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附 錄
附錄A 英文文獻
DEFLECTION TEST AND TRANSMISSION ERROR MEASUREMENT
TO IDENTIFY HYPOID GEAR WHINE NOISE
J. H. YOON1), B. J. CHOI1), I. H. YANG1) and J. E. OH2)*
1)Graduate School of Mechanical Engineering, Hanyang University, Seoul 133-791, Korea
2)School of Mechanical Engineering, Hanyang University, Seoul 133-791, Korea
(Received 5 March 2009; Revised 13 September 2010)
ABSTRACT?Hypoid gears are commonly used in rear-drive and 4WD (4 Wheel Drive) vehicle axles. Investigating their sensitivity to deflections is one of the most important aspects of their design and optimization procedures. Therefore, a deflection test was performed in this study in the actual gear mounting using completely processed gear. This test covered the full operating range of gear loads from “no load” to “peak load”. Under peak load, the contact pattern extended to the tooth boundaries without showing a concentration of the contact pattern at any point on the tooth surface. The transmission error was tested under an axle assembly triaxial-real-car-load condition.
KEY WORDS : Hypoid gear, Deflection test, Transmission error, Gear whine noise, Axle
1. INTRODUCTION
The axle in vehicle driving systems was used primarily in small trucks, special vehicles, or buses, when FF (Front-engine Front-drive) vehicles were popular. However, as the FR (Front-engine Rear-drive), 4WD (4 Wheel Drive), or AWD (All Wheel Drive) type driving systems have been adopted in RV and SUV vehicles, which have gradually become more common since 2000, and in middle-sized or large luxury vehicles, the performance of the axle has constantly improved. As such, the importance and role of the axle continues to increase. In fact, in vehicles with improved performance, the overall indoor noise was also greatly reduced due to the use of low-noise technology, unlike in existing diesel vehicles (Lee et al., 2007; Park etal., 2008; Sim et al. , 2006). However, the gear noise in the transmission and axle, which had been masked, is increasing and has become a significant challenge. To develop a low-noise axle, the transmission error due to the input torque variation in hypoid gear must be measured; in particular, the engineers who modify the teeth to develop low-noise axles need the transmission errors of the gears in direct relation to the tooth geometry. There has been no report, however, of studies in Korea that aim to measure the transmission errors in axles. In Japan, case studies on trans-mission error measurements (Kato, 2003) were reported, but the measurement precision was imperfect. The current method of measuring torque variation is presently under examination. There have also been theories about and experimental evaluation of deflection (Coleman, 1975; Kolivand et al., 2006), but the development of the tooth
geometry through the application of such theories is insufficient. Therefore, in this study, the causes of hypoid gear whine noise were identified by measuring the transmission errors under load variation and by developing experimental methods to measure the triaxle transmission errors. The results of the deflection test with the tooth geometry development of the hypoid gears that were used in the axles were then compared with the interpretation results and tests that were conducted using Gleason's T900
2. DEFLECTION TEST
2.1. Introduction
To design axles, the deflection of the driving and the driven gears and the tooth contact pattern under the torque were measured. Figure 1 shows a picture of the experiment in which the deflection was measured. The tooth contact pattern was measured by applying an appropriate volume of a gear-marking compound to the gears before the two sets of gear teeth were engaged with each other to turn and by copying the imprint on the gears with tape after turning. The tooth contact pattern was then checked. Figure 2 shows the measured tooth contact pattern.
Figure 1. Deflection measurement check. Figure 2. Tooth contact check.
2.2. Positions of the Deflection Measurement and the Axle Noise Section of Input Torque Conditions on the Vehicle
The Hypoid gear rotation direction and torque direction are shown in Figure 3. The measurement position in the direction test is shown in Figure 4, and the axes (E, P, G, and α) of the hypoid gears are shown in Figure13. Except for the upper/lower and right/left torsions of the pinion and ring gears and the displacement, the real deflections were measured with a trigonometric function (Coleman, 1975). This test result also included tooth deflection. Moreover, each displacement sensor was fixed and measured based on the inner bearing assembly of the pinion gear. Because the input revolution in the direction test was 5~10 rpm and because oil was not used, the test was performed with the low revolution to prevent the teeth from being damaged by the heat generated in the surface of the gear under the torque condition.
Figure 3. Hypoid gear rotation direction and torque direction.
Figure 4. Displacement indicator measuring point and indicator anchorage point.
The noise section and the actual input torque that were measured under various driving conditions (W.O.T.: Wide Open Throttle; S.W.O.T.: Semi-Wide Open Throttle; Coast: Full Close Throttle Deceleration).
Figure 5 shows a diagram of a device that measures the input torque in the axles of vehicles. Figure 6 is a graph that shows the input torque measurement for S.W.O.T. and coast driving conditions. Table 1 shows the noise section of the input torque values under coast driving conditions. It can be seen that the input torque in the gear whine noise section is between ?22.5 and ?7.2 kg·m in real vehicles. To develop the tooth geometry with minimum transmission error under these input torque conditions, the transmission error under such input torque must be measured.
Figure 5. Measurement setup of the axle input for the vehicle torque.
Table 1. Axle input torque by test mode.
Figure 6. Axle input torque of S.W.O.T. (semi-wide open throttle) and coast test modes.
3. TRANSMISSION ERROR
3.1. Transmission Error Measurement
The general way to measure the transmission error of the hypoid gear in axles and of the helical gear in the transmission gear is to conduct the single flank test (www.gleason.com). In this test, Gleason’s 600HTT equipment is used to measure the transmission error of the gear pair. The experimental equipment is shown in Figure 7.
This equipment has the following limitation: its use in the single-flank test requires that the test be performed under a low input torque/revolution speed (20 N·m /60 rpm). It can, however, check the quality of the manufactured gear pair very effectively at the manufacturing site.
Figure 8 shows how the results of the experiment were analyzed. If the pinion to be measured revolves while engaged with the gears, the rotational angular velocity of each gear should be measured using a rotation angle meter whose resolution power is at least 30 times the number of gear teeth. After calculating the long and short waves
separately according to the numbers of the pinion and gear teeth (Figure 22), the transmission error of the average tooth mesh is computed to derive the resultant value. In addition, the transmission error for each gear order can be identified by calculating each spectrum for each set of time data through the FFT process.
Figure 7. Experimental setup for the single-flank measurement of the hypoid gear
Figure 8. Transmission error measurement system: Gleason single-flank tester
3.2. Triaxial Transmission Error Measure
The single flank test discussed in Section 3.1 was conduced to evaluate the biaxial transmission error of the two gears. This test is inappropriate to determine the cause analysis of hypoid gear whine noise for the following reasons. First, the torque condition is low, and the deflection under the torque is not applied due to the structural limitations of the equipment. In fact, it is impossible to evaluate the transmission error under high torque because the equipment being tested is fixed to each axis by frictional jigs, not by bolts. Second, it is impossible to identify the cause of the gear whine noise because the deflection under the input torque is not applied.
Figure 9 shows the engagement error meter that utilizes the revolution angle measurement. The transmission error is calculated from the revolution data of the revolution angle meter installed on the extension line of the pinion and gear axes. To prevent motor-side disturbance, the driving method with couplings and belts is utilized, but the measured value tends to change due to the revolutionary vibration of the transmission error.
Figure 9. Conventional transmission error tester
Figure 10. Transmission error measurements by angular velocity using laser sensors.
To make up for this disadvantage, a method of measuring the transmission error using laser sensors was suggested, as shown in Figure 10. This transmission error measurement method stabilized the revolution of the axle input by using a flywheel, and it calculated the transmission error by measuring the angular-velocity variation with the use of laser sensors. This method, however, has the following disadvantages: (1) there must be a transparent hole in the body of the axle so that laser sensors can be used; (2) oil cannot be used to prevent errors due to the irregular reflection of the laser angular-velocity meter. Because the two aforementioned measurement methods use two revolution angle and angular-velocity meters by applying the single-flank test method, the precision of the measurement is reduced due to the transmission errors generated by the revolution of the differential gear, which results from the differential movement of the right/left axis generated with the fixed output axis of one side. Therefore, in this study, the revolution angles of the three axes on the axle were measured to make up for the aforementioned disadvantages of the proposed method. The transmission errors in the input torque section of the axle, which has noise sections in vehicles, were measured using the triaxial transmission error evaluation. This method of evaluating the triaxial transmission error of the axle may also be applied to FF manual transmission and its axle. Figure 11 shows the processes of configuring and computing the triaxial transmission error, and Figure 12 is a diagram of the actual triaxial transmission error measurement experiments. Three ring encoders (ERM280) of HEIDENHAIN with three Rotec E- DR counter boards were used on the input, LH output, and RH output of the axle. Each encoder rotation signal was calculated with RAS software by Rotec. Because a revolutionary angle meter has an angle revolution power of 20480 per revolution, it was possible to measure the transmission error with a high precision: 200 or more times the number of gear teeth (30~80) to be measured.
Figure11. Hardware and software schematic diagram of the triaxial-transmission-error tester.
Figure 12. Triaxial-transmission-error measurements using a rotary encoder.
4. DEFLECTION UNDER THE INPUT TORQUE
4.1. Deflection under Input Torque of the Automobile
Figure 13 shows the coordinate system of the hypoid gear. Figure 14 shows the results of the deflection test under the axle input torque of the E (offset direction), P (pinion
direction), and G (gear direction) axis, and Figure 15 shows the α angle. Table 2 shows the result of the gear tooth contact test under the input torque. The variation of the tooth contact shows spreads out toward the heel as the torque increases in the typical Toe Bias In pattern. According to the input torque, the P axis tends to show a +
direction on the drive side of the gear contact tooth when accelerating a vehicle, and a ? direction on the coast side of the contact gear when decelerating a vehicle. The generated deflection was between 0.02 mm and ?0.025 mm. In the case of the G axis, both the accelerating tooth (drive side) and the decelerating tooth (coast side) were deflected in the same direction, and the deflection was 0.042 mm when decelerating (coast) and 0.018 mm when accelerating, which means that deflection is two times more sensitive when decelerating (coast). For the E axis, the deflection was 0.03 mm when accelerating (drive), which is lower than ?0.045 mm when decelerating. For the α axis, it was 89.96 when decelerating (drive), which means the
deflections are more sensitive than when accelerating (drive).
Figure 13 Axial coordinate of the hypoid gear. Figure 14 EPG axial deflection test results.
Figure 15. α-axial deflection test result. Figure 16. Triaxial rpm measurement results in the time domain.
4.2. Triaxial Transmission Error Measurement Results
Eleven axle pinion gears and 43 gear teeth were used in the test. As in Figure 11, the
results of the triaxial transmission error measurement shown in Figure 16 show the measured revolution number of the time axis of the three channels (input, LH output, RH output) in the hardware. The average rpm of the two output axis rpms that were measured is shown in Figure 17. The average rpm of the two output axes was calculated because the ratio of the output axis rpm to the input rpm is always stable mechanically because the output axis is connected to the differential gear at the center. Therefore, when measuring the transmission error of the three axes of the axle, the average rpm of the gear can be calculated by computing the average of the two rpms because there is a difference between LH and RH. Figure 18 shows the angular displacement over time. This wave form resulted from the measurement of each dis-
placement against the pinion gear with the revolution of the pinion gear, i.e., it is not the averaged result. Figure 19 shows that the short wave passed through the high pass
filter and the long wave through the low pass filter in the total signal. Here the long wave represents the runout volume of the pinion gear, and the short wave represents the transmission error of the pinion gear. Like Figure 19, Figure 20 shows the transmission error of the gear. Figure 21, on the other hand, shows the averaged transmission error of the tooth pitch when the pinion and gears rotate while engaged with each other. Generally, the transmission error was analyzed against the 1st = A1, 2nd = A2, and 3rd = A3 orders, which corresponded with the mash order of the pinion, by analyzing the result of the FFT shown in Figure 21. The values of each order were the representative values of the transmission errors of the pinion and gears.
Table 2. Tooth contact pattern results. Figure 17. LH and RH output shaft rpm averaging results in the time domain.
Figure 18. Total signal by reference input Figure 19. Total signal and long and short
pinion gear rpm signal. waves of the pinion gear.
Figure 20. Total signal and long and short Figure 21. Average tooth pitch result.
waves of the gear.
5. DESCRIPTION OF THE DEVELOPMENT OF COAST NOISE BY DEFLECTION DATA
5.1. Coast Noise Development
To identify the cause of the coast noise that occurs during driving, the transmission er-
ror due to input load was measured. Figure 22 shows the transmission error measure-
ment results. The major cause for coast noise was the high transmission error of 14 μ rad or above in the zone of the torque that works as the input torque to the axle as the vehicle decelerates. The rectangular dotted line indicates the torque zone that is associated with the axle input. To reduce the noise that occurs during coasting, as shown in Figure 23, the transmission errors for each input torque were compared with a 0.1~0.15 mm lengthened pattern on the coast side. The results from the deflection test of E, P, G, a n d α were applied using the S/W of Gleason Hypoid gear. In Figure 24, the calculation results of the transmission error for each input load before and after the change in the length of the coast side pattern were compared. The gear was produced by verifying the corrected gear teeth on the coast side with the calculation results that the transmission error value is lowered in the torque zone where the noise occurs as the vehicle coasts. Figure 25 shows the results from the comparison between the gear teeth of the coast noise gear and long contact pattern gear. In the figure, the top plot compares results from the coast side noise gear and long contact pattern gear on the drive side, while the bottom compares results on the coast side. The points that show the difference between two gear teeth are indicated with a rectangular dotted line. From point 3 to point 9 in the heel direction, the teeth value is relatively negative (‘?’) and continues to be lowered in the heel direction. The axle was assembled with long contact pattern gear, and the transmission error at axle ass’y was measured. Figure 26 compares the transmission error results from the coast noise gear axle ass’y and the long contact pattern gear axle ass’y across the input torque. The rectangular dotted line indicates the zone to which the axle input torque is applied when the vehicle decelerates. It is consistent with the transmission error calculation results in Figure 24. Figure 27 shows the measurement results of interior noise when the vehicle decelerates. In the zones from 80 to 90 kph, 95 to 110 kph and 120 to 130 kph, where coast noise was problematic, the noise level was reduced by 5~8 dB (A).
Figure 22. Transmission error of coast Figure 23. Development method of coast
noise axle test result. noise hypoid gear.
Figure 24. Transmission error calculation res- Figure 25. Comparison of coast
ult of coast noise gear and long contact pattern. noise gear and long contact pattern
tooth profile measurement results.
Figure 26. Transmission error measurement Figure 27. Car test results of coast noise
results of the coast noise axle and long co- axle and long contact pattern axle #1 and
ntact pattern axle. #2.
6. CONCLUSION
To identify the gear whine noise in the axle composed of a hypoid gear and reduce the noise in a decelerating vehicle, the corrected gear teeth and transmission error measures were compared by applying the amount of deflection in the input torque zone of the noise occurring zones. The gear produced based on these results also confirmed that the transmission error from input torque shows the same trend in axle ass’y. In addition, the noise level was reduced by 5~8 dB (A) in the actual vehicle in the noise-occurring zone. These findings suggest that the occurrence of hypoid gear whine noise will be minimized if, based on these results, the target range of the axle input torque for the development of optimal hypoid gear is measured and set as the range of axle input torque and if the amount of transmission error from input torque is verified analytically for corrected teeth gear; moreover, the consequences of applying the deflection measurement results and reflected onto the product are determined.
REFERENCES
Coleman, W. (1975). Analysis of mounting deflections on bevel and hypoid gears. SAE Paper No. 750152.
Kato, N. (2003). Measuring method of transmission error of final reduction gearboxes and gear noise occurrence mechanism. JSME, 69 , 230 ?235.
Kolivand, M., Hannaneh, A. and Soltani, N. (2006). Retaining hypoid gear performance characteristics with differ- ential housing and shafts deflections. ASME, IMechE 2006-13216, 361 ?369.
Lee, Y. Y., Park, S. G. and Oh, J. E. (2007). A study on vibration transfer path identification of vehicle driver’s position by multi-dimensional spectral analysis. Trans.Korean Society for Noise and Vibration Engineering, 17 , 741?746.
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