|
|
- 2015
新的柔性结合部法向接触刚度和接触阻尼方程
|
Abstract:
以修正分形几何学理论和赫兹法向接触力学方程为基础,推导出了柔性结合部法向接触刚度与阻尼方程。假设峰元顶端的曲率半径为变量,提出了一种全新的求导函数而非偏导函数的求解方法,建立了单峰元与平面接触的法向接触刚度方程。数值模拟表明:峰元承担的法向弹性载荷与其顶端的变形量之间符合非线性幂函数凹弧关系;降低表面粗糙度或增加法向接触载荷都将增大实际接触面积;当表面粗糙轮廓分形维数在较小范围内时,实际接触面积随着表面粗糙轮廓分形维数的增加而增大,而当表面粗糙轮廓分形维数在较大范围内时,实际接触面积随着表面粗糙轮廓分形维数的增加而变小;降低表面粗糙度或增加表面粗糙轮廓分形维数与法向接触载荷皆将增加法向接触刚度;法向接触阻尼随着表面粗糙轮廓分形维数的增加先减小后增大;当表面粗糙轮廓分形维数小于临界值时,法向接触阻尼随着分形粗糙度的增大而增大,而当表面粗糙轮廓分形维数超过转折点时,法向接触阻尼随着分形粗糙度的增大而减小;当法向接触载荷增大时,法向接触阻尼略微减小。
Equations of normal contact stiffness and damping for flexible joint interface were built up following the modified fractal geometry theory and Hertz normal contact mechanics expression. Supposing the curvature radius at the tip of the asperity is a variable, a completely new calculating method of differential function, not partial differentiable function, was established to solve the normal contact stiffness equation when an asperity contacted a plane. The digital simulation reveals that there is a nonlinear power function concave arc relationship between asperity’s normal elastic load and its tip deformation. The real contact area may increase by reducing the surface roughness or increasing the normal contact load. The real contact area increases with the fractal dimension of a surface in the smaller fractal dimension of a surface rough profile, while decreases with the fractal dimension of a surface in the larger fractal dimension of a surface rough profile. The normal contact stiffness will increase by reducing the surface roughness or increasing the fractal dimension of a surface rough profile and the normal contact load. The normal contact damping decreases at first and then increases with the increase of the fractal dimension of a surface rough profile. When the fractal dimension of a surface rough profile is less than the critical value, the normal contact damping increases with the fractal roughness. When the fractal dimension of a surface rough profile exceeds the turning point, the normal contact damping will decrease with the fractal roughness. As the normal contact load increases, the normal contact damping decreases slightly
| [1] | ［1］田红亮, 钟先友, 秦红玲, 等. 依据各向异性分形几何理论的固定结合部法向接触力学模型 ［J］. 机械工程学报, 2013, 49(21): 108？？122. |
| [2] | TIAN Hongliang, ZHAO Chunhua, ZHU Dalin, et al. Analysis and validation on normal connection dynamic stiffness of bolted joint interface ensemble ［J］. Journal of Xi’an Jiaotong University, 2012, 46(9): 31？？36. |
| [3] | TIAN Hongliang, ZHU Dalin, QIN Hongling. Normal static elastic stiffness of fixed contact interface ［J］. Chinese Journal of Applied Mechanics, 2011, 28(3): 318？？322. |
| [4] | ［20］田红亮, 方子帆, 赵春华, 等. 依据修正GW理论的结合部法向接触研究 ［J］. 华中科技大学学报: 自然科学版, 2014, 42(6): 38？？42, 47. |
| [5] | TIAN Hongliang, FANG Zifan, ZHAO Chunhua, et al. Normal contact of joint interface using revised GW theory ［J］. Journal of Huazhong University of Science and Technology: Natural Science Edition, 2014, 42(6): 38？？42, 47. |
| [6] | ［21］尤晋闽, 陈天宁. 结合面法向动态参数的分形模型 ［J］. 西安交通大学学报, 2009, 43(9): 91？？94. |
| [7] | ［23］JIANG Shuyun, ZHENG Yunjian, ZHU Hua. A contact stiffness model of machined plane joint based on fractal theory ［J］. ASME Journal of Tribology, 2010, 132(1): 1？？7. |
| [8] | ［4］田红亮, 赵春华, 朱大林, 等. 金属材料结合部法切向刚度修正与实验验证 ［J］. 农业机械学报, 2012, 43(6): 207？？214. |
| [9] | ［5］田红亮, 朱大林, 秦红玲, 等. 结合部法向载荷解析解修正与定量实验验证 ［J］. 农业机械学报, 2011, 42(9): 213？？218. |
| [10] | TIAN Hongliang, CHEN Congping, FANG Zifan, et al. Tangential stiffness model for joint interface adopting the revised fractal geometric theory ［J］. Journal of Xi’an Jiaotong University, 2014, 48(7): 46？？52. |
| [11] | ［12］田红亮, 刘芙蓉, 方子帆, 等. 结合部静摩擦因数修正与定量实验验证 ［J］. 农业机械学报, 2013, 44(10): 282？？293. |
| [12] | TIAN Hongliang, LIU Furong, FANG Zifan, et al. Correction of static friction coefficient for joint interface and quantitative test confirmation ［J］. Transactions of the Chinese Society for Agricultural Machinery, 2013, 44(10): 282？？293. |
| [13] | ［13］田红亮, 赵春华, 方子帆, 等. 金属材料表面静摩擦学特性的预测研究: 理论模型 ［J］. 振动与冲击, 2013, 32(12): 40？？44, 66. |
| [14] | TIAN Hongliang, ZHAO Chunhua, FANG Zifan, et al. Predication investigation on static tribological performance of metallic material surfaces: theoretical model ［J］. Journal of Vibration and Shock, 2013, 32(12): 40？？44, 66. |
| [15] | ［14］田红亮, 刘芙蓉, 赵春华, 等. 金属材料表面静摩擦学特性的预测研究: 实验佐证 ［J］. 振动与冲击, 2014, 33(1): 209？？220. |
| [16] | ［18］田红亮, 刘芙蓉, 方子帆, 等. 引入各向同性虚拟材料的固定结合部模型 ［J］. 振动工程学报, 2013, 26(4): 561？？573. |
| [17] | ［19］TIAN Hongliang, LI Bin, LIU Hongqi, et al. A new method of virtual material hypothesis？？based dynamic modeling on fixed joint interface in machine tools ［J］. Elsevier International Journal of Machine Tools ＆ Manufacture, 2011, 51(3): 239？？249. |
| [18] | ［22］田红亮, 方子帆, 朱大林. 赫兹点接触133年 ［J］. 三峡大学学报: 自然科学版, 2014, 36(2): 88？？97. |
| [19] | TIAN Hongliang, FANG Zifan, ZHU Dalin. 133 years of Hertz point contact ［J］. Journal of China Three Gorges University: Natural Sciences, 2014, 36(2): 88？？97. |
| [20] | TIAN Hongliang, LIU Furong, ZHU Dalin. Dynamic properties of four NET Euler？？Bernoulli straight beam ［J］. Journal of China Three Gorges University: Natural Sciences, 2013, 35(4): 85？？93. |
| [21] | YOU Jinmin, CHEN Tianning. Parameters identification for joint surfaces of cantilever beam ［J］. Journal of Xi’an Jiaotong University, 2008, 42(11): 1323？？1326. |
| [22] | TIAN Hongliang, ZHAO Chunhua, FANG Zifan, et al. Improved model of tangential stiffness for joint interface using anisotropic fractal theory ［J］. Transactions of the Chinese Society for Agricultural Machinery, 2013, 44(3): 257？？266. |
| [23] | ［10］田红亮, 方子帆, 朱大林, 等. 固定接触界面切向静弹性刚度问题研究 ［J］. 应用力学学报, 2011, 28(5): 458？？464. |
| [24] | ［17］田红亮, 朱大林, 秦红玲. 结合面静摩擦因数分形模型的建立与仿真 ［J］. 应用力学学报, 2011, 28(2): 158？？162. |
| [25] | TIAN Hongliang, ZHU Dalin, QIN Hongling. Fractal model of static friction coefficient of joint interface and its simulation ［J］. Chinese Journal of Applied Mechanics, 2011, 28(2): 158？？162. |
| [26] | TIAN Hongliang, LIU Furong, FANG Zifan, et al. Immovable joint surface’s model using isotropic virtual material ［J］. Journal of Vibration Engineering, 2013, 26(4): 561？？573. |
| [27] | YOU Jinmin, CHEN Tianning. Fractal model for normal dynamic parameters of joint surfaces ［J］. Journal of Xi’an Jiaotong University, 2009, 43(9): 91？？94. |
| [28] | ［24］兰国生, 张学良, 丁红钦, 等. 基于分形理论的结合面改进接触模型 ［J］. 农业机械学报, 2011, 42(10): 217？？223, 229. |
| [29] | LAN Guosheng, ZHANG Xueliang, DING Hongqin, et al. Modified contact model of joint interfaces based on fractal theory ［J］. Transactions of the Chinese Society for Agricultural Machinery, 2011, 42(10): 217？？223, 229. |
| [30] | ［25］田红亮, 刘芙蓉, 朱大林. 4种NET欧拉？膊？努利直梁的动力学特性 ［J］. 三峡大学学报: 自然科学版, 2013, 35(4): 85？？93. |
| [31] | ［26］尤晋闽, 陈天宁. 悬臂梁平面结合面参数的识别技术研究 ［J］. 西安交通大学学报, 2008, 42(11): 1323？？1326. |
| [32] | TIAN Hongliang, ZHONG Xianyou, QIN Hongling, et al. Normal contact mechanics model of fixed joint interface adopting anisotropic fractal geometrical theory ［J］. Journal of Mechanical Engineering, 2013, 49(21): 108？？122. |
| [33] | ［2］田红亮, 钟先友, 赵春华, 等. 区分弹性与塑性变形的结合面法向校正模型 ［J］. 机械工程学报, 2014, 50(17): 107？？123. |
| [34] | TIAN Hongliang, ZHONG Xianyou, ZHAO Chunhua, et al. Normal revised model of joint interface distinguishing elastic and plastic deformation ［J］. Journal of Mechanical Engineering, 2014, 50(17): 107？？123. |
| [35] | ［3］陈保家, 李力, 田红亮, 等. 基于性能退化的刀具可靠性评估 ［J］. 三峡大学学报: 自然科学版, 2013, 35(6): 87？？91. |
| [36] | CHEN Baojia, LI Li, TIAN Hongliang, et al. Performance degradation？？based reliability estimation for cutting tools ［J］. Journal of China Three Gorges University: Natural Sciences, 2013, 35(6): 87？？91. |
| [37] | TIAN Hongliang, ZHAO Chunhua, ZHU Dalin, et al. Modification of normal and tangential stiffness for joint interface with metallic material and experimental validation ［J］. Transactions of the Chinese Society for Agricultural Machinery, 2012, 43(6): 207？？214. |
| [38] | TIAN Hongliang, ZHU Dalin, QIN Hongling, et al. Modification of normal load’s analytic solutions for joint interface and quantitative experimental verification ［J］. Transactions of the Chinese Society for Agricultural Machinery, 2011, 42(9): 213？？218. |
| [39] | ［6］田红亮, 赵春华, 朱大林, 等. 整个螺栓结合部的法向连接动刚度及试验验证 ［J］. 西安交通大学学报, 2012, 46(9): 31？？36. |
| [40] | ［7］田红亮, 朱大林, 秦红玲. 固定接触界面法向静弹性刚度 ［J］. 应用力学学报, 2011, 28(3): 318？？322. |
| [41] | ［8］田红亮, 赵春华, 方子帆, 等. 微动结合部的一次加载过程 ［J］. 振动与冲击, 2014, 33(13): 40？？52. |
| [42] | TIAN Hongliang, ZHAO Chunhua, FANG Zifan, et al. One loading process of fretting joint interface ［J］. Journal of Vibration and Shock, 2014, 33(13): 40？？52. |
| [43] | ［9］田红亮, 赵春华, 方子帆, 等. 基于各向异性分形理论的结合面切向刚度改进模型 ［J］. 农业机械学报, 2013, 44(3): 257？？266. |
| [44] | TIAN Hongliang, FANG Zifan, ZHU Dalin, et al. Investigation on tangential static elastic stiffness of fixed contact interface ［J］. Chinese Journal of Applied Mechanics, 2011, 28(5): 458？？464. |
| [45] | ［11］田红亮, 陈从平, 方子帆, 等. 应用改进分形几何理论的结合部切向刚度模型 ［J］. 西安交通大学学报, 2014, 48(7): 46？？52. |
| [46] | TIAN Hongliang, LIU Furong, ZHAO Chunhua, et al. Prediction of static friction performance of metallic material surfaces with experimental proof ［J］. Journal of Vibration and Shock, 2014, 33(1): 209？？220. |
| [47] | ［15］田红亮, 赵春华, 方子帆, 等. 基于各向异性分形几何理论的摩擦非线性数学模型 ［J］. 振动与冲击, 2013, 32(23): 135？？144. |
| [48] | TIAN Hongliang, ZHAO Chunhua, FANG Zifan, et al. Mathematical model of nonlinear friction based on anisotropic fractal geometric theory ［J］. Journal of Vibration and Shock, 2013, 32(23): 135？？144. |
| [49] | ［16］田红亮, 赵春华, 方子帆, 等. 基于修正分形理论的结合面静摩擦模型 ［J］. 华中科技大学学报: 自然科学版, 2013, 41(11): 71？？75. |
| [50] | TIAN Hongliang, ZHAO Chunhua, FANG Zifan, et al. Static frictional model for joint interface using revised fractal theory ［J］. Journal of Huazhong University of Science and Technology: Natural Science Edition, 2013, 41(11): 71？？75. |
