Novel application of mapping method from small displacement torsor to tolerance: Error optimization design of assembly parts

2021 ◽  
pp. 095440542110632
Author(s):  
Xiaokai Mu ◽  
Bo Yuan ◽  
Yunlong Wang ◽  
Wei Sun ◽  
Chong Liu ◽  
...  
Keyword(s):  
Optimization Design ◽  
Mechanical Systems ◽  
Small Displacement ◽  
Manufacturing Cost ◽  
Manufacturing Error ◽  
Assembly Accuracy ◽  
Small Displacement Torsor ◽  
Machine Parts ◽  
Assembly Error ◽  
Error Optimization

The manufacturing/assembly error of machine parts is a key factor that influences the performance and economy of mechanical systems. To achieve high assembly precision and performance on the basis of low manufacturing accuracy and cost, this study primarily optimizes the assembly error of machine parts. First, the small displacement torsor is used to characterize the small deformation between the mating surfaces of parts. Subsequently, to realize the combination of small displacement torsor and tolerance, the small displacement torsor with manufacturing error and assembly deformation is mapped to the tolerance domain. Second, based on the relationship between small displacement torsor and tolerance, an assembly error optimization model is established on the basis of the conventional tolerance-cost model, considering the emergence of manufacturing error and assembly deformation. Third, aiming at the high-pressure rotor for aeroengines, the error optimization design of assembly is carried out developed with the assembly accuracy requirement as the constraint condition, and the total costs of the manufacturing and assembly processes as the objective. The optimization results indicate that the manufacturing error range of each mating surface after optimization changes, from small to large, under the premise of ensuring the product’s performance, which verifies that the difficulty in processing parts is reduced, and that the efficiency of parts processing is also improved. Meanwhile, the relative manufacturing cost after optimization is reduced by 6.79%, which reflects the economic requirements to a certain extent. The content of this article provides the necessary design basis and reference for the realization of high assembly accuracy of mechanical systems, under low cost requirements from the design perspective.

scholarly journals A Coordination Space Model for Assemblability Analysis and Optimization during Measurement-Assisted Large-Scale Assembly

2020 ◽  
Vol 10 (9) ◽  
pp. 3331 ◽  
Author(s):  
Zhizhuo Cui ◽  
Fuzhou Du
Keyword(s):  
Large Scale ◽  
Least Squares Method ◽  
Measurement Data ◽  
Optimization Method ◽  
Small Displacement ◽  
Analysis Method ◽  
Assembly Quality ◽  
Space Model ◽  
Assembly Accuracy ◽  
Small Displacement Torsor

The assembly process is sometimes blocked due to excessive dimension deviations during large-scale assembly. It is inefficient to improve the assembly quality by trial assembly, inspection, and accuracy compensation in the case of excessive deviations. Therefore, assemblability prediction by analyzing the measurement data, assembly accuracy requirements, and the pose of parts is an effective way to discover the assembly deviations in advance for measurement-assisted assembly. In this paper, a coordination space model is constructed based on a small displacement torsor and assembly accuracy requirements. An assemblability analysis method is proposed to check whether the assembly can be executed directly. Aiming at the incoordination problem, an assemblability optimization method based on the union coordination space is proposed. Finally, taking the space manipulator assembly as an example, the result shows that the proposed method can improve assemblability with a better assembly quality and less workload compared to the least-squares method.

An Analysis Model to Predict Rotation Accuracy of High-Precision Spindles Considering Part Errors and Deformation

2017 ◽  
Author(s):  
Yanhui Sun ◽  
Jun Hong ◽  
Junkang Guo ◽  
Yanfei Zhang ◽  
Shaoke Wan ◽  
...  
Keyword(s):  
High Precision ◽  
Design Stage ◽  
Small Displacement ◽  
Analysis Model ◽  
Transformation Matrices ◽  
Beam Elements ◽  
Fea Model ◽  
Small Displacement Torsor ◽  
Variation Propagation ◽  
Error Accumulation

High-precision spindles have significant influence on the machining precision and finishing quality largely due to their motion errors. However, the analysis of rotation accuracy is quite not easy in design stage because of the neglecting of geometric errors and deformations of parts in the traditional dimension chains. Hence, a theoretical analysis model is built in present study to do the prediction. The 3D error accumulation path is recognized by Datum Flow Chain (DFC) and the key tolerances are modeled by Small Displacement Torsor (SDT). Thereafter, the variation propagation is conducted by Homogeneous Transformation Matrices (HTM) and the geometric misalignment in the spindle is calculated. Then, an FEA model is built with Timoshenko beam elements and the deformation is calculated after the geometric misalignment is applied to the model. As spindle rotates, the trajectory of the spindle nose is obtained. Finally, the Monte Carlo (MC) method is used to get the distribution and the range of motion errors. To verify the feasibility and reliability of the analysis model, the radial and axial motion errors of a double supported high-precision spindle are analyzed.

Semantic Representation of Flatness Based on ALC(R) and Mathematical Definition

2013 ◽  
Vol 662 ◽  
pp. 961-965
Author(s):  
Yun Feng Xie ◽  
Yu Lu Du ◽  
Yan Ru Zhong ◽  
Yu Chu Qin
Keyword(s):  
Semantic Representation ◽  
Heterogeneous Systems ◽  
Mathematical Representation ◽  
Small Displacement ◽  
3D Cad ◽  
Logical Language ◽  
Small Displacement Torsor ◽  
Tolerance Specification ◽  
Representation Language ◽  
Important Significance

The information of form tolerances in existing 3D CAD systems is just a kind of symbol and text which is lack of engineering semantic at present. Therefore, a reasonable explanation and Semantic representation of form tolerances has very important significance. In order to reduce the uncertainty and support the semantic interoperability in tolerance specification design, an approach for mathematical representation of flatness based on the Small Displacement Torsor (SDT) is proposed. Based on this, a representation of flatness using description logical language ALC(R) with concrete domain is proposed. Then flatness information is formalized using OWL, an ontology representation language devised by W3C, to be shared and interoperated between heterogeneous systems by building OWL ontology. At last, there is a practical example to verify the feasibility of this approach.

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.

Force Equilibrium Approach for Linearization of Constrained Mechanical System Dynamics

2003 ◽  
Vol 125 (1) ◽  
pp. 143-149 ◽  
Author(s):  
Ju Seok Kang ◽  
Sangwoo Bae ◽  
Jang Moo Lee ◽  
Tae Oh Tak
Keyword(s):  
Mechanical Systems ◽  
Nonlinear Dynamic Analysis ◽  
Differential Algebraic Equations ◽  
Dynamic Equations ◽  
Small Displacement ◽  
Algebraic Equations ◽  
Small Motion ◽  
Constrained Mechanical Systems ◽  
External Forces ◽  
Force Equilibrium

The purpose of this study is to derive a linearized form of dynamic equations for constrained mechanical systems. The governing equations for constrained mechanical systems are generally expressed in terms of Differential-Algebraic Equations (DAEs). Conventional methods of linearization are based on the perturbation of the nonlinear DAE, where small amounts of perturbations are taken to guarantee linear characteristics of the equations. On the other hand, the proposed linearized dynamic equations are derived directly from a force equilibrium condition, not from the DAEs, with small motion assumption. This approach is straightforward and simple compared to conventional perturbation methods, and can be applicable to any constrained mechanical systems that undergo small displacement under external forces. The modeling procedure and formulation of linearized dynamic equations are demonstrated by the example of a vehicle suspension system, a typical constrained multibody system. The solution is validated by comparison with conventional nonlinear dynamic analysis and modal test results.

Intelligent Optimization Design of the Cutting Unit’s Transmission System of a Shearer Based on Robustness

2021 ◽  
pp. 2158009
Author(s):  
Hongbin Gao ◽  
Junjun Chen
Keyword(s):  
Optimization Design ◽  
Design Method ◽  
Harmonic Balance Method ◽  
Optimization Method ◽  
Transmission System ◽  
Gear Transmission ◽  
Manufacturing Cost ◽  
Tooth Width ◽  
Gear Transmission System ◽  
Cutting Unit

To improve the robustness of the shearer cutting part and reduce the manufacturing cost, in this study, the gear transmission system of a shearer’s cutting unit can be divided into three basic components: single-gear-on-one-shaft form, the planetary reduction form, and double-gears-on-one-shaft form. The dynamic differential equations of each structure are established in this study, and the volume functions of the three basic components are obtained. The characteristics of the internal excitation of the gear transmission system are analyzed, and a scheme for solving the motion parameters of each component is formulated based on the harmonic balance method. Based on the parameters, such as tooth width, tooth number, and modulus, as optimized variables, a robust optimization method minimizing the multi-parameter evaluation function, which is weighted linearly by dimensionless vibration and volume of the gear transmission system, is presented. The gear transmission system of a sample shearer’s cutting unit is optimized using the proposed method. The results show that the transmission system’s size decreases by 5.4%, the drum’s maximum torsional acceleration decreases by 17.8%, and the first gear’s maximum torsional acceleration decreases by 9.6%. Thus, we conclude that the optimum design method decreases a shearer’s manufacturing cost and decreases the cutting unit’s failure rate.

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.

An on-line compensation method of a metrology-integrated robot system for high-precision assembly

2016 ◽  
Vol 43 (6) ◽  
pp. 647-656 ◽  
Author(s):  
Yifan Jiang ◽  
Xiang Huang ◽  
Shuanggao Li
Keyword(s):  
High Precision ◽  
Degrees Of Freedom ◽  
Compensation Method ◽  
Assembly Process ◽  
Robot System ◽  
Feed Forward ◽  
Content Type ◽  
Assembly Accuracy ◽  
On Line ◽  
Assembly Error

Purpose The purpose of this paper is to propose an on-line iterative compensation method combining with a feed-forward compensation method to enhance the assembly accuracy of a metrology-integrated robot system (MIRS). Design/methodology/approach By the integration of a six degrees of freedom (6DoF) measurement system (T-Mac), the robot’ movement can be tracked with real-time measurement. With the on-line measured data, the proposed iterative compensation for absolute positioning and the feed-forward compensation for relative linear motion are integrated into the assembly process to improve the assembly accuracy. Findings It is found that the MIRS exhibits good performance in both accuracy and efficiency with the application of the proposed compensation method. With the proposed assembly process, a component can be automatically aligned to the target in seconds, and the assembly error can be decreased to 0.021 mm for position and 0.008° for orientation on average. Originality/value This paper presents a 6DoF MIRS for high-precision assembly. Based on the system, a novel on-line compensation method is proposed to enhance the assembly accuracy. In this paper, the assembly accuracy and the corresponding distance parameter are given by a series of experiments as reference for assembly applications.

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