scholarly journals Kinematic Accuracy Method of Mechanisms Based on Tolerance Theories

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Li Zhang ◽  
Hong Nie ◽  
Xiaohui Wei
Keyword(s):  
Tolerance Analysis ◽  
Functional Element ◽  
Physical Models ◽  
Small Displacement ◽  
Tolerance Design ◽  
Dimensional Chain ◽  
Movement Accuracy ◽  
Kinematic Accuracy ◽  
Tolerance Model ◽  
Joint Clearances

Traditional tolerance analysis is mostly restricted to static analysis. However, tolerances of different components also affect the movement accuracy in a mechanism. In this paper, the idea of kinematic tolerance analysis is advanced. In the interest of achieving movement precision considering tolerance, a kinematic Jacobian model is established on the basis of a traditional dimensional chain and an original Jacobian model. The tolerances of functional element (FE) pairs are expressed as small-displacement screws. In addition, joint clearances resulting from tolerance design also influence the kinematic accuracy, and they are modeled by FE pairs. Two examples are presented to illustrate the rationality and the validity of the kinematic tolerance model. The results of the two examples are shown, and the discussion is presented. A physical model of the 2D example is also built up in 3DCS software. Based on the discussion, a comparison between the statistical and physical models is carried out, and the merits and demerits of both are listed.

scholarly journals Tolerance Design and Robust Study for The Joint Clearances of Landing Gear Retraction Mechanisms

2020 ◽  
Vol 10 (14) ◽  
pp. 4856 ◽  
Author(s):  
Li Zhang ◽  
Hong Nie ◽  
Xiaohui Wei
Keyword(s):  
Landing Gear ◽  
Tolerance Design ◽  
Robust Analysis ◽  
Kinematic Accuracy ◽  
Landing Gears ◽  
Joint Clearances ◽  
Tolerance Theory

Joint clearances inevitably affect the kinematic accuracy and robustness of landing gear retraction mechanisms. However, the complexity and uncertainty of the clearances lead to difficulty in establishing mathematic models and analyzing effects. In the interest of assessing the clearance effects on the kinematic accuracy of landing gears, an integrated tolerance theory is proposed in this paper. In the theory proposed, Jacobian–Torsor model is combined with robust analysis to establish the kinematic accuracy model and predict the influences of clearances. The overall steps to apply the theory presented in practice are given. A typical landing gear retraction mechanism is chosen for the case study and the results show that the tendencies of clearances can be observed. Through the process of tolerance design, robust study, and tolerance redesign, the kinematic accuracy is significantly improved. The integrated tolerance theory proposed and the study conducted will provide designers new insights for the clearance analysis of landing gear mechanisms.

Computer-Aided Monte Carlo Aircraft Tolerance Design Based on UG

2011 ◽  
Vol 338 ◽  
pp. 300-303
Author(s):  
Chang Hong Guo ◽  
Ping Xi ◽  
Zhen Yu Wang ◽  
Xing Dong Li
Keyword(s):  
Monte Carlo ◽  
Three Dimensional ◽  
Integrated Design ◽  
Tolerance Analysis ◽  
Digital Design ◽  
Tolerance Design ◽  
Computer Aided ◽  
Design And Manufacture

Along with the CAD technology being popularized, three-dimensional design of aircraft is ultimately realized into digital design. However, aircraft tolerances have not been designed by computer. They are mainly based on lots of manual calculations and not coordinated with integrated design and hold back the development of aircraft digital design and manufacture technologies. This paper introduces how to develop computer-aided aircraft tolerance analysis and distribution modules on UG and introduces Monte Carlo tolerance analysis technology. Running instances of aircraft tolerance design are illustrated in the paper.

A small displacement torsor model for tolerance analysis in a workpiece-fixture assembly

2009 ◽  
Vol 223 (8) ◽  
pp. 1005-1020 ◽  
Author(s):  
J N Asante
Keyword(s):  
Effective Means ◽  
Experimental System ◽  
Tolerance Analysis ◽  
Geometric Error ◽  
Small Displacement ◽  
Small Displacement Torsor ◽  
Set Up ◽  
Workpiece Setup ◽  
Feature Constraints

Workpiece geometric error, locator geometric error, and clamping error are factors that influence workpiece setup in workpiece fixturing. These errors accumulate and propagate during fixturing. They may be the reason for a machined feature being out of tolerance after machining. This paper presents a methodology for modelling and analysing the combined effect of these errors on a machined feature. Deviation of a machined feature due to the combined errors is expressed in terms of the small displacement torsor parameters. Given a tolerance on the machined feature, constraints are specified for that feature to establish a relationship between the tolerance zone of the feature and the torsor parameters. These constraints provide boundaries within which the machined feature must lie. This is used for tolerance analysis of the machined feature. A case study example was used to illustrate the approach. An experimental system was also set up to verify the analytical model. The results show that this approach offers an effective means for fixturing tolerance analysis.

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.

scholarly journals A Tolerance Analysis Approach Based on Robot Kinematics

2011 ◽  
Vol 2-3 ◽  
pp. 352-357
Author(s):  
Xiu Heng Zhang ◽  
Hong Yi Liu ◽  
Zhong Luo
Keyword(s):  
Three Dimensional ◽  
Mathematical Expression ◽  
Tolerance Analysis ◽  
Analysis Approach ◽  
Robot Kinematics ◽  
Small Displacement ◽  
Functional Requirement ◽  
Percentage Contribution ◽  
Cad Cam ◽  
Functional Features

This paper presents a tolerance modeling approach based on robot kinematics theory within CAD/CAM system. Based on the differential kinematics theories, each feature of characteristics including size tolerance and geometrical tolerance was established as a corresponding small displacement torsor. In order to express the relation between the small displacement of all functional features and the functional requirement, the final expression was represented to establish the projection of analysis of the tolerance chain. A mathematical expression was obtained by the mean instead of single points, and the constraints can be represented by interval using the standard deviation, not limit deviations. After having identified the unit components and the functional requirement from the tolerance chain, we obtained the percentage contribution of each unit feature to the functional requirement. A percentage contribution can help designer to decide which tolerance is tighten or loosen. The application of the tolerance analysis approach in a simple three-dimensional sample was also discussed in this paper.

A Comparison Study of Mathematical Models for Tolerance Analysis

2013 ◽  
Vol 765-767 ◽  
pp. 759-762
Author(s):  
Jian Xin Yang ◽  
Zhen Tao Liu ◽  
Ben Zhao
Keyword(s):  
Tolerance Analysis ◽  
Mathematical Representation ◽  
Small Displacement ◽  
Propagation Mechanism ◽  
Comparison Study ◽  
Worst Case ◽  
Geometric Tolerance ◽  
Geometric Tolerances ◽  
Small Displacement Torsor ◽  
Comprehensive Comparison

This paper reviews two major models (Small Displacement Torsor, Deviation and Clearance Domain) for 3D functional tolerance analysis and compares them. The underlying mathematical representation of geometric tolerances can be classified as inequalities and multi-variate region. The corresponding algebraic or geometric tolerance propagation mechanism of each model is briefly introduced for worst-case and statistical tolerancing. Through a comprehensive comparison of these models, this paper gives some suggestions for choosing the appropriate method for a given tolerancing problem.

Tolerance Design for Four-Bar Function Generating Mechanisms with Joint Clearances Using Taguchi Method

2010 ◽  
Vol 118-120 ◽  
pp. 517-521 ◽  
Author(s):  
Xian Zhen Huang ◽  
Yi Min Zhang ◽  
Hao Lu ◽  
Le Tang ◽  
He Li
Keyword(s):  
Taguchi Method ◽  
Design Parameters ◽  
Tolerance Design ◽  
Function Generator ◽  
Function Generation ◽  
Joint Clearances ◽  
Generation Mechanisms ◽  
Sensitivity Maps

This paper presents a method for tolerance design of four-bar function generating mechanisms with joint clearances using Taguchi method. Based on previous studies made by other researchers, we propose a model to quantify the effects of uncertain factors on the accuracy of four-bar function generating mechanisms. Taguchi’s approach is applied to select the optimal tolerance ranges for the design parameters of function generation mechanisms. Sensitivity maps are plotted to provide an insight to the effects of parameter errors on the performance variances of four-bar function generating mechanisms. To illustrate the efficiency of the proposed methodology, the tolerance design of a four-bar function generator with joint clearances is discussed.

Gear-tolerance optimization based on a response surface method

2018 ◽  
Vol 42 (3) ◽  
pp. 309-322
Author(s):  
Rui Xu ◽  
Kang Huang ◽  
Jun Guo ◽  
Lei Yang ◽  
Mingming Qiu ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Response Surface ◽  
Response Surface Method ◽  
Tolerance Analysis ◽  
Optimization Method ◽  
Small Displacement ◽  
Tooth Contact Analysis ◽  
Tolerance Optimization ◽  
Surface Method ◽  
Low Efficiency

To address the low efficiency of gear-tolerance analysis and optimization, a gear-tolerance optimization method based on a response surface method (RSM) and optimization algorithm is presented. A gear-tolerance mathematical model, including profile deviation, pitch deviation, and geometric deviation, was developed by combining traditional profile modeling with a small displacement torsor (SDT) method. Based on this mathematical model, a tooth-contact analysis method, which takes a variety of deviations into account, and a program to compute transmission error were developed. Using the RSM and a genetic algorithm, a gear-tolerance optimization model was created to consider a variety of gear tolerances as design variables and process cost as an optimization objective. An example of gear-tolerance optimization was analyzed, and the result indicates that the method presented in this paper may help improve the efficiency of gear-tolerance optimization and is practicable for precision gear design.

A small displacement torsor model for 3D tolerance analysis of conical structures

2014 ◽  
Vol 229 (14) ◽  
pp. 2514-2523 ◽  
Author(s):  
Sun Jin ◽  
Hua Chen ◽  
Zhimin Li ◽  
Xinmin Lai
Keyword(s):  
Three Dimensional ◽  
Tolerance Analysis ◽  
Dimensional Euclidean Space ◽  
Small Displacement ◽  
Analysis Method ◽  
Tolerance Zone ◽  
Geometric Tolerances ◽  
Small Displacement Torsor ◽  
Conical Surfaces ◽  
Conical Structures

The small displacement torsor model is a classic three-dimensional tolerance analysis method. It uses three translational vectors and three rotational vectors to represent tolerance information in three-dimensional Euclidean space. However, the target features of this model mainly focused on planes and cylinders in previous studies. Little attention is invested to conical features and their joints which are used widely and more complex than the planar and cylindrical features. The objective of this article is to present a three-dimensional mathematical method of tolerance representation about conical surfaces and their joints based on the small displacement torsor model, and propose a mathematical model of variations and constraint relations of components of the small displacement torsor for conical surfaces caused by geometric tolerances limited by its tolerance zone. In addition, a simple example involving conical structures is used to demonstrate three-dimensional conical tolerance propagation. Both deterministic and statistical results are obtained by this model.

Sign in / Sign up

Export Citation Format

Share Document