1、 STD-AGMA 75FTM4-ENGL 1975 W Ob87575 D004b87 338 I 95FTM4 An Experimental Test Stand to Measure Loaded Transmission Error in Fine-Pitch Plastic Gears by: Sivakumar Sundaresan, David Castor and Kenneth Price, Eastman Kodak American Gear TECHNICAL PAPER COPYRIGHT American Gear Manufacturers Associatio
2、n, Inc.Licensed by Information Handling ServicesAn Experimental Test Stand to Measure Loaded Transmission Error in Fine-Pitch Plastic Gears Sivakumar Sundaresan, David Castor and Kenneth Price, Eastman Kodak nie statements and opinions contained herein are those of the author and should not be const
3、rued as an official action or opinion of the American Gear Manufacturers Association. Abstract This paper describes a developed experimental test stand to measure transmission error in fme-pitch gears. The paper introduces the imporrance of &ansmission mr in office equipment that have uniform motion
4、 requirements. Transmission error is computed by measuring the phase merence between the driver shaft and the driven shaft using optical encoders. The test stand has a variable operating center distance and can apply shaft aiignment errors in both parallel and skew directions. Results from the test
5、stand show the effect of gear elemental errors, transmitted load, and shaft misalignment on transmission mor in fine-pitch piastic gears. - Copyright O 1995 American Gear Manufacnirers Association 1500 King Street, Suite 201 Aiexandria, Virginia, 22314 October, 1995 ISBN: 1-55589-652-9 COPYRIGHT Ame
6、rican Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesSTD-AGMA 75FTMq-ENGL 1995 D b87575 0004b9 LOO E An Experimental Test Stand to Measure Loaded Transmission Error in Fine-Pitch Plastic Gears Sivakumar Sundaresan, Engineer - Project Development Kenneth R. Price, Engine
7、er - Project Development David A. Castor, Supervisor - Power Transmissions Mechanical Engineering Competency Center Kodak Equipment Manufacturing Division Eastman Kodak Company, Rochester, NY 14653-5823 1 INTRODUCTION The need for a photographic-quality image from a color printer or a color copier d
8、emands the movement of the media be uniform and precise. Any variation in the uniform motion of a drive can cause scan lines on an image to be closer together at a slower transport speed, and farther apart at a faster transport speed. often, these variations are periodic in nature and result in peri
9、odic bands of varying density on an image. Entities like gear mesh frequency and shaft frequency are directly related to the distance between the bands on an image. However, the relationship between the amount of density variation in an image and the amount of non-uniform motion in a drive train is
10、not known. This presents a need to measure the non-uniform motion of a gear drive. Additionally, stringent low-acoustic noise requirements in work areas have resulted in a need to study the noise and vibration characteristics of power transmissions in office equipment. In the past few years, researc
11、hers have linked gear mesh induced noise and vibration to the static transmission error in a gear mesh. Welboum (1977) defined static transmission error as the ”the difference between the actual position of the output gear and the position it would occupy if the gear drive is perfect.” This definiti
12、on of static transmission error provides a direct measure of non-uniform motion in a gear drive. Commercially available systems that measure transmission error did not meet our need to measure transmission error in finepitch gears under changes in center distance, at low values of torque, and for sd
13、 variations in shaft alignment. This paper describes a test stand designed to address this need. The rest of this paper is organized as follows: Section 2 describes the mechanical drive system layout of the test stand. Section 3 presents the transmission error measuring system. Section 4 discusses s
14、ample measurement results on finepitch plastic gears. Section 5 concludes this paper with our directions for future work. 2 MECHANICAL DRIVE SYSTEM LAYOUT would meet the following requirements: Our objective was to design a test stand that 1. 2. 3. 4. 5. Measure transmission error for gear meshes th
15、at have non-unity gear ratios Measure transmission error for gear meshes at various values of center distance Measure transmission error for gear meshes at various low values of torque Measure transmission error under variations in parallel and skew alignment Measure non-uniform motion in other driv
16、e components, such as timing belt pulleys and couplings The test stand was designed to meet all of these requirements. The test stand can apply mesh torque between 5 and 90 oz-inches at angular speeds between 5 and 100 rpm. The transmission COPYRIGHT American Gear Manufacturers Association, Inc.Lice
17、nsed by Information Handling Servicesspeed, gear ratio speed, gear ratio, and torque I T torque Servo Encoder ANAYZER i- Fig. 1 Schematic sketch of the test stand error measuring system can measure transmission error when the angular velocity of the gears is less than 100 rpm. The mounting center di
18、stance can be varied from O to 4.5 inches. The test stand can apply errors in paraiiel alignment and skew alignment up to 5 degrees. The drive control can accommodate the change in direction of rotation of the output drive member when timing belt pulleys or couplings are used instead of gears. This
19、section gives a detaiied description of the mechanical layout of the test stand. The test stand consists of the following two mechanical assemblies: Drive Side Assembly (DSA) and Load Side Assembly (SA). Figure 1 shows the schematic sketch of the test stand. The two assemblies are mounted on a pneum
20、atic table. The load side assembly is rigidly mounted on the table and the drive side assembly can be moved on the table to achieve the required meshing center distance. A precisely ground, rigid steel plate is mounted in front of the table to provide a reference/datum plane for the test stand. The
21、load side assembly and drive side assembly are aligned using the reference plane. The drive side assembly consists of a servo- controlled DC motor, three optical encoders, and a driver shaft with a 0.400 inch bore. The DC motor is servoantroiled for constant velocity using a 5OOO-line optical encode
22、r that is mounted on the motor shaft. An 18OOO-line optical encoder (drive measurement encoder) provides the angular position of the driver shaft for transmission error computation. The test gears are mounted on arbors that are inserted into the 0.400 inch bore on the driver shaft and clamped using
23、split-hub clamps. The mounting frame that holds the DC motor, encoders, and driver shaft can be moved in Y direction a maximum of 0.025 inches (X-Y plane represents the plane of the air table) by deflecting thin steel plates that act as flexures. This provides a method to change center distance by s
24、mall amounts when gears are mounted on shafts. The mounting frame can also be rotated about the Z-axis (in the plane of the table) to achieve parallel alignment 2 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesFig. 2 Mounting frame in the drive side a
25、ssembly errors up to 5 degrees. The amount of parallel alignment error is measured using an optical encoder mounted at the pivot point of rotation. Figure 2 shows the mounting frame and illustrates how it can be moved in the Y direction and rotated in the X-Y plane. The load side assembly consists o
26、f a servo- controlled DC motor, three optical encoders, and a driven shaft with a 0.400 inch bore. The DC motor is servo-controlled using a 5000-line optical encoder that is mounted on the motor shaft. The DC motor applies torque in the system. An 18000-line optical encoder (load measurement encoder
27、) provides the angular position of the driven shaft for transmission error computation. The test gears are mounted on xbors that are inserted into the 0.400 inch bore on the driven shaft and clamped using split-hub clamps. The mounting frame that holds the DC motor, encoders, and driven shaft can be
28、 rotated about the Y-axis (in the vertical plane perpendicular to the plane of the air table) to vary skew alignment error. The amount of skew alignment error is measured using an optical encoder mounted at the pivot point of rotation. Figure 3 illustrates the rotation of the mounting frame about th
29、e Y-axis. The main drive controller is an IBM PC-based software that uses inputs such as drive speed, gear ratio, torque, and direction of rotation to calculate the control parameters for the drive and load motors. Torque is varied by changing the current to the load motor. Initial analysis of the s
30、ervo-control provided us with the non-uniform motion characteristic of the drive and load motors. This information helps in identifying the non-gear induced non-uniform motion in the transmission error results from the test stand. The current output from the drive motor servo is also used to monitor
31、 the torque experienced by the drive motor. 3 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services - STD*AGMA 95FTM4-ENGL 1995 a Ob87575 0004b72 7T5 a Fig. 3 Mounting frame in the load side assembly 3 TRANSMISSION ERROR MEASURING SYSTEM The transmission er
32、ror is computed by measuring the phase difference between the two shafts using optical encoders. J. D. Smith (1988), R. E. Smith (1984), and Hochmm and Houser (1994) have applied similar techniques to measure transmission error in coarse pitch, parallel-axis gears. The transmission error measuring s
33、ystem evaluates the transmission error by perfonning the following calculation: TE = e2-e1- N1 N2 The drive measurement encoder and load measurement encoder output no00 square wave pulses per revolution using quadrature, and one index pulse per revolution. The two pulse trains are divided by integer
34、 numbers using puise dividing circuits to equalize the two pulse frequencies. In general, the driver pulse train and driven pulse train are divided by the number of teeth on the driven gear and the driver gear respectively. A phase comparator using a flip-flop with a response time of 20 nanoseconds,
35、 measures the phase difference between the pulse trains from the drive and load measurement encoders. The output from the phase comparator is a square wave between +lo V with a variable mark space ratio. This output signal is filtered using a four-pole low- pass filter and is analyzed using a signal
36、 analyzer. The maximum transmission error that can be measured using this technique corresponds to the angular distance between two adjacent pulses. For example, if the load pulse train is divided by 32 for a driven gear with a one-inch base radius, there will be 2250 (= 72000/32) pulses in one revo
37、lution of driven gear. Hence, one puise corresponds to 0.16 (= 360/2250) degrees of rotation of the driver gear. The maximum transmission error in a oneinch base radius gear that can be measured when the puise train is divided by 32 is 0.0028 inches (= 1.0 * 0.16 * x / 180). Normally , a pulse from
38、the load puise train appears between two adjacent pulses in the drive pulse train. When smaJi gears with large errors are tested, the phase difference between the two puise trains can exceed the distance between two adjacent pulses. In other words, between two adjacent pulses in the pulse train from
39、 the drive measurement encoder, there may not lie a pulse in the pulse train from the load measurement encoder. Such situations require the need to further divide 4 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesSTD-AGHA 95FTM4-ENGL 1995 W the pulses
40、from the drive and load measurement * encoders proportionately. Division of the pulse train by a large number could result in a lower number of pulses per gear tooth available for transmission error computation. Care should be taken to maintain sufficient sampling pulses per tooth mesh in order to s
41、tudy the effect of variations in the gear tooth on transmission error. A time delay circuit is used to delay one pulse train with respect to the other, so that zero value for transmission error corresponds to the situation when one pulse train is 180 degrees out of phase with the other. The measurem
42、ent encoders output 72 pulses per revolution of the shaft. One pulse corresponds to 0.005 degrees (18 arc seconds) of revolution of the shaft. As the transmission error is computed by measuring the phase difference between the pulse trains from the two measurement encoders, the achievable resolution
43、 is finer than 18 arc seconds. The once-per-revolution index pulse from the encoders mounted on the shaft is used to trigger the signal analyzer when time averaging of transmission error is performed. When there is a need to measure transmission error in the orders domain instead of time or frequenc
44、y domain, the pulse train from the 18000-line drive measurement encoder is used to trigger the external sampling option in the signal analyzer. 4 EXPERIMENTAL RESULTS in general, the transmission error for a gear mesh contains a once-per-tooth component (and its harmonics) superimposed over a once-p
45、er- revolution of the gear (or pinion) component. The once-per-tooth component can be caused by the variations in tooth profile, deviations in tooth spacing, and errors in tooth alignment. The once- per-revolution component is caused by the accumulated pitch deviation (may or may not be caused by ru
46、nout) in the gear. In addition to the once-per-tooth and once-per-revolution component, transmission error may also contain components that may be traced back to errors in the drive mechanism of the gear cutting (or grinding) machine. This section presents results for gears that were inspected on th
47、e transmission error test stand. Transmission error is measured in degrees of rotation of the output gear. Section 4.1 describes how the test stand can be used to measure cumulative pitch variation in ultrafine-pitch gears. Section 4.2 illustrates the use of the test stand to measure transmission er
48、ror for gear drive trains that have multiple meshes. Section 4.3 shows the effect of load and shaft misalignment on transmission error in plastic gears. 4.1 Measurement of Cumulative Pitch Variation The transmission error test stand measures cumulative pitch variation in finepitch gears by applying
49、averaging techniques in external sampling mode (orders domain). In orders domain, time is replaced by the angular position of the shaft and frequency is replaced by orders. A component of the signal that occurs n times per revolution of the shaft is said to be at the nth order. The pulse train (72 pulses/rev) from the drive measurement encoder is used to trigger the external sampling of the signal analyzer. The index pulse from the drive motor control encoder is used to trigger the start of each record (sample) in the signal analyzer. Figure 4 compares the cumulative pitch
