基于二阶滑移边界条件的螺旋槽干气密封润滑气膜性能研究
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摘要
随着对螺旋槽干气密封性能研究的不断深入，其应用范围也从高速高压扩大到低速低压。在低速低压工况下，干气密封端面间动压效果差，使得气膜厚度较薄，端面间难以建立稳定气膜而产生干摩擦，导致严重磨损，由此引发了关于低速和低压条件下干气密封端面间滑移流问题的研究。本文根据已经建立的一阶线性滑移边界条件，通过理论分析构建干气密封槽内气体流的二阶非线性滑移边界条件，进而通过实验测寻影响非线性滑移边界条件各参数间的定量关系，推到出稀薄气体流的二阶非线性动力学方程，并分析二阶非线性边界滑移条件各参数对密封性能的影响，揭示干气密封系统中蕴函的复杂的非线性动力学行为。主要研究内容和结论如下：
应用二阶非线性滑移边界条件推导出修正的广义雷诺方程，并用PH线性化方法、迭代法对非线性雷诺方程近似求解，得到泄漏量的近似解析式。继而通过工程实例利用Maple程序计算了不同转速和压力下的泄漏量数值，并与一阶线性滑移边界条件下的泄漏量和实验数值进行了对比。结果表明：二阶非线性滑移边界条件下的泄漏量值比一阶线性滑移边界条件下的泄漏量值更加接近实验数值，特别是在低速、低压工况下更加明显。
应用二阶非线性滑移边界条件推导出修正的广义雷诺方程，并用PH线性化方法、迭代法对非线性雷诺方程近似求解，得到气膜推力的近似解析式，继而对其进行气膜厚度的求导，得到气膜刚度的近似解析式。并利用Maple程序计算不同转速和压力下的气膜刚度数值，并与一阶线性滑移边界条件下的气膜刚度和试验数值进行对比。结果表明：随着气膜厚度的增加，二阶非线性滑移边界条件下的气膜刚度随之减小，且呈非线性关系；随着介质压力、转速的增加，气膜刚度也随之增加，且呈线性关系；二阶非线性滑移边界条件下的气膜刚度数值比一阶线性滑移边界条件下的气膜刚度数值更接近试验数值，其计算精度较高，特别是在低速、低压工况下更加明显。因此在低速低压釜用轴端干气密封中将应用二阶速度滑移条件下的流体力学理论来进行优化设计，指导工程应用。
应用二阶非线性滑移边界条件推导出修正的广义雷诺方程，并用PH线性化方法、迭代法对非线性雷诺方程近似求解，得到气膜推力的近似解析式。并对其进行气膜厚度的求导，得到气膜刚度的近似解析式。继而利用多目标优化方法构建了气膜刚度与泄漏量之比的协调函数，对该目标函数进行近似求解，获得最佳的螺旋槽几何参数值。利用Maple程序计算了不同介质压力和转速下的气膜刚度、泄漏量的数值且与实验数值进行了对比。结果表明：几何参数优化的干气密封样机测试数值与理论计算数值误差较小，说明运用二阶非线性滑移边界条件计算出的理论数值具有较好的精度。
在干气密封试验台上对螺旋槽干气密封系统进行了试验研究，展示了干气密封样机和干气密封试验台摄影图，为了保证试验结果的准确性，采取了必要的系统抗干扰措施。通过对优化出螺旋槽干气密封样机进行测试得到微尺度端面流场参数（泄漏量、气膜厚度、气膜压力）实验值，通过与滑移边界条件下的干气密封理论性能参数值进行对比，得到二阶非线性滑移边界条件下的理论流场参数比一阶线性滑移边界条件下的理论流场参数更加接近于实验值，特别是在高速、高压下更为明显，从而验证了本文理论的正确性。
With spiral grooved dry gas seal performance researched unceasingly, its applicationscope is from the high peed and pressure expanded to low speed and pressure. At low speedand pressure, the dynamic pressure effect of dry gas seal face is weaked, which make gas filmthickness thinner and make end face produce dry friction and serious wear, because it isdifficult to establish stable gas film. It results in the research of dry gas seal face sliding flowproblem at low speed and pressure. In this paper, the second-order nonlinear sliding boundaryconditions of the gas flow in dry gas seal slots is constructed on the first-order linear slipboundary condition and theoretical analysis. Then it measures the quantitative relationship ofthe parameters influencing nonlinear sliding boundary conditions by the experiment andconstructs the nonlinear dynamical equation of the rarefied gas flow, which analyse howparameters influence the sealing performance and reveals the complex nonlinear dynamicbehaviorin of the dry gas seal system. The main contents and conclusion are summarized asfollow:
To address this issue, a modified generalized Reynolds equation is derived with thesecond-order nonlinear slip boundary condition, and the approximate analytic leakage isobtained by solving the nonlinear Reynolds equation with the linear PH method and iterativemethod. Maple program developed with this proposed method was used to compute theleakage values under the different rotational speed and pressure of an engineering instance,and it is compared to the results obtained with the first-order linear slip boundary conditionand the experimental measurements. The results demonstrate that the leakage valuesestimated with the second-order nonlinear slip boundary condition are closer to theexperimental values than that estimated with the first-order linear slip boundary condition.Especially in low-speed and low-pressure conditions, the estimated values with second-ordernonlinear slip boundary condition are significant better than with the first-order linear slipboundary condition.
To address this issue, a modified generalized Reynolds equation is derived with thesecond-order nonlinear slip boundary condition, and the approximate analytic gas film thrustis obtained by solving the nonlinear Reynolds equation with the linear PH method anditerative method. Then, the approximate analytic gas film stiffness is obtained by gas filmthrust derivativing of the gas film thickness. Maple program developed with this proposedmethod is used to compute the gas film stiffness values under the different rotational speedand pressure of an engineering instance, and it is compared to the results obtained with the first-order linear slip boundary conditions and the experimental measurements. The resultsdemonstrate that the gas film stiffness values estimated with the second-order nonlinear slipboundary condition decreases with the gas film thickness increasing, and it is the nonlinearrelationship between the stiffness and thickness of gas, and the gas film stiffness increaseswith the pressure and rotate speed of the medium increasing, and it is the linear relationshipbetween the gas film stiffness and the pressure and rotate speed of the medium, and the gasfilm stiffness values estimated with the second-order nonlinear slip boundary condition arecloser to the experimental values than that estimated with the first-order linear slip boundarycondition, and it has the higher calculation accuracy. Especially in low-speed andlow-pressure conditions, the estimated values with second-order nonlinear slip boundarycondition are significant better than with the first-order linear slip boundary condition. Theoptimization design by hydromechanics theory with the second-order nonlinear slip boundarycondition in shaft dry gas seal of the low-speed and low-pressure conditions can guideengineering application.
The modified generalized Reynolds equation was derived under the second ordernonlinear slip boundary conditions. The nonlinear Reynolds equation was solved to obtain theapproximate solution of gas film thrust by using the PH linearization method, iterative method.Then, gas film stiffness approximate solution was obtained by derivativing gas film thickness.And a trade-off function of rigidity-to-spillage ratio was derived and the optimized geometricparameters were acquired by solving the objective function. Then the gas film stiffness valuesand Leakage values were calculated under the different media pressure and rotational speedby using Maple Program according to an engineering instance, which were compared with theexperimental values. The results show that: Testing values of dry gas seal prototype under theoptimized geometric parameters closed to theoretical numerical calculation. It explained thattheoretical numerical values of the second order nonlinear slip boundary conditions had goodprecision.
The spiral groove dry gas seal system was studied in the dry gas seal test bench, andshowed real figure of the dry gas seal test bench. In order to ensure the accuracy of the testresults, it takes the necessary anti-interference measures system. The experimental values ofmicroscale end flow parameters are obtained by optimization of the spiral groove dry gasseals prototype.Through the experimental data and the theoretical data contrasted, thetheoretical data on the second-order linear slip boundary conditions is closer to theexperimental value, especially at high speed and high pressure, which verify the correctnessof the theory in this paper.
应用二阶非线性滑移边界条件推导出修正的广义雷诺方程，并用PH线性化方法、迭代法对非线性雷诺方程近似求解，得到泄漏量的近似解析式。继而通过工程实例利用Maple程序计算了不同转速和压力下的泄漏量数值，并与一阶线性滑移边界条件下的泄漏量和实验数值进行了对比。结果表明：二阶非线性滑移边界条件下的泄漏量值比一阶线性滑移边界条件下的泄漏量值更加接近实验数值，特别是在低速、低压工况下更加明显。
应用二阶非线性滑移边界条件推导出修正的广义雷诺方程，并用PH线性化方法、迭代法对非线性雷诺方程近似求解，得到气膜推力的近似解析式，继而对其进行气膜厚度的求导，得到气膜刚度的近似解析式。并利用Maple程序计算不同转速和压力下的气膜刚度数值，并与一阶线性滑移边界条件下的气膜刚度和试验数值进行对比。结果表明：随着气膜厚度的增加，二阶非线性滑移边界条件下的气膜刚度随之减小，且呈非线性关系；随着介质压力、转速的增加，气膜刚度也随之增加，且呈线性关系；二阶非线性滑移边界条件下的气膜刚度数值比一阶线性滑移边界条件下的气膜刚度数值更接近试验数值，其计算精度较高，特别是在低速、低压工况下更加明显。因此在低速低压釜用轴端干气密封中将应用二阶速度滑移条件下的流体力学理论来进行优化设计，指导工程应用。
应用二阶非线性滑移边界条件推导出修正的广义雷诺方程，并用PH线性化方法、迭代法对非线性雷诺方程近似求解，得到气膜推力的近似解析式。并对其进行气膜厚度的求导，得到气膜刚度的近似解析式。继而利用多目标优化方法构建了气膜刚度与泄漏量之比的协调函数，对该目标函数进行近似求解，获得最佳的螺旋槽几何参数值。利用Maple程序计算了不同介质压力和转速下的气膜刚度、泄漏量的数值且与实验数值进行了对比。结果表明：几何参数优化的干气密封样机测试数值与理论计算数值误差较小，说明运用二阶非线性滑移边界条件计算出的理论数值具有较好的精度。
在干气密封试验台上对螺旋槽干气密封系统进行了试验研究，展示了干气密封样机和干气密封试验台摄影图，为了保证试验结果的准确性，采取了必要的系统抗干扰措施。通过对优化出螺旋槽干气密封样机进行测试得到微尺度端面流场参数（泄漏量、气膜厚度、气膜压力）实验值，通过与滑移边界条件下的干气密封理论性能参数值进行对比，得到二阶非线性滑移边界条件下的理论流场参数比一阶线性滑移边界条件下的理论流场参数更加接近于实验值，特别是在高速、高压下更为明显，从而验证了本文理论的正确性。
With spiral grooved dry gas seal performance researched unceasingly, its applicationscope is from the high peed and pressure expanded to low speed and pressure. At low speedand pressure, the dynamic pressure effect of dry gas seal face is weaked, which make gas filmthickness thinner and make end face produce dry friction and serious wear, because it isdifficult to establish stable gas film. It results in the research of dry gas seal face sliding flowproblem at low speed and pressure. In this paper, the second-order nonlinear sliding boundaryconditions of the gas flow in dry gas seal slots is constructed on the first-order linear slipboundary condition and theoretical analysis. Then it measures the quantitative relationship ofthe parameters influencing nonlinear sliding boundary conditions by the experiment andconstructs the nonlinear dynamical equation of the rarefied gas flow, which analyse howparameters influence the sealing performance and reveals the complex nonlinear dynamicbehaviorin of the dry gas seal system. The main contents and conclusion are summarized asfollow:
To address this issue, a modified generalized Reynolds equation is derived with thesecond-order nonlinear slip boundary condition, and the approximate analytic leakage isobtained by solving the nonlinear Reynolds equation with the linear PH method and iterativemethod. Maple program developed with this proposed method was used to compute theleakage values under the different rotational speed and pressure of an engineering instance,and it is compared to the results obtained with the first-order linear slip boundary conditionand the experimental measurements. The results demonstrate that the leakage valuesestimated with the second-order nonlinear slip boundary condition are closer to theexperimental values than that estimated with the first-order linear slip boundary condition.Especially in low-speed and low-pressure conditions, the estimated values with second-ordernonlinear slip boundary condition are significant better than with the first-order linear slipboundary condition.
To address this issue, a modified generalized Reynolds equation is derived with thesecond-order nonlinear slip boundary condition, and the approximate analytic gas film thrustis obtained by solving the nonlinear Reynolds equation with the linear PH method anditerative method. Then, the approximate analytic gas film stiffness is obtained by gas filmthrust derivativing of the gas film thickness. Maple program developed with this proposedmethod is used to compute the gas film stiffness values under the different rotational speedand pressure of an engineering instance, and it is compared to the results obtained with the first-order linear slip boundary conditions and the experimental measurements. The resultsdemonstrate that the gas film stiffness values estimated with the second-order nonlinear slipboundary condition decreases with the gas film thickness increasing, and it is the nonlinearrelationship between the stiffness and thickness of gas, and the gas film stiffness increaseswith the pressure and rotate speed of the medium increasing, and it is the linear relationshipbetween the gas film stiffness and the pressure and rotate speed of the medium, and the gasfilm stiffness values estimated with the second-order nonlinear slip boundary condition arecloser to the experimental values than that estimated with the first-order linear slip boundarycondition, and it has the higher calculation accuracy. Especially in low-speed andlow-pressure conditions, the estimated values with second-order nonlinear slip boundarycondition are significant better than with the first-order linear slip boundary condition. Theoptimization design by hydromechanics theory with the second-order nonlinear slip boundarycondition in shaft dry gas seal of the low-speed and low-pressure conditions can guideengineering application.
The modified generalized Reynolds equation was derived under the second ordernonlinear slip boundary conditions. The nonlinear Reynolds equation was solved to obtain theapproximate solution of gas film thrust by using the PH linearization method, iterative method.Then, gas film stiffness approximate solution was obtained by derivativing gas film thickness.And a trade-off function of rigidity-to-spillage ratio was derived and the optimized geometricparameters were acquired by solving the objective function. Then the gas film stiffness valuesand Leakage values were calculated under the different media pressure and rotational speedby using Maple Program according to an engineering instance, which were compared with theexperimental values. The results show that: Testing values of dry gas seal prototype under theoptimized geometric parameters closed to theoretical numerical calculation. It explained thattheoretical numerical values of the second order nonlinear slip boundary conditions had goodprecision.
The spiral groove dry gas seal system was studied in the dry gas seal test bench, andshowed real figure of the dry gas seal test bench. In order to ensure the accuracy of the testresults, it takes the necessary anti-interference measures system. The experimental values ofmicroscale end flow parameters are obtained by optimization of the spiral groove dry gasseals prototype.Through the experimental data and the theoretical data contrasted, thetheoretical data on the second-order linear slip boundary conditions is closer to theexperimental value, especially at high speed and high pressure, which verify the correctnessof the theory in this paper.
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