Analysis and Synthesis of Mechanical Error in Cam-Follower Systems

1982 ◽  
Vol 104 (1) ◽  
pp. 52-62 ◽  
Author(s):  
S. S. Rao ◽  
S. S. Gavane
Keyword(s):  
Nonlinear Programming ◽  
Dynamic Response ◽  
Confidence Level ◽  
Manufacturing Cost ◽  
System Parameters ◽  
Analysis And Synthesis ◽  
Cam Follower ◽  
Programming Techniques ◽  
Allowable Error ◽  
Synthesis Procedure

A method of evaluating the mechanical error in the kinematic and dynamic response of cam-follower systems is presented based on probability principles. The error is analyzed for the three-sigma band of confidence level. A synthesis procedure, using nonlinear programming techniques, of distributing tolerances on geometrical and other system parameters is discussed. The objective of the synthesis problem is to minimize a measure of the manufacturing cost for specified maximum allowable error in the kinematic or dynamic response of the cam-follower system. The application of analysis and synthesis procedures is demonstrated with reference to a disc cam with translating roller follower.

Analysis and Synthesis of Mechanical Error in Geneva Mechanisms—A Stochastic Approach. Part 2: Internal Geneva Mechanism

1982 ◽  
Vol 104 (1) ◽  
pp. 72-77 ◽  
Author(s):  
S. S. Rao ◽  
S. S. Gavane
Keyword(s):  
Probability Theory ◽  
Nonlinear Programming ◽  
Stochastic Approach ◽  
Analysis Procedure ◽  
Numerical Examples ◽  
Kinematic Characteristics ◽  
Analysis And Synthesis ◽  
Programming Techniques ◽  
Synthesis Procedure

Because of error of manufacture and assembly, the output kinematic characteristics of a Geneva mechanism will be different from the desired ones. In this paper an analysis procedure is developed to find the error in acceleration and jerk of internal Geneva mechanisms from the viewpoint of probability theory. A synthesis procedure, using nonlinear programming techniques, of distributing tolerances and clearances in the mechanism for specified maximum allowable errors in acceleration and jerk is discussed. The application of analysis and synthesis procedures is demonstrated by means of numerical examples.

Analysis and Synthesis of Mechanical Error in Geneva Mechanisms—A Stochastic Approach. Part 1: External Geneva Mechanism

1982 ◽  
Vol 104 (1) ◽  
pp. 63-71 ◽  
Author(s):  
S. S. Rao ◽  
S. S. Gavane
Keyword(s):  
Probability Theory ◽  
Nonlinear Programming ◽  
Stochastic Approach ◽  
Analysis Procedure ◽  
View Point ◽  
Numerical Examples ◽  
Kinematic Characteristics ◽  
Analysis And Synthesis ◽  
Programming Techniques ◽  
Synthesis Procedure

Because of error of manufacture and assembly, the output kinematic characteristics of a Geneva mechanism will be different from the desired ones. In this paper an analysis procedure is developed to find the error in acceleration and jerk of external Geneva mechanisms from the view-point of probability theory. A synthesis procedure, using nonlinear programming techniques, of distributing tolerances and clearances in the mechanism for specified maximum allowable errors in acceleration and jerk is discussed. The application of analysis and synthesis procedures is demonstrated by means of numerical examples.

Error Analysis of Cam-Follower Systems: A Probabilistic Approach

1984 ◽  
Vol 198 (3) ◽  
pp. 155-162 ◽  
Author(s):  
S S Rao
Keyword(s):  
Error Analysis ◽  
Probabilistic Approach ◽  
Random Variables ◽  
Stochastic Approach ◽  
Geometrical Parameters ◽  
Manufacturing Costs ◽  
Actual Output ◽  
Analysis And Synthesis ◽  
Cam Follower ◽  
Synthesis Procedure

The actual output kinematic characteristics of a cam-follower system will be different from the theoretical (desired) ones due to errors in manufacture and assembly. A method of evaluating the mechanical error in the kinematic response of cam-follower systems is presented using a stochastic approach. The tolerances on cam profiles and other geometrical parameters are treated as random variables that influence the mechanical error. The equations necessary for the mechanical error analysis of a planar cam-follower system (disc cam with translating roller follower) are derived. The equations for a spatial cam-follower system (globoidal cam with oscillating cylindrical follower) are also given at the end. An optimal synthesis procedure is outlined for the allocation of tolerances so as to minimize the manufacturing costs while satisfying a constraint on the maximum mechanical error in the kinematic response of cam-follower systems. The application of analysis and synthesis procedure is demonstrated with reference to a disc cam with translating roller follower.

Mechanical Separation Phenomena in Picking Mechanisms of Fly-Shuttle Looms

1976 ◽  
Vol 98 (3) ◽  
pp. 835-839 ◽  
Author(s):  
F. D. Hart ◽  
B. M. Patel ◽  
J. R. Bailey
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Operating Conditions ◽  
Equivalent Stiffness ◽  
Noise Emission ◽  
System Parameters ◽  
Response Characteristics ◽  
Cam Follower ◽  
Mechanical Separation ◽  
Dynamic Response Characteristics

Mechanical separation between cam and pick ball in fly-shuttle looms gives rise to impact and vibration which causes significant noise emission. Elimination of separation is analyzed using a mathematical model which simulates the dynamic response characteristics of the system. Parameters considered in the study include equivalent stiffness, mass, and damping of the system, amplitude of excitation, effect of preload provided by a retaining spring, and operating frequency. Combinations of system parameters and operating conditions which give rise to separation are predicted by examining the contact force developed between cam and cam-follower. Equations and graphs are presented that specify the preload required to eliminate separation as a function of the system parameters.

Analysis and Synthesis of Mechanical Error in Universal Joints

1990 ◽  
Author(s):  
J. L. Cagney ◽  
S. S. Rao
Keyword(s):  
Probability Distribution ◽  
Real World ◽  
Probability Distributions ◽  
Manufacturing Cost ◽  
Universal Joint ◽  
Accuracy Requirement ◽  
Output Error ◽  
Manufacturing Errors ◽  
Analysis And Synthesis ◽  
Limiting Value

Abstract The modeling of manufacturing errors in mechanisms is a significant task to validate practical designs. The use of probability distributions for errors can simulate manufacturing variations and real world operations. This paper presents the mechanical error analysis of universal joint drivelines. Each error is simulated using a probability distribution, i.e., a design of the mechanism is created by assigning random values to the errors. Each design is then evaluated by comparing the output error with a limiting value and the reliability of the universal joint is estimated. For this, the design is considered a failure whenever the output error exceeds the specified limit. In addition, the problem of synthesis, which involves the allocation of tolerances (errors) for minimum manufacturing cost without violating a specified accuracy requirement of the output, is also considered. Three probability distributions — normal, Weibull and beta distributions — were used to simulate the random values of the errors. The similarity of the results given by the three distributions suggests that the use of normal distribution would be acceptable for modeling the tolerances in most cases.

Fuzzy Analysis of Geometric Tolerances Using Interval Method

2006 ◽  
Vol 220 (4) ◽  
pp. 489-497 ◽  
Author(s):  
W Wu ◽  
S S Rao
Keyword(s):  
Mechanical System ◽  
Current Approach ◽  
Distribution Functions ◽  
Manufacturing Cost ◽  
Mechanical Assembly ◽  
Geometric Dimensioning And Tolerancing ◽  
Analysis And Synthesis ◽  
Linear Interval ◽  
Linear Interval Equations ◽  
And Performance

The quality and performance of any mechanical system are greatly influenced by the GD&T (geometric dimensioning and tolerancing) used in its design. A proper consideration of the various types of tolerances associated with different components could not only satisfy the assembly requirements, but also minimize the manufacturing cost. To satisfy the design and functional specifications, one has to know how various tolerance patterns affect the manufacturability and assemblability of the designed parts. Therefore, a thorough understanding of how different forms of mechanical tolerances interact with each other becomes a must for designers and manufacturers. The effects of form, orientation, and position tolerances on the kinematic features and dimensions of mechanical systems are analysed using a new approach, based on fuzzy logic, in this article. In this approach, the α-cut method is used with the mechanical tolerances concerned as intervals. The proposed approach represents a more natural and realistic way of dealing with uncertain properties like geometric dimensions. A typical mechanical assembly system involving form, orientation, and position tolerances is used as an illustrative example. As the fuzzy approach leads to systems of non-linear interval equations, a modified Newton-Raphson method is developed for the solution of these equations. The current approach is found to be effective, simple, and accurate and can be extended to the analysis and synthesis of any uncertain mechanical system where the probability distribution functions of the uncertain parameters are unknown.

Computerized Selection of Optimum Machining Conditions for a Job Requiring Multiple Operations

1978 ◽  
Vol 100 (3) ◽  
pp. 356-362 ◽  
Author(s):  
S. S. Rao ◽  
S. K. Hati
Keyword(s):  
Nonlinear Programming ◽  
Mathematical Programming ◽  
Machine Tools ◽  
Machining Conditions ◽  
Coupling Constraints ◽  
Programming Techniques ◽  
Mathematical Programming Problems ◽  
The Individual ◽  
The Cost ◽  
Selection Of

The problem of determining the optimum machining conditions for a job requiring multiple operations has been investigated. Three objectives, namely, the minimization of the cost of production per piece, the maximization of the production rate and, the maximization of the profit are considered in this work. In addition to the usual constraints that arise from the individual machine tools, some coupling constraints have been included in the formulation. The problems are formulated as standard mathematical programming problems, and nonlinear programming techniques are used to solve the problems.

Sign in / Sign up

Export Citation Format

Share Document