Dimensional Tolerance Allocation of Stochastic Dynamic Mechanical Systems Through Performance and Sensitivity Analysis

1993 ◽  
Vol 115 (3) ◽  
pp. 392-402 ◽  
Author(s):  
S. J. Lee ◽  
B. J. Gilmore ◽  
M. M. Ogot
Keyword(s):  
Sensitivity Analysis ◽  
Probabilistic Models ◽  
General Procedure ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Tolerance Allocation ◽  
Stochastic Dynamic ◽  
Link Length ◽  
Analysis And Design ◽  
Dynamic Mechanical

Uncertainties due to random dimensional tolerances within stochastic dynamic mechanical systems lead to mechanical errors and thus, performance degradation. Since design standards do not exist for these systems, analysis and design tools are needed to properly allocate tolerances. This paper presents probabilistic models and methods to allocate tolerances on the link lengths and radial clearances such that the system meets a probabilistic and time dependent performance criterion. The method includes a general procedure for sensitivity analysis, using the effective link length model and nominal equations of motion. Since the sensitivity analysis requires only the nominal equations of motion and statistical information as input, it is straight forward to implement. An optimal design problem is formulated to allocate random tolerances. Examples are presented to illustrate the approach and its generality. This paper provides a solution to the tolerance allocation problem for stochastic dynamically driven mechanical systems.

Dimensional Tolerance Allocation of Stochastic Dynamic Mechanical Systems Through Performance and Sensitivity Analysis

1990 ◽  
Author(s):  
S. J. Lee ◽  
B. J. Gilmore ◽  
M. M. Ogot
Keyword(s):  
Sensitivity Analysis ◽  
Probabilistic Models ◽  
General Procedure ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Tolerance Allocation ◽  
Stochastic Dynamic ◽  
Link Length ◽  
Analysis And Design ◽  
Dynamic Mechanical

Abstract Uncertainties due to random dimensional tolerances within stochastic dynamic mechanical systems lead to mechanical errors and thus, performance degradation. Since design standards do not exist for these systems, analysis and design tools are needed to properly allocate tolerances. This paper presents probabilistic models and methods to allocate tolerances on the link lengths and radial clearances such that the system meets a probabilistic and time dependent performance criterion. The method includes a general procedure for sensitivity analysis, using the effective link length model and nominal equations of motion. Since the sensitivity analysis requires only the nominal equations of motion and statistical information as input, it is straight forward to implement. An optimal design problem is formulated to allocate random tolerances. Examples are presented to illustrate the approach and its generality. This paper provides a solution to the tolerance allocation problem for stochastic dynamically driven mechanical systems.

A Probabilistic Tolerance Allocation Method for Dynamic Mechanical Systems With Periodic Response and Discontinuous Forcing Functions

1995 ◽  
Author(s):  
F. Zhang ◽  
B. J. Gilmore ◽  
A. Sinha
Keyword(s):  
Combustion Engine ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Optimization Procedure ◽  
Tolerance Allocation ◽  
Radial Clearance ◽  
Time Varying ◽  
Link Length ◽  
Design Variables ◽  
Forcing Functions

Abstract Tolerance allocation standards do not exist for mechanical systems whose response are time varying and are subjected to discontinuous forcing functions. Previous approaches based on optimization and numerical integration of the dynamic equations of motion encounter difficulty with determining sensitivities around the force discontinuity. The Alternating Frequency/Time approach is applied here to capture the effect of the discontinuity. The effective link length model is used to model the system and to account for the uncertainties in the link length, radial clearance and pin location. Since the effective link length model is applied, the equations of motion for the nominal system can be applied for the entire analysis. Optimization procedure is applied to the problem where the objective is to minimize the manufacturing costs and satisfy the constraints imposed on mechanical errors and design variables. Examples of tolerance allocation are presented for a single cylinder internal combustion engine.

Analysis and Optimal Design of Spatial Mechanical Systems

1987 ◽  
Author(s):  
H. Ashrafeiuon ◽  
N. K. Mani
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Design ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Design Sensitivity ◽  
General Purpose ◽  
Design Sensitivity Analysis ◽  
Analysis And Design ◽  
Spatial Systems

Abstract This paper presents a new approach to optimal design of large multibody spatial mechanical systems. This approach uses symbolic computing to generate the necessary equations for dynamic analysis and design sensitivity analysis. Identification of system topology is carried out using graph theory. The equations of motion are formulated in terms of relative joint coordinates through the use of velocity transformation matrix. Design sensitivity analysis is carried out using the Direct Differentiation method applied to the relative joint coordinate formulation for spatial systems. Symbolic manipulation programs are used to develop subroutines which provide information for dynamic and design sensitivity analysis. These subroutines are linked to a general purpose computer program which performs dynamic analysis, design sensitivity analysis, and optimization. An example is presented to demonstrate the efficiency of the approach.

Analysis and Optimal Design of Spatial Mechanical Systems

1990 ◽  
Vol 112 (2) ◽  
pp. 200-207 ◽  
Author(s):  
H. Ashrafiuon ◽  
N. K. Mani
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Design ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Design Sensitivity ◽  
General Purpose ◽  
Design Sensitivity Analysis ◽  
Sensitivity Analyses ◽  
Spatial Systems ◽  
Spatial System

This paper presents a new approach to optimal design of large multibody spatial mechanical systems which takes advantage of both numerical analysis and symbolic computing. Identification of system topology is carried out using graph theory. The equations of motion are formulated in terms of relative joint coordinates through the use of a velocity transformation matrix. Design sensitivity analysis is carried out using the direct differentiation method applied to the relative joint coordinate formulation for spatial systems. The symbolic manipulation program MACSYMA is used to automatically generate the necessary equations for both dynamic and design sensitivity analyses for any spatial system. The symbolic equations are written as FORTRAN statements that are linked to a general purpose computer program which performs dynamic analysis, design sensitivity analysis, and optimization, using numerical techniques. Examples are presented to demonstrate reliability and efficiency of this approach.

A Computer-Aided Environment for Analysis and Design of Mechanical Systems

1991 ◽  
Author(s):  
Hamid M. Lankarani ◽  
Behnam Bahr ◽  
Saeid Motavalli
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
General Purpose ◽  
Design System ◽  
Integrated Analysis ◽  
Algebraic Equations ◽  
Efficient Design ◽  
Analysis And Design ◽  
Wide Range

Abstract This paper presents the description of an ideal tool for analysis and design of complex multibody mechanical systems. It is in the form of a general-purpose computer program, which can be used for simulation of many different systems. The generality of this computer-integrated environment allows a wide range of applications with significant engineering importance. No matter how complicated the mechanical system under consideration is, a numerical multibody model of the system is constructed. The governing mixed differential/algebraic equations of motion are automatically formulated and numerically generated. State-of-the-art numerical techniques and computational methods are employed and developed which produce in the response of the system at discrete time junctures. Postprocessing of the results in the form of graphical images or real-time animations provides an enormous aid in visualizing motion of the system. The analysis package may be merged with an efficient design optimization algorithm. The developed integrated analysis/design system is a valuable tool for researchers, design engineers, and analysts of mechanical systems. This computer-integrated tool provides an important bridge between the classical decision making process by an engineer and the emerging technology of computers.

Probabilistic Tolerance Allocation for the Dynamics of an Internal Combustion Engine With a Flexible Connecting Rod

1997 ◽  
Author(s):  
F. Zhang ◽  
B. J. Gilmore ◽  
A. Sinha
Keyword(s):  
Internal Combustion Engine ◽  
Combustion Engine ◽  
Equations Of Motion ◽  
Optimization Procedure ◽  
Internal Combustion ◽  
Tolerance Allocation ◽  
Radial Clearance ◽  
Connecting Rod ◽  
Link Length ◽  
Design Variables

Abstract Tolerance allocation standards do not exist for mechanical systems with flexibility and whose response are time varying, subjected to discontinuous forcing functions. Previous approaches based on optimization and numerical integration of the dynamic equations of motion encounter difficulty with determining sensitivities around the force discontinuity. The Alternating Frequency/Time approach is applied here to capture the effect of the discontinuity. The effective link length model is used to model the system and to account for the uncertainties in the link length, radial clearance and pin location. Since the effective link length model is applied, the equations of motion for the nominal system can be applied for the entire analysis. Optimization procedure is applied to the problem where the objective is to minimize the manufacturing costs and satisfy the constraints imposed on mechanical errors and design variables. Examples of tolerance allocation are presented for a single cylinder internal combustion engine with a flexible connecting rod.

A Sparsity-Oriented Approach to the Dynamic Analysis and Design of Mechanical Systems—Part 1

1977 ◽  
Vol 99 (3) ◽  
pp. 773-779 ◽  
Author(s):  
N. Orlandea ◽  
M. A. Chace ◽  
D. A. Calahan
Keyword(s):  
Computer Simulation ◽  
Dynamic Analysis ◽  
Numerical Solutions ◽  
Sparse Matrix ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Front Suspension ◽  
Analysis And Design

The work described herein is an extension of sparse matrix and stiff integrated numerical algorithms used for the simulation of electrical circuits and three-dimensional mechanical dynamic systems. By applying these algorithms big sets of sparse linear equations can be solved efficiently, and the numerical instability associated with widely split eigenvalues can be avoided. The new numerical methods affect even the initial formulation for these problems. In this paper, the equations of motion and constraints (Part 1) and the force function of springs and dampers (Part 2) are set up, and the numerical solutions for static, transient, and linearized types of analysis as well as the modal optimization algorithms are implemented in the ADAMS (automatic dynamic analysis of mechanical systems) computer program for simulation of three-dimensional mechanical systems (Part 2). The paper concludes with two examples: computer simulation of the front suspension of a 1973 Chevrolet Malibu and computer simulation of the landing gear of a Boeing 747 airplane. The efficiency of simulation and comparison with experimental results are given in tabular form.

The Incorporation of Arc Boundaries and Stick/Slip Friction in a Rule-Based Simulation Algorithm for Dynamic Mechanical Systems with Changing Topologies

1993 ◽  
Vol 115 (3) ◽  
pp. 423-434 ◽  
Author(s):  
Inhwan Han ◽  
B. J. Gilmore ◽  
M. M. Ogot
Keyword(s):  
High Speed ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Coefficient Matrix ◽  
Design Tool ◽  
Simulation Algorithm ◽  
Kinematic Constraint ◽  
Stick Slip ◽  
Rule Based ◽  
Dynamic Mechanical

Many dynamic mechanical systems, such as parts-feeders and percussive power tools, are described by equations of motion which are discontinuous. The discontinuities result from kinematic constraint changes which are difficult to foresee, especially in presence of impact and friction. A simulation algorithm for these types of systems must be able to algorithmically predict and detect the kinematic constraint changes without any prior knowledge of the system’s motion. This paper presents a rule-based approach to the prediction and detection of kinematic constraint changes between bodies with arc and line boundaries. A new type of constraint change, constraint exchange, is characterized. When arc contact exists, stick/slip friction is the difference between pure rolling and rolling with slip. Therefore, stick/slip friction is included in the algorithm. A force constraint is applied to the equations of motion when additional kinematic constraints due to friction would render the coefficient matrix singular. The efficacy of the rule-based simulation algorithm as a design tool is demonstrated through the design and experimental validation of a parts-feeder. The parts-feeder design is validated through two means: (1) a frame-by frame comparison of simulation results with the part motion recorded by high speed video and (2) actual testing.

A Numerical Method for the Dynamic Analysis of Mechanical Systems in Impact

1977 ◽  
Vol 99 (3) ◽  
pp. 665-673 ◽  
Author(s):  
R. E. Beckett ◽  
K. C. Pan ◽  
S. C. Chu
Keyword(s):  
Dynamic Analysis ◽  
Numerical Method ◽  
Numerical Technique ◽  
General Procedure ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Method Of Solution ◽  
Hertz Law ◽  
Impact Phase ◽  
Force Displacement

This paper develops a general procedure for solving mechanism problems where intermittent separations and impacts can occur between mating parts. The numerical technique employed to solve the problem identifies the onset of separation and gives the behavior of the mechanism during separation and impact. The Hertz law is used to find force displacement relationships in impact. Equations of motion are generated by using Hamilton’s principle. A key contribution of this paper is the development of a general approach to the handling of constraint conditions that occur during the separation and impact phase of the motion. Example problems are solved to illustrate the generality and breadth of the method of solution.

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