A Versatile Cam Profile for Controlling Interface Force in Multiple-Dwell Cam-Follower Systems

2012 ◽  
Vol 134 (9) ◽  
Author(s):  
Forrest W. Flocker
Keyword(s):  
Closed Form ◽  
High Speed ◽  
Maximum Magnitude ◽  
Design Objective ◽  
Standard Equation ◽  
Negative Acceleration ◽  
Cam Follower ◽  
Cam Profile ◽  
Harmonic Analyses ◽  
Spreadsheet Software

Cam follower systems are widely used in manufacturing because of their precise motion and ability to easily dwell. The cam typically drives a follower in some precise motion needed to accomplish a manufacturing task. Presented in this paper is a closed-form modified trapezoidal cam motion function with adjustable positive and negative acceleration. The profile is suitable for multiple-dwell cam and follower applications. The profile is particularly applicable to high-speed cams in which the follower acceleration is a primary design objective. The main benefit of the profile is that it allows cam designers to easily set limits on the positive and negative acceleration to achieve design objectives. Additional benefits are that the cycle jerk is continuous and that the cam designer can control the maximum magnitude of jerk. The motion program is presented in closed-form for easy implementation in standard equation-solver or spreadsheet software. Dynamic and harmonic analyses are presented to illustrate the benefits of the profile.

Synthesis of cam profile using classical splines and the effect of knot locations on the acceleration, jump, and interface force of cam follower system

2011 ◽  
Vol 225 (12) ◽  
pp. 3019-3030 ◽  
Author(s):  
U Chavan ◽  
S Joshi
Keyword(s):  
Displacement Function ◽  
Physical Parameters ◽  
Spline Curves ◽  
Design Variables ◽  
Negative Acceleration ◽  
Positive Acceleration ◽  
Large Jump ◽  
Cam Follower ◽  
Displacement Profile ◽  
Cam Profile

Large positive acceleration against a load creates cam follower interface force that can cause excessive wear. Negative acceleration tends to reduce the cam follower interface force, and if the negative acceleration is sufficiently large, jump between the cam and follower can occur. Hence, these are the two main concerns of cam designers. This study presents a new approach to adjust the acceleration, interface force, and jump in the early phase of cam design. Knot locations of polynomial pieces of spline curves are considered as design variables which gives variety of cam profiles. Here, design process starts from displacement profile and there is no need for predefined acceleration curves. A single dwell cam displacement function is defined by classical spline curve, made up of four polynomial pieces that are tied together at their ends, called knots. Specifications of these knots are considered for synthesis and analysis of cam follower system. Mathematical relation between interface force and knot locations is presented as wear and jump models. These models are useful to reduce wear and jump by proper placement of the knots on the basis of interface force. By dynamic simulation of cam follower system, cam curves are drawn for different cases of knot locations and good resemblance was found with theoretical curves. This study suggests the cam designers have the added option to control the kinematic and dynamic quantities without changing the physical parameters of cam follower system.

Influence of Varying Cam Profile and Follower Motion Event Types on Parametric Vibration and Stability of Flexible Cam-Follower Systems

1994 ◽  
Vol 116 (1) ◽  
pp. 298-305 ◽  
Author(s):  
A. I. Mahyuddin ◽  
A. Midha
Keyword(s):  
Closed Form ◽  
Numerical Algorithm ◽  
Parametric Instability ◽  
Excitation Amplitude ◽  
Companion Paper ◽  
Valve Train ◽  
Positional Error ◽  
Parametric Stability ◽  
Cam Follower ◽  
Cam Profile

A method to study parametric stability of flexible cam-follower systems, based on Floquet theory, as well as a closed-form numerical algorithm to compute periodic response of the system, have been developed in a companion paper. These are applied to an automotive valve train, modeled as a single-degree-of-freedom vibration system. The inclusion of the transverse and rotational flexibilities of the camshaft results in a system that is governed by a linear, second-order, ordinary differential equation with time-dependent coefficients. In this paper, the parametric stability of the system is studied, and the results are presented in the form of parametric stability charts. The regions of instability are plotted on the nondimensionalized frequency and excitation (amplitude) parameter plane. The maximum positional error of the follower motion, analyzed by the closed-form numerical algorithm, enables a novel presentation of three-dimensional stability and response charts. Stability of the system is investigated for three types of follower motion events and four different cam profiles. The effect of damping on parametric instability is also studied. A comparative study of these event and cam profile types reveals some very interesting and hitherto unknown results.

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.

A Closed-Form Solution for Minimizing the Cycle Time in Motion Programs With Constant Velocity Segments

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Forrest W. Flocker ◽  
Ramiro H. Bravo
Keyword(s):  
Closed Form ◽  
Cycle Time ◽  
Constant Velocity ◽  
Closed Form Solution ◽  
Form Solution ◽  
Industrial Robots ◽  
General Applicability ◽  
Negative Acceleration ◽  
Cam Follower ◽  
Time Subject

An important need for some dynamic systems is to design a periodic motion program that has a constant velocity segment for a specified time. A few examples of such systems are cam-follower systems used in continuous motion manufacturing, linear actuators, space-based scanners, and industrial robots. In this paper, the closed-form solution is given for a motion program that minimizes the cycle time subject to user-specified limits on positive and negative acceleration and jerk. The main benefit of minimizing cycle time is to maximize the throughput. Two motion programs that address the problem are presented and critically examined. For general applicability, the solution is presented in dimensionless form and an example is given to show its implementation to a typical problem. Conclusions regarding the profiles are drawn and given.

Mathematical modeling and simulation of high-speed cam mechanisms to minimize residual vibrations

2014 ◽  
Vol 228 (13) ◽  
pp. 2402-2415 ◽  
Author(s):  
Halit Kaplan
Keyword(s):  
Mathematical Modeling ◽  
High Speed ◽  
Internal Combustion Engines ◽  
Combustion Engine ◽  
Internal Combustion ◽  
Combustion Engines ◽  
Dimensionless Analysis ◽  
Multipliers Method ◽  
Cam Follower ◽  
Cam Profile

Mathematical modeling, simulation, and optimum design of equivalent one degree-of-freedom high-speed cam mechanisms used for internal combustion engines are investigated in this study. The dynamic equation governing the dynamic behavior of a typical high-speed cam–follower system of an internal combustion engine has been simplified using dimensionless analysis method. The resulting model is then used to find the optimum cam shape to reduce the residual vibrations in the follower part of the system. The Lagrange multipliers method is utilized to minimize the sum of squared error (deviation from the cam profile) over one period under continuity and smoothness constraints.

A Versatile Acceleration-Based Cam Profile for Single-Dwell Applications Requiring Cam-Follower Clearance During Dwell

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Forrest W. Flocker
Keyword(s):  
Closed Form ◽  
Velocity Function ◽  
Manufacturing Operations ◽  
Equation Solving ◽  
Cam Follower ◽  
Cam Profile

Presented in this paper is an asymmetric acceleration-derived cam motion program suitable for single-dwell cam-follower systems with clearance between the cam and follower during dwell. Asymmetric rise and fall is included as this is desirable in certain manufacturing operations and machines that require a quick rise or fall. The motion program for the cam-follower actuation is derived from the follower acceleration so that designers can control the ratio of the magnitudes of positive and negative accelerations. This provides cam designers more control over the cam-follower interface force and therefore more control over factors such as cam wear and the potentially destructive phenomenon known as “follower jump.” The motion program used to close and open the clearance gap is derived from a velocity function, allowing more control of follower inertia during the important clearance closing event. The motion program is presented in closed-form, suitable for implementation in standard engineering equation-solving software.

A Versatile Acceleration-Based Cam Profile for Single-Dwell Applications Requiring Cam-Follower Clearance During Dwell

2011 ◽  
Author(s):  
Forrest W. Flocker
Keyword(s):  
High Speed ◽  
Internal Combustion Engines ◽  
Internal Combustion ◽  
Combustion Engines ◽  
Velocity Function ◽  
Gas Leakage ◽  
Poppet Valve ◽  
Equation Solving ◽  
Cam Follower ◽  
Cam Profile

Presented in this paper is a cam motion program suitable for single-dwell cam-follower systems with built-in clearance between the cam and follower during the dwell portion of the cycle. This makes the motion program particularly well-suited to applications such as valve trains in internal combustion engines in which cam-follower clearance is necessary to ensure proper seating of a poppet valve, preventing gas leakage across the seal. The motion program for the cam follower is derived from the follower acceleration function so that designers can control the ratio of the magnitudes of positive and negative accelerations. This provides cam designers more control over the cam-follower interface force and therefore more control over factors such as cam wear and the potentially destructive phenomenon known as “follower jump.” Included in the motion program is asymmetric rise and fall that allows different times for these events. The follower acceleration is designed to be smooth enough to provide continuous jerk throughout the actuation phase, thereby tending to reduce undesirable residual vibrations. The motion program used to close and open the clearance gap is derived from a velocity function, allowing more control of follower inertia during the important clearance closing event. The motion program is presented in a form appropriate for implementation in standard engineering equation-solving software, giving the cam designer easy control over important parameters in high-speed cam-follower systems.

Assessment of the Dynamic Quality of a Class of Dwell-Rise-Dwell Cams

1981 ◽  
Vol 103 (4) ◽  
pp. 793-802 ◽  
Author(s):  
F. Y. Chen
Keyword(s):  
High Speed ◽  
Amplification Factor ◽  
Response Characteristics ◽  
Vibrational Response ◽  
The Past ◽  
Acceleration Amplification ◽  
Cam Follower ◽  
Cam Profile ◽  
Dynamic Quality

A number of new cam profiles of the dwell-rise-dwell type have been proposed by different researchers in the past two decades. They were claimed as efficient cam curves suitable for high-speed applications. This paper re-examines these profiles with regard to the important vibrational response characteristics when they are applied as motion excitations to a cam-and-follower system. The severity of the dynamic response of the cam follower to the motion excitation of a cam will be measured by a dimensionless quantity known as the normalized acceleration amplification factor (NAAF). A simplified response envelop for the residual vibration of NAAF versus the fundamental period is constructed so that an assessment of the merit of any given cam profile can be made qualitatively and quantitatively.

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.

Sign in / Sign up

Export Citation Format

Share Document