Input Torque Balancing Using an Inverted Cam Mechanism

[+] Author and Article Information
Bram Demeulenaere

Mechanical Engineering Department, Katholieke Universiteit Leuven, Leuven, Belgiumbram.demeulenaere@mech.kuleuven.ac.be

Joris De Schutter

Mechanical Engineering Department, Katholieke Universiteit Leuven, Leuven, Belgiumjoris.deschutter@mech.kuleuven.ac.be

Throughout this paper, the term original system will denote the mechanism to be input torque balanced, whereas the compensated system is the ensemble of the original and the ITB mechanism.

The shape of the rotor and the carriage are determined based on the mass parametrization approach discussed in Sec. 4.

J. Mech. Des 127(5), 887-900 (Oct 14, 2004) (14 pages) doi:10.1115/1.1876452 History: Received December 02, 2003; Revised October 14, 2004

Input torque balancing through addition of an auxiliary, input torque balancing mechanism, is a well-known way for reducing drive speed fluctuations in high-speed cam-follower mechanisms. This paper develops a methodology to design and optimize the so-called inverted cam mechanism (ICM), a simple, cam-based input torque balancing mechanism. It was already introduced in the 1950s, but the design methodologies proposed by Meyer zur Capellen (1964) and Michelin (1979) are, respectively, erroneous or too rough an approximation, and are corrected here. The describing equation that governs the ICM cam design, is shown to be a second-order, nonlinear, ordinary differential equation. It is solved by parameterizing its solution as a finite Fourier series, the coefficients of which are determined through a nonlinear least-squares problem. Based on this methodology, an ICM is designed for input torque balancing a high-speed, industrial cam-follower mechanism. The ICM’s design parameters result from a design optimization, which aims at obtaining a compact and technologically feasible mechanism. The optimization problem is solved using a design chart, which is efficiently created based on a nondimensionalized analysis.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Inverted cam mechanism: kinematic scheme

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Figure 2

Design example (ω=900rpm): dimensionalized (left ordinate axis) and nondimensionalized (right ordinate axis) desired cam follower position, velocity, and acceleration

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Figure 3

Design example (ω=900rpm): (a) Mc (N m) (full line) and Mo (N m) (dashed line); (b) corresponding torque residual Mc+Mo (N m)

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Figure 4

Design example (ω=900rpm): dimensionalized (left ordinate axis) and nondimensionalized (right ordinate axis) ICM pitch radius and its first two derivatives

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Figure 5

Design example: Jeq, Jeq,min, and Jeq,o

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Figure 6

Design example: resulting ICM configuration. Both the X and the Y-axis are expressed in m. The solid boundary indicates the cam against which the upper rolling body rolls. The thin boundary, shown in the left part, and hidden behind the solid boundary in the right part, indicates the cam against which the lower rolling body rolls.

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Figure 7

Design example (ω=900rpm): comparison of ICM input torque contributions: (a) component due to r∙ṙ; (b) component due to ṙ∙r̈, and (c) total input torque Mc

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Figure 8

Shape parametrization: front (a) and top (b) view of the rotor and front (c) and top (d) view of the carriage (with the outer bearing ring of diameter Rb present)

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Figure 9

Design example: design chart (ω=900rpm). The lowest Jeq-values are situated in the lower left corner. The highest values are found in the upper right corner. The contour lines {100,500,1000} indicate Nmin-values (N). The contour lines {0,0.08} indicate t*-values (m).

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Figure 10

Design example (ω=900rpm): contour plots of (a) rmax−rmin (m), (b) ṙmax (m/s), and (c) r̈max(m∕s2) as a function of ξ0 and rmax




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