Keywords

1 Introduction

Machining still has a great presence in a wide variety of industry sectors, being the main provider of high-precision and quality parts for industries such as aeronautics, aerospace, railway, automobile, and shipbuilding [1]. As such, the machining process is the subject of various studies in many aspects, such as the optimization of manufacturing parameters [2], tool life extension [3, 4], cutting forces analysis [5, 6] (which can provide valuable information regarding process stability and productivity), or by applying various management strategies and philosophies to optimize processes and operations [7]. Behind every part order, there is a quote request made to several companies, a budgeting process, a negotiation, and an award. Budgeting can be a very time-consuming task as it involves a detailed analysis of its geometry, necessary tools, fastening, tool wear, machine, and worker time, as well as all the other costs related to industrial activity, which include costs associated with health, cleanliness, facilities, and security [8, 9]. In the machining sector, it is increasingly common to resort to subcontracting these budgeting services by companies that only carry out the assembly of their final products [10]. As such, this work has as its main objective to elaborate a framework that allows, in a quick and easy manner, to predict/determine the production cost of machined parts, thus enabling the elaboration of budgets related to these parts, without the need for any employee with high qualifications. Thus, the waste that this task normally introduces in the activities of part manufacturing companies is eliminated. Indeed, automating this task is very important as it consumes time and resources. Furthermore, this task is of high importance in responding to customer requests, but represents a necessary cost to the companies, which must be reduced as much as possible, improving the companies’ competitiveness. This is even more important considering that most companies that work under subcontract are SME that do not possess a high number of resources, and they are requested by a high number of potential customers, however, in many cases, these companies are not awarded the work. However, customers deserve an accurate and fast response, which is given through a detailed proposal.

The use of management philosophies and strategies can bring many advantages to the company, for example, the Lean philosophy is quite used, being one of its goals de reduction of waste [11]. If budgeting is carried out without automated procedures, it generates waste of time, which must be reduced. Moreover, the proposal to the customer can suffer delays due to manual procedures. Several Lean tools have been used to optimize processes and operations in numerous companies linked to a wide variety of industry sectors, some of them focusing on automating processes and avoiding the waste of resources. Velmurugan et al. [7] improved the machining process flow and sped up the operations flow using time optimization methods and by standardizing the work, achieving a better line balancing of the machining cells. There seems to be a lot of examples in the literature on how Lean tools can be used to eliminate waste, increasing process efficiency, by optimizing cycle time [12], optimizing toolpath [13], which not only can reduce cycle time but improve productivity, or even by employing a correct machine selection to produce parts [14]. However, there are not many studies conducted about budgeting operations, which are quite important to the life of small, medium, and large companies. In the present work, a simple and inexpensive tool for determining the production cost of machined parts will be presented, the developed tool is able to calculate the production cost based on the amount of required material for part production, and by considering the production time of each part (considering all stages of part production). With the production cost, the user of this tool can provide fast and accurate budgets to customers, thus improving their relations while increasing competitiveness.

Following this introduction, this work will be divided into three main sections, starting with Sect. 2, where the methodology adopted for the development of the cost-estimation tool will be shown, including all the considered equations for operation time determination. Followed by Sect. 3, where the results of the tool implementation will be shown, finally ending with Sect. 4, where the conclusions drawn from this work will be presented.

2 Methodology

A tool for the cost-estimation of machined parts was developed, calculating the production cost of each part based on the preparation and production times, as well as the amount of required material for the machining of each part. This enables the tool to provide accurate budgets in a fast manner, especially when compared to the conventional budgeting process. This tool is also created taking into considerations the companies’ resources (place where the tool will be used), both in terms of manpower, machinery and even the type of orders usually received. A model was created and validated in a part manufacturing company, where the main cause for budget errors was high part variability, that were produced in small series. This high variability also induces a greater budgeting time, as the budgeter needs to carefully study each part to be produced. As previously mentioned, the calculation of the cost was based on the estimation of machining time, based on the part’s final dimensions, as well as the required amount of material to produce said part. The presented calculations were applied mainly for milling operations, due to the type of machines considered in the case study. In addition to these calculations, a part complexity level list was created, which are dependent on the part’s detail level, geometry and machining operations/strategy used. These levels would influence the times estimated by the developed tool, including the drawing, part preparation, machine setup and finishing times.

Fig. 1.
figure 1

Flowchart for required material volume calculation method

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The model determines the cost by considering inputs such as the client requests and part information (drawings) (stage 1), needed volume of material based on the part’s dimensions (stage 2) and the machining strategy (stage 3). Furthermore, a part complexity level is added (stage 4), which will influence not only the machining times, but will also influence setup, preparation and finishing times. After this complexity level is defined, an estimation of total part production time is made (stage 5), which is then used to calculate the total production cost (considering the material volume as well) of the machined parts (stage 6), thus enabling the company to provide an accurate budget (final). The material volume calculation and part complexity level definition stages are more complex than the others, as these stages are dependent on various factors. For example, the volume of material is determined based on the final part’s dimensions, with a higher margin being applied to wider parts. Figure 1 shows the used method for determining the required material volume to produce the part.

The determined material volume is then used to estimate its cost, based on current market prices. Figure 2 shows the diagram of the method used for part complexity level definition.

Fig. 2.
figure 2

Flowchart of the method adopted for the part complexity level determination

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Machining time equations were adopted for each of the operations that were considered, these are dependent on the machining parameters, tools, and part’s dimensions. The considered operations were side-milling; face-milling; end-milling; drilling; boring and threading.

The calculation method adopted for the determination of machining time is going to be presented, for each of the mentioned operations. Regarding the machining time for side-milling, the part’s exterior perimeter (Pext) is calculated, considering its length and width values. Secondly, the minimum required number of roughing passes (R.P.) is determined, by Eq. (1), considering the part’s thickness (t, in mm) and the radial depth of cut (ae, in mm). Finishing operations are considered as well, with the number of finishing passes (F.P.) being calculated by Eq. (2), considering part’s thickness, and cutting tool diameter (Øtool, in mm).

$$ R.P. = \left( {\frac{t}{{a_{e} }}} \right) $$
(1)
$$ F. P. = \left( {\frac{t}{{0.5 \times \emptyset_{tool} }}} \right) $$
(2)

The total machining time for side-milling operations (TS.M, in minutes) can be calculated according to Eq. (3). In addition to the determined values, this equation considers the feed rate value used during machining.

$$ T _{S.M.} = \frac{{P_{ext} \times \left( {R.P. + F.P.} \right) }}{{V_{f} }} $$
(3)

As for the calculation of face-milling operation time, the total machining time depends on the number of passes needed to face a determined area, the number of face-milling passes (Fa.P.) is determined by dividing the material’s width by the chosen ae value. Then, the total facing length (F.L., in mm) is calculated, based on the part’s length (lp, in mm), the tool’s diameter and the number of facing passes, as shown in Eq. (4).

$$ F.L. = \left( {l_{p} + \emptyset_{tool} } \right) \times Fa.P $$
(4)

The machining times for these operations are divided into two, one regarding the first face-milling time (T1F.M., in minutes), and second face-milling time (T2F.M., in minutes). These are calculated as seen in Eqs. (5) and (6). These two equations are used as in some cases, depending on the ap, this being 1 mm for the first operation and 5 mm for the second one.

$$ T1 _{F.M.} = \frac{F.L. }{{V_{f} }} $$
(5)
$$ T2 _{F.M.} = \frac{{F.L. \times \left( \frac{5}{ae} \right) }}{{V_{f} }} $$
(6)

Regarding end-milling operations, the machining time is calculated based on the value of the radial depth of cut ae, usually 40% of the tool’s diameter. The distance performed by the tool during the process, which depends on the machined cavity. After determining the distance that the tool moves per increment (E.l., in mm), this value is multiplied by the number of increments needed to machine the cavity (obtained by the ap value), thus obtaining the total end-milling distance (E.L., in mm). The end-milling time (TE.M., in minutes) is then calculated according to the Eq. (7), which is also used to determine end-milling finishing operation’s total time.

$$ T. _{E.M.} = \frac{E.L. }{{V_{f} }} $$
(7)

The drilling time depends on the tool’s diameter, the hole’s depth (D, in mm), the rotational speed (N, in RPM) and feed per rotation (f, in mm/rotation) that are used during machining. During drilling, the tool performs a series of plunges, quickly retracting and then resuming cutting for a few millimetres, repeating this cycle until the end of drilling. The number of plunges (Plunge) that are required can be calculated according to Eq. (8) (result needs to be rounded up and 1 plunge should be added to the result). This value can then be used to determine total drilling length (D.L., in mm) as shown in Eq. (9). With the values obtained from these equations, the drilling time (TD., in minutes) can be calculated following Eq. (10).

$$ Plunge = \frac{D }{{\emptyset_{tool} }} $$
(8)
$$ D.L. = \mathop \sum \limits_{n = 1}^{Plunge} n \times \emptyset_{tool} \times 2 $$
(9)
$$ T_{D.} = \frac{{\left( {\frac{D.L.}{f} } \right)}}{N} $$
(10)

Regarding boring and threading operations, the total operation time (TThread, in minutes) is calculated based on the depth of the hole (D), the feed per rotation (f) and the rotational speed (N), being calculated by Eq. (11).

$$ T _{Thread} = \frac{{\left( {2 \times \frac{D}{f} } \right)}}{N} $$
(11)

Regarding finishing operation’s time, Eq. (12) was adopted (Tfinishing, in minutes). These times are calculated based on the parts dimension (lp - length and wp – width), as well as the part’s thickness (t) and the feed rate that was adopted (Vf).

$$ T_{finishing} = \frac{{\left( {4 \times lp } \right) + \left( {4 \times wp} \right) + \left( {4 \times t} \right) }}{{V_{f} }} $$
(12)

The developed cost-estimation tool also calculates and considers the preparation and other finishing operation times for the final part’s total cost. There are three main steps on the preparation process: (1) CAD 2D/3D (computer-aided design); (2) CAM (Computer Aided Manufacturing); and finally, the (3) Machine Setup. The CAD step is divided into two main ones, 2D technical drawings and 3D drawings. A base time for each of these steps would was determined, these being 5 and 15 min, respectively, adding x (equal to complexity level) minutes of additional operation time for each detail added to the drawing. For the CAM and Machine setup steps, it was determined that 10 min would be added for each step that implies part extraction from the machine. As previously mentioned, part complexity level will inflate the total operation times required for part production, these inflation factors can be seen in Table 1.

Table 1. Part complexity and respective inflation factor
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3 Implementation Results and Discussion

For the validation of the developed cost estimation tool, several experimental tests were conducted, comparing the estimated machining times (for all the considered production stages), with the experimentally registered times. 11 parts of different complexity levels were produced and compared (guaranteeing a minimum of one test for each complexity level). The developed tool considers the estimated production times to calculate the overall machining cost of each part. The percent deviation from the real times vs predicted times for each production stage can be observed in Table 2.

Table 2. Average percent deviation estimated operations times vs experimental times
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The tool offers accurate predictions (14%) in terms of machining time. This is quite satisfactory, as the machining times heavily impact on cost of machined parts [15, 16]. Higher deviation in time predictions for finishing operations were observed, due to the high variability related to these operations [17] due to CAM step. Higher complexity parts also produced higher deviations; however, these were considered acceptable. Thus, this tool can determine the total production cost of different parts, enabling the provision of fast and accurate budgets to customers.

4 Conclusion

Through this work it was developed an accurate and fast way to the estimation of the total cost of a machined part, enabling the fast provision of budgets to customers.

  • Preparation, machining and finishing operation times for the produced parts are considered for the overall process cost-estimation. An accurate prediction of machining times is highly important, as they heavily influence the process’ cost;

  • The estimation of these machining times is performed based on the operations being carried out by the machines employed in this study;

  • By creating a part complexity level to be attributed to each part, offers some level of standardization, thus reducing the cost-estimation time and, consequently the budgeting time required. This application considers the part complexity level to perform calculations, as it affects all stages of part production;

  • This tool was validated in a company setting, registering an average positive percent deviation from the real machining times of 14%, However, a decrease in estimation accuracy was registered for higher levels of part complexity (especially for finishing operations).

The registered results are satisfactory, the developed tool exhibits high accuracy for predicting production times and costs, enabling a faster budgeting process. There is, however, room for improvement, mainly regarding the predictions associated with finishing operations, however, this can be corrected/improved by performing additional validation and experimental tests. Despite this, the tool is quite versatile and may be used for multiple machines, with the ability to be programmed for determining machining times for different operations.