THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING DESIGN OF SPUR-GEARS OF "ZYTEL" NYLON RESIN Keith W. Hall Associate Professor of Mechanical Engineering Herbert H. Alvord Associate Professor of Mechanical Engineering November, 1958 IP-335

ABSTRACT This paper presents a method of calculating the load carrying capacity of gears made of duPont "Zytel" nylon resin. A number of design recommendations are given, and the use of gears of "Zytel" in a helical gear speed reducer is described. ii

TABLE OF CONTENTS Page ABSTRACT............. *............. ii LIST OF FIGURES o........................................... iv INTRODUCTION...... *.......... *............................... 1 MATERIAL.*...................................................... 1 TEST MACHINES.............................................. 2 TEST GEARS......,...................................... 6 TESTS AND RESULTS...................................... 8 LOAD CARRYING CAPACITY OF GEARS OF "ZYTEL"t................... 23 OTHER DESIGN RECOMMENDATIONS*............* s *................... 32 ADDITIONAL INVESTIGATIONS AND RESULTSO........*... *.......... 534 iii

LIST OF FIGURES Figure Page 1 "Zytel" Nylon Resin 2.5% Moisture Content............. 3 2 Effects of Temperature on Physical Properties of ZYTEL 101............................................ 4 5 Schematic Layout of Test Machine...................... 5 4 Test Machine......................................... 7 5 Test Gears with Hob Cut Teeth....................... 9 6 Test Gears with Molded Teeth.......................... 10 7 Molded Gear, Sectioned to Show Ring Gate............ 11 8 Fatigue Life of 16 Pitch Hob Cut Gear Teeth,.......... 13 9 Fatigue Life of 32 Pitch Hob Cut Gear Teeth............ 14 10 Fatigue Life of 20 Pitch Molded Gear Teeth............ 15 11 Fatigue Life of 32 Pitch Molded Gear Teeth,........ 16 12 Fatigue Failure of 20 Pitch Molded Gear Teeth, Not Annealed......................................... 18 13 Fatigue Failure of 20 Pitch Molded Gear Teeth, Annealed,...,..................................... 19 14 Tooth Form Factor Y for Load Near Pitch Point......... 21 15 Recommended Max. Allowable Stresses for Molded Gear Teeth.................................. 22 16 Values of Design Factor K for Use with Lewis Equation and Design Charts............................. 25 17 Design Chart for 16 Pitch Gears.................... 27 18 Design Chart for 20 Pitch Gears....................... 28 19 Design Chart for 32 Pitch Gears...................... 29 20 Design Chart for 48 Pitch Gears........................ 30 21 Helical Pinion and Gear, Hob Cut,...................... 35 22 Helical Gear Speed Reducer Test Stand,,*.............. 5 23 Temperature Rise of Gear Teeth....................... iv

INTRODUCTION The main objective of this paper is to present a method of calculating the load carrying capacity of spur gears of "Zytel", and to show how this method was established. However, this might well be called a progress report on the work being done at the University of Michigan to establish reliable design methods for gears made of this material. This work is being sponsored by the Polychemicals Dept. of E. I. duPont de Nemours and Company, and is still going on at the time of this writing. Leading up to the main objective, it is felt desirable to present some information on the "Zytel" nylon resins, to describe the experimental program which has been conducted with gears of "Zytel", and to show some of the test results from which the load carrying capacity has been established. "Zytel" nylon resin, the test equipment, and some preliminary results were described in paper 56-SA-43, presented at the ASME semi-annual meeting at Cleveland, June, 19568 To present a complete picture of what has been done to date, some of the first parts of that paper are repeated here. MATERIAL "Zytel" is a nylon resin manufactured by E. I. duPont de Nemours & Company. It is thermo-plastic, and is supplied in the form -of granulated powder from which many articles can be molded by conventional molding techniques. The molded material has relatively light weight, is rigid and tough, has a low coefficient of friction, and good resistance to abrasion. -1

-2"Zel." is made in several nylon molding powder compositions, of which "Zytel"'101 is recommended for mechanical parts. All of the information in this paper refers to "Zytel" 101, but to avoid needless repetition, the suffix 101 has been omitted. Typical physical properties of this material are shown in Figure 1. These physical properties are considerably affected by temperature. For example, Figure 2 shows how the yield strength decreases with increase in temperature, while the impact strength increases. The physical properties are also somewhat affected by the moisture content of the molded material. The physical properties shown in Figure 1 are for material which has been conditioned to have 21% moisture by weight. This represents the amount of moisture absorbed at equilibrium, with air at 50% R. H. and 73~F, TEST MACHINES To carry on the test work required to establish the load carrying capacity of gears of "Zytel, five identical test machines were designed and built. These machines operate on the "'ack-to-back", or "four-square" principle, with two pair of gears in each machine loaded against each other. In this way the driving motor supplies only the power to overcome friction and windage in the machine. A schematic layout of the test machine is shown in Figure 3. The gears t be toested are mounted on hollow shafts supported in ball bearings. Two steel teorsion. bars connect the hollow shafts. A

FIGURE 1 "Zytel" Nylon Resin 2..5% Moisture Content Tensile Strength 73~F 11,200 psi Yield Strength 73~F 8,500 psi Elongation 73 F 300 % Modulus of Elasticity 73~F 175,000 psi Shear Strength 73~F 8,000 psi Impact Strength, Izod 73~F 2.0 ft-lb/in. Hardness, Rockwell 73~F R 108, M59 Specific Gravity 73~F 1.14

16,000 -- ----- 1 4.5 YIELD STRENGTH z 14,000 - 4.0 12.000 - 3.0 a 5 10,000 3.0 2,00 tI / x" I I 1 1~ " 8,000 2 V 8,000 ------- ------------- 2.5 w Lw 6,000 2.0 in 4,000 1.5 IMPACT STRENGTH, IZOD 2,000 -- 1.0 0 0.5 -80 -40 0 40 80 120 160 200 240 280 320 TEMPERATURE, ~F Figure 2. Effects of Temperature on Physical Properties of ZYTEL 101

/-BEARING SUPPORT FRICTION COUPLING. OUTER HALF — TEST GEAR FRICTION COUPLING, INNER HALF I SPACER GEAR SHAFT LONG TORSION BAR \J1 SHORT TORSION BAR PIN ~- GEAR SHAFT FLEXURE PLATE SPACER DRIVEN SHROUD TEST GEAR DRIVING SHAFT Figure 3. Schematic Layout of Test Machine

-6friction coupling at the right end is used to twist the torsion bars, thus providing the desired load on the gear teeth, Figure 4 shows one of the test machines, with the friction coupling in the foreground and the driving motor behind. The bearing supports for the right hand shaft of Figure 4 are movable, thus allowing various sizes of gears to be tested. The gears shown in the machine have 22" pitch diameters, which might aid in visualizing the actual size of the test machine. Load is applied to the gear teeth by twisting the friction coupling with a system of small wire ropes and weights operating on the pulleys shown in the foreground of Figure 4. After clamping the friction coupling with the screws provided, the wire ropes are removed to allow the couplings to rotate. Lead shot in buckets is used as the weight. Any desired twisting moment can be applied to the coupling by changing the amount of shot in the buckets. Each machine is individually driven by a constant speed motor through a speed variator, providing a 600 to 5000 rpm speed range. An individual oil mist lubricating.system is provided on each test machine to lubricate gears and bearings. TEST GEARS A fairly large variety of gears have been tested. Many of the gears were machined from molded disks of "Zytel". The teeth of these gears were cut with hobs after the disks had been machined to size, Pitch diameters of these cut gears ranged from 1.375" to 3.75",

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-8with diametral pitches of 16, 20, 32 and 48. Figure 5 shows an assortment of such gears. All but a few had a 20~ pressure angle and full depth teeth, with face widths varying from 7/32" to 7/16". Accuracy limits of the teeth of these gears ranged from AGMA Commercial Class 2 to Precision Class 1, with most of the teeth being within the limits of Commercial Class 2 or 3. In addition to the cut gears described above, 2-~" diameter 20 pitch and 32 pitch gears having molded teeth have been tested. These gears, which are shown in Figure 6, also have a 20~ pressure angle, with full depth teeth and 1/2" face width. The web which joins the hub and rim is 1/8" thick. A single cavity mold, with a ring gate at the hub was used to form these test gears. The action of the ring gate can be fairly well visualized from Figure 7, which shows a gear sectioned through the gate before its removal. The molded 20 and 32 pitch teeth were within the accuracy limits of Commercial Class 1 and 2 respectively, and it is felt that this accuracy would have been difficult to obtain without a ring gated moldo TESTS AND RESULTS An extensive life testing program was first conducted with the machined gears having cut teeth, since variations in gear diameter, diametral pitch, face width, pressure angle, etc., can be most easily accomplished with cut teeth. Pitch line velocities ranged from 785 to 3730 ft/min, both with and without lubrication of the teeth. In some cases pairs of identical gears ran together, while in others small pinions were used with larger gears.

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-12During this work the machines ran continuously, 24 hours per day, being stopped only occasionally for visual inspection or to replace broken gears. When a gear failed, that gear and the gear with which it meshed were replaced and this was counted as a single failure. During most of the test work, the teeth were lubricated with oil mist. When no lubrication was desired, the oil mist system was turned off, and the bearings were lubricated with grease. The gears were generously lubricated with oil at the start of the no-lubrication tests, but were not lubricated thereafter. Ambient temperature and humidity were not controlled at any time. The temperature varied from 68~ to 92~F, and the relative humidity varied from 29 to 85% while the test work was in progress. Some of the results obtained with the gears having cut teeth are shown in Figures 8 and 9. Similar but less extensive data were obtained for 20 and 48 pitch gears having cut teeth. Figures 10 and 11 show the results obtained with the 20 and 32 pitch gears having molded teeth. Some of these gears had been tested as molded, with no subsequent treatment. Others had been moisture conditioned, and still others had been annealed. Figure 11 shows that the life of the 32 pitch molded gears was considerably greater at any given load than that of the gears with cut teeth. However, Figure 10 does not show this samI increase in life for the 20 pitch molded teeth as compared to those with hob cut teeth. It is believed that the relatively poor showing of the 20 pitch molded teeth, particularly at the higher stresses, was due to the presence of residual stresses in the rim of most of the molded gears tested, and to

10 I I I I I I I I I FATIGUE LIFE OF 16 PITCH GEAR TEETH 9 - - - 0 Lub. NoLub. 0 0 8 -- 0 40 Teeth, 1635 Ft./Min. 0El 40 Teeth, 785 Ft./Min. On n) 7 - A A 27 t 60 Teeth, 3730 Ft/Min. W Lubricated t -. 785 Ft./Min.2 F 40 Teeth, 3270 Ft/Min. 2 FAILURES u( 6 _ 27 60 Teeth, 1635 Ft/Min. 0 5 _ Z -# -!T *^ j ^ T l > ^ A ^ 1 "^ ^ ~ ^ - ~ -?CD -I I \ C 2 FAILURES T FAILU, M ILIN -.... e.i e Fatu N't Lu br cated Ft/Min W N~ot Lubricatd ENot Lubricated 1635 Lubricated3730 Ft/Min,.1635 Ft./MIn. / ~ ~ j-785 Ft./Min. 1 3J _ <2 C.) I 2 4 6 8 10 20 50 100 200 500 1000 CYCLES TO FAILURE, MILLIONS Figure 8. Fatigue Life of 16 Pitch Hob Cut Gear Teeth

10 I I I I I 1I I I I I I I 1 FATIGUE LIFE OF 32 PITCH GEAR TEETH 9 ___ _- ___ _a..j| ]: 1 l l l | | t | | | |^~~~~ Lub. NoLub. 0 8 - -- --- 0 64 Teeth, 1635 Ft./Min. 0 *.t 4 * (i * 0 64 Teeth, 7 85 Ft. /Min. ( 7 f ------- — [ - - ------ - -- _ _ * 56 C120 Teeth, 373OFt/Min. ~ I ^^r -' "nj/ * - In o 6U m' 64 Teeth, 16785 Ft./Min. Z- 1 | 2 FAILURES (7/32 Face Width) C 0 00 D ~. Z I 2 FAILURES I I I o ~ ~ ~ ~~~CCEa / FI- NOT A FAILURE- - g~Z~~Fgr 4 Fatigue Life of 32 Pitch___ ___A STOPPED TEST w4 m c 0 w3 3 0 I 2 4 6 8 10 20 50 100 200 500 1000 CYCLES TO FAILURE, MILLIONS Figure 9. Fatigue Life of 32 Pitch Hob Cut Gear Teeth

It0 o -I l I 11111 FATIGUE LIFE OF 20-PITCH ZYTEL GEAR TEETH 9 ---- -- — _J_ —-[ —-- -- _i iii, Lub. No Lub. c0 * L 0 O 50 Teeth, As Molded - 8 O 0 50. Teeth, Molded, Moisture 0 ^ f v *, Conditioned 8^ I h "3 Foilures 7 ___. t_ / 120 Pitch Molded A 50 Teeth, Molded, Annealed 0) |, ~__t i i / ITeeth, Lubricated g l 2 _ 1^-^, l > | /t All Velocities 1635 Ft/Min. (t i al sll|_ l l l l l llll L etLbiae l Failures 05 o 5: K.! 1 1u 111 1..- A J5 4 6 —- -- — 0. 50_1-O _-'"'O 1 I ITeeth, Lubricated 4 F i 2 4 6 8 10 20 50 100 200 500 1000 Figure 10. Fatigue Life of 20 Pitch MolIded Gear Teeth Figure 10o Fatigue Life of 20 Pitch Molded Gear Teeth

10 I I I I I I Il.. 1II I II I FATIGUE LIFE OF 32-PITCH ZYTEL GEAR TEETH Lub. No Lub _/) |^ r| < l l |2 Failures * 0 80 Teeth, As Molded a.8 Z lues o I 0 T i htI IK I I I I! I I I U 0 80 Teeth, Moded, Moisture o I Conditioned 0 All Velocities 1635 Ft/Min. 7 U) ~ > [ | 32 Pitch, Molded 5 | 432PitchMelded Teeth,_I Ntc ot a FilureLNot Lubricated j ~ JJ | l~''JStopped Test C 5 ----- U - \~-^-1z i C 4 3 I I _ _ i I - I, I ti I - ti 0 1 t —ilL —_ ^/ — _- IL 1 2 4 6 8 10 20 50 100 200 500 IOOQ jFigure 1.:Fatgue Life of 32 Pitch 32 Pitch, Hob Cute....Teeth, Lubricted and... _____ _ _____ _Not Lubricated I - I 2 4 6 8 10 20 50 100 200 500 (000 CYCLES TO FAILURE, MILLIONS Figure 11. Fatigue Life of 32 Pitch Molded Gear Teeth

-17the thin web which did not provide enough support for the rim and teeth at high loads. Evidence of residual stresses being present can be seen in Figures 12a, b and c, which show failures of some of the 20 pitch molded gears. Rather than failing at the root of a tooth in a typical bending fatigub failure, the gears of Figure 12a and b failed by breaking through the rim. This type of failure was preceded by the formation of cracks at the roots of the teeth, as shown in Figure 12c. It was not uncommon to have these cracks form at the root of virtually every tooth on the gear after a relatively short period of operation. The gears would then continue to run for a long period of time, during which time one or more of the cracks would progress through the rim to the web. When the crack reached the web, a piece generally broke out to end the test. When the 20 pitch gears were annealed to remove the residual stresses, the life of the gears was considerably increased, and the line of Figure 10 is drawn to represent the test results obtained with the annealed gears. The annealed gears failed at the root in a typical fatigue failure as shown in Figure 15. At higher loads there was evidence of distortion of the 1/8" thick web of the 20 pitch gears, and it was believed that this adversely affected the life of the 20 pitch molded gears. Nevertheless, the molded teeth showed a definite improvement over the cut teeth in the sizes tested. Although no 16 or 48 pitch molded gears were tested, it

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-20was concluded that molded gears of those pitches should have somewhat greater life at any given load than the cut teeth tested. This line of reasoning was followed to establish allowable stress curves of Figure 15. The stresses plotted in Figures 8 through 11 were calculated by the Lewis Equation for bending stress in a gear tooth: FP S = -—, (1) where S = bending stress, psi F = tangential force on tooth, lbs f = face width, inches Y = form factor, load near pitch point The above equation considers all the load to be carried by one tooth when in contact near the pitch point. A photographic analysis of the teeth under load, both stationary and in motion, showed this is essentially the condition which exists with the 16 pitch teeth, With smaller teeth, however, some of the load is carried by the adjacent teeth. Nevertheless, the above equation is simple to use, and calculating the stress in this manner results in the points falling along a straight line within the range of random error deviation. The form factor Y was calculated from the tabulated figures on page 477 of Buckingham's "Analytical Mechanics of Gears", McGrawHill. Buckingham's values have been multiplied by 3.1416, to obtain the values shown in Figure 14.

-21FIGURE 14 Tooth Form Factor Y for Load Nbar Pitch Point Number 20~ Full- 20~ Stubof Teeth Depth Form Depth Form 15 0.556 16- 0.578 17 0.587 18 -- 0.603 19 ----- 0.616 20 0.544 0.628 22 0.559 0.648 24 0.572 0.664 26 0.588 0.678 28 0.597 0.688 30 o.6o6 0.698 34 0. 628 o.714 38 0.651 0.729 43 0.672 0.739 50 o.694 0.758 60 0.713 0.774 75 0.735 0.792 100 0.757 0.808 150 0.779 0.830 300 0.801 0.855 Rack 0.823 0.881

10 in. 1 1 10 7 I I I I I I I I I I I I I I I I i I i' I I I REGOMMENDED MAXIMUM ALLOWABLE STRESSES FOR 9 - - - - - MOLDED ZYTEL GEAR TEETH- -- _ n 20~ PRESSURE ANGLE, FULL DEPTH,. 8 --- OIL LUBRICATED --- 0 0 0 7 7..,.. 0 - -- - ---------- ---- -_ —W 6 ( U) /-48 Pitch 42 Pitch —. ro Z4. I I I __..- I0_h LLJ3.4 I:2 4 6810 20 50 100 200 500 1000 CYCLES TO FAILURE, MILLIONS Figure 15. Recommended Max. Allowable Stresses for Molded Gear Teeth

LOAD CARRYING CAPACITY OF GEARS OF "ZYTEL" The Lewis equation which was used to calculate the stresses in the gear teeth can also be used to calculate the load carrying capacity of the teeth by using the test data to establish allowable stresses. However, this equation is generally more useful when rewritten in either of the following forms: SD fYK (2) 2 P (2) where T = torque gear can transmit, lb-in S = allowable stress, psi, from Figure 15 D = pitch diameter of pinion, inches f = face width, inches Y = form factor for pinion, from Figure 14 K = design factor, from Figure 16 P = diametral pitch or: HP = S D f K (3) 126,000 P where HP = horsepower gear can transmit N = pinion speed, RPM What are considered to be maximum recommended stresses for molded and lubricated teeth are shown in Figure 15. To provide a reasonable margin of safety, the lines shown in Figure 15 have been reduced 25% from the lines which represented failure of the gears on test. Figure 15 shows higher allowable stresses for small teeth than for large teeth. This is in part due to the fact that the load is -23

distributed among more teeth when the teeth are small, even though the method of calculation considers the entire load to be carried by one tooth. Furthermore, the larger teeth tend to run at a higher temperature than the smaller teeth. This has the effect of weakening the larger teeth It should be kept in mind that Figure 15 shows the maximum stresses which should be used when the load is reasonably steady with virtually no shock or impact loading. These should be used with reasonable judgment by the designer, and should be further reduced to compensate for overloading, impact or shock loading, or other such conditions of operation. The design factor K, shown in Figure 16, compensates for those cases where cut teeth may be used instead of molded teeth, for lack of lubrication, and for velocities in excess of 4000 ft/min. Other than this, no correction need be made for velocity. It would seem that the use of Equation 2 or 3 to determine either the torque or horsepower capacity of gears of "Zytel" is fairly straight forward, hence no examples are given. Within reasonable limits, it should be possible to approximate allowable stresses for pitches other than those shown in Figure 15, It would seem unwise, however, to carry this to extremes and use the data of Figure 15 to establish allowable qtresses for teeth which are much larger than those tested. The combination of large loads and high sliding velocities encountered in large teeth might exceed some limiting value not reached with the teeth tested, beyond which the teeth

-25FIGURE 16 Values of Design Factor K for Use with Lewis Equatioh and Design Charts Lubri- Velocity Factor Teeth cation ft/min. Pitch K molded yes below 4000 16-48 1.00 molded yes above 4000 16-48 0.85 molded no below 1635 16-20 0.70 molded no above 1635 16-20 0.50 molded no below 4000 32-48 0.80 cut yes below 4000 16-48 0.85 cut yes above 4000 16-48 0.72 cut no below 1635 16-20 o.60 cut no above 1635 16-20 0.42 cut no below 4000 32-48 0.70

-26may fail by surface deterioration rather than by bending fatigue. In such a case, the load carrying capacity would be limited by resistance to wear rather than. by bending fatigue strength. It would also seem unwise to apply the stresses of Figure 15 to teeth having pitches finer than 48, unless the dimensions of the teeth are very carefully controlled. Small errors could greatly reduce the carrying capacity of such small teeth. To facilitate the design of gear teeth of "Zytel", Equation 2 and the stresses of Figure 15 have been combined to form the design charts of Figures 17, 18, 19 and 20. These design charts can be used to establish the torque capacity of any given gear, or can be used to establish the size of gear required to transmit a given torque. A design factor K, from Figure 16, is used with the charts to increase the torque which must be transmitted, or to decrease the torque which the gear is capable of transmittingo A few brief examples will illustrate how the charts are used. Example l: A 32 pitch pinion having a 1/2" face width is to transmit a torque of 54 lb inches at 1760 RPM. The teeth will be formed by molding, and will be lubricated. A life of 100 million revolutions is desired. What should be the pitch diameter of this pinion? Figure 16 shows a design factor of 1.0 for molded and lubricated teeth with a pitch line velocity below 4000 ft/min, hence the design torque will be the same as the actual torque, 54 lb-inches.

16 20 24 28 32 36 40 44 48 52 56 60 64 0 100 200 300 400 500 NUMBER OF TEETH IN PINION PINION TORQUE, LB.-IN.0 1.5 2.0 2.5 3.0 3.5 PINION ORQUE, LB-IN. 1.0 1.5 2.0 2.5 3.0 3.5 4.0 PITCH DIAMETER. INCHES Figure 17. Design Chart for 16 Pitch Gears

0 ~ ~~ 1 20) 25 303A0 45 5 5 60 6 0 7 ol ~~~~~37_ 1 1 1 X~~ 4`~~~~~~~~~4 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0 15 20 25 30 35 40 45 50 55 60 65 70 5 0 100 200 300 400 500 NUMBER OF TEETH IN PINION PINION TORQUE, LB-IN. 1 1. 20 3"; 1.5 2.0 25 3.0 3.5 PITCH DIAMETER, INCHES Figure 18. Design Chart for 20 Pitch Gears

- - - I AII -I ~ 1 I I y / I - 16 24 32 40 48 56 64 72 80 88 96 104 112 0 50 100 150 200 250 NUMBER OF TEETH IN PINION PINION TORQUE, LB.-IN. PINION TORQUE, B.-IN0.5 1.0 1.5 2.0 2.5 3.0 3.5 PITCH DIAMETER, INCHES Figure 19. Design Chart for 32 Pitch Gears

JiYll llllllllI I -Hll I I I I I I I I I I I I I I I I. o o I. 16 24 32 40 48 56 64 72 80 88 96 104 112 0 16 32 48 64 80 NUMBER OF TEETH IN PINION PINION TORQUE, LB-IN. 2.0 PITCH DIAMETER, INCHES Figure 20. Design Chart for 48 Pitch Gears O 16 32 48 64 80 NUMBER OF TEETH IN PINION~~~~~~~~~~LS

315The solution is shown by the dashed lines of Figure 19, the Design Chart for 32 pitch teeth. The dashed line is started at 54 lb-inch on the torque scale, is extended upward to intersect the 1/2" face line, then is drawn horizontally to the right to intersect the 100 million cycle line, then downward to find the number of teeth to be 68, and the pitch diameter 2.125 inches. Example 2: What diameter would be required for the pinion of the preceding example if the teeth had been formed by hobbing, and were to operate with no lubrication? Figure 16 shows a design factor of 0.70 for 32 pitch cut teeth without lubrication. Then the design torque will be: Design torque -5 = 77. lb-in 0.70 The solution is similar to that of Example 1, except that the line is started at 77^1 lb-in on the torque scale, thus resulting in a pitch diameter of 3.0 inches, with 96 teetho Example 3: What torque could the pinion of Example 1 transmit if the teeth were not lubricated? Figure 16 shows a design factor of 0.80 for 32 pitch molded gears without lubrication when the velocity is below 4000 ft/min. Then the torque which the pinion can. transmit will be: torque = 54 lb-in x 0.80 = 43.2 lb-in.

-32As when calculating the load capacity of the gears by means of Equations 2 or 3, the results obtained from the design charts should be modified by the judgment of the designer to allow for impact or overloading which may be anticipated. OTHER DESIGN RECOMMENDATIONS The following design recommendations are based on information obtained from various tests and investigations with gears of "Zytel"*: 1. Size of Teeth: As with metal gears, it is desirable to use the smallest teeth which are strong enough to transmit the necessary power. The limitations of the load carrying calculations should be considered when determining the size of teeth to be used. 2. Pressure Angle and Tooth Form: Full depth teeth with a 20~ pressure angle appear to be quite satisfactory. The full depth teeth may be strengthened by making the blank oversize, but this must not be carried to extremes, since the strength gained by making the tooth thicker at its base may be more than offset by the weakening effect of higher temperature caused by the increased normal force and sliding velocity. The 16 pitch, 27 tooth, 200 pressure angle gears made with blank diameters 1/16" oversize had greater life than these same gears made with standard full. depth teetho Similar gears with 20~ stub teeth, and with 30~ stub teeth, had less life than the 20~ full depth teeth,

-333. Accuracy of Manufacture: It is desirable to have the teeth as accurately made as is reasonably possible. The life of the gears are shortened when the teeth are not accurately formed and spaced. 4. Backlash: Backlash must be provided, but performance does not seem to be affected by reasonable variations in backlash. Recommended backlash, measured at room temperature, is given below: Diametral Pitch Backlash, inches 16 0.004 - 0.006 20 0.003 - 0.005 32 and finer 0.002 - 0.004 For high speed or very heavy load operation, which may heat the teeth) the backlash should be somewhat more liberal than the values listed. 5* Gear Proportions: Rims, webs, and hubs should be rather generously proportioned to provide ample support for the teeth. This is especially important if the teeth are to be heavily loaded. In general the rim thickness beneath the root of the teeth should be at least 3 times the thickness of the teeth at the pitch circle, the web thickness should be about equal to the rim thickness, the hub diameter at least 1~ times the shaft diameter, and the hub length at least equal to the shaft diameter.

-34If the gear is large and the teeth are to be heavily loaded, it is better to mount the gear of "Zytel" on a metal flange rather than key or spline the gear directly to the shaft, Molded gears should be designed to reduce or eliminate the formation of residual stresses, and the mold should preferably have a ring gate to maintain concentricity. 6. Treatment after Molding: The gears should be fully annealed after molding if there is any evidence of residual stresses being present. It is better to design the gear to prevent the formation of these stresses, rather than to rely on the annealing to remove the stresses, since the annealing process may affect the accuracy of the teeth if the residual stresses are not uniformly distributed, ADDITIONAL INVESTIGATIONS AND RESULTS A considerable amount of experimental work has been done in addition to the life testing previously described. Some of the most interesting is work including here. From a rather extensive wear testing program carried on with cut gears, it was concluded that tooth wear is insignficant in the sizes tested, whether the teeth are or are not lubricated. Inspection of a number of the molded gears after long periods of operation showed that this was also true for the molded teeth. To try out the load carrying calculations on something other than the test machines, a Boston helical gear speed reducer was equipped with the helical pinion and gear of "Zytel" shown in Figure 21. These

-35-................................................ -........................................................................................................................................................................................................................................................................................................................................................................................................................................... I............................................................................................................ -.................................................................................................................................................................................................................................................................................................................................................................................................................. M.N. Figure 21. Helical Pinion and Gear,, Hob Cut............................................................................................................................................................................................................. : I I.. 1. I I I I 1.11.1- 111 -.............................................................................................. X.-%v................................................................................................................................................................................................................................................................. --- --.....

-36have a normal pitch of 12, with 19 and 57 teeth, and a 23.56~ helix angle. The pinion is 0,030" oversize on the outside diameter, while the gear is this same amount undersize. The face widths for the pinion and gear are 2.25" and 2.0" respectively. The gears of "Zytel" replaced 10 pitch steel gears with face widths of 2,25" and 2.50". With the steel gears the reducer had a rating of 10 HP at 1760 RPM of the pinion. The gears of "Zytel" transmitted 7- HP at 1760 RPM for 2091 hours before failure. This represents 221 million revolutions of the pinion, or cycles of tooth loading, at a calculated pinion tooth bending stress of 2560 psi, and is in substantial agreement with predicted life based on our test machine data. Figure 22 shows the gears installed in the speed reducer. A vane pump, driven by a roller chain is used to load the speed reducer. The gears of "Zytel" survived the shearing off of all the teeth in the sprocket mounted on the reducer, and an oil leak in the gear housing which allowed the teeth to run without lubrication for an extended period of time. Figure 23 shows some results of an investigation of gear tooth temperature. The temperature shown were obtained by operating the gears under load for a period of time to allow the temperature to become stabilized, then stopping the machine quickly and measuring the tooth temperature with a thermocouple imbedded in a cork holder contoured to fit the space between the teeth, This work was done with gears having cut teeth, and the ambient temperature was approximately 80 ~F,

-37130 I TEMPERATURE RISE OF ZYTEL GEAR TEETH 120 - - I I I 0 V 2946 Ft/Min. -/ - 16 P, 27 60Teeth, Lub 110 16 —-16 PI 27 60Teeth, No Lub. 1>~VI328/Mn, Vi. i V3928 Ft/Min. z90 _,, 70 r-. 1 - -- 7- Velz2946Ft./Min/ 50 M/ LI I. a I' Ve.2946./Min.71964'2Ft./Min. 40 Wg ~~aVel. ~ 946 nlkt/VI964 Ft./Min.-9 0 2 3 4 5 6 7 8 9 10 CALCULATED BENDING STRESS OO 100 PSI Figure 23. Temperature Rise o Gear Teeth 0 2 3 4 5 6 7 8 9 10 CALCULATED BENDING STRESS-^- 1000 PSI Figure 23. Temperature Rise of Gear Teeth

At any particular bending stress, the temperature increase was considerably greater for the lubricated 16 pitch teeth than for the. lubricated 32 pitch teeth running at the same velocity. This is to be expected, since for the same stress, the 16 pitch teeth carry a much greater load than do the 32 pitch teeth. Furthermore, the sliding velocity is somewhat greater for the 16 pitch teeth. This combination of greater load and sliding velocity could logically account for the higher temperature of the 16 pitch teeth. It is felt that the higher temperature of the larger teeth accounts in part for the lower stresses at which lhese larger teeth fail. However, no simple method of predicting the temperature rise has been established. Some experimental work concerning the application of "Zytel" to gearing is continuing at the present time, although the life testing program is now being concentrated on a new material. Gears of "Zytel" meshing with steel gears are under test, and an investigation of the relationship of sliding velocity, contact pressure, friction coefficient, and wear is in progress. Results will be published when available. In the meantime, it is hoped that the information in this paper will be useful to those who may design gears of "Zytel".