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
Kunzmann H, Pfeifer T, Schmitt R, Schwenke H, Weckenmann A (2005) Productive metrology-adding value to manufacture. CIRP Ann 54(2):155–168
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
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
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
Stojadinović SM, Majstorović VD (2019) An intelligent inspection planning system for prismatic parts on CMMs. Springer International Publishing, Cham
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
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
Shunmugam MS (1986) On assessment of geometric errors. Int J Prod Res 24(2):413–425
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
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
Samuel GL, Shunmugam MS (2000) Evaluation of circularity from coordinate and form data using computational geometric techniques. Precis Eng 24(3):251–263
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
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
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
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
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
Yang XS (2010) Engineering optimization: an introduction with metaheuristic applications. Wiley, Hoboken
Whitley D (1994) A genetic algorithm tutorial. Stat Comput 4(2):65–85
Eberhart R, Kennedy J (1995) Particle swarm optimization. In: Proceedings of the IEEE international conference on neural networks. Citeseer, Vol 4, pp 1942–1948
Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8(1):687–697
Ghafil HN, Jármai K (2020) Dynamic differential annealed optimization: New metaheuristic optimization algorithm for engineering applications. Appl Soft Comput, p 106392
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
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
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
ANSI (1995) Dimensioning and Tolerancing, ANSI Y 14.5, ASME, New York
ANSI (1995) Mathematical Definitions of Dimensioning and Tolerancing Principles, ANSI Y 14.5, ASME, New York
ISO/TS 12781–2 (2003) Geometrical product specifications (GPS)—Flatness—Part 2: Specification operators
Rajagopal K, Anand S (1999) Assessment of circularity error using a selective data partition approach. Int J Prod Res 37(17):3959–3979
ISO/DIS 1101–1996 (1996) Technical drawings—Geometrical Tolerancing, ISO, Geneva
ISO (2017) 1101: Geometrical Product Specification (GPS)—Geometrical tolerancing — Tolerances of form, orientation, location and run-out
Fana KC, Lee JC (1999) Analysis of minimum zone sphericity error using minimum potential energy theory. Precis Eng 23(2):65–72
Samuel GL, Shunmugam MS (1999) Evaluation of straightness and flatness error using computational geometric techniques. Comput Aided Des 31(13):829–843
Zhang Q, Fan KC, Li Z (1999) Evaluation method for spatial straightness errors based on minimum zone condition. Precis Eng 23(4):264–272
Xiuming L, Zhaoyao S (2008) Evaluation of straightness error using convex polygon [J]. Mech Sci Technol Aerosp Eng, p 6
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
Yue WL, Wu Y (2008) Evaluation of spatial straightness errors based on multi-target optimization. Opt Precis Eng 16(8):1423–1428
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
Zhu L, Ding Y, Ding H (2006) Algorithm for spatial straightness evaluation using theories of linear complex Chebyshev approximation and semi-infinite linear programming
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
Cox MG, Siebert BR (2006) The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty. Metrologia 43(4):S178
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
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
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
Cho S, Kim JY (2012) Straightness and flatness evaluation using data envelopment analysis. Int J Adv Manuf Technol 63(5):731–740
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
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
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
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
Mao J, Cao YL (2006) Evaluation method for spatial straightness errors based on particle swarm optimization [J]. J Eng Des 5:291–294
Zhang K (2008) Spatial straightness error evaluation with an ant colony algorithm. In: 2008 IEEE international conference on granular computing. IEEE, pp 793–796
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
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
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
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
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
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
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
Zhang K, Wang S (2011) Form errors evaluation based on a hybrid optimization algorithm. JCP 6(8):1605–1612
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
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
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
Damodarasamy S, Anand SAM (1999) Evaluation of minimum zone for flatness by normal plane method and simplex search. IIE Trans 31(7):617–626
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
Lei XQ, Li F, Tu XP, Wang SF (2013) Geometry searching approximation algorithm for flatness error evaluation. Opt Precis Eng 21(5):1312–1317
Wang M, Xi L, Du S (2014) 3D surface form error evaluation using high definition metrology. Precis Eng 38(1):230–236
Zhu X, Ding H (2002) Flatness tolerance evaluation: an approximate minimum zone solution. Comput Aided Des 34(9):655–664
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
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
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
Hermann G (2007) Robust convex hull-based algorithm for straightness and flatness determination in coordinate measuring. Acta Polytechnica Hungarica 4(4):111–120
Lee MK (2009) An enhanced convex-hull edge method for flatness tolerance evaluation. Comput Aided Des 41(12):930–941
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
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
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
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
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
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
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
Cui C, Li B, Huang F, Zhang R (2007) Genetic algorithm-based form error evaluation. Meas Sci Technol 18(7):1818
Wang DX, Wen XL, Wang FL (2012) A differential evolutionary algorithm for flatness error evaluation. AASRI Procedia 1:238–243
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
Tseng HY (2006) A genetic algorithm for assessing flatness in automated manufacturing systems. J Intell Manuf 17(3):301–306
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
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
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
Mikó B (2021) Assessment of flatness error by regression analysis. Measurement 171:108720
Pathak VK, Singh AK (2017) Effective form error assessment using improved particle swarm optimization. Mapan 32(4):279–292
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
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
Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: 2009 World congress on nature & biologically inspired computing (NaBIC). IEEE, pp 210–214
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
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
Weber T, Motavalli S, Fallahi B, Cheraghi SH (2002) A unified approach to form error evaluation. Precis Eng 26(3):269–278
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
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
Huang FG, Zheng YJ (2008) A method for roundness error evaluation based on area hunting. Acta Metrologica Sinica 29(2):117–119
Zhu LM, Ding H, Xiong YL (2003) A steepest descent algorithm for circularity evaluation. Comput Aided Des 35(3):255–265
Xiuming L, Zhaoyao S (2010) Evaluation of roundness error from coordinate data using curvature technique. Measurement 43(2):164–168
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
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
Xiuming L, Zhaoyao S (2008) Application of convex hull in the assessment of roundness error. Int J Mach Tools Manuf 48(6):711–714
Gadelmawla ES (2010) Simple and efficient algorithms for roundness evaluation from the coordinate measurement data. Measurement 43(2):223–235
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
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
Lei X, Zhang C, Xue Y, Li J (2011) Roundness error evaluation algorithm based on polar coordinate transform. Measurement 44(2):345–350
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
Chen MC, Tsai DM, Tseng HY (1999) A stochastic optimization approach for roundness measurements. Pattern Recogn Lett 20(7):707–719
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
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
Sun TH (2009) Applying particle swarm optimization algorithm to roundness measurement. Expert Syst Appl 36(2):3428–3438
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
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
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
Srinivasu DS, Venkaiah N (2017) Minimum zone evaluation of roundness using hybrid global search approach. Int J Adv Manuf Technol 92(5):2743–2754
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
Rossi A, Lanzetta M (2013) Optimal blind sampling strategy for minimum zone roundness evaluation by metaheuristics. Precis Eng 37(2):241–247
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
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
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
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
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
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
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
Liu W, Fu J, Wang B, Liu S (2019) Five-point cylindricity error separation technique. Measurement 145:311–322
Liu W, Zeng H, Liu S, Wang H, Chen W (2018) Four-point error separation technique for cylindricity. Measure Sci Technol 29(7):075007
Liu W, Zhou X, Li H, Liu S, Fu J (2020) An algorithm for evaluating cylindricity according to the minimum condition. Measurement 158:107698
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
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
Lao YZ, Leong HW, Preparata FP, Singh G (2003) Accurate cylindricity evaluation with axis-estimation preprocessing. Precis Eng 27(4):429–437
Lai HY, Jywe WY, Liu CH (2000) Precision modeling of form errors for cylindricity evaluation using genetic algorithms. Precis Eng 24(4):310–319
Geem ZW (2009) Music-inspired harmony search algorithm: theory and applications, vol 191. Springer, Berlin
Yang Y, Li M, Wang C, Wei Q (2018) Cylindricity error evaluation based on an improved harmony search algorithm. Scientific Programming
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
Mao J, Cao Y, Yang J (2009) Implementation uncertainty evaluation of cylindricity errors based on geometrical product specification (GPS). Measurement 42(5):742–747
Weihua N, Zhenqiang Y (2013) Cylindricity modeling and tolerance analysis for cylindrical components. Int J Adv Manuf Technol 64(5–8):867–874
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
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
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
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
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
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
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
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
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
Xianqing L, Zuobin G, Mingde D, Weimin P (2015) Method for sphericity error evaluation using geometry optimization searching algorithm. Precis Eng 42:101–112
Wang M, Cheraghi SH, Masud AS (2001) Sphericity error evaluation: theoretical derivation and algorithm development. IIE Trans 33(4):281–292
He G, Liu P, Guo L, Wang K (2014) Conicity error evaluation using sequential quadratic programming algorithm. Precis Eng 38(2):330–336
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
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
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
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
Zheng Y (2020) A simple unified branch-and-bound algorithm for minimum zone circularity and sphericity errors. Measure Sci Technol 31(4):045005
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
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
Chatterjee G, Roth B (1998) Chebychev approximation methods for evaluating conicity. Measurement 23(2):63–76
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
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
Wen X, Song A (2004) An immune evolutionary algorithm for sphericity error evaluation. Int J Mach Tools Manuf 44(10):1077–1084
Wen XL, Huang JC, Sheng DH, Wang FL (2010) Conicity and cylindricity error evaluation using particle swarm optimization. Precis Eng 34(2):338–344
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
Rossi A, Chiodi S, Lanzetta M (2014) Minimum centroid neighborhood for minimum zone sphericity. Precis Eng 38(2):337–347
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
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
Mao J, Zhao M (2013) An approach for the evaluation of sphericity error and its uncertainty. Adv Mech Eng 5:208594
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
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
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
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
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
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.
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
Jain NK, Nangia U, Jain J (2018) A review of particle swarm optimization. J Institut Eng India Ser B 99(4):407–411
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
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
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
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
Slowik A, Kwasnicka H (2017) Nature inspired methods and their industry applications—Swarm intelligence algorithms. IEEE Trans Industr Inf 14(3):1004–1015
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
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67
Dhiman G, Kumar V (2017) Spotted hyena optimizer: a novel bio-inspired based metaheuristic technique for engineering applications. Adv Eng Softw 114:48–70
Dhiman G, Kumar V (2018) Emperor penguin optimizer: a bio-inspired algorithm for engineering problems. Knowl-Based Syst 159:20–50
Dhiman G, Kumar V (2018) Multi-objective spotted hyena optimizer: a multi-objective optimization algorithm for engineering problems. Knowl-Based Syst 150:175–197
Dhiman G, Kumar V (2019) Seagull optimization algorithm: Theory and its applications for large-scale industrial engineering problems. Knowl-Based Syst 165:169–196
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
Dhiman G, Kaur A (2019) STOA: a bio-inspired based optimization algorithm for industrial engineering problems. Eng Appl Artif Intell 82:148–174
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
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
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
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
Dhiman G (2020) MOSHEPO: a hybrid multi-objective approach to solve economic load dispatch and micro grid problems. Appl Intell 50(1):119–137
Dhiman G (2019) ESA: a hybrid bio-inspired metaheuristic optimization approach for engineering problems. Eng Comput, PP 1–31
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
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
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
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
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
Dhiman G, Garg M (2020) MoSSE: a novel hybrid multi-objective meta-heuristic algorithm for engineering design problems. Soft Comput 24(24):18379–18398
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
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
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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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DOI: https://doi.org/10.1007/s11831-021-09610-w