基于改进雅可比旋量模型的大尺寸薄壁壳体装配偏差分析与调控

doi:10.12141/j.issn.1000-565X.230636

摘要/Abstract

摘要：

大尺寸薄壁壳体尺寸和质量大，容易变形，装配精度要求苛刻。为满足航天器壳体对接装配的高精度需求，需对壳体装配偏差进行主动预测和调控。该文以某大型薄壁壳体为研究对象，采用小位移旋量法对舱段关键特征误差进行表征，得到舱段几何误差的旋量表达式以及旋量参数之间的约束关系，建立了考虑壳体关键特征误差的并联和串联装配链累积路径，并基于雅克比旋量理论对舱段装配偏差进行表征，得到基于改进雅克比旋量的舱段装配偏差传递模型。利用蒙特卡洛模拟方法对改进的雅可比旋量模型的装配阶差合格率进行数值模拟，并与仿真分析结果进行对比，提出一种量化各类误差贡献度的计算方法。以加工总成本最小为优化目标，以各类误差的变化关系和装配阶差要求为约束条件，提出一种考虑误差贡献度的舱段公差优化分配策略。对优化前后的舱段装配成功率和装配阶差合格率进行对比，发现该文方法可使壳体装配阶差合格率由原来的88.12%提高到99.56%。该文提出的研究方法可为设计人员进行主动公差设计提供理论参考。

关键词: 壳体装配, 装配偏差, 雅可比旋量, 公差建模, 公差优化

Abstract:

The large-size thin-walled shell has large size and mass, and is easy to deform with strict assembly accuracy requirement. In order to meet the high-precision requirement of spacecraft shell docking assembly, it is necessary to actively predict and control the shell assembly deviation. In this paper, a large thin-walled shell is taken as the research object. Based on the small displacement spinor method, the key characteristic errors of cabin are characterized, the geometric error spinor expression of the cabin and the constraint relationship between the spinor parameters are obtained. Then, the cumulative paths of parallel and series assembly chains considering the key feature errors of the shell are established, the assembly deviation of the cabin is characterized based on the Jacobian spinor theory, and an assembly deviation transfer model of the cabin based on the improved Jacobian spinor is obtained. Moreover, the Monte Carlo simulation method is used to numerically simulate the shell assembly step difference qualification rate of the improved Jacobian-Torsor model, with the results being compared with the simulation analysis results. Based on which, a calculation method for quantifying the contributions of various errors is proposed. Finally, by taking the minimum total processing cost as the optimization objective, and the variation relationship of various errors as well as the requirements of assembly order difference as the constraint conditions, an optimal allocation strategy for cabin tolerance considering the error contribution is proposed. The success rate of cabin assembly and the qualified rate of assembly order difference before and after the optimization are then compared, finding that the proposed method increases the qualified rate from the original 88.12% to 99.56%. The research method proposed in this paper provides theoretical reference for designers to carry out active tolerance design.

Key words: shell assembly, assembly deviation, Jacobian-Torsor, tolerance modeling, tolerance optimal allocation

中图分类号:

TH161.7

宜亚丽, 杨泽宇, 卫锐, 赵敏杰, 金贺荣. 基于改进雅可比旋量模型的大尺寸薄壁壳体装配偏差分析与调控[J]. 华南理工大学学报(自然科学版), 2024, 52(12): 32-42.

YI Yali, YANG Zeyu, WEI Rui, ZHAO Minjie, JIN Herong. Analysis and Control of Assembly Deviation of Large-Size Thin-Walled Shell Based on Improved Jacobian-Torsor Model[J]. Journal of South China University of Technology(Natural Science Edition), 2024, 52(12): 32-42.

图/表 18

图1

图2

图3

图4

图5

图6

图7

图8

图9

表1

旋量参数的标准差"

参数类型	标准差		标准差
$Δ ω s i$	$1 . 6 ˙ × 10 - 2$	$Δ α h i$	$1 . 4 ˙ × 10 - 3$
$Δ α s i$	$1.114 827 × 10 - 4$	$Δ β h i$	$1 . 4 ˙ × 10 - 3$
$Δ β s i$	$1.114 827 × 10 - 4$	$Δ ω d i$	$1 . 6 ˙ × 10 - 3$
$Δ u h i$	$1.08 3 ˙ × 10 - 2$	$Δ α d i$	$1.114 827 × 10 - 4$
$Δ υ h i$	$1.08 3 ˙ × 10 - 2$	$Δ β d i$	$1.114 827 × 10 - 4$

表1

图10

图11

图12

图13

表2

各类误差的贡献度"

误差名称		各类误差的贡献度/%
误差名称		$Δ u 2 → 3$	$Δ υ 2 → 3$	$H$
壳体直径误差		0.00	0.00	69.66
壳体特征误差	平面	54.30	75.53	19.84
壳体特征误差	定位孔	33.20	14.85	7.10
变形误差		12.90	9.62	3.40

表2

表3

壳体特征的公差优化分配结果"

尺寸类型	尺寸与公差/mm			尺寸类型	尺寸与公差/mm
尺寸类型	初始	再分配		尺寸类型	初始	再分配
直径ϕD	$300 - 1 + 1$	$300 - 0.5 + 0.5$	位置度ϕt		0.05	0.05
直径ϕT_h	$100 + 0.015$	$100 + 0.01$	垂直度T		0.10	0.05

表3

图14

图15

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