气浮陀螺仪干扰力矩影响因素研究
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摘要
随着惯性导航技术的发展及其应用领域的扩大,惯性系统对陀螺仪漂移精度的要求也越来越高。同时,越来越多的新型陀螺仪逐渐发展起来,例如:静电陀螺仪、激光陀螺仪、光纤陀螺仪、振动陀螺仪和微机械陀螺仪等。凭借技术成熟和成本低廉等优势,传统结构的气浮陀螺仪仍然在惯性导航领域发挥着不可替代的作用。然而,受到加工技术等方面的限制,国内气浮陀螺仪生产合格率和稳定性都较低,这大大降低了生产效率、增加了生产成本。影响气浮陀螺仪漂移精度的因素很多,如加工误差等引起的涡流力矩和陀螺仪浮子组件质心位置热不稳定性引起的干扰力矩等。这些干扰力矩对漂移精度的影响错综复杂,一直制约着气浮陀螺仪精度的提高。因此,如何有效地控制诸因素引起的干扰力矩以进一步提高气浮陀螺仪漂移精度是目前迫切需要解决的关键问题。
本文介绍了气浮陀螺仪漂移误差模型,分析了引起陀螺仪K0和K1项漂移系数增大的影响因素。其中,引起气浮陀螺仪气膜不均匀流动的加工误差等因素影响K0项漂移系数,而陀螺仪浮子组件质心位置的热不稳定性是影响K1项漂移系数的主要因素。因此,针对以上问题着重研究了诸因素对气浮陀螺仪干扰力矩的影响规律,进而为提高陀螺漂移精度提供理论指导。
文中所研究的气浮陀螺仪各部分气膜分别采用柱坐标和笛卡尔坐标表达式,即:气浮陀螺仪止推气膜部分和节流狭缝部分使用柱坐标系表达式,而浮子径向承载气膜部分则可以展开成笛卡尔坐标系表达式,通过相容性变换实现了柱坐标系与笛卡尔坐标系表达式的统一,进而建立了相同形式的数学表达式。基于气体静压润滑雷诺方程式,利用有限元方法,推导了求解气浮陀螺仪气膜压力分布的有限元方程组。基于Christensen粗糙表面随机模型,分别推导了考虑纵向和横向表面粗糙度的雷诺方程。在求得陀螺仪气膜压力数值解的基础上,给出了根据有限元节点压力求解气浮陀螺仪涡流力矩和径向承载能力的计算公式。利用商业数学软件MATLAB,编写了求解雷诺方程的有限元程序,实现了上述因素对气浮陀螺仪涡流力矩影响的研究,以及气膜压力分布结果的可视化输出。
气浮陀螺仪加工和装配中产生的形状误差是K0项漂移系数的重要影响因素。本文建立了气浮陀螺仪浮子椭圆形误差、浮子三棱形误差、节流狭缝平行度误差以及浮子径向偏心率的数学模型,并将模型代入有限元方程中,求得了以上因素对气浮陀螺仪气膜压力分布的影响规律,进而分析了其对涡流力矩的影响,提出了有效控制涡流力矩的方法。此外,还分析了气膜厚度和供气压力对陀螺涡流力矩的影响规律,并且得到了气浮陀螺仪节流狭缝宽度和气膜厚度的合理匹配数值。利用图像处理涡流力矩测试仪,检测了若干陀螺组件的涡流力矩数值,一定程度验证了仿真的合理性。
因为气浮陀螺仪的气膜厚度很薄,而且涡流力矩是一个敏感量,所以表面粗糙度引起的气浮陀螺仪浮子周围气膜压力分布变化将对涡流力矩产生影响。建立了表面粗糙度轮廓算术平均偏差与雷诺方程式中表面粗糙度参数的联系,利用推导的考虑表面粗糙度的雷诺方程,研究了表面粗糙度大小和方向对气浮陀螺仪涡流力矩的影响规律。
气浮陀螺仪浮子组件质心位置的热稳定性是K1项漂移系数的重要影响因素。本文建立了气浮陀螺仪浮子组件的有限元模型,通过节点约束方程,建立了螺钉预紧力模型,并利用螺钉刚度、螺钉预紧力和螺钉拧紧力矩公式,计算了螺钉预紧力模型与螺钉拧紧力矩的对应关系。模拟了变化温度场中,不同大小的螺钉预紧力对陀螺浮子组件质心位置稳定性的影响,得到了螺钉预紧力的合理数值。通过对特征时间点的变形云图和应力分布规律的分析,提出了改善浮子组件性能的合理建议。
With development of inertial navigation technology and expansion of application domain, required precision of gyroscope in inertial system becomes very high. At the same time, more and more new type of gyroscope appeared, such as electrostatic gyroscope, laser gyroscope, optical fiber gyroscope, vibratory gyroscope and micro mechanical gyroscope. Depending mature technology and low cost, air-floated gyroscope still plays an irreplaceable role in inertial navigation field. However, by the restriction of machining technology, qualified rate and stability of air-floated gyroscope are unsatisfactory. This problem reduces production efficiency, and increases the cost. There are many factors influencing drift precision of air-floated gyroscope, such as vortex torque caused by manufacturing error and disturbing interference torque caused by thermal instability of center of mass of float module. So, how to control the factors influencing drift precision effectively is the key problem.
This paper introduced the drift error model of air-floated gyroscope and the factors making K0 and K1 drift coefficient increase. Manufacturing error causing inhomogeneous flow in gas film of air-floated gyroscope influences K0 drift coefficient, while, thermal instability of center of mass of float module influences K1 drift coefficient. So, in this paper, the factors influencing the interference torque have been studied.
Different parts of gas film studied in this paper are usually expressed in cylindrical coordinate and Cartesian coordinate respectively. The thrust part and slot part are usually expressed in cylindrical coordinate, while, radial loading part can be expressed in Cartesian coordinate after expanded into plane. By consistency transformation, the uniform expression of cylindrical coordinate and Cartesian coordinate is obtained. In order to achieve the pressure distribution in gas film, finite element equation is deduced based on aerostatic Reynolds Equation. Then, Reynolds Equation including longitudinal and transverse surface roughness is deduced based on Christensen’s roughness model. The formulas solving the vortex torque and bearing capacity are presented at last. Finite element program used to solve Reynolds Equation is composed by using MATLAB, which is commercial mathematic software. Then research of these factors influencing vortex torque can be achieved expediently, and visual output of gas film pressure distribution can be obtained.
The shape error generated during manufacturing and assembling process is important factor influencing K0 drift coefficient. In this paper, mathematic models of float oval error, float three-lobing error, slot disalignment error and radial eccentricity ratio are established. Then put these models into finite element equation, and effect of these factors on pressure distribution in gas film is obtained. After that, effect of these factors on vortex torque is analyzed and method controlling vortex torque is put forward. Further, effect of gas film thickness and air supply pressure on vortex torque is also studied, and reasonable matching value of slot width and gas film thickness is obtained. By using vortex torque test instrument, vortex torque of several gyroscopes is measured, and the rationality of emulation is verified.
The gas film thickness is very small and vortex torque is quite sensitive, so pressure distribution variation caused by surface roughness will influence vortex torque at a certain extent. In this paper, relation between average arithmetic deviation of surface roughness and parameter of surface roughness in Reynolds Equation is established. Effect of magnitude and direction of surface roughness on vortex torque is studied by using Reynolds Equation including surface roughness.
Thermal stability of center of mass of float module is important factor influencing K1 drift coefficient. Finite element model of air-floated gyroscope is established, and screw pretightening force model is established by using nodal restraint equation. By using screw stiffness and pretightenting force equation, relation between screw pretightenting force in finite model and screw tighten torque is obtained. Then, effect of different pretightening force on the stability of center of mass in variable temperature field is studied, and reasonable screw pretightening force is obtained. At last, the deformation nephogram and stress distribution at the key time points is analyzed, and proper suggestion is put forward.
本文介绍了气浮陀螺仪漂移误差模型,分析了引起陀螺仪K0和K1项漂移系数增大的影响因素。其中,引起气浮陀螺仪气膜不均匀流动的加工误差等因素影响K0项漂移系数,而陀螺仪浮子组件质心位置的热不稳定性是影响K1项漂移系数的主要因素。因此,针对以上问题着重研究了诸因素对气浮陀螺仪干扰力矩的影响规律,进而为提高陀螺漂移精度提供理论指导。
文中所研究的气浮陀螺仪各部分气膜分别采用柱坐标和笛卡尔坐标表达式,即:气浮陀螺仪止推气膜部分和节流狭缝部分使用柱坐标系表达式,而浮子径向承载气膜部分则可以展开成笛卡尔坐标系表达式,通过相容性变换实现了柱坐标系与笛卡尔坐标系表达式的统一,进而建立了相同形式的数学表达式。基于气体静压润滑雷诺方程式,利用有限元方法,推导了求解气浮陀螺仪气膜压力分布的有限元方程组。基于Christensen粗糙表面随机模型,分别推导了考虑纵向和横向表面粗糙度的雷诺方程。在求得陀螺仪气膜压力数值解的基础上,给出了根据有限元节点压力求解气浮陀螺仪涡流力矩和径向承载能力的计算公式。利用商业数学软件MATLAB,编写了求解雷诺方程的有限元程序,实现了上述因素对气浮陀螺仪涡流力矩影响的研究,以及气膜压力分布结果的可视化输出。
气浮陀螺仪加工和装配中产生的形状误差是K0项漂移系数的重要影响因素。本文建立了气浮陀螺仪浮子椭圆形误差、浮子三棱形误差、节流狭缝平行度误差以及浮子径向偏心率的数学模型,并将模型代入有限元方程中,求得了以上因素对气浮陀螺仪气膜压力分布的影响规律,进而分析了其对涡流力矩的影响,提出了有效控制涡流力矩的方法。此外,还分析了气膜厚度和供气压力对陀螺涡流力矩的影响规律,并且得到了气浮陀螺仪节流狭缝宽度和气膜厚度的合理匹配数值。利用图像处理涡流力矩测试仪,检测了若干陀螺组件的涡流力矩数值,一定程度验证了仿真的合理性。
因为气浮陀螺仪的气膜厚度很薄,而且涡流力矩是一个敏感量,所以表面粗糙度引起的气浮陀螺仪浮子周围气膜压力分布变化将对涡流力矩产生影响。建立了表面粗糙度轮廓算术平均偏差与雷诺方程式中表面粗糙度参数的联系,利用推导的考虑表面粗糙度的雷诺方程,研究了表面粗糙度大小和方向对气浮陀螺仪涡流力矩的影响规律。
气浮陀螺仪浮子组件质心位置的热稳定性是K1项漂移系数的重要影响因素。本文建立了气浮陀螺仪浮子组件的有限元模型,通过节点约束方程,建立了螺钉预紧力模型,并利用螺钉刚度、螺钉预紧力和螺钉拧紧力矩公式,计算了螺钉预紧力模型与螺钉拧紧力矩的对应关系。模拟了变化温度场中,不同大小的螺钉预紧力对陀螺浮子组件质心位置稳定性的影响,得到了螺钉预紧力的合理数值。通过对特征时间点的变形云图和应力分布规律的分析,提出了改善浮子组件性能的合理建议。
With development of inertial navigation technology and expansion of application domain, required precision of gyroscope in inertial system becomes very high. At the same time, more and more new type of gyroscope appeared, such as electrostatic gyroscope, laser gyroscope, optical fiber gyroscope, vibratory gyroscope and micro mechanical gyroscope. Depending mature technology and low cost, air-floated gyroscope still plays an irreplaceable role in inertial navigation field. However, by the restriction of machining technology, qualified rate and stability of air-floated gyroscope are unsatisfactory. This problem reduces production efficiency, and increases the cost. There are many factors influencing drift precision of air-floated gyroscope, such as vortex torque caused by manufacturing error and disturbing interference torque caused by thermal instability of center of mass of float module. So, how to control the factors influencing drift precision effectively is the key problem.
This paper introduced the drift error model of air-floated gyroscope and the factors making K0 and K1 drift coefficient increase. Manufacturing error causing inhomogeneous flow in gas film of air-floated gyroscope influences K0 drift coefficient, while, thermal instability of center of mass of float module influences K1 drift coefficient. So, in this paper, the factors influencing the interference torque have been studied.
Different parts of gas film studied in this paper are usually expressed in cylindrical coordinate and Cartesian coordinate respectively. The thrust part and slot part are usually expressed in cylindrical coordinate, while, radial loading part can be expressed in Cartesian coordinate after expanded into plane. By consistency transformation, the uniform expression of cylindrical coordinate and Cartesian coordinate is obtained. In order to achieve the pressure distribution in gas film, finite element equation is deduced based on aerostatic Reynolds Equation. Then, Reynolds Equation including longitudinal and transverse surface roughness is deduced based on Christensen’s roughness model. The formulas solving the vortex torque and bearing capacity are presented at last. Finite element program used to solve Reynolds Equation is composed by using MATLAB, which is commercial mathematic software. Then research of these factors influencing vortex torque can be achieved expediently, and visual output of gas film pressure distribution can be obtained.
The shape error generated during manufacturing and assembling process is important factor influencing K0 drift coefficient. In this paper, mathematic models of float oval error, float three-lobing error, slot disalignment error and radial eccentricity ratio are established. Then put these models into finite element equation, and effect of these factors on pressure distribution in gas film is obtained. After that, effect of these factors on vortex torque is analyzed and method controlling vortex torque is put forward. Further, effect of gas film thickness and air supply pressure on vortex torque is also studied, and reasonable matching value of slot width and gas film thickness is obtained. By using vortex torque test instrument, vortex torque of several gyroscopes is measured, and the rationality of emulation is verified.
The gas film thickness is very small and vortex torque is quite sensitive, so pressure distribution variation caused by surface roughness will influence vortex torque at a certain extent. In this paper, relation between average arithmetic deviation of surface roughness and parameter of surface roughness in Reynolds Equation is established. Effect of magnitude and direction of surface roughness on vortex torque is studied by using Reynolds Equation including surface roughness.
Thermal stability of center of mass of float module is important factor influencing K1 drift coefficient. Finite element model of air-floated gyroscope is established, and screw pretightening force model is established by using nodal restraint equation. By using screw stiffness and pretightenting force equation, relation between screw pretightenting force in finite model and screw tighten torque is obtained. Then, effect of different pretightening force on the stability of center of mass in variable temperature field is studied, and reasonable screw pretightening force is obtained. At last, the deformation nephogram and stress distribution at the key time points is analyzed, and proper suggestion is put forward.
引文
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