Application of Optimal Control Theory to the Synthesis of High-Speed Cam-Follower Systems. Part 1: Optimality Criterion

1983 ◽  
Vol 105 (3) ◽  
pp. 576-584 ◽  
Author(s):  
M. Chew ◽  
F. Freudenstein ◽  
R. W. Longman
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Dynamic Response ◽  
Optimal Control Theory ◽  
High Speed ◽  
Integrated Approach ◽  
Optimization Criterion ◽  
Design Stage ◽  
Trade Offs ◽  
Cam Follower

The synthesis of the parameters governing the dynamic response of high-speed cam-follower systems ideally involves an integrated approach capable of carrying out the tradeoffs necessary to achieve optimum dynamic response in the design stage. These trade-offs involve a balance between the system characteristics at the output and at the cam-follower interface. In this investigation optimal-control theory has been demonstrated to be a useful tool in developing such a tradeoff. Part 1 describes the development of an optimization criterion while Part 2 describes the application of optimal-control theory to the evaluation of system parameters satisfying the optimization criterion.

Application of Optimal Control Theory to the Synthesis of High-Speed Cam-Follower Systems. Part 2: System Optimization

1983 ◽  
Vol 105 (3) ◽  
pp. 585-591 ◽  
Author(s):  
M. Chew ◽  
F. Freudenstein ◽  
R. W. Longman
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Contact Stress ◽  
Optimal Control Theory ◽  
High Speed ◽  
System Optimization ◽  
Design Parameters ◽  
Numerical Examples ◽  
Cam Follower

This part is concerned with the determination of optimum values of the design parameters of cam-follower systems according to the criterion developed in Part 1. The nonlinearities associated with the optimization of contact stress, pressure-angle, and friction-dependent forces, which create difficulties in the simpler approaches, can be tolerated in the optimal-control-theory formulation, which is developed in this investigation. The procedure for the optimization of tuned D-R-D and D-R-R-D cams has been described and the results illustrated by means of numerical examples.

A CAD Package for High-Speed Cam Design Based on Direct Multiple Shooting Optimal Control Techniques

2004 ◽  
Author(s):  
Sebastian Mennicke ◽  
Richard W. Longman ◽  
Meng-Sang Chew ◽  
Hans Georg Bock
Keyword(s):  
Optimal Control ◽  
High Speed ◽  
Optimality Criteria ◽  
Iterative Refinement ◽  
Valve Train ◽  
Design Stage ◽  
Multiple Shooting ◽  
Cam Design ◽  
Trade Offs ◽  
Highly Nonlinear

High-speed automotive valve train design requires realistic models of the valve train. However, this frequently results in highly nonlinear systems with discontinuities and constraints. Optimality criteria and trade-offs for the designs are frequently performed through a process of simulation and iterative refinement. This paper presents CamOE, a cam design optimization package based on direct multiple shooting optimal control theory, incorporating structured sequential quadratic programming. The code allows the designer to incorporate the constraints of importance and to consider and synthesize appropriate optimality criteria. This allows him or her to synthesize the cam profile at the design stage without resorting to a tedious trial-and-error design process. This paper presents CamOE as a software environment that permits rapid feedback to the designer through the process of numerical experiments in specifying criteria and constraints on the automotive valve train.

A Variable-Speed Method for Reducing Residual Vibrations in Elastic Cam-Follower Systems

2003 ◽  
Vol 125 (3) ◽  
pp. 480-482 ◽  
Author(s):  
Yan-An Yao ◽  
Hong-Sen Yan ◽  
Ce Zhang
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Vibration Control ◽  
Optimal Control Theory ◽  
Variable Speed ◽  
Design Point ◽  
Parameter Variations ◽  
Cam Follower ◽  
Speed Method

This paper applies the concept of variable speeds to vibration control of elastic cam-follower systems. A multi-design-point approach, based on optimal control theory, is developed for selecting suitable input speed functions of the cam that can reduce both primary and residual vibrations of the output in elastic cam-follower systems despite parameter variations. A design example is given to verify the feasibility of the approach.

The Design of High-Speed Dwell-Rise-Dwell Cams Using Linear Quadratic Optimal Control Theory

1994 ◽  
Vol 116 (3) ◽  
pp. 867-874 ◽  
Author(s):  
B. C. Fabien ◽  
R. W. Longman ◽  
F. Freudenstein
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
High Speed ◽  
Numerical Procedure ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Trajectory Sensitivity ◽  
Cam Design ◽  
Quadratic Optimal Control

This paper uses linear quadratic optimal control theory to design high-speed Dwell-Rise-Dwell (D-R-D) cams. Three approaches to D-R-D cam design are compared. In the first approach the cam is designed to be optimal at a fixed operating speed, i.e., a tuned cam design is obtained. In the second approach the cam profile is determined by minimizing a sum of quadratic cost functions over a range of discrete speeds, thus producing a cam-follower system which is optimal over a range of speeds. The third technique uses trajectory sensitivity minimization to design a cam which is insensitive to speed variations. All design methods are formulated as linear quadratic optimal control problems and solved using an efficient numerical procedure. It is shown that the design techniques developed can lead to cams that have significantly lower peak contact stress, contact force and energy loss when compared to a polydyne cam design. Furthermore, the trajectory sensitivity minimization approach is shown to yield cams that have lower residual vibration, over a range of speeds, when compared to a polydyne cam design.

Subdivision of Machining Stable Region Based on Vibration Frequencies

2011 ◽  
Vol 291-294 ◽  
pp. 1921-1924 ◽  
Author(s):  
Qing Hua Song ◽  
Xing Ai
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
High Speed ◽  
Stability Limit ◽  
Stable Region ◽  
Vibration Frequencies ◽  
High Speed Milling

Vibration frequencies during high-speed milling processes are investigated. Based on the resonant theory and three critical stats of phase position of successive two cutter teeth, six kinds of spindle speeds are shown, which divide the stable region in stability limit diagram into four parts. Furthermore, using optimal control theory, a novel stable region is proposed, which divides the region into three parts (unconditional stable, optimal stable, and conditional stable region).

Optimum Balancing of Combined Shaking Force, Shaking Moment, and Torque Fluctuations in High-Speed Linkages

1984 ◽  
Vol 106 (2) ◽  
pp. 242-251 ◽  
Author(s):  
T. W. Lee ◽  
C. Cheng
Keyword(s):  
High Speed ◽  
Optimization Technique ◽  
Integrated Approach ◽  
Optimization Techniques ◽  
Theoretical Development ◽  
Design Stage ◽  
Heuristic Optimization ◽  
Analytical Mechanics ◽  
Trade Offs ◽  
Shaking Moment

This paper presents an analytical and computer-aided procedure on the balancing of high-speed linkages. The method allows for the trade-offs necessary to achieve optimum dynamic response of the linkage in the design stage. These trade-offs involve a balance among the shaking force, the shaking moment, bearing reactions, and input-torque fluctuations by mass distribution of the links or counterweighting the linkage. Analytical mechanics and heuristic optimization techniques have been demonstrated to be useful tools in developing such a trade-off. The first part of this paper concerns the development of an optimality criterion in which an integrated approach is presented using both the Lagrangian and the Newtonian formulations, and consequently, a higher computational efficiency is achieved. Based on this theoretical development, the remainder of the paper focuses on the formulation of an optimization problem for linkage balancing and the solution of the problem by the Heuristic Optimization Technique of Lee and Freudenstein. The theory and computation are illustrated by numerical examples in the case of four-bar linkages.

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