1、 - - STD-AGHA 97FTM4-ENGL 1997 0687575 0005080 485 97FTM4 Measurements and Predictions of Plastic Gear I Transmission Errors with Comparisons to the Measured Noise of Plastic and Steel Gears by: Leonard Liauwnardi, Caterpillar, Inc., Dr. Donald R. Houser and Dr. Anthony Luscher, Ohio State Universit
2、y TECHNICAL PAPER COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesMeasurement and Predictions of Plastic Gear Transmission Errors with Comparison to the Measured Noise of Plastic and Steel Gears Leonard Liaumardi, Caterpillar, Inc., Dr. Donald R Houser
3、 and Dr. Anthony Luscher, Ohio State University plie statements and opinions contained herein are those of the author and should not be construed as an officiai action or opinion of the American Gear Manufacturers Association. Abstract in recent years, plastic gears have found their popularity as re
4、placements for metal gears in selected, lightly loaded applications. Many studies have been done in the area of plastic gearing such as plastic material selection, injection molding and load capacity of plastic gears. Severai historical papers imply that plastic gears are “quieter“ than steel gears.
5、 Yet, there have been few studies that focus on studying the transmission errors of plastic gears and relating these errors to the noise that is generated. This paper focuses on the transmission error and sound pressure level measurements of several plastic gear sets and compares experimental static
6、 transmission error measurements to computer predictions. Based on the experimental results, in plastic gears the tooth contact is more susceptible to occurring off the line of action due to excessive tooth deflection. This directly affecs the transmission error behavior. A computer program that con
7、siders off line of action contact is used to accurately predict static transmission error for the experimental plastic gears. According to previous studies on metal gears, there is a correlation between mesh harmonics of transmission error and sound pressure level. This study presents results used t
8、o check this correlation in plastic gears. The comparison of the ratio of sound level to transmission for the plastic gears and steel gears with similar overail geometry specifications is also presented. Copyright O 1997 American Gear Manufacturers Association Aiexandria, Virginia, 22314 1500 King s
9、treet, suite 201 November, 1997 ISBN: 1-55589-698-7 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services, STD-AGMA 97FTM4-ENGL 1997 b87575 0005082 258 m Measurements and Predictions of Plastic Gear Transmission Errors with Comparisons to the Measured Noise
10、 of Plastic and Steel Gears Leonard Liauwnardi, Caterpillar, Inc. Dr. Donald R. Houser, e Ohio State UniversiS, Dr. Anthony Luscher, e Ohio State University Introduction In recent years, plastic gears have found their popularity as replacements for metal gears in selected, lightly loaded application
11、s. Many studies have been done in the area of plastic gearing such as plastic material selection, injection molding processes, and load capacity of plastic gears. Many historical papers imply that plastic gears are “quieter” than steel gears. Yet, there have been few studies that focus on making the
12、 comparison of the transmission error and sound pressure level of plastic and steel gears, as is done in this paper. Research Obiectives There are two main objectives of this paper. 1) The first is the measurement of transmission error of two different plastic gear sets and then to compare these mea
13、surements with analytical predictions of static transmission error. 2) The second objective is to compare the relationships between measured sound pressure level with transmission error of plastic gears (Nylon and Acetal) and steel gears that have similar overall geometries, loads and speeds. Plasti
14、c Gear Manufacturine Overview Plastic gears can be produced by a variety of manufacturing methods. Thermoplastics can be machined from rod stock. Polymer rods are first formed via standard extrusion processes. In some of these rods, a metal insert is included to form a strong hub for the gear. Then
15、a sophisticated cutting machine is used to slowly cut the tooth profiles. Machine cut plastic gears are usually made for prototyping testing purposes. Since extremely small quantities of the test gears used in this study were produced, they were machined from plastic rod stock. Therefore, the manufa
16、cturing errors of these gears are more typical of those observed in metal gears. Net shape manufacturing processes are more common with plastic gears since these processes are much more economical. Compression molding is used to produce thermosetting polymer gears. The complimentary process for ther
17、moplastics is injection molding. This process allows the cost-effective production of plastic gears in high volume. Furthermore, compound gears can be easily produced in a single mold thus reducing part count. Manufacturing inaccuracies of gears produced with these processes differ greatly from thos
18、e of machined gears. For instance, gating methods greatly affect part shape and shrinkage is of major concern. It is not the intent of this paper to address these issues, but techniques similar to those that are used in this paper could be applied to net shape manufactured plastic gears. Measurement
19、 Methodolow Test Rig The major part of this experimental study was conducted on the Variable Center Distance Test Rig located at the Ohio State University i. The gears were continuously lubricated during the test, however an important variable. operational temperature, was not monitored. in this exp
20、eriment, eight different 1 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services STD-AGHA 97FTM4-ENGL 1797 Ob87575 0005083 17Li = signals were simultaneously recorded while the test rig was running: a) signals from four sound pressure level meters placed 45
21、 inches above the test rig, b) a pulse signai from a tachometer that measured shaft speed, c) the output of a gearbox housing accelerometer. d) the sum of the two angular accelerometers of the pinion and the sum the two angular accelerometers of the gear. The data were recorded so that they could be
22、 analyzed fbrther using a spectrum analyzer. More details on these measurements are given below. Transmission Error Measurement Transmission error is defined as the deviation of the position of the driven gear hm the position that it would occupy if both driven and driving gear were infnitely stiff
23、and had perfkt involute profiles. Transmission error may be expressed in angular units or as a hear displacement along the line of action. The following are the respective equations for linear and angular transmission error acceleration: where kp = the base radii of the pinion RBG = the base radius
24、of the gear NG = number of teeth on the gear Np = number of teeth on the pinion +p = pinion angular acceleration 4 = gear angular acceleration accelerometers were mounted at the end of the gear and pinion shafts, but resonances caused dynamic measurement errors 3. Y + Y t afA, - Figure 1. Schematic
25、of Accelerometers Mounted on the Test Gears To obtain the transmission error displacement, the transmission error acceleration has to be integrated twice. The double integration can be performed in the time domain or in the frequency domain by using a pseudo integration method. In this research, the
26、 pseudo integration technique is preferred because it is easy to implement with a spectnim analyzer and does not sacrifice accuracy. The pseudo integration method involves dividing the Fast Fourier Transform spectrum of transmission error acceleration by the square of the corresponding frequency (Eq
27、. 2) By double-inkgratmg both sides of each equation, one can obtain the transmission error in displacement units (effectively by removing the double dots above each term). The transmission error measurement methods that have been implemented in the past on this rig include the use of torsional acce
28、lerometers, opticai encoders and tangentially mounted translational accelerometers 2. In this research, two translational accelerometers are mounted on the arbor where the gear is mounted (shown schematically in Figure 21. The advanage of ths arrangement is that the arbor is manufctured as where g =
29、 gravitationai acceleration (idsec) K = calibration gain (Voltlg) o = corresponding frequency of each discrete signai (radsec) a1 = acceleration of accelerometer 1 a2 = acceleration of accelerometer 2 a3 = acceleration of accelerometer 3 t = acceleration of accelerometer 4 rp = radial distance from
30、the pinion shaft center to the accelerometer neutrai axis one piece with the mounting surce located adjacent to the test gear, therefore minimizing the possibility of shaft compliances and resonances affecting the measurement. In a previous study, the translational The translational accelerometers a
31、re calibrated while they are mounted on the gear and the rig is running at low speed. This rotating motion causes the two 180 apart accelerometers to measure flg 2 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesSTD-AGMA 77FTMi-ENGL 1777 0.5 4 gravitat
32、ional acceleration at shaft frequency. These signals are amplified and then input to a signal analyzer where frequency spectra similar to those shown in Figure 2 are displayed. The lower trace of Figure 2 shows the sum of the accelerometer signals. Because accelerations due to gravity at shaft frequ
33、ency are i80 degrees out of phase with one another, their sum should go to zero when the frequency spectra are added (last part of Figure 2). However, the portions of the signai at mesh frequency and its harmonics all add. During calibration, the gains of the individual transducers are adjusted to g
34、ive zero output at shaft frequency. -1 - 4- - Figure 2. Frequency Spectra of Accelerometer Signals from the Pinion Shaft Sound Pressure Level Measurement It has been widely accepted that transmission error is a major contributor to gear noise. Munro 4 showed that measured sound pressure level and me
35、asured transmission error increase as the torque is increased. In this study, transmission error and sound pressure level were measured simultaneously in an attempt to show a similar relationship between both quantities as a function of torque. The sound pressure level was measured with four sound l
36、evel meters iocated approximately 45 inches above the gearbox. The average of these four sound level meters is used as the sound pressure that is mentioned in the remainder of this paper. = b87575 0005084 O20 Exoenmental Procedure The experimental study started by inspecting the leads and profiles o
37、f the gears that would be tested. This inspection was performed on the Coordinate Measurement Machine in the Mechanical Engineering Department, The Ohio State University. Four leads and profiles were taken on teeth separated by 90. The average of these measurement results was used to represent the l
38、ead and profile each gear in subsequent modeling. The sources of transmission error can be divided into two major components: a portion caused by manufacturing error and a portion caused by tooth deflection. Tooth deflection in this context consists of not on ,I I t : 1 : i . . ; .- -: . I . _-_._-_
39、 . -, . 2 : : : P 2 14 20 -4 O 9 i 20 8 E 5 14 4 . , ,I: . . - - . -_ .-. urn11 13 15 17 19 21 23 25 27 29 31 33 ROLLANOLB, dap Figure A - Profile Check of Acetal Pinion Teeth LEFT 30.664 dq 1 .d,III 1 9 O 2 17 2 : 24 9 .r( O O i 24 E I l7 9 1 xm10 12 14 16 18 10 22 24 26 28 30 ROLL ANCLE, dw Figure
40、 B - Profile Check of Acetal Gears LBPT U 2 14 4 g 20 O a i 20 2 14 . .- . -*.x+ (I-+-. -. . ._._. 1-11 13 15 17 19 21 23 25 27 29 31 33 ROL AULS, dg Figure C - Profile Check of Nylon 616 Pinion Teeth 1997 b87575 0005092 LT7 LEFP i i .i,. ;.i. - . - - . - . iiiiiliiiiiil.iii.iii-l-i.-lii _I_.L_ i 24
41、 8 17 9 H .-c-.-s . J)-.-.(-. .-(- . + . ., . -._ .-* . + . + )-.(. - -,-, . - . .- . -. -.-.- -.-. m.10 12 14 16 18 20 22 24 26 26-T ROLL MK;LE, daq Figure D - Profile Check of Nylon 616 Gear Teeth Figure E - Profile Check of Pinion Steel Teeth I I ., Figure F - Profile Check of Gear Steel Teeth 11 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services
