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Computerized tolerance techniques
Computers ind. Engng Vol. 21, Nos 1--4, pp. 165-172, 1991 Printed in Great Britain. All rights reserved
0360-8352/91 $3.00 + 0.00 Copyright © 1991 Pergamon Press pie
COMPUTERIZED TOLERANCE TECHNIQUES
MohAmmad Elhamul Huq and Hong-Chao Zhang
Department of Industrial Engineering Texas Tech University, Lubbock, Texas. 1984) in 1812 for the U.S. Army are amomg the earliest examples of massproduced items with interchangeable parts. These part are built by the use of m a t c h e d or c o m m o n fixtures, t o o l s and gages, w h i c h d u p l i c a t e d each part or process. These parts did not use s t a n d a r d m e a s u r e s , such as inches or millimeters.
ABSTRACT The i n t e n s e g l o b a l c o m p e t i t i o n to produce quality product at low cost has led m a n y i n d u s t r i a l n a t i o n s to consider m e c h a n i c a l tolerances as a key factor to bring about cost savings as well as be c o m p e t i t i v e . In the l a s t t w o d e c a d e s , not enough r e s e a r c h w o r k has b e e n done in the area of tolerance techniques. In this paper, a comprehensive summary of the state of the art and the projection of future trends in tolerance techniques is p r e s e n t e d to help m a k e a decision c o n c e r n i n g the improvement techniques today and to aid in guiding r e s e a r c h for t h e future. T h i s p a p e r r e v i e w s the s t a t u s of t h e o r y and practice about how manufacturing and assembly processes are characterized for relating tolerances to process or production cost. The s p e c i f i c a t i o n of t o l e r a n c i n g on the d i m e n s i o n of the m a n u f a c t u r e d part has a significant impact on the final production cost. Tight tolerances can r e s u l t in e x c e s s i v e p r o c e s s cost, w h i l e loose t o l e r a n c e s m a y lead to i n c r e a s e d w a s t e and a s s e m b l y problems. This paper systematically reviews the state of art by classifying the p a p e r s w r i t t e n so far into three categories. The categories are tolerance chain technique, tolerances based on analysis and synthesis, and t o l e r a n c e s b a s e d on c o s t - t o l e r a n c e algorithms and design methods. Future areas of research and the unresolved issues have been presented that will s e r v e as a g u i d i n g l i g h t for t h e researcher to investigate and bring about the solution in future.
S i n c e the W o r l d W a r II i n d u s t r y has witnessed a skyrocketing rise in accuracy requirement in e q u i p m e n t design for use in the industry. These requirements have stemmed directly from the increases in stress levels under which mechanical and electrical equipment is called upon to perform as well as the production of quality product at competitive prices. These requirements have led to the development of new and highly sophisticated gage and measurement tools.
INTRODUCTION
A tolerance c h a i n is b a s e d on manual t e c h n i q u e s d e v e l o p e d at the start of the century. Due to tedious and laborious c a l c u l a t i o n involved, the m e t h o d was not p o p u l a r till the e x p l o s i o n of c o m p u t e r t e c h n o l o g y ,
In order to control the d i m e n s i o n of machined parts, tolerancing charts have been used as early as 1950. The technique was mostly used in aircraft industry (Marks 1953) and the automobile industry (Anderson 1956). Due to the c o m p l e x i t y of the c h a r t itself and t h e e x c e s s i v e t i m e a n d e f f o r t r e q u i r e d to learn and p r a c t i c e the technique, it was not very popular in the industry. A u t h o r s like J o h n s o n (1954), Mooney (1955), Wade (1967), Gadzala (1959) p r o p o s e d d i f f e r e n t m e t h o d s to s i m p l i f y the charting technique. However, the t o l e r a n c e chart technique is still time-consuming and e r r o r prone. In 1982, Sack reported the use of tolerance chart in an a u t o m a t i c process-planning system. This report opened up a new and e f f i c i e n t w a y of c o m p u t e r i z e d t o l e r a n c e c h a r t i n g or c h a i n t e c h nique. T h i s p a p e r d e a l s w i t h t h e state of art s u r v e y of t o l e r a n c i n g techniques. TOLERANCE CHAIN TECHNIQUE
Tolerances w e r e f i r s t u s e d on engineering drawing at about the turn of century. It may be recalled that muskets built by Eli W h i t n e y (Lange 165
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which r e s u l t e d in the birth of computer aided t o l e r a n c i n g techniques. A c c c o r d i n g to Bjorke (1978), tolerance chart can also be interpreted as a c a s e of i n t e r r e l a t e d tolerance chain w i t h c o m m o n links. Bjorke, in his book about computer aided tolerancing, u s e s a u n i f i e d m e t h o d for t o l e r a n c e c a l c u l a t i o n and has developed an i n t e r a c t i v e computer p r o g r a m T O L T E C H by w h i c h real life t o l e r a n c e c a l c u l a t i o n s can be performed. B j o r k e u s e s the c o n c e p t of chain in calculation of tolerances. A chain is a sequence of elements such that each element in the sequence has one e n d p o i n t in c o m m o n w i t h its p r e d e s s o r in sequence and its other endpoint in common with its successor in a sequence. Chains can be elementary, simple, and interrelated (Fig. i). In the c a l c u l a t i o n of t o l e r a n c e control, the concept of sum dimension is used. In m e c h a n i c a l a s s e m b l i e s , some d i m e n s i o n s affect the function of t h e a s s e m b l y more than other dimensions. These dimension are denoted functional d i m e n s i o n or sum dimensions (Fig.2) . Statistical c a l c u l a t i o n is h e a v i l y u s e d in the control and distribution of t h e tolerances. K a r o l i n and A h l u w a l i a ( 1 9 8 6 ) h a v e developed a software called CATCcomputer aided tolerance control system, w h i c h employs graphic techn i q u e s for the a n a l y s i s of p r o c e s s t o l e r a n c e s . The r e s u l t of c o m p u t e r aided tolerances analysis is presented in the form of computer generated chart (Fig.3). Computer aided dimensional planning software developed by Davies and X i a o q i n g (1988) is also based on t o l e r a n c e chart method. It uses a m a t r i x - t r e e c h a i n m e t h o d to realize the trace p r o c e d u r e s on the c o m p u t e r to m a k e p o s s i b l e c a l c u l a tions and a d j u s t m e n t s of t o l e r a n c e s in the p r o c e s s of d i m e n s i o n a l planning. In t h i s s o f t w a r e , initial t o l e r a n c e s are being assigned based
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Huq and Zhang: Computerized Tolerance Techniques considers alternative machine selection within the desired tolerance range, p r o c e s s capabilities constraint on tolerance value, variation in manufacturing cost, and the optimization of interdependent tolerance stackup. The advantages of t h i s method are 1. It is e a s y connections between tional dimensions•
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2. It is h e l p f u l to c o r r e c t l y calculate dimensional chains. 3. It is capable of checking the c o r r e c t n e s s of final dimensions and tolerances against part designs and the s u f f i c i e n c y of a l l o w a n c e for operations and thus finding out problems (if any ) existing in process plans. The disadvantages of this method is discussed by Zhang and Mei (1991). The Zhang and Mei paper comes up with a new m e t h o d of analysis that takes care of the disadvantages, which are as follows: i. It d o e s not d i s c u s s o p e r a tional dimensioning from the point of view of NC machines. The selection of datum elements, setups, o p e r a t i o n dimensioning s h o u l d be d e t e r m i n e d before a p p l y i n g O p e r a t i o n Dimension Tolerancing Chain to NC machines.
2. In order for NC machines to perform accurately, the NC programming should include all start and end co-ordinates of tool movement for all operational dimension. 3. A l s o , d u e to a c c u r a c y requirement, the paper does not discuss any fixtures requirements to facilitate the operation. Another computer based analysis software using tolerancing system b a s e d on ISO on s i z e and p o s i t i o n tolerance was developed by Weill and Bourdet (1986). The theory behind the a l g o r i t h m in this s o f t w a r e was developed by Bourdet and is in contrast to traditional tolerance chain theories; it c o n s i d e r s tolerances of p o s i t i o n as w e l l as t o l e r a n c e s of machining• It makes a clear distinction between independent and dependent variables. It takes into account the main factors influencing tolerancing, i.e, m a c h i n i n g errors, setting errors, w o r k p i e c e p o s i t i o n i n g errors, and w e a r of tools, and it proposes an optimization strategy for the d e t e r m i n a t i o n of setting dimensions. One advantage of this software is t h a t it c a n be i n s t a l l e d on a m i c r o - c o m p u t e r , m a k i n g it f l e x i b l e and accessible to small size industries. F u t u r e d e v e l o p m e n t of t h i s s o f t w a r e m a y include 3 - D i m e n s i o n a l tolerancing.
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A N A L Y S I 8 AND S Y N T H E S I S OF T O L E R A N C I N G
As r e g a r d s t h e p a p e r s b a s e d on analysis and synthesis of tolerancing, T.C. Woo and W. Lee (1990) may be c o m m e n d e d for d e v e l o p i n g a new procedure for tolerance synthesis by distributing tolerances so as to satisfy the stackup condition. Figure 4 shows the basic scheme for tolerances synthesis. As a global criterion, c o s t m i n i m i z a t i o n is u s e d . P r o b a b i l i s t i c concept for synthesis and analysis are introduced. In terms of tolerance and dimensions, areas of i n t e r e s t to m a n u f a c t u r i n g a n d to design are defined as t o l e r a n c e region and safe region, respectively. Also, Woo (1989) provides a branch and bound based algorithm for ensuring optimum selection of tolerances using various manufacturing process, m i n i m i z a t i o n of m a n u f a c t u r i n g cost under constraint of tolerance stackup. From the t o l e r a n c e analysis point of view, the two most common methods, worst case and root sum squares, are discussed by Greenwood and Chase (1988) (Fig.5). Further, Greenwood and Chase (1987) p r o p o s e d a new m e t h o d c a l l e d U n i f i e d model of t o l e r a n c e s analysis based on p r o c e s s mean shifts. It i n c l u d e s w o r s t case and root mean square as extreme cases, and anything can be simulated between these extreme conditions with significant improvement in the model. With regard to the computer simulation software TOLCON developed by Lehthihet and Dindelli (1989). TOLCON is based on mathematical relationship between functional requirement (resultant parts) and the individual part or dimensions. The system provides a library of d i s t r i b u t i o n s to model stochastic dimensions or process in t o l e r a n c i n g . T h e n it u s e s Monte Carlo simulation for combinat i o n of s t o c h a s t i c variables and gives a graphical output. COST T O L E R A N C E A L G O R T I H M S
Lastly, p a p e r s u s i n g t o l e r a n c e s based on cost-tolerance algorithm and The design method are discussed. authors Wu and Elmaraghy (1988) have, in their paper, mentioned the importance of proper selection of design tolerance of manufactured parts as a key element to increase productivity, c o n t r o l p r o d u c t q u a l i t y and y i e l d significant savings. The authors discussed eight tolerance analysis model and f i v e c o s t - t o l e r a n c e function model such as S u t h e r l a n d function, reciprocal square function, exponential function, and M i c h r a l - S i d d a l l function. Chase and Greenwood (1990) had done contribution from the design
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Huq and Zhang: Computerized Tolerance Techniques point of view in tolerances analysis. Figure. 6 shows the r e l a t i o n s h i p of t o l e r a n c e to b o t h e n g i n e e r i n g a n d manufacturing. In their paper, they discuss tolerance allocation using o p t i m i z a t i o n t e c h n i q u e s viz c o s t versus tolerance function, tolerances allocation by langrange multipliers, and o t h e r t e c h n i q u e s . The author s u g g e s t s t h a t in o r d e r to m a k e advanced tolerances analysis and optimization methods available for tolerance allocation by designers, quality control t e c h n i q u e s m u s t be used to d e t e r m i n e p r o c e s s c a p a b i l i t i e s and track cost. Figure. 7 shows the typical cost-versus-tolerance function. D o n g a n d S o o m (1989) h a v e d e scribed a p r o d u c t i o n c o s t - p r e c i s i o n model to be used for optimal tolerance design. A tolerance design o p t i m i z a t i o m is formulated based on m i n i m u m cost for d i m e n s i o n chain as well as for related dimension chain. An expert system approach is used for methods of classifying and utilizing limited production data, determining parameters of production cost-precision relations, and automatic associating design tolerances. The author illustrates the design problem by an example. Oswald and Blake (1989) describe a new method of estimating part cost as a function of tolerance. First, specific costs are determined for stated tolerances for an example part. These data are then fitted to a series of cost-tolerance models that
currently in use, and the results analyzed for accuracy. A means of a d a p t i n g a c o s t - t o l e r a n c e m o d e l to account for specific aspects of p r o d u c t i o n p r o c e s s e s is d e s c r i b e d . Kim a n d K n o t t (1988) h a v e u s e d a pseudo-Boolean approach to determining least cost tolerances. Analysis of tolerances is considered from two points of view; first is the arithmetic approach, u s i n g the i n t e g e r programming approach as suggested by O s t w a l d and Huang (1977). Second is aspect, which is c o n s i d e r e d the nature of the variance of the tolerances of the components in the assembly. The author uses arithmetic and statistical model with examples. M i c h a e l and S i d d a l l ( 1981, 1982 ) proposes an approach that integrates the r e l a t i o n s h i p between the design and the production departments based on the theory of nonlinear optimization. It attempts to cope with the problem of o p t i m a l l y allocating tolerances in a m a n u f a c t u r i n g process. In order to minimize the production cost with allowance for system scrap percentage, the upper and lower limits of the random variables of an e n g i n e e r i n g system are assigned. An important distinction between the design and the manufacturing scrap is explained, and the cell technique is utilized to estimate efficiently the system scrap. Sayed and Kheir (1985) have developed a computer program for m i n i m u m cost t o l e r a n c e a s s i g n m e n t . are are
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The software accepts a systems topology, n o m i n a l component values, a figure-of-merit for system performance, a n d i n f o r m a t i o n relating a component cost to its tolerance. The output of the p r o g r a m includes the set of component tolerances that will p r o d u c e the least e x p e n s i v e d e s i g n with i00 p e r c e n t yield. The a u t h o r uses an example from electronics to explain the technique.
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TRENDS
Present theories on m e c h a n i c a l tolerances such as vector tolerancing, v a r i a t i o n a l geometry, nonparametric tolerancing are still in infancy and need further development, refinement, and validation. There is a need for c o m p a r a t i v e analysis for these different theories. Future research should be addressed to the d e v e l o p m e n t of s o u n d m a t h e m a t i c a l foundation for computer representation of t o l e r a n c e s in parts, assemblies, and in algorithms for different tasks such as analysis and synthesis of part tolerances on those of assembly, and m a n u f a c t u r i n g process plans.
It is worthwhile to mention that current standard ANSI Y 14.5 (1983) and ISO does have lot of misintrepret a t i o n and a m b i g u i t i e s . T h e r e is a need to d e t e r m i n e the m a t h e m a t i c a l definition for these standards. The representation-free and noncomputatonal d e f i n i t i o n will r e d u c e the dependencies on special conditions and coordinate the system and the choices of origin, thus making the standards more versatile and user friendly. Also, due to advances in computer technology, the traditional inspection methods s u c h as f u n c t i o n a l gaging are being replaced by computer assisted inspection methods like CMM, laser, t h e o d o l i t e , optical gaging machine. There are no standard procedures and algorithms for these c o m p u t e r i z e d inspections methods to perform tolerance inspections on the manufactured part or assembly. Potential research areas are the development of surface point density, curve and s u r f a c e f i t t i n g a l g o r i t h m from different m e a s u r i n g systems used in the industry. F u t u r e t r e n d s in t h i s p a p e r covers the topics about AI techniques most of the w o r k done have been the development of expert systems. EXDEM (Janakiram 1989) developed on ICC2900 computer at IIT New Delhi is based on rule based expert system. The system developed assigns tolerances on d i m e n s i o n s of p a r t s a u t o m a t i c a l l y and captures the reasoning of designer as well as manufacturer in determining the suitable tolerance values. A n o t h e r e x p e r t s y s t e m d e v e l o p e d by Manivannan and Egbelu is R O S C A T (1989) a rule based system. It uses ISO s p e c i f i c a t i o n of fits for manufacture of rotational components with interference, clearance and transition fit types. It is implemented on an I B M 4 3 8 1 s y s t e m u s i n g L I S P V M language. Further, the application of n e u r a l n e t w o r k s in c o m p u t e r a i d e d tolerancing has yet to be seen. Another area where further investigation is needed is in manufacturing process variability. It is well r e c o g n i z e d t h a t for the p a r t s and assemblies to satisfy the specified tolerances, the manufacturing process must be selected, set up, and maintained well within the tolerable limits in v i e w of the t e n d e n c i e s of most m a n u f a c t u r i n g process to drift and exhibit dispersion due to inherent v a r i a b i l i t i e s of w o r k p i e c e and tool materials, and processing parameters. The current state of knowledge of m a n u f a c t u r i n g process variabilities should be significantly improved if this vital data are to be useful for statistical tolerancing. Process
Huq and Zhang: Computerized Tolerance Techniques models that describe capabilities and variabilities m u s t be d e v e l o p e d . Systematic m e t h o d o l o g i e s are needed for modeling processes for the purpose of evaluating processing alternative for given tolerances.
171
Fainguelunt, D., Weill, R°, and Bourdet, P., 1986, "Computer Aided Tolerancing and Dimensioning in Process Planning," Annals of CIRP, vol 35, pp. 381-386. G a d z a l a , J.L., 1959 , " D i m e n sional control i_nnPrecision Manufacturinq," McGraw-Hill, New York.
SUMMARY
In t h i s p a p e r , a s u r v e y of t h e state-of-the-art of t o l e r a n c i n g is discussed. Tolerance techniques have been classified into three major categories. Each c a t e g o r y has been discussed in detail, and the areas of future research have been pinpointed. Futhermore, the p o t e n t i a l areas of future research as described in this p a p e r w i l l o p e n up a n e w e r a of r e s e a r c h in the a r e a of t o l e r a n c e technique. About 30 papers have been read and referenced in this paper.
REFERENCES
:
A h l u w a l i a , R.S., and Karolin, A.V., 1986, "CATC- a Computer Aided Tolerance Control System," Journal of Manufacturing Systems, 3, pp. 153160. American National Institute (ANSI, 1983)
Standard
Irani, S.A., Mittal, R.O., and Lehtihet, E.A., 1989, "Tolerance Chart Optimization," Int. Journal of Production Research vol. 27, no. 9, pp. 1531-1552. Johnson, A., 1954, "Index tolerance chart s i m p l i f i e s p r o d u c t i o n , " The Tool Enaineer, 32(2), pp. 53-62, February. Kim, S.H., and Knott, K., 1988, "A psuedo-boolean approach to determining least cost tolerances," International J o u r n a l of p r o d u c t i o n Research, vol. 26, no. i, pp. 157-167. Lange, J. C. , 1 9 8 4 , Design Dimensionina with Computer Graphics ADDlication., Marcel Dekker Inc., New york. Lee, W., and Woo, T.C., 1989, "Optimum Selection of Discrete Tolerances," Journal of Mechanisms, Transmissions, and Automation in Design, vol. iii, June, pp. 243-249.
Anderson , J . F . ,Jr. 1 9 5 6 , "Assembly tolerance charts save time and m o n e y , " The Tool Enaineer, 37(6), pp. 95-97, Dec.
Lee, W., and Woo, T.C., 1990, "Tolerances: Their Analysis and Synthesis," J o u r n a l of E n u i n e e r i n a for Industry vol. 112, pp. 113-119.
Bjorke, O., 1989, Computer-Aided Tolerancinq 2nd edition., ASME Press, New York.
L e h t i h e t , E.A., and D i n d e l l i , B.A., 1989, "TOLCON: M i c r o c o m p u t e r based module for Simulation of Tolerances," M a n u f a c t u r i n g Review vol.3, Sep.
Chase, K.W.,and Greenwood, W.H., 1988, "Design Issues in Mechanical Tolerances Analysis," Manufacturina Review vol. i, no. i, pp. 50-59. C h a s e , K.W. , a n d G r e e n w o o d , W.H., 1987, "A new Tolerance Analysis Method for Designers and Manufacturers," Journal of Engineering for Industry, vol. 109, pp. 112-116. Chase, K.W., Greenwood, W.H. and et al. 1990, "Least cost Tolerances Allocation for Mechanical Assemblies with A u t o m a t e d Process Selection," Manufacturina Review , vol. 3, no. i, pp. 44-59. Dong, Z., a n d S o o m A., 1989, "Optimal Tolerancing Design with Automatic Incorporation of Manufacturing Knowledge," IIE I n t e a r a t e d Systems Conference.
Marks, C.J., 1953, " T o l e r a n c e Chart control production machining", American Machinist 97(5), March, pp.l14-116. Manivannan, S., and Egbelu, P.J., 1989, "A Knowledge Based System for the S p e c i f i c a t i o n of M a n u f a c t u r i n g Tolerances," Journal o_ffManufacturinq System vol. 8, no. 2, pp. 153-160. Micheal, W., Siddal, J.N., 1981, "The O p t i m i z a t i o n Problems with Optimal Tolerance Assignment and Full Acceptance," ASME MeGhanical Design, 842-845. ,"The
TR~N i Journal o_~f vol. 103, Oct, pp.
Michael, W., Siddal, Optimal Tolerance
J.N., 1982 Assignment
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With Less Than Full Acceptance, "ASME TRANS: Journal of Mechanical Desiun, vol. 104, Oct, pp. 855-860. M o o n e y , C.T., 1955, " H o w to adjust tolerance charts", The Tool Enaineer , 35(4), pp. 75-81, Oct. Oswald, P.F., Blake,M.O., 1989, "Estimating Cost Associated with Dimensional Tolerance," Manufacturing Review vol. 2, no.4, pp. 277-282. Oswald, P.F., Huang J., 1977, "A method for Optimal Tolerance Selection," J o u r n a l of E n u i n e e r i n g for Industry, August, pp. 358-363. Parkinson, D.B.,1982, "The application of Reliability Methods to Tolerancing," Journal of Mechanical Design, vol. 104, pp. 613-617. SacK Jr., C.F., 1982 " Computer managed process planning - a bridge b e t w e e n CAD and CAM ," A U T O F A C T 4, Philadelphia, Pennsylvania, pp. 7.157.31, 30 November - 2 December. Syed, S.E., Kheir, N.A., 1985, "An efficient Techniques for Minimumcost Tolerancing Assignment, "Simulation , April. Wade, O.R., 1967, Tolerance Control i__nnDesign and Manufacturing, New York, Industrial Press. Inc. Weil, R., 1988, " I n t e g r a t i n g Dimensional and Tolerancing in Computer-Aided Process Planning," Robotics and ComDuter-Inteurated Manufacturing , vol. 4, no. 1/2, pp. 41-48. Wu , Z., and Ehlmaraghy, H.A., 1988, "Evaluation of Cost-Tolerances Algorithms for D e s i g n T o l e r a n c e s Analysis and Synthesis," Manufacturina Review vol.
I, no. 3, pp.168-178.
X i a o q i n g , T., D a v i e s , B.J., 1988, " C o m p u t e r A i d e d D i m e n s i o n a l Planning ," International Journal of Research voi.26, pp. 283-297. Zhang, Y.Z., Zhang, J.K.L., et al. 1989, " O p e r a t i o n a l Dimensional and T o l e r a n c e s C a l c u l a t i o n in CAPP System for Precesion Manufacturing ,,, Annals of CIRP , 38(1). Zhang, H.C., Mei, J., et al. 1991, "Operational Dimensioning and Tolerancing in CAPP," Annals of CIRP vol. 40/1 (To appear).
0360-8352/91 $3.00 + 0.00 Copyright © 1991 Pergamon Press pie
COMPUTERIZED TOLERANCE TECHNIQUES
MohAmmad Elhamul Huq and Hong-Chao Zhang
Department of Industrial Engineering Texas Tech University, Lubbock, Texas. 1984) in 1812 for the U.S. Army are amomg the earliest examples of massproduced items with interchangeable parts. These part are built by the use of m a t c h e d or c o m m o n fixtures, t o o l s and gages, w h i c h d u p l i c a t e d each part or process. These parts did not use s t a n d a r d m e a s u r e s , such as inches or millimeters.
ABSTRACT The i n t e n s e g l o b a l c o m p e t i t i o n to produce quality product at low cost has led m a n y i n d u s t r i a l n a t i o n s to consider m e c h a n i c a l tolerances as a key factor to bring about cost savings as well as be c o m p e t i t i v e . In the l a s t t w o d e c a d e s , not enough r e s e a r c h w o r k has b e e n done in the area of tolerance techniques. In this paper, a comprehensive summary of the state of the art and the projection of future trends in tolerance techniques is p r e s e n t e d to help m a k e a decision c o n c e r n i n g the improvement techniques today and to aid in guiding r e s e a r c h for t h e future. T h i s p a p e r r e v i e w s the s t a t u s of t h e o r y and practice about how manufacturing and assembly processes are characterized for relating tolerances to process or production cost. The s p e c i f i c a t i o n of t o l e r a n c i n g on the d i m e n s i o n of the m a n u f a c t u r e d part has a significant impact on the final production cost. Tight tolerances can r e s u l t in e x c e s s i v e p r o c e s s cost, w h i l e loose t o l e r a n c e s m a y lead to i n c r e a s e d w a s t e and a s s e m b l y problems. This paper systematically reviews the state of art by classifying the p a p e r s w r i t t e n so far into three categories. The categories are tolerance chain technique, tolerances based on analysis and synthesis, and t o l e r a n c e s b a s e d on c o s t - t o l e r a n c e algorithms and design methods. Future areas of research and the unresolved issues have been presented that will s e r v e as a g u i d i n g l i g h t for t h e researcher to investigate and bring about the solution in future.
S i n c e the W o r l d W a r II i n d u s t r y has witnessed a skyrocketing rise in accuracy requirement in e q u i p m e n t design for use in the industry. These requirements have stemmed directly from the increases in stress levels under which mechanical and electrical equipment is called upon to perform as well as the production of quality product at competitive prices. These requirements have led to the development of new and highly sophisticated gage and measurement tools.
INTRODUCTION
A tolerance c h a i n is b a s e d on manual t e c h n i q u e s d e v e l o p e d at the start of the century. Due to tedious and laborious c a l c u l a t i o n involved, the m e t h o d was not p o p u l a r till the e x p l o s i o n of c o m p u t e r t e c h n o l o g y ,
In order to control the d i m e n s i o n of machined parts, tolerancing charts have been used as early as 1950. The technique was mostly used in aircraft industry (Marks 1953) and the automobile industry (Anderson 1956). Due to the c o m p l e x i t y of the c h a r t itself and t h e e x c e s s i v e t i m e a n d e f f o r t r e q u i r e d to learn and p r a c t i c e the technique, it was not very popular in the industry. A u t h o r s like J o h n s o n (1954), Mooney (1955), Wade (1967), Gadzala (1959) p r o p o s e d d i f f e r e n t m e t h o d s to s i m p l i f y the charting technique. However, the t o l e r a n c e chart technique is still time-consuming and e r r o r prone. In 1982, Sack reported the use of tolerance chart in an a u t o m a t i c process-planning system. This report opened up a new and e f f i c i e n t w a y of c o m p u t e r i z e d t o l e r a n c e c h a r t i n g or c h a i n t e c h nique. T h i s p a p e r d e a l s w i t h t h e state of art s u r v e y of t o l e r a n c i n g techniques. TOLERANCE CHAIN TECHNIQUE
Tolerances w e r e f i r s t u s e d on engineering drawing at about the turn of century. It may be recalled that muskets built by Eli W h i t n e y (Lange 165
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which r e s u l t e d in the birth of computer aided t o l e r a n c i n g techniques. A c c c o r d i n g to Bjorke (1978), tolerance chart can also be interpreted as a c a s e of i n t e r r e l a t e d tolerance chain w i t h c o m m o n links. Bjorke, in his book about computer aided tolerancing, u s e s a u n i f i e d m e t h o d for t o l e r a n c e c a l c u l a t i o n and has developed an i n t e r a c t i v e computer p r o g r a m T O L T E C H by w h i c h real life t o l e r a n c e c a l c u l a t i o n s can be performed. B j o r k e u s e s the c o n c e p t of chain in calculation of tolerances. A chain is a sequence of elements such that each element in the sequence has one e n d p o i n t in c o m m o n w i t h its p r e d e s s o r in sequence and its other endpoint in common with its successor in a sequence. Chains can be elementary, simple, and interrelated (Fig. i). In the c a l c u l a t i o n of t o l e r a n c e control, the concept of sum dimension is used. In m e c h a n i c a l a s s e m b l i e s , some d i m e n s i o n s affect the function of t h e a s s e m b l y more than other dimensions. These dimension are denoted functional d i m e n s i o n or sum dimensions (Fig.2) . Statistical c a l c u l a t i o n is h e a v i l y u s e d in the control and distribution of t h e tolerances. K a r o l i n and A h l u w a l i a ( 1 9 8 6 ) h a v e developed a software called CATCcomputer aided tolerance control system, w h i c h employs graphic techn i q u e s for the a n a l y s i s of p r o c e s s t o l e r a n c e s . The r e s u l t of c o m p u t e r aided tolerances analysis is presented in the form of computer generated chart (Fig.3). Computer aided dimensional planning software developed by Davies and X i a o q i n g (1988) is also based on t o l e r a n c e chart method. It uses a m a t r i x - t r e e c h a i n m e t h o d to realize the trace p r o c e d u r e s on the c o m p u t e r to m a k e p o s s i b l e c a l c u l a tions and a d j u s t m e n t s of t o l e r a n c e s in the p r o c e s s of d i m e n s i o n a l planning. In t h i s s o f t w a r e , initial t o l e r a n c e s are being assigned based
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Huq and Zhang: Computerized Tolerance Techniques considers alternative machine selection within the desired tolerance range, p r o c e s s capabilities constraint on tolerance value, variation in manufacturing cost, and the optimization of interdependent tolerance stackup. The advantages of t h i s method are 1. It is e a s y connections between tional dimensions•
to find real related opera-
2. It is h e l p f u l to c o r r e c t l y calculate dimensional chains. 3. It is capable of checking the c o r r e c t n e s s of final dimensions and tolerances against part designs and the s u f f i c i e n c y of a l l o w a n c e for operations and thus finding out problems (if any ) existing in process plans. The disadvantages of this method is discussed by Zhang and Mei (1991). The Zhang and Mei paper comes up with a new m e t h o d of analysis that takes care of the disadvantages, which are as follows: i. It d o e s not d i s c u s s o p e r a tional dimensioning from the point of view of NC machines. The selection of datum elements, setups, o p e r a t i o n dimensioning s h o u l d be d e t e r m i n e d before a p p l y i n g O p e r a t i o n Dimension Tolerancing Chain to NC machines.
2. In order for NC machines to perform accurately, the NC programming should include all start and end co-ordinates of tool movement for all operational dimension. 3. A l s o , d u e to a c c u r a c y requirement, the paper does not discuss any fixtures requirements to facilitate the operation. Another computer based analysis software using tolerancing system b a s e d on ISO on s i z e and p o s i t i o n tolerance was developed by Weill and Bourdet (1986). The theory behind the a l g o r i t h m in this s o f t w a r e was developed by Bourdet and is in contrast to traditional tolerance chain theories; it c o n s i d e r s tolerances of p o s i t i o n as w e l l as t o l e r a n c e s of machining• It makes a clear distinction between independent and dependent variables. It takes into account the main factors influencing tolerancing, i.e, m a c h i n i n g errors, setting errors, w o r k p i e c e p o s i t i o n i n g errors, and w e a r of tools, and it proposes an optimization strategy for the d e t e r m i n a t i o n of setting dimensions. One advantage of this software is t h a t it c a n be i n s t a l l e d on a m i c r o - c o m p u t e r , m a k i n g it f l e x i b l e and accessible to small size industries. F u t u r e d e v e l o p m e n t of t h i s s o f t w a r e m a y include 3 - D i m e n s i o n a l tolerancing.
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A N A L Y S I 8 AND S Y N T H E S I S OF T O L E R A N C I N G
As r e g a r d s t h e p a p e r s b a s e d on analysis and synthesis of tolerancing, T.C. Woo and W. Lee (1990) may be c o m m e n d e d for d e v e l o p i n g a new procedure for tolerance synthesis by distributing tolerances so as to satisfy the stackup condition. Figure 4 shows the basic scheme for tolerances synthesis. As a global criterion, c o s t m i n i m i z a t i o n is u s e d . P r o b a b i l i s t i c concept for synthesis and analysis are introduced. In terms of tolerance and dimensions, areas of i n t e r e s t to m a n u f a c t u r i n g a n d to design are defined as t o l e r a n c e region and safe region, respectively. Also, Woo (1989) provides a branch and bound based algorithm for ensuring optimum selection of tolerances using various manufacturing process, m i n i m i z a t i o n of m a n u f a c t u r i n g cost under constraint of tolerance stackup. From the t o l e r a n c e analysis point of view, the two most common methods, worst case and root sum squares, are discussed by Greenwood and Chase (1988) (Fig.5). Further, Greenwood and Chase (1987) p r o p o s e d a new m e t h o d c a l l e d U n i f i e d model of t o l e r a n c e s analysis based on p r o c e s s mean shifts. It i n c l u d e s w o r s t case and root mean square as extreme cases, and anything can be simulated between these extreme conditions with significant improvement in the model. With regard to the computer simulation software TOLCON developed by Lehthihet and Dindelli (1989). TOLCON is based on mathematical relationship between functional requirement (resultant parts) and the individual part or dimensions. The system provides a library of d i s t r i b u t i o n s to model stochastic dimensions or process in t o l e r a n c i n g . T h e n it u s e s Monte Carlo simulation for combinat i o n of s t o c h a s t i c variables and gives a graphical output. COST T O L E R A N C E A L G O R T I H M S
Lastly, p a p e r s u s i n g t o l e r a n c e s based on cost-tolerance algorithm and The design method are discussed. authors Wu and Elmaraghy (1988) have, in their paper, mentioned the importance of proper selection of design tolerance of manufactured parts as a key element to increase productivity, c o n t r o l p r o d u c t q u a l i t y and y i e l d significant savings. The authors discussed eight tolerance analysis model and f i v e c o s t - t o l e r a n c e function model such as S u t h e r l a n d function, reciprocal square function, exponential function, and M i c h r a l - S i d d a l l function. Chase and Greenwood (1990) had done contribution from the design
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Huq and Zhang: Computerized Tolerance Techniques point of view in tolerances analysis. Figure. 6 shows the r e l a t i o n s h i p of t o l e r a n c e to b o t h e n g i n e e r i n g a n d manufacturing. In their paper, they discuss tolerance allocation using o p t i m i z a t i o n t e c h n i q u e s viz c o s t versus tolerance function, tolerances allocation by langrange multipliers, and o t h e r t e c h n i q u e s . The author s u g g e s t s t h a t in o r d e r to m a k e advanced tolerances analysis and optimization methods available for tolerance allocation by designers, quality control t e c h n i q u e s m u s t be used to d e t e r m i n e p r o c e s s c a p a b i l i t i e s and track cost. Figure. 7 shows the typical cost-versus-tolerance function. D o n g a n d S o o m (1989) h a v e d e scribed a p r o d u c t i o n c o s t - p r e c i s i o n model to be used for optimal tolerance design. A tolerance design o p t i m i z a t i o m is formulated based on m i n i m u m cost for d i m e n s i o n chain as well as for related dimension chain. An expert system approach is used for methods of classifying and utilizing limited production data, determining parameters of production cost-precision relations, and automatic associating design tolerances. The author illustrates the design problem by an example. Oswald and Blake (1989) describe a new method of estimating part cost as a function of tolerance. First, specific costs are determined for stated tolerances for an example part. These data are then fitted to a series of cost-tolerance models that
currently in use, and the results analyzed for accuracy. A means of a d a p t i n g a c o s t - t o l e r a n c e m o d e l to account for specific aspects of p r o d u c t i o n p r o c e s s e s is d e s c r i b e d . Kim a n d K n o t t (1988) h a v e u s e d a pseudo-Boolean approach to determining least cost tolerances. Analysis of tolerances is considered from two points of view; first is the arithmetic approach, u s i n g the i n t e g e r programming approach as suggested by O s t w a l d and Huang (1977). Second is aspect, which is c o n s i d e r e d the nature of the variance of the tolerances of the components in the assembly. The author uses arithmetic and statistical model with examples. M i c h a e l and S i d d a l l ( 1981, 1982 ) proposes an approach that integrates the r e l a t i o n s h i p between the design and the production departments based on the theory of nonlinear optimization. It attempts to cope with the problem of o p t i m a l l y allocating tolerances in a m a n u f a c t u r i n g process. In order to minimize the production cost with allowance for system scrap percentage, the upper and lower limits of the random variables of an e n g i n e e r i n g system are assigned. An important distinction between the design and the manufacturing scrap is explained, and the cell technique is utilized to estimate efficiently the system scrap. Sayed and Kheir (1985) have developed a computer program for m i n i m u m cost t o l e r a n c e a s s i g n m e n t . are are
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The software accepts a systems topology, n o m i n a l component values, a figure-of-merit for system performance, a n d i n f o r m a t i o n relating a component cost to its tolerance. The output of the p r o g r a m includes the set of component tolerances that will p r o d u c e the least e x p e n s i v e d e s i g n with i00 p e r c e n t yield. The a u t h o r uses an example from electronics to explain the technique.
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TRENDS
Present theories on m e c h a n i c a l tolerances such as vector tolerancing, v a r i a t i o n a l geometry, nonparametric tolerancing are still in infancy and need further development, refinement, and validation. There is a need for c o m p a r a t i v e analysis for these different theories. Future research should be addressed to the d e v e l o p m e n t of s o u n d m a t h e m a t i c a l foundation for computer representation of t o l e r a n c e s in parts, assemblies, and in algorithms for different tasks such as analysis and synthesis of part tolerances on those of assembly, and m a n u f a c t u r i n g process plans.
It is worthwhile to mention that current standard ANSI Y 14.5 (1983) and ISO does have lot of misintrepret a t i o n and a m b i g u i t i e s . T h e r e is a need to d e t e r m i n e the m a t h e m a t i c a l definition for these standards. The representation-free and noncomputatonal d e f i n i t i o n will r e d u c e the dependencies on special conditions and coordinate the system and the choices of origin, thus making the standards more versatile and user friendly. Also, due to advances in computer technology, the traditional inspection methods s u c h as f u n c t i o n a l gaging are being replaced by computer assisted inspection methods like CMM, laser, t h e o d o l i t e , optical gaging machine. There are no standard procedures and algorithms for these c o m p u t e r i z e d inspections methods to perform tolerance inspections on the manufactured part or assembly. Potential research areas are the development of surface point density, curve and s u r f a c e f i t t i n g a l g o r i t h m from different m e a s u r i n g systems used in the industry. F u t u r e t r e n d s in t h i s p a p e r covers the topics about AI techniques most of the w o r k done have been the development of expert systems. EXDEM (Janakiram 1989) developed on ICC2900 computer at IIT New Delhi is based on rule based expert system. The system developed assigns tolerances on d i m e n s i o n s of p a r t s a u t o m a t i c a l l y and captures the reasoning of designer as well as manufacturer in determining the suitable tolerance values. A n o t h e r e x p e r t s y s t e m d e v e l o p e d by Manivannan and Egbelu is R O S C A T (1989) a rule based system. It uses ISO s p e c i f i c a t i o n of fits for manufacture of rotational components with interference, clearance and transition fit types. It is implemented on an I B M 4 3 8 1 s y s t e m u s i n g L I S P V M language. Further, the application of n e u r a l n e t w o r k s in c o m p u t e r a i d e d tolerancing has yet to be seen. Another area where further investigation is needed is in manufacturing process variability. It is well r e c o g n i z e d t h a t for the p a r t s and assemblies to satisfy the specified tolerances, the manufacturing process must be selected, set up, and maintained well within the tolerable limits in v i e w of the t e n d e n c i e s of most m a n u f a c t u r i n g process to drift and exhibit dispersion due to inherent v a r i a b i l i t i e s of w o r k p i e c e and tool materials, and processing parameters. The current state of knowledge of m a n u f a c t u r i n g process variabilities should be significantly improved if this vital data are to be useful for statistical tolerancing. Process
Huq and Zhang: Computerized Tolerance Techniques models that describe capabilities and variabilities m u s t be d e v e l o p e d . Systematic m e t h o d o l o g i e s are needed for modeling processes for the purpose of evaluating processing alternative for given tolerances.
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SUMMARY
In t h i s p a p e r , a s u r v e y of t h e state-of-the-art of t o l e r a n c i n g is discussed. Tolerance techniques have been classified into three major categories. Each c a t e g o r y has been discussed in detail, and the areas of future research have been pinpointed. Futhermore, the p o t e n t i a l areas of future research as described in this p a p e r w i l l o p e n up a n e w e r a of r e s e a r c h in the a r e a of t o l e r a n c e technique. About 30 papers have been read and referenced in this paper.
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Standard
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