本研究探討五軸加工的最佳急衝度設定以及急衝度對加工表面品質的影響。工件表面品質和加工速度是生產自由曲面模具的挑戰，對此研究者提出限制急衝度以生成平滑的運動軌跡，藉此抑制機台振動發生，但此舉會影響加工速度。因此在選擇急衝度時需同時考慮表面品質及加工效率。且檢測曲面多軸加工面品質，需有客觀判斷方式，及事前評估與預測，因此本研究提出下列策略以為因應:

一、五軸急衝度之最佳化選擇策略:本研究將伺服軸位置迴路頻寬作為追隨命令限制，配合各軸單節路徑長度進行急衝度計算，提出五軸急衝度之最佳化匹配選擇策略；並以量測五軸加工後表面粗糙度作為面品質檢測依據。使用本研究所設計之單葉片模具作為實際切削，實驗結果證明本研究所建議之五軸急衝度組合可獲最佳加工面品質。與單軸急衝度最大化結果相比，可降低8.3%數值。
二、自由曲面工件之表面品質檢測: 藉由影像處理技術對加工表面影像分析，以加工所殘留痕跡出現頻率作為特徵，發現良好的加工結果會在頻譜圖上有較明顯的峰値，代表顯著地刀具痕迹可作為性能的檢測指標；而不良加工的表面影像具有較多的邊帶(side-band)頻率，使得頻譜上頻率不具有倍頻特性，代表軸之間配合不佳。
三、整合加工性能預測系統: 綜整前兩項研究結果，使用機器學習之支持向量機配合神經網路架構提出整合加工性能預測系統，包含
(1)表面粗糙度預測模組，由加工表面影像之影像特徵值預估表面粗糙度數值，總體平均誤差為0.272%；
(2)加工表面影像特徵預測模組，由軸急衝度參數與加工路徑參數預測加工表面影像之特徵值，包含相關性、能量、同質性、和熵、總和方差及相關性的訊息量度六項參數，總體平均預測誤差為1.114%，最後結合(1)與(2)的整合預測系統之預測誤差結果平均預測誤差為0.730%；
(3)精加工總時間預測模組，同樣由機台急衝度參數與加工路徑參數可預測出總加工時間，14組的平均誤差為0.472%。

本研究所提出之最佳急衝度參數選擇策略，可應用於多軸加工機台以及自由曲面模具加工，有助於現場操作員發揮機台最佳化性能；在無需添加新檢測設備下，亦可提供智慧化生產之機台自動設定與最後品質檢測。而本研究所提出的整合預測系統，可提供使用者執行實際加工前評估製造性能，並且可以減少切削參數設定時之試誤測試時間，適合在曲面表面工件及小批量和高參數差異的智慧製造生產。

This study investigates the best jerk settings in five-axis machining and the influence of jerk settings on the surface quality of machining. Improved surface quality of the workpiece and increased manufacturing speeds are the challenges facing the better manufacture of free-form surface molds, and this study addresses those problems. Researchers have proposed limiting jerk values to guarantee smooth motion trajectories, which can avoid the need to suppress vibration and damage to the machine equipment. But this would sacrifice manufacturing speed. Therefore, it is necessary to consider the balance between surface quality and processing efficiency when selecting a jerk value. In addition, there is no objective judgment method for detecting the quality of the multi-axis machining surface of curved surfaces, and best practices for the pre-evaluation and prediction of performance have not been developed. Jerk values can only be adjusted and improved based on experience. In order to solve the aforementioned problems, this research proposes the following strategies as a response:

1. The optimal selection strategy for five-axis jerk values: This study takes 　the servo axis position loop bandwidth as the tracking command ability limit, calculates jerk values according to the path length of each axis, and proposes the best matching five-axis jerk value selection strategy. The surface roughness after five-axis machining is taken as the metric for surface quality inspection. A single-blade mold designed in this study has been used as the testing mold. The experimental results prove that the five-axis jerk combination recommended by this research does obtain the best surface quality. Compared with the result of maximizing single-axis jerking, roughness values can be reduced by 8.3%.
2. Surface quality inspection of free-form surface workpieces: One can analyze the processed surface image with image processing technology, and use the frequency of residual traces as a representative feature. It is found that a good processing result will have a more obvious peak value on the spectrogram, which indicates the tool traces can be used as a significant performance indicator. Poorly processed surface images have more side-band frequencies, so that the frequencies on the frequency spectrum do not have harmonic frequency characteristics, which is a representative feature of poor matching between the axes while manufacturing.
3. An integrated processing performance prediction system: Based on the first two results, an integrated processing performance prediction system is proposed using machine learning support vector machines and neural network architecture. It includes:
(1) Surface roughness prediction modules, in which surface features of 　 the image are processed to predict a surface roughness value, and which produce an overall average system error of 0.272%.
(2)A processed surface image feature module, which predicts the feature value of the processed surface image from the axis jerking parameters and the processing path parameters. The six parameters of the information measurement index included correlation, energy, homogeneity, sum entropy, sum variance and the correlation information measure. The overall average error is 1.114% and the prediction error result of the integrated prediction system combining (1) and (2) has an average error of 0.730%;
(3) A prediction module for total finishing time. The total processing time can also be predicted from the machine jerking parameters and processing path parameters. The average error of the 14 groups is 0.472%.

The strategy for selecting the best jerk parameters proposed by this research can be applied to all multi-axis machining machines and free-form surface mold processing. This decision-making method will help on-site operators to maximize the performance of their machines and allow automatic machine setting and final quality testing of intelligent production systems without the need to add new detecting equipment. The integrated prediction system proposed by this research can also provide users with the ability to evaluate manufacturing performance before performing actual operations, and reduce trial and error testing time when cutting parameters are set. It is very suitable for curved surface workpieces, small batches and high parameter differences in smart manufacturing production applications.

[1] Chiu, H. W., & Lee, C. H. (2017). Prediction of machining accuracy and surface quality for CNC machine tools using data driven approach. Advances in Engineering Software, 114, 246-257.
[2] Sencer, B., Ishizaki, K., & Shamoto, E. (2015). High speed cornering strategy with confined contour error and vibration suppression for CNC machine tools. CIRP Annals, 64(1), 369-372.
[3] Zhang, Y., Ye, P., Wu, J., & Zhang, H. (2018). An optimal curvature-smooth transition algorithm with axis jerk limitations along linear segments. The International Journal of Advanced Manufacturing Technology, 95(1-4), 875-888.
[4] Chiu, H. W., & Lee, C. H. (2020). Intelligent machining system based on CNC controller parameter selection and optimization. IEEE Access, 8, 51062-51070.
[5] Sencer, B., & Tajima, S. (2017). Frequency optimal feed motion planning in computer numerical controlled machine tools for vibration avoidance. Journal of Manufacturing Science and Engineering, 139(1), 011006.
[6] Sun, Y., Zhao, Y., Bao, Y., & Guo, D. (2014). A novel adaptive-feedrate interpolation method for NURBS tool path with drive constraints. International Journal of Machine Tools and Manufacture, 77, 74-81.
[7] Ha, C. W., & Lee, D. (2017). Analysis of embedded prefilters in motion profiles. IEEE Transactions on Industrial Electronics, 65(2), 1481-1489.
[8] Sencer, B., & Shamoto E. (2012). The effect of jerk parameter of the reference motion trajectory on the oscillatory behavior of feed drive systems. Proceedings of JSPE Semestrial Meeting 2012 JSPE Spring Conference, The Japan Society for Precision Engineering, 261-262.
[9] Erkorkmaz, K., & Altintas, Y. (2001). High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation. International Journal of machine tools and manufacture, 41(9), 1323-1345.
[10] Dumanli, A., & Sencer, B. (2018). Optimal high-bandwidth control of ball-screw drives with acceleration and jerk feedback. Precision Engineering, 54, 254-268.
[11] Zhang, L., & Du, J. (2018). Acceleration smoothing algorithm based on jounce limited for corner motion in high-speed machining. The International Journal of Advanced Manufacturing Technology, 95(1-4), 1487-1504.
[12] Zhang, Y., Ye, P., Wu, J., & Zhang, H. (2018). An optimal curvature-smooth transition algorithm with axis jerk limitations along linear segments. The International Journal of Advanced Manufacturing Technology, 95(1-4), 875-888.
[13] Zhang, Y., Zhao, M., Ye, P., & Zhang, H. (2019). A G4 continuous B-spline transition algorithm for CNC machining with jerk-smooth feedrate scheduling along linear segments. Computer-Aided Design, 115, 231-243.
[14] Hashemian, A., Bo, P., & Bartoň, M. (2020). Reparameterization of ruled surfaces: toward generating smooth jerk-minimized toolpaths for multi-axis flank CNC milling. Computer-Aided Design, 127, 102868.
[15] Li, H., Wu, W. J., Rastegar, J., & Guo, A. (2019). A real-time and look-ahead interpolation algorithm with axial jerk-smooth transition scheme for computer numerical control machining of micro-line segments. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 233(9), 2007-2019.
[16] Altintas, Y., Yang, J., & Kilic, Z. M. (2019). Virtual prediction and constraint of contour errors induced by cutting force disturbances on multi-axis CNC machine tools. CIRP Annals, 68(1), 377-380.
[17] Erkorkmaz, K., & Altintas, Y. (2001). High speed CNC system design. Part III: high speed tracking and contouring control of feed drives. International Journal of Machine Tools and Manufacture, 41(11), 1637-1658.
[18] Trumper, D. L., & Lu, X. (2007). Fast tool servos: advances in precision, acceleration, and bandwidth. In Towards Synthesis of Micro-/Nano-systems. Springer, 11-19.
[19] Lin, C. Y., & Lee, C. H. (2017). Remote servo tuning system for multi-axis CNC machine tools using a virtual machine tool approach. Applied Sciences, 7(8), 776.
[20] Kim, D., & Jeon, D. (2012). Feed-system autotuning of a CNC machining center: Rapid system identification and fine gain tuning based on optimal search. Precision engineering, 36(2), 339-348.
[21] Duong, T. Q., Rodriguez-Ayerbe, P., Lavernhe, S., Tournier, C., & Dumur, D. (2019). Contour error pre-compensation for five-axis high speed machining: offline gain adjustment approach. The International Journal of Advanced Manufacturing Technology, 100(9-12), 3113-3125.
[22] Mansour, S. Z., & Seethaler, R. (2017). Feedrate optimization for computer numerically controlled machine tools using modeled and measured process constraints. Journal of Manufacturing Science and Engineering, 139(1), 011012
[23] Suzuki, T., Yoshikawa, K., Hirogaki, T., Aoyama, E., & Ikegami, T. (2019). Improved method for synchronizing motion accuracy of linear and rotary axes under constant feed speed vector at end milling point–investigation of motion error under NC-commanded motion–. International Journal of Automation Technology, 13(5), 679-690.
[24] Kim, J., & Kim, C. (2011). Influence of machine vibration on surface generation in ultra precision machining. Proceedings of the ICOMM, 497-501.
[25] Chiu, H. W., & Lee, C. H. (2020). Intelligent machining system based on CNC controller parameter selection and optimization. IEEE Access, 8, 51062-51070.
[26] Tounsi, N., Bailey, T., & Elbestawi, M. A. (2003). Identification of acceleration deceleration profile of feed drive systems in CNC machines. International Journal of machine tools and manufacture, 43(5), 441-451.
[27] Nishio, K., Sato, R., & Shirase, K. (2012). Influence of motion errors of feed drive systems on machined surface. Journal of advanced mechanical design, systems, and manufacturing, 6(6), 781-791.
[28] Jiang, Y., Han, J., Xia, L., Lu, L., Tian, X., & Liu, H. (2020). A decoupled five-axis local smoothing interpolation method to achieve continuous acceleration of tool axis. The International Journal of Advanced Manufacturing Technology, 111(1), 449-470.
[29] Bi, Q., Shi, J., Wang, Y., Zhu, L., & Ding, H. (2015). Analytical curvature-continuous dual-Bézier corner transition for five-axis linear tool path. International Journal of Machine Tools and Manufacture, 91, 96-108.
[30] Nieslony, P., Krolczyk, G. M., Wojciechowski, S., Chudy, R., Zak, K., & Maruda, R. W. (2018). Surface quality and topographic inspection of variable compliance part after precise turning. Applied Surface Science, 434, 91-101.
[31] Jiang, X. J., & Whitehouse, D. J. (2012). Technological shifts in surface metrology. CIRP annals, 61(2), 815-836.
[32] Bharathi, S., & Ratnam, M. M. (2019). Evaluation of 3D Surface Roughness of Milled Surfaces using Laser Speckle Pattern. In IOP Conference Series: Materials Science and Engineering, 530(1), 012022.
[33] Ali, J. M., Jailani, H. S., & Murugan, M. (2019). Surface roughness evaluation of milled surfaces by image processing of speckle and white-light images. In Advances in manufacturing processes, Springer, Singapore, 141-151.
[34] Sato, Y., Nakanishi, T., Sato, R., Shirase, K., Oda, M., & Nakayama, N. (2016). Study on the evaluation method for finished surface based on human visual characteristic. In 2016 International Symposium on Flexible Automation (ISFA), IEEE, 428-431.
[35] Martínez, S. S., Vázquez, C. O., García, J. G., & Ortega, J. G. (2017). Quality inspection of machined metal parts using an image fusion technique. Measurement, 111, 374-383.
[36] Cuka, B., Cho, M., & Kim, D. W. (2018). Vision-based surface roughness evaluation system for end milling. International Journal of Computer Integrated Manufacturing, 31(8), 727-738.
[37] Xie, X. (2008). A review of recent advances in surface defect detection using texture analysis techniques. ELCVIA: electronic letters on computer vision and image analysis, 7(3), 1-22.
[38] Hasegawa, S., Sato, R., & Shirase, K. (2016). Influences of geometric and dynamic synchronous errors onto machined surface in 5-axis machining center. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 10(5), JAMDSM0071.
[39] Nishio, K., Sato, R., & Shirase, K. (2012). Influence of motion errors of feed drive systems on machined surface. Journal of advanced mechanical design, systems, and manufacturing, 6(6), 781-791.
[40] Tang, L., & Landers, R. G. (2011). Predictive contour control with adaptive feed rate. IEEE/ASME Transactions On Mechatronics, 17(4), 669-679.
[41] Da, N., Gb, T., & Kc, V. (2014). Study on the relationship between surface roughness of AA6061 alloy end milling and image texture features of milled surface. Procedia Engineering, 97, 150-157.
[42] Wuest, T., Weimer, D., Irgens, C., & Thoben, K. D. (2016). Machine learning in manufacturing: advantages, challenges, and applications. Production & Manufacturing Research, 4(1), 23-45.
[43] Asiltürk, I., & Çunkaş, M. (2011). Modeling and prediction of surface roughness in turning operations using artificial neural network and multiple regression method. Expert systems with applications, 38(5), 5826-5832.
[44] Özel, T., & Karpat, Y. (2005). Predictive modeling of surface roughness and tool wear in hard turning using regression and neural networks. International journal of machine tools and manufacture, 45(4-5), 467-479.
[45] Zain, A. M., Haron, H., & Sharif, S. (2010). Prediction of surface roughness in the end milling machining using artificial neural network. Expert Systems with Applications, 37(2), 1755-1768.
[46] Morala-Argüello, P., Barreiro, J., & Alegre, E. (2012). A evaluation of surface roughness classes by computer vision using wavelet transform in the frequency domain. The International Journal of Advanced Manufacturing Technology, 59(1-4), 213-220.
[47] Ramesh, R., Kumar, K. R., & Anil, G. (2009). Automated intelligent manufacturing system for surface finish control in CNC milling using support vector machines. The International Journal of Advanced Manufacturing Technology, 42(11-12), 1103-1117.
[48] Kayabaşi, O., & Ertürk, Ş. (2019). On-line surface roughness prediction by using a probabilistic approach for end-milling. IEEE Access, 7, 143490-143498.
[49] Batista, M. F., Rodrigues, A. R., & Coelho, R. T. (2017). Modelling and characterisation of roughness of moulds produced by high-speed machining with ball-nose end mill. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 231(6), 933-944.
[50] Lambrechts, P., Boerlage, M., & Steinbuch, M. (2005). Trajectory planning and feedforward design for electromechanical motion systems. Control Engineering Practice, 13(2), 145-157.
[51] Yang, H., Wang, Z., Zhang, T., & Du, F. (2020). A review on vibration analysis and control of machine tool feed drive systems. The International Journal of Advanced Manufacturing Technology, 107, 503–525.
[52] Haralick, R. M., Shanmugam, K., & Dinstein, I. H. (1973). Textural features for image classification. IEEE Transactions on systems, man, and cybernetics, 6, 610-621.
[53] Arizmendi, M., Fernández, J., de Lacalle, L. L., Lamikiz, A., Gil, A., Sánchez, J. A., Campa F.J. & Veiga, F. (2008). Model development for the prediction of surface topography generated by ball-end mills taking into account the tool parallel axis offset. Experimental validation. CIRP annals, 57(1), 101-104.
[54] Beale, M. H., Hagan, M. T., & Demuth, H. B. (2010). Neural network toolbox™ user's guide. The MathWorks, Natick, MA, USA.
[55] Chang, C. C., & Lin, C. J. (2011). LIBSVM: A library for support vector machines. ACM transactions on intelligent systems and technology (TIST), 2(3), 1-27.
[56] He K., Zhang X., Ren S., Sun J. (2016). Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, 770-778.
[57] Selvaraju R. R., Cogswell M., Das A., Vedantam R., Parikh D., & Batra D. (2017). Grad-cam: Visual explanations from deep networks via gradient-based localization. In Proceedings of the IEEE international conference on computer vision, 618-626.
[58] Zhou B., Khosla A., Lapedriza A., Oliva A., Torralba A. (2016). Learning deep features for discriminative localization. In Proceedings of the IEEE conference on computer vision and pattern recognition, 2921-2929.
[59] Ngerntong, S., & Butdee, S. (2020). Surface roughness prediction with chip morphology using fuzzy logic on milling machine. Materials Today: Proceedings, 26, 2357-2362.
[60] Urbikain, G., & de Lacalle, L. L. (2018). Modelling of surface roughness in inclined milling operations with circle-segment end mills. Simulation Modelling Practice and Theory, 84, 161-176.
[61] Xie, N., Zhou, J., & Zheng, B. (2018). An energy-based modeling and prediction approach for surface roughness in turning. The International Journal of Advanced Manufacturing Technology, 96(5-8), 2293-2306.
[62] Sekulic, M., Pejic, V., Brezocnik, M., Gostimirović, M., & Hadzistevic, M. (2018). Prediction of surface roughness in the ball-end milling process using response surface methodology, genetic algorithms, and grey wolf optimizer algorithm. Advances in Production Engineering & Management, 13(1), 18-30.
[63] Marani, M., Songmene, V., Zeinali, M., Kouam, J., & Zedan, Y. (2020). Neuro-fuzzy predictive model for surface roughness and cutting force of machined Al–20 Mg 2 Si–2Cu metal matrix composite using additives. Neural Computing and Applications, 32(12), 8115-8126.
[64] Beemaraj, R. K., Chandra Sekar, M. S., & Vijayan, V. (2020). Computer vision measurement and optimization of surface roughness using soft computing approaches. Transactions of the Institute of Measurement and Control, 42(13), 2475-2481.
[65] Patel, D. R., Kiran, M. B., & Vakharia, V. (2020). Modeling and prediction of surface roughness using multiple regressions: A noncontact approach. Engineering Reports, 2(2), e12119.