permanent recording on the associated Leeds and Northrup high-speed potentiometer recorder embodying a synchronous drive. For the elevated-temperature work, an electrically heated furnace controlled by a Wilson-Maeulen controller with on-off relays was used (see Fig. 29)o Chromel-Alumel thermocouples were used to measure the temperature in close proximity of the spring both in an angular and longitudinal distribution so as to get an accurate indication of the test temperature (see Fig. 27). For the low-temperature work, a mixture of solid carbon-dioxide and methyl alcohol was used. The entire lower portion of the fixture assembly was submerged in a container of the mixture, and temperature stability was maintained throughout all tests at 1.10~F. A Leeds and Northrup portable millivolt potentiometer was used to measure the millivolt differences for the determination of the test temperature. Fo CONCLUSIONS A feasible bimetallic coil.-spring system can be constructed in which the spring constant is independent of temperature within approximately 0.5% over the temperature range of from -65F to 600~Fo A temperatureindependent system is possible within 2.0% over the range of from -lOO0F to 700~ Fo G. RECOMMENDATIONS More testing is recommended to insure the reliability and reproducibility of bimetal spring systems such as studied in this program, Also, since very little relaxation work was done during this project9 extensive experimental work should be done in this area to determine fully the relaxation characteristics of such bimetal systems. The possibility of a coating, to be applied to the nickel alloy materials to prevent elevated-temperature scaling revealed during the course of this project should be investigated. More work should be done on springs in series. 19

IV o ANALYSIS OF BELLEVILLE SPRING WASHERS AS A MEANS OF PRODUCING A SPRING HAVING A CONSTANT SPRING-RATE VERSUS TEMPERATURE Ao INTRODUCTION The motivation behind the analysis of Belleville spring washers is basically that behind the analysis of coil springs, namely, to combine materials possessing positive and negative thermoelastic coefficientso Two additional important reasons for investigating Belleville spring washers are (1) their immense versatility in producing from a given material and thickness a spring of any desirable characteristics simply by a slight variation of the spring height, and (2) that the combinations of materials can easily be effected by simple substitution in their stacking, either series or parallel as indicated in Figo 30Q The method of stacking used for all tests throughout the project was that of series, mostly because of the greater friction present in parallel combinations. The series combination of washers were effected by two means: (1) stacking by use of spacer plates; (2) stacking by means of welding washers together. The latter method makes possible the use of the temperature-dependent bimetallic effects to increase spring stiffness versus temperature. Methods of stacking and bimetallic effects will be further explored below..Five basic materials were used in all tests, namely, 304 and 430 stainless steels and 31%9 42% and 50% Ni-balance Fe alloyso All materials were heat-treated at 12000F for 2 hours and air-cooledo B. THEORETICAL CONSIDERATIONS The basic theory for Belleville spring washers has been known for quite some timeo Several papers about, and. refinements of, their analysis have been written. One of the most complete and best known is that by Almen and Laszlo (5)o The analysis of the washers considered here will be based entirely on their resultso The geometrical notation used here is indicated in Figo 31o On the basis of the investigations by Almen and Laszlo (5), the load-deflection equation for a simply supported washer, loaded uniformly around the inside diameter in compression, may be written as P (1-2)Ma2 [(h-5)(h-l-)t + t3] (10) 21

The maximum stress in the upper edge is a = E~ [cl(h-) + ct] (11) (1-2)Ma2 The maximum stress in the lower edge is a _= E [cl(h-L) c2t] (12) ( 1-2)Ma2 2 where P = applied load, a = stress, 5 = deflection, E = modulus of elasticity, = Poisson's ratio, a = outside radius, h = free height, and t = thickness, M, cl, and c2 are functions of the outside-to-inside diameter ratio a as follows 1 = q+l2- (1) M lI a-l n aJ (13 c = -( - 1 b (14) \In a / T Rn a c2 (a-) (1) T rn a where a = and b = inside radius, The stress equations (11) and (12) above have often been observed to result in considerable error. A more exact analysis of Belleville spring washers by W-mpner (6) has substantiated the load-deflection equation (10) given here and greatly improved the stress equationso However, time did not permit their application to this investigation~ To insure use in the elastic range, all washers investigated were tested for yield datao Considering Eq. (10), letting A = E/(1-l2)Ma2, and differentiating with respect to 5 to obtain the slope of a load-deflection curve, or the spring constant k, one obtains k -= A (h-)(h-2)t + tl - t (16) Letting ko = the slope of the load-deflection curve at room temperature, the ratio of k at any temperature to ko becomes 22

k = A ([(h-5)(h-l) t + t3] -5t[ - 5]) ( (17) ko t ([(h-)(h-) t +t3] - t[3h -] A2 2 Now if we calculate the slopes of a load-deflection curve at a corresponding deflection for the same h and t values, then k =A E(l-o2) ) ko AA Eo(1-12) This relation excludes any changes in h or t due to thermal expansion which are extremely, small. Equation (18) indicates that the dimensionless ratio k/ko versus temperature is independent of spring geometry and a function of material properties onlyo This is as expectedo But Eq. (18) also indicates a very basic difference between the temperature behavior of a Belleville spring washer and a coil spring. The temperature behavior of a coil spring is a function of only one elastic constant, G, the shear modulus, whereas the temperature behavior of a Belleville spring washer is a function of two elastic constants, E and. (or G). Considering Eq. (18) again, it will be noted that, if E decreases with temperature, the effect is to lower the ratio k/ko. At the same time, the k/ko ratio will tend to increase with temperature if p increases with temperatureo For the materials investigated here, on the basis of comparison of the curves for the elastic constants, Fig. 33 and those of the ratios k/ko versus temperature, Figso 34 and 35, it appears that if the thermoelastic coefficients m and e are positive, the thermal coefficient of Poisson's ratio is negative, and for materials of negative m and e, the thermal coefficient of Poisson's ratio is positiveo This cannot be said of all materials, however, and must be determined in each individual caseo This effect is substantiated by Figso 36 and 32 where E/Eo and k/ko versus temperature are plotted for 430 stainless steel and 50% Ni-balance Fe. Note from these curves that wherever the thermoelastic coefficients are negative, the Poisson effect is to increase the k/ko ratio, and whenever the thermoelastic coefficients are positive, the Poisson effect is to decrease the k/ko ratio Mathematically, this can be explained by considering a biaxial state of stress (Fig. 37) of an element, which is the state of stress in Belleville spring washerso Considering the strain in an arbitrary direction, say the x-direction, then the strain from generalized Hooke's Law may be written as Cx = E (x-ay)e 23

Thus, although a decreasing strain, an increasing Poisson's ratio tends to decrease the strain. Physically this means that it is possible to obtain optimum performance from a given material in a Belleville spring washer. Thus if a single material could be found, although possessing a decreasing modulus versus temperature, whose slope of a modulus versus temperature curve was small, and if the thermal coefficient of Poisson's ratio was positive, it might be possible to make a spring out of a single material to withstand temperature effects. This effect certainly should be further investigated. The above point is fairly well illustrated by the dimensionless ratio of k/ko versus temperature for 50% Ni-balance Fe (Fig. 32). As previously mentioned, where the thermoelastic coefficients are negative, the k/ko ratio is increased, and where the thermoelastic coefficients are positive, the ratio is lowered. The net effect is a flattening of the curve to a reasonably constant value. Through the temperature range of approximately 75-850~F, the maximum deviation of k/ko is less than 1.5%. Thus this particular Ni-Fe alloy certainly demands consideration as a single material for springs to withstand temperature effects. The remainder of the analysis of Belleville spring washers was carried out entirely experimentally. First, the dimensionless ratios k/ko versus temperature were determined for each of the five materials available. Second, the individual curves of load versus deflection for each of the washers available with various h and t values were determined at room temperature. On the basis of these two sets of curves and the expression for the equivalent spring constant of series combinations of springs n 1 1 k~e ki ) where i = 1,2,...n, ke k i i=l washers of different materials were put together and tested versus temperature. C. ELASTIC MODULI For completeness, the three elastic moduli versus temperature which were determined are included in Fig. 33. In any future work of this type, the static values of E, G. p should be one of the first things determined. These values would allow a close check between theory and experiment. These values were not determined for this report because we did not have the equipment available to determine the static values of elastic moduli The work had to be done by an outside source which was unable at the time to determine these datao 24

D, DIMENSIONLESS RATIOS k/ko VERSUS TEMPERATURE FOR 304 AND 430 STAINLESS STEELS AND 31%, 42%, 50% NICKEL-BALANCE IRON ALLOYS The dimensionless ratios of k/ko versus temperature for each of the five materials used in tests are included in Figs. 34 and 35. The curves for the two stainless steels were determined on the basis of Eqo (18) from the experimentally determined values of the elastic moduli. The values of Possion's ratio were determined from available data in the literature. The curves of the three iron-nickel alloys were determined directly by experiment, E. INDIVIDUAL WASHER DATA Each washer available was tested at room temperature for individual loaddeflection datao The resulting curves are included in FigSo 38, 39 and 41-50o All washers used throughout the project were of a standard 150-in, OD and 0,75-ino IDo Washers of various h/t ratios and of different stock thickness were tested for each material, The values of stock thickness and h/t ratios are listed on each figure, The washers were simply supported and loaded uniformly around the inside diameter in compression. It was necessary to correct experimental, data for deflections of the test fixtures. All values plotted are corrected~ The calibration curve for the load cell and fixtures used in tests is included in Fig. 40. Some of these load-versus-deflection curves for the individual washers exhibit an irregular behavior in the initial loading period because the base of the washers was not perfectly flat. This effect can be eliminated by preloading. Friction was present in the loading due to the method of support. To eliminate the effect of friction the loop curves of load versus deflection for loading and unloading were obtained, A mean value was then used, as the friction effect would be in opposite directions for loading and unloadingo In any future work it would be desirable to design a support which would minimize friction, F. COMBINATIONS OF WASHERS Combinations of washers will be discussed on the basis of their method of stacking, either (1) by use of spacer plates, or (2) by welding washers together 25

1, Stacking by Use of Spacer Plates —This method of stacking is illustrated in Figo 51o Results of tests of combinations effected by this method are included in Figs. 52 and 53. It is to be noted from these graphs that the experimental values are within approximately 1% of the predicted values determined on the basis of the load-deflection curves for the individual washers, the k/ko ratios versus temperature for the individual materials, and the expression for the equivalent spring constant in series n k = -, where i = 1,2,.. n. i=l Figure 52 further indicates that both the experimental and predicted values of k/k0 versus temperature are within 1% deviation over the temperature range 72-800~F. Figure 53 substantiates that it is possible to obtain a k/ko ratio versus temperature greater than one over the entire temperature range 721000~F. Thus a constant k/ko ratio over this entire range of temperature is entirely possible. Time did not permit further investigation of what, exactly, should be the combination of washers, This particular method of stacking produces considerable friction. As previously pointed out, loop curves of load versus deflection for loading and unloading were obtained to eliminate the friction effecto A proper choice of lubricants and spacer material would certainly minimize this effect and should be carefully considered for any future work. No lubricant was used in these tests~ Further, the spacer material, which was hardened tool steel, scaled considerably at high temperatures. Some type of glass might be quite useful for spacer material to minimize the above-mentioned. effects, 2. Stacking by Welding Washers Together.-This method of stacking is illustrated in Figs. 54 and 55. Results of tests of combinations effected by this method are included in Figs. 56-59. It cannot be said for this method of stacking that the load-deflection equation (10) is valid, since of course the boundary conditions of the washer support are changedo But elastic constants would probably enter in the exact relation in the same manner, If so, then the dimensionless ratio k/ko would be of the same formo This seems to be substantiated in Fig0 56, where the predicted values of the k/ko ratio on the basis of free supports are plotted against experimental results of the welded combinationo If Eqo (18) for k/ko versus temperature for free supports is true for welded supports, then Fig. 56 further shows the advantage of bimetallic effects in welded combinations. The thermal coefficients of expansion versus temperature for the materials used in the combination of Fig. 56 are plotted in Fig0 57. Figure 56 shows that the experimental value is greater than the predicted value at all times, But the agreement between experimental and 26

predicted values is very close at the temperature when the thermal coefficients of expansion are equal, and the deviation is the greatest of the highest temperature where the thermal coefficients of expansion differ considerablyo Although the difference of these thermal coefficients is quite large at lower temperatures also, their absolute values are considerably lesso Since the load-deflection equation is nonlinear the deflections due to the bimetallic effects should be greatest when their magnitudes are maximum, which is at the highest temperature. This is substantiated by Fig. 56o A major effect of welding to be considered in design is that it increases the initial stiffness of the spring koo For the springs fabricated by welding, ko was increased by approximately 100%l This of course could be varied considerably either way, depending on fabrication since the initial stiffness of the spring ko can be adjusted accordinglyo Many combinations of washers can accomplish a constant k/ko ratio versus temperatureo In contrast to the individual washers whose behavior is a function of the thermoelastic coefficients only, combinations have two variables: (1) the number of each kind of washer, and (2) the individual values of ko to weigh in these effects. Go TEST APPARATUS All fixtures and equipment used for tests of Belleville spring washers were the same as those used for tests of coil springs, Fixtures and equipment involved have been discussed thoroughly in Section II. 27

APPENDIX I ANALYSIS OF TUBE-CORE BIMETALLIC SYSTEM Consider a system composed of a thin walled tube in which the inside is filled to a snug fit with a second material. For the analysis to follow the tube is composed of a material with a negative thermoelastic coefficient and the core of a material with positive thermoelastic coefficient. Using Eq. (3a) one may express the independence of spring on temperature as k1o(c1+mkl) + k2o(Ce2+mk2) = 0 (19) where Glo d 4O k I o:= 64 lnl (20) for a solid round wire cross section, and G20(d2 o d ) ) k20 G= (21) 64Rn2 for a tubular round wire cross section (Refer to Ref. 3 for derivation of these spring constants.) Equation (21) has presumed the inside diameter of the tube and the wire diameter of the coil to be equal. For a configuration of this nature nH = n2, T1 = 2 so Eq. (19) after substitution of Eq. (20) and Eq. (21) and rearrangement becomes i209 = Glo (l1+mkl) +1 (22) d lo/ G20 (o2+mk2) For a specific case taking Inconel X as the tube material and 400% nickel-60% iron alloy as the core material, (/_ = _ -90x01) ( 3+155) + dlo (11. 5x106) (10-165) 29

(d ) = (0.60) + 1 d20o = 1.61, d (d = 16. ^61,= 1.126 Taking dlo = 3/32 in., d2o = 0.106 in. EXPERIMENTAL RESULTS OF TUBE-CORE BIMETALLIC SYSTEM Inconel X tubing of outside diameter 0,119 in, and inside nominal diameter of 3/32 in. was used with 40% nickel-60* iron alloy to experimentally check the feasibility of such a composite spring. Figs. 61 and 62 shows this spring and Fig. 63 shows the test results, Note that although the diameter ratio is incorrect as demanded by Eq. (22) the temperature variation is relatively slight with the variation at 500OF being approximately 2%. 30

APPENDIX II SAMPLE CALCULATIONS FOR BIMETAL COIL SPRING SYSTEMS (a.) ~,0! stainless steel-)4O% nickel alloy. Using Eq. (9), one can size the individual springs for the system. Taking for 304 stainless steel mk = -275xl0-6/~F and assuming a 40% nickel alloy spring with c < 9, where mk = +155xlO-6/~F, one has for 02 1OxlO-6/ F, ail = 3xO-6/~F 3- ('d2 4 (10-275) (11.5/6.9) (D1i = d 1i ( 3+155) (n2/nl) Now assuming d = d nd n2 = nl the above reduces to _ 3 (D2) = +(1.68)(1.67) = 2.80 D2 = 1.141 D1 Choosing Dlo (outside diam of inner coil) = 13/16 in. or 0.81,D1 = 0.72 in. D2 = (1.41)(0.72) = 1.015 D2o = 1.015 +.094 = 1.11; c2 -= 10.85 So the sizing would be with 8 active turns in each spring,40O nickel, OD = 0.81, n- 8, d = 3/32; 304 stainless steel, OD = 1.11, n = 8, d = )/32, with both springs having the same pitch. (b) Inconel X spring temper-40% nickel alloy. Again assuming c < 9 for the 40% nickel spring, one may write Eq. (9) as D2 = - /d2 (10-165) (11.5/6.9)' " (3+155) (n2/nl) Assuming d2 = d and n2 = nl as before 31

D2) = + (0.98) (1.67) = 1.64 \Di2 D2 = 1.18 D1 Choosing as before Dlo = 0.81 so that I1D = 0.72, D2 = 0.85. The outside diameter of the inner coil is 0,81 and the inside diameter of the outer coil is 0.766 in. This is not possible because there would be interference of the two coils. If one restricts the wire diameter and the number of active coils to be the same, the coil diameters of the two springs becomes impractically large. At this point one may make several choices. For example, let d2= 0.112, di = 0.09375 n2 = 9, n1 = 10 Then (' ( 0.112- (0,98) (1-67) D11 0.09375 (9/10) (D2) = (2o4) (o0.98) (185) = 3.70 2 =- 1.545 D1 Letting Dlo = 0.75 so that D1 = 0,656, cl = 70, D2 = (1.545)(o.656) =.o0 D20 = 1.01 + 0,112 M 1.12; c2 = 9~00 STRESS CALCULATION To stay within the proportional limit during testing, the total spring loads were calculated as follows: l6PR Tmax = -d3 K 32

where P - total spring load, lbR - mean coil radius, in. d - wire diameter, ino K - Wahl stress factor, nondimensional Solving for the total allowable load in case (a) above, using 12,500 lb/in.2 as the allowable shear stress, (12,5) (0) (3/32) = 7 lb (16) (0.36) (1.19) The specific torsional resilience for 40% nickel alloy, as mentioned in the introduction, is at room temperature S.R = (1,0 113 in. -lb/in_3 2G (2)(609x106) 33

APPENDIX III ANALYSIS AND EXPERIMENTAL PROCEDURES FOR DETERMINATION OF DYNAMIC SHEAR MODULUS The basic idea is that through use of a torsional vibratory system, the shear modulus will be reflected in the frequency of vibration. For a torsional system assuming (a) no damping, end effects or cross-coupling vibration, (b) perfect elasticity and no geometry variations, and (c) infinitely rigid support for hanging wire, the linearized equation of motion for a circular wire spring is: JG IG + - = 0 (23) L where I - moment of inertia of end mass about axis of rotation (in.-lbf-sec2) 9 - angular displacement (radians) J - polar moment of inertia of wire (in.4) G - wire shear modulus (lb/ino2) L - free length of wire (in.) - time derivative (sec-1) (a) can be written as + p29 = (24) where p2 JG IL From the above, the shear modulus may be calculated as 128jtIL I G = 1 (25) d4 T2 where d - wire diameter (in.) T - period of oscillation of pendulum (sec) Hence, by measurement of the period of oscillation and by measurement or calculation of the moment of inertia of the effective oscillating mass, the shear modulus may be calculated. 35

The experimental set-up (see Figs. 65 and 66) consisted of a vertical tubular furnace heated by electric current passing through Nicrome coil windings. The ceramic tube which enclosed the pendulum suspension wire was insulated and the furnace proper was suspended from an aluminum framework. The pendulum with associated holding fixtures for gripping the suspension wire was suspended and secured against any movement to a heavy torsion plate by use of a steel taper pin. The torsion plate was part of the furnace-suspension framework; hence the supporting frame of great torsional rigidity. The pendulum with associated gripping fixtures consisted of the following (from top to bottom): a, A steel tube approximately 1-1/2-in. OD 2ft long, one end of which fastens to the torsion plate by use of a taper pin. At the other end is a special expansioncontraction insert which slides inside the tube and is secured by a threaded holding collar. b. The expansion-contraction insert is used to grip the material specimen (in wire form) which has in some suitable way been imbedded in cylindrical plugs which slip snugly into the cylindrical central portion of the insert. The top expansion-contraction insert has on the inner cylindrical portion a shallow groove to secure a wire to which thermocouples are attached for sensing the temperature in close proximity. Naturally, thermocouples could not be applied to the pendulum suspension wire for fear of changing the natural frequency. The thermocouple supports were made out of stainless-steel welding rod approximately 1/16 ino in diameter. Three ChromelAlumel thermocouples were used to sense the temperature in close proximity of the pendulum wire. c. Next is the pendulum suspension wire made of the material for which the shear modulus is desiredo The specimens had a free length of approximately 10-12 ino and a diameter of not greater than 3/16 in, Most of the work done was with 1/8-in.-diam wire and smaller. Forced onto both ends of the wire are stainless-steel (type 304) plugs, o75-in.-diam by.75 ino long, cylindrical in form, do Next is the lower expansion-contraction insert with threaded holding collar and tube much like the upper portiono The major difference between the top and

bottom tube sections is 3 thermocouple-wire access holes in the top assembly. The thermocouple wires run centrally through the upper tube from the thermocouple holding wire and out to a potentiometer for measuring millivolt differences. A circularly symmetric mass is attached by a taper pin to the bottom tube assembly. The furnace was heated by a 220-v, a-c, single-phase supply in conjunction with a temperature controller and on-off relay. For low-temperature work, the furnace was replaced by a special copper cylinder with seals adequate to contain a mixture of solid carbon dioxide and methyl alcohol. By using this mixture a temperature of approximately -110~F was obtained. Figure 66 shows testing at this temperature. A Leeds and Northrup portable millivolt potentiometer was used to read the millivolt differences and was accurate to within ~53F at 10000F. The period of torsional vibration was obtained by taking the total time for 50 complete oscillations by means of a stop-watch:.and dividing the total time by 50. 37

REFERENCES 1. Koster, W., Ztsch. Metallkde, 35, 194-199 (1943). 2. Vosteen, L. F., NACA Technical Report 4348, August, 1958. 3. Wahl, A. M., Mechanical Springs, Peyton Publishing Company, 1944. 4. International Nickel Co. Tech. Bull. T-35. 5. Almen, J. 0., and Laszlo, A., "Uniform-Section Disk Springs," ASME, 58, 305-14 (1936). 6. Wempner, G. A., "The Conical Disk Spring," Proc. U.S. National Cong. Appl. Mech., 473-78 (1958). 39

0 77 122 212 302 392 482 572 662 752 842 932 1022 25 60% Ni T 24 -o —CM 23 50% Ni / / Tc 1110~ (0) 22 ox (D,___x-___ 0 21 45% Ni L 20 19 25 30% Ni 24 23 0) 22 0 / x 36% Ni 9. W 20 19~ 40% Ni - 0 100 200 300 400 500 600 700 800 900 1000 TEMPERATURE - OF Fig. 1. Young's modulus versus temperature for iron-nickel family between 30% and 60% nickel. 40

12. 00 11.00!z 10. 00 x 9.00 0 r' c 8.00 < Q - 430 Stainless Steel O-Run 1 O-Run 2 (5)- 49%Nickel (Hy Per) l > O^ 2)- Hy-Mu 80 V -Run 1 V -Run 2 ^ Run 1 A Run 2 C1 | | (D - "Iso-elastic" ( )- 40o Nickel-60% Iron 6. 00 () 49 Nickel (Simonds Saw Co) O Run 1 * Run 2 a Run3 ( - 390- Nickel-61% Iron O Run 1 Run 2 5.00 -150 0 100 200 300 400 500 600 700 800 900 1000 11C TEM PERATURE OF Fig. 2. Dynamic shear modulus versus temperature.

15. 00 - S~-8i6 (12 - Tantaloy -- Run 1 Run 2 ^14. -00NS 25 A-286 14- Inconel X (annealed) Q - 504 Stainless Steel A Run l 0 Run 2 () - Haynes 25 () - 561 Nickel-64% Iron 0 Run 1 Q Run 2 N 13.00 jX 12.00 o- 11.00 Flow 4::-I, P0 < 10. 00 9. 00 8. 00 -150 0 100 200- 300 400 500 600 700 800 900 1000 1100 TEMPERATURE 0F Fig. 5. Dynamic shear modulus versus temperature.

Fig. 4. 40 nickel alloy compression spring Wire diater 0.1 in., outside diameter 0.98 in. 43

Fig. 5. 40)o nickel alloy coils. Wire diameter 3/32 in., c = 9.0, n = 9-1/2, p = 9/64 in. (on left); wire diameter 3/32 in., c = 9.0, n = 4-2/3, p = 9/64 in. (on right). Note surface scaling. Fig. 6. 40% nickel alloy coils. Wire diameter 3/32 in., c = 7.0, n= 15^, P = 9/64 in. (on left); wire diameter 3/32 in., c = 6.95, n = 10, p = 9/64 in (on right)..ii~?!iiii!?!i!!!k i~:i i~:-: iiiiii: -:: - i - Ii_;-i::;jii — I.. 44~~~~~~~~~~~'~~:.-_I

i iiiiii-iiii:_ iiii~iiiii-iii —i-.....::.-.: i-i-::: i- i-i-i --—:-::-~-. —.. —::::::::::::::::::::::::::::::::::::::j:::j:: i-::i-iiii~i~i............................iiiii Fig.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. 7. Incone......in tepe cois- Wir.dimeer./3.in..=..0 n = 15, p = 9/64 in. (on left); wire diameter 3/32 in, c = 9.0, n =~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~................ 9-1/2, p __i~i~i-::::_:-:::-::;:ii~i~i_ =:.:_ 9/64: -:-:::-::in.:_:_:-:::-:- (middle),: wire::::::: diameter. 3/32:ilii-i~i-i:-;::i~ii~ii~i-i~iiii,:i.... 9.0...6..............: r; k i i i i i > E F i i i y i E i E E E. E it i:E i i E i E E 7 i i: E i g E E * E E 2 E. E E i. E E i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...... i i — EE:-'-;- -:'':'':;-.:-'-: -':':i -:.Sl00 -:'-.-0':::i::i -:-:: --— l.-:0.-gg~~ -::::::i -ig iii-~ -— igET~iE0 —gl.-004.igE-0000000.iED iiE S.:004.0000EES —;0.fit.0g.igiTE —-EES.-02.-00E.0 00-00ATiitE-00-. *E-idES -gi.E-iE i E-EiE:iE iEE iL-: iERiEE-E~g E ES!if if E E: i. ET~i-i: iEi-i~........ —.......i.i... —.-......-..::t:.:-:::-:~.::-:::-:.::,:000-:-::400-;. —;;:::::- E-::..00.-..::g::::::::_:-::000 W: t;:kE:__:E:.S:.:: i::XtE-::;:::::j::400i:::.:-t::4A:: i-:l:::-:::ES:- t-SE, ti-;g:-.; t::- -:_j-iii-~i.gi;i:i~i - EiSi~i:_;B ri-: Ei:i: _iS~~E!-ii _.- ii!.e~t!;:i~ii-E:4SEitEEiiSEEE~iE ii:4tl' tSi0000-:!h-;i-i iii -i~ii S i:i00-E-;i~i EE i; idiSE i i -E- E; i:::::::-: - i::-i- i-E..0 —..~iiiijgiiiiiiii' -00.:_-i.j ~-:-:S~~-000.00- -::g - i::-::i:-0 -:::::-t i::-00 -::::,-0 - -::i:-:::::::: -:::::::;:-:iii: -::::i:::-: -: - -: - -:-g-.:-:: g-g. -g-iiii,.:-::- 0:-gg-iii -:.:E - g iij:-:::-.-;:;- l- -0- i:00 -E-E;:i-00 i al - i W: i:.:i~iiiii~ ~ ~~i -E-i:::-:::Ei:2:::E:B::::::::::::::::::::E::::::::::-E ~ ~:-:::i::::i~i-::i-:::i:::i-:i:-::::::::~:~::.:E::::-i -: -:iE:::: * D - ai::8:-.-s:~a- ~:B::a~: ~;:B: E B::i:: H:: a::-~a:-.a:: i H.:- 00::;.iB... i i;-....:.::...:, B t i Fig, 7. Inconel X spring temper coils. Wire diameter 7/7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ in.,................ p = 9/64 in. ton right)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..;: it:' i;:: I- -:- -:i:::: -i i-i~~i,:iligii; 0 lii i-i4-lgi 3 | -i a~i- ig i iB i0iB Biii' B BB' ii iBi eiaBiiBai'Biii i Bi iiiii' i-i ii'' B B' iiB iB' s jiB;->:-v ~:: si- s::~i~-i~i ii~ii-i | 2BSBi-aB a _ T -asaaB: si: s:BB:ssB B-i i i;si i i i i;ili iii i:~ Fig. 8, Inconel X spring temper coils. Wire diameter j/j~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ in., c = 7.0,~~~~~~~~~~~~~~~~~~~~...... iB gsB: Bfpg Bs 9/64 Sia: B:B: aeft); wa:e diaBB | s [:BB B _ Te 7/3 BBB BB B:BB C s:BB: s::s:: s:::;s:;S:;igng: gB; S.gBS;Ba: B;B B~s BB BB;;.BB.B s n B.,, p = 9/6B is. # s,<, i sIs E ale); s B s s EB i e di. #gg # sE | a r B/~,B _ B. -, c fi s 0 E _ a: Sg $ B s: s:, -.......... 3333a-gs$3$33sgs$33333$ s-$ $B 3$BB$3$Big | [$ sha$$ a $$ <$... * S'>;M. l,* B. hS,' -.- *'Ag' -, < x; ^... < m... 0. z D. a a Fe <a E.x -.-;-, f~~~~~~~~~~~~~~~~~~~~~~~~~~fe 9,-.a.-. sR......,...,.. >.,. - Fig. 8* Inconel X s~~~~~~~~~~~~~~~~~~~~~~~~~~~~pring temper coils. Wire diameter 3/3 inc=70 n = 15, p = 9/64 in. (on le~~~~~~~~~~~~~~~~t); wire diameter 3/32 in., c = 7.0, n =wre 10,ter3/3 in, C= 90.9n in (on right).~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.,n 6

Symbol I O * 100 V 1i -, v -. TM-5 TM-10 TT-5 TT-10 TM-Large Console TT-Table Model 7 iF 6 O TM Instron -/ r 5 - 10 lb Full Scale -: TM Instron-\ 34 - 5 lb Full Scale \ \/^^<\/ ~ TT Instron f~ [,, \ ~10 lb Full Scale 3 ^^^ } TT Instron 2 5- 0^^ 4 I|mmmmmmmm ^i-mmm~~~5 lb Full Scale $ L1 0 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 MACHINE AND FIXTURE DEFLECTION, IN. Fig. 9. Load versus deformation for Instron testing machines with test fixtures.

70,000. 1.0 in. 60, 000 /~ / ^^'700rF 50 000 x 40, 000 / LU ~t:/:/d OQ Room Temperature 30, 000 - 700~F 70~F 700~F Proportion Limit 25,000 psi 25,000 psi Ultimate Strength 85,000 psi 67,300 psi 20, 00010,000 0 0. 001 0.002 0. 003 0. 004 0. 005 STRAIN, IN./IN. Fig. 10. Stress-strain diagrams for 40% nickel-60% iron alloy at 70 and 700~F. Material annealed before tests at 1200~F for 2 hours. 47

OQ1 O-eT L fOTTe TGTO^lu *UO ~ JapJooDJ q paoSJ; se BuTcds TTOO Jo ond;qno uoT;q lTJGp-poe *T11 *'TdI _ ~''j' p^^uiio-o'^ /'^ -~~~- — i1-2-i _ _ i_ L;1df/ P/v l,'y ~, -,,/LTj,'41 r /(7~/0.' -iI0 p7....'_........L_,,,,N/.d?,,,..1,,.' _!" *T,'L j —' -1 f s'o jAyap / s I ~ -~~-.....1 ~~.{~~~1 A ~ ~O ~ 1/~1 - -: - \ \ i;-':jldulr/ i~ ~- f _-1~1_. -~_-!_ _ _:i - it~~~~~~~~~~~~~~~~ —-'L -.. I Ii. -c. i. — T..:.;~ / I /:. ~..n4 -\_ _ _ ~__' — *1/: _. I _ i r__~_^ _ ~_~_ _.I _ _ _ ___ __ __:______' - - ^Z __i~~~~~_ ^ 1 12..-^ - / " I I'iI1.' lI l t iT 4- -..... ~ - ~- - --..J. ^ -Ili i 4.......... t-'- z-! —-~'~'''t —-' --''- -- 1 -0 0 1 ~~ ~~ X + A —. ~~ ~/-^-4 [.- ~ -i -. * -. -- t - - - ^ 1-, I ~1^- ~ ~/ ~ ^ yI ~- _ 1 / \ __ __- __ ^__ _ _ ___ _ ___ _ ___ ^ ___ _ ___ ^ ____ " -'-!!'."]~ ~ 1 _^! ^ -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~iii__l^/ _l__^/____l^ ____.___._..________.~~11:1~~~ _ -L -hl^ia r "' " ~^ ~ "' " " ~ ~ ^ ~ \ ~ ~' ~\ "'. ^ ~ ~~~~~~~~~~~:li.-.-.. \^ ^^ -i.^ \ ^ ^ ^ ^ ~-^-.~~~~~~~~~~~~~~~~~~~~~~" ~ ~ " " T t ~ ~ T r~1~

6t',o69 -e ROTTI T-I:O'TU %0O *'aGpJooaG Xq paosq. se SuTlads TTOO JO q.0nc no uoqoaGTJGp-pOo *TZl *ST.;::-...... it_/.4 -_ti — SZ'n Jf 7 p ^uo t^:W -fl+ -F~-i -T^F- 4T^ t^T HA _. X _ _iS /I/ _ _4_ H_;;1 r/p |-Xi rs i - - - - ------ *13'/ CIS3YP/ tllj I~l.-:: 511 Q:;:.. I"J/"'It -JI ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~-.e'i ( —-/ )A Ivr4D( I f H i.... -l y^ 1f ~~ "'.1~'~ "~~"\'.........-~: i. 1...............:~'~i ~'" H' i -lf 1 — 1_ - - -_ _ 1 ——.'........ i.0 -- X I-.f~ ~ _ Ll.; S 7 -........;... - i 100 |r-~ — t-1 -!-i4-l-j -T L.| S gX |r ii \-.] - - " -' —' I I~_ ~S I ___0 14 f I | f -~| f X I-~T ~ -T1 ~ 0- - ^ - ~^ —1-: -i ^.-l —i —---.I J — -:.:: — |:: -— |' r_ i-':|t Ti |':;-'L ~ I.';lF't! I -:-F, |.- - - T 1.:.' [.... L:4.1 IT i 4. -,-.. i1 1 -,. 1 |,I,|r., rF1-,4 ti -' |-l.-i. 1 0 / / 0 4 2 0 -

15.20 I I II I V Run 1 V Run 2 TV 15.00- T 14. 80 / V - V 0.4 and 1.6 lb used fZ^~~~~ |^ ~~~~~ / for k calculation -14.60 -,14.40 014.20 \ C) 0^ |^' RS /^c,"9' 1 and 3.75 lb used for LO 14 00 v -v k calculation 0o 8 0 0 13. 80o un 1 13. 60 _,9 13. 40 13. 20 100 200 300 400 500 600 700 TEMPERATURE OF Fig. 13. Spring constant-temperature diagram for 40% nickel alloy coil springs. 5o

I I I I.I! I Spring Index 9.00 27. 60 Active Coils 4-2/3 Wire Diam 0.09375 Pitch 9/64 E Outside Diam 0.938 c2 c = 9.0, n = 4-2/3 27.20 Z<0 26.80 / H z o o Q 0, 26.40 LUi C^) ^ QQ /0 O Run 1 0/^~~ 0/^ ~E Run 2 26.00 1 and 4 lb used for k calculation 25, 60 0 100 200 300 400 500 600 700 TEMPERATURE OF Fig. 14. Spring constant-temperature diagram for 40% nickel alloy coil spring.

I I ~II II I I I I 40% Nickel-60% Iron Inconel X Spring Temper 304 Stainless Steel Symbol c n d p Symbol c n d Symbol c n d l I e 16.95 10 13/32 9764 I 7.0 10 329 6.80 1-3/4 1/8 3/1 < 77.06 4-2/3 3/32 9/64 e 7.0 15 3/32 9/64 10.32 8 3/32 9/64 5 7.65 10 3/32 9/64 I 8.25 15 3/32 3/16 a 11.17 8 3/32 9/64 7.65 8 3/32 9/64 9.18 9 012 0.16 n - number of active coils (D 8.38 3-4/5 3/32 3/16 9.40 8 1/8 0.17 d = wire diameter inches a 9.0 15 3/32 9/64 < 9.80 7 1/8 0.19 1. 10 9.0 4-2/3 3/32 9/64 * 9.13 20 0.074 0.15 p - pitch of spring coil, inches 1. 10 e 9.0 4-2/ 3/32 9/64 93 ko20 - spring constant at 70~F, lb/in. e 9.0 9-1/2 3/32I 9/64 ~ O L| 11.06 |4-3/4 |3/32| 9/ 1640 0 _ 40l Nick el-6 Iron P0! I I N0 L 1 o Inconel yX (spring tempe n 0. 90 | Symbols indicate distribution of experimental data and are not actual experimental points. 304 Stainless Steel 0. 80 -100 0 100 200 300 400 500 600 700,~ ~ ~- -TEMPERATURE F Fig. 15. Nondimensional spring constant versus temperature for 40% nickel alloy, Inconel X spring temper and 304 stainless-steel coil springs. ~aJ Incoriel X spring temper and 304 stainless-steel coil springs.

7, I I I I I! 1 mk Range 40% Nickel, C < 9 4155x106/F -110'F to 550~F 40% Nickel, C - 9 +135xl10-/F -110F to 550'F _~ —~~~ ~Inconel X, spring temper -165x10lO~/F -llO1F to 700'F 304 Stainless Steel -275x106/F 700F to 700F v1v C~9 C99 -< ~~ 40< Nickel —60 Iron C-) m-^~~~ ~ Inconel X c: 1.00,-J Oa L 9 0 ig 16 odmesoa prn osan essteprtr fr4%ncklaly Inconel X (spring temper) z 0.90 __ 304 Stainless Steel 0. 80 ~ 1 1 1 I ~ -100 0 100 200 300 400 500 600 700 TEMPERATURE OF Fig. 16. Nondimensional spring constant versus temperature for 40% nickel alloy, Inconel X spring temper and 304 stainless-steel coil springs. Lines indicate average of data shown in Fig. 15.

0. 99 0.,98 -0.9/? Run 2 -0.96 116 ^- -~~~~~~~~~~~~~~~~~~~0.95 00 16 Hy-Per 49 (49% Ni-51% Fe) 115 Free Length 1.0 IL^ ^ ~~~~~C ~~~~~Outside Diam 0.97 Wire Dimi 0.125 114 p7 ~~~~~~~~~~~~Run 1 113 2: I ~,Run 2 Ln ~~L 110 Inl 108 1 I I 1I 0 100 200 300 400 500 600 700 TEMPERATURE, 0F UJ -i-n ^^^ ^ ^ ^ CQ ~ ~ tin lio hr at i a~ Fig. 17. Plot of spring constant and nondinensional spring constant versus temperature for 49% nickel-balance iron coil spring.

Symbol 4o nickel, c = 7.65, n = 8, d= 3/32, p = 9/64 paralleled with 304 stainless steel c = 11.17, n = 8, d = 3/32, p = 9/64 40% nickel, c = 7.65, n = 8, d = 332, p = 964 paralleled with 304 stainless steel, c = 10.32, n = 8, d = 3/32, p = 9/64 o 40 nickel, c = 6.95, n = 10, d = 3/32, p = 9/64 paralleled with Inconel X (S.T.) c = 9.18, n = 9, d = 0.112, p = 0.16 0~~~~~o 40% nickel, c = 7.65, n = lO, a = 3/32, p = 9/64 paralleled with V ___ Inconel X (S.T.) c = 9.80, n = 7, d = 1/8, p = 0.19 40% nickel, c = 7.65, n = 10, d = 3/32, p T 9/64 paralleled with Z~ __~_ |~O Inconel X (S.T.) c = 9.40, n = 8, d = 1/8, p =0.18 1.04 o * _ 1.02 a2 k/ko =1 \.f l 1 O 0 - --— 0t —:1 o r - 0.98 0 0.96 -100 0 100 200 300 400 500 600 700 TEMPERATURE OF Fig. 18. Nondimensional spring constant versus temperature for bimetal coil spring systems tested.

Fig. 19. 40% nickel alloy c = 6.95, n = 10, d = 3/32 in., p = 9/64 in. paralleled with Inconel X spring temper c = 9.18, n = 9, d = 0.112 in., p = 0.16 in. Fig. 20. 40% nickel alloy c = 7.65, n = 8, d = 3/32 in., p = 9/64 paralleled with 304 stainless steel c = 11.17, n = 8, d = 3/32 in., p = 9/64 in. 56

T3 = const. Severe Relaxation Constant Temperature T2 = const. T, Stress. Moderate Relaxation T- = const. T3> T2 >T Little or No Relaxation Time Fig. 21. Stress relaxation diagram. k ______ _____ _ _Tmax = const. = T k_ Tmax = const. = T2 tmax = const. = T3 T3 >T2> T1 Constant Temperature Time Fig. 22. Spring constant "relaxation" diagram. 5c

vs 0o Fig. 23. Instron testing machine type TTCLM1. Fig. 24. Instron testing machine table model Type TM with associated furnace and control equipment.

g_ I | I lup S~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~iEiiiiill~_:_ ls'- I::iii':' Fig. 25. Instron testing machine TTCLMi1 with furnace and test fixtures in place. 59

Fig. 26. Spring loading apparatus. 1. Load cell. 9. Thermocouple leads. 2. Securing pin on load cell 10. Asbestos packing. to pull rod coupling. 11. Compression pipe. 3. Extension jacket. 12. Upper spring bearing piece. 4. Pull rod. 13. Test spring. 5. Furnace hangar support. 14. Asbestos packing. 6. Machine cross head. 15. Furnace. 7. Drive screw. 16. Thermocouple heads. 8. Compression pipe head piece. 17. Spring holding plug. 60

Fig. 27. Lower test fixtures showing spring. 61

__ balance amp. -ca librated amp. controls" sec I attenuator sec 2 load cell, _........ [I cross head recorder load test spring T ^-~- ----- stspringcrosshead movement.*L~~~, ~synchronously driven chart LOAD WE I GH ING SYSTEM in ge r drive box selsyn motor ^ actual position + ampli L. dyne selsyn Ca speed ^ servo & TF = desired position c amp mag, change sync. clutch gears motor zr up and down vaies o^~ ~speed Fig. 28. Schematic diagram of testing apparatus. 62

Maeulen ]+ ~ Controller O~~ II I 1 Controller Furnace Temperature M230v a.c. 1 ph Motor Sensing Thermocouple Gear L C H Box GE Relay,, i~,,, 230v a~c. 1 ph GE Relay i X Bulletin 709SP, Size 0, Form 2, Type 1 Cat. 3656o63-GR3 2 H 2 2 L T I C L i~i Furnace Allen Bradley Automatic Motor Starter Bulletin 709SP, Size 0, Form 2, Type 1 Fig. 29. Schematic diagram of furnace control. 63

Parallel Series Fig. 30. Parallel and series stacking of Belleville spring washers. 00 Dc lO.D h I. D. Fig. 31. Geometrical notation of Belleville spring washers. 64

1.1 1.0 0 _ 01 o0.9 oJ 0 \J} o I -~0.8Legend A E/Eo 0 k/ko 0. 7 0.6 I i I I Il I 50 150 250 350 450 550 650 750 850 950 TEMPERATURE OF Fig. 32. Dimensionless ratios k/ko and E/Eo versus temperature for 50% nickel-balance iron alloy where ko and Eo are values of spring constant and elastic modulus at 70~F.

1.1 0.9 0 OL d 0.8 Legend A 430 Stainless Steel 0 304 Stainless Steel. 7 O 50% Ni-balance Fe 0.6 50 150 250 350 450 550 650 750 850 950 TEMPERATURE OF Fig. 33. Elastic modulus versus temperature for 430 stainless steel, 304 stainless steel and 50% nickel-balance iron alloy.

30 LU at v 26 LU ar'Y C) ~24 CI\ 22 Legend LU A 430 S-tainless Steel 0 304 Stainless Steel 20 ~30 50 Ni-balance Fe 18 50 150 250 350 450 550 650 750 850 950 TEMPERATURE OF Fig. )34. Dimensionless ratio k/k0 versus temperature for 450 stainless steel, 304 stainless steel and 50% nickel-balance iron alloy.

1. 2 1.I O.O o 0. 9 0. 8 Legend A 42% Ni-balance Fe 0 31% Ni-balance Fe 0.7 0.6 I I I I I 50 150 250 350 450 550 650 750 850 950 TEMPERATURE OF Fig. 35. Dimensionless ratio k/ko versus temperature for 42% nickelbalance iron and 31% nickel-balance iron alloys.

1. 0 0 LU 0. 9 0 \0 - 0. 8 Legend A E/E0 0. 7 0 k/ko 0. 6 50 150 250 350 450 550 650 750 850 950 TEMPERATURE OF Fig. 36. Dimensionless ratios k/ko and E/Eo versus temperature for 430 stainless steel where ko and EQ are values at 70'F.

Fig. 57. Biaxial state of stress. Fig 37. Biaxial state of stress 7o

O50~O 40 30 30 Z / 20 / h/t = 0.871 t = 0.031 in. 10 ~ v h/t = 2.801 t = 0.031 in. 0 200 400 600 800 1000 1200 1400 1600 DEFLECTION X 105 IN INCHES Fig. 38. Load versus deflection for 42% nickel-balance iron alloy washers.

500 530 - 40 M 30 0 9/ h/t = 1.774 t = 0.01 in. DEFLECTION X 10 IN INCHES Fig. 39. Load versus deflection for 42% nickel-balance iron alloy washers.

10 - 7 0V 9 4 3 1 0 20 40 60 80 100 120 140 160 180 DEFLECTION X 105 IN INCHES Fig. 40. Test load versus test fixture deflection for 5/16-in.-diameter pull rod, load cell "C."

500 40 30 C 20 / h/t = 3.065 t = 0.031 in. 10- 0 200 400 600 800 1000 DEFLECTION X 105 IN INCHES Fig. 41. Load versus deflection for 430 stainless steel washer at 70~F. 74

50 - 40 0 30 20 o h/t = 1.031 t = 0.032 in. h/t = 1. 938 t = 0.02 in. 10 ~t0 ^9 ^ (~D h/t = 2.938 t = 0.032 in. 0 L 0 200 400 600 800 1000 1200 1400 1600 1800 DEFLECTION X 105 IN INCHES Fig. 42. Load versus deflection for 50% nickel-balance iron alloy washers at 70F.

40 C30 - 20 Q/ /t = 1.032 t = 0.031 in. 10 () h/t = 1.871 t = 0.031 in. 0 200 400 600 800 1000 1200 1400 1600 1800 DFFIECTION X 105 IN INCHES Fig. 43. Load versus deflection for 304 stainless steel washers at 70~F.

50 ( h/t = 2.591 t = 0.022 in. O(t) h/t = 1.773 t = 0.022 in. 4() h/t = 1.045 t = 0.022 in. 40 30._J 20 10 0 I I I III 0 200 400 600 800 1000 1200 1400 1600 1800 2000 DEFLECTION X 105 IN INCHES Fig. 44. Load versus deflection for 31% nickel-balance iron alloy washers at 70~F.

0.6 6 h@ 0.52 0.4-, 3 0. 3/ Y (Q h/t = 0.75 t = 0.010 in. -|^ -^ (g)~ h/t = 1.30 t = 0.010 in. 0.2 O _ ^ (^6) h/t = 0.26 t = 0.010 in. 0.1 - 0.0 0 200 400 600 800 1000 1200 1400 1600 DEFLECTION X 105 IN INCHES Fig. 45. Load versus deflection for 42% nickel-balance iron alloy washers at 70~F.

1.6 1.2 0. I 0.8 J (17) h/t = 0.542 t = 0.014in. ^ ~' y^^^ Q^^ (^d~ ~ ~ ~ ~ ~ ~ ~ ~ ~h1) h= 1.000 t = 0,04 in. 0.J 4 h = 1143 t = m0.014 in. 0.40 0 200 400 600 800 1000 1200 1400 0 200 400 600 800 1000 1200 1400 0 200 400 600 800 1000 1200 DEFLECTION X 10' IN INCHES Fig. 46. Load versus deflection for 50% nickel-balance iron alloy washers at 700F.

(20 h/t = 2.60 t = 0.015 in. () h/t = 2.155 t = 0.015 in. 10 (G2) h/t = 1.400 t = 0.015 in. z8/ - 0 o 0 4/ - 0 200 400 600 800 1000 1200 1400 1600 1800 DEFLECTION X 105 IN INCHES Fig. 47. Load versus deflection for 304 stainless steel washers at 70~F.

2,0 1.6, 1.2 0. 0. 0 0 200 400 600 800 1000 1200 1400 DEFLECTION X 105 IN INCHES Fig. 48. Load versus deflection for 304 stainless steel washers at 700F.

28 20 16 V) 0, 12 86) h/t = 1.666 t = o.o18 in. 4 h/t) = 2.222 t = 0.018 in. (28) h/t = 2.666 t = o.o18 in. 0 0 200 400 600 800 1000 1200 1400 1600 DEFLECTION X 100 IN INCHES Fig. 49. Load versus deflection for 430 stainless steel washers at 70F..

6.0 5. 0 0 4. 0 3- 0 OD / (^0) ^^^^.~~(0) h/t = 0.63 5 t = 0.018 in. 2. 0.. Oh/t = 0.3 t = o.o8 in. O 1h/t = 1.111 t = 0o.018 in. 1. 0 0 200 400 600 800 1000 1200 1400 1600 DEFLECTION X 10i IN INCHES Fig. 50. Load versus deflection for L350 stainless steel washers at 70'F.

Fig. 51. Belleville spring washers stacked using spacer plates. 84

1 Washer 430 Stainless Steel h = 0.095 t = 0.031 in. 1 Washer 42% Ni-balance Fe 1i 05 h = 0.087 t = 0.031 in. 1. 05 Washers stacked by spacer plates. 0. 95 Legend 0 Predicted 0. 90 A Experimental 0.85 50 150 250 350 450 550 650 750 850 950 TEMPERATURE OF Fig. 52. k/ko versus temperature for washer combinations using spacer plates.

1 Washer 50% Ni-balance Fe h = 0.094 t = 0.032 in. 2 Washers 42% Ni-balance Fe o h = 0.087 t = 0.031 in. Washers stacked by spacer plates 1. I 0039 0. 9 Legend O Predicted Experimental 0. 8 0. 7 50 150 250 350 450 550 650 750 850 950 TEMPERATURE OF Fig. 53. k/ko versus temperature for washer combinations using spacer plates.

Fig. 54. Belleville spring washers stacked by means of welding. Fig. 55. Belleville spring washers stacked by means of welding. 87

6 Washers 42% Ni-balance Fe h = 0.087 t = 0.031 in. 4 Washers 430 Stainless Steel h =0.095 t = 0.031 in. All heat-treated 2 hr at 1200*F Stack height after welding = 1.135 in. Spot welded 3 places Legend Series stacked 0 Expe-imental 0 -1 Predicted 1.1 ko = 1678 lb/in. at 72"F 0. 9 Max. deviation from room temperature value = 3.5% Bimetal effect on two OD joints 0.8 0 100 200 300 400 500 600 700 800 900 1000 TEMPERATURE OF Fig. 56. k/ko versus temperature for washer combinations stacked by means of welding.

5 Washers 42% Ni-balance Fe h = 0.087 t = 0.031 in. 4 Washers 430 Stainless Steel h = 0.095 t = 0.031 in. 1 Washer 50% Ni-balance Fe h = 0.094 t = 0.032 in. All heat-treated 2 hr at 1200~F Stack height after welding = 0.795 in. Spot welded 3 places o Series stacked 1.1 1. I 0. 9 0. ko = 1256 lb/in. at 72-F Max. deviation from room temperature value = 3% Bimetal effects on two OD joints 0. 8 0.1 I I 0 100 200 300 400 500 600 700 800 900 1000 TEMPERATURE OF Fig. 57. k/ko versus temperature for washer combinations stacked by means of welding.

6 Washers 42% Ni-balance Fe h = 0.087 t = 0.031 in. 4 Washers 304 Stainless Steel h = 0.093 t = 0.031 in. All heat-treated 2 hr at 1200'F Stack height after welding = 0.805 in. Spot welded 3 places Series stacked 0 1.1I.I0.9ko = 1591 lb/in at 720F Max. deviation from room temperature value = 4.0% No bimetal effect 0.8O. 7(I *0 100 200 300 400 500 600 700 800 900 1000 TEMPERATURE OF Fig. 58. k/ko versus temperature for washer combinations stacked by means of welding.

4 Washers 42% Ni-balance Fe h = 0.087 t = 0.031 in. 4 Washers 50% Ni-balance Fe h = 0.094 t = 0.032 in. All heat-treated 1 hr at 1000"F Stack height after welding = 0.860 in. Continuous welding joints Series stacked 1.1 1. I 0. 9 ko= 4192 lb/in. at 72~F 0. 8 Max. deviation from room temperature value = 7.8% No bimetal effect 0.70.60.5 I I I l! l l O. 50 0 100 200 300 400 500 600 700 800 TEMPERATURE 0F Fig. 59. k/ko versus temperature for washer combinations stacked by means of welding.

xl- CDC 0 LUL 0r) LU 2f ~ C) -4LU 0~~~~~~Legend ~~~~~~~~~~2 ~~~0 42% Ni-balance Fe A 430 Stainless Steel 50 150 250 350 450 550 650 750 850 950 TEMPERATURE OF Fig. 60. Coefficients of thermal expansion versus temperature for 430 stainless steel and -2% nickel-balance iron alloy.

Fig. 61. Bimetal system composed of Inconel X thin- Fig. 62. End detail of Inconel X —40 nickelwalled tubing 0.09375 in. ID, 0.119 in. OD with core balance iron alloy bimetal tube-core configura40% nickel-balance iron alloy 0.09375 in. diameter. tion. Note core and jacket. Outside diameter 1.0 in., n = 9-1/2. View before test.

Calculated from Curve 1. 00 -_ Shown Below 0.99 o 0.98 0.97 0.96 0.95 ~ 39.50, 39.00 lw_ ~ o9. o ~- -o.-. CD) z 38.50 L 38. 00 0 38.00 3_ ~ LU 1L 37.50-.. o 3 700 0 100 200 300 400 500 600 700 800 TEMPERATURE, OF Fig. 63. Spring constant versus temperature for Inconel X-40% nickel-balance iron alloy tube-core configuration coil spring. Initial heat treatment at 1200~F for 2 hours.

O. D. - OUTSIDE DIAMETER iOo D. _ D - MEAN COIL DIAMETER O~ ~. D. I.D. -.INSIDE DIAMETER D. ~ ^| d - WIRE DIAMETER 1.. D, p - PITCH | |i! | L - FREE LENGTH Fi. 4.Col prngdeintinkech-. i I LI Fig. 64. Coil spring definition sketch. 95

3/4 steel plate outline of furnace 16" DIA;i ii ^^ ~^1 ~! / 35" long ^ ^^1 3/4' \\ I /test specimen taper pin i frame holes (3) for thermocouple wiires Ii CT\ ~~~~~~~~~~~~~~~~~~~~~83' ________ oscillating mass Fig. 65. Schematic diagram of torsion pendulum apparatus. Fig. 66. Shear modulus testing at -1100F.

THE UNIVERSITY OF MICHIGAN, Ann Arbor, Michi- UNCLASSIFIED THE UNIVERSITY OF MICHIGAN, Ann Arbor, Michi- UNCLASSIFIED gan. WIDE-RANGE-TEMPERATURE SPRINGS, by J. I gan. WIDE-RANGE-TEMPERATURE SPRINGS, by J. Ormondroyd, H.E. Gascoigne, J.H. Enns, and P. Ormondroyd, H.E. Gascoigne, J.H. Enns, and P. G. Kessel. 97 P. inc. figs., tables, and I G. Kessel. 97 p. inci. figs., tables, and refs. (Project 9-(8-7360); (Task 73605)(ASD refs. (Project 9-(8-7360); (Task 73605)(ASD TR 61-566)(Contract- No. AF 33(616)-6284). TR 6l-566)(Contract No. AF 33(616)-6284). I~ IJ~~~UNCLASSIFIED REPORT UNCLASSIFIED REPORT Bimetallic spring systems of 40l% nickel-60% Bimetallic spring systems of 40% nickel-60o iron alloy combined with Inconel-X and type iron alloy combined with Inconel-X and type 50stilssteexiichrceitc 04 stainless steel exhibit characteristics stainless steel exhibitcharacteristics suitable for applications from -650F to 600oF. suitable for applications fiom -650F to 6000F. In this range the spring constant is held In this range the spring constant is held within ~0.25%. within +0.25%. The general theory of bimetallic, tempera- j The general theory of bimetallic, temperature independent helical coil and Belleville ture independent helical coil and Belleville type springs is presented. The bimetallic UNCLASSIFIEDtype springs is presented. The bimetallic UNCLASSIFIED over ( over ) systems tested show that a temperature inde- UNCLASSIFIED systems tested show that a temperature inde- UNCLASSIFIED pendent spring is feasible although working pendent spring is feasible although working stresses must be maintained at relatively low stresses must be maintained at relatively low levels. levels. I F-WPB-j1J 61 IUNCLASSIFIED \I UNCLASSIFIED AF-WP-B-JUL 61 iM AF-WP-B-JUL 61 iM /j- __ _____ ______ _____ _ ____ ________ ____ ____ _ __ ___ _ __ __ ___ ___ ____ ___ _________ ______ __ ____ _______ ___

tt* — - - -- -- - ----- ------------ -. - - - - - ITHE UNIVERSITY OF MICHIGAN, Ann Arbor, Michi- UNCLASSIFIED TH UNIVERSITY OF MICHIGAN, Ann Arbor, Michi- UCLASSIFIED Igan. WIDE-RPANGE-TEMPERATtURE SPRINGS, by J.. gan. WIDE-RANGE-TEMPERATURE SPRINGS, by J. Ormondroyd, H.E. Gascoigne, J.H. Enns, and P. Ormondroyd, H.E. Gascoigne, J.H. Enns, and P. G. Kessel. 97 p. incl. figs., tables, and I G. Kessel. 97 p. inc. figs., tables, and refs. (Project 9-(8-7360); (Task 73605)(ASD refs. (Project 9-(8-7 0); (Task 73605)(ASD TR 61-566)(Contract No. AF 33(616)-6284). I refs. (Project 9-(8-7360); (Task 73605)(ASD | TR 61-566)(Contract No. AF 33(616)-6284). | |TR 61-566)(Contract No. AF 33(616)-6284). UNCLASSIFIED REPORT UNCLASSIFIED REPORT Bimetallic spring systems of 40O nickel-60 * Bimetallic spring systems of 40% nickel-60% iron alloy combined with Inconel-X and type iron alloy combined with Inconel-X and type 304 stainless steel exhibit characteristics 304 stainless steel exhibit characteristics suitable for applications from -65~F to 600oF. suitable for applications f!om -65~F to 600~F. In this range the spring constant is held. In this range the spring constant is held within +0.25o. within +0.25%. The general theory of bimetallic, tempera- The general theory of bimetallic, temperature independent helical coil and Belleville ture independent helical coil and Belleville type springs is presented. The bimetallic NC type springs is presented. The bimetallic systems tested show that a temperature inde- UNCLASSIFIED systems tested show that a temperature inde- UNCLASSIFIED pendent spring is feasible although working pendent spring is feasible although working stresses must be maintained at relatively low stresses must be maintained at relatively low levels. levels.!AFg UNCLAJSS IlIFID 6 I UNCLASSIFIEDI UCLAII AF-WP-B-JUL 61 1M AF-WP-B-JUL 61 1M ^ ______ ___ ____ _ ____ ___________ ___ _ __ __ _ __ __ ___ ___ _____ ___ ____ o __________)__ ________ o ___~___ ___) I\p ~I "

THE UNIVERSITY OF MICHIGAN, Ann Arbor, Michi- UNCLASSIFIED TE UNIVERSITY OF MICHIGAN Ann Arbor, Michi- UNCLASSIFIED gan. WIDE-RANGE-TEMPERATUTRE SPRINGS., by-J. ITE~IEST FMCIAAnAbr ih-UJ~SFE gao. WIDE-RANGE-TEERATURE SPRINGS, by gan. WIDE-RANGE-TEMPERATURE SPRINGS, by J. iOrmondroyd, H.E. Gascoigne, 3J.H. Enns, and P. Ormondroyd, H.E. Gascoigne, J.H. Enns, and P. G. Kessel. 97 p. inci. figs., tables, and G. Kessel. 97 p. incl. figs., tables, and refs. (Project 9-(8-7360); (Task 73605)(ASD refs. (Project 9-(8-76o0); (Task 73605)(ASD ITR 61-66)(Contract No. AF 33(66)-628). TR 61-566)(Contract No. AF 33(6l6)-6284). jUNCLASSIFIED REPORT jUNCLASSIFIED REPORT Bimetallic spring systems of 40O nickel-60% Bimetallic spring systems of 40% nickel-60% iron alloy combined with Inconel-X and type iron alloy combined with Inconel-X and type 3O11 stainless steel exhibit characteristics 304 stainless steel exhibit characteristics suitable for applications from -650F to 600oF. suitable for applications f~om -60F to 6000F. In this range the spring constant is held In this range the spring constant is held Iwit-hin ~0.25%. { within +0.25%. The general theory of bimetallic, tempera- The general theory of bimetallic, temperature independent helical coil and Belleville ture independent helical coil and Belleville type springs is presented. The ( )UNCLASSIFIED type springs is presented. The bimetallic I ~~~UNCLASSIFIE~D UNCLASSIFIED ( over o $- ( ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~over systems tested show that a temperature inde- UNCLASSIFIED systems tested show that a temperature inde- UNCLASSIFIED pendent spring is feasible although working pendent spring is feasible although working stresses must be maintained at relatively low stresses must be maintained at relatively low levels, levels. AF-WF-B- 61 M UNCLASSIFIED UNCLASSIFIED A-W-~- 61~~~~~ ~ __ _ __ __ __ _. __. _ _ _ 4^ ~ - _ _ __ _ __AF-WP-B-JUL 61 I_ C —---- - ------ - --— 4 — --- _- _ __I_ _ - __

~ - ii -- - - - -t --- -- -- ----- - -- ---- ---- -.- -- - THE UNIVERSITY OF MICHIGAN, Ann Arbor, Michi- UCLNCLASSIASSIFIED gan. WIDE-RANGE-TEMPERATURE SPRINGS, by J. gan. WIDE-RANGE-TEMPERATURE SPRINGS, by J. Ormondroyd, H.E. Gascoigne, J.H. Erns, and P. Ormondroyd, H.E. Gascoigne, J.H. Enns, and P. G. Kessel. 97 p. inci. figs., tables, and G. Kessel. 97 P. incl. figs., tables, and refs. (Project 9-(8-7360); (Task 73605)(ASD refs. (Project 9-(8-7360); (Task 7360o5)(ASD TR 6l-566)(Contract No. AF 33(6i6)-6284). TR 6l-566)(Contract No. AF 33(616)-6284). jUNCLASSIFIED REPORT UNCLASSIFIED REPORT Bimetallic spring systems of 40% nickel-60% j Bimetallic spring systems of 40)% nickel-60% iron alloy combined with Inconel-X and type iron alloy combined with Inconel-X and type 304 stainless steel exhibit characteristics 304 stainless steel exhibit icharacteristics suitable for applications from -650F to 600~F. suitable for applications from -650F to 6000F. In this range the spring constant is held In this range the spring constant is held I within +0.25. I within +0.25%. The general theory of bimetallic, tempera- The general theory of bimetallic, temperature independent helical coil and Belleville ture independent helical coil and Belleville type springs is presented. The bimetallic type springs is presented. The bimetallic UNCLASSIFIED UNCLASSIFIED ( over) (over ) systems tested sow tat a temperature inde- UNCLASSIFIED systems tested show that a temperature inde- UNCLASSIFIED pendent spring is feaible although workingsystems teested show that a temperature independent spring is feasible although working pendent spring is feasible although working stresses must be maintained at relatively low j stresses must be maintained at relatively low levels. levels. AF-WF-B-AL 61 1M UNCLASSIFIED I UNCLASSIFIED 6 AF-WI-B-5jL 61 iM ~~~~~~~~~~~~~~~~~~AF-WP-B8JUL 61 IM- -- ___