PSI - Issue 42

Omar D. Mohammed et al. / Procedia Structural Integrity 42 (2022) 1607–1618 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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3.4. Misalignment variation Gear misalignment which is directly related to the stiffness of the connected rotating parts and the structural housing, is usually compensated by the tooth flank microgeometry. In the studied gear transmission model, the misalignment of every engaged gear is mainly affected by all other engaged gears in that driving mode, and also the structural housing stiffness. One of the worth considering cases is the misalignment variation. When a rotating part stiffness is varying over time, the obtained misalignment is changing accordingly. A differential gear drive can be seen as a good example of this case. Depending on the differential design, the stiffness can vary for different rotation angles. The variation in differential stiffness will affect the misalignment of the connected ring gear. As shown in Fig.7, the differential has two big holes on two opposite sides, and by rotating the differential, the stiffness varies, and the misalignment will vary accordingly. In the studied model, the misalignment is obtained in two angular positions apart from each other by 90 o . The obtained misalignment values for different torque levels are shown in Table 3 for both the studied positions of 0 o and 90 o . At the positions of 0 o and 90 o , the misalignment was obtained as -0.0062 mm and 0.0131 mm respectively at 1000 Nm load. Therefore, the maximum resulted stresses are different, as shown in Table 4. PPTE for different torque levels was obtained for the studied positions of 0 o and 90 o , and with higher torque levels the PPTE shows more difference, see Fig.8.

Fig.3 PPTE and stress results of Gear1-Ring engagement on the drive flank

4. Gear Failure and Safety Factor Calculations To ensure the durability of a designed gear it is important to make fatigue life assessment and calculate safety factors. Safety factors can be calculated using the generated stresses and the given load collective data. To ensure successful and safe operation, the designed gear must survive under the subjected load collective test. The load collective data should simulate the real service speed, time and load spectrum. The selected microgeometry modifications should produce the lowest possible PPTE over the torque range and must show accepted safety factors to survive gear failure. There are various cumulative damage methods (Fatemi & Vang 1998, Schoenborn et.al. 2015), however, the Palmgren-Miners Rule is the most applied cumulative damage method in the European automotive industry (Schoenborn et.al. 2015). The Palmgren-Miners Rule was used in the current research for calculating the total cumulative damage of every gear load case. As illustrated in Fig.9, the total damage Dtot can be obtained from the sum of the load spectrum damage. The Dtot should not exceed the allowable damage Dalw to avoid failure occurrence. Fatigue damage is the ratio of the number of cycles to the number of cycles till failure. Therefore, the theoretical