Advance in Impact Force Model Research with Evolution of Newton Restitution Coefficient
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摘要: 为了辨识间隙铰链处碰撞力的适用范围,更加准确地描述机械系统中普遍存在的碰撞现象及其对机械系统动态特性的影响规律,以牛顿碰撞恢复系数作为评价指标,以间隙铰链处轴、轴承间的碰撞和恢复过程为例,在不同恢复系数下和碰撞力模型下进行数值模拟及对比分析。研究发现,不同碰撞恢复系数下各模型碰撞过程的最大碰撞力、最大变形量及实际碰撞恢复系数差异较大。因此,实际选择碰撞力模型时应依据碰撞初始条件和材料特性等进行综合考虑。Abstract: In order to identify the application scope of impact force models in clearance joint, and more accurately describe the collision phenomenon in mechanical system, the Newton restitution coefficient is defined as evaluation index, and the joint of journal-bearing is used as example. Then a great number of numerical results are presented based on different impact force models with different coefficient of restitution. It can be concluded that the maximum value of impact force and deformation, as well as actual restitution have obvious difference for different impact forces, so the selection of impact force model should be considered comprehensively with initial collision conditions and material properties.
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Key words:
- clearance joint /
- collision /
- impact force model /
- Newton restitution coefficient
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表 1 不同碰撞力模型在3种恢复系数值下的最大碰撞力
碰撞力模型 最大碰撞力/N Cr = 0.3 Cr = 0.5 Cr = 0.8 Hertz 2136.033 2136.033 2136.033 Liu 2305.168 2305.168 2305.168 H-C 1943.499 1929.073 1975.844 L-N 1928.888 1933.646 1986.405 Gonthier 2207.553 1993.206 1945.774 Flores 2308.516 2006.623 1952.949 Bai 1459.471 1382.348 1405.777 Wang 2362.823 2166.395 2111.053 表 2 不同碰撞力模型在3种恢复系数值下的最大变形量
碰撞力模型 最大变形量/mm Cr = 0.3 Cr = 0.5 Cr = 0.8 Hertz 0.00585 0.00585 0.00585 Liu 0.00538 0.00538 0.00538 H-C 0.00478 0.00500 0.00545 L-N 0.00506 0.00517 0.00548 Gonthier 0.00387 0.00450 0.00528 Flores 0.00368 0.00444 0.00534 Bai 0.00677 0.00752 0.00871 Wang 0.00363 0.00412 0.00490 表 3 Cr = 0.3时不同碰撞力模型实际恢复系数及相对误差
碰撞力模型 初始速度/
(m·s−1)分离速度/(m·s−1) 实际恢复系数及误差 Cr′ 误差/% Hertz 0.5 0.5 1 0 Liu 0.5 0.5 1 0 H-C 0.5 −0.2906 0.5812 93.7333 L-N 0.5 −0.3421 0.6842 128.0667 Gonthier 0.5 −0.1521 0.3042 1.4 Flores 0.5 −0.1281 0.2562 14.6 Bai 0.5 −0.1634 0.3268 8.9333 Wang 0.5 −0.1634 0.3268 8.9333 表 4 Cr = 0.5时不同碰撞力模型实际恢复系数及相对误差
碰撞力模型 初始速度/
(m·s−1)分离速度/
(m·s−1)实际恢复系数及误差 Cr′ 误差/% Hertz 0.5 0.5 1 0 Liu 0.5 0.5 1 0 H-C 0.5 −0.3315 0.663 24.585 L-N 0.5 −0.3626 0.7252 31.054 Gonthier 0.5 −0.2439 0.4878 2.501 Flores 0.5 −0.2352 0.4704 6.293 Bai 0.5 −0.2413 0.4826 3.605 Wang 0.5 −0.2413 0.4826 3.605 表 5 Cr = 0.8时不同碰撞力模型恢复系数及对应相对误差
碰撞力模型 初始速度(m·s−1) 分离速度(m·s−1) 实际恢复系数及误差 Cr′ 误差/% Hertz 0.5 0.5 1 0 Liu 0.5 0.5 1 0 H-C 0.5 −0.4164 0.8328 4.1 L-N 0.5 −0.4236 0.8472 5.9 Gonthier 0.5 −0.384 0.768 4 Flores 0.5 −0.3943 0.7886 1.425 Bai 0.5 −0.3937 0.7874 1.575 Wang 0.5 −0.3937 0.7874 1.575 -
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