三轴气浮台气体球轴承静态特性及涡流力矩的研究
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摘要
静压气体球轴承能够提供三自由度低摩擦的运动工况,是卫星三轴仿真气浮台的关键部件。球轴承的静态特性及涡流力矩的大小直接影响三轴气浮台的性能指标。本文针对具有良好动态特性的环面节流静压气体球轴承,通过理论分析和实验验证的方式,研究了静态特性及制造安装误差对涡流力矩的影响,为球轴承的设计、制造及安装提供了指导依据。主要研究内容包括以下几个方面:
给出了气体球轴承三维模型的求解方法。考虑到球轴承气膜厚度方向的尺度远小于其他两个方向的特点,在网格划分时,主要采用适合大纵横比的六面体和棱锥形单元,并将结构化网格与非结构化网格相结合,大大减少了网格的数量,提高了计算效率。利用有限体积法对三维稳态可压缩Navier-Stokes方程进行离散,并将适用于可压缩气体的改进的SIMPLE算法用于离散方程的求解,得到了球轴承气膜内的压力场和速度场。
给出了环面节流静压气体球轴承静态特性指标的计算方法,对球轴承的压力分布、速度分布、承载力、静态刚度和质量流量特性进行了计算分析。通过与基于经典二维雷诺方程的有限元法的计算结果进行对比,验证了本文提出的三维模型求解方法的准确性。研究了制造误差对球轴承静态特性的影响,结果表明在加工过程中应尽量避免球头尺寸的负偏差及长球面型误差,可以适当存在球头尺寸的正偏差和扁球面型误差;可以适当存在球窝尺寸的负偏差和长球面型误差,而尽量避免球窝尺寸的正偏差和扁球面型误差。针对传统环面节流静压气体球轴承静态刚度较小的缺点,提出了一种新型的高刚度过盈型环面节流静压气体球轴承,计算表明该轴承具有承载力大、静态刚度高、耗气量小等优点。
研究了球轴承的制造安装误差对涡流力矩的影响。给出了涡流力矩的计算方法,对比了不同网格划分方式的计算精度,分析了供气孔的直径和位置误差、球头圆度误差及球窝的安装误差对涡流力矩的影响。研究表明现有加工条件可以满足供气孔的加工精度,但为达到球轴承的涡流力矩指标,球头的加工和球窝的安装精度很难保证。本文的研究为球轴承设计制造时公差的选择提供了理论依据,为球窝的安装提出了精度要求。
提出了减小气体球轴承涡流力矩的补偿方法。对由于供气孔加工误差及球窝安装误差引起的涡流力矩,采用供气孔独立供气的方式进行补偿。对于球头圆度误差引起的涡流力矩,通过调整气浮平台的质心位置进行补偿。研究表明补偿后的涡流力矩明显减小。研究了气体介质及轴承工作点对涡流力矩的影响,结果表明以氮气作为工作介质可以使涡流力矩稍有减小,但成本较高,因此选用空气作为轴承的工作介质。并指出为减小球轴承制造误差引起的涡流力矩,应尽量选取供气压力低、中心气膜厚度小的工作点。
建立了承载力特性和涡流力矩实验台,对静压气体球轴承的承载力特性、球窝安装误差引起的涡流力矩及独立供气对涡流力矩的补偿进行了实验研究。承载力特性的实验结果与理论计算结果基本吻合,表明本文提出的环面节流静压气体球轴承的承载力计算方法是正确的。设计制造了低成本的复合材料球窝,并成功应用于涡流力矩实验台。在球窝安装误差引起的涡流力矩的实验中,由于球轴承制造误差的存在,导致实验测得的涡流力矩大于理论计算值,但二者的变化趋势基本一致。在独立供气对涡流力矩的补偿实验中,设计制造了新的球窝供气组件,提出了采用独立供气的方式补偿球窝安装误差引起的涡流力矩的方法,实验结果表明补偿效果很好,补偿后的涡流力矩仅为补偿前的7.92%。
Externally pressurized spherical air bearings can offer a nearly torque-free environment, perhaps as close as possible to that of space, and for this reason it is the key component of the ground-based three-axis test-bed for simulation of spacecraft dynamics and control. The static characteristic of spherical air bearings and the vortex torque affect the performance of the test-bed directly. In this dissertation, externally pressurized spherical air bearings with inherent compensation possessing good dynamic characteristics are studied by means of theoretical analysis and experimental validation.. The static characteristics as well as the impact of manufacturing and installation errors on vortex torque are investigated, which can provide guidance for the design, manufacturing and installation of spherical air bearings. The main contents of this dissertation consist of the following parts.
First, the calculation method of three-dimensional model for spherical air bearings is given. Since the air film thickness is usually far smaller than the size of the other two directions, the hexahedral unit and pyramid unit fitting for large aspect ratio are mainly used when performing grid division, and the structured as well as unstructured grids are combined, which greatly reduces the number of grids and improve the computational efficiency. An finite-volume method is adopted to discretize the three-dimensional steady-state compressible Navier-Stokes equations, and the modified SIMPLE algorithm suitable for the compressible gas is applied to solve the discretized governing equations. The pressure field and velocity field inside of the gas film of spherical air bearings are obtained.
Secondly, the solution is proposed for the static characteristic of externally pressurized spherical air bearings with inherent compensation. The pressure distribution, velocity distribution, bearing capacity, static stiffness and mass flow characteristic of spherical air bearings are studied. By comparing with the results of the finite element method based on the classic two-dimensional Reynolds equation, the validity of the three-dimensional finite volume method proposed in this dissertation is verified. The impact of manufacturing error on the static characteristic of spherical air bearings is analyzed, studies show that the negative dimension error and the prolate spheroid-type error should be avoided when machining the ball head, whereas the positive dimension error and the oblate spheroid-type error are acceptable to some extent. Similarly, the negative dimension error and the prolate spheroid-type error should be avoided when machining the ball socket, whereas the positive dimension error and the oblate spheroid-type error are acceptable to some extent. In view of the shortcoming of the smaller static stiffness of traditional externally pressurized spherical air bearings with inherent compensation, a new style of spherical bearing structure called over-filled externally pressurized spherical gas bearings is developed. Studies show that the new-style over-filled spherical gas bearing has the advantage of larger bearing capacity, higher static stiffness and smaller air consumption.
Thirdly, the impact of the manufacturing error of the spherical air bearing on the vortex torque is studied. The calculation method of vortex torque is given, the computing accuracies of different forms of grid division are compared, and the impacts of the air intake diameter and location errors, the ball head roundness error as well as the ball socket installation error on the vortex torque are analyzed. Studies show that, under the current processing conditions, the difficulty of air intake machining is possible to overcome, however, in order to achieve the desired vortex torque, the manufacturing precision of the ball head and the installation precision of the ball socket are hard to ensured. The investigation in this dissertation will provide some theoretical guideline for the tolerance choice in the design and manufacturing of spherical air bearings, and puts forward some requirements for the installation precision of the ball socket.
Fourthly, a method of vortex torque compensation is put forward to reduce the vortex torque of spherical air bearings. For the vortex torque caused by air intake processing errors and ball socket installation errors, the compensation is realized by independent air supply of the air intake. For the vortex torque arising from the ball head roundness error, the compensation is realized by adjusting the center of mass of the test-bed. The compensation effect is proved good, and the vortex torque significantly descends after compensation. The impacts of gas medium and the operating point on vortex torque are studied, results show that the usage of nitrogen can reduce the vortex torque slightly at the expense of much higher cost, therefore, air is chosen as the gas medium for air bearings. It also points out that, to reduce the vortex torque caused by manufacturing errors, the operating point with lower air supply pressure and smaller center film thickness is preferred.
Last, the test-bed for bearing capacity characteristic and vortex torque is established. The bearing capacity, and the vortex torque caused by ball socket installation error, as well as the vortex torque compensation provided by independent air supply of externally pressurized spherical air bearings are studied. The experimental results of bearing capacity characteristics coincide with the theoretical results, indicating that the proposed calculation method of bearing capacity characteristics is correct. A low-cost composite ball socket is designed and manufactured, which is applied in the vortex torque test-bed successfully. In the experiment for the vortex torque caused by the ball socket installation error, the existence of the manufacturing error of the spherical air bearing leads to the greater vortex torque measured experimentally compared with the theoretical values, but the overall trends are basically the same. In the experiment for the vortex torque compensation provided by independent air supply, a new set of socket components is designed and manufactured, and the method is proposed to use independent air supply mode to compensate the vortex torque caused by the ball socket installation error. Experimental results show that the compensation effect is distinct, the vortex torque after compensation is only 7.92 per cent of the original value.
给出了气体球轴承三维模型的求解方法。考虑到球轴承气膜厚度方向的尺度远小于其他两个方向的特点,在网格划分时,主要采用适合大纵横比的六面体和棱锥形单元,并将结构化网格与非结构化网格相结合,大大减少了网格的数量,提高了计算效率。利用有限体积法对三维稳态可压缩Navier-Stokes方程进行离散,并将适用于可压缩气体的改进的SIMPLE算法用于离散方程的求解,得到了球轴承气膜内的压力场和速度场。
给出了环面节流静压气体球轴承静态特性指标的计算方法,对球轴承的压力分布、速度分布、承载力、静态刚度和质量流量特性进行了计算分析。通过与基于经典二维雷诺方程的有限元法的计算结果进行对比,验证了本文提出的三维模型求解方法的准确性。研究了制造误差对球轴承静态特性的影响,结果表明在加工过程中应尽量避免球头尺寸的负偏差及长球面型误差,可以适当存在球头尺寸的正偏差和扁球面型误差;可以适当存在球窝尺寸的负偏差和长球面型误差,而尽量避免球窝尺寸的正偏差和扁球面型误差。针对传统环面节流静压气体球轴承静态刚度较小的缺点,提出了一种新型的高刚度过盈型环面节流静压气体球轴承,计算表明该轴承具有承载力大、静态刚度高、耗气量小等优点。
研究了球轴承的制造安装误差对涡流力矩的影响。给出了涡流力矩的计算方法,对比了不同网格划分方式的计算精度,分析了供气孔的直径和位置误差、球头圆度误差及球窝的安装误差对涡流力矩的影响。研究表明现有加工条件可以满足供气孔的加工精度,但为达到球轴承的涡流力矩指标,球头的加工和球窝的安装精度很难保证。本文的研究为球轴承设计制造时公差的选择提供了理论依据,为球窝的安装提出了精度要求。
提出了减小气体球轴承涡流力矩的补偿方法。对由于供气孔加工误差及球窝安装误差引起的涡流力矩,采用供气孔独立供气的方式进行补偿。对于球头圆度误差引起的涡流力矩,通过调整气浮平台的质心位置进行补偿。研究表明补偿后的涡流力矩明显减小。研究了气体介质及轴承工作点对涡流力矩的影响,结果表明以氮气作为工作介质可以使涡流力矩稍有减小,但成本较高,因此选用空气作为轴承的工作介质。并指出为减小球轴承制造误差引起的涡流力矩,应尽量选取供气压力低、中心气膜厚度小的工作点。
建立了承载力特性和涡流力矩实验台,对静压气体球轴承的承载力特性、球窝安装误差引起的涡流力矩及独立供气对涡流力矩的补偿进行了实验研究。承载力特性的实验结果与理论计算结果基本吻合,表明本文提出的环面节流静压气体球轴承的承载力计算方法是正确的。设计制造了低成本的复合材料球窝,并成功应用于涡流力矩实验台。在球窝安装误差引起的涡流力矩的实验中,由于球轴承制造误差的存在,导致实验测得的涡流力矩大于理论计算值,但二者的变化趋势基本一致。在独立供气对涡流力矩的补偿实验中,设计制造了新的球窝供气组件,提出了采用独立供气的方式补偿球窝安装误差引起的涡流力矩的方法,实验结果表明补偿效果很好,补偿后的涡流力矩仅为补偿前的7.92%。
Externally pressurized spherical air bearings can offer a nearly torque-free environment, perhaps as close as possible to that of space, and for this reason it is the key component of the ground-based three-axis test-bed for simulation of spacecraft dynamics and control. The static characteristic of spherical air bearings and the vortex torque affect the performance of the test-bed directly. In this dissertation, externally pressurized spherical air bearings with inherent compensation possessing good dynamic characteristics are studied by means of theoretical analysis and experimental validation.. The static characteristics as well as the impact of manufacturing and installation errors on vortex torque are investigated, which can provide guidance for the design, manufacturing and installation of spherical air bearings. The main contents of this dissertation consist of the following parts.
First, the calculation method of three-dimensional model for spherical air bearings is given. Since the air film thickness is usually far smaller than the size of the other two directions, the hexahedral unit and pyramid unit fitting for large aspect ratio are mainly used when performing grid division, and the structured as well as unstructured grids are combined, which greatly reduces the number of grids and improve the computational efficiency. An finite-volume method is adopted to discretize the three-dimensional steady-state compressible Navier-Stokes equations, and the modified SIMPLE algorithm suitable for the compressible gas is applied to solve the discretized governing equations. The pressure field and velocity field inside of the gas film of spherical air bearings are obtained.
Secondly, the solution is proposed for the static characteristic of externally pressurized spherical air bearings with inherent compensation. The pressure distribution, velocity distribution, bearing capacity, static stiffness and mass flow characteristic of spherical air bearings are studied. By comparing with the results of the finite element method based on the classic two-dimensional Reynolds equation, the validity of the three-dimensional finite volume method proposed in this dissertation is verified. The impact of manufacturing error on the static characteristic of spherical air bearings is analyzed, studies show that the negative dimension error and the prolate spheroid-type error should be avoided when machining the ball head, whereas the positive dimension error and the oblate spheroid-type error are acceptable to some extent. Similarly, the negative dimension error and the prolate spheroid-type error should be avoided when machining the ball socket, whereas the positive dimension error and the oblate spheroid-type error are acceptable to some extent. In view of the shortcoming of the smaller static stiffness of traditional externally pressurized spherical air bearings with inherent compensation, a new style of spherical bearing structure called over-filled externally pressurized spherical gas bearings is developed. Studies show that the new-style over-filled spherical gas bearing has the advantage of larger bearing capacity, higher static stiffness and smaller air consumption.
Thirdly, the impact of the manufacturing error of the spherical air bearing on the vortex torque is studied. The calculation method of vortex torque is given, the computing accuracies of different forms of grid division are compared, and the impacts of the air intake diameter and location errors, the ball head roundness error as well as the ball socket installation error on the vortex torque are analyzed. Studies show that, under the current processing conditions, the difficulty of air intake machining is possible to overcome, however, in order to achieve the desired vortex torque, the manufacturing precision of the ball head and the installation precision of the ball socket are hard to ensured. The investigation in this dissertation will provide some theoretical guideline for the tolerance choice in the design and manufacturing of spherical air bearings, and puts forward some requirements for the installation precision of the ball socket.
Fourthly, a method of vortex torque compensation is put forward to reduce the vortex torque of spherical air bearings. For the vortex torque caused by air intake processing errors and ball socket installation errors, the compensation is realized by independent air supply of the air intake. For the vortex torque arising from the ball head roundness error, the compensation is realized by adjusting the center of mass of the test-bed. The compensation effect is proved good, and the vortex torque significantly descends after compensation. The impacts of gas medium and the operating point on vortex torque are studied, results show that the usage of nitrogen can reduce the vortex torque slightly at the expense of much higher cost, therefore, air is chosen as the gas medium for air bearings. It also points out that, to reduce the vortex torque caused by manufacturing errors, the operating point with lower air supply pressure and smaller center film thickness is preferred.
Last, the test-bed for bearing capacity characteristic and vortex torque is established. The bearing capacity, and the vortex torque caused by ball socket installation error, as well as the vortex torque compensation provided by independent air supply of externally pressurized spherical air bearings are studied. The experimental results of bearing capacity characteristics coincide with the theoretical results, indicating that the proposed calculation method of bearing capacity characteristics is correct. A low-cost composite ball socket is designed and manufactured, which is applied in the vortex torque test-bed successfully. In the experiment for the vortex torque caused by the ball socket installation error, the existence of the manufacturing error of the spherical air bearing leads to the greater vortex torque measured experimentally compared with the theoretical values, but the overall trends are basically the same. In the experiment for the vortex torque compensation provided by independent air supply, a new set of socket components is designed and manufactured, and the method is proposed to use independent air supply mode to compensate the vortex torque caused by the ball socket installation error. Experimental results show that the compensation effect is distinct, the vortex torque after compensation is only 7.92 per cent of the original value.
引文
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38杜金名,卢泽生,孙雅洲.空气静压轴承各种节流形式的比较.航空精密制造技术. 2003, 39(6): 4~7
39郭良斌,王祖温,包钢,李军.新型环面节流静压气体球轴承动特性分析.中国机械工程. 2004, 15(23): 2069-2073
40 1 T.L.COREY, C.M.TYLER, H.H.ROWAND, E.M.KIPP. Behavior of Air in the Hydrostatic Lubrication of Loaded Spherical Bearings. Trans. of ASME,Journal of Basic Engineer. 1956, 78:893~898
41 JOHN H.Laub, ROBERT H.NORTON. Externally Pressurized Spherical Gas Bearings. ASLE TRANSACTIONS. 1961, 172~180
42刘暾,刘育华.气体静压球轴承的精确数值计算.哈尔滨工业大学科学研究报告. 1982,118:7
43刘暾,刘育华,陈世杰.静压气体润滑.哈尔滨工业大学出版社,1990:122-153
44刘暾,彭春野,葛卫平等.小孔节流气体静压润滑的离散化和计算收敛.摩擦学学报. 2001, 21(2):139-142
45安旭,穆怀哲,徐丰仁.气体静压球面轴承的设计计算与实验研究.全国第一届精密机械系统与元件设计学术会,上海, 1986:12
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47郭良斌,包钢,王祖温等.环面节流静压气体球轴承承载力特性的实验研究.武汉大学学报(工学版). 2005, 38(4):68-70
48郭良斌,王祖温,包钢等.新型环面节流静压气体球轴承压力分布的实验研究.摩擦学学报. 2005, 25(4):364-368
49 D.F.WILCOCK. Design and Performance of Gas-Pressurized, Spherical, Space-Simulator Bearings. Transactions of the ASME. 1965, (9): 604-612
50 Gu A. A Derivation of the viscous torque on a fluid-film supported spinning sphere. Journal of Lubrication Technology. 1973, (4): 536-538
51贺晓霞,高钟毓,王永梁.静压气体球轴承支承球形转子的干扰力矩分析.中国惯性技术学报. 2002, 10(12):56~61
52姚英学,杜建军,刘暾等.制造误差对气体静压轴承涡流力矩影响分析方法研究.航空学报. 2003, 24(2):124~128
53秦冬黎,姚英学.小孔节流动静压混合气体润滑球轴承的干扰力矩分析.润滑与密封. 2007, 32(4): 131~135
54 Giovanni Cimatti. Existence and Uniqueness for Nonlivear Reynolds Equations. International Journal of Engineering Science. 1986, 24(5): 827~834
55 A. Z. Szeri. Some Extensions of the Lubrication Theory of Osborne Reynolds. Tran. of ASME, Journal of Tribology. 1987, 109(3): 21~35
56 W. A. Gross. Perturbation Solutions for Gas-Lubricating Films. Tran. of ASME, Journal of Basic Engineering. 1961, 83(2): 139~144
57 Ausman. J. S. An Improved Analytical Solution for Self-Acting Gas-Lubricated Journal Bearings of Finite Length. Trans. of ASME, Journal of Basic Engineering. 1961, 83(2): 188~194
58 S. Ramachandra. Solution of Reynolds Equation for a Full Finite Journal Bearing. Trans. of ASME, Journal of Basic Engineering. 1961, 83(4): 589~594
59 J. A. Schmitt. Asymptotic Methods for a General Finite Width Gas Slider Bearing. Trans of ASME, Journal of Lubrication Technology. 1978, 100(2): 254~260
60 M. Anaya-Dufresne, G. B. Sinclair. Some Exact Solutions of Reynolds Equation. Tran. of ASME, Journal of Tribology. 1995, 117(3): 560~562
61 B. C. Majumdar. On the General Solution of Externally Pressurized Gas Journal Bearings. Trans. of ASME, Journal of Lubrication Technology. 1972,94(4): 291~296
62 M. M. Reddi, T. Y. Chu. Finite Element Solution of the Steady-State Compressible Lubrication Problem. Trans. of ASME, Journal of Lubrication Technology. 1970, 92(3):495~503
63 S. S. Wadhwa, R. Sinhasan and D. V. Singh. Analysis of Externally Pressurized Gas Bearings by a Incremental Finite Element Method. Wear. 1981, 69(2): 133~141
64李子才,戴锷.气体轴承压力的数值计算——求解Reynolds方程的非线性有限元及其误差分析.力学学报. 1980, (2): 158~168
65刘暾,刘育华,史小文.气体静压轴承的有限元数值解法.光学机械. 1984, (2):23~29
66 S. H. Nguyen. p-Version Finite Element Analysis of Gas Bearings of Finite Width. Trans. of ASME, Journal of Tribology. 1991, 113(3): 417~420
67朱自强.应用计算流体力学.北京航空航天大学出版社,2002: 1~12
68 M.C.Pandian. A New Method for the Numerical Solution of the Reynolds Equation for Gas-Lubrication Slider Bearings. Journal of Engineering Mathematics. 1985, 19(3):3~19
69古林卓嗣.多重格子法による動圧気体軸受数値解析の高速化.日本機械学会論文集(C編)62巻604号. 1996, 62(12):.4636~4643
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