Optimisation of subtractive rapid prototyping process parameters using response surface methodology

Subtractive rapid prototyping machine is the most suitable tool to manufacture a polymer based prosthetic part because it is able to achieve a low surface roughness value for a complex and customised part. Many investigations have been conducted to explain the relation among the surface roughness value, the material rate removal, and the subtractive rapid prototyping process parameters. It is important to find the optimum process parameters in order to achieve the most efficient and productive process. However, none of the research found in the literature optimises the subtractive rapid prototyping process parameters in fabricating polycarbonate part. Therefore, this research aims to find the optimum process parameters to achieve the lowest arithmetic average of surface roughness value of the polycarbonate part in maximum material removal rate. In this research, the response surface methodology is implemented to optimised feed rate, step-over, and depth of cut of the subtractive rapid prototyping process. This research finds the feed rate, step-over, and depth of cut values that can be used to achieve the best result in manufacturing of polycarbonate material.


Introduction
Polycarbonate material has been applied for various prosthetic products due to the fact that it is strong, tough, and transparent thermoplastic material. A prosthetic product is mostly an intricate product and customized for each patient. As a result, the feasible process to fabricate the product is by using rapid prototyping. Rapid prototyping process can be performed by using subtractive or additive methods. Subtractive rapid prototyping is carried out by implementing high speed milling process to cut the raw material in order to produce the part. Meanwhile, additive rapid prototyping carried out by depositing materials layer by layer to build the shape of the part. For a certain type of prosthetic parts such as a socket of prosthetic leg that require a specific surface roughness and dimensional accuracy, the subtractive rapid prototyping is preferable to be implemented. The main purpose of subtractive rapid prototyping is to achieve the required minimum surface roughness and dimensional error in the maximum material rate removal. Therefore, the optimisation of subtractive rapid prototyping process parameters in fabricating polycarbonate materials is considered as a significant problem and needs to be tackled. This paper only describes the optimisation of subtractive rapid prototyping processes to achieve the maximum material removal rate and the minimum surface roughness. The novelty of this research lies in optimising the subtractive rapid prototyping process parameters to achieve the Based on the literature review, the aim of this research is to optimize the process parameters in subtractive rapid prototyping to achieve the half of the arithmetic average of surface roughness values of the Fused Deposition Modelling, which is maximum of 0.0075 mm (7.5 µm), in the maximum material rate removal of polycarbonate material.

Methodology
Response Surface Methodology is implemented in this research to develop several mathematical models and validate the models. The shape and the dimensions of the polycarbonate material specimen fabricated by using the subtractive rapid prototyping process are shown in Fig. 1. Roland MDX 40 is used as the subtractive rapid prototyping machine. The machine is assisted by CAM Modela Player 4.0 software to generate the tool path from the STL format model. A carbide solid square end mill with 5 mm diameter is used as the cutting tool. In order to move the cutting tool, the software uses zigzag cut type. Different parameter values for roughing and finishing processes are determined based on the tools catalogue and interview with the expert. Table 1 shows the roughing parameter value of the subtractive rapid prototyping. Three levels of value for depth of cut, feed rate, and step-over are designed for finishing process. The value of each level for each parameter as shown in Table 2 is determined based on the machine specification, literature study, and the preliminary experiment. The subtractive rapid prototyping is performed under dry operating condition. The spindle for finishing process is 10000 rpm and the entry speed for finishing process is 4 mm/s. The polycarbonate material is assumed to be always homogeneous. Then, the cutting temperature is assumed to be always constant. Finally, the tool wear is assumed to occur after performing three roughing and finishing processes.  measured by using a stopwatch. The arithmetic average of surface roughness is measured by using Mitutoyo SJ 210 with 0.01 µm of accuracy at Industrial Metrology Laboratory of University of Surabaya. Two direction of arithmetic average of surface roughness measurement is conducted, which are horizontal and vertical directions. After the measurement process, the measured data is analyzed by using MINITAB release 14 software.

Results and discussion
The design of the first order experiment are shown in Table 3. The first order experiment involves all two level factors using 2 3 factorial design with additional 5 center points. The result of the first order experiment is showed in Based on the result of the validation step, the first order models are not adequate as a linear regression model. For that reason, the second order experiment for material removal rate, vertical arithmetic average of surface roughness, and horizontal arithmetic average of surface roughness must be conducted. The central composite design is used to determine the number of the second order experiment run. The design and result of the second order experiment is shown in Table 4. By using the experiment result shown in Table 4, the prediction model of material removal rate, vertical arithmetic average of surface roughness, and horizontal arithmetic average of surface roughness are shown in Eq. 1, Eq. 2, and Eq. 3. . According to the result of the validation step for the second order experiment, the developed equations can be used as the best prediction model.
The aim of this research is to determine the feed rate, step over, and depth of cut in subtractive rapid prototyping to achieve the maximum material rate removal of polycarbonate material and the arithmetic average of surface roughness less than or equal to 7.5 µm. The multiple response optimizer based on desirability approach is used to maximize the material rate removal and minimize the horizontal and vertical arithmetic average of surface roughness [17]. The result shows that the optimum condition achieved when the feed rate, step-over, and depth of cut are set in 18.70 mm/s, 0.54 mm, and 0.46 mm respectively. The maximum material removal rate achieved by implementing these parameters is 2.3672 mm 3 /s. The achieved horizontal and vertical arithmetic averages of surface roughness are 3.5842 µm and 7.4867 µm respectively.

Conclusions
The goal of this research is to optimize the subtractive rapid prototyping parameters for polycarbonate material by implementing the response surface methodology in order to achieve the maximum material rate removal of polycarbonate material and achieve the horizontal and vertical arithmetic average of surface roughness less than or equal to 7.5 µm at the same time. The optimized feed rate, step over, and depth of cut for the subtractive rapid prototyping are found to be 18.70 mm/s, 0.54 mm, and 0.46 mm respectively. By implementing these parameters, the achieved material removal rate is 2.3672 mm 3 /s and the maximum achieved vertical arithmetic average of surface roughness is 7.4867 µm.