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.

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.

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.

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.

Dynamic Analysis of Mechanical Systems With Time-Varying Topologies: Part 1 — Dynamic Model and Stability Analysis

1990 ◽  
Author(s):  
Yu Wang
Keyword(s):  
Stability Analysis ◽  
Dynamic Model ◽  
Local Stability ◽  
Global Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Time Varying ◽  
Discrete Equations ◽  
Local Stability Analysis ◽  
Multiple Collisions

Abstract A model is developed for analyzing mechanical systems with a pair of bodies with topological changes in their kinematic constraints. It is built upon the concept of Poincaré map rather than following the traditional methods of differential equations. The model provides a set of well-defined and naturally-discrete equations of motion and is capable of giving physical insights of dynamic characteristics of deadbeat convergence of multiple collisions and periodic or chaotic responses. The development of dynamic model and a local stability analysis are presented in Part 1, and the global analysis and numerical simulation are discussed in Part 2.

scholarly journals Dynamic Modeling and Vibration Characteristics Analysis of Deep-Groove Ball Bearing, Considering Sliding Effect

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2408
Author(s):  
Fanjie Li ◽  
Xiaopeng Li ◽  
Dongyang Shang
Keyword(s):  
Ball Bearing ◽  
Equations Of Motion ◽  
Constant Load ◽  
Vibration Characteristics ◽  
Vibration Response ◽  
System Model ◽  
Radial Clearance ◽  
Time Varying ◽  
Deep Groove ◽  
Deep Groove Ball Bearing

To study the vibration characteristics of deep-groove ball bearing, considering the influence of sliding, the dynamic model of the DGB 6205 system is established in this paper. The DGB 6205 system model includes the movement of the bearing inner ring in the X and Y directions, the rotation of the cage, the rotation movement of each ball, the revolution movement of each ball and the movement along the radial direction of each ball. Based on the system model, the differential equations of motion of the system are established, and the correctness of the model is verified by experiment. The slip characteristics of the DGB 6205 system are studied by numerical simulation. At the same time, the influence of time-varying load on the vibration characteristics of the system is studied. Then, the sensitivity of system parameters is analyzed. The results show that the sliding speed between the ball and the inner raceway is greater than that between the ball and the outer raceway. The radial vibration response of DGB 6205 system under time-varying load is less than that under constant load. The increase of radial clearance will increase the vibration response of DGB 6205 system.

Effect of Backlash on Vibration Spectrum in Spur Gearboxes Incorporating Sleeve Bearings

1991 ◽  
Author(s):  
Fawzi M. A. El-Saeidy
Keyword(s):  
Fourier Transform ◽  
Time Domain ◽  
Vibration Spectrum ◽  
Equations Of Motion ◽  
Analysis Procedure ◽  
Radial Clearance ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Gearbox Vibration ◽  
Center Distance

Abstract An Analytical model is presented to simulate effect of tooth backlash on vibration spectrum of spur gearboxes incorporating sleeve bearings. Included in the model are: elasticity of shafts, friction between meshing teeth, interaction between gearbox casing and internals, and time-varying tooth backlash (backlash is a function of operating center distance), mesh stiffness (stiffness is calculated based on the strain energies of the tooth that is treated as a cantilever beam of involute shape) and Hertzian mesh damping. The bearing forces are calculated with consideration of bearing radial clearance and system vibrations. The analysis is applied to a single stage gearbox and equations of motion are numerically integrated to obtain system reponse in time domain. This response is transformed into frequency domain (vibration spectrum) using Fast Fourier Transform (FFT) algorithm and samples of the results are shown for different values of tooth backlash. The results show that backlash has a pronounced effect on gearbox vibration and study provides an analysis procedure for predicting such effects.

scholarly journals Dynamic Modeling and Stability Analysis of Mechanical Systems with Time-Varying Topologies

1993 ◽  
Vol 115 (4) ◽  
pp. 808-816 ◽  
Author(s):  
Yu Wang
Keyword(s):  
Stability Analysis ◽  
Dynamic Modeling ◽  
Local Stability ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Time Varying ◽  
Kinematic Constraints ◽  
Discrete Equations ◽  
Local Stability Analysis ◽  
Multiple Collisions

A model is developed for analyzing mechanical systems with a pair of bodies with topological changes in their kinematic constraints. It is built upon the concept of a Poincare´ map rather than following the traditional methods of differential equations. The model provides a set of well-defined and naturally-discrete equations of motion and is capable of giving physical insights of dynamic characteristics of deadbeat convergence of multiple collisions and periodic or chaotic responses. The development of a dynamic model and a local stability analysis are presented.

Optimal Design of the Mechanical Systems Using Parametric Technique & MBS (Multi-Body Systems) Software

2012 ◽  
Vol 463-464 ◽  
pp. 1129-1132 ◽  
Author(s):  
Cătălin Alexandru
Keyword(s):  
Optimal Design ◽  
Tracking System ◽  
Mechanical Systems ◽  
Great Influence ◽  
Optimization Procedure ◽  
Energetic Efficiency ◽  
Design Objective ◽  
Design Variables ◽  
Solar Tracking ◽  
Multi Body

The paper approaches the optimal design of the mechanical systems based on parametric technique in MBS (Multi-Body Systems) environment. The optimization process is developed in five steps: parameterizing the virtual model for creating the relations between the objects (points, markers, bodies, constraints, forces), defining the design variables, defining the design objective and constraints, performing parametric studies in order to identify the sensitivity of the design objective at the modification of the design variables, and optimizing the model on the basis of the main design variables (with great influence on the design objective). For applying the optimization procedure, a solar tracking system used for increasing the energetic efficiency of the photovoltaic modules has been considered. The study is performed by using the MBS environment ADAMS of MSC Software.

scholarly journals Impact Dynamics Analysis of Mobile Mechanical Systems

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1776
Author(s):  
Sorin Dumitru ◽  
Andra Constantin ◽  
Cristian Copilusi ◽  
Nicolae Dumitru
Keyword(s):  
Mechanical System ◽  
Combustion Engine ◽  
Mechanical Systems ◽  
Free Fall ◽  
Radial Clearance ◽  
Connecting Rod ◽  
Element Analysis ◽  
Multi Body ◽  
The Impact ◽  
Two Bodies

The current paper focuses on the impact phenomenon analysis, in the case of multi-body mechanical systems undergoing fast motion, due to the presence of some manufacturing and mounting errors or due to some accident during the transport mechanical systems. Thus, the impact phenomenon was analyzed in two cases, the first one consisting of a two bodies, namely, a free-fall body brought in contact with the other considered fixed in space and the second case, which is a complex one, when the analyzed bodies are components of a multi-body mechanical system. The research main objective is to analyze the impact generated between the two bodies through three methods, i.e., the analytical method, a virtual prototyping method accomplished with MSC Adams software and a method based on finite element analysis with Ansys and Abaqus software. A dynamic model of the impact force was developed, which allows to make a comparison of the numerical results obtained through the abovementioned methods. As a multi-body mechanical system, it was considered a mechanism from an internal combustion engine from which the radial clearance between the piston bolt and connecting rod head of the considered mechanism was analyzed.

Optimal Design of Mechanical Systems With Constraint Violation Stabilization Method

1985 ◽  
Vol 107 (4) ◽  
pp. 493-498 ◽  
Author(s):  
C. O. Chang ◽  
P. E. Nikravesh
Keyword(s):  
Optimal Design ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Design Procedure ◽  
Optimization Procedure ◽  
Design Sensitivity ◽  
System Response ◽  
Stabilization Method ◽  
Sensitivity Matrix ◽  
Constraint Violation

This paper presents a comprehensive optimal design procedure for constrained dynamic systems. The constraint violation stabilization method for dynamic analysis of mechanical systems is briefly reviewed. A direct differentiation method is used to form the equations of design sensitivity analysis based on a constraint violation stabilization method. The sensitivity equations and the equations of motion are integrated simultaneously to obtain the system response, as well as the state sensitivity matrices. All integrations are performed using a multistep predictor-corrector method. The first order design sensitivity matrix is used to calculate the gradient of cost function and the performance constraint during the optimization procedure. An optimization routine is linked to the analysis/sensitivity algorithm. Two examples are given which illustrate the effectiveness of this method for determining the optimal design of a system.

Sign in / Sign up

Export Citation Format

Share Document