Designing Dynamically Compensated and Robust Cam Profiles With Bernstein-Be´zier Harmonic Curves

1998 ◽  
Vol 120 (1) ◽  
pp. 40-45 ◽  
Author(s):  
L. N. Srinivasan ◽  
Q. Jeffrey Ge
Keyword(s):  
High Speed ◽  
Design Procedure ◽  
Vibration Characteristics ◽  
Resonant Vibrations ◽  
Residual Vibration ◽  
Numerical Examples ◽  
Polynomial Curves ◽  
Harmonic Content ◽  
Cam Follower ◽  
Design Speed

This paper deals with the problem of designing dynamically compensated cam profiles to minimize residual vibrations in high-speed cam-follower systems. The traditional Polydyne method is modified and extended to achieve significant improvement in residual vibration characteristics. First, cam displacement curves are represented by Bernstein-Be´zier harmonic curves as opposed to polynomial curves. These recently developed harmonic curves are low in harmonic content and therefore the resulting cam profiles are less prone to induce resonant vibrations in the follower system. Second, the design procedure is expanded such that the residual vibrations of the resulting cam-follower system is not only extinguished at the design speed but also made insensitive to speed variations. Numerical examples are given in the end.

Designing Dynamically Compensated and Robust Cam Profiles With Bernstein-Bézier Harmonic Curves

1997 ◽  
Author(s):  
Lakshmi N. Srinivasan ◽  
Q. Jeffrey Ge
Keyword(s):  
High Speed ◽  
Design Procedure ◽  
Vibration Characteristics ◽  
Resonant Vibrations ◽  
Residual Vibration ◽  
Numerical Examples ◽  
Polynomial Curves ◽  
Harmonic Content ◽  
Cam Follower ◽  
Design Speed

Abstract This paper deals with the problem of designing dynamically compensated cam profiles to minimize residual vibrations in high-speed cam-follower systems. The traditional Polydyne method is modified and extended to achieve significant improvement in residual vibration characteristics. First, cam displacement curves are represented by Bernstein-Bézier harmonic curves as opposed to polynomial curves. These recently developed harmonic curves are low in harmonic content and therefore the resulting cam profiles are less prone to induce resonant vibrations in the follower system. Second, the design procedure is expanded such that the residual vibrations of the resulting cam-follower system is not only extinguished at the design speed but also made insensitive to speed variations. Numerical examples are given in the end.

Synthesis of Inertially Compensated Variable-Speed Cams

2003 ◽  
Vol 125 (3) ◽  
pp. 593-601 ◽  
Author(s):  
B. Demeulenaere ◽  
J. De Schutter
Keyword(s):  
High Speed ◽  
Design Procedure ◽  
Variable Speed ◽  
Speed Variation ◽  
Design Choice ◽  
Cam Follower ◽  
Speed Fluctuation ◽  
Novel Design

Traditionally, cam-follower systems are designed by assuming a constant camshaft speed. Nevertheless, all cam-follower systems, especially high-speed systems, exhibit some camshaft speed fluctuation (despite the presence of a flywheel) which causes the follower motions to be inaccurate. This paper therefore proposes a novel design procedure that explicitly takes into account the camshaft speed variation. The design procedure assumes that (i) the cam-follower system is conservative and (ii) all forces are inertial. The design procedure is based on a single design choice, i.e., the amount of camshaft speed variation, and yields (i) cams that compensate for the inertial dynamics for any period of motion and (ii) a camshaft flywheel whose (small) inertia is independent of the period of motion. A design example shows that the cams designed in this way offer the following advantages, even for non-conservative, non-purely inertial cam-follower systems: (i) more accurate camshaft motion despite a smaller flywheel, (ii) lower motor torques, (iii) more accurate follower motions, with fewer undesired harmonics, and (iv) a camshaft motion spectrum that is easily and robustly predictable.

C 2 Piecewise Bézier Harmonics for Motion Specifications of High-Speed Cam Mechanisms

1996 ◽  
Author(s):  
Q. J. Ge ◽  
L. Srinivasan
Keyword(s):  
High Speed ◽  
Robot Manipulators ◽  
Ease Of Use ◽  
High Frequencies ◽  
Harmonic Content ◽  
Cam Follower

Abstract This paper deals with the problem of specifying motions for high-speed cam mechanisms where reduction of vibration is a major concern, ft presents Bézier harmonic curves and C2 piecewise Bézier 3-harmonic curves for synthesizing cam-follower motions with low-harmonic content. As examples, these curves have been applied to the synthesis of Rise-Dwell-Return (RDR) cam motion program to demonstrate the flexibility and ease-of-use of the curves. It has also been shown that these curves have considerably lower harmonic contents than those of 3-4-5 polynomials at high frequencies. The results are useful for motion specifications of high-speed machinery including not only cam mechanisms but robot manipulators as well.

Synthesis and Steady State Analysis of High-Speed Elastic Cam-Follower Linkages With Concentrated Masses: Part I — Theory

1991 ◽  
Author(s):  
Hsin-Ting J. Liu ◽  
Donald R. Flugrad
Keyword(s):  
Steady State ◽  
Iterative Procedure ◽  
High Speed ◽  
Linear Ordinary Differential Equations ◽  
Periodic Linear ◽  
Cam Follower ◽  
Cam Profile ◽  
Concentrated Masses ◽  
Design Speed ◽  
Steady State Solutions

Abstract A cam driving a lumped inertia through a massless, elastic, slider-crank follower linkage with two concent rated masses located at the pin joints is considered. An iterative procedure taking the elasticity, damping, and changing geometry of the linkage into account is developed for synthesizing the cam profile to produce a desired output motion at a given design speed. The steady state solutions for the inhomogeneous, periodic, linear, ordinary differential equations are solved numerically by Hsu’s method.

Synthesis and Steady State Analysis of High-Speed Elastic Cam Follower Linkages by a Finite Element Method

1991 ◽  
Author(s):  
Hsin-Ting J. Liu ◽  
Donald R. Flugrad
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Speed ◽  
The Finite Element Method ◽  
Linear Ordinary Differential Equations ◽  
Periodic Linear ◽  
Cam Follower ◽  
Cam Profile ◽  
Design Speed ◽  
Element Method

Abstract A cam driving a lumped inertia through an elastic slider-crank follower linkage with a curved beam coupler is considered. An iterative procedure utilizing the finite element method developed by Midha et al. (1978) is used to synthesize the cam profile to produce a desired output motion at a given design speed and damping coefficient. Nonlinear terms are neglected producing inhomogeneous. periodic, linear, ordinary differential equations. Response of the synthesized linkages are simulated and found to be satisfactory at the design conditions.

Residual Vibration Criteria Applied to Multiple Degree of Freedom Cam Followers

1981 ◽  
Vol 103 (4) ◽  
pp. 702-705 ◽  
Author(s):  
J. L. Wiederrich
Keyword(s):  
Modal Analysis ◽  
Vibration Characteristics ◽  
Vibration Response ◽  
Degree Of Freedom ◽  
Operating Speed ◽  
Residual Vibration ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Cam Follower

The vibration characteristics of a cam motion are generally presented by plotting the single degree of freedom residual vibration as a function of normalized operating speed. In this paper it is shown that by applying the methods of modal analysis, these residual vibration characteristics can be extended to the characterization of the vibration response of a multiple degree of freedom cam follower system.

Steady-State Residual Vibrations in High-Speed, Dwell-Type, Rotating Disk Cam-Follower Systems

2005 ◽  
Vol 127 (1) ◽  
pp. 12-17 ◽  
Author(s):  
Stephen F. Felszeghy
Keyword(s):  
Steady State ◽  
High Speed ◽  
Transient Analysis ◽  
Linear Models ◽  
Initial Conditions ◽  
Rotating Disk ◽  
Residual Vibration ◽  
Transient Vibration ◽  
Closed Form Solutions ◽  
Cam Follower

Followers driven by high-speed, dwell-type, rotating disk cams can exhibit undesirable residual vibrations during dwell. These vibrations have been studied with linear models mostly using results from transient vibration analysis, assuming quiescent initial conditions. Here, the residual vibrations are studied with closed-form solutions to the steady-state vibrations obtained with a circular convolution integral. The steady-state vibrations, which can extend over the entire cam cycle, are periodic and continuous. It is shown that significant differences exist between the residual vibration results obtained from steady-state analysis and those obtained from transient analysis. The undamped steady-state vibrations exhibit resonances. Away from the resonance conditions, the steady-state residual vibration amplitudes are consistently smaller than those predicted by transient analysis. The results from the two approaches agree quantitatively only for relatively stiff and damped follower systems.

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.

scholarly journals Part-optimized forming by spatially distributed vaporizing foil actuators

2021 ◽  
Author(s):  
Marlon Hahn ◽  
A. Erman Tekkaya
Keyword(s):  
Process Design ◽  
High Speed ◽  
Specific Impulse ◽  
Design Procedure ◽  
Mathematical Optimization ◽  
Starting Point ◽  
Spatially Distributed ◽  
Lower Tool ◽  
A Minor ◽  
Charging Energy

AbstractElectrically vaporizing foil actuators are employed as an innovative high speed sheet metal forming technology, which has the potential to lower tool costs. To reduce experimental try-outs, a predictive physics-based process design procedure is developed for the first time. It consists of a mathematical optimization utilizing numerical forming simulations followed by analytical computations for the forming-impulse generation through the rapid Joule heating of the foils. The proposed method is demonstrated for an exemplary steel sheet part. The resulting process design provides a part-specific impulse distribution, corresponding parallel actuator geometries, and the pulse generator’s charging energy, so that all process parameters are available before the first experiment. The experimental validation is then performed for the example part. Formed parts indicate that the introduced method yields a good starting point for actual testing, as it only requires adjustments in the form of a minor charging energy augmentation. This was expectable due to the conservative nature of the underlying modeling. The part geometry obtained with the most suitable charging energy is finally compared to the target geometry.

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