金属橡胶环与圆锥轴承组合支承转子系统振动性能研究
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摘要
圆锥动静压滑动轴承综合了动压轴承和静压轴承的优点，能够同时承受径向及轴向载荷，具有启动平稳、轴向间隙容易调整、高速时摩擦功耗较小等特点，在高速旋转机械中的应用愈来愈广泛。然而支承在油膜轴承中的高速转子，由于受不平衡质量或者外界干扰等因素的影响，在通过临界转速区或者运行时常会出现剧烈的振动，由于油膜的特性还会产生“自激振动”，从而使转子系统丧失动力稳定性。为了实现对高速旋转机械振动的控制，金属橡胶干摩擦阻尼减振构件因其阻尼性能好、重量轻、且易制成各种形状、环境适应能力强、可调节刚度等一系列优点在该领域得到了成功的应用。
本文针对圆锥动静压轴承支承的高速转子系统，提出用金属橡胶环作为弹性阻尼支承，设计了金属橡胶环与圆锥动静压轴承组合支承高速转子系统，研究了该系统的金属橡胶环动力学参数计算方法、圆锥动静压轴承的油膜力特性、系统模型的建立以及系统参数设计的方法等，并对该组合支承高速转子系统进行了振动性能实验研究。
基于对金属橡胶单元体力学实验结果，建立了金属橡胶单元体非成型方向和成型方向的迟滞恢复应力数学模型，基于此模型，推导出了金属橡胶环径向和轴向动力学参数计算的数学表达式。理论和实验研究了金属橡胶环结构参数与动力学参数的关系，实验结果与理论仿真结果具有较好的一致性，证明了理论模型的正确性。研究结果表明，金属橡胶环动刚度和阻尼的大小与振动幅值和频率有关，预变形和相对密度对径向动刚度和能量耗散系数有重要影响，径向动刚度和能量耗散系数在数值上比轴向大许多。
对金属橡胶环与圆锥动静压轴承组合支承中的轴承油膜力进行了相关研究。考虑润滑油膜轴向速度、紊流和热效应等因素，推导了极坐标系下圆锥动静压轴承的广义雷诺方程、能量方程及相关表达式，采用有限差分法对方程进行离散，利用帕坦卡正系数法则对离散化方程系数及常数项进行处理，数值计算得到了油膜三维压力场和温度场，研究了轴承温升、间隙等参数对轴承性能的影响，数值计算了油膜刚度系数和阻尼系数。对该轴承的静压浮起、动压润滑和流量特性进行相关实验研究，理论与实验研究具有较好的一致性，证明了理论分析的正确性。
建立了圆锥动静压轴承转子系统刚性支承和金属橡胶环与圆锥动静压轴承组合支承转子系统的运动微分方程，提出了基于H_∞理论的系统数学模型，给出了H_∞性能指标γ意义下的振动抑制效果评估指标及动力稳定性判别准则，H_∞性能指标γ越小系统对不平衡干扰力的抑制能力越强，系统响应振幅越小。考虑金属橡胶环模型参数不确定性，通过具体算例，提出了基于H_∞性能指标γ意义下的金属橡胶环最佳动力参数设计方法，仿真结果与H_∞理论计算值对比证明了基于H_∞理论的系统模型的正确性。
研制了金属橡胶环与圆锥动静压轴承组合支承高速转子系统实验台。对比实验研究了圆锥动静压轴承刚性支承以及金属橡胶环弹性支承的高速转子系统振动性能，研究表明，圆锥动静压轴承在工作时，存在着剧烈的自激振动而导致系统失稳，供油压力对圆锥动静压轴承高速转子系统稳定区域有影响，提高供油压力有助于扩大转子系统稳定区域，但是稳定区域扩大能力有限。当系统加入金属橡胶环弹性支承时，由不平衡干扰力产生的系统基频振动随之减小，系统产生自激振动的转速明显提高，系统稳定区域扩大，随着供油压力的增大，系统稳定区域提高的愈明显，当圆锥动静压轴承与金属橡胶环动力参数达到合理地匹配时，金属橡胶干摩擦阻尼能有效地消耗振动能量，降低系统的振动，有效扩大系统稳定区域，实验研究结果与理论分析具有很好的一致性。
本文的研究对金属橡胶环与圆锥动静压轴承组合支承系统在工业各领域高速旋转机械中的实际应用，奠定了理论及实验基础，具有重要的理论意义和实际应用价值。
Conical hybrid (hydrodynamic-hydrostatic) bearing has the advantages ofdynamic pressure bearing and aero-static bearing, such as the capability of bearingthe axial and radial load, steady start, easy adjustment for axial clearance, lessfrictional power loss in high-speed rotation, etc. These advantages had widden itsapplication in high speed rotation machines. However, the rotor supported byjournal bearing may generate severe vibration when it runs across the critical speedcaused by the unbalanced mass or the external disturbance. The nonlinearity of oilfilm force may also generate the self-excited vibration which may lead to theinstability of the rotor system. In order to control the vibration of high-speedrotating machinery, the damping elements made of Metal Rubber (MR) materialhave been widely used in the field of vibration reduction because of its gooddamping performance, light weight, accessibility to produce elements with variousshapes, suitability of severe environment, adjustable stiffness, and so on.
In the present study, a high speed rotor system with combined supportconsisted with conical hybrid sliding bearing and MR ring was designed. Thecalculation method for the dynamic characteristics of MR ring, the lubricationperformance of conical hybrid bearing, the systematic modeling and designingmethods of this system have been researched. The dynamic characteristics of thiscombined bearing high-speed system have been studied experimentally.
Based on the experimental results of MR segment,model building was used tobuild a hysteretic restoring stress mathematical model of MR microelement innon-molding direction and shaping direction. The expression for the nonlinearhysteresis force versus relative density was derived, and a formula for thecalculation of dynamics parameters of MR damping ring was deduced. The dynamicparameters of MR ring were tested which shows the accordance with the theoreticalsimulation results. Theoretical and experiment results show that the frequency andamplitude of vibration are dependent on the stiffness and damping of MR ring. Thepreloaded deformation and relative density of the ring have great influence on itsradial dynamic stiffness and energy dissipation. The radial stiffness and energydissipation factor are greater numerically than those in axial direction.
The oil film force of conical hybrid sliding bearing in the combined supportwas researched. With consideration of the effects of parameters of turbulence,thermal effect and axial velocity, the generalized Reynolds’ equation, energycontrol equation and the oil film lubrication related expressions in polar coordinatesystem were derived, and then discretized using finite difference method which coefficients and constants were treated using Patankar positive coefficientprincipals. The three dimensional pressure field and temperature distribution wereanalyzed numerically. The effects of bearing clearance on the performance ofjournal bearing, as well as the stiffness and damping coefficients of the bearing,were studied. The static pressure, hydrodynamic lubrication and flow characteristicswere tested experimentally. The theoretical results show good agreements with theexperimental results which prove the correctness of the theory.
The differential equations of motion for the rotor system with rigid support andcombined support were set up separately. A systematic model based on H_∞theorywas presented. Based on this, a criterion for evaluating the effect of vibrationcontrol and dynamic stability considering the index γ for H_∞theory was proposed.The smaller the index γ for H_∞theory is, the stronger the capability of the system toprevent the disturbance of unbalanced forces is, and the smaller the amplitude of thesystem response is. Through a specific example, index γ for the description of H_∞performance and trail-and-error were used to optimize the parameters for thedynamic design, considering uncertainty of the MR damping ring. The accordanceof simulated and experimental results based on H_∞show the validity of themodeling method.
The MR–conical hybrid sliding bearing-high-speed rotor test system was setup. The dynamic characteristics of the conical hybrid sliding bearing with a rigidsupport and a support with a MR ring were compared. Results show that for anoperational conical hybrid sliding bearing at operational stage, it may may generateself excitation and cause the systematic instability. The oil supply pressure to therotor system has a significant effect on the stability range of the system. Theimprovement of oil supply pressure is beneficial to expand this range, but it haslimit to make this range widened. When the MR damping ring is put into the elasticsupport, the primary frequency of the system caused by the unbalanced mass wasreduced, and the frequency for self excitation was increased obviously, whichindicates that the stability range became large. With the increase of oil supplypressure, the system of regional stability was improved significantly. When theparameters of conical hybrid sliding bearing and MR ring to dynamic parametersare matched reasonably, the vibration energy can be dissipated effectively, whichreduces the vibration of the system, improves the system stable speed essentially.The test results show good agreement with the theoretical analysis results.
The experimental and theoretical results of this paper are beneficial to thefurther application of MR–conical hybrid sliding bearing joint support in highspeed rotating machinery.
本文针对圆锥动静压轴承支承的高速转子系统，提出用金属橡胶环作为弹性阻尼支承，设计了金属橡胶环与圆锥动静压轴承组合支承高速转子系统，研究了该系统的金属橡胶环动力学参数计算方法、圆锥动静压轴承的油膜力特性、系统模型的建立以及系统参数设计的方法等，并对该组合支承高速转子系统进行了振动性能实验研究。
基于对金属橡胶单元体力学实验结果，建立了金属橡胶单元体非成型方向和成型方向的迟滞恢复应力数学模型，基于此模型，推导出了金属橡胶环径向和轴向动力学参数计算的数学表达式。理论和实验研究了金属橡胶环结构参数与动力学参数的关系，实验结果与理论仿真结果具有较好的一致性，证明了理论模型的正确性。研究结果表明，金属橡胶环动刚度和阻尼的大小与振动幅值和频率有关，预变形和相对密度对径向动刚度和能量耗散系数有重要影响，径向动刚度和能量耗散系数在数值上比轴向大许多。
对金属橡胶环与圆锥动静压轴承组合支承中的轴承油膜力进行了相关研究。考虑润滑油膜轴向速度、紊流和热效应等因素，推导了极坐标系下圆锥动静压轴承的广义雷诺方程、能量方程及相关表达式，采用有限差分法对方程进行离散，利用帕坦卡正系数法则对离散化方程系数及常数项进行处理，数值计算得到了油膜三维压力场和温度场，研究了轴承温升、间隙等参数对轴承性能的影响，数值计算了油膜刚度系数和阻尼系数。对该轴承的静压浮起、动压润滑和流量特性进行相关实验研究，理论与实验研究具有较好的一致性，证明了理论分析的正确性。
建立了圆锥动静压轴承转子系统刚性支承和金属橡胶环与圆锥动静压轴承组合支承转子系统的运动微分方程，提出了基于H_∞理论的系统数学模型，给出了H_∞性能指标γ意义下的振动抑制效果评估指标及动力稳定性判别准则，H_∞性能指标γ越小系统对不平衡干扰力的抑制能力越强，系统响应振幅越小。考虑金属橡胶环模型参数不确定性，通过具体算例，提出了基于H_∞性能指标γ意义下的金属橡胶环最佳动力参数设计方法，仿真结果与H_∞理论计算值对比证明了基于H_∞理论的系统模型的正确性。
研制了金属橡胶环与圆锥动静压轴承组合支承高速转子系统实验台。对比实验研究了圆锥动静压轴承刚性支承以及金属橡胶环弹性支承的高速转子系统振动性能，研究表明，圆锥动静压轴承在工作时，存在着剧烈的自激振动而导致系统失稳，供油压力对圆锥动静压轴承高速转子系统稳定区域有影响，提高供油压力有助于扩大转子系统稳定区域，但是稳定区域扩大能力有限。当系统加入金属橡胶环弹性支承时，由不平衡干扰力产生的系统基频振动随之减小，系统产生自激振动的转速明显提高，系统稳定区域扩大，随着供油压力的增大，系统稳定区域提高的愈明显，当圆锥动静压轴承与金属橡胶环动力参数达到合理地匹配时，金属橡胶干摩擦阻尼能有效地消耗振动能量，降低系统的振动，有效扩大系统稳定区域，实验研究结果与理论分析具有很好的一致性。
本文的研究对金属橡胶环与圆锥动静压轴承组合支承系统在工业各领域高速旋转机械中的实际应用，奠定了理论及实验基础，具有重要的理论意义和实际应用价值。
Conical hybrid (hydrodynamic-hydrostatic) bearing has the advantages ofdynamic pressure bearing and aero-static bearing, such as the capability of bearingthe axial and radial load, steady start, easy adjustment for axial clearance, lessfrictional power loss in high-speed rotation, etc. These advantages had widden itsapplication in high speed rotation machines. However, the rotor supported byjournal bearing may generate severe vibration when it runs across the critical speedcaused by the unbalanced mass or the external disturbance. The nonlinearity of oilfilm force may also generate the self-excited vibration which may lead to theinstability of the rotor system. In order to control the vibration of high-speedrotating machinery, the damping elements made of Metal Rubber (MR) materialhave been widely used in the field of vibration reduction because of its gooddamping performance, light weight, accessibility to produce elements with variousshapes, suitability of severe environment, adjustable stiffness, and so on.
In the present study, a high speed rotor system with combined supportconsisted with conical hybrid sliding bearing and MR ring was designed. Thecalculation method for the dynamic characteristics of MR ring, the lubricationperformance of conical hybrid bearing, the systematic modeling and designingmethods of this system have been researched. The dynamic characteristics of thiscombined bearing high-speed system have been studied experimentally.
Based on the experimental results of MR segment,model building was used tobuild a hysteretic restoring stress mathematical model of MR microelement innon-molding direction and shaping direction. The expression for the nonlinearhysteresis force versus relative density was derived, and a formula for thecalculation of dynamics parameters of MR damping ring was deduced. The dynamicparameters of MR ring were tested which shows the accordance with the theoreticalsimulation results. Theoretical and experiment results show that the frequency andamplitude of vibration are dependent on the stiffness and damping of MR ring. Thepreloaded deformation and relative density of the ring have great influence on itsradial dynamic stiffness and energy dissipation. The radial stiffness and energydissipation factor are greater numerically than those in axial direction.
The oil film force of conical hybrid sliding bearing in the combined supportwas researched. With consideration of the effects of parameters of turbulence,thermal effect and axial velocity, the generalized Reynolds’ equation, energycontrol equation and the oil film lubrication related expressions in polar coordinatesystem were derived, and then discretized using finite difference method which coefficients and constants were treated using Patankar positive coefficientprincipals. The three dimensional pressure field and temperature distribution wereanalyzed numerically. The effects of bearing clearance on the performance ofjournal bearing, as well as the stiffness and damping coefficients of the bearing,were studied. The static pressure, hydrodynamic lubrication and flow characteristicswere tested experimentally. The theoretical results show good agreements with theexperimental results which prove the correctness of the theory.
The differential equations of motion for the rotor system with rigid support andcombined support were set up separately. A systematic model based on H_∞theorywas presented. Based on this, a criterion for evaluating the effect of vibrationcontrol and dynamic stability considering the index γ for H_∞theory was proposed.The smaller the index γ for H_∞theory is, the stronger the capability of the system toprevent the disturbance of unbalanced forces is, and the smaller the amplitude of thesystem response is. Through a specific example, index γ for the description of H_∞performance and trail-and-error were used to optimize the parameters for thedynamic design, considering uncertainty of the MR damping ring. The accordanceof simulated and experimental results based on H_∞show the validity of themodeling method.
The MR–conical hybrid sliding bearing-high-speed rotor test system was setup. The dynamic characteristics of the conical hybrid sliding bearing with a rigidsupport and a support with a MR ring were compared. Results show that for anoperational conical hybrid sliding bearing at operational stage, it may may generateself excitation and cause the systematic instability. The oil supply pressure to therotor system has a significant effect on the stability range of the system. Theimprovement of oil supply pressure is beneficial to expand this range, but it haslimit to make this range widened. When the MR damping ring is put into the elasticsupport, the primary frequency of the system caused by the unbalanced mass wasreduced, and the frequency for self excitation was increased obviously, whichindicates that the stability range became large. With the increase of oil supplypressure, the system of regional stability was improved significantly. When theparameters of conical hybrid sliding bearing and MR ring to dynamic parametersare matched reasonably, the vibration energy can be dissipated effectively, whichreduces the vibration of the system, improves the system stable speed essentially.The test results show good agreement with the theoretical analysis results.
The experimental and theoretical results of this paper are beneficial to thefurther application of MR–conical hybrid sliding bearing joint support in highspeed rotating machinery.
引文
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