Optimal_design_of_gears

Optimal_design_of_gears - Page 1 of 8 EML 3005: MECHANICAL...

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Page 1 of 8 EML 3005: MECHANICAL DESIGN OPTIMAL DESIGN OF SPUR AND HELICAL GEARS Nagaraj K. Arakere Mechanical & Aerospace Engineering University of Florida Summary A simple closed-form procedure is presented for designing minimum-weight spur and helical gear sets. The procedure optimizes bending and surface fatigue strengths of gear teeth, to arrive at minimum weight gears. The method does not take into account effects of scuffing, heat generation, and lubrication conditions like oil temperature, elasto-hydrodynamic film thickness and flash temperature, since they are outside the scope of the class. Introduction Gear design is a process of synthesis where gear geometry, materials, heat treatment, manufacturing methods and lubrication are selected to meet the performance requirements of a given application. The designer must design the gearset with adequate resistance to contact fatigue (pitting resistance) and bending fatigue to transmit the required power for design life. With the simple procedure presented here, one can select materials and heat treatment and optimize gear geometry to satisfy constraints of weight, size and configuration. It is assumed that the gear ratio m G is known. The gear designer can minimize noise level and operating temperature by minimizing the pitchline velocity and sliding velocity. This is done by specifying high gear accuracy and selecting material strengths consistent with maximum material hardness, to obtain minimum size gearsets with teeth no larger than necessary to balance pitting resistance and bending strength. Gear design is not the same as gear analysis. Existing gear sets can only be analyzed, not designed. While design is more challenging than analysis, current textbooks do not provide procedures for designing minimum weight gears. They usually recommend that the number of teeth in the pinion be chosen based solely on avoiding undercut. This does not result in minimum weight gearsets. Optimum Number of Pinion Teeth The optimum number of teeth maximizes the load capacity of a gearset. Figure 1 shows that load capacity is limited by surface fatigue (contact stress), bending fatigue and scuffing failure depending on the number of teeth. There is also a lower limit to the number of teeth, below which undercut occurs. The shaded zone in Fig. 1 is bounded by all three-failure modes curves and the undercut limit. We will only consider bending and contact fatigue for optimal design. Notice that the surface fatigue curve is not a function of number of teeth, while in contrast the bending fatigue curve depends strongly on the number of pinion teeth and decreases rapidly with increasing number of teeth. . Maximum load capacity occurs at point “A” where pitting resistance and bending strength are balanced. With more pinion teeth (to the right of point A) load capacity is controlled by
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Optimal_design_of_gears - Page 1 of 8 EML 3005: MECHANICAL...

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