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Management and Production Engineering Review

Volume 1 • Number 3 • September 2010 • pp. 56–62

TECHNICAL AND ECONOMIC COEFFICIENTS

OF MULTI-DIRECTIONAL PRODUCTION

OF PARTS BY INCREMENTAL METHODS

Edward Pająk, Maciej Kowalski, Radosław Paszkiewicz, Radosław Wichniarek,

Przemysław Zawadzki, Adam Dudziak

Poznan University of Technology, Institute of Mechanical Technology, Poland

Corresponding author:

Radosław Wichniarek

Poznan University of Technology

Institute of Mechanical Technology

Piotrowo 3, 60-965 Poznan, Poland

phone: +48 61 6652052

e-mail: [email protected]

Received: 3 May 2010 Abstract

Accepted: 27 July 2010 The present article contains results research of production accuracy and strength properties

of parts manufactured with application of Rapid Prototyping technology. A proposition of

synthetic technical-economic coefficient for model preparation is presented which will be used

for determining direction of layer deposition during multi-directional construction of models

with FDM method.

Keywords

rapid prototyping, multi-directional, accuracy, strength properties.

Introduction

Shortening time between commencement of de-sign works and starting up of production is one of themost important factors in competitiveness of eachcompany. The cycle of technical preparation of pro-duction has significant share in that time, as well asin the costs of the project. Since it is common thatmore and more perfect computer hardware and soft-ware is used, it makes it possible to create DigitalMock Up of a product model. Multi-functional con-figurations integrated with DMU enable performingstatistic and dynamic analyses of designed product aswell as simulations related to its operation. In a greatdeal of cases it is recommended that a physical mod-el of the product, its part or a functional prototypeshould be constructed as an element of technical cy-cle of preparing production. Construction of a model(prototype) with use of Rapid Prototyping technol-ogy on the basis of virtual CAD-3D models is usual-ly sufficiently representative, and time and costs ofsuch construction remain at much favourable levels

than when making a model with use of traditionalmechanical technologies.

The Fig. 1 above shows the place where mod-el is created in the chain leading from productionpreparation to delivery of the product to customer.Pursuant to the diagram, currently there are manyvarious technologies of Rapid Prototyping (RP), andparts executed with use of the technologies have dif-ferent values of a given feature. It is important toensure that the values of features which are requiredby a customer are as similar to product features aspossible, and the product features – to the valuesof features of prepared model. This concerns main-ly the values of features which characterize accuracyand strength. Nevertheless, the said convergence isnot always possible, since it depends on the materialof which the model is made, as well as technology ofconstruction. Application of the RT technology ex-ceeds beyond construction of a real model; it focuseson creating tools (e.g. forms) used for making readyparts, mostly in the case of individual or job-lot pro-duction (Fig. 2).

56


Fig. 1. Properties of real model.

Fig. 2. Application of incremental technologies (preparedacc. to [1, 6, 7]).

The article describes investigation of selected fea-tures of real models created with use of FDM (FusedDeposition Modelling) technology in the conditionsof anisotropic1 material layer deposition. Technical-economic coefficients which allow to determine thelevel of conformity of the features of created realmodel with features of product manufactured for cus-tomer are prepared on their basis.

Plan of the experiment

Investigation was performed on the samples pre-pared with use of the FDM method on the deviceDimension BST 1200 made of ABS material.

The scope of testing covered the following(Fig. 3):– measuring strength properties of a part, with theassumption of anisotropic material layer disposi-tion,– measuring accuracy of manufacturing of a part,with the assumption of anisotropic material layerdisposition,– measuring part production time.

Fig. 3. Technical-economic coefficient of model prepara-tion technology.

Preparing of a real model with use of a specif-ic RP technology depends on required features ofthe model (accuracy and strength), as well as ongeneral economic factors. Due to that, the synthet-ic technical-economic coefficient (CTE) prepared fora given technology will be equal to the sum of the fol-lowing coefficients: strength (ST), accuracy (A) andcost (E) multiplied by the weights of coefficient froma given group (wST , wA, wE).

CTE = ST × wST + A × wA + E × wE . (1)

The value of that coefficient may facilitate se-lection of model orientation in the FDM machineworkspace (or application of multi-directional layerdisposition technology) which is the most favourablefrom the point of view of criteria determined byweights. The choice of adequate orientation shouldbe enabled by obtaining the most favourable modelfeatures similar to required features, with the possi-ble shortest time of execution and minimum costs.

Investigation of model strength coefficient

Strength investigation enables determining theST coefficient, one of the coefficients which defines

1The concept anisotropic layer disposition will be used in the event of constructing the same elements, however, for each

of them layers will be disposed from different directions. The concept of multi-directional layer disposition is used in the

event when change of layer disposition direction is possible when producing building a part.

Volume 1 • Number 3 • September 2010 57


synthetic coefficient CTE. The measurements wereperformed on universal measuring devices INSTRON4481, INSTRON 1115, INSTRON PW5. Samplesmade of ABS material with use of RP – FDM tech-nology were used for research. Research was per-formed on samples of rectangular section and dimen-sions pursuant to standards for given conditions oftesting, and on samples of circular section. Results ofinvestigation which part is presented in Fig. 4 showthat the strength coefficient ST, in the event of bend-ing (STR) reaches its maximum value in the eventof load acting perpendicularly to the disposed layers(STR = 1.0). In that case there may be also some sig-nificant deformations of model. On the other hand,in the event of other direction of construction, riskof model deformations is significantly smaller (com-pare graphs from the measuring equipment – Fig. 4).Research performed on two sections, and particular-ly their statistic analysis shows that the value of thecoefficient is also influenced by the shape of cross sec-tion of STR sample (similar problem is analysed inthe article [2, 3]).

Fig. 4. Results of tensile strength testing of samples pro-duced by disposing layers lengthwise and crosswise to

load.

Investigation of the strength coefficient in thecase of compression loads is presented in Fig. 5.The testing was performed on samples of circularsection and dimensions ø30 mm×45 mm. Compres-sion strength of models constructed with use of theFDM method is comparable irrespective of the direc-tion of layer disposition. Therefore, the coefficient ofstrength ST does not have to consider the coefficientrelated to compression loads.

Fig. 5. Results of compression strength testing of sam-ples created by placing layers lengthwise and crosswise

to load.

Required features of real models are often con-nected with bending strength and impact resistance.Coefficients of those strength features (STZ) shouldbe therefore taken into consideration when preparingstrategy of placement of created models. Results ofbending strength testing are presented in Fig. 6.

Fig. 6. Results of bending strength testing of samplesproduced by disposing layers lengthwise and crosswise to

load.

For example on Fig. 6 maximum value of coeffi-cient STZ = 1, 0 for lengthwise disposing layers (big-ger value of bending strength). Value of coefficientST is calculate as average STS and STZ coefficient.

Investigation of model production

accuracy coefficient

Accuracy of model production will be character-ized by volume error (similar problem is analysedin the article [4, 5]). It is defined as a difference be-tween the volume of material used for production of

58 Volume 1 • Number 3 • September 2010


a model and the volume resulting from computer rep-resentation (3D model) of the model. Figure 3 showsthat the final accuracy of model production and theaccuracy coefficient prepared on that basis (markedas A) is a result of superposition of various errors inmodel production. They have impact on the quali-ty of external model surfaces (roughness of externalsurfaces), accuracy of dimensions, and weight of theproduct. Model production errors were grouped inthe following two categories: external model errorsand internal model errors. Causes of the above errorsare various, some of them does not have any signifi-cance for a customer, others condition the possibilityof using the model. Therefore, by defining the finalcoefficient of accuracy of model production (A), itwill be also necessary to introduce weights which de-fine importance of specific group of errors occurringin the model for the customer.

External errors of model production

External errors of model production include: con-version error, staircase error and error of division intolayers.Error of conversion to STL format (∆STL) is

connected with recording geometry of surface usual-ly with use of a network of triangles (triangulation).Conversion error mainly relates to mapping a circle,or part of it (chordal error – Fig. 7a) and conse-quently entire part (Fig. 7b).

a) b)

Fig. 7. Error of conversion to STL format; a) chordalerror, b) model error.

Error of conversion ∆STL depends on the coeffi-cient of segmentation (tessellation value); by usinglower coefficient of segmentation (seg), we obtainsmaller chordal error, and thus smaller conversionerror. CAD 3D model was mapped by a real modelwith higher accuracy (Fig. 8).However, decreasing the coefficient of segmenta-

tion is connected with exponential increase of con-version process time. Coefficient of error conversionto STL format ASTL = 1, 0, when chordal error isequal 0.

Fig. 8. Solid model (left right corner) and mesh modelsproduced with various segmentation coefficient (seg).

Staircase error (∆S) of a model is connectedwith technology of model production layer-by-layer(Fig. 9a and Fig. 9b). It occurs less frequently inmodels which external surfaces are parallel to direc-tion of placing layers (this is mostly the purpose ofmulti-directional disposition of model layers).

a)

b)

Fig. 9. a) The essence of staircase error; b) Impact ofthickness of disposed layer on the value of staircase er-

ror.

Staircase error (∆S) may be reduced by reducingthe thickness of disposed layer (Fig. 9b), however,



this results in extension of model production time.In this case AS = 1, 0.

Error of division into layers (∆W ) is another ex-ternal model volume error. Its essence is shown inFig. 10.

Fig. 10. Error of division into layers.

Error of division into layers is connected withconstruction of RP devices. Figure 11 shows an ex-ample of producing a model of part of defined dimen-sion “h”. Assuming that it will be produced withthickness of disposed layer g = 0.25 mm, in theevent that the dimension is h = 2.0 mm, the num-ber of disposed layers equals 8. In this case coeffi-cient of division layers AW = 1, 0. In the event thath = 2.8 mm, the number of disposed layers of thick-ness g = 0.25mm equals 11.2. The device control sys-tem rounds the number up and disposes 12 layers. Insuch a case error of division is higher (Fig. 11). In thiscase coefficient error of division layers AW = 0.93(AW = 2.8 mm/2 layers × 0.25 mm) = 0.93).

Fig. 11. Number of disposed layers.

When discussing the error of division, one shouldalso mention the error of rejecting extreme layerswhich shape and surface do not allow to producea closed outline and fill it. In such a situation, controlsoftware rejects extreme layers and this way gener-ates volume error (Fig. 12).

Fig. 12. Error of rejecting extreme layers – model (a),photograph of sample (b).

Internal errors of model production

Internal errors of model production are connect-ed with the method of filling the interior of disposedlayer (Fig. 13). The figure shows magnified struc-ture of a single layer of real model constructed withuse of FDM technology. FMD device control soft-ware first places a “thread” of material of width “h”to create an external outline of the model and thenfills that outline with “threads” of material accordingto standard path programmed in the device controlsoftware.

a)

b)

Fig. 13. Illustration of internal error; h – width of singlematerial thread, r1 and r2 – external and internal radiusof real model corner, g – layer thickness, r3 – radius of

material thread rounding.



Research showed that volume error is almost al-ways of negative value. This means that the volumeof material used for producing a real model is usuallysmaller than the volume of virtual CAD 3D model,however, this depends chiefly on the model shape.Multi-directional layer disposition in RP technolo-gy contributes to reducing of volume error (internalerrors of model production not include to calculatecoefficient of accuracy A).

Testing economic coefficient

of model production

The criterion of economic coefficient of modelproduction is determined by incurred direct costs.They depend mostly upon the quantity of consumedmaterial (material of model and material of support)and time of production of a real model. The errorof conversion to format ∆STL is possible to reduce,when in this case increase time of production. Sim-ilary we can reduce of staircase error ∆S by reduc-ing the thickness of disposed layers. In this case in-crease time of production and direct cost of produc-tion (Fig. 14).

Fig. 14. Comparison of model production time with useof disposed layer thickness of 0.33 mm and 0.25 mm

Research of multi-directional layer disposition inproduction of real models do not allow to unequivo-cally evaluate the economic efficiency of that process.It is not possible due to vast possibilities of creatingvarious shapes of models and a lot of alternative di-rections of disposing layers in such models.

Summary

The concept of multi-directional layer disposi-tion in model production with application of RapidPrototyping technology requires adequate situationof model in relation to the head spreading materi-al, and thus determining direction of disposing sub-sequent layers. Choice of the direction in relationto anisotropic properties of the model influences itsstrength properties, accuracy and costs of model pro-duction. Modifications of numerical value of the tech-nical and economic coefficient (resulting from modifi-cation of its components) depend on the direction oflayer disposition in real model production (α). HenceCTE = f(α).

CTE(α) = {[STS(α) + STz(α)]/2} × wSt

+{[ASTL + AS(α) + AW ]/3} × wA + E(α) × wE .

Thanks to the analysis of modifications ofCTE(α) it is possible to adopt the most favourableorientation of a model in the device workspace, whichmakes it possible to come to the most favourablecompromise between parameters of strength, accu-racy and costs of model production. Therefore, itenables preparing individual strategy of material lay-er disposition for each case of required properties ofa model.

The work was supported by the Polish Min-istry of Science and High School – project number3390/B/T02/2009/36.

References

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