EXPERIMENTAL INVESTIGATION OF CHAIN TENSION AND ROLLER SPROCKET IMPACT FORCES IN ROLLER CHAIN DRIVES James C. Conwell Department of Mech icalEngineering Louisiana State University Baton Rouge, LA 70803 G. E Johnson Design Laboratory Mechanical Engineering and Applied Mechanics University of Michigan Ann Arbor, MI 48109-2125

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DESIGN, CONSTRUCTION, AND INSTRUMENTATION OF A MACHINE TO MEASURE TENSION AND IMPACT FORCES IN ROLLER CHAIN DRIVESi James C. Conwell Department of Mechanical Engineering Louisiana State University Baton Rouge, LA 70803 G. E. Johnson Design Laboratory Mechanical Engineering and Applied Mechanics University of Michigan Ann Arbor, MI 48109-2125 Glen_E._Johnson@um.cc.umich.edu ABSTRACT Most previous experimental investigations of chain drive dynamics have been completed on the classical four-square test machine (also referred to as a chain speeder in the industry). In this paper we discuss the design and construction of a new test machine configuration that offers some advantages over the traditional design. The new machine and attendant instrumentation provide more realistic chain loading, and allow link tension and roller - sprocket impact monitoring during normal operation. The incorporation of an idler sprocket allows independent adjustment of test span length and preload. The angle at which rollers approach an instrumented sprocket can also be adjusted. Drawbacks of the new configuration (compared to the four-square design) are that the support structure may not be as rigid and the additional sprockets (idler sprocket and instrumented sprocket) add kinematic complexity. lThis paper is based on the Ph.D. dissertation research conducted by the first author under the direction of the second author at Vanderbilt University, completed in December 1989.

NOMENCLATURE a Pitch Angle of a Sprocket e(t) Time response of a dynamic system h(t) Time-based transfer function of a dynamic system i(t) Time-based input to the dynamic system E(w) Frequency response of a dynamic system H(w) Frequency domain transfer function I(w) Frequency input to the dynamic system

INTRODUCTION Chain drives are among the oldest of the basic machine elements. In spite of their widespread use, in 1984 Freudenstein observed that were not well understood. Freudenstein's observations, coupled with the desire on the part of the auto industry to better understand chain drives in order to reduce engine and power transmission development time, have lead to a renaissance in theoretical and experimental investigation, including studies by Chen and Freudenstein (1988), Wang (1992), Wang et al (1992), Kim (1990), Kim and Johnson (1992a and 1992b), Choi and Johnson (1992a and 1992b), Conwell, Johnson, and Peterson (1992a, 1992b, 1992c), and Veikos and Freudenstein (1992a and 1992b). Chain drive dynamics became of interest to the automobile industry with the rise in importance of noise, vibration, and harshness (NVH). Chain drives offer non-slip, light weight, inexpensive, compact power transmission compared to belts or gears, but usually at the cost of increased noise and vibration. A brief history of chain drives and the important milestones in their practical development through the late twentieth century can be found in Conwell (1989). Today, three types of chains are commonly found: roller chains, silent chains and engineering steel chains. The new test machine was designed specifically to investigate roller chains, so the remainder of this discussion will be limited to chains of this type. Chain drives were poorly understood through the 1980's for a variety of reasons, including the polygonal action, nontrivial sprocket geometry, intentional clearances and unintentional dimensional variations due to manufacturing tolerances, friction, and the large number of bodies that make up the typical chain and sprocket system. The manufacture of roller chains has been standardized by the American National Standards devoted to the study of roller drive chain behavior was given by Bartlett (1935). Bartlett developed a new approach to rating roller chain drives based upon sprocket impact loads and experience. Bremer (1947) reported on marine applications and analyzed the various loads on chain drives. Staments (1951) considered the fundamental loads on chain drives using an optical strain gage. Most modem work can be directly traced to Binder's (1956) classical text. In his work, Binder both documented and extended the work of many early chain investigators. Polygonal action has been one of the most studied chain drive topics. Morrison (1952), Mahalingham (1952), Okoshi and Uehara (1959a and 1959b) and Bouillon and Tordion (1965) all reported on this phenomenon. Ryabov (1968) and Chew (1985) modeled the inertia effects on impact forces in chain drives, while Radzimovsky (1955) developed an 'equalizing' linkage in an attempt to minimize the impact. Turnbull and Fawcett (1975) completed an approximate kinematic analysis of roller chain drives. Recent research on chain drives has been conducted at the University of Michigan (Johnson), Pennsylvania State University (Wang), University of Texas (Marshek), Chalmers University of Technology (Gerbert) and Columbia University (Freudenstein). Marshek and his students (1978, 1982, 1983a, and 1983b) determined quasi-static chain and sprocket load distributions. Chen and Freudenstein (1988) completed an approximate kinematic analysis of the roller chain drive. Veikos and Freudenstein (1992a and 1992b) developed a lumped mass dynamic model based on Lagrange's equations of motion and also studied chain drive vibrations. Wang's work is based on a continuous model of the axially moving material and he has studied the stability of chain spans subject to periodic

sprocket excitations (Wang 1992) and the effect of impact intensity on chain drive vibrations (Wang, et al, 1992). Gerbert studied the tooth load distribution of seated and unseated roller chains and timing belts and made several important observations about the effects of friction and elasticity. Kim and Johnson (1992a and 1992b) developed a detailed model of the roller - sprocket contact mechanics that allowed the first determination of actual pressure angles and a multi-body dynamic simulation based on Kane's dynamic equations. Choi and Johnson (1992a and 1992b) incorporated the effects of impact, polygonal action, and chain tensioners into the axially moving material model and studied transverse vibration of chain spans. Much work has been completed, but much work remains. The remainder of this article is devoted to the physical description of our test machine, along with its attendant general purpose instrumentation. CHAIN DRIVE EVALUATION MACHINE Design of the New Test Machine The new test machine was designed to load the chain drive up to three horsepower over a wide range of chain speeds, with adjustable center distance between sprockets, and with an adjustable angle of approach for engagement of the chain with an instrumented sprocket. An assembly drawing of the test machine is presented in Figure 1. Table 1 contains a list of components of the test machine, with letters referenced in Table 1 corresponding to parts located in Figure 1. A primary advantage of the'new load scheme and geometry is that the center distance in one of the chain spans is independent of chain tension. The length can be measured with a pair of machinist's dividers and adjusted as required. Another advantage is that an instrumented idler with adjustable angle of approach can measure the dynamic interactions between rollers and sprocket teeth. A third advantage of the design is that it allows overhung sprocket mounting so that a strain gage can be mounted on a link side plate and can be connect with a wiring harness to strain monitoring instrumentation. Drive Train The test machine is powered by a three-phase, 208 volt, three horsepower electric motor (K). The drive shaft of the test machine is supported by a welded steel bracket (G) and is driven by the motor through a V-Belt (I) and sheave (F). The motor is mounted on an adjustable frame (H). The adjustable base can accommodate different size motor drive shaft sheaves; different drive sheaves provide different linear chain speeds. Furthermore, the frame allows quick adjustment of the drive belt tension to compensate for any belt stretch that may occur. The motor mounts were selected to reduce transmission of shock to the motor base. The motor has a 'no-load' operating speed of 1740 revolutions per minute. On/off control of the motor is accomplished by a NEMA size 0 motor starter (AA). Chain Loading Preloading the chain is accomplished through the use of an idler/tensioner sprocket assembly (V). This assembly consists of a twelve tooth idler sprocket, a load cell and an adjustment track which permits the vertical location of the center line of the sprocket to be varied. The load cell is an integral part of the assembly and can instantly measure the vertical force being applied to the shaft of the idler/tensioner sprocket.

The preload chain tension was calibrated as a function of the output of the integral load cell. During experiments, once the desired preload tension is reached, the idler/tensioner assembly is locked into position. The power transmission component of the chain load is obtained by placing external loads on the resistive shaft (X). A sheave (W) is mounted on the resistive shaft. This pulley, via a V-belt (L), drives a countershaft assembly (M,P) which in turn drives a 60 ampere automobile alternator (S). The countershaft assembly allows the alternator to turn at a higher speed than the resistive shaft. Furthermore, by changing the pulleys mounted on the countershaft (M), it is possible to maintain a constant speed of the alternator. This arrangement allows tests to be conducted for a range of linear chain speeds with constant torque transmission. To vary the torque transmitted by the test chain drive, electricity produced by the alternator is passed through a load box with 15 three ohm switched resistors wired in parallel. The torque transmitted by the chain (and required to rotate the resistive sprocket) can be varied by altering the number of resistors switched into the alternator circuit. During the operation of the test machine, the speed of the alternator is 4500 RPM. The alternator produces approximately 13.6 V DC at this speed. The vertical location of the resistive shaft assembly can be varied. The shaft assembly can be moved along the vertical support (J), while the support arm (U) can be slid along the main support beam (Z), permitting the use of a variety of test sprockets (D), while maintaining the horizontal aspect of the upper chain span. Additionally, the horizontal position of the resistive shaft can be varied, although it was maintained in a fixed position throughout the experiments. Chassis and Frame The baseplate of the machine (N) is cold-rolled, quarter-inch thick steel plate, while the main structural members (Z) are three-inch I beams. These materials were chosen for their stiffness, their good machining characteristics and their low cost. The main structural members are welded together and bolted to the base plates. The resistive shaft assembly (Y) is mounted on a structure of 3/4-inch cold-rolled round steel members (J) and (U). The center distance between the resistive sprocket and the test sprocket (D) can be adjusted, as can the height of the resistive sprocket. The drive shaft, the countershaft and the resistive shaft are supported by 3-inch wide, 3/8-inch hot rolled steel plates. All of the shafting in the test machine is constructed of 5/8-inch cold rolled steel rounds, chosen for both strength and surface finish. Test Machine Instrumentation An IBM 80286 based computer with 80287 math coprocessor is used to control and monitor the experiments through an IBM Data Acquisition and Control Adapter (IBM DACA board) and an IBM General Purpose Interface Bus Adapter (IBM GPIB board). The primary use of the DACA board is the determination of the rotation speed of the instrumented sprocket (D). A photon coupled interrupter module is placed across the instrumented sprockets so that the teeth of the sprocket intermittently block the beam across the interrupter as the sprocket rotates. The output of the interrupter module is 0.8 V DC when the beam is not blocked, but rises very quickly to 6.0 V DC once the beam is blocked. The DACA board is used to both power and monitor the voltage output of the photon interrupter. If the number of teeth on the instrumented

instrument and the sampling rate of the DACA board are known, then the speed of the instrumented sprocket can be readily determined. The GPIB is defined by ANSI/IEEE Standard 488-1978. The data were collected with the aid of a Bruel and Kjaer (B&K) 2032 dual channel spectrum analyzer. This analyzer can be totally controlled via the GPIB bus. Serial polls can be requested from the 2032, providing a means of updating status as well as error checking. One of the most useful capabilities of the 2032 is the ability to store a data file of measurement results in an external storage medium (e.g., the hard drive on a computer). The 2032 has the capability to perform realtime analysis as well as process previously collected data. Tension Monitoring The tension in a link is monitored by means of a strain gage mounted on the link side plate (a quarter bridge). The strain gage is connected to a Vishay/Ellis (V/E) 20A Digital Strain Indicator by a wiring harness to condition the output of the strain gage. The features of the V/E 20A are an isolated DC power supply for gage excitation, bridge completion circuits to achieve initial bridge balance and calibration, a fixed gain DC differential amplifier and a digital voltmeter readout. The V/E 20A has excellent shielding and is almost immune to electrical noise common found in the vicinity of motors and other electronic equipment. The V/E 20A output (plus or minus 5 volts DC) can be fed directly from the strain indicator to the B&K 2032. Figure 3 presents a schematic drawing of the instrument connections for the chain tension experiments. The tension on each link varies throughout the operation of the chain drive. A gross variation occurs as the chain moves from the tight span to the loose span and back again. High frequency variation occurs due to impact, and span stiffness and span length variations that take place as the rollers engage and disengage with the sprockets. It is likely that this cyclic loading of the links strongly affects chain life descriptors like stretch, wear, and fatigue, and other performance descriptors like noise and vibration. Impact Monitoring To illustrate the mechanism of impact in roller chain drives, Figure 2 shows a chain wrapping around a sprocket. Roller A is shown seated on the sprocket. As the sprocket continues to turn, the chain link joining rollers A and B articulates about the pin joint of roller A. After the sprocket has rotated an angle equal to the pitch angle of the sprocket (a), roller B approaches and impacts the sprocket at the next subsequent tooth recess. As the sprocket continues to turn, this event repeats itself. The magnitude of the impulsive force at impact is numerically equal to the product of the effective mass (the mass involved in the impact), the relative velocity between a roller and the sprocket tooth recess and the reciprocal of the time for the event to occur. In order to measure the impact force, an instrumented sprocket support and frame was incorporated into the machine. Referring again to Figure 1, this instrumented sprocket assembly is indicated by the letters A, B and C with the actual instrumented sprocket as letter D. Each of the instrumented sprocket brackets are two-force members, joined to the main superstructure of the machine and to each other with pinjoints. As two-force members, they can only transmit loads applied along their length. The two support brackets are arranged orthogonally with respect to each other. Each of the support brackets has a load cell included as an integral part of the bracket. As a roller element seats onto the instrumented sprocket (D), an impact force occurs. This impact force is immediately resolved into the two orthogonal directions (horizontal and vertical) through the use of the two force members, while the magnitude of the force in each direction is determined by the load cell.

Each load cell is an aluminum ring with four strain gages. Two of the gages are mounted on the exterior of the ring and two on the interior in order to increase load cell output and sensitivity. The output from each load cell is fed into a Vishay-Ellis 20A digital strain indicator, which also provides the excitation for the strain gage bridge. The output of the strain indicators is then fed into the B&K 2033 (the signal from the vertical load cell is monitored by Channel A and the signal from the horizontal load cell is monitored by Channel B). The photocell is powered by the IBM computer and its output during the experiment is monitored by the DACA board. Additionally, the computer controls the spectrum analyzer throughout the experiment. Figure 4 presents a schematic drawing of the instrument connections for the impact force experiments. Determination of the Impact Input Force From Measurement of the Output Spectra The response of virtually any linear system can be related to the system input through a transfer function. In the time domain, this relationship can be expressed as: t e(t) = fi(t)h(t - t)dt (1) 0 where e is the response of the system, h is the impulse response or unit sample response, and i is the system input. In the frequency domain, equation (1) becomes: E(w) = H(w) * I(w) (2) It is customary to work with equation (2), i.e., in the frequency domain. If the input to the system is known, then the response of the system can be measured. It is then a simple matter to deduce the system transfer function. The transfer functions for both the horizontal and vertical load rings were experimentally determined by this strategy. In experiments, the system response can be measured, and the known system transfer functions can then be used to deduce the input excitation, i.e., the impact force associated with the conditions of the experiments. Conversion Of The Machine From Tension Measurement to Impact Measurement The sprocket support structure can be changed from an arrangement where the sprockets are supported by one bearing on each side to an arrangement where the sprocket is overhung. In the first position the impact force can be measured. In the overhung position, the wiring harness from the link side plate strain gage is free to move around the chain span (at least until the helix that the wires wind themselves into is ready to fail - on the order of one minute). This allows the tension measurement. A General Electric H21B1 photon coupled interrupter module is used as a locator device in order to provide a reference point for each data cycle. A sketch of the experimental setup is shown below, followed by a representative strain gauge output data. SUMMARY In this paper we have presented the essential features of the new test machine. The new machine offers significant advantages that allow more data collection options than have been

traditionally available. Data obtained with the new test machine will be reported in another article and can also be found in Conwell (1989). ACKNOWLEDGMENT After the test machine had been built, the National Science Foundation provided support for experiments through grants no. MSM-88-12957 and MSS-89-96293. This support is gratefully acknowledged. REFERENCES American National Standards Institute, 1972, "Transmission Roller Chains and Sprocket Teeth," ANSI Standard B29. 1, New York, NY. Bartlett, G.M., 1935, "A New Basis for the Rating of Roller Chain Drives," Trans. ASME, V. 57, Number 3, pp. 97. Binder, R.C., 1956, Mechanics of the Roller Chain Drive, Prentice-Hall, Englewood Cliffs, NJ. Bouillon, G., and Tordion, G.V., 1965, "On Polygonal Action in Roller Chain Drives," Trans. ASME J. Engineering for Industry, V. 87B, pp. 243-250. Bremer, N.C., 1947, "Heavy Duty Chain Drives for Marine Propulsion Service," Trans. ASME, V. 69, pp. 441-452. Chen, C-K, and Freudenstein, F., 1988, "Toward a More Exact Kinematics of Roller Chain Drives," Trans. of the ASME J. Mechanisms. Transmissions and Automation in Design, V. 110, No. 3, pp. 269-275. Chew, M., 1985, "Inertia Effects of a Roller-Chain on Impact Intensity," Trans. ASME J. Mechanisms, Transmissions and Automation in Design, V. 107, pp. 123-130. Choi, W. and Johnson, G. E., 1992a, Vibration of Roller Chain Drives at Low. Medium and High Operating Speeds, MEAM Technical Report Number 92-08, University of Michigan, Ann Arbor, Michigan. Choi, W. and Johnson, G. E., 1992b, Transverse Vibrations of a Roller Chain Drive with Tensioner, MEAM Technical Report Number 92-09, University of Michigan, Ann Arbor, Michigan. Conwell, J. C., 1989, An Examination of Transient Forces in Roller Chain Drives, Ph.D. Dissertation, Vanderbilt University, Nashville, TN. Eldiwany, B.H. and Marshek, K.M., 1984, "Experimental Load Distributions for Double Pitch Steel Roller Chains on Steel Sprockets," Mechanism and Machine Theory, Volume 19, Number 6, pp. 449-457.

Freudenstein, F., 1984, "Machine Dynamics: Some Thoughts on Research Initiatives," Trans. ASME J. Mechanisms. Transmissions. and Automation in Design, V. 106, No. 3, pp 264 - 266. J Gerbert, G., et al, 1978, "Load Distribution in Timing Belts," Trans. ASME J. of Mechanical Design, V. 100, pp. 208-215.,Ij 3J. J? JGerbert, G., 1989, "Tooth Action in Chain and Timing Belt Drives," Proceedings of the International Power Transmission and Gearing Conference, Volume 1 ASME, Book 10288A - 1989, pp 81 - 89. Kim, M. S., 1990, Dynamic Behavior of Roller Chain Drives at Moderate and High Speeds, Ph.D. dissertation, University of Michigan. Kim, M. S., and Johnson,G. E., 1992a, Mechanics of Roller Chain-Sprocket Contact, MEAM Technical Report Number 92-06, University of Michigan, Ann Arbor, Michigan. Kim, M. S., and Johnson, G. E., 1992b, A General Multi-Body Dynamic Model to Predict the Behavior of Roller Chain Drives at Moderate and High Speeds, MEAM Technical Report Number 92-07, University of Michigan, Ann Arbor, Michigan. Mahalingam, S., 1858, "Polygonal Action in Chain Drives," J. Franklin Institute, Number 1, pp. 23 -28. *Marshek, K.M., 1978, "On the Analyses of Sprocket Load Distribution," Mechanism and Machine Theory, Volume 14, pp. 135-139., Morrison, R.A., 1952, "Polygonal Action in Chain Drives," Machine Design, Volume 24, pp. 155 -159. UNaji, M. and Marshek, K.M., 1983a, "Analysis of Sprocket Load Distribution," Mechanism and Machine Theory, Volume 18, Number 5, pp. 349-356. Naji, M. and Marshek, K.M., 1983b, "Experimental Determination of the Roller Chain Load Distribution," Trans. ASME J. Mechanisms. Transmissions and Automation in Design, V. 105, pp. 331-338. Okoshi, M. and Uehara, K., 1959a, "Study on the Uneveness of Transmission Roller Chains, First Report," Journal of the Japan Society of Precision Engineering, Volume 25, Number 9, pp. 425-431.

Okoshi, M. and Uehara, K., 1959b, "Study on the Uneveness of Transmission Roller Chains, Second Report," Journal of the Japan Society of Precision Engineering, Volume 25, Number 10, pp. 552-558. Radzimovsky, E.I., 1955, "Eliminating Pulsations in Chain Drives," Product Engineering, Volume 26, pp. 153-157. Ross, M.O. and Marshek, K.M., 1982, "Four-Square Sprocket Test Machine," Mechanism and Machine Theory, Volume 17, Number 5, pp. 321-326. Ryabov, G.K., "Inertial Effects of Impact Loading in Chain Drives," Russian Engineering Journal, Volume 48, Number 8, pp. 17-19. Staments, W.K., 1951, "Dynamic Loading of Chain Drives," Trans. ASME, July 1951, pp. 655-665. Turnbull, S.R., and Fawcett, J.N., "An Approximate Kinematic Analysis of the Roller Chain Drive," Proceedings of the Fourth World Congress on Theory of Machines and Mechanisms, pp. 907 -911. Veikos, N. C. and Freudenstein, F. 1992a, "On the Dynamic Analysis of Roller Chain Drives: Part 1- Theory", Mechanism- Design and Synthesis, DE-vol. 46, edited by Kinzel et al, ASME, NY, 1992, pp.431-438. Veikos, N. C. and Freudenstein, F., 1992b, "On the Dynamic Analysis of Roller Chain Drives: Part 2,", Mechanism Design and Synthesis, DE-vol. 46, edited by Kinzel et al, ASME, NY, 1992, pp.439-450. Wang, K. W., 1992, "On the Stability of Chain Drive Systems Under Periodic Sprocket Oscillations," Trans. ASME J. Vibration and Acoustics, Vol. 114, pp 119 - 126. Wang, K. W., et al, 1992, "On the Impact Intensity of Vibrating Axially Moving Roller Chains," Trans. ASME J. Vibration and Acoustics, Vol. 114, pp 397 - 403.

TABLE 1 PARTS LIST FOR THE CHAIN TEST MACHINE Part Letter Part Description A Strain Gauge/Load Ring Assembly B Isolated Sprocket Bracket C Isolated Sprocket Support D Mechanically Isolated Sprocket E Drive Sprocket F Drive Pulley G Drive Shaft Support Assembly H Electric Motor Adjustable Base I Drive Belt J Resistive Sprocket Vertical Support K 3 HP Electric Motor L Countershaft Drive Belt M Countershaft Pulleys N Machine Base plates O I-Beam Horizontal Supports P Countershaft Support Assembly Q Alternator Drive Bracket R Alternator Support Bracket S Alternator T Resistive Sprocket Support Plate U Resistive Sprocket Support Arm V Idler/Tensioner Sprocket Assembly W Countershaft Drive Pulley X Resistive Sprocket Y Resistive Pulley Shaft Support Z Main Superstructure Support Beam AA NEMA Size 0 Motor Starter

Figure 1. Schematic drawing of the new test machine. Roller A Roller B Chain Pitch P Figure 2: Roller B is about to seat, causing an impact force between roller B and the sprocket.

POSITION PHOTOCELL OUTPUT CHAIN STRAIN GAGE B&K 2032 IBM AT | - l I INSTRUMENT CONTROL AND DATA TRANSFER Figure 3: Schematic drawing of the instrumentation for the measurement of the chain tension.

HORIZONTAL LOAD CELL SPEED PHOTOCELL INFORMATION I INSTRUMENT CONTROL AND DATA TRANSFER Figure 4: Schematic drawing of the instrumentation for the measurement of the impact force.

Experimental Investigation of Link Tension and Roller - Sprocket Impact in Roller Chain Drives James C. Conwelll Department of Mechanical Engineering Louisiana State University Baton Rouge, LA 70803 G. E. Johnson Design Laboratory Mechanical Engineering & Applied Mechanics University of Michigan Ann Arbor, MI 48109-2125 ABSTRACT This paper presents the results from a recent experimental investigation into the dynamic behavior of roller chain drives. A strain gage mounted on a link side plate was used to measure the force in the link side plate during normal operation over a wide range of linear chain speeds and preloads. The test machine also included a specially instrumented idler sprocket that allowed the measurement of the horizontal and vertical components of the bearing reaction force. The roller - sprocket impact force was then determined with an experimentally determined transfer function approach facilitated by a Bruel & Kjaer 2032 dual channel spectrum analyzer. Observations about the data include: * As is typically assumed, under quasi-static conditions, dynamic effects can be neglected without introducing significant error. ~ As chain speed increases, dynamic effects become increasingly important. * As is the case for belt drives, the average tight side chain tension can be expressed in the classical form of the preload, the driven load, and the load due to centrifugal force with only modest error over a wide range of linear chain speeds. * The tension in a chain link increases very rapidly as the link exits the driven sprocket. The increase from loose side to tight side average tension occurs over less than two sprocket teeth. * The tension in a chain link decreases very rapidly as the link enters the drive sprocket. The decrease from tight side to average loose side tension occurs over less than two sprocket teeth. * Transient spikes are present in the tension data at the point where the link exits the driven sprocket and at the point where the link enters the driven sprocket. * Impact force tends to increase as chain tension increases, however the relationship is not monotonic. tThis paper is based on the Ph.D. dissertation of the first author which was completed under the direction of the second author at Vanderbilt University, December 1989.

* Impact force tends to increase as chain speed increases, however the relationship is not monotonic. * For a chain traveling in the horizontal direction, the vertical component of the impact force is much larger than the horizontal component. * The magnitude of the horizontal component of the impact force increases more rapidly than the magnitude of the vertical component as the chain speed increases, indicating that the angle of impact (as measured from a vertical line) increases as chain speed increases. INTRODUCTION Several investigators have studied the forces that exist in a chain link during operation of the chain drive (Staments (1951), Radzimovsky (1955), Binder (1956), Ryabov (1968), Turnbull and Fawcett (1975), Naji and Marshek (1983a and 1983b), Eldiwany and Marshek (1984), Chew (1985), Chen and Freudenstein (1988), Wang (1992), Wang et al (1992), Kim and Johnson (1992a and 1992b), Choi and Johnson (1992a and 1992b), Veikos and Freudenstein (1992a and 1992b), and Gerbert (1978 and 1989)). As a link moves around the drive, the forces in the link vary. In the most general case, these forces go from a high level on the 'tight' side of the chain, reduce in magnitude as the link engages with and then rotates around the drive sprocket to the 'loose' side of the chain, and then increase in magnitude as the link moves around the driven sprocket and returns to the tight side. Furthermore, when a link leaves the span and engages with a sprocket, an impact force occurs due to the relative velocity between the roller and sprocket. It has been proposed that these forces are responsible for the stretch, wear, fatigue, noise, and vibration that occur in chain drives. Until now these forces have never been experimentally measured throughout the link's cycle from tight to loose and back again. To enable direct measurements of the link tension and impact forces, a new test machine was designed and built. The design details and the instrumentation attendant to the machine are described in a companion article in this journal. The experiments described here were completed with the new test machine and with standard ANSI number 40 riveted steel roller chain and 40B12 sprockets. Link tension data were collected first. Then the test machine was reconfigured and impact data were collected. In the remainder of this paper, the experimental methods and the data that were collected are presented and discussed. For the purpose of this discussion, an experimental run is defined as an experiment conducted for a specific chain speed, dynamic chain loading, and chain preloading. An experimental group is all of the experimental runs conducted at a specific chain speed. An experimental group consists of 36 experimental runs. A total of four experimental groups (for a total of 144 experimental runs) were conducted. Data are tabulated in the Appendix. More complete details of the experiments and instrumentation can be obtained by consulting Conwell (1989). LINK TENSION Procedure The procedure developed to measure the chain side plate force is outlined below. 1. Set preload. Monitor output from the link side plate strain gauge. 2. Configure Bruel & Kjaer 2032 (B&K 2032).

3. Set resistance level for alternator circuit. Position photocell power on. 4. Place B&K 2032 in time history mode to act as high speed, high accuracy A/D converter. 5. Five seconds after B&K 2032 is placed in time history mode, turn on test machine. Run test machine for 30 seconds. Five seconds after test machine shut off, take B&K 2032 out of time history mode. 6. While B&K 2032 is in time history mode, write data to Intel 80286 based computer controlling the equipment. Once a particular experimental run is completed, place additional information in this data file concerning the time and date of the test and the overall status of the data. 7. Check data for existence of overload condition prior to beginning a new test. Overload indicates invalid test run. Discard data if overload was present. 8. Remove resistance from alternator and preload from chain. The entire test procedure was automated and controlled by an Intel 80286 based personal computer. This facilitated repeatability and consistency. Once an experimental group was completed, the test machine was dismantled, the speed was changed, and all calibrations were checked. The machine was then reassembled in preparation for the next experimental group. During the course of an experimental run, the link on which the strain gauge is mounted travels around the chain loop (from loose to tight and back again) many times. Data from the tight sight of the chain span were separated from the data collected on the loose side of the chain span. Average values for chain side plate force were determined for both the tight and loose spans. Link Tension Data and Discussion Figures la through Id present the time averaged force in the tight side of the chain (as a function of torque transmitted) for the four linear chain speeds tested. These data can also be found in the Appendix in tabulated form. As would be expected, the data indicate that the addition of the preload tends to shift the tension in the tight side of the chain by the amount of the preload. The value of the tight side tension was predictably sensitive to the linear chain speed. For example, the time averaged tight side tension at a sprocket speed of 1400 rpm is approximately 8 pounds higher than the time averaged tight side tension at a sprocket speed of 800 rpm for comparable pre- and external loading. Consider the free body diagram of the load sprocket shown in Figure 2. The model often posed for this case is simply Tt =(M / Rp) + Ti (1) where M is the external moment acting on the sprocket, Rp is the pitch radius of the sprocket, and Tt and Ti are the tight and loose side tensions respectively. If the experimentally preset external moment, and the experimentally measured time averaged loose side tension are substituted into equation (1), it is possible to use equation (1) to predict the tight side tension. These calculated results are presented in juxtaposition with the experimentally measured time averaged values for tight side tension in Figures 3a through 3d. The addition of a term that is proportional to the square of the linear chain speed allows fairly accurate prediction of the time averaged tight side tension, i.e., Tt = Preload + (M / Rp) +.00304wV2 (2a)

where w is the weight per unit length of chain in pounds per inch, V is the linear speed of the chain in inches per second, and other terms are as defined before. The coefficient on the third term of equation (2a) was determined by regression analysis. If the weight per unit length in equation (2a) is replaced by the mass per unit length divided by the acceleration of gravity, the equation becomes Tt = Preload + (M / Rp) + 1.17mV2 (2b) Incorporation of a term including the product of the mass per unit length and the square of the linear speed has been previously introduced to account for the centrifugal force in the general axially moving material problem (Mote, 1965). The constant of proportionality is dependent on the stiffness of the pulley (in this case sprocket) mounting system relative to the stiffness of the span of the moving material. For a simple single span system, the axially moving material model predicts that as the stiffness of the mounting becomes large relative to the stiffness of the span of moving material, the constant of proportionality approaches zero. As the stiffness of the mounting becomes small relative to the stiffness of the span of moving material, the constant of proportionality approaches unity. The constant of proportionality in equation (2b) is greater than unity, but this does not violate any physical principals. Beikmann, Perkins, and Ulsoy (1992) have shown that values larger than unity are possible for belt systems with two pulleys and a tensioner. It is even possible to predict negative constants of proportionality for some geometric configurations, indicating the presence of a static instability. Another possible explanation for the large constant of proportionality is the fact that there is no place for the effects of impact to be introduced in this model, except through the centrifugal force term. Accordingly, the constant of proportionality for the centrifugal force term will tend to be overestimated. Prediction of the constant of proportionality has been historically difficult. Typically, some approximate value has been assumed based on "experience." General guidelines which give approximate values for the constant of proportionality as a function of chain type, chain span, and qualitative mounting structure details would be useful and should be the subject of a future investigation. The study by Beikmann, Perkins, and Ulsoy (1992) is a seminal step toward realization of this goal. Load Distribution on the Sprockets The way that the chain force changes as the link moves from either span onto and around either sprocket has long been of interest. Binder (1956) was the first to formally report on this phenomenon. Marshek et al. (1984) presented load distribution data for quasi-static experiments. Kim and Johnson (1992a and b) present an analytical model that very accurately maps the data reported in Marshek et al. (1984). In the present study, realistic chain speeds were used, and dynamic effects were clearly important. Inertial effects, impact, friction, clearances, tolerances, alignment, and preloading are likely to all become increasingly important as chain speed increases. Typical data for one cycle around the loop (seated on load sprocket, exiting load sprocket, in tight chain span, over idler, in tight chain span, entering drive sprocket, seated on drive sprocket, exiting drive sprocket, in loose chain span, entering load sprocket) are shown in Figure 4a and 4b. There were clear and repeatable spikes at the point where the link leaves the load sprocket and at the point where the link enters the drive sprocket. There were no spikes at either the entry or the exit points on the idler sprocket, indicating that these spikes correspond to transient forces associated with rapid changes in the link tension. A second and related observation about the data is that the transition from the tight side tension to the loose side tension took place in the space of less than two links at the point of entry onto the drive sprocket. Similarly, the transition from the loose side tension to the tight

side tension took place in less than two links at the point of exit from the load sprocket. These results agree with the experimental observations made by Staments (1951) in his early experiments, and contradict the predictions that would be made by Binder's (1956) analytical model. IMPACT FORCE Procedure The procedure developed to measure the impact force as a roller seats on the sprocket is outlined below. 1. Preload upper chain span. Monitor output from the idler sprocket support load cells. 2. Turn on machine and place resistance across alternator circuit. 3. Configure Bruel & Kjaer 2032 dual channel spectrum analyzer (B&K 2032) to monitor frequency domain response of idler sprocket support load cells. 4. Power the speed photocell. The photocell and the computer controlling the experiment determine the rotational speed of the instrumented sprocket. 5. Warm up test machine for five minutes. 6. A total of 1500 spectra are averaged from both load cells. A spectrum is defined by 2048 points sampled at the Nyquist criterion rate. For this experiment, 4096 points per second were received by the analyzer. While the analyzer is averaging data, the speed photocell is intermittently polled and the rotational speed of the instrumented sprocket is determined. 7. Stop test machine and remove power from the speed photocell. Transfer data from the B&K 2032 to a computer file. Include in the file the time and date of the test, the speed of the instrumented sprocket, and the X,Y pairs (the frequency and the output from the load ring corresponding to this frequency) from the averaged spectra. To complete the next run, these steps are repeated. The entire test procedure was automated and controlled by an Intel 80286 based personal computer. This facilitated repeatability and consistency. Once an experimental group was completed, the load cells were removed from the test machine, the chain was replaced, the speed was changed, and the calibration was checked. The machine was then reassembled in preparation for the next experimental group. Impact Data and Discussion The data collected allow the determination of the impact force spectrum for various chain tensions and instrumented sprocket speeds. The strategy is based on an experimentally determined transfer function approach facilitated by the Bruel & Kjaer 2032 dual channel spectrum analyzer. Typical frequency domain data and results are presented in Figure 5. To obtain the transfer function, linear behavior was assumed, a known input excitation was applied to the sprocket, and the system response was measured. The transfer function is just the response divided by the input. Following this approach, transfer functions were obtained for both the horizontal and the vertical load cells. In subsequent experiments, the system response was measured, and the input (i.e., the impact force) was determined by dividing the response by the transfer function.

Magnitude of the Impact Force The impact force data can be presented in a three dimensional plot (see Figure 6) where impact force is shown as a response surface mapped over sprocket speed and chain tension. Raw data are presented in the Appendix. The impact force ranges from a low value of 6 pounds (800 rpm, 20 pound preload, 57.61 inch pounds of torque transmitted) to a high of 125 pounds (1400 rpm, 70 pound preload, 37.63 inch pounds of torque transmitted). Referring to Figure 6, as the tension in the chain span increases, the impact force also tends to increase. The impact force also tends to increase as the sprocket speed increases. However, neither relationship is monotonic. Data points contrary to these trends are dispersed throughout the space and their location(s) are likely to be related to the specific geometric details of the apparatus (possibly due to linear and/or nonlinear vibration phenomena in the system). This will be the subject of future investigations. A very steep rise in impact force was observed for increasing sprocket speed in the vicinity of 100 radians/sec and also in the vicinity of 120 radians/sec. We suggest that these data indicate the complexity of the relation between the impact force and the other system variables. Further research into the relation between the impact force and the mode shapes of the chain span, center distances, tension, chain speed, friction, clearances, tolerances, and alignment will be necessary before the impact phenomenon can be fully explained. A detailed analytical study of chain span vibration is presently being conducted by Choi and Johnson at the University of Michigan. The data can be summarized by an empirical equation obtained by regression analysis, i.e. Impact Force; -.0000303T +.012892c2T - 1.37118coT + 47.43351T +.00074603 -.25491Xo2 + 28.02622c) - 989.466 (3) where o is the angular velocity of the sprocket in radians per second and T is the chain tension in pounds. (In these experiments, the instrumented idler sprocket was set in the tight side of the chain span). The average difference between the impact force as computed by equation (3) and the impact force as measured in the experiment was 1.1068 pounds. Equation (3) is presented graphically in Figure 7. Angle of Impact Since the two load cells were mounted on two force members, the angle of the impact force is readily determined. The largest component of impact force was always detected by the vertical load cell. At 800 rpm, the angle of impact was approximately 11~ from the vertical. At 1000 rpm, the angle of impact was approximately 13~ from the vertical. At 1200 rpm, it was approximately 15.3~. At 1400 rpm, it was approximately 18~. These data indicate that the roller seating process is clearly speed dependent. This might be exploited through the design of special sprocket seat geometries for critical applications. This should be investigated further. CONCLUSION The data presented here provide a basis for further investigation in order to develop explicit phenomenological explanations of the behavior of chain drives. The following specific conclusions can be drawn from the data.. As is typically assumed, under quasi-static conditions, dynamic effects can be

neglected without introducing significant error. * As chain speed increases, dynamic effects become increasingly important. * As is the case for belt drives, the average tight side chain tension can be expressed in the classical form of the preload, the driven load, and the load due to centrifugal force with only modest error over a wide range of linear chain speeds. * The tension in a chain link increases very rapidly as the link exits the driven sprocket. The increase from loose side to tight side average tension occurs over less than two sprocket teeth. * The tension in a chain link decreases very rapidly as the link enters the drive sprocket. The decrease from tight side to average loose side tension occurs over less than two sprocket teeth. * Transient spikes are present in the tension data at the point where the link exits the driven sprocket and at the point where the link enters the driven sprocket. * Impact force tends to increase as chain tension increases, however the relationship is not monotonic. * Impact force tends to increase as chain speed increases, however the relationship is not monotonic. * For a chain traveling in the horizontal direction, the vertical component of the impact force is much larger than the horizontal component. * The magnitude of the horizontal component of the impact force increases more rapidly than the magnitude of the vertical component as the chain speed increases, indicating that the angle of impact (as measured from a vertical line) increases as chain speed increases. ACKNOWLEDGMENTS The authors gratefully acknowledge the support of the National Science Foundation through grants no. MSM-88-12957 and MSS-89-06293. We also wish to acknowledge the value of discussions with Messrs. S. Peterson, R. McReynolds, and G. Walker of Vanderbilt University, Messrs. N. Miller and F. Rasmussen of Bruel and Kjaer Instruments, Mr. R. Carroll of Sign Management Consultants, and Mr. K. Goodwin of Sverdrop Technologies. REFERENCES Beikmann, R. S., Perkins, N. C., and Ulsoy, A. G., 1992, "Free Vibration Analysis of Automotive Serpentine Belt Accessory Drive Systems," Proceedings of the 1992 CSME Mechanical Engineering Forum, Montreal, Canada, June, 1992, pp. 118-123. Binder, R. C., 1956, Mechanics of the Roller Chain Drive, Prentice-Hall, Englewood Cliffs, NJ.

Chen, C-K, and Freudenstein, F., 1988, "Toward a More Exact Kinematics of Roller Chain Drives," Trans. ASME J. Mechanisms. Transmissions and Automation in Design, Volume 110, No. 3, pp. 269-275. Choi, W. and Johnson, G. E., 1992a, Vibration of Roller Chain Drives at Low. Medium and High Operating Speeds, MEAM Technical Report Number 92-08, University of Michigan, Ann Arbor, Michigan. Choi, W. and Johnson, G. E., 1992b, Transverse Vibrations of a Roller Chain Drive with Tensioner, MEAM Technical Report Number 92-09, University of Michigan, Ann Arbor, Michigan. Conwell, J. C., 1989, An Examination of Transient Forces in Roller Chain Drives, Ph.D. Dissertation, Vanderbilt University, December 1989. Eldiwany, B. H. and Marshek, K. M., 1984, "Experimental Load Distributions for Double Pitch Steel Roller Chains on Steel Sprockets," Mechanism and Machine Theory, Volume 19, Number 6, pp. 449-457. Gerbert, G., et al, 1978, "Load Distribution in Timing Belts," Trans. ASME J. Mechanical Design, V. 100, pp. 208-215. Gerbert, G., 1989, "Tooth Action in Chain and Timing Belt Drives," Proceedings of the International Power Transmission and Gearing Conference, Volume 1, ASME, Book 10288A - 1989, pp 81 Kim, M. S., 1990, Dynamic Behavior of Roller Chain Drives at Moderate and High Speeds, Ph.D. dissertation, The University of Michigan, 1990, 122 pp Kim, M. S., and Johnson,G. E., 1992a, Mechanics of Roller Chain-Sprocket Contact, MEAM Technical Report Number 92-06, University of Michigan, Ann Arbor, Michigan. Kim, M. S., and Johnson, G. E., 1992b, A General Multi-Body Dynamic Model to Predict the Behavior of Roller Chain Drives at Moderate and High Speeds, MEAM Technical Report Number 92-07, University of Michigan, Ann Arbor, Michigan. Marshek, K. M., 1978, "On the Analyses of Sprocket Load Distribution," Mechanism and

Machine Theory, Volume 14, pp. 135-139. Mote, C. D., Jr., 1965, "A Study of Band Saw Vibrations," Journal of the Franklin Institute, Vol. 279, no. 6, pp. 430-444. Naji, M. and Marshek, K. M., 1983a, "Analysis of Sprocket Load Distribution," Mechanism and Machine Theory, Volume 18, Number 5, pp. 349-356. Naji, M. and Marshek, K. M., 1983b, "Experimental Determination of the Roller Chain Load Distribution," Trans. ASME J. Mechanisms. Transmissions and Automation in Design, Volume 105, pp. 331-338. Radzimovsky, E. I., 1955, "Eliminating Pulsations in Chain Drives," Product Engineering, Volume 26, pp. 153-157. Staments, W. K., 1951, "Dynamic Loading of Chain Drives," Trans. ASME, July 1951, pp. 655-665. Turnbull, S. R., and Fawcett, J. N., "An Approximate Kinematic Analysis of the Roller Chain Drive," Proceedings of the Fourth World Congress on Theory of Machines and Mechanisms, pp. 907-911. Veikos, N. C. and Freudenstein, F. 1992a, "On the Dynamic Analysis of Roller Chain Drives: Part 1- Theory", Mechanism Design and Synthesis, DE-vol. 46, edited by Kinzel et al, ASME, NY, 1992, pp.431-438. Veikos, N. C. and Freudenstein, F., 1992b, "On the Dynamic Analysis of Roller Chain Drives: Part 2,", Mechanism Design and Synthesis, DE-vol. 46, edited by Kinzel et al, ASME, NY, 1992, pp.439-450. Wang, K. W., 1992, "On the Stability of Chain Drive Systems Under Periodic Sprocket Oscillations," Trans. ASME J. Vibration and Acoustics, Vol. 114, pp 119 - 126. Wang, K. W., et al, 1992, "On the Impact Intensity of Vibrating Axially Moving Roller Chains," Trans. ASME J. Vibration and Acoustics, Vol. 114, pp 397 - 403.

APPENDIX This appendix lists the data collected during the experiments described in this paper. The data are grouped according to the rotational speeds of the instrumented sprocket (800, 1000, 1200 and 1400 RPM). The following terms are used throughout this appendix: Sprocket Speed - The rotational speed of the instrumented sprocket. Preload - The amount of preload, in pounds, placed in the upper chain span prior to each test. Torque - The amount of torque, in inch-pounds, transmitted by the chain drive during an experimental run. Chain Force - The average chain force, in pounds, determined from the data collected during the experiment. Impact Force - The impact force, in pounds, measured during the experiment.

800 RPM Data SDrocket Speed (RPM) Preload (Ibs) Torque (in-lbs) 798.112 796.937 795.367 793.593 791.323 788.630 798.277 797.272 795.785 793.988 792.071 789.776 798.234 796.941 795.364 793.661 791.477 789.110 797.871 796.499 794.893 793.151 790.735 788.250 797.742 796.204 794.828 792.944 790.366 787.771 797.185 795.900 794.231 792.831 790.549 787.889 20 20 20 20 20 20 30 30 30 30 30 30 40 40 40 40 40 40 50 50 50 50 50 50 60 60 60 60 60 60 70 70 70 70 70 70 27.61 32.19 37.63 41.77 45.99 57.61 27.61 32.19 37.63 41.77 45.99 57.61 27.61 32.19 37.63 41.77 45.99 57.61 27.61 32.19 37.63 41.77 45.99 57.61 27.61 32.19 37.63 41.77 45.99 57.61 27.61 32.19 37.63 41.77 45.99 57.61 Chain Force (Ibs) Impact Force (Ibs) 36.9733 15.397 38.9635 15.06 41.912 13.556 44.091 11.564 46.824 10.815 51.927 6.82 47.1751 12.222 48.732 13.129 50.941 12.493 53.912 11.163 56.811 13.409 62.127 13.11 57.223 16.714 58.744 17.897 60.983 17.29 64.012 16.18 66.932 19.23 72.141 18.23 67.119 21.45 68.814 22.02 70.721 18.64 74.132 17.311 76.855 9.02 83.512 8.31 77.252 21.443 79.242 21.737 80.933 19.001 85.311 19.325 87.144 19.413 94.030 13.904 87.523 25.02 89.621 24.504 91.521 20.951 95.442 23.522 95.427 23.746 105.02 15.65

1000 RPM Data Sorocket Speed (RPM) Pretoad (Ibs) Torque (in-lbs) Chain Force (lbs) Impact Force (lbs) 787.151 984.975 981.945 979.170 975.620 971.343 985.105 983.685 981.523 978.097 974.667 971.535 985.431 982.476 980.697 978.569 975.080 972.658 984.554 982.440 980.160 977.137 973.362 970.344 984.290 982.329 979.795 977.543 972.709 969.911 983.877 981.877 979.417 976.445 972.867 969.584 20 20 20 20 20 20 30 30 30 30 30 30 40 40 40 40 40 40 50 50 50 50 50 50 60 60 60 60 60 60 70 70 70 70 70 70 27.61 32.19 37.63 41.77 45.99 57.61 27.61 32.19 37.63 41.77 45.99 57.61 27.61 32.19 37.63 41.77 45.99 57.61 27.61 32.19 37.63 41.77 45.99 57.61 27.61 32.19 37.63 41.77 45.99 57.61 27.61 32.19 37.63 41.77 45.99 57.61 38.2463 40.1735 43.158 45.731 48.321 53.6181 48.6321 50.921 53.421 54.921 57.921 65.001 58.451 61.031 63.151 65.314 68.314 74.511 68.215 70.421 73.851 74.801 78.711 83.923 78.316 80.164 84.631 85.117 87.932 94.520 88.724 90.051 94.211 94.991 96.541 106.301 27.74 28.708 29.686 28.336 25.277 21.924 26.186 21.294 34.462 35.249 32.911 31.308 29.664 22.244 29.984 12.523 15.416 13.352 14.562 36.023 46.409 25.838 19.226 27.961 34.432 28.004 36.06 31.795 40.827 43.731 55.837 54.575 48.641 46.477 35.946 37.212

1200 RPM Data Sprocket Speed (RPM) Prlnoad ( Ihb Torque (in-lbs) Chain Force (lbs) Impact Force (Ibs) 1147.518 1145.014 1142.779 1139.911 1137.196 1133.737 1145.543 1142.647 1140.379 1138.062 1135.036 1131.848 1145.008 1142.245 1140.062 1136.959 1134.015 1130.475 1144.116 1141.733 1138.906 1136.108 1133.149 1129.767 1143.221 1140.979 1138.296 1135.234 1132.116 1129.331 1142.706 1139.363 1136.047 1132.624 1129.869 1126.615 20 20 20 20 20 20 30 30 30 30 30 30 40 40 40 40 40 40 50 50 50 50 50 50 60 60 60 60 60 60 70 70 70 70 70 70 27.61 32.19 37.63 41.77 45.99 57.61 27.61 32.19 37.63 41.77 45.99 57.61 27.61 32.19 37.63 41.77 45.99 57.61 27.61 32.19 37.63 41.77 45.99 57.61 27.61 32.19 37.63 41.77 45.99 57.61 27.61 32.19 37.63 41.77 45.99 57.61 39.8823 41.8515 44.745 47.728 49.868 55.7145 49.5311 52.248 53.921 57.311 59.767 65.237 60.354 61.531 64.318 68.012 70.317 74.921 70.121 70.991 74.815 77.814 80.824 85.012 80.041 80.513 85.210 86.999 89.931 96.130 91.423 92.131 94.721 97.241 101.421 106.017 35.561 39.655 30.544 27.713 15.145 6.635 64.174 61.139 58.285 53.073 49.410 43.227 79.911 76.659 72.985 65.949 64.937 43.651 127.842 103.44 100.207 82.131 70.401 84.842 120.5855 93.685 90.379 89.565 76.734 74.310 116.375 105.120 91.729 93.129 83.282 78.072

1400 RPM Data Sprocket Speed (RPM) 1335.587 1332.206 1331.098 1328.077 1324.237 1320.399 1333.468 1331.762 1328.783 1326.847 1323.883 1319.846 1333.504 1331.941 1328.783 1326.622 1322.981 1318.839 1332.007 1330.167 1326.411 1323.742 1320.642 1317.268 1330.213 1327.251 1325.282 1322.683 1320.295 1315.979 1330.152 1328.026 1323.791 1322.522 1318.082 1314.898 Pretoad (Ibs) Torque (in-lbs) 20 27.61 20 32.19 20 37.63 20 41.77 20 45.99 20 57.61 30 27.61 30 32.19 30 37.63 30 41.77 30 45.99 30 57.61 40 27.61 40 32.19 40 37.63 40 41.77 40 45.99 40 57.61 50 27.61 50 32.19 50 37.63 50 41.77 50 45.99 50 57.61 60 27.61 60 32.19 60 37.63 60 41.77 60 45.99 60 57.61 70 27.61 70 32.19 70 37.63 70 41.77 70 45.99 70 57.61 Chain Force (Ibs) Impact Force (Ibs) 41.7975 39.557 43.5675 43.21 46.5605 39.585 49.644 43.242 51.578 49.887 57.603 39.649 52.3011 51.835 54.176 51.984 56.213 57.701 58.920 52.481 61.375 66.826 67.922 58.616 61.542 55.465 63.211 54.755 65.911 60.221 69.311 56.55 71.042 63.79 76.711 61.296 72.850 59.075 73.644 61.659 76.429 56.310 79.714 64.661 82.013 52.481 87.940 54.365 81.623 74.07 84.515 77.231 87.361 89.610 88.930 103.816 92.341 91.705 97.581 95.555 91.854 96.82 94.131 107.392 96.250 125.557 99.112 123.489 101.832 106.812 106.821 100.832

,) z D 0 aO) LI FI C) TJ 0 LL UL. 140.00 - 120.00 100.00 - 80.00 - 60.00 - 40.00 - 20.00 -,n rN r ooooo 20 POUND CHAIN PRELOAD o ooa 30 POUND CHAIN PRELOAD """" 40 POUND CHAIN PRELOAD ~ ooo 50 POUND CHAIN PRELOAD +++++ 60 POUND CHAIN PRELOAD xxx x 70 POUND CHAIN PRELOAD + + 0 0 A a o o a 0 0 0 0 0 U.uu 20 25 30 35 40 45 50 55 TORQUE TRANSMITTED BY CHAIN DRIVE (IN-LBS) 60 Figure la. Time averaged force in the tight side of the chain as a function of transmitted torque and chain preload for a nominal instrumented sprocket speed of 800 rpm

140.00 - (E D 120.00 -0 o z 100.00o CL IJl @ 80.00 -I FIE C 60.00 LLI IZ z 40.00 -o 20.00 LL 00000 00000 A A A A A 0 000 ++~+++ 20 POUND 30 POUND 40 POUND 50 POUND 60 POUND 70 POUND x CHAIN CHAIN CHAIN CHAIN CHAIN CHAIN PRELOAD PRELOAD PRELOAD PRELOAD PRELOAD PRELOAD + + + 0o 0 A 0 O 0 O 0 0 0 0 U.UU 20 20 25 30 TORQUE 35 40 45 TRANSMITTED BY CHAIN DRIVE 50 55 (IN-LBS) I I 60 Figure lb. Time averaged force in the tight side of the chain as a function of transmitted torque and chain preload for a nominal instrumented sprocket speed of 1000 rpm

140.00 r) Q, 120.00 0 0 -z 100.00 Li Un @ 80.00 HI D 60.00 Iz 40.00 0L El ooooo 20 a a o 30 A A A 40 o 0 0 050 +++++ 60 x x x 70 POUND POUND POUND POUND POUND POUND CHAIN CHAIN CHAIN CHAIN CHAIN CHAIN PRELOAD PRELOAD PRELOAD PRELOAD PRELOAD PRELOAD 1( 3 3 0o 0 0 n o o 0 0 o 0.00 - 2 o l.0 I I I i I I I I I I I 1 1 1 l - 25 30 TORQUE I r T T r i Ii i T i l I i i I I I i i I I I I I I I 1 1 I 1 T 1 1 1 i 1 1i 35 40 45 50 55 TRANSMITTED BY CHAIN DRIVE (IN-LBS) 60 Figure Ic. Time averaged force in the tight side of the chain as a function of transmitted torque and chain preload for a nominal instrumented sprocket speed of 1200 rpm

140.00 - ooooo 20 POUND CHAIN PRELOAD - 00000 30 POUND CHAIN PRELOAD uc - "a"" -40 POUND CHAIN PRELOAD ooooo o50 POUND CHAIN PRELOAD ) 120.00 - + ++ + 60 POUND CHAIN PRELOAD ~o x ~~xx 70 POUND CHAIN PRELOAD z: a_ 100.00 x - +0+ IC + + ox: o~~~~~~~ 80.00 T'5~~~~~~~~~~~~~~~ A 0 _ A CD 0 0 I 60.00 0 0 1, 2z 0 -- - O~~~~~~0 ar 40.00 L0 20.00 I I I I I.,,,,, I I I i I, I I I I I I I I I I I I I I I I 20 25 30 35 40 45 50 55 60 TORQUE TRANSMITTED BY CHAIN DRIVE (IN-LBS) Figure Id. Time averaged force in the tight side of the chain as a function of transmitted torque and chain preload for a nominal instrumented sprocket speed of 1400 rpm

TIGHT SIDE TENSION RESISTIVE SPROCKET LOOSE SIDE TENSION Figure 2. Free body diagram of driven sprocket.

140.00 - oU) D 120.00 <n LL0 a9 80.00 I "_ 60.00 Lw. — z 40.00 (ro 20.00 -LL. ~ o ooooo EXPERIMENTAL VALUES A,^," PREDICTED VALUES (FROM EQUATION (5)) 0 0 A 0 A 0 A 0 0 0 A O 0 A 2a 2 0 A o A 0 A 0 A 0 a a 0 a 0 A 0 A 0 A 0 A 0 A 0 A 2 0 o a 8 0 A 0 A a a 0 A 0 A 0 A 0 A u.UU 784 784 786 788 ROTATIONAL 790 SPEED 792 794 796 798 OF INSTRUMENTED SPROCKET (RPM) 800 Figure 3a. Experimentally determined tight side chain tension compared to tight side chain tension calculated by Equation (1) for a nominal instrumented sprocket speed of 800 rpm.

140.00 n CL z 100.00 LU lJ cn Q 80.00 I ( 60.00 LJ Fz 40.00 LiJ O p0 20.00 L_ o oooo EXPERIMENTAL VALUES "^AAA PREDICTED VALUES (FROM EQUATION (5)) 0 — I — 4 il. 0 A 0 A O a 0 A 0 A 0 A 0 46 0 A 0 A a A 0 A 0 A 0 A 0 o A A 0 A 0 A 0 0 A 0 O A 0 A 0 A 0~ A 0 A 0 A 1 0 0 A 0 A O A 0 0 A A 0 A 0 0 0.00 I 964 964 I11 11 1 I I I i r r I 1 1ii 1 I II I i l r l l l ' 11 7 111 11 i i I lll l lll 968 972 976 980 984 988 ROTATIONAL SPEED OF INSTRUMENTED SPROCKET (RPM) Figure 3b. Experimentally determined tight side chain tension compared to tight side chain tension calculated by Equation (1) for a nominal instrumented sprocket speed of 1000 rpm.

4 A r fA I 0 Q_ Z1 a_ ui n LLJ hLL w 0 L - qU.UU - 20.00 - 00.00 - 80.00 - 60.00 - 40.00 - 20.00 - 0.00 1120 ooooo EXPERIMENTAL VALUES a"^^^ PREDICTED VALUES (FROM EQUATION (5)) 0 0 0 A A 0 0 A A 0 A 0 A a 0 0 a 0 A A A 0 0 A A 0 A 0 A 0 I 0 A 0 A 0 A A 0 0 0 A A 0 0 A A A 0 0 a 0 A A 0 0 A A 0 0 A 1125 1130 1135 1140 1145 1150 ROTATIONAL SPEED OF INSTRUMENTED SPROCKET (RPM) Figure 3c. Experimentally determined tight side chain tension compared to tight side chain tension calculated by Equation (1) for a nominal instrumented sprocket speed of 1200 rpm.

140.00 - E) 0 - D 120.00 - o L100.00 - (n 60.00 CL J - z 80.00 - I LL z 40.00 -LU! (9 o 20.00 - [L o oooo EXPERIMENTAL VALUES "^"" PtREDICTED VALUES (FROM EQUATION (5)) 0 A 0 0 A 0 0 a 0 A 0 0 A 0 A 0, A 0 0 A 0 A 0 A A o 0 A L0 A a o A A 0 a 0 A 0 A 0 6 A 0 0 A 0 A A 0 0 A 0 A I 0.00 {,TTT 1305 I II I Ii II I I I I I I I I I I I lT l l l ITT 1 1 Ir 1 I I I I I I 1 1310 1:315 1320 1325 1330 1335 1340 ROTATIONAL SPEED OF INSTRUMENTED SPROCKET (RPM) Figure 3d. Experimentally determined tight side chain tension compared to tight side chain tension calculated by Equation (1) for a nominal instrumented sprocket speed of 1400 rpm.

60.00 z o 50.00 i — 30.00 30.00 o LAJ 20.00 10.00o......:..................... 0.00 0.02 0.04 0.56 0.68 0.106""0.'.2 NORMAIZED TIME/POSmON Figure 4a. Typical output from strain gage mounted on link side plate over one complete cycle around the loop. CHAI MOTION / 11 FORCE IN TIGHT sE OF CHAIN! I. PREOAD LEVEL I I ~ f a a 1..~~~~~~~~~~~~~~~~~~ I b c d =OSTMIO IN TIE CHAD StAN Figure 4b. Typical time averaged chain force as a function of position in the chain span.

0.00 o -20.00,. -40.00 z -60.00 a, -80.00 a UJ -100.00 -120.00 0.. 400.00 800.00 1200.00 1600.00 FREQUENCY (HERTZ) Figure 5a. Typical experimentally measured output spectrum from vertical load cell. 5.00 - z U U U0 0 o * oo C 3.00 ' N 0 2.00 Z 1.00 0.00.. ' Figure 5b. Vertical load cell transfer function.

40.00 Or) c 30.00 z o az o c 20.00 z D z o L 10.00 o.oo00 0.000 400. 000 00.800.000 1200.000 1600.000 FREQUENCY (HERTZ) Figure 5c. Typical spectrum of the force applied to the sprocket by the rollers.

>m DR.- <I 4:7i.1 '-~S Figure 6. Experimentally measured impact force as a function of sprocket speed and chain -tension.

<I \ 11 ' Figure 7. Impact force as a function of sprocket speed and chain tension as predicted by Equation (3).

THE UNIVERSITY OF MICHIGAN DATE DUE o — 3 (~KIS