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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3.1. Dependency in gear design A double or even triple dependency gear systems are already applied in gear transmissions. Double dependency means a gear is in engagement with two other gears, as illustrated in Fig. 1, while triple dependency involves the engagement with three other gears. This type of design layout imposes different restrictions in both the macro- and the microgeometry designs. By considering the double dependency case, explained in Section 2, the driven Ring Gear is in engagement with both Gear 1 and Gear 2. In this case, the design consistency must exist, which means the design parameters of the driven Ring Gear are set in agreement with the other two driving gears to fulfil the requirements of both engagements. The dependency in gear design can be further explained as follows. 3.1.1 Macrogeometry design A double dependency case involves three dependent gears, as illustrated in Fig.1. The macrogeometry parameters of the three studied dependent gears must be designed to fulfil the design requirements of both engagements Gear 1-Ring and Gear 2-Ring. The macrogeometry parameters of module, helix angle and pressure angle must be set in common by having the same value for the three dependent gears. Several macrogeometry parameters are discussed here from the dependency perspective as follows. Table 1: The main macrogeometry parameters used in the studied model Parameter Gear 1 Gear 2 Driven Ring Gear Number of teeth 17 23 79 Normal module, mm 2.6 Normal pressure angle, deg. 21 Normal helix angle, deg. 30 (left helix) 30 (left helix) 30 (right helix) Face width, mm 34 34 33 Operating centre distance, mm 142 151 Modulus of Elasticity, GPa 206 Poisson’s ratio 0.3 Table 2: The studied microgeometry design cases. G1-RG engagement, Drive G1-RG engagement, Coast G2-RG engagement, Drive Design A_G1-D Design A_G1-C Design A_G2-D G1 RG G1 RG G2 RG fHa (µm) -7 10 fHa (µm) -7 10 fHa (µm) 0 10 ca (µm) 9 3 ca (µm) 9 3 ca (µm) 2 3 caa (µm) 15 17 caa (µm) 15 17 caa (µm) 11 17 Dca (mm) 56.72 233.85 Dca (mm) 56.72 233.85 Dca (mm) 76.62 233.85 Roll angle (deg) 38.2 21.2 Roll angle (deg) 38.5 21.2 Roll angle (deg) 38 21.2 fhb (µm) 0 0 fhb (µm) 0 0 fhb (µm) 0 0 cb (µm) 8 7 cb (µm) 8 7 cb (µm) 2 7 G1-RG engagement, Drive G1-RG engagement, Coast G2-RG engagement, Drive Design B_G1-D Design B_G1-C Design B_G2-D G1 RG G1 RG G2 RG fHa (µm) 0 10 fHa (µm) 5 10 fHa (µm) 10 10 ca (µm) 15 3 ca (µm) 13 4 ca (µm) 3 3 caa (µm) 20 17 caa (µm) 20 17 caa (µm) 11 17 Dca (mm) 56.72 233.85 Dca (mm) 56.72 233.85 Dca (mm) 76.62 233.85 Roll angle (deg) 38.2 21.2 Roll angle (deg) 38.2 21.2 Roll angle (deg) 38 21.2 fhb (µm) 0 0 fhb (µm) 40 60 fhb (µm) 20 0 cb (µm) 13 7 cb (µm) 11 17 cb (µm) 10 7 ● Gear module: the gear module value is essentially based on the selected number of teeth and the given centre distance. The gear module must have one value for the engaged gears, and thus all the three dependent gears, in the studied model, must have the same module. ● Helix angle: increasing the helix angle is limited by the generated axial force and root stresses. Furthermore, manufacturing issues might be obtained with high helix angles. On the other hand, a low contact ratio will be