Design of an optimal damper to minimize the vibration of machine tool structures subject to random excitation
The vibration of machine tools during machining adversely affects machining accuracy and tool life, and therefore must be minimized. The cutting forces for stable turning are generally known to be random, and hence excite all the resonance modes. Of all these modes, those that generate relative motions between a cutting tool and a workpiece are of concern.This paper presents a new approach for designing an optimal damper to minimize the relative vibration between the cutting tool and workpiece during stable machining. An approximate normal mode method is employed to calculate the response of a machine tool system with nonproportional damping subject to random excitation. The major advantage of this method is that it reduces the amount of computation greatly for higher-order systems when responses have to be calculated repeatedly in the process of optimization. An optimal design procedure is presented based on a representative lumped parameter model that can be constructed by using existing experimental or analytical techniques. The two-step optimization procedure based on the modified pattern search and univariate search effectively leads the numerical solution to the global minimun irrespectively of initial values even under the existence of many local minima.
Dynamic analysis of machine tool structureswith applied damping treatment
Abstract Machine tool structures have been analysed in the past using finite element method to study and improve their rigidity. The structural damping of the machine tool structure plays an important role in governing the dynamic properties of the structure. However, it has been reported that attempts have been made experimentally to establish that improvement can be attained by applied damping treatment using viscoelastic layers. A theoretical study on the vibrations of machine tool structures with applied damping treatment has been carried out in this investigation using a conventional beam element. The complex nature of the Young's modulus of the layer material has been accounted for in the derivation of the stiffness matrix. Simultaneous iteration technique has been extended to evaluate the complex eigenvalues. Models of milling machine, radial drilling machine and lathe have been analysed for their natural frequencies and loss factors. Influence of layering treatment on the natural frequencies and loss factors has been discussed. In addition to uniform layering, staggering of layers have also been attempted.
Estimation of structural parameters from dynamic test data
Parameters for a lumped linear model approximating a distributed elastic structure are determined from dynamic test data comprised of several mode shapes and frequencies. Measurement errors, nonlinear response, and nonmeasurable quantities such as mode slope components are accommodated. Some mass and stiffness parameters may be known accurately, whereas the remainder are to be estimated. The method entails minimizing a quadratic function of the difference between corresponding modes and frequencies of the theoretical model and the test specimen. This technique was applied to some actual vibration test data, and the special techniques that are required to overcome convergence problems are described.