薄壁零件高速铣削过程中非线性振动的研究
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摘要
现代国防装备中，如航天飞行器、飞机、火箭、卫星等所用的特殊材料和特殊型面的构件，用传统加工不可能达到理想精度要求，必须采用多轴联动、高速、高精度的数控机床进行加工。因此，高性能的数控机床对国防现代化和我国汽车工业的高速发展起着至关重要的作用，它所带来的技术和产品已经关系到我国经济的发展和国防的进步。但是在高速切削金属零件过程中发生的强烈振动，会恶化被加工零件的表面质量，影响被加工零件的加工精度，使零件的废品率提高，严重时会破坏机床主轴，造成重大的经济损失。随着国防事业的发展，对型面特殊的，质量轻，柔度大的铝合金零件的需求不断增大，也对高速铣削加工数控中心提出了更高的要求。
因此，目前高速铣削过程中开口薄壁零件的非线性振动问题日益突出，逐渐成为了限制高速铣削加工生产技术水平和生产效率的主要问题。对高速铣削过程中薄壁零件非线性问题的研究有着重要的理论意义和工程实际价值。本文主要采用理论研究和数值分析相结合的方法对于切削力作用下的高速铣削中薄壳和薄板零件的非线性振动、分叉和混沌动力学特性进行研究。论文的主要研究内容有以下几方面。
(1)高速铣削过程中薄壳零件的动力学建模
研究了高速铣削过程中航空发动机叶片的非线性振动问题，发动机叶片柔度大，并且受到切削力的作用，基于高速铣削过程中加工发动机叶片的工作状态，利用Hamilton原理建立了切削力作用下高速铣削过程中薄壳类零件的非线性动力学方程。选取了第一阶模态和第二阶模态，利用Galerkin方法对所得到的薄壳构件的偏微分方程进行了离散，得到了两自由度非线性动力学方程，用来描述系统的运动。
(2)高速铣削过程中薄壳零件非线性动力学特性的研究
分别考虑了主参数共振情况下1:1内共振和1:2内共振的情况，利用多尺度方法得到了系统的四维平均方程。基于四维平均方程，利用数值方法研究了高速铣削过程中薄壳零件的非线性动力学行为以及动态分叉特性。数值结果表明，系统的非线性动态响应幅值随着外激励的增加而非线性增加。在特定参数情况下，第二阶模态的幅值有可能大于第一阶模态的幅值。所以，只考虑第一阶模态并不能全面的反映系统非线性振动情况。通过随外激励变化的分叉图，发现系统呈现出混沌运动→周期运动→单倍周期运动→多倍周期运动→概周期运动→混沌运动的交替变化过程。从所得到的系统阻尼参数分叉图中可以看出，阻尼系数对系统的动态响应有着很大的影响，随着阻尼系数的增加系统的运动趋于稳定的周期运动。因此，可以适当的调节系统的阻尼用来抑制混沌运动的出现。
(3)高速铣削过程中薄板类零件的非线性振动和混沌运动的研究
利用Hamilton原理建立了高速铣削过程中薄板零件的非线性动力学方程。选取了第一阶模态和第二阶模态，利用Galerkin方法对所得到的切削力作用下薄板零件的偏微分方程进行了离散，得到了薄板零件的两自由度非线性动力学方程。
分别考虑主参数共振情况下1:1内共振和1:3内共振情况，利用多尺度方法得到系统的四维平均方程。基于四维平均方程，利用数值方法研究了高速铣削过程中薄板零件的非线性动力学行为及动态分叉特性。数值结果表明，系统在外激励作用下存在着混沌运动、周期运动和概周期运动。从所得到的随系统阻尼参数变化的分叉图中可以看出，阻尼系数对系统的动态响应有很大的影响。
(4)高速铣削过程中时滞参数对系统非线性振动的影响
时滞现象普遍存在于切削加工中，本文分别研究了高速铣削薄壳零件和高速铣削薄板零件非线性动力学问题中时滞的影响。根据四维平均方程，通过数值分析，研究了时滞参数对系统非线性振动的影响。通过固定其他参数并改变时滞参数，发现系统存在周期运动，混沌运动和概周期运动。系统对时滞参数的改变非常敏感，可以通过改变时滞参数来抑制系统混沌运动的出现。
The equipments that are used for modern national defense, spacecraft, aircraft,rockets, satellites, are normal made of special materials with complex finishing surfaces.The components of these equipments are impossible to be manufactured by traditionalmachines but rather by multi axis CNC machine with high speed, and high precision.Therefore, the CNC machines with high performance play a vital role in themodernization of national defense, modern aircraft and automobile industry. Thehigh precision workpieces related to the progress of China's economic development andnational defense. In the process of high speed milling, however, the thin walledworkpieces frequently have strong vibrations which can result in poor surface finishing,high rejection rate, even the machine axis damage. With the rapid development of nationaldefense, the requirement of workpieces with light weight, low stiffness and good surfaceare bloomed. So that the new technology of CNC machine are corresponding demanded.
Research on the nonlinear vibrations of thin walled workpieces during high speedmilling becomes more and more important in engineering. In this paper, the nonlinearvibrations of thin walled workpieces subjected to the cutting force in high speed millingprocess are studied by using theoretical and numerical methods. The main research field ofthis dissertation is introduces as follows.
(1) Modelling of the shell shaped workpiece during high speed milling process isestablished.
During the process of machining engine blades, the workpiece with low stiffness hasstrong vibrations which result in poor surface finishing, high rejection rates and machinedamage. Based on the milling process, the shell shaped workpiece is modeled as acantilevered thin shell subjected to the cutting force with time delay effects. Equations ofmotion are derived by using Hamilton principle based on the classical shell theory. Theresulting nonlinear partial differential equations are reduced to a two degree of freedomnonlinear system by applying the Galerkin’s approach.
(2) Nonlinear vibrations of the shell shaped workpiece during high speed millingprocess is investigated.
The averaging method is used to obtain two sets of the four dimensional averagedequations by considering the1:1and1:2internal resonances, respectively. Using thenumerical method, dynamics of the cantilevered shell shaped workpiece is studied under dumping coefficient and forcing excitation. It is concluded that there exit complexnonlinear behaviors including the chaotic motion, periodic and quasi periodic motions. Itis observed from the bifurcation diagram of forcing excitation that with the increase of theamplitude of the non dimensional forcing excitation, the motions of the cantileveredshell shaped workpiece demonstrate the following pattern: chaotic motion→periodicmotion→quasi periodic motion→chaotic motion. The nonlinear dynamic behavior of theshell shaped workpiece form the chaotic motion is controlled by varying the amplitude ofthe damping coefficient.
(3) Nonlinear vibrations, bifurcations and chaos of the thin plate workpiece duringhigh speed milling process are studied.
Because of the cutting force in the milling process, the thin plate workpiece vibratestrongly. Based on the cutting process, the thin plate workpiece is modeled as acantilevered thin plate subjected the cutting force. Applying the Hamilton principle, theequations of motion of the thin plate workpiece are derived based on Kirchhoff platetheory. Utilizing the Galerkin’s approach, the resulting equations are reduced to atwo degree of freedom nonlinear system. The method of Asymptotic Perturbation isutilized to obtain two sets of four dimensional averaged equations by considering1:1and1:3internal resonances, respectively. Using numerical simulations, the influence ofdifferent parameters on nonlinear vibrations of the thin plate workpiece is detected. It isconcluded that there exist complex nonlinear behaviors including chaotic motion, periodicmotion and periodic n motion. The motion of the system is very sensitive by varying thedumping coefficient.
(4) The influences of time delay effects on the thin walled workpiece duringhigh speed milling process are analyzed.
The statuses of the system in the past or a certain time before have impact on thecurrent system. There exists a time lag. The time delay effects frequently happen in thecutting system. In this study, based on the four dimensional averaged equations, theinfluence of time delay parameters on the thin walled workpiece is numerically analyzed.It is stated that nonlinear behaviors of the thin walled workpiece is sensitive on thevarying time delay parameters.
因此，目前高速铣削过程中开口薄壁零件的非线性振动问题日益突出，逐渐成为了限制高速铣削加工生产技术水平和生产效率的主要问题。对高速铣削过程中薄壁零件非线性问题的研究有着重要的理论意义和工程实际价值。本文主要采用理论研究和数值分析相结合的方法对于切削力作用下的高速铣削中薄壳和薄板零件的非线性振动、分叉和混沌动力学特性进行研究。论文的主要研究内容有以下几方面。
(1)高速铣削过程中薄壳零件的动力学建模
研究了高速铣削过程中航空发动机叶片的非线性振动问题，发动机叶片柔度大，并且受到切削力的作用，基于高速铣削过程中加工发动机叶片的工作状态，利用Hamilton原理建立了切削力作用下高速铣削过程中薄壳类零件的非线性动力学方程。选取了第一阶模态和第二阶模态，利用Galerkin方法对所得到的薄壳构件的偏微分方程进行了离散，得到了两自由度非线性动力学方程，用来描述系统的运动。
(2)高速铣削过程中薄壳零件非线性动力学特性的研究
分别考虑了主参数共振情况下1:1内共振和1:2内共振的情况，利用多尺度方法得到了系统的四维平均方程。基于四维平均方程，利用数值方法研究了高速铣削过程中薄壳零件的非线性动力学行为以及动态分叉特性。数值结果表明，系统的非线性动态响应幅值随着外激励的增加而非线性增加。在特定参数情况下，第二阶模态的幅值有可能大于第一阶模态的幅值。所以，只考虑第一阶模态并不能全面的反映系统非线性振动情况。通过随外激励变化的分叉图，发现系统呈现出混沌运动→周期运动→单倍周期运动→多倍周期运动→概周期运动→混沌运动的交替变化过程。从所得到的系统阻尼参数分叉图中可以看出，阻尼系数对系统的动态响应有着很大的影响，随着阻尼系数的增加系统的运动趋于稳定的周期运动。因此，可以适当的调节系统的阻尼用来抑制混沌运动的出现。
(3)高速铣削过程中薄板类零件的非线性振动和混沌运动的研究
利用Hamilton原理建立了高速铣削过程中薄板零件的非线性动力学方程。选取了第一阶模态和第二阶模态，利用Galerkin方法对所得到的切削力作用下薄板零件的偏微分方程进行了离散，得到了薄板零件的两自由度非线性动力学方程。
分别考虑主参数共振情况下1:1内共振和1:3内共振情况，利用多尺度方法得到系统的四维平均方程。基于四维平均方程，利用数值方法研究了高速铣削过程中薄板零件的非线性动力学行为及动态分叉特性。数值结果表明，系统在外激励作用下存在着混沌运动、周期运动和概周期运动。从所得到的随系统阻尼参数变化的分叉图中可以看出，阻尼系数对系统的动态响应有很大的影响。
(4)高速铣削过程中时滞参数对系统非线性振动的影响
时滞现象普遍存在于切削加工中，本文分别研究了高速铣削薄壳零件和高速铣削薄板零件非线性动力学问题中时滞的影响。根据四维平均方程，通过数值分析，研究了时滞参数对系统非线性振动的影响。通过固定其他参数并改变时滞参数，发现系统存在周期运动，混沌运动和概周期运动。系统对时滞参数的改变非常敏感，可以通过改变时滞参数来抑制系统混沌运动的出现。
The equipments that are used for modern national defense, spacecraft, aircraft,rockets, satellites, are normal made of special materials with complex finishing surfaces.The components of these equipments are impossible to be manufactured by traditionalmachines but rather by multi axis CNC machine with high speed, and high precision.Therefore, the CNC machines with high performance play a vital role in themodernization of national defense, modern aircraft and automobile industry. Thehigh precision workpieces related to the progress of China's economic development andnational defense. In the process of high speed milling, however, the thin walledworkpieces frequently have strong vibrations which can result in poor surface finishing,high rejection rate, even the machine axis damage. With the rapid development of nationaldefense, the requirement of workpieces with light weight, low stiffness and good surfaceare bloomed. So that the new technology of CNC machine are corresponding demanded.
Research on the nonlinear vibrations of thin walled workpieces during high speedmilling becomes more and more important in engineering. In this paper, the nonlinearvibrations of thin walled workpieces subjected to the cutting force in high speed millingprocess are studied by using theoretical and numerical methods. The main research field ofthis dissertation is introduces as follows.
(1) Modelling of the shell shaped workpiece during high speed milling process isestablished.
During the process of machining engine blades, the workpiece with low stiffness hasstrong vibrations which result in poor surface finishing, high rejection rates and machinedamage. Based on the milling process, the shell shaped workpiece is modeled as acantilevered thin shell subjected to the cutting force with time delay effects. Equations ofmotion are derived by using Hamilton principle based on the classical shell theory. Theresulting nonlinear partial differential equations are reduced to a two degree of freedomnonlinear system by applying the Galerkin’s approach.
(2) Nonlinear vibrations of the shell shaped workpiece during high speed millingprocess is investigated.
The averaging method is used to obtain two sets of the four dimensional averagedequations by considering the1:1and1:2internal resonances, respectively. Using thenumerical method, dynamics of the cantilevered shell shaped workpiece is studied under dumping coefficient and forcing excitation. It is concluded that there exit complexnonlinear behaviors including the chaotic motion, periodic and quasi periodic motions. Itis observed from the bifurcation diagram of forcing excitation that with the increase of theamplitude of the non dimensional forcing excitation, the motions of the cantileveredshell shaped workpiece demonstrate the following pattern: chaotic motion→periodicmotion→quasi periodic motion→chaotic motion. The nonlinear dynamic behavior of theshell shaped workpiece form the chaotic motion is controlled by varying the amplitude ofthe damping coefficient.
(3) Nonlinear vibrations, bifurcations and chaos of the thin plate workpiece duringhigh speed milling process are studied.
Because of the cutting force in the milling process, the thin plate workpiece vibratestrongly. Based on the cutting process, the thin plate workpiece is modeled as acantilevered thin plate subjected the cutting force. Applying the Hamilton principle, theequations of motion of the thin plate workpiece are derived based on Kirchhoff platetheory. Utilizing the Galerkin’s approach, the resulting equations are reduced to atwo degree of freedom nonlinear system. The method of Asymptotic Perturbation isutilized to obtain two sets of four dimensional averaged equations by considering1:1and1:3internal resonances, respectively. Using numerical simulations, the influence ofdifferent parameters on nonlinear vibrations of the thin plate workpiece is detected. It isconcluded that there exist complex nonlinear behaviors including chaotic motion, periodicmotion and periodic n motion. The motion of the system is very sensitive by varying thedumping coefficient.
(4) The influences of time delay effects on the thin walled workpiece duringhigh speed milling process are analyzed.
The statuses of the system in the past or a certain time before have impact on thecurrent system. There exists a time lag. The time delay effects frequently happen in thecutting system. In this study, based on the four dimensional averaged equations, theinfluence of time delay parameters on the thin walled workpiece is numerically analyzed.It is stated that nonlinear behaviors of the thin walled workpiece is sensitive on thevarying time delay parameters.
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