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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obtained by decreasing the helix angle. All dependent gears must have the same helix angle value, regardless of whether the helix direction is left or right hand. ● Pressure angle: decreasing the pressure angle is limited by the cutter life and by obtaining larger base circle diameters which impose a stub tooth with relatively lower contact ratio. On the other hand, increasing the pressure angle is limited by the generated bearing load due to the increase of the radial force and by getting pointy tooth tip thickness. ● Number of teeth: the number of teeth should be selected by satisfying the gear ratio requirements for both engagements, with considering the hunting ratio condition. Having a hunting gear ratio in a gear pair ensures that the number of teeth of the two gears will have no common factors between them, and that will avoid the coincidence of their frequency orders. In the double dependency case, the number of teeth of the three gears must be set to ensure a hunting gear ratio of both engagements. ● Tip and root diameters: the tip and root diameters of the driven ring gear should be set by avoiding any contact below the root form diameter in both engagements. ● Operating centre distance: the design of the driven ring gear should be set in consistence with the two driving gears to meet the given shaft centre distances. Any change in the centre distance due to profile shifting or tooth correction will change the standard centre distance to the operating centre distance, and this will change other parameters to the operating (working) ones accordingly. ● Face width: there is no dependency in setting the face width, see Table 1. The most important thing to mention here is that the active face width should fulfil the stresses and contact ratio requirements. Table 3: Torque and misalignment for the studied load cases. G1-D (L1) Misalig. (mm) G1-D (L2) Misalig. (mm) G1-C Misalig. (mm) G2-D Misalig. (mm) T (Nm) stiff. 0 stiff. 90 T (Nm) stiff. 0 stiff. 90 T (Nm) stiff. 0 T (Nm) stiff. 0 100 0.0023 0.00344 40 0.0029 0.00212 70 -0.017 100 -0.002 200 0.00136 0.00451 80 0.002478 0.00222 140 -0.030111 200 -0.0036 300 0.00041 0.00559 120 0.002056 0.00232 210 -0.043222 300 -0.0052 400 -0.0005 0.00666 160 0.001634 0.00241 280 -0.056333 400 -0.0068 500 -0.0015 0.00773 200 0.001212 0.00251 350 -0.069444 500 -0.0084 600 -0.0024 0.00881 240 0.00079 0.00261 420 -0.082555 600 -0.01 700 -0.0034 0.00988 280 0.000368 0.00271 490 -0.095666 700 -0.0116 800 -0.0043 0.01095 320 -0.000054 0.00281 560 -0.108777 800 -0.0132 900 -0.0053 0.01202 360 -0.000476 0.0029 630 -0.121888 900 -0.0148 1000 -0.0062 0.0131 400 -0.0009 0.003 700 -0.135 1000 -0.0164 Microgeometry design Microgeometry defines all modifications from the nominal tooth profile, as illustrated in Fig.2. Gear tooth design in the micro-scale is a crucial task for gear design engineers. Tooth load distribution, actual contact ratio, PPTE, contact stresses, and root bending stresses are all affected by the tooth flank microgeometry design. In the current research the dependency effect was studied. Two different microgeometry designs, namely Design A and B which are stated in Table 2, were used for Gear 1 and Gear 2. For Gear 1-Ring engagement, as seen in Fig.3, design A_G1-D shows lower PPTE at the low torque levels (L2) and slightly lower stresses than design B_G1-D, but Design B_G1-D offers lower PPTE at the high torque levels (L1). However, using the same Ring Gear microgeometry for Gear 2-Ring engagement with adding a basic microgeometry set of Gear 2, which is named design A_G2-D, shows significantly high PPTE and stresses, see Fig.4 and 6c. Therefore, the microgeometry should be designed by considering this dependency. Design B_G2-D can then be presented by optimizing the microgeometry design of Gear 2 and keeping the same Ring Gear design to avoid any changes on Gear1-Ring engagement. The gear dependency adds a restriction in design. The microgeometry design of the driven ring gear has to be set in consistence with the two driving gears to fulfil the stress and PPTE requirements of both engagements. It is recommended in such case to start with a basic set of microgeometry design for the ring gear, which is the common gear in this case. The required modifications should be more on both driving gears than the driven ring gear. If the modifications are not enough for obtaining the required results, certain modifications can be added to the ring gear. 3.1.2