Selection of Optimum Assembly Gap Tolerance for Motor Assembly

Abstract

The parts in the motor assembly are divided into two types: fixed and variable. The tolerances of the fixed parts cannot be changed and the tolerances of the variable parts are calculated using three methodologies such as ME boost, ANFIS, and Cost function optimization.ME boost is an Excel add in used to calculate the tolerances of the variable parts. ANFIS is a neural network based optimization tool in matlab. Cost function is formulated for the variable parts in the assembly and optimized to calculate the tolerances. Then the tolerance for the assembly gap is calculated. The tolerances for the gap from the three methodologies are compared and optimum tolerance is considered for manufacturing.

Introduction

I. INTRODUCTION

The acceptable variation in the dimension of a part is called tolerance. Tolerances are of two types: unilateral tolerance and bilateral tolerance. Unilateral tolerances are symmetric on both the sides of the dimension whereas bilateral tolerances are non-symmetric on both sides of the dimension. In this work unilateral tolerances are considered. Gap is formed in few assemblies due to variation in dimensions. The procedure to calculate the tolerances for the gap is discussed in this paper. There are two types of parts in the assembly: fixed parts and the variable parts. In this paper three methodologies are used to calculate the tolerances for the variable parts. A loop diagram is used to represent the assembly gap along with the parts of the assembly. The dimensions of the parts from left to right in the loop diagram are considered positive and the dimensions of the parts from right to left in the loop diagram are considered negative.

In this paper,                                                   

1. The tolerances for the variable parts are calculated using three methodologies
2. Tolerance for the gap is calculated
3. The tolerances calculated using different methodologies is compared and optimum tolerance is selected.

II. RELATED WORK

Many researchers have been working on this topic since last two decades. A lot of literature is available and some related work is presented here. A workable analytical method for locating the optimum set of dimensional tolerances that minimizes the manufacturing costs is presented by Speckhart (1972) [3]. The technique of applying statistical methods to tolerance analysis of assemblies is described by Nigam and Turner (1995) [4]. An approach based on a new method called fuzzy comprehensive evaluation method and optimization through genetic algorithm is proposed by Ji et al. (2000) [5]. The distribution of tolerance on the component dimension of a complex assembly is found by Kumar et al. (2009) [8]. A new method called as decision support process along with Taguchi loss function to calculate the assembly gap tolerances is proposed by Abhishek Kumar et al. (2010) [6][7].  

III. METHODOLOGIES

A. ME Boost

ME boost is an excel add-in and has several modules such as Strength of materials, Mechanical design, Kinematics & Dynamics, Fluids, and Unit conversion. It covers a wide range of Mechanical Engineering areas. In the Mechanical design module of ME boost there is a sub module called tolerance calculator. The tolerance calculator interface is shown in the figure 1.

The distribution of tolerances is assumed normal and the mean dimension, standard deviation, sigma range, and the name of the part are given as inputs to calculate the tolerance.

B. ANFIS

The abbreviation for ANFIS is Adaptive Network based Fuzzy Interface System. It was developed based on Takagi-Sugeno fuzzy interface system in the form of artificial neural network in 1995 by Jang. It comprises of fuzzy IF-THEN rules and it can learn all kind of functions and approximates them. In anfis, the ambiguity of decisions is converted to mathematical models. This helps in the easy interpretation of the decisions. It is user friendly and has fewer errors. It is an inbuilt tool in matlab and can be used using simple commands such as anfisedit and fuzzy. The anfis edit command is used to train the network and the fuzzy command is used to predict the output for given inputs. The mean dimensions and standard deviations of the fixed parts are the inputs and the tolerances of the fixed parts are the outputs.

???????C. Cost Function Optimization

The cost function is

???????D. Fuzzy Comprehensive Evaluation Method [2]

In the Fuzzy Comprehensive Evaluation Method, the following fuzzy factors are taken into consideration:

1. Dimension Size (DS): The total length of the part.
2. Geometric Structure (GS): The shape of the part.
3. Material Machinability (MM): Degree of the machinability of the part.

4. Process Accuracy (PA): The degree of machining accuracy of the part.

The tolerance for the gap is calculated using three methodologies: ME boost, ANFIS, Cost function optimization. In ME boost and anfis the inputs are mean dimension and standard deviation. In the cost function optimization, the cost function is formulated using the machinability calculated using fuzzy comprehensive evaluation method and the cost function is optimized for minimum cost.

Conclusion

This work shows the calculation of assembly gap tolerances using three methodologies and their comparison. The tolerance calculated using cost function optimization is less and it results in greater assembly quality with optimum costs. The tolerance calculated using ME boost and anfis have very less difference. These tolerances can also be considered for manufacturing.

References

[1] Dimensioning and tolerancing handbook by Paul J. Drake, McGraw Hill publications. [2] Madhavi Reddy G V, Sreenivasulu Reddy A, “Assembly gap tolerance calculation using ANFIS and Cost function optimization”, IJRASET, Volume 10, Issue II, 2022. [3] F. H. Speckhart, “Calculation of tolerance based on a minimum costs approach”, Journal of Engineering for Industry, 5, pp. 447– 453, 1972. [4] Swami D Nigam, Joshua U Turner, “Review of statistical approaches to tolerance analysis”, Computer Aided Design, Volume 27, Issue 1, January 1995. [5] Ji, S., Li, X. and Cai, H., 2000. Optimal Tolerance Allocation Based on Fuzzy Comprehensive Evaluation and Genetic Algorithm. Manufacturing Review, 1 (1): pp. 50-59. [6] Abhishek Kumar, Lorens Goksel, Seung-Kyum Choi. \"Tolerance Allocation of Assemblies Using Fuzzy Comprehensive Evaluation and Decision Support Processes\", Volume 1: 36th Design Automation Conference, Parts A and B, 2010. [7] Abhishek Kumar, Seung-Kyum Choi, Lorens Goksel. \"Tolerance allocation of assemblies using fuzzy comprehensive evaluation and decision support process\", The International Journal of Advanced Manufacturing Technology, 2010. [8] Kumar, M. S., Kannan, S. M., & Jayabalan, V. (2009a). A new algorithm for optimum tolerance allocation of complex assemblies with alternative processes selection. The International Journal of Advanced Manufacturing Technology, 40(7-8), 819-836. [9] C. Qinghong, “Fuzzy comprehensive evaluation of design variables in mechanical reliability”, Fuzzy Techniques and Application (I), pp. 492–497, Beijing Aerospace University, 1994.

Copyright

Copyright © 2022 Madhavi Reddy G V, Vani S, Sreenivasulu Reddy A. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.