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Journal of ZheJiang University (Engineering Science)  2025, Vol. 59 Issue (11): 2259-2268    DOI: 10.3785/j.issn.1008-973X.2025.11.004
    
Predictive modeling and adaptive optimization method for ball screw whirling milling process
Chao LIU1,2,3(),Hao DING1,Juanjuan ZHENG1,4,Shaofu HUANG1,3,Zuqing LUO1,Gang SHEN1
1. School of Mechanical and Electrical Engineering, Anhui University of Science and Technology, Huainan 232000, China
2. State Key Laboratory of Mechanical Transmission for Advanced Equipment, Chongqing University, Chongqing 400030, China
3. Institute ofEnvironment-friendly Materials and Occupational Health, Anhui University of Science and Technology, Wuhu 241003, China
4. College of Mathematics and Statistics, Chongqing University, Chongqing 400030, China
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Abstract  

An adaptive dynamic optimization hybrid model that combined improved sparrow search algorithm for optimizing backpropagation (ISSA-BP) and non-dominated sorting genetic algorithm--III (NSGA-III) was proposed to address the highly nonlinear problem between machining parameters and various indicators in whirling milling. The effect of five improvement strategies, population size, and the ratio of searchers to vigilantes on the sparrow search algorithm was compared, and an appropriate network structure was determined. Then an ISSA-BP prediction model with four indicators was established. The predictive performance of the proposed ISSA-BP model was compared with four other algorithms. The relative prediction errors for all four indicators were less than 2%, verifying the superiority of the model. The ISSA-BP model was encapsulated and embedded into NSGA-III as a fitness prediction function, and the Pareto optimal solution set was solved, which provided guidance for improving machining stability and ensuring machining quality in screw whirling milling.



Key wordswhirling milling      predictive modeling      multi-objective optimization      non-dominated sorting genetic algorithm-III(NSGA-III)     
Received: 27 October 2024      Published: 30 October 2025
CLC:  TG 62  
Fund:  国家自然科学基金资助项目(52205321, 52275228, U21A20125);安徽理工大学环境友好材料与职业健康研究院 (芜湖) 资助项目(ALW2021YF06); 安徽理工大学研究生创新基金资助项目(2023CX2077).
Cite this article:

Chao LIU,Hao DING,Juanjuan ZHENG,Shaofu HUANG,Zuqing LUO,Gang SHEN. Predictive modeling and adaptive optimization method for ball screw whirling milling process. Journal of ZheJiang University (Engineering Science), 2025, 59(11): 2259-2268.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.11.004     OR     https://www.zjujournals.com/eng/Y2025/V59/I11/2259


丝杠旋铣预测建模与自适应优化方法

针对丝杠旋铣加工参数与各指标之间的高度非线性问题,提出融合改进麻雀搜索算法优化反向传播(ISSA-BP)和非支配排序遗传算法(NSGA-III)的自适应动态优化混合模型. 对比5种改良策略、种群规模及搜索者与警戒者比例对麻雀搜索算法的影响,确定适宜的网络结构,建立4个指标的ISSA-BP预测模型. 通过与其他4种算法的预测性能对比可知,提出的ISSA-BP模型对4个指标的预测相对误差均低于2%,验证了模型的优越性. 将ISSA-BP模型封装嵌入NSGA-III作为适应度预测函数,求解得到帕累托最优解集,为丝杠旋铣加工在提升加工稳定性、保障加工质量方面提供指导.


关键词: 旋风铣削,  预测建模,  多目标优化,  非支配排序遗传算法(NSGA-III) 
Fig.1 Schematic diagram of whirling milling processing
Fig.2 Cutting force and vibration acquisition process
Fig.3 Roughness and residual stress measuring device
序号Vt/
(m·min?1)
Ma/
mm
NFmax/
N
av/gRa/
nm
σr/
MPa
A1600.0631640.471143.6308
A21000.0631460.441132.8250
A31400.0631540.388107.8400
A41800.0631220.393116.5455
B11400.043750.395117.692
B21400.0631540.388107.8400
B31400.0831930.378126.8370
B41400.1032160.374204.6415
C11400.0621800.359109.8410
C21400.0631540.388107.8400
C31400.0641610.41392.3329
C41400.0661300.49481.7260
Tab.1 Plan and result of single-factor experiment
序号Vt/
(m·min?1)
Ma/
mm
NFmax / Nav/gRa/
nm
σr/
MPa
1600.0631640.471143.6308
2800.0631480.464142.9235
31000.0631460.441132.8250
41200.0631510.412119.1316
51400.0631540.388107.8400
61600.0631470.378104.9453
71800.0631220.393116.5455
81400.043750.395117.692
91400.0531210.392111.0326
101400.0631540.388107.8400
111400.0731770.383111.8373
121400.0831930.378126.8370
131400.0932050.375156.5306
141400.132160.374204.0415
151400.0621800.359109.8410
161400.062.51590.375112.7325
171400.0631540.388107.8400
181400.063.51600.497.9387
191400.0641610.41392.3329
201400.0651790.44569.5198
211400.0661300.49481.7260
Tab.2 Interpolated parameter and result based on single-factor experiment
映射名称映射公式 映射范围
Logistic$ {x_{i+1}} = \mu {x_i} (1 - {x_i}),\mu \in (0,4] $[0,1.0]
Circle$ {x_{i+1}} = \text{mod} [{x_i}+0.2 - 0.5 \sin \;(2{\text{π}} {x_i})/(2{\text{π}}) ,1] $[0,1.0]
Sine$ {x_{i+1}} = \mu \sin\; (\text {π} {x_i}),\mu \in [0,1.0] $[0,1.0]
Singer$ \begin{gathered} {x_{i+1}} = \mu (7.86{x_i} - 23.31x_i^2+28.75x_i^3 - 13.303x_i^4) \\ \mu \in (0.9,1.08) \\ \end{gathered} $[0,1.0]
Cubic$ {x_{i+1}} = \rho (1 - x_i^2) $[0,1.0]
Tab.3 Several common chaotic mappings
Fig.4 Comparison of SSA improvement strategies
Fig.5 Effect of population size on ISSA-BP model
Fig.6 Model prediction performance for percentage of various searchers and scouters
Fig.7 Violin plots comparing RMSE of five algorithms across four indicators
Fig.8 Performance comparison of five algorithmic models under four performance evaluation standards
Fig.9 Comparison of R2 under five algorithms
算法F/N算法av/g
MAEMSERMSEMAPER2MAEMSERMSEMAPER2
BP8.6263.27.956.280.870BP0.00646.63×10?50.00811.540.952
ISSA-BP1.199.263.040.740.991ISSA-BP0.00033.42×10?60.00180.120.999
PSO-BP3.5537.86.152.490.960PSO-BP0.00181.54×10?50.00390.4690.989
GWO-BP4.3342.66.533.220.950GWO-BP0.00363.20×10?50.00560.570.984
MFO-BP3.8936.26.022.30.964MFO-BP0.00202.61×10?50.00510.480.992
算法Ra/nm算法$\sigma_{\mathrm{r}} $/MPa
MAEMSERMSEMAPER2MAEMSERMSEMAPER2
BP3.0121.174.606.700.880BP33.10986.531.49.280.82
ISSA-BP1.031.681.291.030.997ISSA-BP8.50133.211.541.710.98
PSO-BP2.3513.563.682.000.984PSO-BP17.34429.720.735.810.93
GWO-BP2.8316.284.032.360.975GWO-BP21.46689.626.257.890.89
MFO-BP3.2014.333.794.170.950MFO-BP18.81488.622.16.140.92
Tab.4 Performance comparison of five algorithm models across four indicators
Fig.10 Flowchart of ISSA-BP-NSGA-III analysis
Fig.11 Pareto optimization frontier graph
Vt/
(m·min-1)
Ma/
mm
NFmax/
N
av/
g
Ra/
nm
σr/
MPa
1400.0875.4161.30.450176.8619
1400.0665.489.80.458175.7238
1400.0754.2115.60.406174.3566
116.70.0713.2131.00.428148.6318
1010.0905.1203.220.504172.2598
1010.0905.3193.00.508174.3601
1400.0663.0108.90.388166.8388
130.80.0744.0119.90.425170.7537
123.50.0772.9135.00.413160.1272
114.50.0914.5195.10.499171.1592
97.30.0985.9192.50.470175.4599
134.90.0724.1110.60.417172.0533
116.40.0663.1124.50.424148.3313
127.10.0663.4113.60.416157.7406
1400.0802.9147.10.373206.8339
106.50.0783.0156.60.443137.1200
1050.0803.5185.70.480144.2362
97.60.0983.5240.30.505132.3303
116.80.1003.7232.90.459153.9485
114.50.0853.7178.80.461154.8479
Tab.5 Pareto solution
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