tóm tắt: Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC

Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.Nghiên cứu ảnh hưởng của một số thông số công nghệ đến quá trình gia công tia lửa điện bề mặt trụ ngoài thép 90CrSi với dung dịch điện môi trộn bột nano SiC.

MINISTRY OF EDUCATION AND TRAINING MINISTRY OF INDUSTRY AND TRADE NATIONAL RESEARCH INSTITUTE OF MECHANICAL ENGINEERING - *** - NGUYỄN MẠNH CƯỜNG RESEARCH ON THE EFFECTS OF SOME PROCESS PARAMETERS ON ELECTRICAL DISCHARGE MACHINING PROCESS OF 90CrSi STEEL EXTERNAL CYLINDRICAL SURFACE USING DIELECTRIC SOLUTION MIXED WITH SiC NANO POWDER SPECIALITY: MECHANICAL ENGINEERING Code: 9520103 SUMMARY OF THE Ph.D THESIS Hanoi - 2023 Hà Nội - 2023 The work was completed at the Institute of Mechanical Engineering - Ministry of Industry and Trade Scientific instructor 1: Assoc Prof Vũ Ngọc Pi Scientific instructor 2: Assoc Prof Lê Thu Quý Reviewer 1: … ….….….….….….….….….….… Reviewer 2: … ….….….….….….….….….….… Reviewer 3: … ….….….….….….….….….….… The thesis is defended in the Doctoral Thesis Evaluation Council of the Institute Place of meeting: National Research Institute of Mechanical Engineering No4, Pham Van Dong Str., Cau Giay Distr., Hanoi, Vietnam At AM , date ……………………… , 2023 Thesis can be found at the following libraries: - Vietnam National Library - Library of Mechanics Research Institute - Library of Thai Nguyen University of Technology LIST OF PUBLICATIONS Thi-Hong Tran, Manh-Cuong Nguyen, Anh-Tung Luu, The-Vinh Do, ThuQuy Le, Trung-Tuyen Vu, Ngoc-Giang Tran, Thi-Tam Do and Ngoc-Pi Vu, Electrical Discharge Machining with SiC Powder-Mixed Dielectric: An Effective Application in the Machining Process of Hardened 90CrSi Steel, Machines (MDPI), July 2020 (SCIE Q2); https://doi.org/10.3390/machines8030036 Vu Ngoc Pi, Do Thi Tam, Nguyen Manh Cuong, Thi-Hong Tran; Multiobjective Optimization of PMEDM Process Parameters for Processing Cylindrical Shaped Parts Using Taguchi Method and Grey Relational Analysis; International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN (P): 2249–6890; ISSN (E): 2249–8001 Vol 10, Issue 2, Apr 2020, pp 669-678 (Scopus Q3) https://issuu.com/tjprc/docs/2-67-1584777249-66.ijmperdapr202066 Tran Thi Hong, Bui Thanh Danh, Nguyen Van Cuong, Le Hong Ky, Nguyen Hong Linh, Nguyen Thi Thanh Nga, Tran Ngoc Giang, Nguyen Manh Cuong*; A Study on Influence of Input Parameters on Surface Roughness in PMEDM Cylindrical Shaped Parts; Materials Science Forum (Volume 1018), January 2021, pp 65-70 (Scopus Q4) https://doi.org/10.4028/www.scientific.net/MSF.1018.65 Tran Thi Hong, Nguyen Van Cuong, Bui Thanh Danh, Le Hong Ky, Nguyen Hong Linh, Vu Thi Lien, Nguyen Thai Vinh, Nguyen Manh Cuong*; MultiObjective Optimization of PMEDM Process of 90CrSi Alloy Steel for Minimum Electrode Wear Rate and Maximum Material Removal Rate with Silicon Carbide Powder; Materials Science Forum (Volume 1018), January 2021, pp 51-58 (Scopus Q4) https://doi.org/10.4028/www.scientific.net/MSF.1018.51 Tran Thi Hong, Nguyen Hong Linh, Nguyen Van Cuong, Bui Thanh Danh, Le Hong Ky, Le Thu Quy, Nguyen Manh Cuong, Vu Ngoc Pi, Do Thi Tam*; Effect of Process Parameters on Machining Time in PMEDM Cylindrical Shaped Parts with Silicon Carbide Powder Suspended Dielectric; Materials Science Forum (Volume 1018), January 2021, pp 97102 (Scopus Q4) https://doi.org/10.4028/www.scientific.net/MSF.1018.97 INTRODUCTION OF DISSERTATION Dissertation title Research on the effects of some process parameters on electrical discharge machining process of 90CrSi steel external cylindrical surface using dielectric solution mixed with SiC nano powder Rationale of the study Electrical discharge machining (EDM) is one of the most popular advanced machining technologies in the world This is an effective machining method that is used to process conductive materials, high hardness, and difficult-to-machine parts For example, parts in aircraft engines, power generation turbines, molds, etc There are several disadvantages of EDM method such as: it cannot machine non-conductive materials; low material removal rate (MRR); the electrode wears out quickly, leading to reduced dimensional accuracy of the machined part There have been many domestically and internationally studies to provide solutions to enhance the performance of EDM process such as: Optimizing machining process parameters; Selecting electrode materials; choosing nano powder materials to mix into the dielectric solution Among the above solutions, performing EDM process with conductive powder mixed into dielectric solution (PMEDM) is the solution that gives very positive results This method has been receiving much attention in EDM research Previous research findings indicate that PMEDM can concurrently improve both productivity and quality of the machining process, hence boosting the electrode's durability However, several issues with this technique remain unresolved, including the powder material, powder size, powder concentration, machining process mechanism, and so on As a result, many scientists have been interested in conducting research on the theoretical fundamentals, as well as optimization and application of this technology PMEDM machining research reveals that this is a very difficult field due to the vast number of process parameters, each of which has a very varied effect on the goal functions Furthermore, numerous optimization methods have been applied in this field, such as the Taguchi method, artificial neural network, target surface approach, and so on The majority of the study has focused on simple optimization problems target However, the PMEDM process's multi-objective optimization problem requires consideration as well Parts with external cylindrical surfaces, such as shaped tablet punches and shaped steel sheet punches, are used in actual manufacturing These parts are typically made of tool alloy steels such as SKD11, SKD61, 90CrSi, and others These are pieces that are difficult to machine using conventional methods Processing this type of detail with the EDM method is a very effective way for processing the aforesaid details A number of research have been conducted on the use of EDM machining to process 90CrSi material parts with curved outer cylindrical surfaces When utilizing EDM, studies have demonstrated clear results in terms of both productivity and surface quality However, no research on PMEDM for details with external cylindrical surfaces made of 90CrSi alloy steel has been conducted to yet From the above analysis, the topic “Research on the effects of some process parameters on electrical discharge machining process of 90CrSi steel external cylindrical surface using dielectric solution mixed with SiC nano powder” is urgent Subjects and research goals of the thesis 3.1 Scope of the study The object of research is the PMEDM process when machining small-sized external cylindrical shaped parts The scope of the study is limited to external cylindrical shaped parts tempered 90CrSi tool steel with a maximum dimension of less than 20 mm Also, the electrode material is red copper and EDM processing with dielectric solution mixed with 500 nm SiC powder 3.2 Objectives of the study Investigation of the effects of input parameters of the PMEDM process including the servo voltage (SV), the discharge current (IP), the pulse on time (T on), the pulse off time (Toff), the powder concentration (Cp) on the surface roughness (Ra), the material removal rate (MRR), and the tool wear rate (TWR) when machining external cylindrical shaped parts with 90CrSi material and the pulse electrode is red copper In addition, finding a reasonable set of input process parameters to achieve the smallest Ra, the highest MRR, or smallest TWR Conducting multi-objective optimization of process parameters to simultaneously achieve smallest Ra, largest MRR and smallest TWR Research methodology Using theoretical research methods combined with experimental methods; Using statistical analysis techniques and develop empirical models; Using the Taguchi method and Gray Relational Analysis (GRA) method for single-objective and multi-objective problems Significances 5.1 Scientific significances This dissertation has contributed to improving knowledge about PMEDM process, especially about PMEDM external cylindrical shaped parts Specifically: - Contribute to clarifying the influence of input process parameters (SV, IP, T on, Toff, Cp) on Ra, MRR, and TWR when machining external cylindrical shaped parts with 90CrSi steel using dielectric solution mixed with SiC nano powder - Formulas have been proposed to predict SR, MRR and TWR when processing with reasonable input process factors - Finding the effectiveness of PMEDM when using SiC nano powder and copper electrodes to process external cylindrical shaped parts - The results of the thesis can be used as a reference for scientific research on PMEDM process 5.2 Practical significances Successfully applied PMEDM method to process small-size external cylindrical shaped parts when using SiC nano powder and copper electrodes The results can be applied to mechanical manufacturing companies when processing tablet punches (or steel plate punches) with external cylindrical shaped surfaces to improve the efficiency of the machining process 5.3 New contributions of the thesis - For the first time, the PMEDM method has been successfully applied to process parts small-size external cylindrical shaped parts when using SiC nano powder and copper electrodes - Evaluating the influence of several input process parameters on SR, MRR, and TWR when machining external cylindrical shaped surface of 90CrSi parts using SiC nano powder dielectric solution and copper electrodes - Solving single-objective and multi-objective optimization problems by applying the Taguchi method and GRA to provide a reasonable set of technological parameters when PMEDM - Proposing empirical formulas to predict SR, MRR, and TWR values when PMEDM CHAPTER OVERVIEW OF ELECTRICAL DISCHARGE MACHINING 1.1 Electrical discharge machining Mechanism of Electrical Discharge Machining Figure 1.1 is a diagram of the principle of EDM process In the EDM process: - Eletrodes are EDM tools; There are many material types used to make electrodes such as: Cu, Cu-Zn alloy, Al, graphite, etc All electrode materials are characterized by good electrical conductivity and easy to machine and create precise shapes Choosing the appropriate Fig 1.1 EDM schematic electrodes is very important as results in high material removal rate, small electrode wear, and low processing costs - Machining parts (workpiece): Part materials in EDM machining must be conductive The ability to conduct electricity, heat, melting point, hardness of the machined part material affects the productivity and quality of processing - Dielectric solution: Dielectric solution has the effect of controlling the discharge process, cooling the surface of the machined part as well as the electrode surface and solidifying the chip, rolling the chip out of the machining area and putting it into the filtering system, absorbing and releasing thermal energy Types of EDM: EDM has the following main types: EDM, wire-EDM, EDM sawing, EDM grinding, EDM drilling Among these types, EDM is the most commonly used machining form today 1.2 Advantages and disadvantages of EDM Advantages: Does not require the tool to have a hardness higher than the hardness of the work piece; Does not cause deformation of machined parts; Able to machine small-sized surfaces with complex shapes; Easy to automate because the machining movements are quite simple; Causes little thermal deformation of machined parts; Disadvantages: Can only process conductive materials; The machined hole surface has a taper; Low productivity and machined surface quality; When increasing MMR, the surface roughness also increases; During the machining process, the electrode is worn, which negatively affects the machining accuracy; 1.3 Process parameters of EDM +) Servo voltage Ud: The voltage in EDM is related to the discharge gap and the insulation of the dielectric solution The voltage at the discharge gap increases continuously until an ion current appears to break down the insulation of the dielectric solution When the current begins to appear, the maximum voltage (U0) decreases and remains in a stable state (Ud) at the discharge gap (Figure 1.2) MMR, TWR and SR increase as voltage increases Fig 1.2: Relation between sevro volatage, +) Discharge current Id: This is one of current and time in EDM the most important input parameters of the EDM machining process High current will increase MRR but also increase TWR and reduce machined surface quality +) Pulse on time Ton: (Figure 1.2) includes delay time (Tde) and spark discharge time (Td) Ton and number of pulse cycles (Tp) per second are important quantities In EDM, the MRR is proportional to the amount of energy used during T on +) Pulse off time Toff: (Figure 1.2) Toff has an impact on material removal productivity and the stability of the machining process 1.4 Productivity, surface quality and machining accuracy +) Productivity: also known as MRR which is determined by the ratio between the volume of workpiece material removed and the processing time +) Tool wear rate TWR: is the amount of electrode material worn out in a unit of processing time +) Quality of machined surface: The surface machined by EDM is characterized by its shape, chemical composition, micro-organization and mechanical properties +) Processing accuracy: Machining dimensional accuracy in EDM is often determined through two parameters: overcut amount (d) and machined surface profile accuracy 1.5 Powder mixed electrical discharge machining (PMEDM) Fig 1.3 PMEDM schematic Fig 1.4 Discharge process of EDM and PMEDM Scientists have researched the impact of combining nano- and micro-sized metal powders or alloys into dielectric solutions in the EDM process (PMEDM) in recent years to improve the machining process while also improving machined surface quality Figure 1.3 depicts the PMEDM method's machining diagram When conductive powder particles are present, the spark discharge process varies dramatically (such as increasing the discharge gap, the number of sparks fired in one phase, and the pulse length (Figure 1.4) 1.6 Literature of EDM and PMEDM 1.6.1 Vietnamese publications - Vu Quang Ha (2012) studied the influence of technological regime on productivity and surface quality when wire EDM cutting Research on electrode profile wear and machined surface quality when EDM was conducted by Tran Quang Huy in 2019 In this work, the author used two types of electrode materials: red copper and plated red copper chromium with machined parts being SKD11 steel - Research to determine the optimal technology mode when EDM machining with different types of electrodes combined with different types of processing materials In his research, Nguyen Van Duc proposed the optimal technological regime when pulsing SKD11 steel with copper electrode material - Tran Thi Hong at al has published some research results on EDM when machining shaped Fig 1.5: External cylindrical shaped parts external cylindrical surfaces when machined by EDM machining 90CrSi steel (Figure 1.5) with copper electrodes In this studies, the influence of input technology parameters (T on, Toff, IP, SV) on output results (Ra, TWR, MRR) was investigated - Banh Tien Long and Nguyen Huu Phan have studied the effect of Ti powder on MRR, TWR, and surface quality of parts From the results of the study, processing SKD61 steel using Ti powder can made a improvement in machining productivity and surface quality compared to when not used the powder Specifically, MRR increased by 474.5%, TWR decreased by 64.4%, Ra decreased by 41.3%, and the number and size of microcracks on the machined surface were smaller Also, the white layer thickness is more uniform and the mechanical properties of the surface layer are enhanced - Le Van Tao et al have conducted a study for evaluating the influence of process parameters when PMEDM SKD61 steel with WC powder on SR The results of the study showed that Ra improved by 53.3%, and microhardness increased by 81.5% 1.6.2 Overseas publications Research on EDM and PMEDM focuses mainly on the following directions: - Improving machining productivity, mainly to increase MRR, and reduce TWR - Improving surface quality after machining using EDM and PMEDM methods to reduce SR, reduce surface microcracks, and increase microhardness of the surface layer a) MRR and TWR in PMEDM - Shabgard et al conducted a study on PMEDM SKD61 with red copper electrodes It was noted that IP and Ton have a great influence on MRR, TWR and SR Accordingly, increasing IP causes MRR, TWR and Ra increase rapidly Also, when T on increases, MRR and Ra increase but TWR decreases sharply - M.L Jeswani investigated PMEDM with mixing graphite powder with Cp = g/l into an oil dielectric solution It was reported that MRR increased by 60% and TWR decreased by 28% - When machining titanium alloy, Chow Han-Ming et al employed SiC powder and Al powder with an oil solvent Their findings demonstrate that incorporating SiC powder and Al powder into the oil dielectric solution increases the discharge gap, resulting in an increase in MRR Similarly, Tzeng Y.F et al processed SKD11 steel with Al, Cr, Cu, and SiC powder It was discovered that the powder concentration, powder size, particle density, and electrical and thermal conductivity of the powder all had a significant impact on the machining process A proper powder concentration will boost MRR while decreasing TWR - H.K Kansal et al performed an optimization study to find optimum input parameters when PMEDM pure Ti material using Si powder It was noted that increasing powder concentration helps improve both MRR and SR Also, it was found that the optimal process mode is Cp = g/l, IP = A - Yoo Seok Kim and Chong Nam Chu investigated PMEDM process with graphite mixed powder to machine small holes with diameter of 100 µm and depth of 300 µm, STS304 steel material From the results, mixing graphite powder in solvent with appropriate concentration can reduce the machining time up to 30.9%, and TWR up to 28.3% for comparing to EDM machining without powder - A.P Tiwary et al evaluated the influence of the concentration of three different powders including copper, nickel and cobalt in the dielectric, deionized water, on the MRR material removal rate and the amount of TWR electrode wear when machining Ti-6Al-4V The recommended optimal input parameters are IP = 1.5A and Cobalt powder concentration is g/l b) Ability to improve machined surface quality of the PMEDM method - Mohri et al investigated the effects of PMEDM process with Si powder with particle size of 10-30μm The obtained results show that the machined surfaces have good wear resistance and small surface roughness (Ra) (2μm) - Yoshiyuki Uno and Arika Okada studied the influence of Si powder on the surface formation mechanism It was reported that Si powder mixed in dielectric solution allows creating product surfaces that have smaller surface roughness than conventional EDM methods - According to Jahan, mixing nano-sized graphite powder into dielectric solution in pulse machining and electric spark milling reduces Ra (can reach 38 nm) Besides, Prihandana noted that microcracks on the machined surface will decrease in both number and size when pulsing with powder mixing - Pichai Janmanee et al conducted a study on PMEDM with Ti powder to improve machined surface quality In their results, the hardness of the processed surface layer of WC material increased significantly when pulsed with a powder concentration of 50 g/l In the layer µm deeper than the surface, the microhardness reaches 1750 HV It is due to the formation of TiC through powder mixing, while if EDM not mix powder, the hardness of the base metal layer only reaches 998 HV To evaluate the influence of powder mixed into diselectric solution on the change of machined surface layer during PMEDM, A Batish and colleagues studied the influence of Al, graphite, Cu and W powders Their results show that, when machining with W powder, the surface hardness is the greatest Also, the microhardness of the PMEDM surface depends on other parameters such as powder material, powder concentration, IP, Ton, electrode material Thus, in studies to improve the efficiency of the electroporation process, the PMEDM method is an effective solution to increase MRR and reduce TWR as well as improve machined surface quality Ra (µm) 3.5 2.5 1.5 0.5 3.434 3.426 3.288 3.653 3.008 2.403 2.5 3.5 4.5 Cp (g/lit) Fig 3.3 Effect of powder concentration on surface roughness To evaluate the effect of mixing powder into a dielectric solution on the quality of the machined surface, the technique of analyzing the machined surface captured by a scanning electron microscope (SEM) was applied A number of SEM samples were selected, including: Pulse sample without powder mixing with the following parameters: Cp = (g/liter); Ton = (µs); Toff =30 (µs); IP =12 (A); SV =35 (V); Average Ra 2.388 (μm) Pulse sample mixed with powder with parameters: Cp = (g/liter); Ton = (µs); Toff = 14 (µs); IP = (A); SV = (V); Average 2,080 (μm) From the SEM analysis results (Figure 3.4), it can be seen that when the pulse is mixed with powder (Figure 3.4b), the number of dents is greater than when there is no powder mixing (Figure 3.4a) Figure 3.5 shows that the number of cracks when machining with powder mixed (2 cracks - Figure 3.5b) is significantly reduced compared to when machining without powder mixing (5 cracks - Figure 3.5a) Figure 3.6 shows the structure of the machined surface layer when machining without powder mixing and with powder mixing a) b) Fig 3.4: Machined surface topography 13 a) b) Fig 3.5 Microscopic cracks on the machined surface The results of measuring the thickness of the white layer on the SEM are given in Table 3.5 for samples when pulsed without mixing powder and Table 3.6 for samples when pulsed with powder mixed Accordingly, the thickness of the whitening layer when machining with powder mixed is lower and more uniform than without powder mixing That leads to better surface quality when machining with powder mixed than without mixing powder a) b) Fig 3.6 Structure and whitening layer on machined surface 14 Table 3.5 Thicknesses of White layers when processed without mixing powder Table 3.6 Thicknesses of White layers when processed with mixing powder +) Determination of optimum input factors for getting minimum SR: To determine a reasonable pulse mode, it is necessary to analyze the variance of the S/N ratio of Ra to find a reasonable level of input parameters Table 3.7 ANOVA of S/N of ̅̅̅̅ 𝑅𝑎 Source Cp Ton Toff IP SV Residual Error Total DF 2 2 17 Seq SS 24.018 8.067 30.207 14.147 17.310 19.694 113.443 Adj SS 24.018 8.067 30.207 14.147 17.310 19.694 Adj MS 4.804 4.033 15.103 7.074 8.655 4.924 F 0.98 0.82 3.07 1.44 1.76 P 0.524 0.503 0.156 0.339 0.283 ANOVA S/N values of Ra are shown in Table 3.7, Table 3.8 and Figure 3.7 From the results, it shows that Cp = g/l (Cp5), Ton = µs (Ton1), Toff = 21 µs (Toff2), IP = A (IP2), SV = V (SV2) are the levels and the values of the input parameters give the largest S/N ratio This is the reasonable level and value of the process parameters to achieve the smallest surface roughness Table 3.8 Influence of input factors on S/N of Ra Level Delta Rank Cp -10.205 -10.216 -10.060 -9.513 -7.386 -11.106 3.721 Ton -8.833 -9.993 -10.417 Toff -9.479 -8.312 -11.451 IP -9.797 -8.638 -10.808 SV -11.077 -8.741 -9.425 1.584 3.139 2.170 2.336 15 Fig 3.7 Effect of main factors on S/N of Ra +) Prediction of surface roughness: ̅̅̅̅𝑂𝑃 ) is determined by the levels of The predicted average surface value (𝑅𝑎 parameters that have a strong influence on the S/N of surface roughness according to the formula: ̅ + 𝑇̅𝑜𝑛1 + 𝑇̅𝑜𝑓𝑓2 + ̅̅̅ ̅̅̅̅ 𝑅𝑎𝑂𝑃 = 𝐶𝑝5 𝐼𝑃2 + ̅̅̅̅ 𝑆𝑉2 − ∗ 𝑇̅𝑅𝑎 (3.4) And we have: ̅̅̅̅ 𝑅𝑎𝑂𝑃 = 2.403 + 2.804 + 2.618 + 2.817 + 2.772 − ∗ 3.202 = 0.606 𝜇𝑚 Experimental results with input parameters: Cp = g/l, Ton = µs, Toff = 21 µs, IP = A, SV = V, the average Ra after experiments is 0.656 µm This value differs 100 (0.656 − 0.606) ∙ = 7.62 % from the predicted value This result shows that, in 0.656 the optimal pulse mode using SiC powder, the surface roughness is reduced by 5.67 times (82.35%) compared to when nano powder is not used Fig 3.8 Normal probability plot Fig 3.9 Probability plot original data +) Evaluate the reliability of the model: The reliability of the model is evaluated through the normal distribution graph (Figure 3.8) and the probability distribution graph of the original data (Figure 3.9) From these figures, it can be seen that the Ra data follow the law of normal distribution 16 3.3.2 Effect of input parameters on MRR Table 3.9 Experimental plan and MRR and S/N No Cp Ton Toff IP SV 10 11 12 13 14 15 16 17 18 0 2 2.5 2.5 2.5 3.5 3.5 3.5 4 4.5 4.5 4.5 10 14 10 14 10 14 10 14 10 14 10 14 14 14 21 30 14 21 30 21 30 14 30 14 21 30 14 30 14 21 30 12 12 4 12 12 8 12 5 4 5 MRR [g/h] Run 0.01921 0.01011 0.24745 0.00341 0.33044 0.03213 0.00179 0.03924 0.33835 0.45369 0.05054 0.00254 0.32517 0.00777 0.00886 0.31019 0.00702 0.00799 Run 0.01925 0.01012 0.24651 0.00339 0.33016 0.03213 0.00178 0.03916 0.33835 0.45233 0.05058 0.00253 0.32488 0.00775 0.00883 0.30989 0.00701 0.00798 Run 0.01925 0.01012 0.24698 0.00340 0.33016 0.03216 0.00179 0.03908 0.33808 0.45278 0.05049 0.00253 0.32547 0.00774 0.00885 0.31019 0.00700 0.00800 S/N -34.3156 -39.8957 -12.1468 -49.3611 -9.6230 -29.8586 -54.9584 -28.1426 -9.4149 -6.8794 -25.9281 -51.9155 -9.7577 -42.2115 -41.0643 -10.1703 -43.0820 -41.9507 Average 0.019241 0.010121 0.246981 0.003404 0.330254 0.032142 0.001787 0.039163 0.338263 0.452930 0.050535 0.002536 0.325175 0.007752 0.008847 0.310090 0.007013 0.007989 The results of determining MRR of experiments according to formula 3.1 and their average value for each option in 18 different runs are presented in Table 3.9 +) Effect of input parameters on MRR The results of calculating the S/N ratio (according to formula 3.5) of 18 ̅̅̅̅̅̅̅ ) are shown experiments are shown in Table 3.9 ANOVA values of average MRR (𝑀𝑅𝑅 as Table 3.10 Table 3.11 and Figure 3.11 show the influence of input parameters on ̅̅̅̅̅̅̅) The influence of the parameters on 𝑀𝑅𝑅 ̅̅̅̅̅̅̅ in % is as follows: IP has pulse arrival (𝑀𝑅𝑅 the largest contribution to MRR (55.98%), followed by T on (9.16%), Toff (8.66%), SV (5.77%) and finally is Cp (2.33%) From Figure 3.10, it can be seen that when machining with a dielectric solution mixed with a concentration of nano powder, the MRR is higher than when machining with a dielectric solution without powder mixed MRR reaches its highest value when Cp is at level (3.5 g/l), at this level MRR increases by 183.11% compared to without powder (Figure 3.12) ̅̅̅̅̅̅̅ Table 3.10 ANOVA of 𝑀𝑅𝑅 ̅̅̅̅̅̅̅ Table 3.11 Effect of input factors on 𝑀𝑅𝑅 17 MRR (g/h) 0.2 0.15 0.1 0.16867 0.12193 0.1264 0.09211 0.113920.10836 0.05 0 2.5 3.5 4.5 Cp (g/lit) ̅̅̅̅̅̅̅ Fig 3.10 Main effects plot for 𝑀𝑅𝑅 Fig 3.11 Relation between Cp and MRR +) Determine the appropriate input factors to achieve the largest MRR According to Table 3.11 and Figure 3.8, nano powder concentration Cp = 3.5 (g/liter) (Cp4), Ton = (µs) (Ton1), Toff = 30 (µs) (Toff3), IP = 12 (A) (IP3), SV = (V) (SV3) are the levels and values of input parameters for the largest MRR This is a reasonable level and value of the input process parameters to achieve the largest MRR +) Predict MRR value ̅̅̅̅̅̅̅𝑂𝑃 ) is determined by the levels of The predicted average MRR value (𝑀𝑅𝑅 parameters that have a strong influence on the S/N of MRR according to the formula: ̅ + 𝑇̅𝑜𝑛1 + 𝑇̅𝑜𝑓𝑓3 + ̅̅̅ ̅̅̅̅̅̅̅ 𝑀𝑅𝑅𝑂𝑃 = 𝐶𝑝4 𝐼𝑃3 + ̅̅̅̅ 𝑆𝑉3 − ∗ 𝑇̅𝑀𝑅𝑅 (3.6) Substituting the number, we have: ̅̅̅̅̅̅̅𝑂𝑃 = 0.16867 + 0.18544 + 0.18151 + 0.28344 + 0.15808 − ∗ 0.121901 𝑀𝑅𝑅 = 0.48954 𝑔/ℎ Conduct validation experiments with the following input parameters: C p = 3.5 (g/l), Ton = (µs), Toff = 30 (µs), IP = 12 (A), SV = (V) we have the average pulse removal capacity received after experiments is 0.442 (g/h) This value is 9.71% different from the predicted value From here it can be seen that with the optimal pulse mode (using nano powder), the ablation productivity increases 4.79 times compared to the average level without using nano powder 0.09211 (g/h) 3.3.3 Effect of input parameters on TWR Table 3.12 Experimental plan and TWR and calculated S/N No Cp 10 11 12 13 14 15 16 17 18 0 2 2.5 2.5 2.5 3.5 3.5 3.5 4 4.5 4.5 4.5 Input parameters Ton Toff IP 10 14 10 14 10 14 10 14 10 14 10 14 14 21 30 14 21 30 21 30 14 30 14 21 21 30 14 30 14 21 12 12 4 12 12 12 8 12 SV Run 5 4 3 5 94.68 14.95 72.89 47.30 179.87 16.81 60.71 43.58 69.63 641.74 41.38 5.79 75.00 5.43 69.67 317.20 14.19 6.18 TWR (mg/h) Run Run 18 91.52 16.67 64.79 46.34 174.58 18.10 58.65 38.91 57.34 657.39 37.93 5.02 64.29 6.07 60.80 292.03 10.32 9.48 97.04 18.97 48.59 46.82 171.93 12.93 59.68 40.47 53.24 636.52 36.21 4.63 71.43 6.71 64.60 312.17 12.90 7.01 Average of TWR 94.412 16.864 62.092 46.821 175.459 15.948 59.680 40.986 60.068 645.217 38.506 5.149 70.238 6.067 65.024 307.133 12.473 7.554 S/N -395.030 -245.804 -359.742 -334.092 -448.851 -241.358 -355.174 -322.624 -356.309 -561.949 -317.240 -142.717 -369.489 -156.910 -362.750 -497.520 -219.913 -177.107 +) Effect of input parameters on TWR: The results of calculating the S/N ratio of 18 experiments are shown in Table 3.12 From the ANOVA analysis results (Table 3.13), it can be seen that Ton is the parameter with the largest percentage influence on TWR with 25.6%; Next is the influence of the parameters Cp (17.5%), Toff (15.29%), IP (13.65%) and SV (7.04%) Table 3.13 ANOVA of effect of input factors o TWR Table 3.14 Order of influence of input parameters on TWR The order of influence of input parameters is described in Table 3.14 From this table, it can be seen that the order of influence of parameters on S/N ratio is Cp, Ton, Toff, IP and SV respectively Fig 3.12 Influence of input parameters on TWR Figure 3.12 describes the influence of parameters on TWR electrode wear rate From the figure, it can be seen that Cp has an effect on TWR Using the appropriate powder concentration can reduce TWR Specifically, with Cp = 4.0 g/l, the amount of wear is smallest, and smaller than without mixing powder +) Determine the appropriate input factors to achieve the smallest TWR Determining reasonable input parameters to achieve the smallest TWR is similar to the case of determining Ra above The appropriate pulse mode to achieve the smallest TWR is: Cp = g/l, Ton = 14 µs, Toff = 21 µs, IP = A, SV = V +) Predict the value of electrode wear rate: ̅̅̅̅̅̅̅𝑂𝑃 ) is determined by the The predicted average electrode wear value ( 𝑇𝑊𝑅 levels of parameters that have a strong influence on the S/N of TWR according to the formula: ̅ + 𝑇̅𝑜𝑛3 + 𝑇̅𝑜𝑓𝑓2 + ̅̅̅ ̅̅̅̅̅̅̅ 𝑇𝑊𝑅𝑂𝑃 = 𝐶𝑝5 𝐼𝑃1 + ̅̅̅̅ 𝑆𝑉1 − ∗ 𝑇̅𝐸𝑊𝑅 (3.11) Thay số: 18 18 18 ∑ 𝑇𝑊𝑅𝐼 +∑𝑖=1 𝑇𝑊𝑅𝐼𝐼 + ∑𝑖=1 𝑇𝑊𝑅𝐼𝐼𝐼 𝑇̅𝑇𝑊𝑅 = 𝑖=1 = 3.857 (𝑚𝑔/ℎ) 54 19 (3.12) To evaluate the determined results, a validation experiment was performed This experiment was performed with the following pulse parameters: C p = (g/l), Ton = 14 (µs), Toff = 21 (µs), IP = (A), SV = (V) The average TWR determination result obtained after experiments is 3,533 mg/h Thus, the error between the predicted results and the experimental results is 8.4 (%) +) Evaluate the reliability of the experimental model: Fig 3.13 Normal probability plot a) b) c) Fig 3.14 Johnson conversion plot for TWR Figure 3.13 shows the normal distribution graph of the residuals It is easy to see that the distributed residuals are scattered and quite close to a normal distribution (oblique straight line) To evaluate more clearly, the Johnson transition plot (Figure 3.14) was used This graph includes figures: Figure 3.14a is the probability distribution graph of the original data Accordingly, there are some original data that not follow 20 the normal distribution rule Figure 3.14b is the result of Anderson-Darling (AD) statistics This figure shows that the data does not follow a normal distribution because the p value of 0.005 is very small compared to the significance level of 0.05 Therefore, it is necessary to use the Johnson transformation to convert the data into data that follows the normal distribution law Figure 3.18c shows the distribution graph of the converted data This figure shows that the conversion data (blue points) are all within the two bounding lines Additionally, the p value of 0.478 is much larger than the significance level of 0.05 In other words, the transformed data follows the law of normal distribution with a very high level, meaning the experimental model is reliable Conclusions of chapter - The influence of parameters on surface roughness Ra is as follows: The influence of Toff is the largest (29.71%); followed by Cp (18.65%), SV (15.43%), IP (11.05%) and finally Ton (10.79%) - Mixing SiC powder into dielectric solution when pulsed reduces Ra of the machined surface (29.86%), increases MRR (358.15%) compared to when pulsed with dielectric solution without mixing powder - A reasonable set of pulse mode parameters to achieve the smallest Ra surface roughness is: Cp = (g/l), Ton = (µs), Toff = 21 (µs), IP = (A), and SV = (V) - A reasonable set of pulse mode parameters to achieve maximum ablation productivity is: Cp = 3.5 (g/l), Ton = (µs), Toff = 30 (µs), IP = 12 (A), and SV = (V) - A reasonable set of pulse mode parameters to achieve the smallest tool wear rate is: Cp = (g/l), Ton = 14 (µs), Toff = 21 (µs), IP = (A), and SV = (V) - Formulas have been built to calculate the optimal values of SR, MRR, and TWR, when process the external cylindrical surface with a dielectric solution mixed with 500 (nm) particle size SiC powder CHAPTER MULTI-OBJECTIVE OPTIMIZATION OF PROCESS PARAMETERS IN ELECTRICAL DISCHARGE MACHINING FOR HARDENED 90CrSi STEEL WITH SiC POWDER-MIXED DIELECTRIC 4.1 Problem Statement This chapter applies multi-objective optimization the input parameters for electrical discharge machining hardened 90CrSi steel with SiC powder-mixed dielectric using single objective functions as Ra, MRR, and TWR The Taguchi method and Gray Relational Analysis are applied to solve the multi-objective optimization problem with the given single objective functions 4.2 Overview of the Taguchi Method and Gray Relational Analysis The Taguchi method and Gray Relational Analysis (abbreviated as Taguchi-Gray) are applied to solve the multi-objective optimization problem Minitab software was utilized for data analysis The procedure for multi-objective optimization problems includes 04 steps is presented as follows: • Step 1: Construct a database in the form of orthogonal arrays 21 • Step 2: Perform Gray Relational Analysis • Step 3: Optimize using the Taguchi method and Gray Relational Analysis • Step 4: Conduct experiments to validate the results 4.3 Multi-objective optimization for cylinder surface with powder-mixed dielectric using Taguchi method and Grey Relational Analysis 4.3.1 Construct the orthogonal arrays database This step was carried out in Chapter 3, where the design and experimentation for three single-objective functions, including minimum Ra, maximum MRR, and minimum TWR, were conducted Table 4.1 presents the orthogonal matrix of input parameters and output results (Ra, MRR, and TWR) Table 4.1 Orthogonal Matrix of Input Parameters and Output Results Surface roughness Electrode Wear Rate Material Removal Rate TWR (mg/h) MRR (mg/h) Ra (m) 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd 2.960 2.930 2.928 94.675 91.519 97.041 19.21 19.25 2.239 2.161 2.383 14.947 16.672 18.972 10.11 10.12 19.25 10.12 5.066 5.117 5.125 72.891 64.792 48.594 247.45 246.51 246.98 2.411 2.434 2.482 47.299 46.344 46.821 3.41 3.39 3.40 2.749 2.839 2.601 179.868 174.578 171.932 330.44 330.16 330.16 4.942 5.200 5.174 16.810 18.103 12.931 32.13 32.13 32.16 2.158 2.232 2.196 60.709 58.651 59.680 1.79 1.78 1.79 3.895 3.882 3.868 43.580 38.911 40.467 39.24 39.16 39.08 3.840 3.733 3.790 69.625 57.338 53.242 338.35 338.35 338.08 2.791 2.620 2.528 641.739 657.391 636.522 453.69 452.33 452.78 3.421 3.559 3.490 41.379 37.931 36.207 50.54 50.58 50.49 2.685 3.068 2.906 5.792 5.020 4.634 2.54 2.53 2.53 2.959 2.795 2.763 75.000 64.286 71.429 325.17 324.88 325.47 2.646 2.670 2.785 5.428 6.067 6.705 7.77 7.75 7.74 1.614 1.655 1.741 69.669 60.802 64.602 8.86 8.83 8.85 3.752 3.613 3.926 317.203 292.028 312.168 310.19 309.89 310.19 4.404 4.298 4.491 14.194 10.323 12.903 7.02 7.01 7.00 2.864 2.732 2.795 6.181 9.477 7.005 7.99 7.98 8.00 4.3.2 Grey relational Analysis The analysis of Gray Relational relationships for multi-objective optimization is carried out as follows: +) Standardization of experimental data This process is performed through the standardized value Zij (0≤Zij≤1), which is determined by the formula: 𝑍𝑖𝑗 = 𝑆𝑁𝑖𝑗 −min(𝑆𝑁𝑖𝑗 ,𝑗=1,2, 𝑘) max(𝑆𝑁𝑖𝑗 ,𝑗=1,2, 𝑛)−min(𝑆𝑁𝑖𝑗 ,𝑗=1,2, 𝑛) where j represents the experiment number (j=18) 22 (4.3) The S/N ratio and the value of Zij corresponding to each output objective are shown in Table 4.2 +) Determine of the gray relational coefficient The gray relational coefficient indicates the difference between the standardized value and the ideal value, determined by the formula: ∆𝑚𝑖𝑛+𝜁Δ𝑚𝑎𝑥 𝛾(𝑘) = (𝑘)+𝜁Δ𝑚𝑎𝑥 (4.4) Δ0𝑗 where, j=1, 2, n; k=1, 2, ….m; n is the number of experiments; k is the number of output objectives ∆ot(k) is the absolute value of the deviation between the current standardized value Zj(k) (the Z-value of the j-th experiment for the k-th objective) and the ideal value Z0(k) (reference value): Δ0𝑗 (𝑘) = ‖𝑍0 (𝑘) − 𝑍𝑗 (𝑘)‖ (4.5) +) Δmin = min‖𝑍0 (𝑘) − 𝑍𝑗 (𝑘)‖ is the minimum value 0j ∀𝑗∈𝑖 ∀𝑘 +) Δmax = max max‖𝑍0 (𝑘) − 𝑍𝑗 (𝑘)‖ is the maximum value 0j ∀𝑗∈𝑖 ∀𝑘 +)  is a discrimination coefficient; ≤  ≤ This coefficient can be adjusted based on the practical requirements of the system In this study  = 0.5 Table 4.2 S/N ratio and standardized Z-value of Ra, TWR MRR S/N Zij TWR MRR reference value 1.000 1.000 1.000 Ra Ra TWR -9.365 -7.093 -14.156 -7.757 -8.728 -14.163 -6.831 -11.780 -11.568 -8.460 -10.858 -9.220 -9.067 -8.631 -4.459 -11.517 -12.866 -8.936 -39.503 -24.580 -35.974 -33.409 -44.885 -24.136 -35.517 -32.262 -35.631 -56.195 -31.724 -14.272 -36.949 -15.691 -36.275 -49.752 -21.991 -17.711 MRR 25.683 20.101 47.853 10.630 50.377 30.141 5.041 31.857 50.585 53.121 34.072 8.074 50.242 17.790 18.936 49.830 16.914 18.051 0.494 0.729 0.001 0.660 0.560 0.000 0.756 0.246 0.267 0.588 0.341 0.509 0.525 0.570 1.000 0.273 0.134 0.539 0.398 0.754 0.482 0.544 0.270 0.765 0.493 0.571 0.491 0.000 0.584 1.000 0.459 0.966 0.475 0.154 0.816 0.918 0.429 0.313 0.890 0.116 0.943 0.522 0.000 0.558 0.947 1.000 0.604 0.063 0.940 0.265 0.289 0.932 0.247 0.271 Ra 0.506 0.271 0.999 0.340 0.440 1.000 0.244 0.754 0.733 0.412 0.659 0.491 0.475 0.430 0.000 0.727 0.866 0.461 j(k) TWR 0.602 0.246 0.518 0.456 0.730 0.235 0.507 0.429 0.509 1.000 0.416 0.000 0.541 0.034 0.525 0.846 0.184 0.082 MRR 0.571 0.687 0.110 0.884 0.057 0.478 1.000 0.442 0.053 0.000 0.396 0.937 0.060 0.735 0.711 0.068 0.753 0.729 +) Determining the average Gray Relational coefficient To transform a single objective function into a multi-objective function, the average gray relational coefficient is calculated as : 𝛾̅𝑗 = ∑𝑚 𝑖=1 𝛾𝑖𝑗 (4.6) 𝑘 23 Table 4.3 presents the gray relational coefficients corresponding to individual objectives and the average gray relational coefficient +) Determining the optimal levels of input parameters: Table 4.3 displays the gray relational coefficients for each experiment and the Table 4.3 gray relational coefficients interaction gray relational coefficients and the averaged gray relational coefficients From the table, experiment number 15, corresponding to the machnining mode with Cp = g/l, Ton = µs, Toff = 30 µs, IP = A, SV = V, has the highest interaction gray relational coefficient (0,634) However, this is not yet the optimal level of factors Using Minitab 19 software, the average gray relational coefficient at various levels of each factor can be determined (Table 4.4 and Figure 4.1) The optimal set of process parameters that achieve both lower surface roughness and "smaller is better" for electrode wear, while achieving "greater is better" for material removal rate, are: Cp5/Ton3/Toff2/IP3/SV2 coresponding with Cp = 4.0 g/l, Ton = 14µs, Toff = 21 µs, IP = 12 A, SV = V (Figure 4.1) The results of the ANOVA analysis, shown in Table 4.5 Inticate that it can be seen that the nano-powder concentration Cp has the strongest impact on the overall objective (39.69%), followed by T off (15.01%), SV (13.69%), IP (13.01%), T on (8.57%) Table 4.4 Influence of Parameters on coefficient of Grey relational Figure 4.1 The influence of key parameters on overall objective 24 Table 4.5 ANOVA Results for Grey relational Coefficient Analysis of Variance for Means Source DF Seq SS Cp 0.023043 Ton 0.004974 Toff 0.008712 IP 0.007556 SV 0.007950 Residual Error 0.005826 Total 17 0.058060 Adj SS 0.023043 0.004974 0.008712 0.007556 0.007950 0.005826 Adj MS 0.004609 0.002487 0.004356 0.003778 0.003975 0.001456 F 3.16 1.71 2.99 2.59 2.73 P 0.144 0.291 0.161 0.190 0.179 C% 39.69 8.57 15.01 13.01 13.69 10.03 100.00 The optimal Grey relational coefficient is determined by the formula: 𝛾𝑜𝑝 = 𝜂𝑚 + ∑5𝑖=1(𝜂̅ − 𝜂𝑚 ) = 𝐶𝑝5 + 𝑇𝑜𝑛3 + 𝑇𝑜𝑓𝑓2 + 𝐼𝑃3 + 𝑆𝑉2 − ∗ 𝑇 (4.7) ̅̅̅̅ where T is the average Grey relational coefficient (T = 0.561), the values C p5, Ton3, Toff2, IP3, SV2 are the Grey relational coefficients of the corresponding parameters at the optimum level, obtained from Table 4.3 According to equation (4.7), ̅̅̅̅ 𝛾𝑜𝑝 = 0.732 Based on the optimal values of the input parameters, the optimal value of the multiobjective function (𝑅𝑎, 𝐸𝑊𝑅, MRR)𝑜𝑝 with three single-objective functions Ra, MRR and TWR are determined by the following formula:: (𝑅𝑎, 𝐸𝑊𝑅, MRR)𝑜𝑝 = ̅̅̅̅ 𝐶𝑝5 + ̅̅̅̅̅̅ 𝑇𝑜𝑛3 + ̅̅̅̅̅̅̅ 𝑇𝑜𝑓𝑓2 + ̅̅̅̅ 𝐼𝑃3 + ̅̅̅̅̅ 𝑆𝑉2 − ∗ 𝑇̅ (4.10) Therefore, (𝑅𝑎)𝑜𝑝 = 2.127 𝜇𝑚; (𝐸𝑊𝑅)𝑜𝑝 = 55.874 𝑚𝑔/ℎ; (MRR)𝑜𝑝 = 265.61 𝑚𝑔/ℎ Table 4.6 Comparing calculations and experiments results Optimal parameters Machining Calculation Experiment Differences properties % Cp5/Ton3/Toff3/IP3/SV2 Cp6/Ton1/Toff3/IP3/SV3 2.127 2.314 8.8 Ra (m) TWR (mg/h) 55.874 53.23 4.7 MRR (mg/h) 265.61 276.53 4.1 GRA value 0.811 0.701 To evaluate the accuracy of the calculation method, three-time repetition experiments was conducted with the optimized set of parameters The experimental results were compared with the optimized calculated, as presented in Table 4.6 The largest error compared to the calculations is 8.8%, corresponding to the surface roughness calculation Therefore, the calculation method can be reliably used to predict the values of the components of the multi-objective function, including Ra, MRR, and TWR Conclusions of chapter - The Taguchi method and Gray Relational Analysis are efficient tools for multiobjective optimizating the EDM process for hardened 90CrSi steel using a copper electrode with SiC powder-mixed dielectric (500 nm) - The influence levels of the parameters on the objective are as follows: The discharge current intensity IP has the highest significant impact (32.63%); followed by voltage potential difference SV (20.47%), nano-powder concentration Cp (11.89%), pulse duration Ton (9.71%), and finally pulse pause time T off (1.04%) 25 - The optimal parameters for machining 90CrSi steel using a copper electrode with a 500 nm SiC nanoparticle-mixed dielectric to achieve the multi-objective functions mentioned above are as follows: Cp = 4.0 (g/l), Ton = 14 (µs), Toff = 21 (µs), IP = 12 (A), SV = (V) - Experimental results have confirmed the suitability of the optimized multiobjective function calculation model for the real EDM process of 90CrSi steel using 500 nm SiC nanoparticles-mixed dielectric - Construct formulas to calculate the multi-objective function for discharging using a copper electrode with SiC powder-mixed dielectric is (Equation 4.10) CONCLUSIONS AND FUTURE RESEARCH WORKS Conclusions The thesis has studied the EDM process when machining the external cylindrical surface of 90CrSi material using a dielectric solution mixed with 500 (nm) SiC powder It can be said that these are the first studies on PMEDM when machining shaped outer cylindrical surfaces From the results of the thesis, the following conclusions have been drawn These conclusions are also new points of the thesis because this is the first research in this field Added knowledge about machining PMEDM in general and PMEDM for shaped outer cylindrical surfaces in particular Successfully built a PMEDM experimental system on the outer cylindrical surface, allowing for experimental research to be carried out to meet the requirements Researched the influence of technological parameters of the PMEDM process on surface roughness, material removal rate, and tool wear rate when processing external cylindrical surface of 90CrSi material with a dielectric solution mixed with SiC powder and using copper electrodes Proposing a set of reasonable process parameters for PMEDM external cylindrical parts in order to achieve three single objective functions, including: minimum surface roughness, maximum material removal rate and minimum electrode wear rate These factors include the powder concentration, the pulse on time, the pulse off time, the current, and the servo voltage : - The input process parameters to achieve the smallest surface roughness are: C p = (g/l), Ton = (µs), Toff = 21 (µs), IP = (A), and SV = (V) - AThe input process parameters to achieve maximum ablation productivity are: C p = 3.5 (g/l), Ton = (µs), Toff = 30 (µs), IP = 12 (A), and SV = (V) - The input process parameters to achieve the smallest tool wear rate are: Cp = (g/l), Ton = 14 (µs), Toff = 21 (µs), IP = (A), and SV = (V) Building formulas to predict the optimal values of SR, MRR and TWR (formulas (3.4), (3.6) and (3.11)) Solving multi-objective optimization problem to find optimal input parameters when PMEDM 90CrSi steel external cylindrical surface with dielectric solution mixed with SiC nano powder by applying Taguchi method and gray relationship analysis The problem consists of three single functions including smallest surface roughness, highest 26 material removal rate and smallest electrode wear rate The optimal set of parameters is: Cp = 4.0 (g/l), Ton = 14 (µs), Toff = 21 (µs), IP = 12 (A), SV = (V) Future research works The thesis has studied PMEDM process when machining the external cylindrical surface of 90CrSi material with dielectric solution mixed with SiC nano powder Some results have been performed as mentioned above However, there are still issues that require further research as follows: - Research on PMEDM process when machining external cylindrical surfaces with different machining materials such as tool steel SKD11, SKD61, HARDOX 500 steel etc - Research on PMEDM process when machining external cylindrical surface using different electrode materials such as graphite, tungsten carbide etc - Evaluate the influence of process parameters on the quality of the surface layer after machining such as microhardness, surface whitening layer, degree of adhesion to the machined surface of powder particles - Research on PMEDM machining combined with ultrasonic vibration 27