Studies Of Nonlinear Vibrations For Thin-walled Workpiece During High-speed Milling Process

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 motionâ†'periodicmotionâ†'quasi periodic motionâ†'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.