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Research Papers

Optimizing Cam Profiles Using the Particle Swarm Technique

[+] Author and Article Information
Ramiro H. Bravo

Forrest W. Flocker

Department of Engineering and Technology,  University of Texas of the Permian Basin, 4901 East University, Odessa, TX 79762flocker_f@utpb.edu

J. Mech. Des 133(9), 091003 (Sep 07, 2011) (11 pages) doi:10.1115/1.4004587 History: Received March 08, 2011; Revised July 01, 2011; Published September 07, 2011; Online September 07, 2011

Cam-follower systems are ideally suited for many machine applications that require a specific and an accurate output motion. The required follower motion is achieved by carefully designing the shape or profile of the cam. Modern profiles are typically synthesized by piecing together a set of trigonometric and/or polynomial functions that satisfy the constraints. For most problems, there are many profile solutions that satisfy the constraints. In this paper, a relatively new optimization technique known as particle swarm optimization (PSO) is applied to the optimization of two different cam problems. The first example is a single-dwell cam in which the magnitude of the negative acceleration is minimized. The second example is a cam with a constant velocity segment in which the cycle time is optimized. The intent is to show the method in two different settings so that the reader can extend it to the optimization of any cam-follower problem. To illustrate the method, first the PSO method is applied to a mathematical function with two independent variables. Then, the method is used to find the cam profile that provides the minimum acceleration in a single-dwell cam using three independent variables. Finally, it is applied to obtain the minimum cycle time of a cam with a constant velocity segment using cubic interpolations and seven or more independent variables. The PSO method was very successful in all the optimization problems discussed in this paper. In the first cam problem, it significantly lowered the level of negative acceleration, while maintaining the positive acceleration at a constrained upper limit. The optimization procedure for the second cam problem found a very elegant five-segment solution. This solution results no matter how many initial segments or independent variables are chosen so long as there are at least five segments. Presented in this paper is the particle swarm optimizing technique that is applicable to many aspects of cam design. Two diverse examples were presented that illustrate how the PSO method can be used effectively in the optimization of cam-follower problems. In both illustrative examples, the PSO method proved to be robust, easy to implement, and suitable for minimizing a wide variety objective functions applicable to the design of cam-follower systems.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

A typical cam-follower arrangement

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Figure 2

A typical double-dwell follower motion program

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Figure 3

Illustration of convergence and swarm density refinement

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Figure 4

Illustration of the mathematical optimization problem

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Figure 5

Swarm behavior during convergence for the mathematical example. (a) Initial swarm distribution; (b) swarm after 600 iterations; (c) swarm after 4000 iterations; (d) swarm after 13,600 iterations.

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Figure 6

Follower motion for a symmetric single-dwell cam

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Figure 7

Kinematics for optimized seventh-degree cam profile. (a) Dimensionless position; (b) dimensionless velocity; (c) dimensionless acceleration; (d) dimensionless jerk.

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Figure 8

Swarm density study for single-dwell cam profile optimization

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Figure 16

Kinematics for the constant velocity profile. (a) Dimensionless position; (b) dimensionless velocity; (c) dimensionless acceleration; (d) dimensionless jerk.

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Figure 15

Optimal acceleration without regard to jerk limits

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Figure 14

Follower shown at the start and end of the constant velocity segment

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Figure 13

Five-segment solution giving the minimum cycle time

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Figure 12

Piecewise linear dimensionless acceleration

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Figure 11

The unknown position function subdivided into six segments

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Figure 10

Motion program for a constant velocity cam-follower system. (a) Physical or actual quantities; (b) dimensionless quantities.

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Figure 9

Form-closed barrel cam driving an axial follower

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