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A Comprehensive Review on Computational Techniques for Form Error Evaluation

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Abstract

In industries, precise measurement of different form errors is critical and challenging for stringent geometric and dimensional control in manufactured part. These form errors have significant influence on the functional performance of an industrial product that arises due the inherent invariability in measurement techniques and manufacturing devices. Several research have been conducted for evaluation of important form errors such as straightness, flatness, circularity, cylindricity and sphericity using different computational methods. The need of computational methods is justified as they minimize calculation time, human errors and provides improved tolerance values in assessment of form errors. In the same context, this paper presents a comprehensive review and discussion on different computational techniques for distinctive form error evaluation in engineering components. The present work mainly focused on aspects of mathematical formulations and the computational techniques i.e., traditional methods and advanced optimization algorithms, employed for precised evaluation of these errors. Based on the detailed review, several future research directions were described. Finally, last section presents concluding remarks on computational methods in modelling and precise evaluation of form error in manufactured components.

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References

  1. Kunzmann H, Pfeifer T, Schmitt R, Schwenke H, Weckenmann A (2005) Productive metrology-adding value to manufacture. CIRP Ann 54(2):155–168

    Article  Google Scholar 

  2. Shin D, Park J, Kim N, Wysk RA (2009) A stochastic model for the optimal batch size in multi-step operations with process and product variability. Int J Prod Res 47(14):3919–3936

    Article  MATH  Google Scholar 

  3. Morse E, Dantan JY, Anwer N, Söderberg R, Moroni G, Qureshi A, Mathieu L (2018) Tolerancing: managing uncertainty from conceptual design to final product. CIRP Ann 67(2):695–717

    Article  Google Scholar 

  4. Pathak VK, Singh AK, Sivadasan M, Singh NK (2018) Framework for automated GD&T inspection using 3D scanner. J Institut Eng Ser C 99(2):197–205

    Article  Google Scholar 

  5. Stojadinović SM, Majstorović VD (2019) An intelligent inspection planning system for prismatic parts on CMMs. Springer International Publishing, Cham

    Book  Google Scholar 

  6. Acko B, McCarthy M, Haertig F, Buchmeister B (2012) Standards for testing freeform measurement capability of optical and tactile coordinate measuring machines. Measure Sci Technol 23(9):094013

    Article  Google Scholar 

  7. Liu F, Xu G, Liang L, Zhang Q, Liu D (2016) Least squares evaluations for form and profile errors of ellipse using coordinate data. Chin J Mech Eng 29(5):1020–1028

    Article  Google Scholar 

  8. Shunmugam MS (1986) On assessment of geometric errors. Int J Prod Res 24(2):413–425

    Article  Google Scholar 

  9. Haghighi P, Mohan P, Kalish N, Vemulapalli P, Shah JJ, Davidson JK (2015) Toward automatic tolerancing of mechanical assemblies: First-order GD&T schema development and tolerance allocation. J Comput Inform Sci Eng, vol 15, no 4

  10. Radlovački V, Hadžistević M, Štrbac B, Delić M, Kamberović B (2016) Evaluating minimum zone flatness error using new method—Bundle of plains through one point. Precis Eng 43:554–562

    Article  Google Scholar 

  11. Samuel GL, Shunmugam MS (2000) Evaluation of circularity from coordinate and form data using computational geometric techniques. Precis Eng 24(3):251–263

    Article  Google Scholar 

  12. Bialas S, Humienny Z, Kiszka K (1998) Relations between ISO 1101 geometrical tolerances and vectorial tolerances—conversion problems. In: Geometric design tolerancing: theories, standards and applications. Springer, Boston, MA, pp 88–99

  13. Gosavi A, Phatakwala S (2006) A finite-differences derivative-descent approach for estimating form error in precision-manufactured parts. J Manuf Sci Eng 128(1):355–359

    Article  Google Scholar 

  14. Kovvur Y, Ramaswami H, Anand RB, Anand S (2008) Minimum-zone form tolerance evaluation using particle swarm optimisation. Int J Intell Syst Technol Appl 4(1–2):79–96

    Google Scholar 

  15. Agarwal A, Desai KA (2020) Predictive framework for cutting force induced cylindricity error estimation in end milling of thin-walled components. Precis Eng 66:209–219

    Article  Google Scholar 

  16. Pathak VK, Singh AK, Singh R, Chaudhary H (2017) A modified algorithm of Particle Swarm Optimization for form error evaluation. Tm Technisches Messen 84(4):272–292

    Article  Google Scholar 

  17. Yang XS (2010) Engineering optimization: an introduction with metaheuristic applications. Wiley, Hoboken

    Book  Google Scholar 

  18. Whitley D (1994) A genetic algorithm tutorial. Stat Comput 4(2):65–85

    Article  Google Scholar 

  19. Eberhart R, Kennedy J (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks. Citeseer, Vol 4, pp 1942–1948

  20. Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8(1):687–697

    Article  Google Scholar 

  21. Ghafil HN, Jármai K (2020) Dynamic differential annealed optimization: New metaheuristic optimization algorithm for engineering applications. Appl Soft Comput, p 106392

  22. Kadhem AA, Wahab NIA, Aris I, Jasni J, Abdalla AN (2017) Computational techniques for assessing the reliability and sustainability of electrical power systems: a review. Renew Sustain Energy Rev 80:1175–1186

    Article  Google Scholar 

  23. Steinhauser MO, Hiermaier S (2009) A review of computational methods in materials science: examples from shock-wave and polymer physics. Int J Mol Sci 10(12):5135–5216

    Article  Google Scholar 

  24. ISO (1983) Technical drawings—geometrical tolerancing—tolerancing of form, orientation, location and run-out-generalities, definitions, symbols, indications on drawings. ISO1101:1983. International Organization for Standardization, Geneva

  25. ANSI (1995) Dimensioning and Tolerancing, ANSI Y 14.5, ASME, New York

  26. ANSI (1995) Mathematical Definitions of Dimensioning and Tolerancing Principles, ANSI Y 14.5, ASME, New York

  27. ISO/TS 12781–2 (2003) Geometrical product specifications (GPS)—Flatness—Part 2: Specification operators

  28. Rajagopal K, Anand S (1999) Assessment of circularity error using a selective data partition approach. Int J Prod Res 37(17):3959–3979

    Article  MATH  Google Scholar 

  29. ISO/DIS 1101–1996 (1996) Technical drawings—Geometrical Tolerancing, ISO, Geneva

  30. ISO (2017) 1101: Geometrical Product Specification (GPS)—Geometrical tolerancing — Tolerances of form, orientation, location and run-out

  31. Fana KC, Lee JC (1999) Analysis of minimum zone sphericity error using minimum potential energy theory. Precis Eng 23(2):65–72

    Article  Google Scholar 

  32. Samuel GL, Shunmugam MS (1999) Evaluation of straightness and flatness error using computational geometric techniques. Comput Aided Des 31(13):829–843

    Article  MATH  Google Scholar 

  33. Zhang Q, Fan KC, Li Z (1999) Evaluation method for spatial straightness errors based on minimum zone condition. Precis Eng 23(4):264–272

    Article  Google Scholar 

  34. Xiuming L, Zhaoyao S (2008) Evaluation of straightness error using convex polygon [J]. Mech Sci Technol Aerosp Eng, p 6

  35. Affan Badar M, Raman S, Pulat PS (2003) Intelligent search-based selection of sample points for straightness and flatness estimation. J Manuf Sci Eng 125(2):263–271

    Article  Google Scholar 

  36. Yue WL, Wu Y (2008) Evaluation of spatial straightness errors based on multi-target optimization. Opt Precis Eng 16(8):1423–1428

    Google Scholar 

  37. Dhanish PB, Mathew J (2007) A fast and simple algorithm for evaluation of minimum zone straightness error from coordinate data. Int J Adv Manuf Technol 32(1):92–98

    Article  Google Scholar 

  38. Zhu L, Ding Y, Ding H (2006) Algorithm for spatial straightness evaluation using theories of linear complex Chebyshev approximation and semi-infinite linear programming

  39. Endrias DH, Feng HY, Ma J, Wang L, Taher MA (2012) A combinatorial optimization approach for evaluating minimum-zone spatial straightness errors. Measurement 45(5):1170–1179

    Article  Google Scholar 

  40. Cox MG, Siebert BR (2006) The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty. Metrologia 43(4):S178

    Article  Google Scholar 

  41. Wübbeler G, Krystek M, Elster C (2008) Evaluation of measurement uncertainty and its numerical calculation by a Monte Carlo method. Measure Sci Technol 19(8):084009

    Article  Google Scholar 

  42. Zhu M, Ge G, Yang Y, Du Z, Yang J (2019) Uncertainty evaluation of straightness in coordinate measuring machines based on error ellipse theory integrated with Monte Carlo method. Measure Sci Technol 31(3):035008

    Article  Google Scholar 

  43. Zhu LM, Ding H, Xiong YL (2003) Distance function based algorithm for spatial straightness evaluation. Proc Institut Mech Eng Part B J Eng Manuf 217(7):931–939

    Article  Google Scholar 

  44. Cho S, Kim JY (2012) Straightness and flatness evaluation using data envelopment analysis. Int J Adv Manuf Technol 63(5):731–740

    Article  Google Scholar 

  45. Orady E, Li S, Chen Y (2000) Evaluation of minimum zone straightness by a nonlinear optimization method. J Manuf Sci Eng 122(4):795–797

    Article  Google Scholar 

  46. Wang BP, Sun DG, Kong LD, Wang XH (2004) A calculating method of straightness error based on genetic algorithms [J]. Acta Metrologica Sinica, p 1

  47. Wen X, Song A (2003) An improved genetic algorithm for planar and spatial straightness error evaluation. Int J Mach Tools Manuf 43(11):1157–1162

    Article  Google Scholar 

  48. Cui C, Li T, Blunt LA, Jiang X, Huang H, Ye R, Fan W (2013) The assessment of straightness and flatness errors using particle swarm optimization. Procedia CIRP 10:271–275

    Article  Google Scholar 

  49. Mao J, Cao YL (2006) Evaluation method for spatial straightness errors based on particle swarm optimization [J]. J Eng Des 5:291–294

    Google Scholar 

  50. Zhang K (2008) Spatial straightness error evaluation with an ant colony algorithm. In: 2008 IEEE international conference on granular computing. IEEE, pp 793–796

  51. Zhang K, Kong X, Luo J, Wang S (2015) Study on straightness error evaluation of spatial lines based on a hybrid ant colony algorithm. Int J Wireless Mobile Comput 8(3):277–284

    Article  Google Scholar 

  52. Wang C, Ren C, Li B, Wang Y, Wang K (2018) Research on straightness error evaluation method based on search algorithm of beetle. In: International workshop of advanced manufacturing and automation. Springer, Singapore, pp 368–374

  53. Ming Y, Dunbing T (2014) Study on the evaluation of straightness error via hybrid least squares and artificial fish swarm algorithm. Mech Sci Technol Aerosp Eng, p 7

  54. Yang SH, Natarajan U, Sekar M, Palani S (2010) Prediction of surface roughness in turning operations by computer vision using neural network trained by differential evolution algorithm. Int J Adv Manuf Technol 51(9):965–971

    Article  Google Scholar 

  55. Luo J, Liu Z, Zhang P, Liu X, Liu Z (2020) A method for axis straightness error evaluation based on improved differential evolution algorithm. Int J Adv Manuf Technol 110(1):413–425

    Article  Google Scholar 

  56. Hongwei Z, Hui C, Zhibing L, Longlong T, Wenhua S (2020) Axis straightness error evaluation of deep hole by least square method. In: 2020 12th international conference on measuring technology and mechatronics automation (ICMTMA). IEEE, pp. 17–21

  57. Mao J, Zheng H, Cao Y, Yang J (2006) Planar straightness error evaluation based on particle swarm optimization. In: Third international symposium on precision mechanical measurements. International Society for Optics and Photonics, Vol 6280, p 62802D

  58. Zhang K, Wang S (2011) Form errors evaluation based on a hybrid optimization algorithm. JCP 6(8):1605–1612

    Google Scholar 

  59. Luo J, Wang Q (2014) A method for axis straightness error evaluation based on improved artificial bee colony algorithm. Int J Adv Manuf Technol 71(5–8):1501–1509

    Article  Google Scholar 

  60. Hui Y, Mei X, Jiang G, Zhao F, Shen P (2019) Assembly consistency improvement of straightness error of the linear axis based on the consistency degree and GA-MSVM-I-KM. J Intell Manuf, pp 1–13

  61. Raghunandan R, Rao PV (2008) Selection of sampling points for accurate evaluation of flatness error using coordinate measuring machine. J Mater Process Technol 202(1–3):240–245

    Article  Google Scholar 

  62. Damodarasamy S, Anand SAM (1999) Evaluation of minimum zone for flatness by normal plane method and simplex search. IIE Trans 31(7):617–626

    Article  Google Scholar 

  63. Li P, Ding XM, Tan JB, Cui JW (2016) A hybrid method based on reduced constraint region and convex-hull edge for flatness error evaluation. Precis Eng 45:168–175

    Article  Google Scholar 

  64. Lei XQ, Li F, Tu XP, Wang SF (2013) Geometry searching approximation algorithm for flatness error evaluation. Opt Precis Eng 21(5):1312–1317

    Article  Google Scholar 

  65. Wang M, Xi L, Du S (2014) 3D surface form error evaluation using high definition metrology. Precis Eng 38(1):230–236

    Article  Google Scholar 

  66. Zhu X, Ding H (2002) Flatness tolerance evaluation: an approximate minimum zone solution. Comput Aided Des 34(9):655–664

    Article  Google Scholar 

  67. Ye RF, Cui CC, Huang FG, Fan W, Yu Q (2012) Minimum zone evaluation of flatness error using an adaptive iterative strategy for coordinate measuring machines data. In: Advanced Materials Research. Trans Tech Publications Ltd, Vol 472, pp 25–29

  68. Tian SY, Huang FG, Zhang B (2009) An evaluation method for flatness error based on region searching [J]. J Huaqiao Univ (Nat Sci), p 5

  69. Xu B, Wang C, Wang W, Huang M (2018) Area searching algorithm for flatness error evaluation. In: 2018 2nd IEEE advanced information management, communicates, electronic and automation control conference (IMCEC). IEEE, pp 690–693

  70. Hermann G (2007) Robust convex hull-based algorithm for straightness and flatness determination in coordinate measuring. Acta Polytechnica Hungarica 4(4):111–120

    Google Scholar 

  71. Lee MK (2009) An enhanced convex-hull edge method for flatness tolerance evaluation. Comput Aided Des 41(12):930–941

    Article  Google Scholar 

  72. Huang J (2003) An efficient approach for solving the straightness and the flatness problems at large number of data points. Comput Aided Des 35(1):15–25

    Article  Google Scholar 

  73. Deng G, Wang G, Duan J (2003) A new algorithm for evaluating form error: the valid characteristic point method with the rapidly contracted constraint zone. J Mater Process Technol 139(1–3):247–252

    Article  Google Scholar 

  74. Štrbac B, Radlovački V, Ačko B, Spasić-Jokić V, Župunski L, Hadžistević M (2016) The use of Monte Carlo simulation in evaluating the uncertainty of flatness measurement on a CMM. J Prod Eng 19(2):69–72

    Google Scholar 

  75. Calvo R, Gómez E, Domingo R (2014) Vectorial method of minimum zone tolerance for flatness, straightness, and their uncertainty estimation. Int J Precis Eng Manuf 15(1):31–44

    Article  Google Scholar 

  76. Yue WL, Wu Y, Su J (2007) A fast evaluation method for minimum zone flatness by means of classifying measured points [J]. Acta Metrologica Sinica, p 1

  77. Wen XL, Zhu XC, Zhao YB, Wang DX, Wang FL (2012) Flatness error evaluation and verification based on new generation geometrical product specification (GPS). Precis Eng 36(1):70–76

    Article  Google Scholar 

  78. Luo J, Wang Q, Fu L (2012) Application of modified artificial bee colony algorithm to flatness error evaluation. Guangxue Jingmi Gongcheng Optics Precis Eng 20(2):422–430

    Article  Google Scholar 

  79. Cui C, Li B, Huang F, Zhang R (2007) Genetic algorithm-based form error evaluation. Meas Sci Technol 18(7):1818

    Article  Google Scholar 

  80. Wang DX, Wen XL, Wang FL (2012) A differential evolutionary algorithm for flatness error evaluation. AASRI Procedia 1:238–243

    Article  Google Scholar 

  81. Zhang M, Liu Y, Sun C, Wang X, Tan J (2020) Precision measurement and evaluation of flatness error for the aero-engine rotor connection surface based on convex hull theory and an improved PSO algorithm. Measure Sci Technol 31(8):085006

    Article  Google Scholar 

  82. Tseng HY (2006) A genetic algorithm for assessing flatness in automated manufacturing systems. J Intell Manuf 17(3):301–306

    Article  Google Scholar 

  83. Zhang K (2009) Study on minimum zone evaluation of flatness errors based on a hybrid chaos optimization algorithm. In: International conference on intelligent computing, Springer, Berlin, Heidelberg, pp 193–200

  84. Yang Y, Li M, Gu JJ (2019) Application of adaptive hybrid teaching-learning-based optimization algorithm in flatness error evaluation. J Comput 30(4):63–77

    Google Scholar 

  85. Zhang K, Luo J (2013) Research on flatness errors evaluation based on artificial fish swarm algorithm and Powell method. Int J Comput Sci Math 4(4):402–411

    Article  MathSciNet  Google Scholar 

  86. Mikó B (2021) Assessment of flatness error by regression analysis. Measurement 171:108720

    Article  Google Scholar 

  87. Pathak VK, Singh AK (2017) Effective form error assessment using improved particle swarm optimization. Mapan 32(4):279–292

    Article  Google Scholar 

  88. Yu X, Huang M (2009) Evaluation of flatness error based on the improved particle swarm optimization. In: 2009 9th international conference on electronic measurement & instruments. IEEE, pp 4–1038

  89. Ilyas Khan M, Ma SY (2014) Efficient genetic algorithms for measurement of flatness error and development of flatness plane based on minimum zone method. In: Advanced materials research. Trans Tech Publications Ltd. Vol 941, pp 2232–2238

  90. Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: 2009 World congress on nature & biologically inspired computing (NaBIC). IEEE, pp 210–214

  91. Abdulshahed AM, Badi I, Alturas A (2019) Efficient evaluation of flatness error from Coordinate Measurement Data using Cuckoo Search optomisation algorithm. J Acad Res 37:51

    Google Scholar 

  92. Jiang YM, Liu GX (2010) A new flatness evaluation-rotation method based on GA. In: Advanced materials research. Trans Tech Publications Ltd., Vol 139, pp 2033–2037

  93. Weber T, Motavalli S, Fallahi B, Cheraghi SH (2002) A unified approach to form error evaluation. Precis Eng 26(3):269–278

    Article  Google Scholar 

  94. Venkaiah N, Shunmugam MS (2007) Evaluation of form data using computational geometric techniques—Part I: circularity error. Int J Mach Tools Manuf 47(7–8):1229–1236

    Article  Google Scholar 

  95. Dhanish PB (2002) A simple algorithm for evaluation of minimum zone circularity error from coordinate data. Int J Mach Tools Manuf 42(14):1589–1594

    Article  Google Scholar 

  96. Huang FG, Zheng YJ (2008) A method for roundness error evaluation based on area hunting. Acta Metrologica Sinica 29(2):117–119

    MathSciNet  Google Scholar 

  97. Zhu LM, Ding H, Xiong YL (2003) A steepest descent algorithm for circularity evaluation. Comput Aided Des 35(3):255–265

    Article  Google Scholar 

  98. Xiuming L, Zhaoyao S (2010) Evaluation of roundness error from coordinate data using curvature technique. Measurement 43(2):164–168

    Article  Google Scholar 

  99. Ding Y, Zhu L, Ding H (2007) A unified approach for circularity and spatial straightness evaluation using semi-definite programming. Int J Mach Tools Manuf 47(10):1646–1650

    Article  Google Scholar 

  100. Cui C, Fan W, Huang F (2010) An iterative neighborhood search approach for minimum zone circularity evaluation from coordinate measuring machine data. Measure Sci Technol 21(2):027001

    Article  Google Scholar 

  101. Xiuming L, Zhaoyao S (2008) Application of convex hull in the assessment of roundness error. Int J Mach Tools Manuf 48(6):711–714

    Article  Google Scholar 

  102. Gadelmawla ES (2010) Simple and efficient algorithms for roundness evaluation from the coordinate measurement data. Measurement 43(2):223–235

    Article  Google Scholar 

  103. Lei XQ, Pan WM, Tu XP, Wang SF (2014) Minimum zone evaluation for roundness error based on geometric approximating searching algorithm. Mapan 29(2):143–149

    Article  Google Scholar 

  104. Jiang Q, Feng HY, OuYang D, Desta MT (2006) A roundness evaluation algorithm with reduced fitting uncertainty of CMM measurement data. J Manuf Syst 25(3):184–195

    Article  Google Scholar 

  105. Lei X, Zhang C, Xue Y, Li J (2011) Roundness error evaluation algorithm based on polar coordinate transform. Measurement 44(2):345–350

    Article  Google Scholar 

  106. Li X, Liu H, Li W (2011) Development and application of α-hull and Voronoi diagrams in the assessment of roundness error. Measure Sci Technol 22(4):045105

    Article  MathSciNet  Google Scholar 

  107. Chen MC, Tsai DM, Tseng HY (1999) A stochastic optimization approach for roundness measurements. Pattern Recogn Lett 20(7):707–719

    Article  Google Scholar 

  108. Wen X, Xia Q, Zhao Y (2006) An effective genetic algorithm for circularity error unified evaluation. Int J Mach Tools Manuf 46(14):1770–1777

    Article  Google Scholar 

  109. Du CL, Luo CX, Han ZT, Zhu YS (2014) Applying particle swarm optimization algorithm to roundness error evaluation based on minimum zone circle. Measurement 52:12–21

    Article  Google Scholar 

  110. Sun TH (2009) Applying particle swarm optimization algorithm to roundness measurement. Expert Syst Appl 36(2):3428–3438

    Article  Google Scholar 

  111. Kumar M, Kumaar P, Kameshwaranath R, Thasarathan R (2018) Roundness error measurement using teaching learning based optimization algorithm and comparison with particle swarm optimization algorithm. Int J Data Netw Sci 2(3):63–70

    Article  Google Scholar 

  112. Rossi A, Antonetti M, Barloscio M, Lanzetta M (2011) Fast genetic algorithm for roundness evaluation by the minimum zone tolerance (MZT) method. Measurement 44(7):1243–1252

    Article  Google Scholar 

  113. Jin L, Chen YP, Lu HY, Li SP, Chen Y (2014) Roundness error evaluation based on differential evolution algorithm. In: Applied mechanics and materials. Trans Tech Publications Ltd., Vol 670, pp 1285–1289

  114. Srinivasu DS, Venkaiah N (2017) Minimum zone evaluation of roundness using hybrid global search approach. Int J Adv Manuf Technol 92(5):2743–2754

    Article  Google Scholar 

  115. Pathak VK, Singh AK (2017) Form error evaluation of noncontact scan data using constriction factor particle swarm optimization. J Adv Manuf Syst 16(03):205–226

    Article  Google Scholar 

  116. Rossi A, Lanzetta M (2013) Optimal blind sampling strategy for minimum zone roundness evaluation by metaheuristics. Precis Eng 37(2):241–247

    Article  Google Scholar 

  117. Meo A, Profumo L, Rossi A, Lanzetta M (2013) Optimum dataset size and search space for minimum zone roundness evaluation by genetic algorithm. Measure Sci Rev 13(3):100–107

    Article  Google Scholar 

  118. Ming Y, Dunbing T, Zhuanping Z, Dongjing X (2013) Evaluation of circularity error based on hybrid improved artificial fish swarm and geometric algorithm. J Nanjing Univ Aeronaut Astronaut, p 4

  119. Lei X, Song H, Xue Y, Li J, Zhou J, Duan M (2011) Method for cylindricity error evaluation using geometry optimization searching algorithm. Measurement 44(9):1556–1563

    Article  Google Scholar 

  120. Venkaiah N, Shunmugam MS (2007) Evaluation of form data using computational geometric techniques—part II: cylindricity error. Int J Mach Tools Manuf 47(7–8):1237–1245

    Article  Google Scholar 

  121. Zhu LM, Ding H (2003) Application of kinematic geometry to computational metrology: distance function based hierarchical algorithms for cylindricity evaluation. Int J Mach Tools Manuf 43(2):203–215

    Article  Google Scholar 

  122. Wang C, Xu BS (2015) Evaluation of cylindricity geometrical error based on calculational geometry. In: Applied mechanics and materials. Trans Tech Publications Ltd., Vol 722, pp 359–362

  123. Zheng P, Liu D, Zhao F, Zhang L (2019) An efficient method for minimum zone cylindricity error evaluation using kinematic geometry optimization algorithm. Measurement 135:886–895

    Article  Google Scholar 

  124. Liu W, Fu J, Wang B, Liu S (2019) Five-point cylindricity error separation technique. Measurement 145:311–322

    Article  Google Scholar 

  125. Liu W, Zeng H, Liu S, Wang H, Chen W (2018) Four-point error separation technique for cylindricity. Measure Sci Technol 29(7):075007

    Article  Google Scholar 

  126. Liu W, Zhou X, Li H, Liu S, Fu J (2020) An algorithm for evaluating cylindricity according to the minimum condition. Measurement 158:107698

    Article  Google Scholar 

  127. Liu D, Zheng P, Wu J, Yin H, Zhang L (2020) A new method for cylindricity error evaluation based on increment-simplex algorithm. Sci Prog 103(4):0036850420959878

    Article  Google Scholar 

  128. Zheng P, Wu JQ, Zhang LN (2017) Research of the on-line evaluating the cylindricity error technology based on the new generation of GPS. Proc Eng 174:402–409

    Article  Google Scholar 

  129. Lao YZ, Leong HW, Preparata FP, Singh G (2003) Accurate cylindricity evaluation with axis-estimation preprocessing. Precis Eng 27(4):429–437

    Article  Google Scholar 

  130. Lai HY, Jywe WY, Liu CH (2000) Precision modeling of form errors for cylindricity evaluation using genetic algorithms. Precis Eng 24(4):310–319

    Article  Google Scholar 

  131. Geem ZW (2009) Music-inspired harmony search algorithm: theory and applications, vol 191. Springer, Berlin

    Google Scholar 

  132. Yang Y, Li M, Wang C, Wei Q (2018) Cylindricity error evaluation based on an improved harmony search algorithm. Scientific Programming

  133. Wen XL, Zhao YB, Wang DX, Pan J (2013) Adaptive Monte Carlo and GUM methods for the evaluation of measurement uncertainty of cylindricity error. Precis Eng 37(4):856–864

    Article  Google Scholar 

  134. Mao J, Cao Y, Yang J (2009) Implementation uncertainty evaluation of cylindricity errors based on geometrical product specification (GPS). Measurement 42(5):742–747

    Article  Google Scholar 

  135. Weihua N, Zhenqiang Y (2013) Cylindricity modeling and tolerance analysis for cylindrical components. Int J Adv Manuf Technol 64(5–8):867–874

    Article  Google Scholar 

  136. Li Q, Ning H, Gong J, Li X, Dai B (2021) A hybrid greedy sine cosine algorithm with differential evolution for global optimization and cylindricity error evaluation. Appl Artif Intell 35(2):171–191

    Article  Google Scholar 

  137. Luo J, Lu JJ, Chen WM, Fu L, Liu XM, Zhang P, Chen JD (2009) Cylindricity error evaluation using artificial bee colony algorithm with tabu strategy. J Chongqing Univ 32(12):1482–1485

    Google Scholar 

  138. Wu Q, Zhang C, Zhang M, Yang F, Gao L (2019) A modified comprehensive learning particle swarm optimizer and its application in cylindricity error evaluation problem. Math Biosci Eng 16(3):1190–1209

    Article  MathSciNet  Google Scholar 

  139. Guo H, Lin DJ, Pan JZ, Jiang SW (2008) Cylindricity error evaluation based on multi-population genetic algorithm. J Eng Graph 29(4):48–53

    Google Scholar 

  140. Lee K, Cho S, Asfour S (2011) Web-based algorithm for cylindricity evaluation using support vector machine learning. Comput Ind Eng 60(2):228–235

    Article  Google Scholar 

  141. Zhang K, Wu H, Luo J (2016) Study on evaluation of cylindricity errors with a hybrid particle swarm optimization-chaos optimization algorithm. J Comput Theor Nanosci 13(1):567–573

    Article  Google Scholar 

  142. Chen Q, Tao X, Lu J, Wang X (2016) Cylindricity error measuring and evaluating for engine cylinder bore in manufacturing procedure. Adv Mater Sci Eng

  143. Peng Y, Lu BL (2013) A hierarchical particle swarm optimizer with latin sampling based memetic algorithm for numerical optimization. Appl Soft Comput 13(5):2823–2836

    Article  Google Scholar 

  144. Samuel GL, Shunmugam MS (2002) Evaluation of sphericity error from form data using computational geometric techniques. Int J Mach Tools Manuf 42(3):405–416

    Article  Google Scholar 

  145. Xianqing L, Zuobin G, Mingde D, Weimin P (2015) Method for sphericity error evaluation using geometry optimization searching algorithm. Precis Eng 42:101–112

    Article  Google Scholar 

  146. Wang M, Cheraghi SH, Masud AS (2001) Sphericity error evaluation: theoretical derivation and algorithm development. IIE Trans 33(4):281–292

    Article  Google Scholar 

  147. He G, Liu P, Guo L, Wang K (2014) Conicity error evaluation using sequential quadratic programming algorithm. Precis Eng 38(2):330–336

    Article  Google Scholar 

  148. Zhang X, Jiang X, Forbes AB, Minh HD, Scott PJ (2013) Evaluating the form errors of spheres, cylinders and cones using the primal–dual interior point method. Proc Institut Mech Eng Part B J Eng Manuf 227(5):720–725

    Article  Google Scholar 

  149. Liu F, Xu G, Zhang Q, Liang L, Liu D (2015) An intersecting chord method for minimum circumscribed sphere and maximum inscribed sphere evaluations of sphericity error. Measure Sci Technol 26(11):115005

    Article  Google Scholar 

  150. Liu F, Xu G, Liang L, Zhang Q, Liu D (2016) Minimum zone evaluation of sphericity deviation based on the intersecting chord method in Cartesian coordinate system. Precis Eng 45:216–229

    Article  Google Scholar 

  151. Mei J, Huang Q, Chen J, Cheng R, Zhang L, Fang C, Cheng Z (2020) A simple asymptotic search method for estimation of minimum zone sphericity error. AIP Adv 10(1):015322

    Article  Google Scholar 

  152. Zheng Y (2020) A simple unified branch-and-bound algorithm for minimum zone circularity and sphericity errors. Measure Sci Technol 31(4):045005

    Article  Google Scholar 

  153. Prisco U, Polini W (2010) Flatness, cylindricity and sphericity assessment based on the seven classes of symmetry of the surfaces. Adv Mech Eng 2:154287

    Article  Google Scholar 

  154. Soman KG, Ramaswami H, Anand S (2009) Selective zone search method for evaluation of minimum zone sphericity. In: International manufacturing science and engineering conference, vol 43628, pp 517–524

  155. Chatterjee G, Roth B (1998) Chebychev approximation methods for evaluating conicity. Measurement 23(2):63–76

    Article  Google Scholar 

  156. Lei XQ, Song HW, Zhou J (2012) The minimum zone evaluation for sphericity error based on the dichotomy approximating. In: Applied mechanics and materials. Trans Tech Publications Ltd., vol 105, pp 1975–1979

  157. Lei XQ, Xue YJ, Li JS, Ma W, Duan MD (2011) Geometrical optimization searching algorithm for evaluating conicity error. In: Key engineering materials. Trans Tech Publications Ltd., Vol 455, pp 320–326

  158. Wen X, Song A (2004) An immune evolutionary algorithm for sphericity error evaluation. Int J Mach Tools Manuf 44(10):1077–1084

    Article  Google Scholar 

  159. Wen XL, Huang JC, Sheng DH, Wang FL (2010) Conicity and cylindricity error evaluation using particle swarm optimization. Precis Eng 34(2):338–344

    Article  Google Scholar 

  160. Xiulan W, Aiguo S (2003) An improved genetic algorithm for sphericity error evaluation. In: International conference on neural networks and signal processing, 2003. Proceedings of the 2003. IEEE, Vol 1, pp 549–553

  161. Rossi A, Chiodi S, Lanzetta M (2014) Minimum centroid neighborhood for minimum zone sphericity. Precis Eng 38(2):337–347

    Article  Google Scholar 

  162. Huang J, Jiang L, Chao X, Ding X, Tan J (2019) Improved sphericity error evaluation combining a heuristic search algorithm with the feature points model. Rev Sci Instrum 90(3):035105

    Article  Google Scholar 

  163. Xuyi S (2019). A sphericity error assessment application based on whale optimization algorithm. In: IOP conference series: materials science and engineering. IOP Publishing, Vol 631, No 5, p 052050

  164. Mao J, Zhao M (2013) An approach for the evaluation of sphericity error and its uncertainty. Adv Mech Eng 5:208594

    Article  Google Scholar 

  165. Huang J, Jiang L, Chao X, Tan J (2018) Minimum zone sphericity evaluation based on a modified cuckoo search algorithm with fuzzy logic. Measure Sci Technol 30(1):015008

    Article  Google Scholar 

  166. Jiang L, Huang J, Ding X, Chao X (2019) Method for spherical form error evaluation using cuckoo search algorithm. In: Tenth international symposium on precision engineering measurements and instrumentation. International Society for Optics and Photonics., Vol 11053, p 110534J

  167. Chen YP, Jin L, Li SP, Song SL, Liang Y (2013) Evaluation of sphericity error using differential evolution method. In: Applied mechanics and materials. Trans Tech Publications Ltd., Vol 423, pp 2132–2135

  168. Balakrishna P, Raman S, Trafalis TB, Santosa B (2008) Support vector regression for determining the minimum zone sphericity. Int J Adv Manuf Technol 35(9–10):916–923

    Article  Google Scholar 

  169. Wang D, Song A, Wen X, Xu Y, Qiao G (2016) Measurement uncertainty evaluation of conicity error inspected on CMM. Chin J Mech Eng 29(1):212–218

    Article  Google Scholar 

  170. Fister Jr I, Yang XS, Fister I, Brest J, Fister D (2013) A brief review of nature-inspired algorithms for optimization. arxiv preprint. arXiv:1307.4186.

  171. Bhoskar MT, Kulkarni MOK, Kulkarni MNK, Patekar MSL, Kakandikar GM, Nandedkar VM (2015) Genetic algorithm and its applications to mechanical engineering: a review. Mater Today Proceed 2(4–5):2624–2630

    Article  Google Scholar 

  172. Jain NK, Nangia U, Jain J (2018) A review of particle swarm optimization. J Institut Eng India Ser B 99(4):407–411

    Article  Google Scholar 

  173. Pant M, Zaheer H, Garcia-Hernandez L, Abraham A (2020) Differential evolution: a review of more than two decades of research. Eng Appl Artif Intell 90:103479

    Article  Google Scholar 

  174. Karaboga D, Gorkemli B, Ozturk C, Karaboga N (2014) A comprehensive survey: artificial bee colony (ABC) algorithm and applications. Artif Intell Rev 42(1):21–57

    Article  Google Scholar 

  175. Neshat M, Sepidnam G, Sargolzaei M, Toosi AN (2014) Artificial fish swarm algorithm: a survey of the state-of-the-art, hybridization, combinatorial and indicative applications. Artif Intell Rev 42(4):965–997

    Article  Google Scholar 

  176. Mohamad AB, Zain AM, Nazira Bazin NE (2014) Cuckoo search algorithm for optimization problems—a literature review and its applications. Appl Artif Intell 28(5):419–448

    Article  Google Scholar 

  177. Slowik A, Kwasnicka H (2017) Nature inspired methods and their industry applications—Swarm intelligence algorithms. IEEE Trans Industr Inf 14(3):1004–1015

    Article  Google Scholar 

  178. Morrison DR, Jacobson SH, Sauppe JJ, Sewell EC (2016) Branch-and-bound algorithms: A survey of recent advances in searching, branching, and pruning. Discret Optim 19:79–102

    Article  MathSciNet  MATH  Google Scholar 

  179. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Article  Google Scholar 

  180. Dhiman G, Kumar V (2017) Spotted hyena optimizer: a novel bio-inspired based metaheuristic technique for engineering applications. Adv Eng Softw 114:48–70

    Article  Google Scholar 

  181. Dhiman G, Kumar V (2018) Emperor penguin optimizer: a bio-inspired algorithm for engineering problems. Knowl-Based Syst 159:20–50

    Article  Google Scholar 

  182. Dhiman G, Kumar V (2018) Multi-objective spotted hyena optimizer: a multi-objective optimization algorithm for engineering problems. Knowl-Based Syst 150:175–197

    Article  Google Scholar 

  183. Dhiman G, Kumar V (2019) Seagull optimization algorithm: Theory and its applications for large-scale industrial engineering problems. Knowl-Based Syst 165:169–196

    Article  Google Scholar 

  184. Kaur S, Awasthi LK, Sangal AL, Dhiman G (2020) Tunicate swarm algorithm: a new bio-inspired based metaheuristic paradigm for global optimization. Eng Appl Artif Intell 90:103541

    Article  Google Scholar 

  185. Dhiman G, Kaur A (2019) STOA: a bio-inspired based optimization algorithm for industrial engineering problems. Eng Appl Artif Intell 82:148–174

    Article  Google Scholar 

  186. Dhiman G, Kaur A (2019) A hybrid algorithm based on particle swarm and spotted hyena optimizer for global optimization. In: Soft computing for problem solving, Springer, Singapore, pp 599–615

  187. Singh P, Dhiman G (2018) Uncertainty representation using fuzzy-entropy approach: Special application in remotely sensed high-resolution satellite images (RSHRSIs). Appl Soft Comput 72:121–139

    Article  Google Scholar 

  188. Dhiman G, Kumar V (2019) KnRVEA: A hybrid evolutionary algorithm based on knee points and reference vector adaptation strategies for many-objective optimization. Appl Intell 49(7):2434–2460

    Article  Google Scholar 

  189. Pathak VK, Srivastava AK (2020) A novel upgraded bat algorithm based on cuckoo search and Sugeno inertia weight for large scale and constrained engineering design optimization problems. Eng Comput, PP 1–28

  190. Dhiman G (2020) MOSHEPO: a hybrid multi-objective approach to solve economic load dispatch and micro grid problems. Appl Intell 50(1):119–137

    Article  Google Scholar 

  191. Dhiman G (2019) ESA: a hybrid bio-inspired metaheuristic optimization approach for engineering problems. Eng Comput, PP 1–31

  192. Dhiman G, Kumar V (2018) Astrophysics inspired multi-objective approach for automatic clustering and feature selection in real-life environment. Mod Phys Lett B 32(31):1850385

    Article  Google Scholar 

  193. Dhiman G, Soni M, Pandey HM, Slowik A, Kaur H (2020) A novel hybrid hypervolume indicator and reference vector adaptation strategies based evolutionary algorithm for many-objective optimization. Eng Comput, PP 1–19

  194. Dhiman G, Garg M, Nagar A, Kumar V, Dehghani M (2020) A novel algorithm for global optimization: Rat swarm optimizer. J Ambient Intell Human Comput, PP 1–26

  195. Dhiman G, Singh P, Kaur H, Maini R (2019) DHIMAN: A novel algorithm for economic D ispatch problem based on optimization met H od us I ng M onte Carlo simulation and A strophysics co N cepts. Mod Phys Lett A 34(04):1950032

    Article  Google Scholar 

  196. Dhiman G, Singh KK, Slowik A, Chang V, Yildiz AR, Kaur A, Garg M (2021) EMoSOA: a new evolutionary multi-objective seagull optimization algorithm for global optimization. Int J Mach Learn Cybern 12(2):571–596

    Article  Google Scholar 

  197. Dhiman G, Garg M (2020) MoSSE: a novel hybrid multi-objective meta-heuristic algorithm for engineering design problems. Soft Comput 24(24):18379–18398

    Article  Google Scholar 

  198. Dehghani M, Montazeri Z, Givi H, Guerrero JM, Dhiman G (2020) Darts game optimizer: A new optimization technique based on darts game. Int J Intell Eng Syst 13:286–294

    Google Scholar 

  199. Dhiman G, Kaur A (2019) HKn-RVEA: a novel many-objective evolutionary algorithm for car side impact bar crashworthiness problem. Int J Veh Des 80(2–4):257–284

    Article  Google Scholar 

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Pathak, V.K., Singh, R. A Comprehensive Review on Computational Techniques for Form Error Evaluation. Arch Computat Methods Eng 29, 1199–1228 (2022). https://doi.org/10.1007/s11831-021-09610-w

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