Optics and Precision Engineering, Volume. 31, Issue 4, 491(2023)
Determination method of optimal measurement area of CNC machine tool on-machine measurement system
Figures & Tables(15)
Fig. 7. Measurement error distribution diagram for sphere measurement
Table 1. Parameter settings of five algorithms
View tableView in ArticleTable 1. Parameter settings of five algorithms
Algorithm Population N Number of iterations M Parameter settings ACO 20 100 Pheromone volatilization
Rou=0.9
Transition probability
constant P0=0.2
Step size
0.1
FA 20 100 Light intensity absorption
coefficient g=1
Initial attraction
beta（）=1
Distance index m=2 DE 20 100 Initial mutation operator
F0=0.5
Crossover operator
CR=0.9
— ABC 20 100 Honey source transformation
coefficient a=1
— — CS 20 100 Discovery probability
pa=0.25
— —
Table 2. Comparison of 50 test results of five algorithms
View tableView in ArticleTable 2. Comparison of 50 test results of five algorithms
Algorithm category
Stuck in a local optimum
Get the optimal value
Average of 50 runs
Standard deviation of 50 runs
FA
yes
7.227 2
7.220 4
0.000 8
ACO
yes
7.223 1
7.211 2
0.000 4
DE
no
7.232 5
7.231 7
0.001 6
ABC
no
7.232 5
7.231 0
0.002 3
CS
no
7.232 5
7.232 0
0.002 7
Table 3. Parameter Settings of three improved CS algorithms
View tableView in ArticleTable 3. Parameter Settings of three improved CS algorithms
Algorithm Population N Number of iterations M Parameter settings Crossover
operator CR
Discovery
probability pa
IA-CS 20 100 Immune replacement probability
P=0.6
— 0.25 QGA-CS 20 100 Binary length
L=3
— 0.25 DE-CS 20 100 Initial mutation operator
F0=0.5
0.9 0.25
Table 4. Comparison of 50 test results of the four algorithms
View tableView in ArticleTable 4. Comparison of 50 test results of the four algorithms
Algorithm Single search time/s Convergent
algebra
Get the optimal value/μm Stuck in a local optimum Average of 50 runs/μm Standard deviation of 50 runs/μm CS 7.232 5 14 7.232 5 no 7.232 0 0.002 7 IACS 6.042 2 11 7.232 5 no 7.231 6 0.003 0 QGACS 7.429 3 7 7.232 5 no 7.231 9 0.002 3 DECS 5.238 2 5 7.232 5 no 7.232 0 0.002 0
Table 5. Algorithm test results of changing initial parameters
View tableView in ArticleTable 5. Algorithm test results of changing initial parameters
DE-CS Total group number N20 40 60 80 100 Single search time/s 6.244 2 12.273 4 18.438 1 24.656 7 30.894 4 Find the optimal solution/μm 7.232 5 7.232 5 7.232 5 7.232 5 7.232 5 Stuck in a local optimum no no no no no Average of 50 runs/μm 7.232 0 7.232 1 7.232 1 7.232 3 7.232 4 Standard deviation of 50 runs/μm 0.002 0 0.001 1 0.001 2 0.000 7 0.000 5 Mutation operator F0 0.2 0.4 0.5 0.8 0.9 Single search time/s 6.154 9 6.129 4 6.135 2 6.171 1 6.139 4 Find the optimal solution/μm 7.232 5 7.232 5 7.232 5 7.232 5 7.232 5 Stuck in a local optimum no no no no no Average of 50 runs/μm 7.230 9 7.230 9 7.231 3 7.231 7 7.231 8 Standard deviation of 50 runs/μm 0.003 1 0.003 0 0.002 3 0.002 0 0.002 1 Crossover operator CR 0.1 0.3 0.5 0.8 0.9 Single search time/s 6.097 5 6.089 6 6.073 4 6.085 5 6.147 6 Find the optimal solution/μm 7.232 5 7.232 5 7.232 5 7.232 5 7.232 5 Stuck in a local optimum no no no no no Average of 50 runs/μm 7.230 9 7.231 0 7.231 0 7.231 1 7.231 2 Standard deviation of 50 runs/μm 0.003 2 0.003 0 0.003 1 0.002 3 0.002 3
Table 6. Comparison of maximum measurement error distribution regions
View tableView in ArticleTable 6. Comparison of maximum measurement error distribution regions
X-axis coordinate
range/mm
Y-axis coordinate
range/mm
Z-axis coordinate
range/mm
Actual measurement
maximum error /μm
Algorithm to solve the maximum error/μm 304.477~313.477 -54.877~-45.877 -268~-258 5.5 7.122 3 340.477~349.477 -54.877~-45.877 -248~-238 4.8 6.202 4 376.477~385.477 -54.877~-45.877 -248~-238 6.3 3.184 8 411.916~420.916 -54.602~-45.602 -288~-278 4.4 1.427 4 411.916~420.916 -90.602~-81.602 -288~-278 5.8 1.510 5 411.916~420.916 -54.602~-45.602 -268~-258 3.6 1.391 9 394.783~403.783 -145.133~-136.133 -268~-258 3.9 0.744 3 430.783~439.783 -145.133~-136.133 -268~-258 3.1 0.710 7 376.418~385.418 -145.036~-136.036 -268~258 6.4 0.813 5 448.783~457.783 -127.133~-118.133 -268~-258 4.5 6.983 9 448.783~457.783 -145.133~-136.133 -268~-258 4.4 6.982 5 466.783~475.783 -145.133~-136.133 -288~-278 5.6 7.589 3
Table 7. Comparison of optimal measurement areas for point measurement
View tableView in ArticleTable 7. Comparison of optimal measurement areas for point measurement
X-axis coordinate range
/mm
Y-axis coordinate range
/mm
Z-axis coordinate range/mm Actual measurement maximum
error/μm
DE-SC solve the maximum
error/μm
331.487 ~ 340.487 -125.042 ~ -116.042 -305 ~ -295 4.5 2.4331 340.487 ~ 349.487 -125.042 ~ -116.042 -305 ~ -295 4.5 2.4331 349.487 ~ 358.487 -125.042 ~ -116.042 -305 ~ -295 4.5 2.4331 322.487 ~ 331.487 -116.042 ~ -107.042 -305 ~ -295 5.0 2.3331 331.487 ~ 340.487 -116.042 ~ -107.042 -305 ~ -295 4.0 2.3331 340.487 ~ 349.487 -116.042 ~ -107.042 -305 ~ -295 4.5 2.3331 322.487 ~ 331.487 -125.042 ~ -116.042 -295 ~ -285 4.5 2.4330 331.487 ~ 340.487 -125.042 ~ -116.042 -295 ~ -285 4.5 2.4330 349.487 ~ 358.487 -125.042 ~ -116.042 -295 ~ -285 5.5 2.4330
Table 8. Comparison of the best measurement areas for circular surface measurement
View tableView in ArticleTable 8. Comparison of the best measurement areas for circular surface measurement
X-axis coordinate range/mm Y-axis coordinate
range/mm
Z-axis coordinate range/mm Actual measurement maximum error /μm DE-SC solve the
maximum error/μm
356.061~365.061 -109.727~-100.727 -263~-253 5.3 3.361 0 374.326~383.326 -129.220~-120.220 -303~-293 5.4 9.120 7 374.061~383.061 -73.727~-64.727 -283~-273 5.7 9.082 0 320.326~329.326 -165.220 ~-156.220 -303~-293 6.0 7.554 7 374.061~383.061 -73.727~-64.727 -243~-233 6.0 9.016 0 320.061~329.061 -109.727~-100.727 -283~-273 6.4 7.698 6
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Shuangshuang ZHANG, Hongtao YANG, Qun MA, Li LI. Determination method of optimal measurement area of CNC machine tool on-machine measurement system[J]. Optics and Precision Engineering, 2023, 31(4): 491
Paper Information
Category: Micro/Nano Technology and Fine Mechanics
Received: Aug. 11, 2022
Accepted: --
Published Online: Mar. 7, 2023
The Author Email: YANG Hongtao (lloid@163.com)
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