平面约束变胞机构构态切换能力的概率评估模型

doi:10.7527/S1000-6893.2022.26843

Abstract

Abstract:

The definition and evaluation of configuration transformation ability as well as the principle of force control during the process of configuration transformation are the research foundation for realizing the stable configuration transformation of metamorphic mechanisms. Considering the randomness of input errors in practical application， the establishment of a probabilistic evaluation model of the configuration transformation ability is the theoretical basis for reducing failure probability of kinematic performance of metamorphic mechanisms. Based on the structure composition principle of the multiconfiguration source metamorphic mechanism that can operate in an under-actuated state， the modularized calculation models are established for force analysis of the augmented Assur groups including metamorphic joints. According to the equivalent resistance gradient model of metamorphic joints， a force analysis model is deduced to describe mechanical control principle of the configuration transformation of constrained metamorphic mechanisms. Furthermore， considering the uncertainties in the link dimensions， masses， and compliance parameters et al， a reliability evaluation method of the configuration transformation moment for the constrained metamorphic mechanism is established. Considering the influence of kinematic failure at the adjacent moment of configuration transformation time， an interval reliability calculation method for the configuration transformation of constrained metamorphic mechanisms is proposed by using the calculation model of system reliability. Finally， the feasibility and effectiveness of the probabilistic evaluation method is verified by taking the metamorphic mechanism of paper folding as an example. This research provides the foundation for the reliability optimization design of the constrained metamorphic mechanism aiming at obtaining the repeatability of the configuration transformation with high probability. It also shows theoretical and practical significance in promoting the application of metamorphic mechanisms.

Key words: planar constrained metamorphic mechanisms, configuration transformation, probability, reliability, equivalent resistance, structure of metamorphic joint

CLC Number:

V328.5

Benqi SUN, Qiang YANG, Zhili SUN, Shujun LI, Hongkun MA, Ruonan WANG. A probabilistic evaluation model for configuration transformation ability of planar constrained metamorphic mechanisms[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(4): 426843.

Figures/Tables 16

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参数	数值	参数	数值	参数	数值
l_AB /mm	N~（180，0.042）	l_BC /mm	N~（360，0.06）	l_CD /mm	N~（240，0.048）
l_CE /mm	N~（360，0.06）	l_EF /mm	N~（210，0.048）	l_AD /mm	315
maxl_AF /mm	870	m_AB /kg	N~（1，0.007）	m_BC /kg	N~（1.5，0.01）
m_CD /kg	N~（1，0.007）	m_CE /kg	N~（1.5，0.01）	m_EF /kg	N~（2，0.013）
m_slider/kg	N~（1，0.007）	J_AB /（kg·m²）	0.002 7	J_BC /（kg·m²）	0.016 2
J_CD /（kg·m²）	0.004 8	J_CE /（kg·m²）	0.016 2	J_EF /（kg·m²）	0.007 35
a/mm	250	k₁/（N·mm^-1）	N~（10，0.1）	d₁/mm	N~（100，0.667）
d₂/mm	N~（120，0.667）	b/mm	76	k₂/（N·mm^-1）	N~（0.5，0.01）
ω₁/（rad·s^-1）	N~（2π，0.01）	α/（°）	N~（120.3，0.167）	Δθ₁/（°）	N~（0，0.067）

参数	第Ⅰ构态	第Ⅱ构态	循环
机构类型	曲柄滑块机构	曲柄摇杆机构	下一循环
主动件转角	-290.2°~-15.2°	-15.2°~69.8°	下一循环
变胞副E夹角	停（120.3°）	120.3°~72.5°	下一循环
滑块位置	598.5~870 mm	停（870 mm）	下一循环
摇杆摆角	停（115.9°）	115.9°~88.8°	下一循环

构态	角度/（°）	μ_Z	σ_Z	β	可靠度	蒙特卡洛
构态Ⅰ	-21	2.581 7	0.519 4	4.970 5	1	1
构态Ⅰ	-20	1.791 8	0.525 6	3.408 8	0.999 7	0.999 6
构态Ⅰ	-19	1.331 4	0.533 7	2.494 7	0.993 7	0.963 3
构态Ⅰ	-18	1.247 4	0.544 0	2.293 0	0.989 1	0.988 6
构态Ⅰ	-17	1.584 6	0.557 0	2.844 9	0.997 8	0.998 1
构态Ⅰ	-16	2.383 2	0.572 9	4.159 9	1	1
切换时刻	-15.2	42.133 6	1.060 6	39.726 2	1	1
构态Ⅱ	-15	132.477 9	3.884 8	34.101 6	1	1

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A probabilistic evaluation model for configuration transformation ability of planar constrained metamorphic mechanisms

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