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TECHNICAL PAPERS

# Computation of Parameters of a Form Grinding Wheel for Grinding of Shaving Cutter for Plunge Shaving of Topologically Modified Involute Pinion

[+] Author and Article Information

EATON Corp., 31900 Sherman Avenue, Madison Heights, MI 48071

J. Manuf. Sci. Eng 127(4), 819-828 (Jan 14, 2005) (10 pages) doi:10.1115/1.2037087 History: Received June 22, 2004; Revised January 14, 2005

## Abstract

The paper is targeting on the finishing of precision gears for low-noise/noiseless transmission for cars and light trucks. Transmission error is the predominant cause of gear noise. The application of a topologically modified pinion results in reduction of transmission error up to two times. The required modification of the pinion tooth surface is provided on a plunge shaving operation with application of a shaving cutter of an appropriate design. A novel approach for computation of parameters of a form grinding wheel for grinding of the shaving cutter for plunge shaving of a precision involute pinion with topologically modified tooth surface is reported in the paper. The developed approach for computation of parameters of the form grinding wheel is focused on application of the shaving cutter grinder with a lack of CNC articulation. The problem under consideration is solved using the DG/K-based approach of part surface machining earlier developed by the author. (The DG/K-approach is based on fundamental results obtained in differential geometry of surfaces, and in kinematics of multi-parametric motion of a rigid body in $E3$ space (See Radzevich, S.P., Sculptured Surface Machining on Multi-Axis CNC Machine. Monograph, 1991, Vishcha Shkola Publishers, Kiev (in Russian). See also Radzevich, S.P., 2001, Fundamentals of Surface Machining. Monograph, Rastan, Kiev (in Russian).) An analytical solution to the problem is discussed in the paper. The solution has been used for developing software for the Mitsubishi ZA30CNC shaving cutter grinder for the needs of the automotive industry. Computer simulation reveals high accuracy of the ground shaving cutter.

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## Figures

Figure 1

Deviations of the desired topologically modified pinion tooth surface Pp.des from the true involute pinion tooth surface Pp

Figure 2

Deviations of the topologically modified lateral tooth surface of the auxiliary phantom rack Rm

Figure 3

The work and the grinding wheel relative motion in shaving cutter grinding operation

Figure 4

Design and dressing of the form grinding wheel

Figure 5

Unit normal vector to the desired grinding wheel surface Tgw

Figure 6

The form grinding wheel axial profile

Figure 7

Application of the Newton-Raphson method for solving equation of contact

Figure 8

Deviations of the actual modified pinion tooth surface from the desired topologically modified pinion tooth surface

Figure 9

Flow-chart for computation parameters of finishing of an involute pinion with topologically of modified tooth surface on ZA30CNC Mitsubishi shaving cutter grinder: block of the desired topologically modified pinion tooth surface (a), block of the desired topologically modified shaving cutter tooth surface (b), block of the actual deviations of the shaving cutter tooth surface (c), and block of the actual deviations of the pinion tooth surface (d)

Figure 10

Effective length Lgw(eff) of the grinding wheel

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