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Cost estimation support tool for vertical high speed machines based on product characteristics and productivity requirements
Int. J. Production Economics 134 (2011) 188–195
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Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe
Cost estimation support tool for vertical high speed machines based on product characteristics and productivity requirements Guillem Quintana, Joaquim Ciurana n ´ s/n, 17071 Girona, Spain Department of Mechanical Engineering and Civil Construction, Universitat de Girona, Av. Lluis Santalo
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 February 2009 Accepted 20 June 2011 Available online 6 July 2011
This work concerns a machine tool selection problem, which consists of selecting the most suitable machine to satisfy manufacturing company requirements. The main goal of this work is to develop a cost estimation support tool for vertical high speed machining centres based on final part and productivity requirements of the company linked with machine tool characteristics available in the catalogues in order to apply the cost model and to calculate machine tool cost estimations. The cost model presented is based on multiple regression analyses and provides reasonably accurate market cost predictions. Applying the proposed cost model will help the user to determine the approximate market cost of the machine and can be especially interesting for decision makers in the preliminary stages of a selection process because it avoids long and costly studies. & 2011 Elsevier B.V. All rights reserved.
Keywords: Decision making Cost Multiple regression analysis Milling machine
1. Introduction The highly competitive global economy forces companies to use new equipment that is continuously introduced into the market with technology advances. An improper technology or machine selection can negatively affect productivity, precision, flexibility and a company’s responsive manufacturing capabilities (Arslan et al., 2004). This increasingly keen competition and shorter demand-to-market times are driving innovative approaches within the product creation process. When considering the factors that decide a product’s success in today’s market, it becomes clear that cost is as crucial as quality and functionality (Layer et al., 2002). Cost estimations are fundamental criteria to make design and manufacturing decisions in engineering. Achieving an estimate requires knowledge and skills. Traditionally, however, engineers give more relevance to performance and technical requirements than cost (Ri!os et al., 2007). A lot of literature has been published about cost engineering (Asiedu and Gu, 1998; AACE International, 1999; Arslan et al., 2004; Scott, 2004; Ri!os et al., 2007) and several research studies have considered cost estimation in very different engineering fields such as the automotive industry (Cavalieri et al., 2004), the aeronautical industry (Greves and Joumier, 2003; NASA, 2004), the moulds and dies industry (Folgado et al., 2010), construction
n
Corresponding author. Tel.: þ34 972 418265; fax: þ34 972 418098. E-mail addresses: [email protected] (G. Quintana), [email protected] (J. Ciurana). 0925-5273/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2011.06.013
(Kim et al., 2004), steel pipe bending (Shtub and Versano, 1999), industrial plant maintenance (Edwards et al., 2000), supply chain network (Zhang and Xia, 2010), product packaging (Zhang and Fuh, 1998) and high-tech equipment (Chou et al., 2010). In recent years there has been constant innovation and technological advances in all production system fields. However, material removal processes are still the most widely used and relevant techniques to produce the final shape of manufactured products and, although other significant manufacturing techniques have emerged, it seems that this relevance will not expire in the near future. New technologies have been introduced in the market and new concepts of metal cutting, e.g. high speed machining (HSM), have been developed. Globalisation has brought new challenges and requirements to the manufacturing sector. Industries are continuously pushed to improve productivity and quality and to reduce costs by increasing material removal rates and machine tool flexibility, capabilities and performance. Machine tools are most important for discrete product manufacturing. Naturally, it becomes necessary to consider machine tools with new and improved technologies when attempting to cater to increased levels of quality and production system parameters (Gopalakrishnan et al., 2004). Selecting the most appropriate machining centre from among the wide range of types and models available is a difficult but very important decision for a manufacturing company (Ic¸ and Yurdakul, 2008). A typical HSM centre for moulds and dies employs a spindle with a top rotational speed of 10,000–20,000 rev/min and feed rates up to 20 m/min. Although such high feed rate values are probably applicable for some light alloy straight cut machining, they have
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little relevance when cutting complex hardened steel cavities, so feed rates of o10 m/min are more commonly used. Acceleration/ deceleration values are arguably more important, and 5–10 m/s2 is desirable for high productivity (Urbanski et al., 2000). The machine tool selection process has been a critical issue for companies for years, because the improper selection of a machine tool might cause many problems and have a negative effect on productivity, precision, flexibility and a company’s responsive manufacturing capabilities. One of the most important challenges in a machine tool selection process is the lack of both reliable data for possible machine tool alternatives and an expert with considerable experience of machine specifications and manufacturing processes (Ayagˇ, 2007). For basic machine tool selection, the first factor to be considered is the cost of the machine, with the main goal being to satisfy production system design requirements and budgetary constraints (Gopalakrishnan et al., 2004). The decision maker should be an expert, or at least be very familiar with the machine properties, to select the most suitable machine from among the increasing number of available alternatives, which can be a highly demanding task (Arslan et al., 2004). The machine selection procedure has been studied by several researchers and from several points of view. A large number of these works are focused on the selection of conventional machine tools (Wang et al., 2000; Chick et al., 2000; Smith et al., 2003; Arslan et al., 2004; Gopalakrishnan et al., 2004; Ic¸ and Yurdakul, 2008; Albertı´ et al., 2010). Arslan et al. (2004) and Gopalakrishnan et al. (2004) also consider high speed machines and their characteristics or specifications. Manufacturing system significance is another very relevant aspect considered by researchers (Arslan et al., 2004; Gopalakrishnan et al., 2004; Wang et al., 2000; Chick et al., 2000). This paper focuses on the machine tool selection problem, which consists of making a decision about the most suitable machine to satisfy the needs of a manufacturing company. The final decision affects the production system performance and selecting an inadequate machine can negatively affect company results. So, this is an important process that may pose some difficulties for the decision maker. The object of this work has been to develop a cost estimation method for vertical high speed machining centres based on the machine characteristics and the final part and productivity requirements. The method applied to develop the cost model is based on previous works studies out by the authors (Quintana et al., 2007; Ciurana et al., 2008). The main novelty of the paper is that the cost estimation is based on the final product and productivity requirements. The models presented in previous works are based on the machine characteristics available in the machine tool catalogues. However, there is a considerable gap between machine tool catalogues and companies’ requirements. In this paper, product characteristics and productivity needs are linked with machine tools available in the catalogues. This is done by integrating references (Quintana et al., 2008; Lo´pez de Lacalle and Lamikiz, 2009) in the cost calculation algorithm. Applying the proposed cost estimation method could be especially interesting for decision makers in the preliminary stages of the selection process.
2. Methodology Now that preliminary considerations have been stated, this section explains the steps followed to achieve the objectives of this work. For an appropriate and successful evaluation and selection, the decision maker may need to analyse a large amount of data and consider many factors. The empirical work carried out consisted of compiling information about the characteristics of vertical high speed machine tools that can be found on the
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market. All the data and information were extracted from the machine tool manufacturers’ catalogues. Compiling these data led to the sample that would subsequently be used to do statistical studies and build the mathematical model. All the data was analysed and studied once the information had been collected. The final sample consisted of 35 different vertical high speed machine tools from eight different companies. ‘‘High speed’’ machines were defined according to the commercial departments of the contacted companies: a spindle capable of rotating at speeds higher than 10,000 rpm. The larger the number of samples, the better the cost model. However, the process of gathering together all the machine tool characteristics, contacting the companies and getting the cost information was too long. For this reason it was necessary to reach a trade-off between the number of samples and the time spent obtaining them. The information collected for each of these 35 entry-level machines are 19 characteristics (independent variables of the statistical studies) and one unique dependant variable (the cost). The 19 characteristics considered for each machine were classified into three groups: 1) Geometric characteristics: work volume, work area, table loading capacity, weight, X axis linear travel, Y axis linear travel and Z axis linear travel. 2) Axis characteristics: positioning accuracy, positioning repeatability, number of axes, rapid traverse in X axis, rapid traverse in Y axis, rapid traverse in Z axis and feed rates also in the three axes. 3) Spindle characteristics: maximum spindle speed, power and torque.
The Nomenclature, denominations and units used for all these data throughout the study are shown in Table 1. Some of the challenges of gathering together all the information required and obtaining a representative sample to carry out the research are explained by Arslan et al. (2004): the lack of standard formats in machine catalogues, the large number of factors to be considered and the introduction of new machine tools together with advancements in the technology makes the problem a highly complex one. This makes it difficult to compare machines of different companies. Selecting machine tools could be difficult because in some cases not all the characteristics of the machines are specified in catalogues or suppliers sometimes use different standards or modes to indicate the same characteristic. It would therefore be very helpful to have a tool of some kind to help make the decision.
Table 1 Nomenclature and units used in this study. Nomenclature V Ar L W A R X, Y, Z Vfrx, Vfry, Vfrz fx, fy, fz S P T E Ma Mm
Work volume (m3) Work area (m2) Table loading capacity (kg) Weight (Kg) Positioning accuracy (mm) Positioning repeatability (mm) Linear axis X, Y, Z, travel (mm) Rapid traverse X, Y, Z (m/min) X, Y, Z, feed rate (m/min) Max. spindle speed (rpm) Power (kW) Torque (Nm) Number of axis Market cost (h) Predicted cost (h)
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3. Cost calculation procedure The goal of this work has been to develop a cost estimation method for vertical high speed machining centres based on machine characteristics and final part requirements. The cost model presented is based on multiple regression statistical analyses. This and the method followed for its implementation are derived from previous research (Quintana et al., 2007; Ciurana et al., 2008). Multiple regression is the most appropriate method of analysis when the research problem includes one unique metric dependant variable that is supposed to be related with more than one metric independent variables. The general purpose of multiple regression analysis is to find out the relationship between several independent (or predictor variables) and a dependant variable (or criterion variable). This relationship could then be used to calculate the dependant variable and eventually predict its value by using the knowledge of values of independent variables (Hair et al., 1999). The general form of a prediction equation for multiple regression is presented in Eq. (1): Y ¼ b0 þ b1 X1 þb2 X2 þ b3 X 3 þ ::: þbn Xn
the suitable machine tool characteristics to produce the part. Some examples of final product requirements are related with the dimensions, geometric complexities, accuracy and repeatability needs of the final part. These characteristics are constrained by the machine tool X, Y and Z axis linear travel, work volume, work area, table loading capacity, number of axes, positioning accuracy and repeatability. Productivity requirements can be measured in terms of the material removal rate, which depends on rapid traverses in X, Y and Z axes, feed rates, spindle speed, power and torque of the machine tool. All these data had to be compiled because these machine tool characteristics are the independent variables of the cost model needed to obtain market machine tool cost predictions that ensure product and productivity needs. The following sections explain procedures implemented to obtain market cost predictions of vertical high speed machines that suit the final product specifications and the productivity requirements. The cost model developed and the procedures to obtain all the required variables to perform predictions are also detailed. 3.1. Cost model
ð1Þ
where Y is the predicted score and represents the dependant variable, X1 is the known score of the first independent variable, X2 is the known score of the second independent variable, etc. The constant, b0, is where the regression line intercepts the Y axis, and is the predicted variable value when all independent values are zero. The rest of the bs are the regression coefficients and represent the variation of the predicted score when the corresponding independent variable Xi varies 1 unit (Hair et al., 1999). This work defines the dependant or predicted variable ‘‘Y’’ as the market cost (Mm) of vertical high speed machine centres. Fig. 1 shows a flowchart of the market cost calculation procedure carried out by the support tool presented in this work. Manufactured product requirements and desired productivity capabilities are the cost model calculation inputs and they determine
The model proposed in Eq. (2) for vertical high speed machine centres consists of characteristics such as volume (V), work area (Ar), positioning accuracy (A), axis linear travels (X), (Y) and (Z), spindle speed (S), table loading capacity (L), feed rate (f) and power (P). As shown in Eq. (2), the market cost (Mm) is a function of the mentioned set of variables Mm (X, Y, Z, A, Ar, V, L, f, S, P). Mm ¼ 36,502:66279,250:13 V14,420:45 Ar þ 20:31 L þ60:76 X þ 164:70 Y31:54 Z5436:54 A þ 333:20 f þ2:96 S þ 2097:37 P
ð2Þ Main statistic indicators were analysed to evaluate and validate the cost model developed and errors were committed when predicting the cost of the machines of the experimental data set (Table 2).
COST ESTIMATION SUPPORT TOOL FOR VERTICAL HIGH SPEED MACHINES User
Final product requirements
Productivity requirements
MACHINE TOOL CHARACTERISTICS
INDEPENDENT VARIABLES DECISION
COST MODEL APPLICATION
Predicted market cost (Mm ) Fig. 1. Flowchart representation of the milling centre market cost calculation procedure.
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Multiple correlation coefficient (r) and multiple correlation square (R2) give good values of the relation between independent variables and the dependant variable. These values indicate accurate predictions for the model developed in this work. The model prediction was checked by adding more independent variables. However, the adjusted coefficient has decreased so it does not give extra prediction power. The independent variables of the market cost prediction model can be classified into three types of characteristics. It contains six geometric characteristics: the volume (V), the work area (Ar), the table loading capacity (L) and the axis linear travels (X), (Y) and (Z); two axis characteristics – the feed rate (f), the positioning accuracy (A) and two spindle characteristics – the maximum spindle speed (S) and the power (P). The user can set these attributes looking at the requirements of the production system (f, S, P) of the company and the characteristics of the parts that have to be produced (V, Ar, L, X, Y, Z, A). The next step is how to decide the value required for each independent variable of the model. 3.2. Final product requirements Final product requirements concern those characteristics that have to be fulfilled by parts manufactured in a milling centre case study. Final part characteristics that have an influence on the Table 2 Cost model MRA outputs. Statistic indicators Multiple r R2 Adjusted R2 Standard error Observations
0.9853 0.9708 0.9586 27,311.74 35
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machine tool characteristics used in the model are volume (V), work area (Ar), table loading capacity (L) and axis linear travels (X), (Y) and (Z) and positioning accuracy (A). As explained by Quintana et al. (2008) all these characteristics influence the blank decision, among others. The cost estimation support tool presented integrates the procedure presented by Quintana et al. (2008) to calculate blank characteristics. The user has to introduce final part requirements and tool extract data required to calculate the market cost prediction. The form screen used to establish the part characteristics and requirements depends on the part typology and is shown in Fig. 2. Some independent variables are extracted from blank dimensional characteristics calculated and proposed by the software proposed by Quintana et al. (2008) such as axis linear travels (X), (Y) and (Z), the volume (V) and the work area (Ar). One independent variable is directly extracted from the data introduced by the user in the input form. The table loading capacity (L) is calculated by multiplying volume (V) and density, which is introduced as material featured by the user in the characterisation form. The aim of the simple method used to define the product requirements is to be able to define very rapidly the principal product characteristics required for the cost model. All the product data required for the cost model can be easily extracted for any kind of workpiece shape, e.g. simple geometrical products or free-form surfaces. The final part selected to apply the method proposed should be the most restrictive in order to ensure that the machine tool to which the cost is calculated is suitable to manufacture any kind of part required by the company. It means that the selected final part dimensions should be the dimensions of the largest part to be manufactured and the accuracy selected should be the highest required. The user can carry out the procedure introducing the characteristics of parts machined by the company in the past (which could be extracted from CAD or CAM files) or applying the
Fig. 2. Characterisation form for prismatic parts.
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characteristics of the parts that company will have to be able to manufacture in the future.
Table 3 Specific power coefficients (K) of several materials. Work material
Specific power coefficient (K)
Structural steels Alloy steels Cast iron Titanium alloy
4–5.7 5.3–7.4 2.5–3.7 4.7–5.1
3.3. Productivity requirements Productivity requirements refer to those capabilities required by the manufacturing system that have to be achieved by the machine tool. The material removal rate (MRR) is usually expressed as the volume of material extracted during one unit of time and depends on process parameters such as axial and radial depths of cut and feed rate (Fig. 3). These process parameters, and others such as spindle speed, are provided by the cutting tool providers in their catalogues and tables. There is a huge variety of cutting tools in terms of shape, size, number of teeth, surface coating, performance, usage, and also a huge variety of manufacturers. Machine tool characteristics used as independent variables in the model are feed rate (f), maximum spindle speed (S) and power (P). As mentioned, these variables are related to required material removal rates which at the same time are mainly restricted by the cutting tool characteristics. There is a relationship between spindle speed and power which is typically expressed using the power/torque curves for the spindles of the machine tools. It is possible to identify feed rate (f) values, spindle speed (S) and power (P) required to make market cost predictions considering productivity requirements and constraints. The procedure used to obtain the data needed by the cost model is a typical method followed to calculate the spindle power requirements of a machine tool and can be found in the catalogues of machine tool manufacturers and are also described in several research studies (Arnone, 1998; Lo´pez de Lacalle and Lamikiz, 2009). The method first considers the cutting parameters that the manufacturers provide for several cutting tools and workpiece material combinations. Surface complexity, accuracy and surface roughness help to determine which operation and cutting tool is needed for roughing, semi-finishing, finishing and super-finishing operations. For simple geometries that require considerable roughing, large-diameter tools with several cutting edges are used. In contrast, small-diameter tools are needed for complex
geometries to ensure high precision requirements or highly smooth surfaces. The cutting speed Vc parameter is usually provided by cutting tool manufacturers. The spindle speed in rpm can be easily calculated from the cutting speed and the tool diameter (D) using the following equation: S¼
Vc 1000 Dp
ð3Þ
The relation between the spindle speed and the feed rate can be easily calculated by applying the next equation: f ¼ fz zS
ð4Þ
where fz is the feed per tooth (mm/z) and z the number of teeth. Once the radial depth of cut (Ae) and axial depth of cut (Ap) are selected, the volume of material removed (MRR) in cm3/min could be calculated with the feed speed (f) as shown in the following equation: MRR ¼
AeApf 1000
ð5Þ
Finally, to provide a certain material removal rate, the machine tool spindle must be able to provide a certain effective power. Tool manufacturers provide a specific power coefficient (K) and the power required in kW can be simply calculated as: P¼
AeApf K 100,000
ð6Þ
Table 3 shows the value of the specific power coefficient (K) for certain typical workpiece materials. As material is introduced by the user in previous steps to calculate independent variables restricted by the final part requirements, material information is already known by the support tool and can be easily used to calculate the effective power required. Feed rate (f), spindle speed (S) and effective power (P) requirements for workpiece machining can be calculated, once we know the required cutting tool, the workpiece material and the strategies employed for roughing and finishing in conventional milling or HSM. It is advisable to use data about roughing operations when axial and radial depths of cut are high and the material has high K coefficient value. Again, the user can carry out the procedure by introducing the parameters used to produce parts machined in the past by the company (for example, using data extracted from CAM files) or applying the parameters that the company will have to use in the future.
4. Support tool
Fig. 3. Schematic representation of the milling process parameters.
Once the cost model is developed as presented in Section 3.1, and the procedures to determine the variables required to achieve the final part requirements and the productivity needs have been established as in Sections 3.2 and 3.3, respectively, it is possible to complete the cost model with the values found for each of the independent variables and predict the market cost of a vertical high speed machine centre that can achieve the manufacturing requirements.
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most critical specifications required. A point to take into consideration is that the model needs real machine tool characteristics. In those cases where the product or productivity needs are not a constraint, the value introduced is adjusted to a realistic value. For example, if the biggest shape required to be machined is very small, or, at least, smaller than typical machine tool tables, the variables X, Y, Z, Ar and V, which are related to the workpiece shape, will be lower than the minimum X, Y, A, Ar and V variables
Once the user has specified the part attributes to machine and the productivity requirements, the support tool predicts market costs for the vertical milling centre that can achieve the requirements described. The whole calculation process is shown in the flowchart given in Fig. 4. It is advisable to use the most restrictive parameters to perform the calculation in order to ensure that market cost prediction applies a vertical milling centre able to achieve the
User
Final product requirements
Productivity requirements
• Geometrical characteristics
• Material removal rates (MRR)
• Accuracy
• Cutting tool characteristics
• Material
• Feed rates
• Surface finish
• Spindle speed • Conventional milling/HSM
X
Y
Z
S
A
BLANK SHAPE REQUIREMENTS CALCULATION
f
Ae
Ap
POWER CONSUMPTION REQUIREMENTS CALCULATION
K
Ar
P
x
V
=
d
L MODEL VARIABLES
X
Y
Z
A
Ar
V
L
S
f
P
MRA COST MODEL Predicted market cost (Mm) Fig. 4. Flowchart representation of the milling centre market cost calculation procedure.
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of the sample. In this case the minimum values of the sample are considered to complete the model as, otherwise, the user would be asking the model for a price of a machine that does not exist. Section 5 presents a case study in which this situation occurs.
5. Case study This section shows a case study using the computer application developed for a vertical milling market cost estimation that is the aim of this work. Fig. 5 shows the part to be manufactured in alloy steel. This part could be manufactured in 2.5 axes. It is a typical part that must be manufactured in a workshop. Observing the final product and productivity requirements, it is possible to establish the values of the prediction model variables and calculate the approximate market cost of the required vertical milling centre. Focusing on the final product requirements, the support tool presented by Quintana et al. (2008) is used to calculate blank characteristics and extract the independent variables (X, Y, Z) applied to axis linear travels, the precision (A), the work area and volume (Ar, V) and the table loading capacity (L). Blank material calculation for the part shown in Fig. 5 begins with running the application. The user chooses the prismatic type then the screen of prismatic typologies is accessed. The form for part characterisation is completed with the required information and the software provides the following information about the required
blank. The part shown in Fig. 5 is solved using a calibrated square steel profile 60 mm wide, 60 mm long and 48 mm high. Information introduced by the user can be used to fulfil the model values. To decide X, Y and Z axis linear travels it is necessary to consider not only the blank shape but also the shape of the vice that is clamped on the machine table. At this stage values are still very low compared with real machine tool X, Y and Z values, and the model is completed with realistic values taking the minimum values from the sample. The same discussion could be applied to accuracy. Accuracy is extracted from the data introduced by the user in the blank calculation software. The working area and volume are calculated with X, Y and Z. The density of alloy steel is 7.80 g/cm3. Considering typical, X, Y and Z axes, working tables, working volumes, accuracy and loading table, the model variables decided are presented in Table 4. Regarding the productivity requirements, S, f and P were calculated following the procedure presented in Section 3.3. The spindle speed considered is S¼20,000 rpm, the feed rate is f¼24 m/min and radial and axial depths of cut are Ae¼ 5 mm and Ap¼1 mm. The power was calculated using Eq. (6) (K¼7.4). Then the power calculated was rounded to a realistic machine tool power based on the sample. By combining all of the independent variables introduced into the model and applying Eq. (2), a machine tool market cost of h115,048.76 is proposed. It is a reasonably accurate market cost prediction as indicated by the correlation coefficients presented in Section 3.1 and it is also verifiable by observing the milling centre market.
6. Conclusions The machine tool selection problem focuses on selecting the most suitable machine to satisfy requirements for a manufacturing company. The final decision affects the production system performance. An inadequate machine tool selection can negatively affect the company business. The most important factor to be considered in the selection process is the machine tool cost. Applying the proposed cost estimation support tool will help the user calculate the approximate market cost of vertical high speed milling centres. Cost model estimation could especially interest decision makers in preliminary stages of the selection process. It becomes an especially useful tool for inexperienced personnel making this type of decision because it reduces the budgetary part of the machine tool selection problem into a process of information entry. Manufactured product requirements and productivity capability desires are used to determine the main characteristics of the required machine tool. These machine tool characteristics are used to complete the cost model and predict the market cost. The support tool presented is an easy and fast one that considers entry-level vertical milling centres. Large and costly studies can be avoided by applying the tool presented. Extra options, extra functions or extra accessories on machine tools are not considered. Company pricing policy, technical assistance, maintaining and support costs, mean time between failures, recycling costs, reliability, environmental impact or machine tool life-cycle costs are also not considered in the model cost.
Fig. 5. Part to produce.
Table 4 Independent variables extracted from the blank decision. Independent variables
X (mm)
Y (mm)
Z (mm)
A (lm)
Ar (m2)
V (m3)
d (g/cm3)
L (kg)
S (rpm)
f (m/min)
K
P (kW)
Blank characteristics Model variables
60 600
60 400
48 350
9 9
0.0036 0.2400
0.00017 0.08400
7.80 7.80
1.35 655
20,000 20,000
24 24
7.4 7.4
8.88 18.5
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The database and the cost model presented should be regularly updated to ensure the quality of the estimations and consider the market cost variation due to factors such as new machine tools and technologies introduced. It would be also very interesting to develop a multi-criteria decision making support tool, focused not only on predicting costs but expanded to also focus on different product and productivity requirements. The method proposed could be applied to develop other cost models and to facilitate making well informed decisions regarding the selection task of other machine tools or process types.
Acknowledgements This research would not have been possible without the ˜ a), FIDIA (Mr. Ramon collaboration of DMG (Mr. Josep Ocan Kortazar), INTERMAHER, which represents MAZAK (Mr. Joan Roca) and MAQUINA CENTRE which represents OKUMA, HURON and ROMI (Mr. Jordi Garrido). We greatly appreciate the time and information provided by these companies References AACE, 1999. International Association for the Advancement of Cost Engineering. Recommended Practices and Standards, 11R-88: Required skills and knowledge of a cost engineer. Albertı´, M., Ciurana, J., Rodriguez, C.A., Ozel, T., 2010. Design of a decision support system for machine tool selection based on machine characteristics and performance tests. Journal of Intelligent Manufacturing. doi:10.1007/s10845009-0286-6. Scott, A., 2004. Skills and Knowledge of Cost Engineering, fifth edition AACE International, Morgantown, West Virginia. Arnone, M., 1998. High Performance Machining. Hanser Gardner Publications, Cincinnati, USA. Arslan, M.C., C - atay, B., Budak, E., 2004. A decision support system for machine tool selection. Journal of Manufacturing Technology Management 15 (1), 101–109. Asiedu, Y., Gu, P., 1998. Product life cycle cost analysis: State of the art review. International Journal of Production Research 36 (4), 883–908. Ayagˇ, Z., 2007. A hybrid approach to machine-tool selection through AHP and simulation. International Journal of Production Research 45 (9), 2029–2050. Cavalieri, S., Maccarrone, P., Pinto, R., 2004. Parametric vs. neural network models for the estimation of production costs: a case study in the automotive industry. International Journal of Production Economics 91 (2), 165–177. Chick, S.E., Olsen, T.L., Sethuraman, K., Stecke, K.E., White, C.C., 2000. A descriptive multi-attribute model for reconfigurable machining system selection examining buyer-supplier relationships. International Journal of Agile Management Systems 2 (1), 33–48. Chou, J., Tai, Y., Chang, L., 2010. Predicting the development cost of TFT-LCD manufacturing equipment with artificial intelligence models. International Journal of Production Economy 128 (1), 339–350.
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Contents lists available at ScienceDirect
Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe
Cost estimation support tool for vertical high speed machines based on product characteristics and productivity requirements Guillem Quintana, Joaquim Ciurana n ´ s/n, 17071 Girona, Spain Department of Mechanical Engineering and Civil Construction, Universitat de Girona, Av. Lluis Santalo
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 February 2009 Accepted 20 June 2011 Available online 6 July 2011
This work concerns a machine tool selection problem, which consists of selecting the most suitable machine to satisfy manufacturing company requirements. The main goal of this work is to develop a cost estimation support tool for vertical high speed machining centres based on final part and productivity requirements of the company linked with machine tool characteristics available in the catalogues in order to apply the cost model and to calculate machine tool cost estimations. The cost model presented is based on multiple regression analyses and provides reasonably accurate market cost predictions. Applying the proposed cost model will help the user to determine the approximate market cost of the machine and can be especially interesting for decision makers in the preliminary stages of a selection process because it avoids long and costly studies. & 2011 Elsevier B.V. All rights reserved.
Keywords: Decision making Cost Multiple regression analysis Milling machine
1. Introduction The highly competitive global economy forces companies to use new equipment that is continuously introduced into the market with technology advances. An improper technology or machine selection can negatively affect productivity, precision, flexibility and a company’s responsive manufacturing capabilities (Arslan et al., 2004). This increasingly keen competition and shorter demand-to-market times are driving innovative approaches within the product creation process. When considering the factors that decide a product’s success in today’s market, it becomes clear that cost is as crucial as quality and functionality (Layer et al., 2002). Cost estimations are fundamental criteria to make design and manufacturing decisions in engineering. Achieving an estimate requires knowledge and skills. Traditionally, however, engineers give more relevance to performance and technical requirements than cost (Ri!os et al., 2007). A lot of literature has been published about cost engineering (Asiedu and Gu, 1998; AACE International, 1999; Arslan et al., 2004; Scott, 2004; Ri!os et al., 2007) and several research studies have considered cost estimation in very different engineering fields such as the automotive industry (Cavalieri et al., 2004), the aeronautical industry (Greves and Joumier, 2003; NASA, 2004), the moulds and dies industry (Folgado et al., 2010), construction
n
Corresponding author. Tel.: þ34 972 418265; fax: þ34 972 418098. E-mail addresses: [email protected] (G. Quintana), [email protected] (J. Ciurana). 0925-5273/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2011.06.013
(Kim et al., 2004), steel pipe bending (Shtub and Versano, 1999), industrial plant maintenance (Edwards et al., 2000), supply chain network (Zhang and Xia, 2010), product packaging (Zhang and Fuh, 1998) and high-tech equipment (Chou et al., 2010). In recent years there has been constant innovation and technological advances in all production system fields. However, material removal processes are still the most widely used and relevant techniques to produce the final shape of manufactured products and, although other significant manufacturing techniques have emerged, it seems that this relevance will not expire in the near future. New technologies have been introduced in the market and new concepts of metal cutting, e.g. high speed machining (HSM), have been developed. Globalisation has brought new challenges and requirements to the manufacturing sector. Industries are continuously pushed to improve productivity and quality and to reduce costs by increasing material removal rates and machine tool flexibility, capabilities and performance. Machine tools are most important for discrete product manufacturing. Naturally, it becomes necessary to consider machine tools with new and improved technologies when attempting to cater to increased levels of quality and production system parameters (Gopalakrishnan et al., 2004). Selecting the most appropriate machining centre from among the wide range of types and models available is a difficult but very important decision for a manufacturing company (Ic¸ and Yurdakul, 2008). A typical HSM centre for moulds and dies employs a spindle with a top rotational speed of 10,000–20,000 rev/min and feed rates up to 20 m/min. Although such high feed rate values are probably applicable for some light alloy straight cut machining, they have
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little relevance when cutting complex hardened steel cavities, so feed rates of o10 m/min are more commonly used. Acceleration/ deceleration values are arguably more important, and 5–10 m/s2 is desirable for high productivity (Urbanski et al., 2000). The machine tool selection process has been a critical issue for companies for years, because the improper selection of a machine tool might cause many problems and have a negative effect on productivity, precision, flexibility and a company’s responsive manufacturing capabilities. One of the most important challenges in a machine tool selection process is the lack of both reliable data for possible machine tool alternatives and an expert with considerable experience of machine specifications and manufacturing processes (Ayagˇ, 2007). For basic machine tool selection, the first factor to be considered is the cost of the machine, with the main goal being to satisfy production system design requirements and budgetary constraints (Gopalakrishnan et al., 2004). The decision maker should be an expert, or at least be very familiar with the machine properties, to select the most suitable machine from among the increasing number of available alternatives, which can be a highly demanding task (Arslan et al., 2004). The machine selection procedure has been studied by several researchers and from several points of view. A large number of these works are focused on the selection of conventional machine tools (Wang et al., 2000; Chick et al., 2000; Smith et al., 2003; Arslan et al., 2004; Gopalakrishnan et al., 2004; Ic¸ and Yurdakul, 2008; Albertı´ et al., 2010). Arslan et al. (2004) and Gopalakrishnan et al. (2004) also consider high speed machines and their characteristics or specifications. Manufacturing system significance is another very relevant aspect considered by researchers (Arslan et al., 2004; Gopalakrishnan et al., 2004; Wang et al., 2000; Chick et al., 2000). This paper focuses on the machine tool selection problem, which consists of making a decision about the most suitable machine to satisfy the needs of a manufacturing company. The final decision affects the production system performance and selecting an inadequate machine can negatively affect company results. So, this is an important process that may pose some difficulties for the decision maker. The object of this work has been to develop a cost estimation method for vertical high speed machining centres based on the machine characteristics and the final part and productivity requirements. The method applied to develop the cost model is based on previous works studies out by the authors (Quintana et al., 2007; Ciurana et al., 2008). The main novelty of the paper is that the cost estimation is based on the final product and productivity requirements. The models presented in previous works are based on the machine characteristics available in the machine tool catalogues. However, there is a considerable gap between machine tool catalogues and companies’ requirements. In this paper, product characteristics and productivity needs are linked with machine tools available in the catalogues. This is done by integrating references (Quintana et al., 2008; Lo´pez de Lacalle and Lamikiz, 2009) in the cost calculation algorithm. Applying the proposed cost estimation method could be especially interesting for decision makers in the preliminary stages of the selection process.
2. Methodology Now that preliminary considerations have been stated, this section explains the steps followed to achieve the objectives of this work. For an appropriate and successful evaluation and selection, the decision maker may need to analyse a large amount of data and consider many factors. The empirical work carried out consisted of compiling information about the characteristics of vertical high speed machine tools that can be found on the
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market. All the data and information were extracted from the machine tool manufacturers’ catalogues. Compiling these data led to the sample that would subsequently be used to do statistical studies and build the mathematical model. All the data was analysed and studied once the information had been collected. The final sample consisted of 35 different vertical high speed machine tools from eight different companies. ‘‘High speed’’ machines were defined according to the commercial departments of the contacted companies: a spindle capable of rotating at speeds higher than 10,000 rpm. The larger the number of samples, the better the cost model. However, the process of gathering together all the machine tool characteristics, contacting the companies and getting the cost information was too long. For this reason it was necessary to reach a trade-off between the number of samples and the time spent obtaining them. The information collected for each of these 35 entry-level machines are 19 characteristics (independent variables of the statistical studies) and one unique dependant variable (the cost). The 19 characteristics considered for each machine were classified into three groups: 1) Geometric characteristics: work volume, work area, table loading capacity, weight, X axis linear travel, Y axis linear travel and Z axis linear travel. 2) Axis characteristics: positioning accuracy, positioning repeatability, number of axes, rapid traverse in X axis, rapid traverse in Y axis, rapid traverse in Z axis and feed rates also in the three axes. 3) Spindle characteristics: maximum spindle speed, power and torque.
The Nomenclature, denominations and units used for all these data throughout the study are shown in Table 1. Some of the challenges of gathering together all the information required and obtaining a representative sample to carry out the research are explained by Arslan et al. (2004): the lack of standard formats in machine catalogues, the large number of factors to be considered and the introduction of new machine tools together with advancements in the technology makes the problem a highly complex one. This makes it difficult to compare machines of different companies. Selecting machine tools could be difficult because in some cases not all the characteristics of the machines are specified in catalogues or suppliers sometimes use different standards or modes to indicate the same characteristic. It would therefore be very helpful to have a tool of some kind to help make the decision.
Table 1 Nomenclature and units used in this study. Nomenclature V Ar L W A R X, Y, Z Vfrx, Vfry, Vfrz fx, fy, fz S P T E Ma Mm
Work volume (m3) Work area (m2) Table loading capacity (kg) Weight (Kg) Positioning accuracy (mm) Positioning repeatability (mm) Linear axis X, Y, Z, travel (mm) Rapid traverse X, Y, Z (m/min) X, Y, Z, feed rate (m/min) Max. spindle speed (rpm) Power (kW) Torque (Nm) Number of axis Market cost (h) Predicted cost (h)
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3. Cost calculation procedure The goal of this work has been to develop a cost estimation method for vertical high speed machining centres based on machine characteristics and final part requirements. The cost model presented is based on multiple regression statistical analyses. This and the method followed for its implementation are derived from previous research (Quintana et al., 2007; Ciurana et al., 2008). Multiple regression is the most appropriate method of analysis when the research problem includes one unique metric dependant variable that is supposed to be related with more than one metric independent variables. The general purpose of multiple regression analysis is to find out the relationship between several independent (or predictor variables) and a dependant variable (or criterion variable). This relationship could then be used to calculate the dependant variable and eventually predict its value by using the knowledge of values of independent variables (Hair et al., 1999). The general form of a prediction equation for multiple regression is presented in Eq. (1): Y ¼ b0 þ b1 X1 þb2 X2 þ b3 X 3 þ ::: þbn Xn
the suitable machine tool characteristics to produce the part. Some examples of final product requirements are related with the dimensions, geometric complexities, accuracy and repeatability needs of the final part. These characteristics are constrained by the machine tool X, Y and Z axis linear travel, work volume, work area, table loading capacity, number of axes, positioning accuracy and repeatability. Productivity requirements can be measured in terms of the material removal rate, which depends on rapid traverses in X, Y and Z axes, feed rates, spindle speed, power and torque of the machine tool. All these data had to be compiled because these machine tool characteristics are the independent variables of the cost model needed to obtain market machine tool cost predictions that ensure product and productivity needs. The following sections explain procedures implemented to obtain market cost predictions of vertical high speed machines that suit the final product specifications and the productivity requirements. The cost model developed and the procedures to obtain all the required variables to perform predictions are also detailed. 3.1. Cost model
ð1Þ
where Y is the predicted score and represents the dependant variable, X1 is the known score of the first independent variable, X2 is the known score of the second independent variable, etc. The constant, b0, is where the regression line intercepts the Y axis, and is the predicted variable value when all independent values are zero. The rest of the bs are the regression coefficients and represent the variation of the predicted score when the corresponding independent variable Xi varies 1 unit (Hair et al., 1999). This work defines the dependant or predicted variable ‘‘Y’’ as the market cost (Mm) of vertical high speed machine centres. Fig. 1 shows a flowchart of the market cost calculation procedure carried out by the support tool presented in this work. Manufactured product requirements and desired productivity capabilities are the cost model calculation inputs and they determine
The model proposed in Eq. (2) for vertical high speed machine centres consists of characteristics such as volume (V), work area (Ar), positioning accuracy (A), axis linear travels (X), (Y) and (Z), spindle speed (S), table loading capacity (L), feed rate (f) and power (P). As shown in Eq. (2), the market cost (Mm) is a function of the mentioned set of variables Mm (X, Y, Z, A, Ar, V, L, f, S, P). Mm ¼ 36,502:66279,250:13 V14,420:45 Ar þ 20:31 L þ60:76 X þ 164:70 Y31:54 Z5436:54 A þ 333:20 f þ2:96 S þ 2097:37 P
ð2Þ Main statistic indicators were analysed to evaluate and validate the cost model developed and errors were committed when predicting the cost of the machines of the experimental data set (Table 2).
COST ESTIMATION SUPPORT TOOL FOR VERTICAL HIGH SPEED MACHINES User
Final product requirements
Productivity requirements
MACHINE TOOL CHARACTERISTICS
INDEPENDENT VARIABLES DECISION
COST MODEL APPLICATION
Predicted market cost (Mm ) Fig. 1. Flowchart representation of the milling centre market cost calculation procedure.
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Multiple correlation coefficient (r) and multiple correlation square (R2) give good values of the relation between independent variables and the dependant variable. These values indicate accurate predictions for the model developed in this work. The model prediction was checked by adding more independent variables. However, the adjusted coefficient has decreased so it does not give extra prediction power. The independent variables of the market cost prediction model can be classified into three types of characteristics. It contains six geometric characteristics: the volume (V), the work area (Ar), the table loading capacity (L) and the axis linear travels (X), (Y) and (Z); two axis characteristics – the feed rate (f), the positioning accuracy (A) and two spindle characteristics – the maximum spindle speed (S) and the power (P). The user can set these attributes looking at the requirements of the production system (f, S, P) of the company and the characteristics of the parts that have to be produced (V, Ar, L, X, Y, Z, A). The next step is how to decide the value required for each independent variable of the model. 3.2. Final product requirements Final product requirements concern those characteristics that have to be fulfilled by parts manufactured in a milling centre case study. Final part characteristics that have an influence on the Table 2 Cost model MRA outputs. Statistic indicators Multiple r R2 Adjusted R2 Standard error Observations
0.9853 0.9708 0.9586 27,311.74 35
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machine tool characteristics used in the model are volume (V), work area (Ar), table loading capacity (L) and axis linear travels (X), (Y) and (Z) and positioning accuracy (A). As explained by Quintana et al. (2008) all these characteristics influence the blank decision, among others. The cost estimation support tool presented integrates the procedure presented by Quintana et al. (2008) to calculate blank characteristics. The user has to introduce final part requirements and tool extract data required to calculate the market cost prediction. The form screen used to establish the part characteristics and requirements depends on the part typology and is shown in Fig. 2. Some independent variables are extracted from blank dimensional characteristics calculated and proposed by the software proposed by Quintana et al. (2008) such as axis linear travels (X), (Y) and (Z), the volume (V) and the work area (Ar). One independent variable is directly extracted from the data introduced by the user in the input form. The table loading capacity (L) is calculated by multiplying volume (V) and density, which is introduced as material featured by the user in the characterisation form. The aim of the simple method used to define the product requirements is to be able to define very rapidly the principal product characteristics required for the cost model. All the product data required for the cost model can be easily extracted for any kind of workpiece shape, e.g. simple geometrical products or free-form surfaces. The final part selected to apply the method proposed should be the most restrictive in order to ensure that the machine tool to which the cost is calculated is suitable to manufacture any kind of part required by the company. It means that the selected final part dimensions should be the dimensions of the largest part to be manufactured and the accuracy selected should be the highest required. The user can carry out the procedure introducing the characteristics of parts machined by the company in the past (which could be extracted from CAD or CAM files) or applying the
Fig. 2. Characterisation form for prismatic parts.
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characteristics of the parts that company will have to be able to manufacture in the future.
Table 3 Specific power coefficients (K) of several materials. Work material
Specific power coefficient (K)
Structural steels Alloy steels Cast iron Titanium alloy
4–5.7 5.3–7.4 2.5–3.7 4.7–5.1
3.3. Productivity requirements Productivity requirements refer to those capabilities required by the manufacturing system that have to be achieved by the machine tool. The material removal rate (MRR) is usually expressed as the volume of material extracted during one unit of time and depends on process parameters such as axial and radial depths of cut and feed rate (Fig. 3). These process parameters, and others such as spindle speed, are provided by the cutting tool providers in their catalogues and tables. There is a huge variety of cutting tools in terms of shape, size, number of teeth, surface coating, performance, usage, and also a huge variety of manufacturers. Machine tool characteristics used as independent variables in the model are feed rate (f), maximum spindle speed (S) and power (P). As mentioned, these variables are related to required material removal rates which at the same time are mainly restricted by the cutting tool characteristics. There is a relationship between spindle speed and power which is typically expressed using the power/torque curves for the spindles of the machine tools. It is possible to identify feed rate (f) values, spindle speed (S) and power (P) required to make market cost predictions considering productivity requirements and constraints. The procedure used to obtain the data needed by the cost model is a typical method followed to calculate the spindle power requirements of a machine tool and can be found in the catalogues of machine tool manufacturers and are also described in several research studies (Arnone, 1998; Lo´pez de Lacalle and Lamikiz, 2009). The method first considers the cutting parameters that the manufacturers provide for several cutting tools and workpiece material combinations. Surface complexity, accuracy and surface roughness help to determine which operation and cutting tool is needed for roughing, semi-finishing, finishing and super-finishing operations. For simple geometries that require considerable roughing, large-diameter tools with several cutting edges are used. In contrast, small-diameter tools are needed for complex
geometries to ensure high precision requirements or highly smooth surfaces. The cutting speed Vc parameter is usually provided by cutting tool manufacturers. The spindle speed in rpm can be easily calculated from the cutting speed and the tool diameter (D) using the following equation: S¼
Vc 1000 Dp
ð3Þ
The relation between the spindle speed and the feed rate can be easily calculated by applying the next equation: f ¼ fz zS
ð4Þ
where fz is the feed per tooth (mm/z) and z the number of teeth. Once the radial depth of cut (Ae) and axial depth of cut (Ap) are selected, the volume of material removed (MRR) in cm3/min could be calculated with the feed speed (f) as shown in the following equation: MRR ¼
AeApf 1000
ð5Þ
Finally, to provide a certain material removal rate, the machine tool spindle must be able to provide a certain effective power. Tool manufacturers provide a specific power coefficient (K) and the power required in kW can be simply calculated as: P¼
AeApf K 100,000
ð6Þ
Table 3 shows the value of the specific power coefficient (K) for certain typical workpiece materials. As material is introduced by the user in previous steps to calculate independent variables restricted by the final part requirements, material information is already known by the support tool and can be easily used to calculate the effective power required. Feed rate (f), spindle speed (S) and effective power (P) requirements for workpiece machining can be calculated, once we know the required cutting tool, the workpiece material and the strategies employed for roughing and finishing in conventional milling or HSM. It is advisable to use data about roughing operations when axial and radial depths of cut are high and the material has high K coefficient value. Again, the user can carry out the procedure by introducing the parameters used to produce parts machined in the past by the company (for example, using data extracted from CAM files) or applying the parameters that the company will have to use in the future.
4. Support tool
Fig. 3. Schematic representation of the milling process parameters.
Once the cost model is developed as presented in Section 3.1, and the procedures to determine the variables required to achieve the final part requirements and the productivity needs have been established as in Sections 3.2 and 3.3, respectively, it is possible to complete the cost model with the values found for each of the independent variables and predict the market cost of a vertical high speed machine centre that can achieve the manufacturing requirements.
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most critical specifications required. A point to take into consideration is that the model needs real machine tool characteristics. In those cases where the product or productivity needs are not a constraint, the value introduced is adjusted to a realistic value. For example, if the biggest shape required to be machined is very small, or, at least, smaller than typical machine tool tables, the variables X, Y, Z, Ar and V, which are related to the workpiece shape, will be lower than the minimum X, Y, A, Ar and V variables
Once the user has specified the part attributes to machine and the productivity requirements, the support tool predicts market costs for the vertical milling centre that can achieve the requirements described. The whole calculation process is shown in the flowchart given in Fig. 4. It is advisable to use the most restrictive parameters to perform the calculation in order to ensure that market cost prediction applies a vertical milling centre able to achieve the
User
Final product requirements
Productivity requirements
• Geometrical characteristics
• Material removal rates (MRR)
• Accuracy
• Cutting tool characteristics
• Material
• Feed rates
• Surface finish
• Spindle speed • Conventional milling/HSM
X
Y
Z
S
A
BLANK SHAPE REQUIREMENTS CALCULATION
f
Ae
Ap
POWER CONSUMPTION REQUIREMENTS CALCULATION
K
Ar
P
x
V
=
d
L MODEL VARIABLES
X
Y
Z
A
Ar
V
L
S
f
P
MRA COST MODEL Predicted market cost (Mm) Fig. 4. Flowchart representation of the milling centre market cost calculation procedure.
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of the sample. In this case the minimum values of the sample are considered to complete the model as, otherwise, the user would be asking the model for a price of a machine that does not exist. Section 5 presents a case study in which this situation occurs.
5. Case study This section shows a case study using the computer application developed for a vertical milling market cost estimation that is the aim of this work. Fig. 5 shows the part to be manufactured in alloy steel. This part could be manufactured in 2.5 axes. It is a typical part that must be manufactured in a workshop. Observing the final product and productivity requirements, it is possible to establish the values of the prediction model variables and calculate the approximate market cost of the required vertical milling centre. Focusing on the final product requirements, the support tool presented by Quintana et al. (2008) is used to calculate blank characteristics and extract the independent variables (X, Y, Z) applied to axis linear travels, the precision (A), the work area and volume (Ar, V) and the table loading capacity (L). Blank material calculation for the part shown in Fig. 5 begins with running the application. The user chooses the prismatic type then the screen of prismatic typologies is accessed. The form for part characterisation is completed with the required information and the software provides the following information about the required
blank. The part shown in Fig. 5 is solved using a calibrated square steel profile 60 mm wide, 60 mm long and 48 mm high. Information introduced by the user can be used to fulfil the model values. To decide X, Y and Z axis linear travels it is necessary to consider not only the blank shape but also the shape of the vice that is clamped on the machine table. At this stage values are still very low compared with real machine tool X, Y and Z values, and the model is completed with realistic values taking the minimum values from the sample. The same discussion could be applied to accuracy. Accuracy is extracted from the data introduced by the user in the blank calculation software. The working area and volume are calculated with X, Y and Z. The density of alloy steel is 7.80 g/cm3. Considering typical, X, Y and Z axes, working tables, working volumes, accuracy and loading table, the model variables decided are presented in Table 4. Regarding the productivity requirements, S, f and P were calculated following the procedure presented in Section 3.3. The spindle speed considered is S¼20,000 rpm, the feed rate is f¼24 m/min and radial and axial depths of cut are Ae¼ 5 mm and Ap¼1 mm. The power was calculated using Eq. (6) (K¼7.4). Then the power calculated was rounded to a realistic machine tool power based on the sample. By combining all of the independent variables introduced into the model and applying Eq. (2), a machine tool market cost of h115,048.76 is proposed. It is a reasonably accurate market cost prediction as indicated by the correlation coefficients presented in Section 3.1 and it is also verifiable by observing the milling centre market.
6. Conclusions The machine tool selection problem focuses on selecting the most suitable machine to satisfy requirements for a manufacturing company. The final decision affects the production system performance. An inadequate machine tool selection can negatively affect the company business. The most important factor to be considered in the selection process is the machine tool cost. Applying the proposed cost estimation support tool will help the user calculate the approximate market cost of vertical high speed milling centres. Cost model estimation could especially interest decision makers in preliminary stages of the selection process. It becomes an especially useful tool for inexperienced personnel making this type of decision because it reduces the budgetary part of the machine tool selection problem into a process of information entry. Manufactured product requirements and productivity capability desires are used to determine the main characteristics of the required machine tool. These machine tool characteristics are used to complete the cost model and predict the market cost. The support tool presented is an easy and fast one that considers entry-level vertical milling centres. Large and costly studies can be avoided by applying the tool presented. Extra options, extra functions or extra accessories on machine tools are not considered. Company pricing policy, technical assistance, maintaining and support costs, mean time between failures, recycling costs, reliability, environmental impact or machine tool life-cycle costs are also not considered in the model cost.
Fig. 5. Part to produce.
Table 4 Independent variables extracted from the blank decision. Independent variables
X (mm)
Y (mm)
Z (mm)
A (lm)
Ar (m2)
V (m3)
d (g/cm3)
L (kg)
S (rpm)
f (m/min)
K
P (kW)
Blank characteristics Model variables
60 600
60 400
48 350
9 9
0.0036 0.2400
0.00017 0.08400
7.80 7.80
1.35 655
20,000 20,000
24 24
7.4 7.4
8.88 18.5
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The database and the cost model presented should be regularly updated to ensure the quality of the estimations and consider the market cost variation due to factors such as new machine tools and technologies introduced. It would be also very interesting to develop a multi-criteria decision making support tool, focused not only on predicting costs but expanded to also focus on different product and productivity requirements. The method proposed could be applied to develop other cost models and to facilitate making well informed decisions regarding the selection task of other machine tools or process types.
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