Tolerance Analysis in Machining: An Approach Combining the Model of Manufactured Part and the Jacobian-Torsor Model

2008 ◽  
Author(s):  
Mojtaba Kamali Nejad ◽  
Alain Desrochers ◽  
Franc¸ois Villeneuve ◽  
Fre´de´ric Vignat
Keyword(s):  
Kinematic Chain ◽  
Tolerance Analysis ◽  
Small Displacement ◽  
Functional Requirements ◽  
Combined Approach ◽  
Functional Elements ◽  
New Approach ◽  
Nominal Model ◽  
Small Displacement Torsor ◽  
Position And Orientation

To perform tolerance analysis in machining, a combined approach which blends the benefits of the Model of Manufactured Part (the MMP model) and the Jacobian-Torsor model is proposed. The former is based on the CAD nominal model, where deviations are described relative to the nominal part using small displacement torsor. The later starts with the kinematic dimension chains and expresses the relative position and orientation of the various components of the chosen kinematic chain by Jacobian matrices. The Jacobian-Torsor model uses interval arithmetic for expressing the possible variation of the functional elements and for calculating the extreme bounds of the functional requirements. In the following sections, the two aforementioned models will first be outlined before the new combined approach for tolerance analysis in machining is presented. This new approach uses the advantages of the MMP model to simulate the machining operation, taking into account positioning and machining defects. Furthermore it takes advantages of the interval-based formulation which has been used in the Jacobian Torsor model. The combined approach is finally applied on an example.

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.

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.

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.

A Comparison Study of Small Displacement Torsor and Analysis Line Methods for Functional Tolerance Analysis

2012 ◽  
Vol 605-607 ◽  
pp. 358-364
Author(s):  
Chun Li Li ◽  
Jian Xin Yang ◽  
Jun Ying Wang ◽  
Wen Xin Ma
Keyword(s):  
Computation Time ◽  
Tolerance Analysis ◽  
General Characteristic ◽  
Worst Case Analysis ◽  
Small Displacement ◽  
Worst Case ◽  
Small Displacement Torsor ◽  
Functional Tolerance ◽  
Tolerance Accumulation ◽  
Analysis Line

Tolerance analysis plays an important role in the stage of product design and has great influences on the product assembly quality and manufacturing costs. Two major methods are used for three-dimensional functional tolerance analysis, which are small displacement torsor and analysis line. A positioning mechanism with two parts is presented for tolerance accumulation calculation. Through the comparison of these two methods on computation processes and results, analysis line method can establish the explicit relationship between the functional requirement and the tolerances of the influential part, which allows finding the accumulation results in the worst-case and statistical conditions. However, it requires the determination of transfer relationship case by case. For small displacement torsor model, it permits a set of inequalities to express the tolerance zones, which yields a linear programming problem. It is applicable to different tolerance chains for its general characteristic. However it is adopted only for the worst-case analysis and requires more computation time.

A CAD model for the tolerancing of mechanical assemblies considering non-rigid joints between parts with defects

2021 ◽  
pp. 095440542110257
Author(s):  
Anis Korbi ◽  
Mehdi Tlija ◽  
Borhen Louhichi
Keyword(s):  
Tolerance Analysis ◽  
Design Stage ◽  
Small Displacement ◽  
Worst Case ◽  
Mechanical Assemblies ◽  
Proposed Model ◽  
Small Displacement Torsor ◽  
Rigid Joints ◽  
Geometrical Defects ◽  
The Ideal

During the design stage, the ideal simulation and visualization of the mechanical assemblies behavior require the modeling of parts with dimensional and geometrical defects. However, the deviations caused by parts deformations can generate an important difference between the ideal assembly and the real product. In this regard, this paper proposes a tolerance analysis method of CAD assemblies considering non-rigid joints between parts with defects. The determination of realistic rigid components with dimensional and geometrical defects is based on the worst case tolerancing approach and the Small Displacement Torsor (SDT) parameters. The Finite Element (FE) computation is executed to determine deformations of realistic non-rigid part models under external loads. Sub-algorithms to define non-rigid joints between realistic parts are developed. The tolerance analysis is established using the realistic CAD assembly. A case study is presented to evaluate the proposed model.

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.

scholarly journals A New Approach to the Solution of Robot Kinematics Based on Relative Transformation Matrices

2016 ◽  
Vol 5 (3) ◽  
pp. 213
Author(s):  
Mohammad Reza Elhami ◽  
Iman Dashti
Keyword(s):  
Robot Manipulator ◽  
Robot Kinematics ◽  
Coordinate Frame ◽  
End Effector ◽  
New Approach ◽  
Transformation Matrices ◽  
The World ◽  
Convenient Approach ◽  
Position And Orientation ◽  
Relative Transformation

In analyzing robot manipulator kinematics, we need to describe relative movement of adjacent linkages or joints in order to obtain the pose of end effector (both position and orientation) in reference coordinate frame. Denavit-Hartenberg established a method based on a 4×4 homogenous matrix so called “A” matrix. This method used by most of the authors for kinematics and dynamic analysis of the robot manipulators. Although it has many advantages, however, finding the elements of this matrix and link/joint’s parameters is sometimes complicated and confusing. By considering these difficulties, the authors proposed a new approach called ‘convenient approach’ that is developed based on “Relative Transformations Principle”. It provides a very simple and convenient way for the solution of robot kinematics compared to the conventional D-H representation. In order to clarify this point, the kinematics of the world known Stanford manipulator has been solved through D-H representation as well as convenient approach and the results are compared.

scholarly journals A New Approach in High Precision Bone Surgery: Semi-Automatic Alignment of an Application-Specific Instrument Guide Adjusted by a Smart Screwdriver

10.29007/bp2d ◽  
2018 ◽  
Author(s):  
Lukas Theisgen ◽  
Sabine Jeromin ◽  
Manuel Vossel ◽  
Sylvain Billet ◽  
Klaus Radermacher ◽  
...  
Keyword(s):  
Kinematic Chain ◽  
Lateral Direction ◽  
Human Errors ◽  
New Approach ◽  
Surgical Workflow ◽  
Bone Surgery ◽  
Handheld Device ◽  
Automatic Alignment ◽  
Cost Efficient ◽  
Application Specific

Robotic surgical systems reduce the cognitive workload of the surgeon by assisting in guidance and operational tasks. As a result, higher precision and a decreased surgery time are achieved, while human errors are minimised. However, most of robotic systems are expensive, bulky and limited to specific applications.In this paper a novel semi-automatic robotic system is evaluated that offers the high accuracies of robotic surgery while remaining small, universally applicable and easy to use. The system is composed of a universally applicable handheld device, called Smart Screwdriver (SSD) and an application specific kinematic chain serving as a tool guide. The guide mechanism is equipped with motion screws. By inserting the SSD into a screw head, the screw is identified automatically and the required number of revolutions is executed to achieve the desired pose of the tool guide.The usability of the system was evaluated according to IEC 60601-1-6 using pedicle screw implementation as an example. The achieved positioning accuracies of the drill sleeve were comparable to those of SpineAssist from Mazor Robotics Ltd., Caesarea (IL) with -0.54 ± 0.93 mm (max: 2.08 mm) in medial/lateral-direction and 0.17 ± 0.51 mm (max: 1.39 mm) in cranial/caudal-direction in the pedicle isthmus. Additionally, the system is cost-efficient, safe, easy to integrate in the surgical workflow and universally applicable to applications in which a static position in one or more DOF is to be adjusted.

Sign in / Sign up

Export Citation Format

Share Document