Automated Setup Planning for Lathe Machining

Journal of Manufacturing Systems Vol. 17/No. 3 1998

Automated Setup Planning for Lathe Machining Samuel H. Huang, The University of Toledo, Toledo, Ohio

Abstract

To improve the performance of CAD/CAM systems, the task of setup planning needs to be automated. Some researchers have addressed this research issue and proposed several automatic setup planning approaches. Most of the proposed approaches generate setup plans based on geometry analysis (tool approach direction analysis) and precedence constraint analysis. Chang proposed a heuristic approach to solve the setup planning problem. 1Features of a component are grouped into clusters based on the commonality of tool approach directions. The clusters are then refined based on precedence constraints. Finally, setup plans are generated heuristically. Other setup planning approaches based on geometry analysis and precedence constraint analysis are: a rule-based approach proposed by Hayes and Wright, 2 an unsupervised learning approach developed by Chen, 3 a hybrid approach suggested by Zhang, Nee, and Ong, 4 and an algorithmic approach presented by Sarma and Wright. s Setup planning and fixturing are two closely related tasks in process planning. To set up a workpiece is to locate the workpiece in a desired position on the machine table. A fixture is then used to provide some kind of a clamping mechanism to maintain the workpiece in position and to resist the effects of gravity and/or operational forces. 6 To develop a practical solution to setup planning, fixturing constraints need to be taken into consideration. The problem of fixturing has been addressed by quite a few researchers. 711 Some researchers studied fixturing as the problem of eliminating kinematic degrees of freedom of a workpiece) ° Others emphasized the fact that fixtures for machining rely on friction force. 8,1~These issues have been integrated into the development of computerized setup planning systems) 3"t5 Another important issue that needs to be considered in setup planning is tolerance analysis. The purpose of setup and fixturing is to ensure the stability and, more importantly, the precision of machining processes. Therefore, an important guideline for

The development of computer-aided design (CAD) and computer-aided manufacturing (CAM) has advanced to the stage where NC (numerically controlled) codes can be automatically generated for components created using a CAD model; however, there still remains a gap between the CAD/CAM environment and the physical machining processes. A critical aspect of this gap is setup planning, which requires extensive experience and is typically performed manually. To improve the performance of CAD/CAM systems, the task of setup planning needs to be automated. This paper presents an automatic approach to setup planning for components machined on a lathe. The problem of setup planning is formulated as a mathematical problem. Issues taken into consideration include geometry analysis, precedence constraint analysis, kinematic analysis, force analysis, and tolerance analysis. An algorithm is then presented to solve the setup planning problem. An example is also given to show the effectiveness of the algorithm. The mathematical formulation of the setup planning problem is theoretically sound, and the algorithm can deal with a variety of turned components with promising results.

Keywords: Setup Planning, Positioning, Workholding, Mathematical Mode/, Algorithm

1. Introduction Computer-aided design (CAD) is now a standard practice in the manufacturing industry. Computeraided manufacturing (CAM) software tools are also commonly used. CAM software tools can automatically generate NC (numerically controlled) codes for components created using a CAD model once machining geometry is specified. State-of-the-art CAM software tools can handle some process planning tasks gracefully, such as operation sequencing and NC tool path generation; however, the success is limited to components that can be machined in a single setup. For components that need to be machined in multiple setups, critical decisions such as setup formation, positioning and workholding, and setup sequencing are usually made by an expert machinist rather than generated by a CAM software tool. In other words, the task of setup planning, which requires extensive experience, is still performed manually.

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and turning tapers; with appropriate attachments, it can be adapted to simple milling or grinding operations. 19 Other special classes of work performed on a lathe include knurling, filing, polishing, and coil winding, z° A lathe is probably the oldest of all the machine tools as well as the most important one in modern metalcutting practice. There are many different types of lathes that vary in size, design, method of drive, arrangement of gears, and purpose. In general, they can be classified as speed lathes, engine lathes, bench lathes, toolroom lathes, turret lathes, automatic lathes, and special-purpose lathes. For more detailed information about different types of lathes, readers may refer to Begeman. 19 Accurate and rigid means of positioning and holding workpieces on lathes are critical requirements for successful turning and other machining operations. The problem of position is closely related to the concept of isostatism. 21 The principle of isostatism means that positioning a workpiece on an isostatic jig confers on it a unique location in space that remains unchanged by removing and replacing the workpiece on its support. It is well known that a workpiece, as a solid object, has six degrees of freedom (three translations along and three rotations around the X, Y, and Z axes) that characterize its location. To locate a workpiece in a definite position, these six degrees of freedom need to be canceled. The method of canceling the degrees of freedom to locate a workpiece, called the principle of isostatism, has been defined as the six-point principle (or 3-2-1 principle) in the field of mechanical engineering. 21,22 To locate a cylindrical workpiece in a definite position, the six-point principle is applied as shown in Figure 1. The workpiece is first located on its surface using four points (1, 2, 3, and 4) and four degrees of freedom (two translations along and two rotations around the Y and Z axes) are canceled. A fifth point (5) is added to cancel the translation along the X axis. Finally, a sixth point (6) is applied to cancel the rotation around the X axis. Note that point 6 acts by friction and requires clamping, which is not strictly isostatic. Of course, isostatic positionhag without friction at the contact points and with punctual contact cannot be realized practically; however, it is an important guideline for designing workholding devices.

setup planning and fixture design is the design tolerance requirements of a component. The issue of tolerance analysis in setup planning cannot be ignored. Huang and Gu 16 and Boerma and Kals ~s provided some heuristic rules for setup planning based on tolerance analysis. Zhang, Huang, and Mei discussed in detail the influence of setup planning on tolerance control and proposed a graphical approach to aid the decision-making process while generating setup plans. ~7 Based on the graphical approach, Huang and Zhang further developed a graph-theoretical approach to setup planning solely based on tolerance consideration. ~s To deal with a variety of situations successfully, all of the analysis issues mentioned previously need to be incorporated into the development of an automatic setup planning system. Each of the prior research works addresses only certain aspects of the setup planning problem. As a result, suboptimal or even awkward setup plans are generated for some precision components. Furthermore, most of the research works focus on setuP planning for milling operations performed on a machining center. Setup planning for turning, boring, and other operations performed on a lathe is largely ignored. This paper presents an automatic approach to setup planning for components machined on a lathe. The issue of position and workholding on a lathe is discussed in Section 2. In Section 3, the problem of setup planning is formulated as a mathematical problem. The issues of geometry analysis, precedence constraint analysis, kinematic analysis, force analysis, and tolerance analysis are taken into consideration. In Section 4, an algorithm is presented to solve the setup planning problem. An example is then given in Section 5 to show the effectiveness of the algorithm. Finally, conclusions are drawn regarding the utility and applicability of the proposed setup planning approach.

2. Positioning and Workholding on a Lathe A lathe is a machine that removes material by rotating the workpiece against a cutter. Although a lathe can be used for many purposes, it is particularly adapted to turning operations for cylindrical workpieces. Other than turning, a lathe can also be used to perform drilling, boring, and reaming operations. In addition, it can be used for cutting threads

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6 (withclamping)

t

/__.x

~

Z

i

ii

i

Y 2

3

4

1

Fiaure 1

Application of Six-Point Principle to Cylindrical Workplece (modified from Halevi and WellF~)

Major types of workholding devices for turning operations are centers and dogs, face drivers, stead)rests and follower rests, mandrels and arbors, faceplates and fixtures, collets, and chucks. There are two different types of lathe machining, namely, between-center machining and chuck-type machining, depending on positioning and workholding methods? 9a3 Between-center machining follows this procedure: (1) locate center holes, (2) drill center holes, (3) mount the workpiece between centers using the pre-drilled holes, (4) face the end faces of the workpiece, and (5) turn the workpiece. 2° This procedure is fairly standard. Thus, setup planning for between-center machining is trivial. On the other hand, chuck-type machining involves a variety of situations and usually requires several setups to obtain the finished component. The setup planning algorithm presented in this paper focuses on setup planning for chuck-type machining.

isfied. Thus, the problem of setup planning can be stated as: given a stock (raw material) and the design requirements of a component, find a plan to transform the stock into the component by performing setup formation, datum selection, and setup sequencing. This problem can be formulated mathematically and solved using an algorithmic approach. The mathematical formulation is presented as follows. Workpieee Geometry A lathe is typically used to machine rotational components. Let F = ~ , j~, ,.., jr,} denote the set of features within a rotational component in which n is the number of features. Here, the term feature refers to a cylindrical, plane, or cone surface of the rotational component. Chamfers, grooves, tapers, threads, and holes are also examples of features. Features that are typically not machined on a lathe, such as keyways, are not considered. Figure 2 shows a rotational component that has 11 features (n = 11). Featuresf,f3,fe, andfn are plane surfaces. Features ~,J~,fi, andJ~ are cylindrical surfaces. FeaturesJ~ and /10 are chamfers, while feature f8 is a cone surface. A component is always made from a stock. Therefore, the stock shape needs to be considered. To make a rotational component, the stock used could be a cast or just a cylinder. In the case of a cast, most of the features exist on the stock. In the case of a cylinder, a number of features (that is, plane surfaces except two end faces) do not exist. A

3. Mathematical Formulation The tasks of setup planning include (1) setup formation, (2) datum selection, and (3) setup sequencing.U The task of setup formation is to group features within a component into sets so that each set of features can be machined in one setup. The task of datum selection is to select locating and clamping surfaces (that is, setup datums) for each setup. The task of setup sequencing is to sequence the setups so that the precedence constraints of machining are sat-

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able for locating or clamping. Cylindrical surfaces are usually used for clamping; however, when the stock is a cylinder, a cone surface of the designed component could be considered a potential clamping surface because it is not yet machined and takes the form of a cylindrical surface. On the other hand, some cylindrical surfaces are not suitable for clamping due to force and torque requirements. For example, in Figure 2, if the stock is a cast, features j~, j~, and f~, are obviously not suitable for locating or clamping. According to an expert machinist, feature j~ is also not suitable for clamping due to force and torque requirements. Only features fl, f2, j~, f,, fr, fT, andJ~ are suitable for locating or clamping. Thus, x = [1 1 1 1 0 1 1 0 0 0 1], X = {f~,f2,f3,f4,A, fT, fH}. Note that the determination of the fixmring vector is based not only on the design of the component but also on the stock shape. During the machining processes, the set of features that are suitable for locating or clamping might change. For example, assume feature fi of the component shown in Figure 2 needs to be threaded. Before it is threaded, f2 can be used for clamping; however, it cannot be used for clamping after threading. Therefore, the set of features that are suitable for locating or clamping is a variable depending on the status of the workpiece. Since the status of the workpiece after the ith setup is described using the set K~, the set of features that are suitable for locating and clamping after the ith setup can be described using the notation X(K~).

stock geometry vector k = [kl kz ... k,] is used to describe the stock shape, in which

1, if feature f~ exists on the stock k~ =

0, otherwise

i = 1, 2, ..., n

Let K0 denote the set of features that exist on the stock. External cylindrical and cone surfaces are considered to exist on the stock. For example, if the component shown in Figure 2 is to be made from a cylindrical stock, then k = [1 1 0 1 0 0 1 1 1 0 1], K0 = [f~,j~, f4,fi,j~,j~,jql].During machining, the shape of the stock might change. Some features that do not exist on the stock will be created after machining. Let Ki denote the set of features that exist after the workpiece was machined in the ith setup. Within a rotational component, some features are suitable for locating or clamping and others are not. This characteristic of the component is described using a focturing vector, x = [xl x2 ... x,], in which

xi =

l, if feature f~ is suitable for locating or clamping 0, otherwise i = 1, 2, ..., n

Let X denote the set of features that are suitable for locating or clamping. To determine the fixturing vector of a component, geometry and force analyses need to be performed. Obviously, cone surfaces, chamfers, grooves, tapers, and threads are not suit-

~

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J ,P~ufw 2 Features of Rotationsl Component

199

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~10

fll

/

Journal of Manufacturing Systems Vol. 17/No. 3 1998

To m a k e sure a cylindrical workpiece has a definite position on a lathe when performing chuck-type machining, a cylindrical surface is n e e d e d for clamping and a plane surface is needed for locating as a result o f kinematic analysis (Figure 1). In other words, one cylindrical surface and one plane surface need to be selected as the setup datums for each setup. Therefore, it is necessary to distinguish cylindrical surfaces from plane surfaces. Cylindrical surfaces within a rotational c o m p o n e n t are described using a cylindrical vector c = [cl Cz ...... cn], in which

described using a cone vector o = [ol o5 ...... on], in which 1, if feature f~ is a cone surface oi =

0, otherwise

00100001],P=

Tool Approach Direction The tool approach direction o f a feature is an unobstructed path that a cutting tool can take to access the feature. 1 A feature may have more than one tool approach direction. As shown in Figure 3, there are two possible tool approach directions (left or right) for features within a rotational c o m p o n e n t that are to be m a c h i n e d on a lathe. (Note that features that need to be approached straight-on, such as grooves, are not considered because usually they cannot be used as clamping surfaces.) Therefore, a feature can be m a c h i n e d (1) only from the left side, (2) only from the right side, and (3) either from the left side or from the right side o f the component. A n algorithm for finding tool approach directions for features within a rotational c o m p o n e n t based on geometry analysis can be found in Zhou. zs Let at, a

i = 1, 2, ..., n

1, if featuref~ is a plane surface 0, otherwise

o = [0000000

1 0 0 01, O = {3~}.

Let C denote the set o f features that are cylindrical surfaces. Plane surfaces within a rotational component are described using a plane vector p = [Pl pz ...... Phi, in which

Pi =

i = 1, 2, ..., n

Let O denote the set o f features that are cone surfaces. For the example part shown in Figure 2, e = [01010010100], C = {f2,J~,fi,3~}, p = [ 1 0 1

1, if featuref~ is a cylindrical surface c~ =

0, otherwise

i = 1, 2, .... n

Let P denote the set o f features that are plane surfaces. As mentioned previously, if the stock is a cylinder, a cone surface o f the designed c o m p o n e n t can be considered a potential clamping surface. Therefore, cone surfaces within a rotational component also n e e d to be distinguished. They are

Right

FiEure 3 Two Tool Approach Directions of Rotational Component

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Journal of Manufacturing Systems Vol. 17/No. 3 1998

two-dimensional vector, denote the tool approach direction of feature f~. The vector at is defined as follows:

Tolerance Factor

As previously mentioned, design tolerance requirements of a component are an important guideline for setup planning. Tolerances of a component can be categorized into local tolerances and relative tolerances. A local tolerance is related only to a single feature and is mainly determined by machine/process capabilities, such as the tolerance of a diameter of a hole. However, a relative tolerance is related to more than one feature and is influenced by not only machine/process capabilities but also by setup planning, such as the tolerance of a dimension between two end faces of a cylinder. Therefore, only relative tolerances of a component need to be analyzed in setup planning. 17 A tolerance can be converted into a tolerance factor by dividing the tolerance value by the representative length. The representative length depends on the type of tolerance and the dimensions of the component. It is calculated in such a way that the tolerance factor represents the tangent of the maximum admissible angle of rotation of the feature concerned. After conversion, the smaller the value of a tolerance factor, the more important the tolerance is. Readers may refer to Boerma and Kals 15 for more details about the converting scheme. When there is more than one tolerance relationship between two features, the total tolerance factor is calculated as

[1 0], i f f can be machined only from the left side of the component

ai =

[0 1], i f f can be machined only from the right side of the component [1 1], i f f can be machined either from the left side or from the right side of the component

Let matrix A =

Ial] a2

an

be the tool approach direction matrix of the rotational component. Let A~, A2, and A3 be the set of features that can be machined from the left side, from the right side, and either from the left side or from the right side of the component, respectively. Thus, A, ~ A2 = A3. For the example part shown in Figure 2, when chuck-type workholding devices are used, features fl, f2, andfa can be machined only from the left side (al = a2 = a 3 = [1 0]), featuresfs, f~,fi, fa, fg, flo, and )q, can be machined only from the right side (as = a6 = a7 = a8 = a9 = a,o = an = [0 1]), while feature f4 can be machined either from the left side or the right side of the component (a4 = [1 1]). Thus, A, = ~ , j ~ , A , A } , A2 = { f 4 , A , f 6 , J ~ , A , J ~ , A O , f l , } , A3 = .,4, ¢'~ A2 = {f4}. The tool approach direction matrix for the part shown in Figure 2 is as follows:

t--

i=l [i

in which t is the total tolerance factor, m is the number of tolerance relationships, and ti is the ith tolerance factor. The relative tolerance information of a component can be represented using a weighted, undirected graph G = (V, E) called a tolerance factor graph. The features within the component are represented as the vertices V= {fl,f2, ...,f,}, where n is the number of features. The relative tolerance information is represented using the weighted edges E = {e~, e2..... v=}, where m is the number of relative tolerances. If features f~ andf~ have a tolerance relationship (i, j = 1, 2, ..., n; i ~ j ) , then ~,J~) E E with the tolerance factor being its weight. Let T = [to] denote the adjacency matrix of tolerance factor graph G. Figure 4 shows a toleranced rotational component (local top erances are omitted). There are six features within

-1 o7 1

01

1

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°i 201

Journal of Manufacturing @stems Vol. 17/No. 3 1998

.

24

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.

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Unit: 1 × 10~ 2.5

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// // //

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Figure 4

Figure 5

Tolerated Rotational Component (local tolerances omitted)

Tolerance Graph and Its Adjacency Matrix for Component Shown in Figure 4

the component. Feature f~ has dimensional tolerances with featureJ~ (12 ___ 0.10) and featurej~ (40 _+ 0.15). FeatureJ~ also has a parallelism tolerance (0.03) with featurefv Feature f4 has a concentricity tolerance (0.02) with featurej~. Featurej~ has a perpendicularity tolerance (0.01) with feature 3q. The tolerance factor graph and its adjacency matrix for this component are shown in Figure 5.

(3) reflects the fact that the setup datums are not machined in that particular setup. Constraint (4) assures that one cylindrical surface and one plane surface are selected as the setup datums for each setup. Constraint (5) warrants that the selected datums are suitable for locating and clamping. All solutions satisfying the constraints are feasible solutions. To find a good solution, tolerance analysis needs to be performed.

Setup Planning The problem of setup planning can be formulated mathematically as finding the sets of features S~ (with features cl and pl as the setup datums), $2 (with features c2 and p2 as the setup datums) .... , S, (with features c, and Pr as the setup datums) to be machined in that sequence, subject to

V i E {1,2 .... ,r}

(2)

c,, p, E St

Vi E {1, 2 .... , r}

(3)

¢i ~ C, Pi E P

Vi E {1, 2 .... , r}

(4)

Ci, Pi E X ( K i _ I )

Vi E {1, 2 .... , r}

(5)

S~CA,,qE

{1,2}

4. Algorithm

Development

In this section, an algorithm is presented that can be used to generate setup plans for rotational components that are manufactured using chuck-type lathe machining. While vector representation expedites computerization, set representation facilitates presentation of the algorithm. Therefore, set representation is adopted in this section. The notations presented in Section 3 that are used in the algorithm development are summarized as follows:

(1)

S~LJS2u...uS, = F

2.5 0 0 7.1 0 0

f K0

Constraint (1) guarantees that all of the features within the component are machined. Constraint (2) ensures that all the features within the same setup have a common tool approach direction. Constraint

X

202

number of features within a rotational component features, i = 1, 2, ..., n set of features that exist on the stock set of features that exist after the workpiece was machined in the ith setup set of features that are suitable for locating or clamping (based on the design of the component and the stock shape)

Journal of Manufacturing Systems Vol. 17/No. 3 1998

X(K,) set of features that are suitable for locating C P 0

At A2

A3 T=

Let S" = S" u {f,}

and clamping after the workpiece was machined in the ith setup set of features that are cylindrical surfaces set of features that are plane surfaces set of features that are cone surfaces set of features that can be machined from the left side of the component set of features that can be machined from the right side of the component set of features that can be machined either from the left side or from the right side of the component [t0]adjacency matrix of the tolerance factor graph, i, j = 1, 2, ..., n

Let ,7* = S* - {f,} Go to statement "If S* = 9 then ..." Else Let a and b denote the number of elements in S" and S", respectively If a ___b then Let S' = S' u S*, S* = 9 , Exit Else Let S" = S" u S*, S* = 9 , Exit This algorithm groups the features within a rotational component into two sets, S' and S". This grouping satisfies constraints (1) and (2). After the features have been grouped into setups, setup datums for each setup need to be selected. The selection of setup datums needs to facilitate tolerance control, namely, features that have tight tolerance relationship need to be mutually dammed. 17,t8 The algorithm for selecting a cylindrical setup datum (denoted c') for setup S" is given as follows:

The first step of setup planning is setup formation. Setup formation is constrained by tool approach directions of features. Since there are two possible tool approach directions for a rotational component, the features within the component can be grouped into two sets. Features that can be machined only from the left side of the component can naturally be grouped into one set. Similarly, features that can be machined only from the right side of the component can be grouped into the other set. For a feature that can be machined either from the left side or right side, it must be assigned to a specific set. The assignment should be based on tolerance consideration, namely, features with tight tolerance relationships should be machined in the same setup, tS"t8 The task of setup formation is completed when all the features are assigned to a specific set. The algorithm for setup formation is given as follows:

LetH= CnXnS" If H = O then LetH= O~X~S" If H , 9 then Go to statement "Find t,~ = min [to] ..." Else Findf~ such that ~

Let S" = At - A3, S" = A2 - A3, S* = A3

t,,i = 0, in which f ,

j=l

ES'~A3nCnX,

If S* = 9 then

f i ES"

If such anfx is found then

Exit

Let S" = S" - {fx}, S" = S" + {fx}

Else

Let c" =f,, Exit

Find t~ = rain [to], in w h i c h f ~ A3 j~ ~ A3 to~O;i,j=l,2

.... , n

Else

If such a t~ is found then

L e t q ( / ] ) = m i n [to], V f E S ' n A , n X, in whichJ~ E S', to ~ 0

Iffy E At then

Find q(f~) = max [q(h)]

Let S '= S" u {f,,}

LetS" = S ' -

Else

203

{f,,}, S " = S " + {f,,}

nC

Journal of Manufacturing Systems Vol. 17/No. 3 1998

Let c" =f~, Exit

Else

Else

Let $1 = S", cl = c", Pl = P" Find t,,y = rain [to], in w h i c h f G H,

Let $2 = S', c2 = c', p~ = p '

f j ~ S',to~O; i , j = l,2, ...,n

Ifc~ ~ X(K1) ORp2 ~ X(KI) then

If such a t~ is found then

Swap S1 with $2, cl with c~, and pl with p2

Let c" =f~, Exit

If c~ ¢~ Ko n X then

Else

Let H~= C n X n

Let c" = f., in which f . ~ H and its diameter is the largest, Exit

If Hc ~ ~ then Let c~ =f~, in whichf~ E Hc and its diameter is the largest

The selection of a plane setup datum for setup S" is similar to the selection of a cylindrical setup datum except that the datum p ' has to be selected from set P instead of set C u O. Thus, setup datums for setup S" can be selected. The selection of setup datums for setup S" follows the same procedure. The sequence of applying this algorithm to the two setups is important w h e n X n A3 n S + = O, in which S + E {S', S"}. In this case, the datum selection algorithrn should be applied to setup S + last. The setup dattmas selected using this algorithm satisfy constraints (3) and (4). Note that in certain situations, this algorithm might find a solution in which both setups share a common cylindrical setup datum. In this particular situation, the component is not suitable for chuck-type machining. Instead, betweencenter machining is recommended. After setup datums are selected, the setups need to be sequenced. The constraint for setup sequencing is the precedence constraint, namely, the availability of the setup datums on the workpiece. In the meantime, the selection of setup sequence needs to facilitate tolerance control, m~8 The algorithm for setup sequencing is given as follows:

Else Let $3 = $2, c3 = c2, P3 = P2 Let $2 = $1, cz = cl, Pz = Pl Let $1 = {c2} Let cl =f~, in whichf~ E C ~ X ~ K0 and it is practical for machining & Letp~ =fy, in whichfy E e n X n K0, {f~,p2}

¢ A,, ~, p2} ¢ As Ifp~ ~ Ko ~ X t h e n Letpa =f., in whichf. E P n X n it is an end face

V f E {c',p', c",p"}, in which

5. Illustrative Example

1=1

In this section, an illustrative example is used to show the effectiveness of the algorithm. The design drawing of the example component is shown in Figure 6a (the unit is mm, surface finish and local tolerances are omitted). There are 11 features within the component, as illustrated in Figure 6b; therefore, n = 11. Assume the stock is a cylinder. Therefore, only featuresfa, f4,fi, fa, j~, andfn exist on the stock,

1, if to ~ O, ~, J}} ¢ S', {f, J]} (Z S"

w° =

$2 n Ko and

After setup sequencing, constraint (5) is also satisfied. The input of the algorithm is obtained by performing geometry analysis, kinematic analysis, and force analysis. The algorithm incorporates tolerance analysis and precedence constraint analysis when generating setup plans. Therefore, the algorithm can generate practical setup plans and can deal with a variety of situations gracefully.

!1

Let d(l~) = Z w o ,

& n Ko

0, otherwise

Find d(f~) = max [d(/~)], in w h i c h f E {c',p', c",p"} Iffx E {c", p"} then Let S, = S', c, = c',p~ =p" Let $2 = S", c~ = c", p2 = p"

Ko = ~ , A , f , , f , , f , , f , , } .

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1998

of the component, while feature f4 can be machined either from the left side or from the fight side of the component. Therefore, A1 = ~,j~,j~,j~}, A2 = {J4,fs, ff,fT,fs,fg,fl0,fn }, A3 = {/4}. The tolerance factors are calculated as shown in Table 1. Thus, the adjacency matrix of the tolerance factor graph is as follows:

t

I

100 9 6 -

1

,W

72-+ 0'10--~ 200+-0.20 ,

"2

240___0.10 q'h ¢,-q

(a) t,

t,

t~

t,

t~

~

t,

t,

t,0

t,1

? 0

(b)

Figure 6 Example Component: (a) Design drawing (surface finish and local tolerances omitted), (b) Feature illustration

Features fl, Y~, ff, and j q! are plane surfaces, features f~, J~, fi, and f9 are cylindrical surfaces, while featurefs is a cone surface. Therefore, P = ~,J~,f~, ]]~}, C = [f~, f~, f~,j~}, and O = {/8}. Based on the design of the component, it is easy to see that featuresf~,J~,j~, andfn are suitable for locating, while featureJ~ is suitable for clamping. FeaturesJ~ andf~0 are chamfers and thus not suitable for locating or clamping. Since the stock is a cylinder, featureJ~, a cone surface, is considered a potential clamping surface. Based on the component design, featuresJ~,fi, andJ~ are not suitable for clamping due to force and torque requirements. However, since the stock is a cylinder, features f~ and f9 are treated as potential clamping surfaces. Therefore, the set of features that are suitable for locating or clamping is determined as X = {fb f~,J~,f~, fT,f~,J~,fn}. Features f~, y~, and j~ can be machined only from the left side of the component, featuresfs, f~,y~,j'~,j~, f~0, and.f~l can be machined only from the right side

X ("--

~

~

~

X ~

~

~

~

~

~

X t "~

?

1

J II

The algorithm presented in Section 4 is applied to the example component as follows: Setup Formation: s" = A, - X3 =

f,,f,,f,o,A,},

205

S* =

S" =As-A3

= 7,}

=

Journal of Manufacturing System Vol. 17/No. 3 1998

Table l

Calculation of Tolerance Factors for Example Component Toleraneed Features

Tolerance Value

Representative L e n g t h

ft,~ f~a,J~ f~,J~ f~,f~

_ 0.20 _+0.10 -+0.10 0.05

96 48 144 40

Since S* = {f4} :;/: O, txy = t49 = 1.25 X 10-3 is found, andf~ =f9 ~ A~, it is determined that s"= s"u

~} = s"u

A,} andS* =s*

- ~}

0.4 / 96 = 4.17 × 0.2 / 48 = 4.17 × 0.2 / 144 = 1.39 x 0 . 0 5 / 4 0 = 1.25 x

10-~ 10 -~ 10-~ 10-~

Since H # O, t~ is not found, and the diameter offi is greater than that offg, it is determined that c" =ft. (4) the selection o f p '

{A} = {A,A,A,A,A,A,A,, =s*

Tolerance Factor

- {f,} = o .

H = P ~ X n S " = {f~,A,A, f n } n {f~,A,A,A,f7, ~ , ~ , ~ 1 } ~ { ~ , ~ , j ~ , ~ , ~ , f l O , ~ l } = {j~,fll}

Since S* = O, the process of setup formation is terminated.

Since H # O and t~ = t63 = 1.39 x 10-3 is found, it is determined that p" =f~.

Datum Selection:

Setup Sequencing:

Since x n ~3 n s ' = 0 L A , A , A , A , A , f , , A , } n {)~} n {]], J~,J~ } = O, the algorithm of datum selection is applied to setup S" first

d0C7) = 0, d ~ ) = 0, d ~ ) = 1, d ~ ) = 3

(1) the selection of c"

Since d(A) > d(A) > d(J~) = dT,f~ =J3. Sincefx =f3 = p " ~ {c",p"}, it is determined that S, = S" = {f~,J~,J~,J~}, ca = c' =J~,p, =p" =f6, $2 = s"= ~ , f , , f ~ , A , f , , A o , A , } , c~ = c" = f,, m = p" = f,.

H:CnXnS "= {f~,f~,fT, fg} n {f~,A,f~,A, fT, f,,A,A,} c~ ~ , A , A } = O Since H = O, the set H is determined as H = O n x c ~ s ' = ~ } n ~ , ~ , f , , A , f ~ , f , , A , A , } c~ {f,,A, jS} = 0 . Again H = 0 . No ~ is found to satisfy the

Since c2 E X(KO andp2 E X(K0, there is no need to swap $1 and $2.

n

condition that Z t~ = 0, in whichf~ E S" n A3 n C n

K, n X = 0 L f , , f i , A , A , A , } c~ 0q, A,A,f,,J~,A, Jg, fn} = {f~,f4,fT, Js, fg, fn}- Since c~ =f7 E K0 n X butpl =f6 ~ Ko n X, it is determined thatpl = f n .

j=l

X, y~ s S". However, it is found that q(f~) = q(J~) = 1.25 X 10-3. Therefore, S " = S " - {f~} = S " - {j]} = ~ , A , f , , A , f , , A , , A , } , s ' = s" + ~ } = s" + {f,} = 0q,A,A,A}, c" =f,.

Therefore, the example component can be machined in two setups as shown in Figure 7. In the first setup, featurej~l is used as the locating surface and feature f7 is used as the clamping surface. FeaturesJ~,3~,f3, and f4 are machined. In the second setup, feature j~ is used as the locating surface and feature f4 is used as the clamping surface. Featuresfs, J6,fi, J~,~,Jl0, and3ql are machined.

(2) the selection of p"

H =PnXnS'=

{fl,A,A, A1} c~ Oet,A,A,A, fT,

A,A,A,} c~ 0q,A,A} = 0q,A} Since H # O and t,~ = t~6 = 1.39 × 10-3 is found, it is determined that p" =J~. (3) the selection of c"

6. Conclusion

H= C AX

More and more CAD/CAM systems are being used by manufacturing companies to improve productivity. Current CAD/CAM systems require

n S " = {f2,A, fT, fg} n { f t , A , A , f ~ , f T ,

A,A,A~} n {A,A,A,A,A, Ao,A,} = {/;,A}

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Journal of Manufacturing Systems Vol. 17/No. 3 1998

to deal with lathe machining. Further research is needed to develop an effective setup planning algorithm for components machined using milling operations on a machining center.

tremendous amounts of user interaction not only during product modeling but also during process planning. Once a component is designed and represented using a CAD model, CAM users need to decide the setups and manufacturing processes involved to machine the component. They can then have the CAM software tool generate NC codes for the component through a sequence of interaction. In other words, most process planning decisions are made by users rather than the CAM software tool. The algorithm presented in this paper can be used to provide automated setup planning capability for CAM software tools, thus improving user productivity. The algorithm takes into consideration the issues of geometry analysis, precedence constraint analysis, kinematic analysis, force analysis, and tolerance analysis. As a result, it can deal successfully with a variety of components machined on a lathe. The drawback of this algorithm is that.it can only be used

References 1. T.C. Chang, Expert Process Planning for Manufacturing (Reading, MA: Addison-Wesley, 1990). 2. C. Hayes and E Wright, "Automating Process Planning: Using Feature Interactions to Guide Search," Journal of Mfg. Systems (v8, nl, 1989), ppl-14. 3. C.L.P. Chert, "Setup Generation and Feature Sequencing Using Unsupervised Learning Algorithm," Proc. of 1993 NSF Design and Mfg. Systems Conf. (vl, 1993), pp981-986. 4. Y.E Zhang, A.Y.C. Nee, and S.K. Ong, "A Hybrid Approach for Setup Planning," Int'l Journal of Advanced Mfg. Technology (vl0, 1995), pp183-190. 5. S.E. Sarrna and P.K. Wright, "Algorithms for the Minimization of Setups and Tool Changes in 'Simply Fixturable' Components in Milling," Journal of Mfg. Systems (v15, n2, 1996), pp95-112. 6. J.I. Karash, "Principles of Locating and Positioning," Handbook of Fixture Design (New York: McGraw-Hill, 1962), pp2-1 to 2-22. 7. D.A. King and A. de Sam Lazaro, "Process and Tolerance Considerations in the Automated Design of Fixtures," Journal of Eng. for Industry (v116, 1994), pp480-486. 8. S.H. Lee and M.R. Cutkosky, "Fixture Planning with Friction," Journal of Eng. for Industry (vl 13, 1991), pp320-327. 9. R.J. Menassa and W.R. DeVries, "A Design Synthesis and Optimization Method for Fixtures with Compliant Elements," ASME Syrup. on Advances in Integrated Product Design and Mfg. (1990), pp203218. 10. Y.C.Chou, V. Chandru, and M.M. Barash, "A Mathematical Approach to Automatic Configuration of Machining Fixtures: Analysis and Synthesis," Journal of Eng. for Industry (v 111, 1989), pp299-306. 11. J.D. Lee and L.S. Haynes, "Finite-Element Analysis of Flexible Fixturing System," Journal of Eng. for Industry (v 109, 1987), pp 134-139. 12. EJ.M. van Houten, "Strategy in Generative Planning of Turning Processes," Annals of CIRP (v35, nl, 1986), pp331-335. 13. H. Sakurai, "Automatic Setup Planning and Fixture Design for Machining," Journal of Mfg. Systems (vl 1, nl, 1992), pp30-37. 14. R.I.M. Young and R. Bell, "Fixturing Strategies and Geometric Queries in Set-up Planning," Int'lJournal of Production Research (v29, n3, 1991), pp537-550. 15. J.R. Boerma and H.J.J. Kals, "FIXES, A System for Automatic Selection of Set-Ups and Design of Fixtures," Annals of CIRP (v37, nl, 1988), pp443-446. 16. X. Huang and P. Gu, "Tolerance Analysis in Setup and Fixture Planning for Precision Machining," Proc. of 4th Int'l Conf. on Computer Integrated Mfg. and Automation Technology, Oct. 10-12, 1994 (Troy, NY: Rensselaer Polytechnic Institute, 1994), pp298-305. 17. H.-C. Zhang, S.H. Huang, and J. Mei, "Operational Dimensioning and Tolerancing in Process Planning: Setup Planning," Int7 Journal of Production Research (v34, n7, 1996), pp1841-1858. 18. S.H. Huang and H.-C. Zhang, "Tolerance Analysis in Setup Planning for Rotational Parts" Journal of Mfg. Systems (v15, n5, 1996), pp340-350. 19. M.L. Begeman, Manufacturing Processes, 4th ed. (New York: Chapman & Hall, 1957). 20. "How to Run a Lathe" (South Bend, IN: South Bend Lathe Works (SBLW), 1956). 21. G. Halevi and R.D. Weill, Process Planning Principles: A Logical Approach (New York: Chapman & Hall, 1995). 22. H.-P. Wang and J.-K. Li, Computer-Aided Process Planning (New York: Elsevier, 1991). 23. S. Cole, A.S. Dinsmore, T.C. Doud, E Ferdinand, G.Y. Gill, T.W. Judson, J.S. Larson, R.M. Perry, and J.M. Sullivan, "Turning and Boring,"

The First Setup

b.N1 b.",l kxl

i~,.e \'wt,~

The SecondSetup

Figure 7 Generated Setup Plan for Example Component Shown in Figure 6

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Journal of Manufacturing Systems Vol. 17/No. 3 1998

Tool and Manufacturing Engineers Handbook, Desk Edition (Dearborn, MI: Society of Mfg. Engineers, 1989), pp23-1 to 23-30. 24. S.H. Huang, "A Graph-Matrix Approach to Setup Planning in Computer-Aided Process Planning (CAPP)," Phi) dissertation (Lubbock, TX; Dept. of Industrial Eng., Texas Tech Univ., 1995). 25. E Zhou, "Form Feature and Tolerance Transfer from 3D Solid Model to a Setup Planning System," master's thesis (Lubbock, TX; Dept. of Industrial Eng., Texas Tech Univ., 1996).

industrial, and manufacturing engineering at the University of Toledo. Before returning to academia m 1998, he was with Unigraphics Solutions Inc. (formerly EDS/Unigraphics), where he held a position of engineering systems engineer and worked in the Unigraphics NC Automation PBU in an effort to develop an architectural framework for next-generation CAM systems. His research interests include CAD/CAM/CAPP integration, application of artificial intelligence (AI) in manufacturing, tolerance analysis for precision manufacturing, and environmentally conscious design and rnanufaeturing. His research papers have appeared in the Journal of Manufacturing Systems, International Journal of Production Research, IEEE Transactions on Systems, Man and Cybernetics, IEEE Transactions on Components, Packaging and Manufacturing Technology, liE Transactions, Computers in Industry, and the Journal of Engineering Design and Automation.

Author's Biography Samuel H. Huang received his BS in instrument engineering from Zhejiang University (ER. China) in 1991 and his MS and Phl) degrees in industrial engineering from Texas Tech University in 1992 and 1995, respectively. Dr. Huang is currently an assistant professor of mechanical,

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