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.

Evaluation of Parametric Vibration and Stability of Flexible Cam-Follower Systems

1994 ◽  
Vol 116 (1) ◽  
pp. 291-297 ◽  
Author(s):  
A. I. Mahyuddin ◽  
A. Midha ◽  
A. K. Bajaj
Keyword(s):  
Equations Of Motion ◽  
Second Order ◽  
Valve Train ◽  
Time Dependent ◽  
Equivalent Model ◽  
System Response ◽  
Parametric Stability ◽  
Order Linear ◽  
Linear Ordinary Differential Equations ◽  
Cam Follower

A method to study parametric stability of flexible cam-follower systems is developed. This method is applied to an automotive valve train which is modeled as a single-degree-of-freedom vibration system. The inclusion of the transverse and rotational flexibilities of the camshaft results in a system governed by a second-order, linear, ordinary differential equation with time-dependent coefficients. This class of equations, known as Hill’s equations, merits special notice in determination of the system response and stability. The analysis includes development of the equivalent model of the system, derivation of its equation of motion, and a method to evaluate its parametric stability based on Floquet theory. A closed-form numerical algorithm, developed to compute the periodic response of systems governed by second-order, linear, ordinary differential equations of motion with time-dependent coefficients, is utilized. The results of this study are presented in a companion paper in the forms of parametric stability charts and three-dimensional stability and response charts.

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.

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.

Spline Based Design of Cam Contours for Improved Dynamic Performance

1993 ◽  
Author(s):  
Holly K. Ault ◽  
James C. Wilkinson
Keyword(s):  
Dynamic Performance ◽  
Integrated Design ◽  
Polynomial Functions ◽  
Piecewise Polynomial ◽  
Cam Design ◽  
Piecewise Polynomial Functions ◽  
Cam Follower ◽  
Cam Profile ◽  
Pitch Curve ◽  
Design And Manufacture

Abstract A method for the integrated design and manufacture of radial plate cams is discussed. Currently, a cam-follower system is designed by specifying constraints on the motion of the follower. The physical cam contour or cam pitch curve are not mathematically defined. The cam is manufactured from the discretized follower motion program. A new method for cam design is proposed which will produce a smooth, mathematically defined cam pitch curve while maintaining the proper constraints on the follower motion. Piecewise polynomial functions in the form of rational and/or non-rational splines may be used. Cams will be manufactured using smoothed profiles and tested for improved dynamic performance. The results of initial investigations of cam profile design for this research are presented.

Dynamic Simulation and Test for the Valve Train Dynamics

2011 ◽  
Vol 117-119 ◽  
pp. 15-19 ◽  
Author(s):  
Cai Yun Guan ◽  
You Ming Chen ◽  
Wen Jie Qin
Keyword(s):  
Dynamic Model ◽  
Contact Stiffness ◽  
Quantitative Agreement ◽  
Measured Data ◽  
Valve Train ◽  
Parameter Determination ◽  
Cam Follower ◽  
Train Dynamics ◽  
Simulation Results

This paper presents the development of a dynamic model of the valve train of one engine. During the parameter determination of the model, finite element method is used to calculate the contact stiffness of the cam-follower . The simulation results of the model are compared with measured data of the valve train at same speed. Excellent quantitative agreement is found between the numerical and experimental results and the validity of the dynamic model can be verified.

Nonlinear Transient Response of a High Speed Driven Valve System and Stresses in Valve Springs for Internal Combustion Engines

1989 ◽  
Vol 111 (3) ◽  
pp. 264-271 ◽  
Author(s):  
K. Nagaya
Keyword(s):  
High Speed ◽  
Internal Combustion Engines ◽  
Three Dimensional ◽  
Beam Theory ◽  
Internal Combustion ◽  
Valve Train ◽  
Combination Method ◽  
Combustion Engines ◽  
Valve System ◽  
Cam Profile

This paper presents a method for solving the dynamic response problems of a driven valve system and the stress problem of valve springs for internal combustion engines. In this system there is hysteresis behavior in the spring constants during the rotation of the cam shaft. To treat this nonlinearity, the rigidity of each section is assumed to be one of a partly linear spring. For the valve trains, the cam profile is complex in general. To treat a general cam profile, this paper applies a combination method of the Fourier expansion, the Laplace transform and the analytical connection methods, and gives a response of valve trains. This paper also presents a theoretical result for the stresses in the valve spring due to the motion of the valve train based on the three dimensional curved beam theory.

Modeling Controlled Articulated Flexible Systems Using Assumed Modes: Part I — Theory

2001 ◽  
Author(s):  
Theodore G. Mordfin ◽  
Sivakumar S. K. Tadikonda
Keyword(s):  
Closed Form ◽  
Structural Model ◽  
Numerical Solutions ◽  
Closed Form Solution ◽  
Flexible Multibody Dynamics ◽  
Companion Paper ◽  
Form Solution ◽  
Control Laws ◽  
Comparison Functions ◽  
Flexible Behavior

Abstract Guidelines are sought for generating component body models for use in controlled, articulated, flexible multibody dynamics system simulations. In support of this effort, exact closed-form and numerical solutions are developed for the small elastic motions of a planar, flexible, single link system, in which the link is represented as an Euler-Bernoulli bar in transverse vibration. The link is connected to ground by a pin joint, and the articulation is controlled by proportional and proprotional/derivative (PD) feedback control laws. The characteristics of the closed-form solution are shown to consist of combinations of the characteristic expressions associated with classical end conditions. A large-articulation flexible body model of a controlled-articulation flexible link is then developed and linearized about an arbitrary reference angle. This model uses the method of assumed modes to represent the flexible behavior of the link. It is shown the model is analytically equivalent to a purely structural model which uses a hybrid set of assumed modes, and that numerical convergence can be investigated in terms of admissible functions and quasi-comparison functions. Numerical evaluation of the use of various types of assumed modes is presented in a companion paper.

Dynamic Modeling of an Overhead Valve Engine CAM-Follower System Using a Resistive Companion Dynamic Simulation Solver

2005 ◽  
Author(s):  
Daniel C. Sloope ◽  
David N. Rocheleau
Keyword(s):  
Mathematical Model ◽  
Dynamic Simulation ◽  
Dynamic Modeling ◽  
Valve Train ◽  
Test Bed ◽  
Virtual Test ◽  
Virtual Test Bed ◽  
Cam Follower ◽  
Valve Engine ◽  
The Mathematical Model

A computer simulation model of the valve train of a Honda GX30 engine was modeled using Virtual Test Bed (VTB), a resistive companion dynamic simulation solver. Traditionally VTB has been exclusive to solving electrical system models but using the resistive companion equivalence of through and across variables, it can be applied to mechanical systems. This paper describes a dynamic simulation of an overhead valve engine cam-follower system using the VTB software application. The model was created to show valve train position, velocity and acceleration to aid in development of a camless engine being developed at the University of South Carolina. The mathematical model was created using governing dynamic equations. Using C++ programming, the mathematical model was transformed into a Virtual Test Bed model. The VTB model successfully shows valve train component position, velocity and acceleration. The significance of this work is its novelty in using the Virtual Test Bed environment to handle dynamic modeling of mechanical systems, whereas to date, VTB has been primarily focused on resistive companion modeling of power electronic systems. This work provides the foundation for using VTB to tackle more complex mechanical models.

Valve Gear Refinement

2000 ◽  
Vol 124 (1) ◽  
pp. 86-90 ◽  
Author(s):  
Jurij Avsec ◽  
Milan Marcic ◽  
Maks Oblak
Keyword(s):  
Mathematical Model ◽  
Cam Design ◽  
Cam Follower ◽  
New Type ◽  
Cam Profile ◽  
Profile Design ◽  
Comparison Of The Results ◽  
The Mathematical Model ◽  
Valve Gear ◽  
Lubrication Properties

This paper describes a new type of valve gear cam—MULTICAM—which consists of seven curves and allows an optimum cam profile design. In order to calculate the cinematic and dynamic values and to assess the minimum oil film thickness in the valve gear, the mathematical model of an ideal valve gear was used. In addition, the comparison of the results between the polysine cam and the new MULTICAM cam design was made. By means of the new cam design the Hertz pressures were reduced at the point of contact between the cam and the cam follower and the lubrication properties at the top of the cam improved.

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.

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