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Int J Adv Manuf Technol (1999) 15:171181 1999 Springer-Verlag London Limited Development of Automated Fixture Planning Systems W. Ma, J. Li and Y. Rong Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA, USA Fixturing is an important manufacturing activity. The computer- aided fixture design technique is being rapidly developed to reduce the lead time involved in manufacturing planning. An automated fixture configuration design system has been developed to select automatically modular fixture components and place them in position with satisfactory assembly relation- ships. In this paper, an automated fixturing planning system is presented in which fixturing surfaces and points are auto- matically determined based on workpiece geometry and oper- ational information. Fixturing surface accessibility, feature accuracy, and fixturing stability are the main concerns in the fixture planning. The system development, the fixture planning decision procedure, and an implementation example are presented in the paper. Keywords: Accuracy; Clamping; Fixture planning; Locating 1. Introduction Fixturing is an important manufacturing activity in the pro- duction cycle. A computer-aided (or automated) fixture design (CAFD) technique has been developed as part of CAD/CAM integration 1. The development of CAFD contributes to the reduction of manufacturing lead time, the optimisation of manu- facturing operations, and the verification of manufacturing pro- cess designs 2. CAFD plays an important role in flexible manufacturing systems (FMS) and computer-integrated manu- facturing systems (CIMS) 3. Figure 1 outlines the activities for fixture design in manufac- turing systems which include three major aspects: set-up plan- ning, fixture planning, and fixture configuration design 4. The objective of set-up planning is to determine the number of set- ups, the position and orientation of the workpiece in each set- up, and also the machining surfaces in each set-up. Fixture planning determines the locating and clamping points on work- piece surfaces. The task of fixture configuration design is to select fixture components and place them into a final configur- Correspondence and offprint requests to: Dr Kevin Rong, Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA 01609-2280, USA. E-mail: rongKwpi.edu Fig. 1. Fixture design in manufacturing systems. ation to fulfil the functions of locating and clamping the workpiece. An automated modular fixture configuration design system has been developed in which, when fixturing surfaces and points are selected on the workpiece model, fixture units are automatically generated and placed into position with the assistance of fixture component assembly relationships 4,5. This paper deals with fixture planning when the fixturing surfaces and positions on the workpiece are selected automatically. Previous papers on fixture design analysis have been pub- lished, but a comprehensive fixture planning system which can be used to generate fixture plans for industrial applications has not been developed. Previous work includes: a method for the automated determination of fixture location and clamping derived from a mathematical model 6; an algorithm for the selection of locating and clamping positions which provide the maximum mechanical leverage 7; kinematic analysis based fixture planning 8,9; a fixturing grade and dependency grade based fixturability analysis 10; automated selection of set-ups 172 W. Ma and Y. Rong with consideration of tolerance factors of orientation errors in fixture design 11, and finally a geometric analysis based 2D fixture planning system 12. In our previous research, fixturing features 13, fixturing accuracy 14,15, geometric constraints 16, and fixturing surface accessibility 17 have been studied. A framework has been developed for set-up planning and fixture design 18. In this paper, an automated fixture planning system, Fix- Planning, is presented where fixturing surfaces and points are determined when the workpiece model and set-up planning information is input to the system. 2. Basic Requirements of Fixture Planning In engineering practice, fixture planning is governed by a number of factors, including workpiece geometric information and tolerance; set-up planning information such as machining features, the machine tool and cutting tools to be used in each set-up; initial and resulting forms of the workpiece in each set-up; and available fixture components. To ensure that the fixture can hold the workpiece in an acceptable position so that the manufacturing process can be carried out according to the design specifications, the following conditions should be satisfied for a feasible fixture plan. 1. The degrees of freedom (DOF) of the workpiece are totally constrained when the workpiece is located. 2. Machining accuracy specifications can be ensured in the current set-up. 3. Fixture design is stable to resist any effects of external force and torque. 4. Fixturing surfaces and points can be accessed easily by available fixture components. 5. There is no interference between the workpiece and the fixture, and between the cutter tool and the fixture. In this investigation, we focus on the first four requirements. Fixture planning is carried out based on the following consider- ations: 1. Although the workpiece geometry can be complex in indus- trial production, in most fixture designs, planar and cylindri- cal surfaces (internal and external) are used as the locating and clamping surfaces because of the ease of access and measurement of these features when the workpiece is fixed. In this investigation, planar and cylindrical surfaces are used in fixture planning. 2. Many CNC machines, especially machining centres, can be used to perform various operations within one set-up. In most cases, the cutting-tool axis of the machine tool is fixed. When considering fixturing stability, the locating sur- faces are preferably those with normal directions opposite to, or perpendicular to, the cutting-tool axis. For clamping features, the normal directions should be in line with, or perpendicular to, the cutting-tool axis, because, in fixture design, clamping forces should be against locators. 3. For the surfaces to be machined, there should exist datum surfaces which serve as position and orientation references from which other dimensions and tolerances are measured. In fixture planning, surfaces with high accuracy grades should be selected preferentially as locating surfaces so that the inherited machining error is minimised and the required tolerances of the machining features are easily attained. 4. In fixture planning, more than one workpiece surface must be selected for the locating and clamping surfaces for restricting the DOF of the workpiece in a set-up. Therefore, besides the conditions for individual surfaces, the combi- nation status of the available locating surfaces is also important for the accurate location of the workpiece. 5. Since the locators and clamps are in contact with the workpiece, the distribution of fixturing points plays a critical role in ensuring fixturing stability. 6. For a feasible fixture design, the fixturing surfaces must be accessible to the fixture components. The usable (effective) area of the fixturing surface should be large enough to accommodate the functional surfaces of the locators and clamps. Besides considering a fixturing surface, the accessi- bility of potential fixturing points on the surface is also important for the determination of the final fixturing point distribution. 3. Fixturing Surfaces The concept of features has been widely used in design and manufacturing. A workpiece to be machined can be viewed as a combination of features such as planes, steps, pockets, slots, and holes. In a particular operation set-up, features used for fixturing the workpiece can be defined as fixturing features or fixturing surfaces. In practice, most fixturing features are planar and cylindrical surfaces. According to the fixturing functions, the fixturing surfaces can be classified into locating, clamping, and supporting features. Unlike design and manufacturing fea- tures, fixturing surfaces are orientation-dependent. They do not play the same role throughout the manufacturing processes. A set of surfaces may serve as fixturing surfaces in a set-up, but may not be used for fixturing or have different fixturing functions in another set-up. The concept of fixturing features allows the fixturing require- ments to be associated with the workpiece geometry. Feature information in a feature-based workpiece model can also be used directly for fixture design purposes. For manufacturing features, the information necessary for describing a fixturing feature contains geometric and non-geometric aspects. The former includes feature type, shape and dimensional parameters, and position and orientation of the workpiece. The latter includes the surface finish, accuracy level and relationships with machining features, and surface accessibility. 3.1 Discretisation of Fixturing Surfaces In most fixture designs, the fixturing features, especially the locating surfaces, are planar and cylindrical surfaces. In order to evaluate fixturing surface accessibility and determine locating/clamping points on fixturing surfaces, a candidate fix- turing surface is sampled into grid-arrayed discrete points with Development of Automated Fixture Planning Systems 173 equal interval T.IfT is small enough, the discrete sample points will be almost continuous. In order to make the sampling algorithm generic, an outer- bounding rectangle on the surface is used as the sampling region. Since in most cases, the primary locating surface is perpendicular to the other locating surfaces, especially in modu- lar fixture designs, the fixturing surfaces are considered as bottom-locating, top-clamping, side-locating, and side-clamping surfaces. For a bottom-locating/top-clamping surface with a normal Z (or 2Z) direction, two edges of the outer-bounding rectangle must be parallel to the X-axis and two other edges parallel to the Y-axis. For a side-locating/clamping surface, there must be two edges parallel to the Z-axis, while the other two edges must be perpendicular to the first two edges. Figure 2 shows an example of sampled candidate fixturing surfaces with the outer-bounding rectangle. With the assumption that the Z-axis is normal to the surface in the surface local coordi- nate system, the points within the outer-bounding rectangle can be represented as: x = X min + T u, u = 1, 2, %, N u y = Y min + T v, v = 1, 2, %, N v (1) where N u and N v are the numbers of points in the X- and Y- directions, respectively, which are: N u = int (X max 2 X min )/T and N v = int Y max 2 Y min )/T. 3.2 Fixturing Surface Accessibility Fixturing surface accessibility is a measure of whether a candi- date fixturing surface is accessible to a regular fixture compo- nent. Three major factors must be taken into account: 1. The geometry of the fixturing surface which involves the effective area and shape of the surface. 2. Possible obstruction of the workpiece geometry along the normal direction and/or around the geometric region of the fixturing surface. 3. The size and shape of the functional fixture components. In practical situations, it is possible that a planar surface of the workpiece has a complex shape and has a full/partial obstruction along its normal direction and/or around its geo- Fig. 2. Sampling of a candidate fixturing surface with an outer-bound- ing rectangle. metric region. It is thus required that the accessibility model should comprehensively reflect these facts so that a reasonably comparable accessibility value can be applied for every candi- date fixturing surface. The surface accessibility is defined as a statistical value based on the point accessibility (PA) of every valid sample point on the surface, where PA consists of two parts: the point self individual accessibility (SIA) and the point neighbour related accessibility (NRA). The SIA corresponds mainly to the isolated accessibility of the fixturing point, whereas the NRA reflects the extended accessibility of the fixturing point. The SIA of a sample point is defined on the basis of three attribute tags. The tag s 1 is used to indicate whether the square test grid with its centre at the current sample point is inside, on, or outside the outer-loop of the fixturing surface. Three discrete values are assigned to represent its status, i.e. 0, 1, and 2, respectively. If there exists obstructive workpiece geometry in the surface normal direction or surrounding the sample point, this affects the surface accessibility at the sample point. For example, as shown in Fig. 3(a), on a candidate bottom-locating surface of a workpiece, sample point p 1 is not accessible because of the obstructive geometry of the workpiece along the bottom-locat- ing direction, and p 2 is not accessible either because of the obstructions surrounding it. To evaluate automatically whether an obstruction exists in the surface normal direction, a virtual volume is generated by extruding the square test grid to a solid entity in the surface normal direction. By employing a technique for detecting the interference between two solid entities, the obstruction can be identified, as shown in Fig. 3(b). The extruding method is a little different for the square Fig. 3. Obstruction checking at virtual sample points on a bottom- locating surface. (Kp i means the extrusion is carried out at point p i along its accessible direction.) 174 W. Ma and Y. Rong test grid on the side-locating/clamping surface, where the square test grid is first stretched along the bottom-locating direction, and then the stretched grid is extruded along the side-locating/clamping direction as illustrated in Fig. 4. The attribute tag s 2 is used for recording the result of obstruction checking at a sample point. When such an obstruction is detected, s 2 = 1, otherwise, s 2 = 0. If the test grid at the sample point is found to be not obstructed, its individual accessibility is largely dependent on the contact area between the test surface and the fixture components, which is represented by the attribute tag s 3 . The definition of s 3 is s 3 = Area 1 T 2 , s 3 P 0, 1 (2) where Area I is the contact area and T is the edge length of the test grid. On the basis of above three attribute tags, the SIA of a sample point p u,v can be given by a numerical value according to the following rules: if s 1 = OutsideOuterLoop, SIA = 21 (inaccessible); if s 1 OutsideOuterLoop AND s 2 = Obstructed, SIA = 2 1 (inaccessible); if bottom-locating/top-clamping AND S 1 OutsideOut- erLoop AND s 2 = NotObstructed, SIA = s 3 ; Fig. 4. Obstruction checking at sample points on a side-locating/ clamp- ing surface. if side-locating/clamping AND s 1 OutsideOuterLoop AND s 2 = NotObstructed, SIA = 0.5 v s 3 ; where v reflects the height effect of the point in side locating/clamping. The accessibility in the surrounding area of the sample point also affects the accessibility of the point. On a fixturing surface, the positional relationship between the current sample point and all the neighbouring sample points can be represented by a3 3 map where P c is the current sample point with a discrete position of (u, v), P 1 | P 8 are 8-neighbour sample points, and their locations are all labelled in Fig. 5. The NRA at sample point p u,v can be calculated using the equation: NRA(u, v) = O 8 k=1 F k 8 (3) where F k is the related-access factor of kth neighbour, which can be determined based on the SIA as well as its measure (s 1 , s 2 , s 3 ). For bottom-locating/top-clamping, F 9 k = 5 21, s 2 (p k ) = 1 0, s 1 (p k ) = 2 and s 2 (p k ) = 0 IA(p k ), s 1 (p k ) 2 and s 2 (p k ) = 0 (4) F k = 5 F 9 k , k = 1, 3, 5, 7 F 9 k , k = 2, 4, 6, 8, F 9 k21 $ 0 and F 9 k+1 $ 0 21, k = 2, 4, 6, 8, F 9 k21 = 2 1orF 9 k+1 = 2 1 (5) For side-locating/clamping, F 9 k = 5 21, s 2 (p k ) = 1, k = 1, 5, 6, 8 20.5, s 2 (p k ) = 1, k = 2, 3, 4 0, s 1 (p k ) = 2 and s 2 (p k ) = 0 SIA(P k ), s 1 (p k ) 2 and s 2 (p k ) = 0 (6) F k = 5 F 9 k , k = 1, 3, 5, 6, 7, 8 F 9 k , k = 2, 4, F 9 3 $ 0 20.5, k = 2, 4, F 9 3 = 20.5 (7) For a valid sample point, once the SIA and NRA are obtained, the PA can also be calculated according to the equation: Fig. 5. 3 3 position map of current point P c and 8-neighbour sample points P 1 | P 8 . Development of Automated Fixture Planning Systems 175 PA = SIA + NRA,ifPA , 0, then PA = 0 (8) From the definitions of SIA and NRA, SIA is in the range of 0 | 1 and NRA is in the range of 21|1. Therefore, PA must be in the range of 21|2. When the value of PA is less than zero, the sample point is severely obstructed and is not a feasible fixturing point. The overall accessibility (OA) of the fixturing surface is defined as the sum of the PA values at all valid sample points, i.e., OA = O N valid PA u,v , sample point p u,v is tested valid (9) As OA is statistically measured by the overall effect of the accessibility of the sample points on the surface, the infor- mation about the effective area and shape complexity of the surface is represented in the model. Generally, the model satisfies the criterion that the surface with the larger OA is more accessible than the one with the smaller OA. 3.3 Generalised Accuracy of the Fixturing Features One of the most important tasks for fixture planing is to guarantee that the tolerance requirements are met when the workpiece is machined. The accuracy of features can be charac- terised by their tolerance and surface finish, and the tolerance between features. Generally, the tolerance of features can be classified into two types: dimensional tolerance and geometric tolerance. The magnitude of the dimensional tolerance may express the relationship between two features on the workpiece. If there is a feature with a tight dimensional tolerance with respect to a machining feature, this implies that the feature may be used potentially as an operational datum, i.e. a locating surface in the set-up. Based on whether a datum feature is needed, the geometric tolerance can be further divided into form tolerance and positional/orientation tolerance. The form tolerance is associated only with the feature itself, which specifies the allowable geometric variation of individual fea- tures. The form tolerance, e.g. surface finish, of a feature affects the suitability of the feature to be the fixturing datum. The positional/orientation tolerance is of the same importance as the dimensional tolerance for fixture planning since it also represents a relationship between features. In order to evaluate the accuracy of a feature and use it efficiently in fixture planning, a generalised feature accuracy grade is applied in this investigation, which is defined as: T g = (w 1 T d + w 2 T p )*(w 3 T f + w 4 T r ) (10) where T d , T p and T f are the dimensional tolerance grade, positional tolerance grade and form tolerance grade, respect- ively; T r is the tolerance grade equivalent to the surface finish of the feature. w 1 , w 2 , w 3 , and w 4 are the weight factors. The multiple operation “*” represents a dominant relationship where a zero value can contribute to the final result, while the operation “+” represents a relatively weak relationship with preferences. T d , T p , T f , and T r can be obtained by applying the algorithms described in 11,18. 4. Development of Automated Fixture Planning Systems An overview of the automated fixture planning system is shown in Fig. 6. The procedure for fixture planning can be divided into five stages, i.e. input, analysis, planning, verification, and output. The input data includes a workpiece CAD model containing the geometric and tolerance information of the features of the workpiece, and set-up planning information including the features