Integrating cylindricity error into tolerance analysis of precision rotary assemblies using Jacobian–Torsor model

2013 ◽  
Vol 227 (11) ◽  
pp. 2517-2530 ◽  
Author(s):  
Ni Weihua ◽  
Yao Zhenqiang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Significant Influence ◽  
Tolerance Analysis ◽  
Small Displacement ◽  
Contact Method ◽  
Functional Requirements ◽  
Form Error ◽  
Cylindrical Parts ◽  
Cylindricity Error

In this study, the cylindricity error was integrated into the tolerance analysis of precision rotary assemblies using Jacobian–Torsor model. The contact method was developed to rapidly determine the actual fitting clearance through the virtual assembling of the mating cylindrical parts using Monte Carlo simulation. By modifying the expressions of small displacement torsors of the cylinder pairs, the actual fitting clearance between the bore and the shaft was taken into account, which overcame the shortage of Jacobian–Torsor model that the form error cannot be processed. The effects of the cylindricity error and the number of lobes on the actual fitting clearance and the functional requirements were analyzed in detail. The results show that the cylindricity error has significant influence on the actual fitting clearance and the final functional requirements, and it should not be ignored in the tolerance analysis for precision rotary assemblies.

Tolerance Analysis Supports Tolerance Assignment

2018 ◽  
Vol 8 (1) ◽  
pp. 1-20
Author(s):  
Wilma Polini ◽  
Andrea Corrado ◽  
Costanzo Cavaliere
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Tolerance Analysis ◽  
Point Of View ◽  
Industrial Plant ◽  
Functional Requirements ◽  
Simulation Approach ◽  
Support Design ◽  
Functional Point ◽  
Tolerance Assignment

This work presents a method to support product design, since it shows how to use together tolerance assignment and analysis for choosing among different set of tolerances assigned to the same product. It starts from tolerance assignment that produces different sets of tolerances for the product components which are all acceptable from a functional point of view. It translates each assigned set of tolerances into one or more groups of tolerances that are recognized by the software used for tolerance analysis. Therefore, the software for tolerance analysis is applied to each group of tolerances by means of a Monte Carlo simulation approach. Finally, the obtained results are intersected or compounded to obtain the trend of product functional requirements that allows to identify the best set of tolerances assigned to the product components. The developed method was applied to a skillet, a platform of an industrial plant that is made of five parts connected by screws. The obtained results show how the developed new method is a valid tool to support design for industrial application.

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.

Application of a Unified Jacobian—Torsor Model for Tolerance Analysis

2003 ◽  
Vol 3 (1) ◽  
pp. 2-14 ◽  
Author(s):  
Alain Desrochers ◽  
Walid Ghie ◽  
Luc Laperrie`re
Keyword(s):  
Three Dimensional ◽  
Tolerance Analysis ◽  
Small Displacement ◽  
Manufacturing Processes ◽  
Functional Requirements ◽  
Tolerance Zone ◽  
Kinematic Chains ◽  
Final Assembly ◽  
Novel Method ◽  
Assembly Constraints

Because of uncertainties in manufacturing processes, a mechanical part always shows variations in its geometrical characteristics (ex. form, dimension, orientation and position). Quality then often reflect how well tolerances and hence, functional requirements, are being achieved by the manufacturing processes in the final product. From a design perspective, efficient methods must be made available to compute, from the tolerances on individual parts, the value of the functional requirement on the final assembly. This is known as tolerance analysis. To that end, existing methods, often based on modeling of the open kinematic chains in robotics, are classified as deterministic or statistical. These methods suppose that the assembled parts are not perfect with regard to the nominal geometry and are rigid. The rigidity of the parts implies that the places of contacts are regarded as points. The validation or the determination of a tolerance zone is therefore accomplished by a series of simulation in specific points subjected to assembly constraints. To overcome the limitations and difficulties of point based approaches, the paper proposes the unification of two existing models: the Jacobian’s matrix model, based on the infinitesimal modeling of open kinematic chains in robotics, and the tolerance zone representation model, using small displacement screws and constraints to establish the extreme limits between which points and surfaces can vary. The approach also uses interval algebra as a novel method to take tolerance boundaries into account in tolerance analysis. The approach has been illustrated on a simple two parts assembly, nevertheless demonstrating the capability of the method to handle three-dimensional geometry. The results are then validated geometrically, showing the overall soundness of the approach.

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.

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.

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