Comparison of Assembly Tolerance Analysis by the Direct Linearization and Modified Monte Carlo Simulation Methods

1995 ◽  
Author(s):  
Jinsong Gao ◽  
Kenneth W. Chase ◽  
Spencer P. Magleby
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Closed Loop ◽  
Great Influence ◽  
Tolerance Analysis ◽  
Linearization Method ◽  
Direct Linearization ◽  
Highly Nonlinear ◽  
Assembly Features ◽  
Assembly Constraints

Abstract Two methods for performing statistical tolerance analysis of mechanical assemblies are compared: the Direct Linearization Method (DLM), and Monte Carlo simulation. A selection of 2-D and 3-D vector models of assemblies were analyzed, including problems with closed loop assembly constraints. Closed vector loops describe the small kinematic adjustments that occur at assembly time. Open loops describe critical clearances or other assembly features. The DLM uses linearized assembly constraints and matrix algebra to estimate the variations of the assembly or kinematic variables, and to predict assembly rejects. A modified Monte Carlo simulation, employing an iterative technique for closed loop assemblies, was applied to the same problem set. The results of the comparison show that the DLM is accurate if the tolerances are relatively small compared to the nominal dimensions of the components, and the assembly functions are not highly nonlinear. Sample size is shown to have great influence on the accuracy of Monte Carlo simulation.

A Second-Order Method for Assembly Tolerance Analysis

1999 ◽  
Author(s):  
Charles G. Glancy ◽  
Kenneth W. Chase
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Nonlinear Analysis ◽  
Closed Loop ◽  
Tolerance Analysis ◽  
Linear Analysis ◽  
Tolerance Allocation ◽  
Input And Output ◽  
Loop Constraints ◽  
Geometric Effects

Abstract Linear analysis and Monte Carlo simulation are two well-established methods for statistical tolerance analysis of mechanical assemblies. Both methods have advantages and disadvantages. The Linearized Method, a form of linear analysis, provides fast analysis, tolerance allocation, and the capability to solve closed loop constraints. However, the Linearized Method does not accurately approximate nonlinear geometric effects or allow for non-normally distributed input or output distributions. Monte Carlo simulation, on the other hand, does accurately model nonlinear effects and allow for non-normally distributed input and output distributions. Of course, Monte Carlo simulation can be computationally expensive and must be re-run when any input variable is modified. The second-order tolerance analysis (SOTA) method attempts to combine the advantages of the Linearized Method with the advantages of Monte Carlo simulation. The SOTA method applies the Method of System Moments to implicit variables of a system of nonlinear equations. The SOTA method achieves the benefits of speed, tolerance allocation, closed-loop constraints, non-linear geometric effects and non-normal input and output distributions. The SOTA method offers significant benefits as a nonlinear analysis tool suitable for use in design iteration. A comparison was performed between the Linearized Method, Monte Carlo simulation, and the SOTA method. The SOTA method provided a comparable nonlinear analysis to Monte Carlo simulation with 106 samples. The analysis time of the SOTA method was comparable to the Linearized Method.

A Comparative Study of Tolerance Analysis Methods

2004 ◽  
Author(s):  
Zhengshu Shen ◽  
Gaurav Ameta ◽  
Jami J. Shah ◽  
Joseph K. Davidson
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Tolerance Analysis ◽  
3 Dimensional ◽  
Analysis Methods ◽  
Simulation Based ◽  
Comprehensive Comparison ◽  
Tolerance Charts ◽  
Assembly Constraints ◽  
Tolerance Accumulation

This paper reviews four major methods for tolerance analysis and compares them. The methods discussed are (1) 1D tolerance charts, (2) variational analysis based on Monte Carlo simulation, (3) vector loop (or kinematic) based analysis, and (4) ASU T-Maps© based tolerance analysis. Tolerance charts deal with tolerance analysis in one direction at a time and ignore possible contributions from the other directions. Manual charting is tedious and error-prone, hence attempts have been made for automation. Monte Carlo simulation based tolerance analysis is based on parametric solid modeling; its inherent drawback is that simulation results highly depend on the user-defined modeling scheme, and its inability to obey all Y14.5 rules. The vector loop method uses kinematic joints to model assembly constraints. It is also not fully consistent with Y14.5 standard. ASU T-Maps based tolerance analysis method can model geometric tolerances and their interaction in truly 3-dimensional context. It is completely consistent with Y14.5 standard but its use by designers may be quite challenging. T-Maps based tolerance analysis is still under development. Despite the shortcomings of each of these tolerance analysis methods, each may be used to provide reasonable results under certain circumstances. No guidelines exist for such a purpose. Through a comprehensive comparison of these methods, this paper will develop some guidelines for selecting the best method to use for a given tolerance accumulation problem.

Mixed Efficient Global Optimization for Time-Dependent Reliability Analysis

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Global Optimization ◽  
Reliability Analysis ◽  
Surrogate Model ◽  
Extreme Value ◽  
Time Dependent ◽  
Efficient Global Optimization ◽  
Highly Nonlinear ◽  
Adaptive Kriging

Time-dependent reliability analysis requires the use of the extreme value of a response. The extreme value function is usually highly nonlinear, and traditional reliability methods, such as the first order reliability method (FORM), may produce large errors. The solution to this problem is using a surrogate model of the extreme response. The objective of this work is to improve the efficiency of building such a surrogate model. A mixed efficient global optimization (m-EGO) method is proposed. Different from the current EGO method, which draws samples of random variables and time independently, the m-EGO method draws samples for the two types of samples simultaneously. The m-EGO method employs the adaptive Kriging–Monte Carlo simulation (AK–MCS) so that high accuracy is also achieved. Then, Monte Carlo simulation (MCS) is applied to calculate the time-dependent reliability based on the surrogate model. Good accuracy and efficiency of the m-EGO method are demonstrated by three examples.

Research on Tolerance Simulation and Improvement of Gas Turbine Generator

2014 ◽  
Vol 1039 ◽  
pp. 99-104
Author(s):  
Jing Liu ◽  
Ming Li ◽  
Gao Wei Zhan
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Gas Turbine ◽  
High Reliability ◽  
Tolerance Analysis ◽  
Analysis Software ◽  
Turbine Generator ◽  
Reliability Calculation ◽  
The Impact ◽  
Assembly Precision

VisVSA is a kind of 3-D tolerance analysis software which offers high reliability calculation based on Monte Carlo simulation. This paper uses VisVSA to improve the design of gas turbine generator. In many factors that affect designing properties, the impact of manufacturing precision and assembly precision through comparative analysis are discussed.

scholarly journals Monte Carlo Simulation Experiments for Engineering Optimisation

2015 ◽  
Vol 2 (1) ◽  
pp. 97
Author(s):  
Robert Anderson ◽  
Zhou Wei ◽  
Ian Cox ◽  
Malcolm Moore ◽  
Florence Kussener
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Tolerance Analysis ◽  
Simulation Experiments ◽  
Practical Applications ◽  
Study Approach ◽  
Good Set ◽  
Robust Process ◽  
And Control

Design of Experiments (DoE) is widely used in design, manufacturing and quality management. The resulting data is usually analysed with multiple linear regression to generate polynomial equations that describe the relationship between process inputs and outputs. These equations enable us to understand how input values affect the predicted value of one or more outputs and find good set points for the inputs. However, to develop robust manufacturing processes, we also need to understand how variation in these inputs appears as variation in the output. This understanding allows us to define set points and control tolerances for the inputs that will keep the outputs within their required specification windows. Tolerance analysis provides a powerful way of finding input settings and ranges that minimise output variation to produce a process that is robust. In many practical applications, tolerance analysis exploits Monte Carlo simulation of the polynomial model generated from DoE’s. This paper briefly describes tolerance analysis and then shows how Monte Carlo simulation experiments using space-filling designs can be used to find the input settings that result in a robust process. Using this approach, engineers can quickly and easily identify the key inputs responsible for transferring undesired variation to their process outputs and identify the set points and ranges that make their process as robust as possible. If the process is not sufficiently robust, they can rationally investigate different strategies to improve it. A case study approach is used to aid explanation and understanding.

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