BENDING LOAD CAPACITY ENHANCEMENT USING ASYMMETRIC TOOTH PROFILE

Outline of the presentation Introduction Geometry Tooth bending stress Numerical analysis Conclusions

Introduction Gears are functional units used for transmission of power in transmission systems. Fine module gears are used for low noise, vibration and for compact size of transmission system. Smaller gears will lead to insufficiency in bending load carrying capacity. This is a serious problem in plastic and sintered gears.

Solutions for bending load enhancement To improve the fatigue strength of the tooth by heat treatment or surface quality improvement. Reduce the maximum bending stress at the root of the tooth by proper fillet profile.

Methods developed for the possible solutions Carburization Shot peening Gear cutter with larger tip corner Changing the profile of tooth root Design of tooth form based on operating situation

Operating conditions of gear In normal involute gear, tooth is in symmetric form. In practical gear units both forward and backward rotations are not required simultaneously. The load and running conditions are different for front and back rotation. Hence two sides of gear tooth are functionally different. One side is loaded for longer period, the opposite side is unloaded or slightly loaded for short duration.

Asymmetric tooth No left right tooth symmetry Pressure angles on both sides are different. Higher pressure angle on drive side for large critical section. Asymmetric tooth side surfaces enables to increase the load capacity and durability for the drive tooth side.

Geometry Pitch radii of pinion and gear Radii of base circles

Tooth bending stress Tooth bending stress in symmetric gears can be estimated by ISO 6336 and DIN 3990. These standards are based on Critical section of tooth is defined by point of tangency with root fillet of a line rotated 30 deg from tooth centerline Compressive stress produced by radial component of tooth is neglected. Total load acts at the tip of the tooth

Tooth model for bending stress

According to the DIN 3990, the maximum bending stress is

Numerical Analysis The stresses occurring over the tooth is analyzed with 2D-FEM. Total tooth load acts at the tooth tip. Analysis is performed with ANSYS. PLANE 82 element is used.

Mechanism Data Power 8 kW Normal module 2 mm Number of teeth on pinion 20 Number of teeth on gear 40 Materials Steel Face width 40 mm

Results of bending stress analysis

Maximum tooth bending stress points

Tooth bending stress results Decrease in stress due to the reduction in tooth height in correspondence to pressure angle Pressure angle Coast/drive side Von mises stress (By FEM) 20/20 210 20/25 178 20/30 169 20/35 153 20/40 136.5

Conclusions The bending stress analyses have been performed with the aid of FEM for asymmetric and symmetric tooth. Asymmetric teeth have better performance than symmetric teeth for bending stress minimization. As pressure angle on drive side increases, the bending stress decreases and bending load carrying capacity increases. The location of maximum bending stress remains the same in FEM.

Applications of asymmetric gears Aerospace applications Mass production transmissions Molded and powder gears

References Alexander Kapelevich, Geometry and design of involute spur gears with asymmetric teeth, Mech. Mach. Theory 35 (2000), pp. 117–130. Kapelevich, A.L., and Shekhtman, Y.V., 2003, “Direct Gear Design: Bending Stress Minimization,” Gear Technol., Sept./Oct., pp. 44-49. A.L. Kapelevich and R.E. Kleiss, Direct gear design for spur and helical involute gears, Gear Technol. (9/10) (2002), pp. 29–35.

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