<p style="text-align: center;"><img src="/ueditor/php/upload/image/20250312/1741783612999240.png" title="1741783612999240.png" alt="6.png"/></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">The three gear meshes shown here carry torque through the transmission in given gear and range shift lever positions. The gear meshes of interest are Gear mesh 1 (18.75 order of input shaft) and Gear mesh 2 (15.1 order of input shaft). The red arrows mark the direction of torque flowing through this multi-axis gearing system.</span></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">Methodology</span></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">Noise Testing and Order Analysis for Source Identification</span></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">Noise data is recorded using a binaural headset along with engine RPM. Different sets of data acquisition were executed corresponding to constant RPMs, engine RPM sweep (from low idle to high idle engine RPM). A sampling rate of 44 kHz is considered. For test data analysis, a frequency resolution of 1 Hz with A-weighting is applied.</span></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">Based on the order analysis, high amplitude orders were identified as shown in Fig. 2. By suppressing those orders in sequence/combination and listening to the sound, dominant orders 15.1 and 18.75 are confirmed for further investigation.</span></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">The noise was specific to the combination of the speed and range lever selection. In the noisy condition, three gear meshes were transmitting torque to the spiral bevel gears connected to the rear axle through the planetary final drive. Based on the number of teeth and power flow, orders were calculated for different gear mesh combinations. It was found that the two identified orders viz 18.75 and 15.1 corresponded to one range gear mesh and one-speed gear mesh which were engaged and transmitted the torque.</span></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">Gear Geometric Parameter Considerations and Virtual Analysis</span></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">Gear Macrogeometry Improvements</span></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">To increase the profile contact ratio in each gear mesh, the modules were reduced, and tip diameters were increased marginally. To prevent contact between the tip and the root of the gear, we first performed theoretical calculations to determine the necessary root clearances. In addition to these manual calculations, we also used advanced simulation software to analyze potential tip-to-root contacts. This analysis considered factors such as increased tip diameters, misalignments, and tooth deflections. The macro geometry improvements also included, in each gear mesh, the gear face width and helix angle increase to achieve a minimum face contact ratio of 1. These design enhancements helped raise the sum of contact ratios to over 2.5 for these helical gears. A summary of these changes is provided in Table 1. These macro geometry changes were in line with the study by Liu et al. (Ref. 1) mentioned earlier.</span></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">To calibrate the simulation model, a gear contact pattern test was conducted on a test bench using masking compounds on the gear flank. The torque through the gear mesh was set to be the same as that in the actual application. Actual torque values in field applications were obtained by strain gauging the transmission shafts and running the tractor in field conditions. This physical test served two purposes: to calibrate the simulation model and to understand contact health issues in one of the two gear meshes. It highlighted the necessity for lead slope correction to achieve centered contact within the application load range. This insight informed the final microgeometry adjustments in the lead direction for the gear mesh of order 18.75 (Gear mesh 1).</span></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">The lead crown values were kept to a minimum to increase effective face contact ratios while ensuring no edge loading, as revealed in the contact pattern studies conducted in the simulation software.</span></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">It became evident that Gear mesh 1, with its offset contact pattern, required lead slope correction. During the development of these lead corrections, it was discovered, through software simulations, that the necessity for lead correction could be reduced by flipping the helix hand due to the change in system deflections. After evaluating the impact on the calculated bearing life, the team opted to modify the helix hand in conjunction with the previously mentioned gear design enhancements.</span></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">As indicated in the literature review (Refs. 5, 6), it is understood that when designing for full load conditions, long tip reliefs offer superior PPTE reduction compared to short tip reliefs. Parametric simulation runs also demonstrated that longer tip reliefs yielded lower PPTE results, with the PPTE outcomes showing less sensitivity to lead and profile microgeometry tolerances. Consequently, the start of tip relief angles was reduced, alongside an increase in tip relief values, to minimize the PPTE. These start-of-tip-reliefs for each of the gear meshes were close to, but slightly less than the working pitch roll angle.</span></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">The simulation results of the macro and micro gear design improvements are presented in the “Verification” section.</span></p><p><br/></p>