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Design of an FDM positioning systemand application of an error-cost

multiobjective optimization approach Marlon Wesley Machado Cunico and Jonas de Carvalho

Department of Mechanical Engineering, University of Sao Paulo, Sao Carlos, Brazil

AbstractPurpose – As a result of the increased number of applications for additive manufacturing technologies and in addition to the demand for partsproduced with high accuracy and better quality, the need for the improvement of positioning and precision equipment in manufacturing has becomeevident. To address this needed improvement, the main goal of this work is to provide a systematic approach for designing additive manufacturingmachines, allowing the identification of the relationship between estimated errors and the cost of equipment. In the same way, this study also intendsto indicate a suitable configuration of a machine as a function of final accuracy and total equipment cost.Design/methodology/approach – To identify the suitable elements of the machine, a numerical model that estimates the final error and relative costof equipment as a function of cost and tolerance of the machine elements was constructed and evaluated. After evaluating this model by comparing itwith first-generation fused deposition modelling (FDM) machines, an optimisation study was performed that focused on the minimisation of both thetotal cost and final equipment error. The optimisation problem was defined in accordance with the goal attainment method, which allowed

identification of the Pareto optimum of the study. The optimisation results were then compared with current equipment concepts, and possibleimprovements and restrictions of the optimised concept were described.Findings – With regard to the evaluation of the numerical model of final error, the general error in the x - and y -direction was observed to have adeviation of 2 mm, while the numerical error in the z -direction was found to be inferior to that of currently used equipment. The optimisation study alsoallowed the identification of the machine elements that provide the minimal error and cost for the equipment, identifying an optimal Pareto of thesystem. In such an optimal case, the average of the final errors for the balanced solution (in which the objective functions have equal importance) wasfound to be 141 mm. In addition, the cost of this solution was 1.57 times higher than the cheapest solution found. Finally, a comparison between theconfiguration of commercial FDM machines and the optimum values was found, highlighting the main points that would possibly provide animprovement to the current concepts and an increase in equipment profitability.Originality/value – Despite the growth of additive manufacturing development, there are still several challenges to overcome to increase the accuracyof the final parts, such as the reduction of mechanical errors. However, in addition to the complexity of this subject, the cost of equipment restricts thedevelopment of new solutions. As a result, a systematic approach to identify a suitable configuration of each machine in accordance with the optimalaccuracy and cost of equipment is needed.

Keywords Layered manufacturing, Product design, Error analysis, Optimisation techniques, Manufacturing systemsPaper type Research paper

The intense growth of additive manufacturing technologies

and their applications in the last few years have given rise to

an increased demand for high accuracy parts. However, the

development of these technologies faces several challenges,

such as the needed increase in quality and strength of the final

products (Gibson et al., 2010; Cunico, 2011). The main goal

of this work is to evaluate a systematic approach for the design

of additive manufacturing equipment in which both cost and

final accuracy of the machine are considered.As the basis of this study, a layout of a positioning system such

as the stereolithography or selective laser sintering equipment

(Gibson et al., 2010) was selected. In these systems, the

displacement of the tool head is a direct result of the action of

mechanical elements and does not to involve mirrors or

galvanometers. Figure 1 shows a schematic of the selected

concept, which is equivalent to a firstgeneration fused deposition

modelling (FDM) machine, such as a 3D Modelerw or FDM

series (Wang, 2010). It is alsointeresting to notethat variations of

this concept were adapted for simultaneous deposition and

polymerisation (SDP), laminated object modeling (LOM) and

3D print technologies. Consequently, this work can also be used

for the improvement of other similar technologies (Gibson et al.,

2010; Cunico, 2011).

For this research, a numerical model that allows the

identification of the cost and final error of the equipment

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/1355-2546.htm

Rapid Prototyping Journal

19/5 (2013) 344–352

q Emerald Group Publishing Limited [ISSN 1355-2546]

[DOI 10.1108/RPJ-11-2011-0117]

The authors would like to acknowledge the financial support of CAPES,in addition to technical support of the Department of Post Graduation inMechanical Engineering of the University of Sao Paulo (campus SaoCarlos), for providing access to infrastructure and laboratory.

Received: 11 November 2011Revised: 26 December 2011, 13 March 2012Accepted: 16 March 2012

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wasstudied.Furthermore, this work presents theevaluation of the

numerical model, which was used to perform an optimisation

study for the minimisation of relative cost and final equipment

error.

The variables considered for the numerical model were the

general tolerance grade for the manufacturing of supports and

structural elements, the tolerance of linear guides and the

accuracy of linear transmission. Similarly, the equipment cost

was estimated as a result of the relative cost of the main

machine elements and manufacturing features.

To construct the numerical model, we applied precision

engineering methods, such as error budgeting, to identify the

final error of the equipment. We also only considered

geometric errors to compose this model, while the cost-

tolerance function was composed of component and

manufacturing costs. In cost-tolerance case, we identified

the regression of the cost-tolerance function components in

addition to applying a simple reciprocal model to find the

manufacturing cost as a function of tolerance (Dong et al.,

1994; Slocum, 1992).

The goal attainment optimisation method was applied to

accommodate multiple objectives of the optimisation study.This method consists of the optimisation of a system composed

of several objective functions. Each of these functions as

weighted according to the importance of that objective in the

optimisation problem. Then, the sensitivity of the optimisation

study was analysed, allowing the Pareto optimum to be

identified, which describes the optimal solutions of cost and

error according to the weighted variation of importance of each

objective (Rao, 2009).

Finally, the optimisation results were compared with

current equipment concepts, and the restrictions of the

improvements of these concepts were discussed.

Materials and methods

To construct the numerical model of final equipment errors,

the tolerances and costs of the main machine components,

such as linear guides, linear bearings and shafts, lead screws,

timing belts and pulleys and ball screws were estimated.

Additionally, a simple reciprocal model was considered to

estimate the relative cost, which includes the manufacturingprocesses as a function of tolerance (Dong et al., 1994).

For the optimisation study, Matlab was used as a

computational tool to solve the theoretical model, along

with the goal attainment method to define the multi-objective

problem. To solve the numerical model, we performed a

Newton modified routine, which identified the local optimum

solution for the numerical system (Rao, 2009).

Machine elements and manufacturing parameters

For the main machine elements of the proposed positioning

system numerical model, we researched the cost and tolerance

of two groups of components: transmission and linear guides.

Figure 2 shows the relationship found between cost and

machine element accuracy, in addition to their respectivetolerance grades (THK, 2011, 2007; Gates, 2011, 2006;

Thomson, 2009a, b; Hiwin, 2008, 2006; Slocum, 1992).

From these results, a regression cost-tolerance curve was

constructed for the transmission elements (Figure 3). This

curve estimates thecost of themachine elements as a function of

tolerance.The confidenceinterval of thisregression mayalso be

verified, although the least square was found to be above 0.90.

In the same way, the relationship between the cost and

tolerance of the linear guide is determined in Figure 4, whose

regression analysis resulted in a least square value equal to

0.966. This value indicates that the confidence of the

regression is suitable for use in the numerical model.

To determine therelative costof manufacturing processes,we

decided to use a simple reciprocal model that indicates the

general relative cost as a function of the manufacturing

tolerance grade. Because the range of this study is bounded by

IT7 and IT1 accuracy grades, it was possible to identify the

numerical model presented in equation (1). In this equation,

the costis shown as a result oftolerance (d ) and sense coefficient

(c0), which determine the referential form of the curve. Then,

we establishedthe sense coefficient to be equal to the IT7 grade

(0.052mm), which resulted in the curve shown in Figure 5

(Dong et al., 1994; Shigley and Mischke, 1996):

Cost ¼ c0 · d 21 ð1Þ

After estimating the cost-tolerance functions of the main

components of the positioning system, we formulated ageneral cost-function equation that takes into account the

manufacturing tolerances, machine element accuracy and the

number of machine elements, as presented in equation (2).

Through the use of this equation, it is also possible to evaluate

other equipment layouts in addition to identifying

the contribution of each component for the final cost of the

equipment:

C total ¼ ðC g x · N ax þ C g y · N a y

þ C g z · N azÞ · w1

þ ðC t x · N bx þ C t y · N b y

þ C t z · N bzÞ · w2 þ C m · w3

ð2Þ

Figure 1 Schematic of a first-generation FDM machine

X

Y

Z

Source: Crump et al. (2009)

Design of an FDM positioning system

Marlon Wesley Machado Cunico and Jonas de Carvalho


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where:

C total is the sum of the machine element and

manufacturing operation costs.C g x, C g y and C g z are the costs of linear guides of the x-, y-, and

z-axes, respectively.C t x, C t y and C t z are the costs of the transmission elements of

the x-, y-, and z-axes, respectively.C m is the relative cost of the manufacturing

operation.

w1 is the weight of the relative cost of the linear

guides.

w2 is the weight of the relative cost of the

transmission elements.

w3 is the weight of the relative cost of the

manufacturing operation.

N ax, N a y and N az

are the quantities of linear guides used in the

model. N bx, N b y and N bz are the quantities of transmission elements

used in the model.

In accordance with the proposed equipment layout, the

quantity of linear guides for the x- and y-axes is equal to 2,

using no linear guide and four transmission elements

Figure 2 Relation of main positioning machine elements, accuracy grade, general error and relative cost

Machine Element Accuracy Grade General Error Relative Cost

normal (c ) 38 µm 1

High (H) 29 µm 1,170731707

normal (c ) 17 µm 1,97597561

High (H) 12 µm 2,173658537

Precision (P) 6 µm 2,498780488

Superprecision (SP) 3 µm 2,999756098

Ultraprecision (UP) 2 µm 3,749634146

Lead Screw IT10 500 µm 1

Timing Belt T10 + Pulley IT7 IT07 100 µm 1,291248207

C10 210 µm 1,552941176

C07 52 µm 1,918425907

C05 23 µm 1,833572453

C03 12 µm 8,3

Linear bearing - Pillow Block

Linear guide - profiled rail

Ball Screw

L i n e a r G u i d e

T r a n s m i s s i o n

Figure 3 Regression curve of transmission elements, accuracy and relative cost

700 µm

600 µm

500 µm

400 µm

300 µm

200 µm

100 µm

0 µm

0.8 1

y = 573,63 x –4.354

R2 = 0.9544

1.2

B a l l S c r e w

- C

1 0

T i m i n g B e l t T 1 0

+ P u l l e y I T 7

B a l l S c r e w - C 7

B a l l S c r e w - C 5

Lead Screw

1.4 1.6 1.8 2

Relative cost

A x i a l E r r o r




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for the z-axis. Similarly, the weight of the cost of the

transmission elements is found to be 3.4, making the general

cost of transmission higher than the linear guide in that

proportion. We also defined the value of the manufacturing cost

weight as 1 to consider the minimal cost necessary to fabricate

the equipment.

It is also important to note that this study focused on

geometric errors, making it primarily useful for the

conceptual design process. In other applications, additional

sources of error should also be studied, such as kinematics,dynamics and thermal errors. Because these errors are caused

by external forces, such as thermal expansion, material

instability, friction, vibration and random sources, they should

be considered in a second step (detailed design), where

detailed specifications can be developed for materials,

dimensions and forces, among other parameters (Venkatesh

and Izman, 2008; Tan et al., 2008; Dornfeld and Lee, 2007;

Slocum, 1992). Therefore, we emphasise that the intention of

this proposal is to help the designer select a suitable machine

layout for the development of a novel positioning system in

the preliminary stages of a project.

Another point of interest is the effect of process parameters

on the final accuracy of the part. These parameters include

deposition and extrusion velocities, extrusion and chamber

temperatures, height of the deposition layer and the trajectory

strategy. Due to the quantity of variables involved in the

process, the reduction of positioning system errors is essential

to avoid either distortions of the process or the interference of

computational compensation of errors (Venkatesh and Izman,

2008; Tan et al., 2008; Tong et al., 2004; Dornfeld and Lee,

2007; Slocum, 1992).

Numerical model

The errors obtained from the theoretical model of a first

generation FDM machine layout (Figure 6) were comparedwith the announced accuracy of FDM 1600 and FDM 8000

for the evaluation of the numerical model of the equipment

final error (Crump et al., 2009; Wang, 2010; Stratasys, 1994,

1998). In this figure, the main axes used in the composition of

the error budgeting model are shown in addition to the main

dimensions of the positioning system. Therefore, it is possible

to determine the axial translation coordinates for the

numerical model.

For the identification of the final error of the system, the

homogeneous transformation matrix (HTM) of each

coordinate system (axis) was multiplied taking into

consideration the translational and rotational errors, as

observed in equation (3) (Venkatesh and Izman, 2008;

Slocum, 1992):RT zerror

¼ T T xerror · yT yerror

· zT zerror ð3Þ

To introduce the errors from the machine elements into the

HTM, the translation and error matrices were determined, as

illustrated in equation (4). In that equation, a T berror is the HTM

from axis “a” to axis “b” considering errors, while aT b · is

the translation matrix from axis “a” to axis “b” without errors.

The error matrix (aE b) considers only geometric error from the

interfacebetween axis “a”and axis “b,” where X , Y and Z arethe

position elements in the x-, y- and z-directions, respectively,

while (1x, 1y, 1z) and (d x, d y, d z) are the rotational and linear

Figure 5 Estimation curve of manufacturing tolerances as a function of relative cost

Figure 4 Regression curve of linear guide elements, accuracy and relative cost

45 µmLinear Bearing - C/H

L i n e

a r g u i d e

n o r

m a l ( C )

L i n e a r g u i d

e H i g h ( H )

L i n e a r g u i d e

P r e c i s i o

n ( P )

L i n e a r g u i d

e

S u p e r p r e c i s i o n

( S P )

L i n e a r g u i d e

U l t r a p r e c i s i o n ( U P )

40 µm

35 µm

30 µm

25 µm

20 µm

15 µm

10 µm

5 µm

0 µm

0.5 1 1.5 2 2.5 3 3.5 4

Relative cost

R a d i a l e r r o r

y = 120.31e –1.132x

R2 = 0.9667




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errorsinthe x-, y-and z-directions,respectively, (Venkatesh and

Izman, 2008; Slocum, 1992):

aT berror ¼a T b · aE b ¼

1 0 0 X

0 1 0 Y

0 0 1 Z

0 0 0 1

26666664

37777775

·

1 21z 1 y d x

1z 1 21x d y

21 y 1x 1 d z

0 0 0 1

26666664

37777775

¼

1 21z 1 y X þ d x

1z 1 21x Y þ d y

21 y 1x 1 Z þ d z

0 0 0 1

266

66664

377

77775

ð4Þ

After applying the main equipment dimensions shown in

Figure 6, the HTM of each axis of the system was found, as

presented in equations (5)-(7). It is important to note that the

errors of those equations were dependent on the machine

element errors and manufacturing tolerances:

FDM 1600!T T xerror ¼

1 21z1 1 y1

1502 X þ d x1

1z1 1 21x1

25 þ d y1

21 y1 1x1

1 50 þ d z1

0 0 0 1

2666664

3777775

FDM 8000!T T xerror ¼

1 21z1 1 y1

2502 X þ d x1

1z1 1 21x1

25 þ d y1

21 y1 1x1

1 50 þ d z1

0 0 0 1

2666664

3777775

ð5Þ

FDM 1600!x T yerror ¼

1 21z2 1 y2

d x2

1z2 1 21x2 1252Y þ d y2

21 y2 1x2

1 225 þ d z2

0 0 0 1

2666664

3777775

FDM 8000!x T yerror ¼

1 21z2 1 y2

d x2

1z2 1 21x2

2252Y þ d y2

21 y2 1x2

1 225 þ d z2

0 0 0 1

26666664

37777775

ð6Þ

Figure 6 FDM machine schematic (schematic basic dimensions) and axes (X , Y , Z , T )

Source: Adapted from Crump et al. (2009)




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FDM 1600! y T zerror ¼

1 21z3 1 y3

2150 þ d x3

1z3 1 21x3

2150 þ d y3

21 y3 1x3 1 225 þ Z þ d z3

0 0 0 1

26666664

37777775

FDM 8000! y T zerror ¼

1 21z3 1 y3 2250 þ d x3

1z3 1 21x3

2250 þ d y3

21 y3 1x3 1 225 þ Z þ d z3

0 0 0 1

26666664

37777775

ð7Þ

Finally, the maximum equipment error can be found from

equation (8), which describes the multiplication of the HTM,

which takes errors into consideration, and the inverse matrix,

which takes into account the expected position of the machine

(Venkatesh and Izman, 2008; Slocum, 1992). In this case,because we have considered the centre of the table as the origin

of the system, the values of ( X , Y , and Z ) are null:

E R ¼ RT zerror ·

21RT z!

d x

d y

d z

1

26666664

37777775

¼

1 0 0 X

0 1 0 Y

0 0 1 Z

0 0 0 1

26666664

37777775

21

·

1 21z 1 y X þ d x

1z 1 21x Y þ d y

21 y 1x 1 Z þ d z

0 0 0 1

2

6666664

3

7777775

ð8Þ

Optimisation of system

For the optimisation study, we applied the goal attainment

method, by defining a problem with multiple objectives. In

addition, a Newton modified algorithm was performed to

solve the cost-error system (Rao, 2009).

Due to the dependency between the tolerance and the cost

of machine elements, we defined seven variables to perform

the optimisation study: C g x ; C g y ; C g z ; C t x ; C t y ; C t z ; and C m. Asthese variables refer to the cost of components and

manufacturing processes, their respective machine element

tolerance values had to be updated in each iteration of the

optimisation study. For this study, only the main dimensions

of the FDM 1600 layout were considered, whereas equipment

with different built areas or layouts implies different

optimisation results.

Equation (9)shows the optimisation problem, which consists

of the minimisation of the total cost and final error. In this

equation, the weight of objective function (w) represents the

importance of each function to the optimisation study:

Minimize! f ðcos t ; error Þ ¼ C total · w þ Error · ð1 2 wÞ

s:t :

1 # C g # 5

1 # C t # 3

1 # C m # 15

ð9Þ

This equation also shows theconstraint functions,which bound

the relative cost of the linear guide between 1 and 5.

Additionally, the cost of the transmission elements was

limited between 1 and 3, while the relative cost of the

manufacturing tolerances could be as great as 15.

Initially, we defined all the variables in the optimisation

study as 1 to identify the local optimum that provided the

lowest values for the relative cost. This definition forced the

optimisation problem to indicate the lowest solutions despite

the existence of other local optimum values.

Results and discussion

To evaluate the numerical model presented in this study,machine elements from commercial equipment were

considered. The model from the study was compared with the

FDM 1600, which is accurate to ^0.127 mm in the x- and

y-directions and 0.254mm in the z-direction, and the FDM

8000, which is accurate to^0.127 mmin the x-and y-directions

and 0.254 mm in the z-direction (Stratasys, 1994, 1998).

The design parameters were specified as Timing belt T10,

IT7 belt pulley, C10 ball screw, linear bearing (normal grade)

and IT4 as the manufacturing tolerance. In addition, the error

budget was found for the machine origin, which was placed at

the centre of the building table.

Table I was constructed by comparing the numerical model

final errorsand theaccuracyof thereferenceequipmentand was

used to identify the equivalency between the numerical modelerror and announced accuracy. For example, although a

deviation of ^2 mm was found in the x- and y-directions, the

average of the errors presents a general divergence between the

numerical model and the FDM machine equal to 2 mm.

After the evaluation of the proposed model, we performed

an optimisation study of the cost-tolerance function. In this

study, the balanced solution indicates the average final is

141.46mm. This value resulted from setting the weight equal

to 0.5, emphasising the equal importance of the objective

functions.

For this solution, a relative cost 1.57 times higher than the

cheapest solution was also found. The machine elements

composing this equipment layout include the linear bearing

(H) for the linear guide in the x- and y-directions, the Ball

screw-C7 for the transmission elements in the x- and

y-directions and the Ball screw-C5 for the z-direction.

Another point that should also be noted is the analysis of the

optimisation sensitivity. The main intention of this analysis was

to identify the behaviour of the optimal values as a function of

the objective function weights. As a result, an Pareto optimum

was found (Figures 3-7), which relates the optimal solutions of

cost and error. In this figure, the value of the balanced

optimisation (w ¼ 0.5) is highlighted as the square point on the

curve.

The maximum value of the average of the final errors was

found when the importance weight was equal to 1. This result,




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which provided the cheapest solution (relative cost ¼ 1),

provided an average error of 733.69 mm, while the minimum

error was found in the y-direction (approximately 718.7 mm).

In Figure 7, it can also be observed that the minimal

average error (37.19 mm) implies an increase of 2.83 times the

equipment cost, which was found for the importance weight

equal to 0. In that case, the deviation of the errors was

0.51 mm, the highest error value found in the z-direction.

It can be noted that this analysis may be relevant for

the identification of the profitability of equipment layout during

the preliminary phases of a project, expressing graphically theadvantages and disadvantages that influence the changes of

accuracy and cost. Additionally, the Pareto optimum also

indicates the limit between feasible and unfeasible solutions,

emphasising the minimal cost that can be achieved for the same

error.

Table II indicates the equivalent machine elements for the

solutions found in the Pareto optimum. Through this table, it is

possible to observethe values of thetotalrelative costs,importance

weight and errors of the respective optimal solutions. In addition,

the design parameters that promote these results are indicated,

such as the tolerances of the manufacturing processes, linear

guides and transmission elements.

Another point that was made apparent in this study is that

currently available equipment are already made with

specifications close to the optimum solutions, which employ

importance weights equal to 0.5 (balanced solution). This

emphasises that the current equipment layout concepts are

already well dimensioned. Despite this finding, if the cost of the

equipment remains constant, the implementation of the optimum

solution would decrease the error by 20 mm. Additionally, this

study also indicates that, for the same error, it is still possible to

decrease the cost of the equipment by 10 per cent.

Moreover, the increase in accuracy regardless of the

reduction of or remaining final error might imply a change in

the layout concept, instead of a simple adjustment of theaccuracy of the machine elements. Therefore, it would be

possible to improve the accuracy of the equipment by almost

120mm, if the relative cost of equipment increased 1.26 times.

It is also important to note that although this study

considered only geometric errors, by ignoring other potential

mechanical, electronic and controlling errors, such as a

dynamics error or motor resolution, this study can be a useful

tool for determining positioning system concepts and

improving the accuracy of additive manufacturing

equipment, such as FDM machines.

Conclusion

This work evaluated a general model for the estimation of the final

error of the layout of a first generation FDM positioning system.

Figure 7 Pareto optimum of optimisation study, relating optimal values of cost function and average of final error

3

2.5

2

1.5

1

0.50

C

o s t

C o s t

100 200 300 400

2

1.9

1.8

1.7

1.6

1.5

balancedsolutions

Optimal Pareto

FDM 1,600

100 125 150 175 200

500

Feasible Solutions

Feasible Solutions

Unfeasible Solutions

600 700 800

Final Error ( m)

Final Error ( m)

Table I Comparison between numerical model and current equipment accuracy

FDM 1600 layout (building area

254 3 245 3 245mm)

FDM 8000 layout (building area

457 3 457 3 609mm)

Error direction Numerical model error Announced accuracy Numerical model error Announced accuracy

x (mm) 20.128 0.127 20.129 0.127

y (mm) 20.126 0.127 20.127 0.127

z (mm) 20.244 0.254 20.249 0.254Average (mm) 0.166 0.169 20.168 0.169




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T a b l e I I D e t e r m i n a t i o n o f m a c h i n e e l e m e n t s a s a f u n c t i o n o f f u n c t i o n w e i g h t s

W e i g h t

X

e r r o r ( m m )

Y e r r o r ( m m

)

Z e r r o r ( m m )

A v e r a g e e r r o r ( m m )

R e l

a t i v e c o s t

M a n u f a c t u r i n g t o l e r a n c e

L i n e

a r g u i d e x y

T r a n s m i s s i o n e l e m e n t x y

T r

a n s m i s s i o n e l e m e n t z

0

2

3 7 . 3

8

2

3 6 . 6

2

2

3 7 . 5

8

3 7 . 1

9

2 . 8

3

I T 1

L i n e a r g u i d e ( U P )

B a l l s c r e w

–

C 5

B a l l s c r e w

–

C 5

0 . 1

2

4 3 . 0

9

2

4 1 . 9

4

2

4 4 . 4

5

4 3 . 1

6

2 . 5

1

I T 2

L i n e a r g u i d e ( S P )

B a l l s c r e w

–

C 5

B a l l s c r e w

–

C 5

0 . 2

2

5 2 . 8

5

2

5 1 . 1

3

2

7 1 . 6

6

5 8 . 5

5

2 . 1

7

I T 2

L i n e a r g u i d e ( P )

B a l l s c r e w

–

C 5

B a l l s c r e w

–

C 7

0 . 3

2

6 3 . 2

4

2

6 0 . 9

9

2

1 0 9 . 5

7 7 . 9

2

1 . 9

4

I T 3

L i n e a r g u i d e ( C )

B a l l s c r e w

–

C 5

T i m i n g b e l t þ

p u l l e y I T 7

0 . 4

2

7 8 . 0

7

2

7 5 . 2

2

2

1 5 6

1 0 3 . 0

9

1 . 7

5

I T 4

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In addition, a systematic approach to select the main machine

elements for similar FDM positioning systems, such as LOM,

SDPand 3DPequipment, was presented. Despite the acceptance

of the high prices of advanced manufacturing, reduction of

manufacturing costs implies an increase in profit of the

equipment, emphasising the importance of this work during the

conceptual design.

A deviation of 2 mm was found by comparing the proposednumerical model, which considered only geometric errors, to

two commercially available equipment units. This deviation

was found to be the average of the final error between the

higher FDM 8000 equivalent model and the lower FDM

1600 equivalent model. This could possibly be the result of

the increase in tolerance as a function of larger dimensions,

despite the use of the same IT grade.

In addition to the identification of cost-accuracy functions,

the minimisation of the optimisation study resulted in a final

error of 37 mm for maximum accuracy. In order for the cost

function to equal the error function, the optimal result was

found to equal 141.46 mm, which is lower than the equivalent

value of the commercial equipment that we used as the basis

of our study (168mm).

The design layout of the solution that obtained the highestaccuracy employs ultra-precision grade linear guides and C5

grade ball screws, in addition to a manufacturing tolerance

equal to an IT7 grade. However, this concept requires an

increase of 2.83 times the total cost of cheapest equipment

concept studied.

Additionally, it was found that the current layout of

commercially available equipment is close to the optimum

solution of the optimisation problem if the weight of the

functions were considered equal at a value of 0.5. This may

indicate that the improvement of FDM accuracy should occur

in parallel with the change of layout design to prevent a

significant increase in the total cost of equipment.

ReferencesCrump, S.S., Batchelder, S.J., Sampson, T., Zinniel, R.L. and

Barnett, J. (2009), “System and method for building three-

dimensional objects with metal-based alloys”, US Patent,

Stratasys, Inc., Edina, MN.

Cunico, M.M.W.M. (2011), “Development of new rapid

prototyping process”, Rapid Prototyping Journal , Vol. 17

No. 2, p. 6.

Dong, Z., Hu, W. and Xue, D. (1994), “New production cost-

tolerance modelsfor tolerance synthesis”, Journalof Engineering

for Industry Transaction of ASME , Vol. 116, pp. 199-206.

D or nf el d, D. A. a nd L ee , D. E. (2 007 ), Precision

Manufacturing , Springer, New York, NY, p. 775.

Gates (2006), Timing Belt Theory, Gates Mectrol, p. 18,

available at: www.gates.com/ (accessed June 2011).

Gates (2011), Urethane Timing Belts and Pulley, Gates

Mectrol, p. 64, available at: www.gates.com/ (accessed

June 2011).

G ibson, I., R osen, D.W. and S tucker, B. ( 20 10 ),

“Photopolymerization processes”, Additive Manufacturing

Technologies, Springer, New York, NY, pp. 61-102.Hiwin (2006), Linear Bearing Technical Information, HIWIN

Linear Motion Products & Technology, p. 252, available at:

www.hiwin.com/ (accessed June 2011).

Hiwin (2008), Ball Screw Technical Information, HIWIN

Linear Motion Products & Technology, p. 252, available at:

www.hiwin.com/ (accessed June 2011).

Rao, S.S. (2009), Engineering Optimization: Theory and

Practice, Wiley, New York, NY.

Shigley, J.E. and Mischke, C.R. (1996), Standard Handbook of

Machine Design, McGraw-Hill, New York, NY, p. 1723.

Slocum, A.H. (1992), Precision Machine Design, SME,

Dearborn, MI, p. 750.

Stratasys (1994), F DM S ys tem D ocu men tat ion,

Reference Manual, Stratasys, Edina, MN.

Stratasys (1998), F DM S ys tem D ocu men tat ion,Reference Manual, Stratasys, Edina, MN.

Tan, K.K., Lee, T.H. and Huang, S. (2008), Precision

Motio n Contr ol: Desig n and Implementat ion, Springer,

New York, NY, p. 272.

THK (2007), Power Linear Bush, THK, p. 12, available at:

www.thk.com (accessed June 2011).

THK (2011), Precision Ball Screws: DIN Standard Compliant

Ball Screw, THK, p. 36, available at: www.thk.com

(accessed June 2011).

Thomson (2009a), Lead Screws, Ball Screws and Ball Splines,

Thomson Linear, p. 252, available at: www.thomsonlinear.

com/ (accessed June 2011).

Thomson (2009b), Thomson Roundrail Linear Guides and

Components, Thomson Linear, p. 268, available at:www.thomsonlinear.com/ (accessed June 2011).

Tong, K., Lehtihet, E.A. and Joshi, S. (2004), “Software error

compensation for rapid prototyping”, Precision Engineering ,

Vol. 28 No. 3, pp. 280-292.

Venkatesh, V.C. and Izman, S. (2008), Precision Engineering ,

McGraw-Hill, New York, NY, p. 418.

Wang, B. (2010), Integrated Product, Process and Enterprise

Design, Vol. 2, Springer, New York, NY, p. 492.

Corresponding author

Marlon Wesley Machado Cunico can be contacted at:

[email protected]




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352

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