多支点测力平台维间耦合误差建模与精度分配

doi:10.13229/j.cnki.jdxbgxb.20231260

摘要/Abstract

摘要：

针对多传感器布置的测力平台耦合误差成因不明、难以削减的问题，以压电式六维测力平台为研究对象，从传感器耦合、装配误差、标定装置全环节分析耦合成因。基于测量原理，建立包含34个影响因素的维间耦合模型，采用敏感性算法筛选并量化各因素影响程度，以耦合误差≤5%量程为目标进行精度容差分配。采样仿真结果表明，分配后各项耦合误差的99%置信上限均满足要求。实验表明，满足容差下平台力输出耦合误差≤3.64%量程，力矩输出耦合误差≤4.80%量程，验证了精度范围的有效性和在耦合误差控制上的实用性。

关键词: 精密仪器及机械, 维间耦合, 测量误差, 大量程六维力, 敏感性分析

Abstract:

In response to the causes of unclear and difficult reduction of coupling errors in force measurement platforms arranged with multiple sensors， this article takes the piezoelectric six axis force measurement platform as the research object， analyzes the coupling causes from the entire process of sensor coupling， assembly error and calibration device. Based on measurement principles， establish an inter dimensional coupling model containing 34 influencing factors， use sensitivity algorithms to screen and quantify the degree of influence of each factor， and accuracy tolerance allocate is performed with a coupling error ≤ 5% of the range as the target. The sampling simulation shows that the 99% confidence upper limit of each coupling error after allocation meets the requirements. Experiment shows that the coupling error of platform force output is ≤ 3.64% of the range under tolerance， and the coupling error of torque output is ≤ 4.80% of the range， which verify the effectiveness of the accuracy range and their applicability in coupling error control.

Key words: precision instrument and machinery, inter-dimensional coupling, measurement error, large range six-axis force, sensitivity analysis

中图分类号:

TH823

张军,王郁赫,姜楠,蔡佳乐,滕玄德,张鹏. 多支点测力平台维间耦合误差建模与精度分配[J]. 吉林大学学报(工学版), 2025, 55(8): 2501-2510.

Jun ZHANG,Yu-he WANG,Nan JIANG,Jia-le CAI,Xuan-de TENG,Peng ZHANG. Modeling and accuracy allocation of inter-dimensional coupling errors in multi pivot force measurement platforms[J]. Journal of Jilin University(Engineering and Technology Edition), 2025, 55(8): 2501-2510.

图/表 16

图1

图2

图3

表1

因素正态分布表"

误差因素项	$σ$ /rad
r₁， r₂， r₃， r₄	0.005 8
$θ x y$ ， $θ x z$ ， $θ y x$ ， $θ y z$ ， $θ z x$ ， $θ z y$	0.011 6
k_xy_1~4， k_xz_1~4， k_yx_1~4， k_yz_1~4， k_zx_1~4， k_zy_1~4	0.016 7

表1

图4

表2

Fx 作用下耦合因素筛选结果"

耦合方向	影响因素
F_y	r_1~4， $θ y x$ ， k_xy_1~4， k_zy_1~4
F_z	$θ z x$ ， k_xz_1~4
M_x	r_1~4， $θ y x$ ， k_xy_1~4， k_xz_1~4， k_zy_1~4
M_y	k_xz_1~4， k_zx_1~4
M_z	r_1~4， $θ y z$ ， k_xy_1~4，k_zx_1~4，k_zy_1~4

表2

图5

表3

Fx 作用下Fy 耦合因素半带宽分配"

耦合因素	数值	耦合因素	数值
r₁	0.007 9	k_xy₃	0.015 6
r₂	0.007 9	k_xy₄	0.015 6
r₃	0.007 9	k_zy₁	0.012 5
r₄	0.007 9	k_zy₂	0.012 5
$θ y x$	0.020 0	k_zy₃	0.012 5
k_xy₁	0.015 6	k_zy₄	0.012 5
k_xy₂	0.015 6

表3

表4

Fx 作用下Mx 耦合因素半带宽分配"

耦合因素	数值	耦合因素	数值
r₁	0.011 7	k_xz₁	0.029 2
r₂	0.011 7	k_xz₂	0.029 2
r₃	0.011 7	k_xz₃	0.029 2
r₄	0.011 7	k_xz₄	0.029 2
$θ y x$	0.030 2	k_zy₁	0.019 0
k_xy₁	0.023 6	k_zy₂	0.049 4
k_xy₂	0.023 6	k_zy₃	0.019 0
k_xy₃	0.023 6	k_zy₄	0.049 4
k_xy₄	0.023 6

表4

图6

表5

表6

图7

表7

装置角度误差测量结果"

项目	$θ x y$	$θ x z$	$θ y x$	$θ y z$	$θ z x$	$θ z y$
F_x /F_y /F_z	0.017 2	0	-0.020 6	-0.014 0	0.008 7	0.006 1
M_x	-0.003 4	—	—	—	—	0.014 8
M_y /M_z	—	—	-0.003 4	0.014 8	—	—

表7

图8

图9

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项目	F_x 耦合输出	F_y 耦合输出	F_z 耦合输出	M_x 耦合输出	M_y 耦合输出	M_z 耦合输出
F_x 加载	—	［-136.79，139.02］	［-222.41，215.41］	［-9.33，9.49］	［-7.69.7.18］	［-7.41，6.56］
F_y 加载	［-136.97，141.55］	—	［-215.35.231.32］	［-7.37，7.58］	［-9.66，10.19］	［-7.31，6.76］
F_z 加载	［-182.68，199.72］	［-192.10，194.09］	—	［-8.91，9.06］	［-8.59，9.39］	［-8.78，9.08］
M_x 加载	［-42.01，40.72］	［-43.63，41.72］	［-0.79，0.75］	—	［-1.97，1.92］	［-11.30，10.48］
M_y 加载	［-39.99，41.91］	［-41.55，44.15］	［-0.73，0.79］	［-1.93，1.96］	—	［-10.32，10.93］
M_z 加载	［-32.02，33.56］	［-40.00，34.31］	［-67.47，68.52］	［-11.87，12.68］	［-13.06，12.64］	—

编号	k_yx	k_zx	k_zy	k_xy	k_xz	k_yz
1	0.010 4	-0.000 4	-0.004 5	0.012 6	-0.014 7	0.019 2
2	0.014 9	-0.004 3	0.001 9	-0.009 3	-0.018 2	-0.011 6
3	-0.008 1	-0.003 2	0.002 0	0.010 4	0.011 2	0.014 7
4	0.002 7	0.003 5	0.002 6	-0.006 4	0.014 1	0.005 4