Journal of Jilin University(Engineering and Technology Edition) ›› 2023, Vol. 53 ›› Issue (10): 2761-2772.doi: 10.13229/j.cnki.jdxbgxb.20211350

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Thermal-force deformation analysis and prediction modeling of CNC gear hobbing machine workbench

Si-bao WANG1,2(),Zhong-zheng GUO1,2,Chi MA1,2,Shi-long WANG1,2   

  1. 1.College of Mechanical and Vehicle Engineering，Chongqing University，Chongqing 400044，China
    2.State Key Laboratory of Mechanical Transmissions，Chongqing University，Chongqing 400044，China
  • Received:2021-12-07 Online:2023-10-01 Published:2023-12-13

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Abstract:

In order to reduce the influence of hobbing workbench deformation on machining accuracy， the thermal and mechanical deformation of the workbench were studied.A Subpopulation Adaptive Mind Evolution Algorithm-Back Propagation Neural Network was proposed for thermal-mechanical deformation prediction of hobbing workbench. The initial value， weight and threshold of BP Neural Network were adjusted by SAMEA， which effectively improved the prediction accuracy. Combining K-means clustering and grey correlation analysis （GRA）， the thermal error input variables were reduced from eight to three. Aiming at the table deformation caused by cutting force in gear hobbing， the cutting force was represented by the current of machine tool spindle and used as the input variable of the prediction model. Experimental results show that the average prediction accuracy of the proposed SAMEA-BP model is 95.1%， and comparison with other models verifies the validity and generalization of the model.

Key words: thermal error, force error, SAMEA-BP neural network, mean clustering algorithm, grey relation analysis

CLC Number: 

  • TH161

Fig.1

Structure diagram of gear hobbing machine"

Fig.2

Thermal deformation of bed"

Fig.3

Space coordinate system of gear hobbing machine"

Fig.4

Gear hobbing chip formation process"

Fig.5

System framework diagram of mind evolutionary algorithm"

Fig.6

Flow chart of SAMEA-BP"

Fig.7

BP neural network structure"

Table 1

Parameter of MEA"

参数取值参数取值
种群大小40子群体数6
优胜子种群数6迭代次数70
临时子种群数6

Table 2

Geometric parameters of hob and gear workpieces"

滚刀参数数值齿轮参数数值
头数2法向模数/mm5.08
旋向左旋法向压力角/（°）20
外径/mm110齿数34
螺旋角5°34′30″齿顶圆直径/mm192
容屑槽数10螺旋角/（°）13
容屑槽类型直槽齿宽/mm30

Table 3

Installation positions of temperature sensors and displacement sensors"

传感器安装/检测位置传感器安装/检测位置
T1小立柱外侧T6刀架侧面
T2Z轴拖板丝杠套T7床身上表面
T3Z轴拖板上部T8环境温度
T4立柱Z轴静压导轨S1工作台X方向
T5电主轴轴承侧面S2工作台Y方向

Fig.8

Physical picture of temperature and displacementacquisition module"

Fig.9

Physical picture of current acquisition module"

Table 4

Processing parameter"

t/minn/（r·min-1）f/（mm·min-1）ap/mm
0~40120126
40~80160147
80~120200168

Fig.10

Three phase current change of spindle"

Fig.11

Change of spindle"

Fig.12

Temperatures of hobbing machine"

Fig.13

Displacement of workbench"

Table 5

K mean clustering-grey relation degree between temperature variable and thermal error"

分组序号K均值聚类分组结果灰色关联度大小
1T1T2T30.7210.9390.735
2T4T70.6880.693
3T5T6T80.7050.6940.687

Fig.14

Prediction and measurement values of X direction"

Fig.15

Residual error of X direction"

Fig.16

Prediction and measurement values of Y direction"

Fig.17

Residual error of Y direction"

Table 6

RMSE of each model"

方向SAMEA-BPMEA-BPPSO-BPGA-BPSAMEA-BP2
X0.37540.50430.72480.92020.5254
Y0.33910.48540.78460.82150.3545

Table 7

Performance comparison of each model"

算 法方 向迭代次数收敛时间/sR2下降梯度
SAMEA-BPX22<0.0010.98460.405
Y27<0.0010.97030.394
MEA-BPX33<0.0010.96340.252
Y27<0.0010.96370.314
PSO-BPX57<0.010.96170.216
Y46<0.010.95640.227
GA-BPX62<0.010.94480.124
Y48<0.010.94950.095
SAMEA-BP2X35<0.0010.98540.301
Y25<0.0010.97190.267

Fig.18

Comparison of generalization performances of X-direction"

Fig.19

Comparison of generalization performances of Y-direction"

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