j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 5 ( 2 0 0 8 ) 338–346

journa l homepage: www.e lsev ier .com/ locate / jmatprotec

A parametric FEA system for fixturing of thin-walledcylindrical components

Yan Wang ∗, Jianfan Xie, Zhijian Wang, Nabil GindyUniversity of Nottingham, UK

a r t i c l e i n f o

Article history:

Received 18 May 2007

Received in revised form

26 October 2007

Accepted 20 November 2007

Keywords:

FEA

Thin-wall

Cylindrical components

a b s t r a c t

Machining of thin-walled components has increasingly become a difficulty for manufactur-

ers. Advanced digital analyses have been developed by many researchers to model, predict

and reduce errors induced by machining processes. Fixtures for thin-walled components

to increase the rigidity of components, improve dynamic performance and reduce machin-

ing cost have been widely used in industries. However, modelling to simulate the impact

of fixture on the quality of thin-walled components is seldom reported. Moreover, today’s

machining shop floors, characterized by a large variety of products in small batch sizes,

require flexible simulation tools that can be quickly reconfigured. Parametric technology is

a key to implement it.

This paper proposed a parametric finite element analysis (FEA) system that can automati-

cally mesh components, assign material properties and boundary condition, and create FEA

Parametric

Abaqus

files ready for calculation with limited human interference. The system is focused on thin-

walled cylindrical components, including straight thin-walled cylinder, conic thin-walled

cylinder and angle-varying thin-walled cylinder. Based on the FE prediction, whether or not

a fixture is required and the impact of a support fixture on the component quality can be

assessed.

to determine the optimal cutting condition during machin-

1. Introduction

Thin-walled components have been widely used in theaerospace, automobile and power industries where weightmatters. In modern global manufacturing, companies areunder enormous pressure to reduce manufacturing cost andimprove component quality. On one side, aggressive machin-ing strategy is often applied on the thin-walled componentsto increase machine removal ratio, leading to larger machin-ing force, thus larger machining deformation and larger profileerror. On the other side, the tolerance on components is tighter

than before. Under such contradictory situations, machiningof thin-walled components has increasingly become a diffi-culty for the manufacturers.

∗ Corresponding author.E-mail address: yan.wang@nottingham.ac.uk (Y. Wang).

0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2007.11.216

© 2007 Elsevier B.V. All rights reserved.

The problem has been addressed by many researchers(Thevenot et al., 2006; Brave et al., 2005; Tsai and Liao,1999; Ratchev et al., 2002, 2004a,b,c,d; Mehdi et al., 2002a,b)using advanced simulation tools for modelling, predicting andreducing errors. The main concerns are focused on two issues:vibration and deformation. Vibration contributes to poor sur-face finish as well as shorter tool life and spindle life, anddeformation is the main contributory factor of dimensionalerror. Regarding the dynamic aspect of the machining of thin-walled components, Thevenot et al. (2006) proposed a model

ing process, in which the dynamic behaviour of workpiecewith respect to tool position was introduced in the stabilitylobes theory. Experimental approach to validate the 3D lobes

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 5 ( 2 0 0 8 ) 338–346 339

Nomenclature

a the oblique angle of conic thin-walled cyinderap the oblique angle of the pth section of angle-

varying thin-walled cylinderb The angle around the z axis of the reference

between two nodes N(i, j, k) and N(i, j, k + 1)BC(i, j, k) Boundary condition, which is the function of

variables i, j and kCS the coordinate system on the centre of the top

surface of the thin-walled cylinderDL element size in the length direction of the com-

ponentDR element size in the radius direction of the com-

ponentDT element size in the thickness direction of com-

ponentE Young’s modulusE1(i, j, k) element vector of element C3D8 and is a func-

tion of i, j and kE2(i, j, k) element vector of element C3D20 and is a func-

tion of i, j and kF machining force specified by userFCi the force boundary condition on component

during the ith stepFIX1 constraint on the bottom end surface of the

componentFIX2 constraint on the top end surface of the com-

ponentID(i, j, k) the identity number of a node and is a function

of i, j and kIDe the identity number of elementIDnm the identity number of the mth node of a ele-

mentL the total length of the straight or conic thin-

walled cylinderLp the length of the pth section of the angle-

varying thin-walled cylinderLET the number of finite element across the cylin-

der thicknessNL the number of nodes in the length direction of

the componentNR the number of nodes in the radius direction of

the componentNT the number of nodes in the thickness direction

of the componentN(i, j, k) node vector and is a function of variables i, j and

kR/R0 Internal radius of the top surface of the thin-

walled cylinderR(i, j, k) The distance from the node N(i, j, k) to the z axis

of the reference coordinate system cylinderS The number of section of the angle-varying

thin-walled cylinderT Thickness of the thin-walled cylinderTLi The tolerance constrains on the component

during the ith stepTol Tolerance in the thickness direction on the

thin-walled cylinder

X(i, j, k) The X value regarding the CS of node N(i, j, k)XS boundary condition on X direction for XY sym-

metryY(i, j, k) The Y value regarding the CS of node N(i, j, k)YS1 boundary condition on Y direction for X sym-

metryYS2 Boundary condition on Y direction for of XY

symmetryZ(i, j, k) The Z value regarding the CS of node N(i, j, k)ˇ The angle of the component in the radius

direction representing the symmetry boundary

condition

� Poisson ratio

construction was reported. Peripheral milling operation wassimulated and the tool was assumed to be more rigid thanthe workpiece. Considering high speed milling, Brave et al.(2005) suggested a method for obtaining the instability lobeswhen both machine structure and machined workpiece havesimilar dynamic behaviours. The method was validated byexperiments.

Due to the deflection of tool and workpiece inducedduring machining operation, the machine tool does notremove material from components as planned, thus, sur-face dimensional error is produced. Tsai and Liao (1999)developed a finite element model along with end millingcutting force model to analyze surface dimensional errorin the peripheral milling of thin-walled workpieces. In themodel, the geometry and thickness variations of the work-piece during machining are taken into account by modellingthe helical fluted end mill with the pre-twisted Timo-shenko beam element. Ratchev et al. conducted extensiveresearch regarding thin-walled structure using finite ele-ment analysis (FEA), covering force modelling for end milling(Ratchev et al., 2004a), material removal simulation (Ratchevet al., 2004b,c) and error compensation (Ratchev et al., 2002,2004d).

The researches in (Thevenot et al., 2006; Brave et al., 2005;Tsai and Liao, 1999; Ratchev et al., 2004a,b,c) were focused onprismatic components under milling operations. The dynamicbehaviour of thin-walled cylindrical components under turn-ing operation was studied by Mehdi et al. (2002a,b), containingtwo parts: simulation (Mehdi et al., 2002a) and experiments(Mehdi et al., 2002b). The simulation part took into accountthe damping due to rubbing between the tool flank andthe machined workpiece surface, and defined the param-eters governing the stability of the cutting process in thecase of thin-walled workpieces. The experimental part vali-dated the simulation by performing the test on thin-walledtubes with steel and aluminum alloy, using different oper-ating condition including dimensions, geometry and settingconditions.

Advanced models with experiment validation were pro-posed in Thevenot et al. (2006), Brave et al. (2005), Tsai and

Liao (1999), Ratchev et al. (2004a,b,c), Mehdi et al. (2002a,b)with the purpose of identifying the problems generated dur-ing thin-walled structure machining. Once the problem hasbeen modeled and predicted, means to reduce errors should

340 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 5 ( 2 0 0 8 ) 338–346

Fig. 1 – Components types and geometry parameters. (a) Straight thin-walled cylinder; (b) conic thin-walled cylinder; and (c)

(

varying angle thin-walled cylinder.

be employed. (Ratchev et al., 2002, 2004d) proposed a methodof error compensation by offsetting the tool path according tothe predicted deflection. This method is effective only if thecomponent is still rigid enough to resist machining forces. It isnot feasible for the very thin-walled monolithic components,which have already been deflected, even when a very smallforce is exerted on the component. For example, Trent Enginecasings are very thin cylindrical components having roughly2 mm thickness against approximately 500 mm diameter andheight. The casings are so flexible, that they deflect evenwhen pushed by fingers. Error compensation by offsettingthe tool path is useless for this type of components. Sup-port fixture is often required to increase component rigidityand improve the dynamic performance of the tool-componentsystem. Moreover, the support fixture allows much increasedmaterial removal rate, leading to improved machining effi-ciency and reduced machining cost. However, the researchregarding support fixture for very thin-walled components isstill lacking.

As components are becoming increasingly less in volumeand larger in variety to cater for customer needs, compo-nents in the same part family are often very similar to eachother. The components geometry can be easily updated inparametric CAD software, e.g. Pro/Engineer, but simulation ofthin-walled components behaviour in machining processesusing finite element analysis (FEA) is still a manual pro-cess and often needs professional skill. The time and effortrequired to build an FEA modelling for each different compo-nent are increasingly becoming unacceptable. A huge amountof time is wasted on doing the repeatable work, which couldbe up to 90% of the total FEA work in many cases. Such a hugeamount of repeatable FEA work can be easily reduced or elim-inated by employing a parametric FEA system. In this paper,a method of parametric FEA system for thin-walled cylindri-cal components is proposed. Based on the FEA, whether ornot a support fixture is needed can be assessed firstly againstthe tolerance requirement. If yes, how to support the compo-nents, and how much improvement the machining strategycan achieve can be further investigated. Written in Visualbasic, the parametric FEA system can undertake four func-

tions automatically with few interactions from the user: (1)node generation, (2) element generation, (3) material prop-erty and boundary condition assignment, (4) steps (loadingsequences).

2. Frame work of the parametric FEAsystem

The types of thin-walled components considered in the sys-tem are straight cylinder (Fig. 1(a)), conic cylinder (Fig. 1(b)) andvarying-angle conic cylinder (Fig. 1(c)). For thin-walled cylin-drical components, it is in general held at this end surface forthe machining of the thin wall. If excessive machining defor-mation is encountered, a fixture is often required to hold thecomponent at this other end to increase the rigidity of thecomponents. If the accuracy requirement of components isstill not achievable, it is necessary to support the thin wall ofcomponent using support fixture, e.g. the fixtures in (Koelling,1998; CPF, in pressa,b).

The assumptions of the parametric FEA system are: elasticdeformation; point force; rigid fixture/support. The machiningforces, deformation and tolerance in the thickness directionare of concern and thus are considered in the FEA. The inputparameters of the FEA system for thin-walled cylindrical partsare composed of

(i) The geometry parameters including thickness T, lengthL, internal radius R of top surface, angle a shown in Fig. 1(b); straight cylinder in Fig. 1(a) is treated as a special caseof conic cylinder with a = 0; the varying angle thin-walledcylinder (Fig. 1 (c)) refers to the conic thin-walled cylinderhaving the same thickness but different angle at differ-ent section, and has variables including a constant wallthickness T, the internal radius R0 of the top surface ofthe component, the number of sections S, for the pth sec-tion, whilst p ∈ [0, S−1], the variables are angle ap, internalradius of the top surface Rp and the length Lp.

(ii) Machining force F and quality requirement (tolerance) Tol.iii) Material parameters including Young’s modulus E and

Poisson ratio v.(iv) Number of elements across the thickness LET. The default

value for this one is 2, which means there are two finiteelements across the thickness direction. However, thiscan be specified by user.

Abaqus is used for the FEA solver. Two types of solid ele-ments are selected for the system: the 1st order brick elementC3D8 and the 2nd order brick element C3D20. The 2nd order

t e c

eaupetdriwibtcberi

3

Atstt

D

wtdb

E

wfn

got

j o u r n a l o f m a t e r i a l s p r o c e s s i n g

lement C3D20 is preferred as it is more computation efficientnd more accurate (ABAQUS, 2004). The 1st order element issed for contact analysis when the 2nd order element is inap-ropriate if local deformation or stress at the contact position,.g. the contact between machine tool and component, needso be predicted accurately. Based on the input information, theeveloped software can generate the FEA input file ready to beun on ABAQUS. From the tolerance constraints Tol, the max-mum machining forces exerted on the components with or

ithout fixture can be estimated. Whether or not the machin-ng force F specified by the user is appropriate can be evaluatedy comparing the deformation induced by the force F with theolerance Tol. Two situations are considered in the software:omponents held at one end surface and component held onoth end surfaces. Since the FEA is parametric, if the geom-try of components is slightly changed, the FEA input can beegenerated automatically. The procedure to generate FEA files detailed in Section 3.

. FEA input file generation

global coordinate system CS (shown in Fig. 1) is built onhe centre of the top end surface of the cylinder. For a userpecified variable LET, which is the number of elements acrosshe thickness, the size of an element on the internal wall ofhe cylinder is pre-defined as

T = T

LET, DL = DT and DR = 1.5DT (1)

here DT, DR and DL are the dimensions of the element acrosshe thickness, around the centre axis and along the lengthirection, respectively, thus, ET, ER and EL, which are the num-ers of elements in these three directions, are

T = LET; EL = Int(

L

DL

)and ER = Int

(ˇR

DR

)(2)

here �, to be explained later, can be � or 1/2�, and theunction Int(number) is used to round a number down to theearest integer.

Mesh generation is the procedure of discretization of solideometry and includes the generation of node and generation

f element. Let NT, NR and NL be the number of node in thehree directions, for the C3D8 element and C3D20 element:

NT = ET + 1, NR = ER + 1 and

Fig. 2 – The node vector N(i, j, k) o

h n o l o g y 2 0 5 ( 2 0 0 8 ) 338–346 341

NL = EL + 1 for C3D8 element (3)

NT = 2 ∗ ET + 1, NR = 2 ∗ ER + 1 and

NL = 2EL + 1 for C3D20 element (4)

The node vector N[i, j, k], where i ∈ [0, NL − 1], j ∈ [0, NT − 1]and k ∈ [0, NR − 1], is represented as

N[i, j, k] = [ID(i, j, k), X(i, j, k), Y(i, j, k), Z(i, j, k)] (5)

where ID(i, j, k), X(i, j, k), Y(i, j, k), Z(i, j, k)] are the node numberand the X, Y, Z values regarding the global coordinate systemCS, respectively, and are functions of variables i, j and k. Theelement vectors are expressed differently for element C3D8and C3D20, which are

E1(i, j, k) = [IDe, IDn1, . . . , IDnm, . . . , IDn8]

for C3D8 element, m ∈ [1, 8] (6)

E2(i, j, k) = [IDe, IDn1, . . . IDnm, . . . , IDn20]

for C3D20 element, m ∈ [1, 20] (7)

where E1 and E2 represent the element vectors of elementC3D8 and C3D20, respectively and IDe is the element ID num-ber, the IDnm is the ID number of the mth node of the elementand is a function of the variables of i, j and k. Sections 3.1 and3.2 explain the automatic generation of node and element forthe C3D8 element and C3D20 elements.

3.1. Node and element generation for C3D8 element

The node number starts from the node whose position is (R,0, 0), and increases firstly in the length direction and secondlyin the thickness direction, and then in the direction aroundthe centre axis. The node number ID(i, j, k) of a node N(i, j, k),where i ∈ [0, NL − 1], j ∈ [0, NT − 1] and k ∈ [0, NR − 1], is

ID(i, j, k) = NLNT k + NL j + i + 1 (8)

As shown in Fig. 2(a), for conic and straight thin-walledcylinder, the Z(i, j, k) of the node N(i, j, k) is

Z(i, j, k) = DL i (9)

f conic thin-walled cylinder.

342 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 5 ( 2 0 0 8 ) 338–346

Fig. 3 – The node vector of angle-varying thin-walled

Fig. 5 – Element E1(i, j, k) and its nodes.

cylinder.

The distance of Node N(i, j, k) to the z axis of the CS, whichis the centre axis of the cylinder, is R(i, j, k):

R(i, j, k) = R + Z(i, j, k) tan(a) + DT j (10)

As shown in Fig. 2(b), let b be the angle around the Z axis ofthe coordinate system CS between nodes next to each other,b = DR/R, then

X(i, j, k) = R(i, j, k) cos(b k) (11)

Y(i, j, k) = R(i, j, k) sin(b k) (12)

For varying-angle thin-walled cylindrical parts, the Z(x, y,z), the z coordinate value of the node N(i, j, k) shown in Fig. 3,is the same as that in Eq. (9). The R(i, j, k) is different from thatin Eq. (10):

R(i, j, k) = R0 + Z(i, j, k)tan(a0) + DT j if 0 < Z(i, j, k) < L0 (13)

R(i, j, k) = Rp +(

Z(i, j, k) −p∑

u=0

Lu

)tan(ap)

+DT j if Z(i, j, k) ∈[

p∑u=0

Lu,

p+1∑u=0

Lu

](14)

Fig. 4 – Flow chart of node generation for C3D8 element.

e

where L0, R0 and a0 are the length, internal radius and angleof the top surface of the top section of component, and Lp,Rp and ap are the length, internal radius and the angle of thepth section of the component, and p ∈ [1, S − 1]. The X and Ycoordinate values of the node N(i, j, k) are the same as thesein Eqs. (11) and (12). The flow chart of the iteration for the ID(i,j, k), X(i, j, k), Y(i, j, k) and Z(i, j, k) of the node N(i, j, k) is shownin Fig. 4 for the 1st order element C3D8.

After the node generation, it is necessary to generate theelement by the software. As shown in Fig. 5, a C3D8 elementE1(i, j, k) is an element composed of eight nodes, starting fromthe node whose node number is ID(i, j, k), where i ∈ [0, NT − 2],j ∈ [0, NL − 2] and k ∈ [0, NR − 2], the IDn1, . . ., IDn8, which arethe node ID numbers of E1(i, j, k) in relation to the i, j and k,is shown in Fig. 5(b). With the initial value of IDe being zero,the flow chart of C3D8 element generation is the same as thatshown in Fig. 4 except the highlighted part, which is changedto

IDe = IDe + 1

IDn1 = ID(i, j, k)

. . .

IDn8 = ID(i + 1, j, k + 1)

E1(i, j, k) = [IDe1, IDn1, . . . , IDn8]

Print E1(i, j, k) to the FEA file

(15)

3.2. Node and element generation for C3D2D element

As shown in Fig. 6, there is a middle node on each of the 12 edgeof the 2nd order solid element C3D20, and there is no node onthe centre of the element surface, in other word, the iterationwill be skipped if any two of the three variables i, j, k are odds,where i ∈ [0, NL − 1], j ∈ [0, NT − 1], the highlighted iterationbody shown in Fig. 4 for a node N(i, j, k) should be modified as

below:

If[any two of the three variables i, j and k are odds = fals

N(i, j, k) = ID(i, j, k), X(i, j, k), Y(i, j, k), Z(i, j, k)]

Print N(i, j, k) to the FEA file

End ifIteration for element generation of E2(i, j, k), i ∈ [0, EL − 1],

j ∈ [0, ET − 1] and k ∈ [0, ER − 1] is similar to Fig. 4 and the high-

lighted body is modified as below, where IDn1, . . ., IDn20, which

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 5 ( 2 0 0 8 ) 338–346 343

Fig. 6 – Element E2(i, j, k) and its nodes.

bou

a

3s

3Ta

3BaoN

B

w“oD(3rnf

s

boundary condition can be represented by the constraints ofY direction on the nodes N Set whose X coordinate value is

Fig. 7 – Symmetry

re the functions of ID(i, j, k), are shown in Fig. 6(b):

IDe2 = IDe2 + 1

IDn1 = ID(2i, 2j, 2k)

. . .

IDn20 = ID(2i, 2j + 2, 2k + 1)

E2(i, j, k) = [IDe1, IDn1, . . . , IDn20]

Print E2(i, j, k) to the FEA file

(17)

.3. Material property and boundary condition andteps

.3.1. Material propertieshe parameters of material property are Young’s modulus End Poisson ratio v, which are input by user.

.3.2. Boundary condition and stepsoundary condition includes displacement and force bound-ry condition. The vector of a boundary condition is a functionf variables i, j, k, where i ∈ [0, NL − 1], j ∈ [0, NT − 1] and k ∈ [0,

R − 1] and is represented as

C(i, j, k) = [Type, N Set, DF1, DF2, Mag] (18)

here “Type = 0” for displacement boundary condition, andType = 1” for force boundary condition; N Set is the noder node set on which the boundary condition is applied,F1 and DF2 are the first and the last constrained DOF

degree of freedom), respectively. DF1 and DF2 are 1, 2 andif the constrained DOF are X, Y and Z regarding the CS,

espectively, DF2 is optional and is left empty if it does

ot exist. Mag is the magnitude of the displacement or the

orce.If the component geometry and boundary condition is

ymmetrical, it is desirable to model part of the component

ndary condition.

geometry with extra boundary condition to reduce the cal-culation time. The variable introduced to represent that partof the component is variable �, which will be automaticallyassigned if the geometry and boundary condition are sym-metrical about the X axis or the Y axis.

3.3.3. Boundary condition—X symmetry (� = �)As shown in Fig. 7(a), if the component geometry and itsboundary condition are symmetrical about the XZ plane ofthe CS, only half of the geometry with extra boundary condi-tion shown in Fig. 7(b) needs to be modelled. The X symmetry

Fig. 8 – Flow chart for boundary conditions and steps.

n g t

344 j o u r n a l o f m a t e r i a l s p r o c e s s i

zero:

YS1 = BC(i, j, k) = [0, N Set, 2, , 0] (19)

where N set = {ID (i, j, 0) and ID (i, j, Int(NR/2)), i ∈ [0, NT − 1],j ∈ [0, NL − 1]}. Y symmetry can be regarded as X symmetry byassigning an appropriate coordinate system CS.

3.3.4. X and Y symmetry (� = 1/2�)If the geometry and force and displacement boundary condi-tion are symmetrical about both the XZ plane and YZ planeof the CS, only 1/4 geometry of the components as shownin Fig. 7(c) should be employed, and for i ∈ [0, NT − 1] andj ∈ [0, NL − 1], the boundary constraints of X and Y symmetryare

XS1 = BC(i, j, k) = [0, N Set, 1, , 0]

where N set = [ID(i, j, 0)] (20)

YS2 = BC(i, j, k) = [0, N Set, 2, , 0],

where N set = [ID(i, j, Int(1/2NR))] (21)

Fig. 9 – Interface of the parametric FEA system. (a) Co

e c h n o l o g y 2 0 5 ( 2 0 0 8 ) 338–346

3.3.5. Held on the bottom end surfaceThe initial condition is that the component is fixed in X, Y,Z directions of the end surface, whose z coordinate value isL for conic cylinder and

∑S−1p=0Lp for angle-varying cylinder

regarding the CS, The boundary condition vector is

FIX1 = BC(i, j, k) = [0, N set, 1, 3, 0] (22)

where N set = {ID(NL − 1, j, k), j ∈ [0, NT − 1] and k ∈ [0, NR − 1]}.

3.3.6. Held on the top end surfaceIf the machining deformation of the component is excessive,a fixture is required to hold the top end surface of the com-ponent whose z coordinate value is zero. In this case, thedisplacement boundary condition is

FIX2 = BC(i, j, k) = [0, N set, 1, 3, 0] (23)

where N set = {ID(0, j, k), j ∈ [0, NT − 1] and k ∈ [0, NR − 1]}.

3.3.7. ToleranceTolerance Tol, a user input variable, is the maximum alloweddeformation in the thickness direction. The tolerance Tol may

nic cylinder and (b) angle-varying conic cylinder.

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 5 ( 2 0 0 8 ) 338–346 345

(Con

bimtti

T

lT

F

wtEf

3Sm

Fig. 9 –

e applied on the nodes on the thin wall of components dur-ng different steps (loading sequence) in order to calculate the

aximum allowed machining forces. Let us assume that theolerance is applied on the node ID(i, 0, 0) where i ∈ [0, NL − 1] inhe ith steps, the boundary condition vector for the tolerances

Li = BC(i, j, k) = [0, ID(i, 0, 0), 1, , Tol] (24)

The maximum allowed machining forces Fmax should beess than the minimal reaction forces on the nodes where theol is applied on:

< Fmax = Min(RF0, . . . , RFi, . . . , RFNL−1) (25)

here RFi is the reaction force on the nodes ID(i, 0, 0) where theolerance Tol is applied. F is the machining forces input by user.q. (25) can be used to assess whether or not the machiningorce specified by the user is acceptable.

.3.8. Force boundary conditionimilar to the boundary condition vector for tolerance,achining force F is applied on the nodes on the thin wall

tinued )

of components during different steps in order to calculate themachining deformation. Assuming the force is applied on thenode ID(i, 0, 0) during the ith step, the boundary conditionvector for the force is

FCi = BC(i, j, k) = [1, ID(i, 0, 0), 1, , F] (26)

To meet the tolerance requirement, the maximum defor-mation Dmax induced by the machining force F on the wall ofthe component should be less than the tolerance Tol:

Dmax = Max(D1, . . . , Di, . . . DNT−1) < Tol (27)

where Di is the deformation induced by machining force F onthe node ID(i, 0, 0). If Eq. (26) cannot be satisfied when both topand bottom surfaces of components are constrained, fixturethat supports components on the thin wall is then required.

3.3.9. StepsThere are NL nodes in the length direction, therefore, NL stepsis applied. The flowchart of steps iteration is shown in Fig. 8.

n g t

r error in the peripheral milling of thin walled workpieces.

346 j o u r n a l o f m a t e r i a l s p r o c e s s i

4. System introduction

After starting the software, the user needs to select thecomponent type: conic thin-walled cylinder or angle-varyingthin-walled cylinder. Since the geometry parameters of thesetwo components are different, the interfaces for the userare slightly different as shown in Fig. 9(a) and (b). The userinterface includes five parts: geometry parameters, materialproperty assignment, force and tolerance assignment, bound-ary condition and mesh generations. Once the user specifiesthe input, an FEA input file is generated and ready for calcu-lation on the FEA solvers.

5. Conclusions

Fixture is an effective means for thin-walled components toreduce deformation, vibration and increase material removalratio. The research regarding fixture for thin-walled com-ponents is seldom reported. It has been recognised thatmodelling of the machining process of thin-walled compo-nents is important. However, the current modelling processis still dedicated and time-consuming, and much of the workto build a simulation is repeatable. Parametric technology forFEA simulation is highly demanded to realise a flexible andreconfigurable manufacturing of the thin-walled components.

In this paper a parametric FEA software system is devel-oped for thin-walled cylindrical components. Three typesof components are considered: straight thin-walled cylin-der, conic thin-walled cylinder and angle-varying thin-walledcylinder. Based on user input, including geometry parametersof the components, material property, boundary condition,tolerance and machining forces, the FEA input file can be gen-erated automatically. Two situations are taken into account:components fixed at one end surface and components fixed atboth end surfaces. After comparing the deformation inducedby machining forces to the tolerance, it is possible to assesswhether a fixture to support the wall of the thin-walled com-ponents is needed.

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