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Benefits of geometric dimensioning and tolerancing
Journal of Materials Processing Technology 78 (1998) 29 – 35
Benefits of geometric dimensioning and tolerancing P. Chiabert *, F. Lombardi, M. Orlando Department of Production Systems and Economics, Politechnic of Torino, Torino, Italy
Abstract This paper focuses on the major benefits of the geometric dimensioning and tolerancing (GD&T) approach to design and inspection activities. This is accomplished by the GD&T description of a simple part by comparing it with a more traditional one. Also, the paper outlines the great impact of the GD&T approach on design for assembly (DFA). Finally, we conclude with some remarks about future standardization and some observations about the current evolution of production systems and integrated software for design and tolerancing in a ‘closed ring structure’. © 1998 Elsevier Science S.A. All rights reserved. Keywords: GD&T; Design for assembly; DFA; Integrated software; Closed ring structure; CAPE; CAQ; CIM
1. Introduction Manufacturing and quality engineers agree that the two major issues for a technical drawing are thoroughness and unambiguity [1 – 6]. In fact, a poor drawing may even double the manufacturing and inspection costs because many engineering changes may be necessary before it defines a functional, manufacturable and inspectable part. In today’s competitive, stringent market, it is not enough to make technical drawings ‘that can be understood’. The designer must make drawings ‘that cannot possibly be misunderstood’. Geometric dimensioning and tolerancing (GD&T) is the keyword. GD&T greatly increases clearness, uniformity and consistency in drawing specifications, thus providing product, process and quality engineers with the same language. Also, GD&T represents a philosophy of dimensioning and tolerancing of a part based on how it functions in the assembly. So, potential product problems will be identified at the design stage, thus eliminating production delays, reworks and related costs. 2. GD&T versus coordinate dimensioning Referring to Fig. 1(a) and (b), let us compare the traditional method of dimensioning by coordinates (Fig. 1(a)) with a GD&T description (Fig. 1(b)) of a simple plate. * Corresponding author. 0924-0136/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S0924-0136(97)00459-7
At a glance, the drawing represented in Fig. 1(a) seems easy to understand. The plate is 6 mm thick, 16 mm wide and 70 mm long. It has two symmetrical through-holes (diameter ¥= 7 mm). The distance between the hole centers is 50 mm. The allowable (symetrical) tolerances are 9 0.2 mm for the linear dimensions and 9 5° for the angular dimensions, respectively. Compared with Fig. 1(a), Fig. 1(b) clearly seems more complicated and more difficult to understand (without specific GD&T training). Why is the GD&T representation better than the traditional coordinate dimensioning? The point is that a correct GD&T representation captures the design intent by providing the designer with better tools in order to say what he means. Furthermore, GD&T clearly and completely shows the functional requirements of the part as well as the method for its inspection [7,8]. For example, both Fig. 1(a) and (b) specify a plate thickness of (69 0.2) mm. But how straight must the plate be? The drawing in Fig. 1(a) says nothing about this: the plate could be within the thickness limits established by the tolerance, yet be significantly bowed and therefore unfit for use in the assembly. By contrast, the drawing in Fig. 1(b) clearly communicates the functional requirements of the part by including a 0.2 mm geometric tolerance for straightness. This geometric tolerance, in addition to the maximum material condition (MMC) modifier, prescribes that the plate must be straight enough to pass between two parallel plates (of
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Fig. 1. (a) The coordinate dimensioning of a plate; (b) the GD&T description of a plate.
a gauge) spaced 6.4 mm (the so-called virtual dimension of the part). Of course, the point-to-point thickness of the plate must still be within the limits established by the implicit tolerance. Let us now compare Fig. 1(a) and (b) from the point of view of hole locations. In the Fig. 1(a), due to the tolerance accumulation, the maximum tolerance for the location of the upper hole is 90.4 mm (instead of 9 0.2 mm). Tolerance accumulation is highly undesirable because the part, although in tolerance, may not fit its counterpart in the assembly. Therefore the designer must assume unnecessary tighter tolerances, which increases production costs. With regard to the inspection process for the part, we are faced with a nasty dilemma. The horns of this dilemma are shown in Fig. 2. In order to position the plate on the datum reference frame (DRF) when checking the location of the holes, what is the inspection sequence? In Fig. 2 (top) the part is related to the datum reference frame by bringing at least three points of a planar face of the part into contact with the datum plane A; then, keeping the part in contact with the plane A, by bringing at least two points of the part into contact with the datum plane B. Finally, keeping the part in contact with both the planes A–B, the relationship is completed by bringing at least one point of the part into contact with the datum plane C. In Fig. 2 (bottom) the positioning sequence is different: A –C–B instead of A – B – C. As we can see, different positioning sequences can yield different results. What is the correct sequence? Coordinate dimensioning says nothing about this.
Let us examine the GD&T approach to positioning the part in the datum reference frame. First of all, three datum features are selected. A datum feature is selected on the basis of its geometric relationship to the toleranced feature and the requirements of the design. To ensure proper assembly, corresponding interfacing features of the mating parts should be selected as datum features. As regards the part shown in the Fig. 1(b), three datum features are selected and identified on the drawing by the corresponding datum feature symbols A, B, C, enclosed in a square. They agree with the principal planar faces of the part.
Fig. 2. Different results, due to different positioning sequences.
P. Chiabert et al. / Journal of Materials Processing Technology 78 (1998) 29–35
The corresponding simulated datums are the planes derived from the physical planar counterparts (datum simulators) of the gauge equipment; the datum features are positioned against the corresponding datum simulators in the order of precedence which is specified, from left to right, in the feature control frame of the geometric tolerance callout and, thus, there are no more dilemmas about part positioning for inspection. Fig. 1(b) shows several dimensions (basic dimensions) enclosed in a rectangle. The basic dimensions, describing the theoretically exact characteristics of the part, are the ‘basis’ from which permissible variations are established by the tolerance callouts in the feature control frames. (Basic dimensions are also used to define gauge dimensions: in this case, the gauge makers tolerances—very small when compared to part tolerances—will apply.) As regards hole positions, the basic dimensions of 8 and 60 mm are used to establish the true location of the upper hole axis from the specified datums C and B. The position tolerance callout, together with the MMC modifier, establishes that, when the hole is at MMC (its smallest diameter ¥ =6.8 mm), its axis must fall within a perfectly cylindrical zone normal to the datum A and located at the true position in the datum reference frame (DRF). Notice that the positional tolerance zone also defines both the limits of the attitude of the hole axis relative to the datum A and the limits of the straightness of the hole axis at MMC. Notice also that whenever a tolerance of position is applied at MMC a bonus tolerance is available. In particular, when the diameter of the hole reaches its maximum value (¥ =7.2 mm, least material condition (LMC)) a bonus tolerance of 0.4 mm is available, and the diameter of the tolerance zone correspondingly increases (¥= 0.6+ 0.4 =1 mm). In order to verify the hole positions, a functional gauge may be used, which simulates the worst case mating part. The MMC condition enables one to use a fixed gauge. The axis of the studs of the gauge are 50 mm apart (basic dimension). The diameter of the studs is ¥=(6.8− 0.6)=6.2 mm (the so called virtual dimension of the hole). In general, a functional fixed gauge represent an ‘intelligent’ go or no-go condition: in fact it implicitly takes into account the bonus tolerance. The three major benefits of functional gauges are : economical to produce (only for simple parts); the part can be checked quickly; no special skill required to interpret the results. The use of functional gauges is not mandatory. Open set-up and paper gauge techniques are often adopted to evaluate a part and to adjust the manufacturing process. When verifying complex parts (i.e. EDM electrodes and others tooling elements used in die production,
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complex body surface elements for the automotive industry, etc.) off-line programmed, portable coordinate measurement machines (CMM) are used which can operate on the shop floor [9–17]. Moreover, CMMs enable consistent monitoring of the production process because deviations in the processes are quickly detected, thus allowing the machine operators and production engineers to interrupt and correct a process before bad parts are produced. In conclusion, three major benefits of the GD&T approach to parts design are summarized as: (i) no tolerance accumulation; (ii) clearly defined inspection process; and (iii) a bonus tolerance is available (when prescribed by the MMC modifier).
3. The GD&T impact on design for assembly The most important benefit of the GD&T approach lies in ensuring, at the design phase, that component parts will assemble into the finished product and function as intended. Without this capability, parts that meet extremes of individual tolerance specifications may pass inspection but still fail to assemble properly. Assembly stacks with geometric tolerances play a fundamental role in such a task. A stack is a chain of vectors aimed at determining the maximum and minimum distance between two features of a part within an assembly. The stack’s calculation enables the designer to analyse the dimensional relationships within an assembly, and so create smarter designs and open up tolerances to the outer limits permitted by the product function. Larger tolerances reduce scrap and other costs of nonconformance. Referring to Fig. 3(a) and (b), we can illustrate the above concepts by means of an example taken from [5]. Fig. 3(a) represents a 3-D CAD model (in the CATIA V4 environment) of a gearbox and Fig. 3(b) represents schematically the longitudinal section of the gearbox. The parts of this assembly have been GD&T dimensioned and toleranced and have not been individually drawn in this context for the sake of brevity. Referring to the Fig. 3(b), the assembly is as follows. On the left, the housing (P00) carries a cover (P03) which houses a ball bearing and a bush. On the right of the housing, the through-hole houses a bush and a sheet steel cup plug (P11). The ball bearing and the bushes hold the main shaft (P04) which supports four gears. The ‘input’ gear (P10), positioned on the right, is supported by two bushes and is idling in the configuration shown (the main shaft cannot rotate in this configuration). Moving to the left of the input gear, we can see a hub (P13), a gear speed sensor (P15) and an ‘output’ gear (P18). The hub, the gear speed sensor and the output gear are rotationally integrated with the main shaft by
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Fig. 3. (a) A 3-dimensional CAD model of the gear box; (b) a schematic longitudinal section of the gear box.
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means of splines and are axially positioned by means of retaining rings and shoulders. The hub holds a collar (P14) which is axially driven by a shift-fork (not represented in the figure). When the fork pushes the collar on the right between the hub and the input gear, the input rotation is transferred to the hub, then to the main shaft and to the other gears. The major diameter of gear P15 skims a speed sensor (P24), clamped to the housing by two retaining rings. Several dimensions have to be analysed in this assembly and some tolerances balanced to minimize production costs. Referring, for example, to the clearance between the major diameter of the gear and the speed sensor, let us assume that the design engineer and the production engineer agree a design goal (in this case the minimum functional clearance, for safety sake) of + 2 mm.Three steps are necessary in order to compute the gear-sensor clearance, indicated by ‘‘?’’ in Fig. 3(b): 1. clearly locate and mark the surfaces that are pressed together when the gear and the speed sensor are moved into the position that gives the extreme minimum condition for the clearance; 2. mark the start point of the stack and assign a positive (conventional) direction for the distances (i.e. the radial vectors making the stack); 3. calculate the resultant of the vectors. The vectors start from the surface of the major diameter of the gear and reach the lower surface of the sensor speed. Stack vectors represent the following dimensions (capital letters from A to Y) in Fig. 3(b): the basic dimensions involved in the stack; the maximum and minimum dimensions of the features involved in the stack; the geometric tolerances of the features involved in the stack. The stack (i.e. the chain of the above vectors) passes through the previously located and marked surfaces. Except for the basic dimensions, each vector of the stack has a maximum and a minimum value and, therefore, the stack has a maximum and a minimum value. The difference between the maximum and minimum values is the tolerance of the stack. In order to document the stack step by step (i.e component by component) a table has to be constructed, called the stack form. Each row of the stack form describes a single component vector of the stack: the start and stop surfaces, the maximum value, the minimum value and the associated tolerance (maximum value minus minimum value). In the last row of the stack form, the accumulated value of the tolerances must correspond to the difference between the maximum and minimum values of the stack (the accumulated value of the maximum and minimum values of the stack components). By comparing the stack results to the design goal to see if they differ, it is possible to adjust the stack
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answer (i.e. the maximum and minimum value of the stack) in order to match the design goal. Firstly, the designer must calculate the total available tolerance (the stack answer minus the design goal), then distribute the total available tolerance among the stack components. The idea is to put the extra tolerances on the components that have the greatest impact on the manufacturing costs. Clearly, assigning extra tolerances is not a simple task, requiring a concurrent input from the design, manufacturing and production engineers. Moreover, one must keep in mind that many stacks involved in the assembly may share several components. Therefore, the distribution of the extra tolerance among the components of a single stack, may alter other stacks that then have to be recalculated and reoptimized. This implies additional costs.
4. Remarks, conclusions and developments GD&T is perfectly in line with the current evolution of the well known geometrical product specifications (GPS) concept. GPS defines, by an engineering drawing, the shape, dimensions and surface characteristics which ensure optimum functioning of the part to be produced, together with the dispersion around the optimum where the function is still satisfactory. We know that in the process of manufacturing workpieces will be produce which are not perfect, showing some deviation from the optimum and from one another. Therefore these workpieces will be measured in order to compare them with the specifications. There is a need to relate: the workpiece as conceived by the designer (the ideal workpiece); the workpiece as manufactured (the actual workpiece); the knowledge of the workpiece as measured (the only possible or practical information on the actual workpiece). To obtain this relationship and to allow mutual interpretation, standards have been developed in the field of GPS to deal with the basic definitions, the symbolic representation, the manufacturing capabilities, and the measured principles and so on. For many years, these GPS standards have been prepared by the Technical Committees (TCs) within national and international organizations for industrial standards; they have been discussed and issued as soon as specific needs in each field were identified, but quite often a global view was missing. This has resulted in standards with a different approach and presentation, and sometimes containing contradictions. There are also gaps between the standards.
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In recognition of this fact the Joint Harmonization Group of ISO/TC 3 (Limits and Fits), ISO/TC 10/SC 5 (Dimensioning and Tolerancing) and ISO/TC 57 (Metrology and Properties of Surfaces) decided to structure the standards dealing with GPS according to a Masterplan which will be used for future standardization. Moreover, the GD&T approach is perfectly in line with the current evolution of production systems. The present demand for ‘just in time’ requires that, right from the design phase, the product has to be functional as well as economic to manufacture and test. In this new scenario, the design engineer, the manufacturing engineer and the production planner must work in a fully integrated, concurrent structure [18–28]. This structure is often referred to as ‘the closed ring structure’. In such a structure, the full integration between design, manufacturing and production should be achieved by means of a common, shared (via a network) data base which stores all the general product specifications of the part. The design engineer, using the functions of group technology and GPS, should be able to benefit by adapting part drawings and other data for an existing part to the new part being designed. With the electronic prototype of the part, the design engineer can perform an exhaustive analysis of the part, not only on the basis of stress–strain analysis, but also on the basis of how the part has to be assembled and inspected for quality. The manufacturing engineer should be able to check the product and the process for manufacturability. If problems arise, the design engineer may be asked to make design changes to the product. Both the design and manufacturing engineers can interact using the common data base and the same language (the GD&T language). When the design is finalized, the same model is used to create the numerical control program to produce the part as well as the numerical control program to drive the CMM on the shop floor. The production planner, upon review of the electronic part’s check-list, can, with a single transaction, release the drawing, the bills of material and the manufacturing and inspection programs to manufacturing and inspection. In recent years integrated high-level software aimed at dimensioning, tolerancing and inspecting parts and assemblies (by CMMs) have come on the market [9,11,13,15,16]. These tools are very promising for: full integration between designing and tolerancing of parts and assemblies; simulation of the inspection process on the ‘virtual product’ in a CAD environment; tolerances optimization and assembly checking; automatic needs evaluation of engineering changes. But, at the present time, the full implementation of such tools in production systems involves some risks:
high market and setting-up costs; difficulties in their cost-effective use; almost always a long setting-up time. A project intended to perform an extended experiment on the capabilities of integrated GD&T software in a fully integrated, closed ring structure has been carried out at the Department of Production Systems and Economics (DSPEA) of the Politechnic of Torino [17] for two years. This project has financially supported by the Ministero della Pubblica Istruzione, the Politechnic of Torino and the Camera di Commercio Industria, Artigianato e Agricoltura (CCIAA) of Torino.The first results of this experiment, involving the experience of a couple of software houses and of several mechanical industries in Italy are referred to in [9,16,17]. Further results will be available in the next year.
References [1] A. Donnarumma, Disegno di Macchine, vol. 1, Masson, Paris, 1996. [2] S. Muraski Johnson, Misunderstanding fires GD&T debate, Mach. Des. April 18 (1994) 69 – 72 [3] A. Krulikowski, GD&T challenges the fast draw, Manuf. Eng. 112 (2) (1994) 27 – 31. [4] A. Krulikowski, Geometric Dimensioning and Tolerancing, a Self-Study Workbook, Effective Training Incorporated, 1994. [5] A. Krulikowski, Tolerance Stacks, a Self Study Course, Effective Training Incorporated, Westland, MI, 1992. [6] E. Chirone, M. Orlando, S. Tornincasa, Il disegno funzionale e le tolleranze geometriche, Proc. IX Convegno Nazionale ADM, Caserta, 27 – 29 September, 1995, pp. 645 – 655. [7] ASME Y14.5M-1994, Dimensioning and Tolerancing. [8] ASME Y14.5.1M-1994, Mathematical Definition of Dimensioning and Tolerancing. [9] P. Chiabert, M. Orlando, S. Tornincasa, Sulla validazione di particolari meccanici in ambiente integrato con processo ad anello chiuso, Proc. IX Convegno Nazionale ADM, Caserta, 27 – 29 September 1995, pp. 17 – 27. [10] J.V. Owen, CMMs on the shop floor, Manuf. Eng. 106 (4) (1991) 66 – 70. [11] P. Diletti, Nuova logica per il controllo dimensionale, Tecnol. Mecc. 4 (1993) 166 – 170. [12] J. Granquist, Closing the loop of mold design, manufacture and inspection, Am. Mach. 4 (1993) 23 – 25. [13] D. Powaser, Linking CAD and CMM, Automation 4 (1994) 52 – 53. [14] R. Aronson, Why test them all?, Manuf. Eng. 115 (5) (1995) 77 – 82. [15] F. Franceschini, M. Luisoni, Controllo delle prestazioni delle macchine di misura a coordinate (Parti I/II), Autom. Integr. Marzo/Aprile (1996) 112 – 118, 114 – 117. [16] P. Chiabert, F. Lombardi, M. Orlando, Gli strumenti per l’ingegneria simultanea nei settori CAPE e CAQ, atti del Seminario Italo-Spagnolo, Napoli, 26 Giugno 1996. [17] M. Orlando, About an integrated approach to the inspection and validation phase of production process, Proc. AMME95 Gliwice-Wisla, 30th November – 1st December 1995, pp. 255–258. [18] S.P. Dutta, G. Abdou, S. Agasaveeran, Performance analysis of network designs in CIM environment, Int. J. Comput. Integr. Manuf. 6 (5) (1993) 293 – 301.
P. Chiabert et al. / Journal of Materials Processing Technology 78 (1998) 29–35 [19] M.D. Reimann, J. Sarkis, An architecture for integrated automated quality control, J. Manuf. Syst. 12 (4) (1993) 341 – 355. [20] M.D. Reimann, J. Sarkis, Design for automating the inspection of manufacturing parts, Comput. Integr. Manuf. Syst. 7 (4) (1994) 269 – 278. [21] A. Gunasekaran, S.K. Goyal, et al., An investigation into the application of group technology in advanced manufacturing systems, Int. J. Comput. Integr. Manuf. 7 (4) (1994) 215 – 228. [22] S.D. Urban, J.J. Shah, et al., A heterogeneous, active data base architecture for engineering data management, Int. J. Comput. Integr. Manuf. 7 (5) (1994) 276–293. [23] E.J. Klages, R.M. Wilson, An automated inspection programming system, Int. J. Comput. Integr. Manuf. 7 (6) (1994) 365 – 374. [24] D.J. Medeiros, G. Thomas, et al., Offline programming of
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coordinate measuring machines, J. Manuf. Syst. 13 (6) (1994) 401 – 411. J.S. Smith, S.B. Joshi, A shop floor controller for computer-integrated manufacturing, Int. J. Comput. Integr. Manuf. 8 (5) (1995) 327 – 339. R.D. Caldwell, Y. Nong, D.A. Urzi, Re-engineering the product development cycle and future enhancements of the computer integrated environment, Int. J. Comput. Integr. Manuf. 8 (6) (1995) 441 – 447. A.L. Arentsen, J.J. Tiemersma and H.J.J. Kals, The integration of quality control and shop floor control, Int. J. Comput. Integr. Manuf. 9 (2) (1996) 113 – 130. F. Franceschini and S. Rossetto, Strumenti e Tecniche di Supporto per la Qualita` nella Progettazione, Technical Report, DSPEA, 1996.
Benefits of geometric dimensioning and tolerancing P. Chiabert *, F. Lombardi, M. Orlando Department of Production Systems and Economics, Politechnic of Torino, Torino, Italy
Abstract This paper focuses on the major benefits of the geometric dimensioning and tolerancing (GD&T) approach to design and inspection activities. This is accomplished by the GD&T description of a simple part by comparing it with a more traditional one. Also, the paper outlines the great impact of the GD&T approach on design for assembly (DFA). Finally, we conclude with some remarks about future standardization and some observations about the current evolution of production systems and integrated software for design and tolerancing in a ‘closed ring structure’. © 1998 Elsevier Science S.A. All rights reserved. Keywords: GD&T; Design for assembly; DFA; Integrated software; Closed ring structure; CAPE; CAQ; CIM
1. Introduction Manufacturing and quality engineers agree that the two major issues for a technical drawing are thoroughness and unambiguity [1 – 6]. In fact, a poor drawing may even double the manufacturing and inspection costs because many engineering changes may be necessary before it defines a functional, manufacturable and inspectable part. In today’s competitive, stringent market, it is not enough to make technical drawings ‘that can be understood’. The designer must make drawings ‘that cannot possibly be misunderstood’. Geometric dimensioning and tolerancing (GD&T) is the keyword. GD&T greatly increases clearness, uniformity and consistency in drawing specifications, thus providing product, process and quality engineers with the same language. Also, GD&T represents a philosophy of dimensioning and tolerancing of a part based on how it functions in the assembly. So, potential product problems will be identified at the design stage, thus eliminating production delays, reworks and related costs. 2. GD&T versus coordinate dimensioning Referring to Fig. 1(a) and (b), let us compare the traditional method of dimensioning by coordinates (Fig. 1(a)) with a GD&T description (Fig. 1(b)) of a simple plate. * Corresponding author. 0924-0136/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S0924-0136(97)00459-7
At a glance, the drawing represented in Fig. 1(a) seems easy to understand. The plate is 6 mm thick, 16 mm wide and 70 mm long. It has two symmetrical through-holes (diameter ¥= 7 mm). The distance between the hole centers is 50 mm. The allowable (symetrical) tolerances are 9 0.2 mm for the linear dimensions and 9 5° for the angular dimensions, respectively. Compared with Fig. 1(a), Fig. 1(b) clearly seems more complicated and more difficult to understand (without specific GD&T training). Why is the GD&T representation better than the traditional coordinate dimensioning? The point is that a correct GD&T representation captures the design intent by providing the designer with better tools in order to say what he means. Furthermore, GD&T clearly and completely shows the functional requirements of the part as well as the method for its inspection [7,8]. For example, both Fig. 1(a) and (b) specify a plate thickness of (69 0.2) mm. But how straight must the plate be? The drawing in Fig. 1(a) says nothing about this: the plate could be within the thickness limits established by the tolerance, yet be significantly bowed and therefore unfit for use in the assembly. By contrast, the drawing in Fig. 1(b) clearly communicates the functional requirements of the part by including a 0.2 mm geometric tolerance for straightness. This geometric tolerance, in addition to the maximum material condition (MMC) modifier, prescribes that the plate must be straight enough to pass between two parallel plates (of
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P. Chiabert et al. / Journal of Materials Processing Technology 78 (1998) 29–35
Fig. 1. (a) The coordinate dimensioning of a plate; (b) the GD&T description of a plate.
a gauge) spaced 6.4 mm (the so-called virtual dimension of the part). Of course, the point-to-point thickness of the plate must still be within the limits established by the implicit tolerance. Let us now compare Fig. 1(a) and (b) from the point of view of hole locations. In the Fig. 1(a), due to the tolerance accumulation, the maximum tolerance for the location of the upper hole is 90.4 mm (instead of 9 0.2 mm). Tolerance accumulation is highly undesirable because the part, although in tolerance, may not fit its counterpart in the assembly. Therefore the designer must assume unnecessary tighter tolerances, which increases production costs. With regard to the inspection process for the part, we are faced with a nasty dilemma. The horns of this dilemma are shown in Fig. 2. In order to position the plate on the datum reference frame (DRF) when checking the location of the holes, what is the inspection sequence? In Fig. 2 (top) the part is related to the datum reference frame by bringing at least three points of a planar face of the part into contact with the datum plane A; then, keeping the part in contact with the plane A, by bringing at least two points of the part into contact with the datum plane B. Finally, keeping the part in contact with both the planes A–B, the relationship is completed by bringing at least one point of the part into contact with the datum plane C. In Fig. 2 (bottom) the positioning sequence is different: A –C–B instead of A – B – C. As we can see, different positioning sequences can yield different results. What is the correct sequence? Coordinate dimensioning says nothing about this.
Let us examine the GD&T approach to positioning the part in the datum reference frame. First of all, three datum features are selected. A datum feature is selected on the basis of its geometric relationship to the toleranced feature and the requirements of the design. To ensure proper assembly, corresponding interfacing features of the mating parts should be selected as datum features. As regards the part shown in the Fig. 1(b), three datum features are selected and identified on the drawing by the corresponding datum feature symbols A, B, C, enclosed in a square. They agree with the principal planar faces of the part.
Fig. 2. Different results, due to different positioning sequences.
P. Chiabert et al. / Journal of Materials Processing Technology 78 (1998) 29–35
The corresponding simulated datums are the planes derived from the physical planar counterparts (datum simulators) of the gauge equipment; the datum features are positioned against the corresponding datum simulators in the order of precedence which is specified, from left to right, in the feature control frame of the geometric tolerance callout and, thus, there are no more dilemmas about part positioning for inspection. Fig. 1(b) shows several dimensions (basic dimensions) enclosed in a rectangle. The basic dimensions, describing the theoretically exact characteristics of the part, are the ‘basis’ from which permissible variations are established by the tolerance callouts in the feature control frames. (Basic dimensions are also used to define gauge dimensions: in this case, the gauge makers tolerances—very small when compared to part tolerances—will apply.) As regards hole positions, the basic dimensions of 8 and 60 mm are used to establish the true location of the upper hole axis from the specified datums C and B. The position tolerance callout, together with the MMC modifier, establishes that, when the hole is at MMC (its smallest diameter ¥ =6.8 mm), its axis must fall within a perfectly cylindrical zone normal to the datum A and located at the true position in the datum reference frame (DRF). Notice that the positional tolerance zone also defines both the limits of the attitude of the hole axis relative to the datum A and the limits of the straightness of the hole axis at MMC. Notice also that whenever a tolerance of position is applied at MMC a bonus tolerance is available. In particular, when the diameter of the hole reaches its maximum value (¥ =7.2 mm, least material condition (LMC)) a bonus tolerance of 0.4 mm is available, and the diameter of the tolerance zone correspondingly increases (¥= 0.6+ 0.4 =1 mm). In order to verify the hole positions, a functional gauge may be used, which simulates the worst case mating part. The MMC condition enables one to use a fixed gauge. The axis of the studs of the gauge are 50 mm apart (basic dimension). The diameter of the studs is ¥=(6.8− 0.6)=6.2 mm (the so called virtual dimension of the hole). In general, a functional fixed gauge represent an ‘intelligent’ go or no-go condition: in fact it implicitly takes into account the bonus tolerance. The three major benefits of functional gauges are : economical to produce (only for simple parts); the part can be checked quickly; no special skill required to interpret the results. The use of functional gauges is not mandatory. Open set-up and paper gauge techniques are often adopted to evaluate a part and to adjust the manufacturing process. When verifying complex parts (i.e. EDM electrodes and others tooling elements used in die production,
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complex body surface elements for the automotive industry, etc.) off-line programmed, portable coordinate measurement machines (CMM) are used which can operate on the shop floor [9–17]. Moreover, CMMs enable consistent monitoring of the production process because deviations in the processes are quickly detected, thus allowing the machine operators and production engineers to interrupt and correct a process before bad parts are produced. In conclusion, three major benefits of the GD&T approach to parts design are summarized as: (i) no tolerance accumulation; (ii) clearly defined inspection process; and (iii) a bonus tolerance is available (when prescribed by the MMC modifier).
3. The GD&T impact on design for assembly The most important benefit of the GD&T approach lies in ensuring, at the design phase, that component parts will assemble into the finished product and function as intended. Without this capability, parts that meet extremes of individual tolerance specifications may pass inspection but still fail to assemble properly. Assembly stacks with geometric tolerances play a fundamental role in such a task. A stack is a chain of vectors aimed at determining the maximum and minimum distance between two features of a part within an assembly. The stack’s calculation enables the designer to analyse the dimensional relationships within an assembly, and so create smarter designs and open up tolerances to the outer limits permitted by the product function. Larger tolerances reduce scrap and other costs of nonconformance. Referring to Fig. 3(a) and (b), we can illustrate the above concepts by means of an example taken from [5]. Fig. 3(a) represents a 3-D CAD model (in the CATIA V4 environment) of a gearbox and Fig. 3(b) represents schematically the longitudinal section of the gearbox. The parts of this assembly have been GD&T dimensioned and toleranced and have not been individually drawn in this context for the sake of brevity. Referring to the Fig. 3(b), the assembly is as follows. On the left, the housing (P00) carries a cover (P03) which houses a ball bearing and a bush. On the right of the housing, the through-hole houses a bush and a sheet steel cup plug (P11). The ball bearing and the bushes hold the main shaft (P04) which supports four gears. The ‘input’ gear (P10), positioned on the right, is supported by two bushes and is idling in the configuration shown (the main shaft cannot rotate in this configuration). Moving to the left of the input gear, we can see a hub (P13), a gear speed sensor (P15) and an ‘output’ gear (P18). The hub, the gear speed sensor and the output gear are rotationally integrated with the main shaft by
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Fig. 3. (a) A 3-dimensional CAD model of the gear box; (b) a schematic longitudinal section of the gear box.
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means of splines and are axially positioned by means of retaining rings and shoulders. The hub holds a collar (P14) which is axially driven by a shift-fork (not represented in the figure). When the fork pushes the collar on the right between the hub and the input gear, the input rotation is transferred to the hub, then to the main shaft and to the other gears. The major diameter of gear P15 skims a speed sensor (P24), clamped to the housing by two retaining rings. Several dimensions have to be analysed in this assembly and some tolerances balanced to minimize production costs. Referring, for example, to the clearance between the major diameter of the gear and the speed sensor, let us assume that the design engineer and the production engineer agree a design goal (in this case the minimum functional clearance, for safety sake) of + 2 mm.Three steps are necessary in order to compute the gear-sensor clearance, indicated by ‘‘?’’ in Fig. 3(b): 1. clearly locate and mark the surfaces that are pressed together when the gear and the speed sensor are moved into the position that gives the extreme minimum condition for the clearance; 2. mark the start point of the stack and assign a positive (conventional) direction for the distances (i.e. the radial vectors making the stack); 3. calculate the resultant of the vectors. The vectors start from the surface of the major diameter of the gear and reach the lower surface of the sensor speed. Stack vectors represent the following dimensions (capital letters from A to Y) in Fig. 3(b): the basic dimensions involved in the stack; the maximum and minimum dimensions of the features involved in the stack; the geometric tolerances of the features involved in the stack. The stack (i.e. the chain of the above vectors) passes through the previously located and marked surfaces. Except for the basic dimensions, each vector of the stack has a maximum and a minimum value and, therefore, the stack has a maximum and a minimum value. The difference between the maximum and minimum values is the tolerance of the stack. In order to document the stack step by step (i.e component by component) a table has to be constructed, called the stack form. Each row of the stack form describes a single component vector of the stack: the start and stop surfaces, the maximum value, the minimum value and the associated tolerance (maximum value minus minimum value). In the last row of the stack form, the accumulated value of the tolerances must correspond to the difference between the maximum and minimum values of the stack (the accumulated value of the maximum and minimum values of the stack components). By comparing the stack results to the design goal to see if they differ, it is possible to adjust the stack
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answer (i.e. the maximum and minimum value of the stack) in order to match the design goal. Firstly, the designer must calculate the total available tolerance (the stack answer minus the design goal), then distribute the total available tolerance among the stack components. The idea is to put the extra tolerances on the components that have the greatest impact on the manufacturing costs. Clearly, assigning extra tolerances is not a simple task, requiring a concurrent input from the design, manufacturing and production engineers. Moreover, one must keep in mind that many stacks involved in the assembly may share several components. Therefore, the distribution of the extra tolerance among the components of a single stack, may alter other stacks that then have to be recalculated and reoptimized. This implies additional costs.
4. Remarks, conclusions and developments GD&T is perfectly in line with the current evolution of the well known geometrical product specifications (GPS) concept. GPS defines, by an engineering drawing, the shape, dimensions and surface characteristics which ensure optimum functioning of the part to be produced, together with the dispersion around the optimum where the function is still satisfactory. We know that in the process of manufacturing workpieces will be produce which are not perfect, showing some deviation from the optimum and from one another. Therefore these workpieces will be measured in order to compare them with the specifications. There is a need to relate: the workpiece as conceived by the designer (the ideal workpiece); the workpiece as manufactured (the actual workpiece); the knowledge of the workpiece as measured (the only possible or practical information on the actual workpiece). To obtain this relationship and to allow mutual interpretation, standards have been developed in the field of GPS to deal with the basic definitions, the symbolic representation, the manufacturing capabilities, and the measured principles and so on. For many years, these GPS standards have been prepared by the Technical Committees (TCs) within national and international organizations for industrial standards; they have been discussed and issued as soon as specific needs in each field were identified, but quite often a global view was missing. This has resulted in standards with a different approach and presentation, and sometimes containing contradictions. There are also gaps between the standards.
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In recognition of this fact the Joint Harmonization Group of ISO/TC 3 (Limits and Fits), ISO/TC 10/SC 5 (Dimensioning and Tolerancing) and ISO/TC 57 (Metrology and Properties of Surfaces) decided to structure the standards dealing with GPS according to a Masterplan which will be used for future standardization. Moreover, the GD&T approach is perfectly in line with the current evolution of production systems. The present demand for ‘just in time’ requires that, right from the design phase, the product has to be functional as well as economic to manufacture and test. In this new scenario, the design engineer, the manufacturing engineer and the production planner must work in a fully integrated, concurrent structure [18–28]. This structure is often referred to as ‘the closed ring structure’. In such a structure, the full integration between design, manufacturing and production should be achieved by means of a common, shared (via a network) data base which stores all the general product specifications of the part. The design engineer, using the functions of group technology and GPS, should be able to benefit by adapting part drawings and other data for an existing part to the new part being designed. With the electronic prototype of the part, the design engineer can perform an exhaustive analysis of the part, not only on the basis of stress–strain analysis, but also on the basis of how the part has to be assembled and inspected for quality. The manufacturing engineer should be able to check the product and the process for manufacturability. If problems arise, the design engineer may be asked to make design changes to the product. Both the design and manufacturing engineers can interact using the common data base and the same language (the GD&T language). When the design is finalized, the same model is used to create the numerical control program to produce the part as well as the numerical control program to drive the CMM on the shop floor. The production planner, upon review of the electronic part’s check-list, can, with a single transaction, release the drawing, the bills of material and the manufacturing and inspection programs to manufacturing and inspection. In recent years integrated high-level software aimed at dimensioning, tolerancing and inspecting parts and assemblies (by CMMs) have come on the market [9,11,13,15,16]. These tools are very promising for: full integration between designing and tolerancing of parts and assemblies; simulation of the inspection process on the ‘virtual product’ in a CAD environment; tolerances optimization and assembly checking; automatic needs evaluation of engineering changes. But, at the present time, the full implementation of such tools in production systems involves some risks:
high market and setting-up costs; difficulties in their cost-effective use; almost always a long setting-up time. A project intended to perform an extended experiment on the capabilities of integrated GD&T software in a fully integrated, closed ring structure has been carried out at the Department of Production Systems and Economics (DSPEA) of the Politechnic of Torino [17] for two years. This project has financially supported by the Ministero della Pubblica Istruzione, the Politechnic of Torino and the Camera di Commercio Industria, Artigianato e Agricoltura (CCIAA) of Torino.The first results of this experiment, involving the experience of a couple of software houses and of several mechanical industries in Italy are referred to in [9,16,17]. Further results will be available in the next year.
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