线性化处理前后开式静压工作台动态特性比较  

Dynamic Characteristic Comparison of Open-type Hydrostatic Worktable both Before and After Linearization

作　　者：赵建华[1] 高殿荣[1] 

机构地区：[1]燕山大学机械工程学院,秦皇岛066004

出　　处：《机械工程学报》2012年第24期158-163,共6页Journal of Mechanical Engineering

基　　金：国家自然科学基金(51075348);河北省自然科学基金(E2011203151);高等学校博士学科点专项科研基金(20101333110002)资助项目

摘　　要：目前,静压支承主要是作为线性系统进行动态性能分析,但线性化造成的误差未进行分析。以多头泵调节下的开式静压工作台为对象,推导出工作台关于压力、流量的非线性微分方程组。一方面,对工作台支承系统进行线性化处理,利用Laplace变换的方法获得了系统的传递函数,采用Routh判据对其进行稳定性判别,并绘制系统的阶跃响应和脉冲响应曲线。另一方面,采用四阶Runge-Kutta法,利用Simulink工具箱搭建非线性系统的框图,并绘制系统的阶跃响应和脉冲响应曲线。对比两种方法得到的阶跃响应曲线,线性化系统与原系统的响应曲线差别较小,精度能够满足正常的工程需要,线性化处理对于多头泵调节下的开式静压工作台是可行的。因此对静压工作台进行动态性能分析,绘制出幅频、相频、动刚度曲线图。所做的研究对比分析两种方法得到的多头泵调节下开式静压工作台的响应结果,为工程的实际应用提供了参考依据。At present,the hydrostatic bearing system,usually considered as the linear system,is mostly researched on the dynamic performance.But the error via linearization transform hasn＇t yet analyzed.Take the open-type hydrostatic worktable based on the multi-head pump for instance,the nonlinear differential equations systems on the pressure and the flow are derived.On the one hand,the hydrostatic bearing system is linearized,and the transfer function via Laplace transform is obtained.The stability is discriminated with Routh criteria,and then the step response curves and the pulse response curves are plotted.On the other hand,the system block diagram of the worktable bearing system is built with fourth-order Runge-Kutta method using Simulink tool box,and the step response curves are plotted.Comparing the response curves obtained separately from two different methods,the difference between the curves is very small,and the precision can meet the demand of the practical engineering,then the linear treatment is valid for the open-type hydrostatic worktable based on the multi-head pump.So the dynamic performance on the worktable is analyzed,and the amplitude-frequency curves,the phase-frequency curves,and the dynamic stiffness-frequency curves are present.The proposed research contrasts the response results of the hydrostatic worktable with two different methods,and provides a basis for the practical engineering.

关 键 词：多头泵 开式静压工作台 非线性微分方程组 LAPLACE变换 四阶Runge-Kutta法 动刚度 

分 类 号：TH133[机械工程—机械制造及自动化]