To improve the measurement accuracy of high-speed and precision motorized spindle rotary error as the research objective, based on the three-point method, an error separation model and an objective optimization function for noise-containing signals are developed. To improve the convergence speed, globally optimize the model objectives, and obtain the best optimization region of the sensor mounting angle, it is proposed that an enhanced adaptive particle swarm optimization algorithm be used. With the improved particle swarm algorithm, the convergence speed was greater than that of the primary particle swarm algorithm by more than 50%. The spindle radial rotation error was experimentally measured and separated using a high-speed vertical machining center, and the deviation between the separation result and the experimental rotation error was 4.5%, indicating that the separation result's accuracy was high. It also proved the correctness and feasibility of the optimization algorithm.
LiZSunBZhuW, et al.Thermal error modeling of motorized spindle and application of miniature radiator in motorized spindle. Int J Adv Manuf Technol2024; 131: 1107–1118.
2.
WangHChenGSunY. Prediction of thermal errors in a motorized spindle in CNC machine tools by applying loads based on heat flux. Proc Inst Mech Eng, Part C: J Mech Eng Sci2024; 238: 264–278.
3.
HaoranYKaiguoF. Co-simulation-based digital twin for thermal characteristics of motorized spindle. Int J Adv Manuf Technol2023; 125: 4725–4737.
4.
HongxunZZhaojunYChuanhaiC, et al.Optimal design of three-stress accelerated degradation test plan for motorized spindle with poor prior information. Metals (Basel)2022; 12: 1996–1996.
5.
YeDXueshiTZhaolongL, et al.A review of key technologies for high-speed motorized spindles of CNC machine tools. Machines2022; 10: 145.
6.
LeeDHKimMGChoNG. Characterization of the sampling in optical measurements of machined surface textures. Proc IMechE, Part B: J Eng Manuf2016; 230: 2047–2063.
7.
LuHZWangZWJiCD, et al.A study of ultraprecision ball rotating displacement measurement using laser focus deviation probes. Proc IMechE, Part B: J Eng Manuf2017; 231: 2504–2510.
8.
ShuQZhuMZLiuXB, et al.Radial error motion measurement of ultraprecision axes of rotation with nanometer-level precision. J Manuf Sci Eng2017; 139: 1–11.
9.
AokiYShigeoO. Research of three-point method roundness error measurement. Precise Mach1966; 32: 27–32.
10.
WhitehouseDJ. Some theoretical aspects of error separation techniques in surface metrology. J Phys E Sci Instrum1976; 9: 531–536.
11.
MaPZhaoCLuX, et al.Rotation error measurement technology and experimentation research of high-precision hydrostatic spindle. Int J Adv Manuf Technol2014; 73: 1313–1320.
12.
ChenGDSunYHAnCH, et al.Measurement and analysis for frequency domain error of ultra-precision spindle in a fly cutting machine tool. Proc IMechE, Part B: J Eng Manuf2018; 232: 1501–1507.
13.
JinLYanZXieL, et al.An experimental investigation of spindle rotary error on high-speed machining center. Int J Adv Manuf Technol2014; 70: 327–334.
14.
HuangPLeeWBChanCY. Investigation of the effects of spindle unbalance induced error motion on machining accuracy in ultra-precision diamond turning. Int J Mach Tools Manuf2015; 94: 48–56.
15.
LeeDHLeeWR. Easy measuring instrument for analyzing the radial and tilt error motions of a rotating shaft. Proc Inst Mech Eng, Part M: J Eng Marit Environ2017; 231: 667–674.
16.
ShiSLinJWangX, et al.A hybrid three-probe method for measuring the roundness error and the spindle error. Prec Eng2016; 45: 403–413.
17.
Kim MGLee DHCho NG. A force sensor with five degrees of freedom using optical intensity modulation for usage in a magnetic resonance field. Meas Sci Technol2013; 24: 045101.
PingMAJianhongLIJianguoOU,et al.Research on multi-step error separation of spindle rotary accuracy. Mech Sci Technol2018; 37: 884–890.
20.
ChenYZhaoXSGaoWG, et al.A novel multi-probe method for separating spindle radial error from artifact roundness error. Int J Adv Manuf Tech2017; 93: 623–634.
21.
KimMGLeeDHChoNG. The 5-degree of freedom setting error calibration algorithm for endpoint device or rotor to manufacture freeform surfaces. In Proceedings-ASPE/ASPEN summer topical meeting: manufacture and metrology of freeform and off-axis aspheric surfaces. Am Soc Precis Eng, Hawaii, USA, 2014, pp.158–161
22.
LeeDHLeeWR. Easy measuring instrument for analyzing the radial and tilt error motions of a rotating shaft. Proc IMechE, Part M: J Eng Marit Environ2017; 231: 667–674.
23.
BaekSKimMLeeD, et al.Multi-probe system design for measuring the roundness and rotation error motion of a spindle using an error separation technique. Proc Inst Mech Eng, Part B: J Eng Manuf2018; 233: 1547–1560.
24.
HailongCDajiangLXinjiangZ, et al.Measurement and analysis of the radial motion error of aerostatic ultra-precision spindle. Measurement (Mahwah N J)2019; 137: 624–635.
25.
ChengbaoZMingZZhongC, et al.Study on error separation of three-probe method. Symmetry (Basel)2022; 14: 866–866.
26.
GangKZhijianZJianzhongY, et al.Roundness error separation based on singularity detection and exact-stop of the spindle in on-machine measurement of spindle rotation error. Mech Syst Signal Process2022; 171: 108647. DOI: https://doi.org/10.1016/j.ymssp.2021.108647.
27.
RuixiangMAWeibinZHUJinZHU, et al.Separation and compensation method for indexing error of rotary table based on Fourier transformation. J Instrum2023; 44: 140–150.
28.
HaitjemaH. Revisiting the multi-step method: enhanced error separation and reduced amount of measurements. CIRP Anal-Manuf Technol2015; 64: 491–494.
29.
SchutteJFKohBIReinboltJA, et al.Evaluation of a particle swarm algorithm for biomechanical optimization. J Biomech Eng2005; 127: 465–474.
30.
SuJQiJWuC, et al.Multi-UAVs target attack based on improved genetic algorithm. In: 2020 39th Chinese control conference (CCC). IEEE,Shenyang, China, 2020, pp.1466–1471.
ZhangYHuBLi JW, et al.Heterogeneous multi-UAVs cooperative task assignment based on GSA-GA. In: 2016 IEEE international conference on aircraft utility systems (AUS). IEEE, Beijing, China, 2016, pp.423–426.
33.
PluhacekMSenkerikRDavendraD. Chaos particle swarm optimization with ensemble of chaotic systems. Swarm Evol Comput2015; 25: 29–35.
34.
TiainenTViitalaR. Effect of positional errors on the accuracy of multi-probe roundness measurement methods. Mech Syst Signal Process2020; 144: 106883. DOI: https://doi.org/10.1016/j.ymssp.2020.106883.
35.
Entropy. New findings in entropy described from Madeira Interactive Technologies Institute (particle swarm optimization: a historical review up to the current developments). J Math2020; 22: 362.
36.
PanahizadehVHamidiEDaneshpayehS, et al.Optimization of impact strength and elastic modulus of polyamide-based nanocomposites: using particle swarm optimization method. J Elastomers Plast2024; 56: 244–261.
37.
LiuBWangLJinYH, et al.Improved particle swarm optimization combined with chaos. Chaos, Solitons Fractals2005; 25: 1261–1271.
38.
SibalijaVT. Particle swarm optimization in designing parameters of manufacturing processes: a review (2008–2018). Appl Soft Comput J2019; 84: 105743.
39.
ZhaolongLWenmingZBoZ, et al.Thermal error modeling of motorized spindle based on particle swarm optimization-SVM neural network. Int J Adv Manuf Technol2022; 121: 7215–7227.
40.
NigatuTDDinkaGTTilahunLS. Convergence analysis of particle swarm optimization algorithms for different constriction factors. FrontAppl Math Stat2024; 10: 1304268. DOI: https://doi.org/10.3389/fams.2024.1304268.
41.
ShiSHaitjemaHWangY, et al.Uncertainty evaluation and reduction in three-probe roundness profile measurement based on the system transfer function. Prec Eng2021; 68: 139–157.
42.
ISO 230-7:2015, Test code for machine tools Part 7: Geometric accuracy of axes of rotation.
43.
ANSI/ASME standard B5.54-2005: methods for performance evaluation of CNC machining centers.
44.
ISO/IEC Guide 98–3: 2008-09: Uncertainty of measurement – Part 3: Guide to the expression of uncertainty in measurement (GUM 1995).
