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Modelling suppression of non-linear machine vibration

Vondrich J., Thöndel E.

Journal of Machine Engineering

2009

Vol. 9, No. 2

45--50

In this paper, the coupled non-linear differential equations of the model of machine as non-linear dynamical two degree of freedom vibrating system including cubic non-linearity are solved. The system consists of the main system and the absorber. Consider the non-linearity dynamical vibrating system as a model machine, which is compiled of a driven motor, gearbox and mechanisms with elastic and damping parts and driven parts. The absorber is used to control the main system vibrations when subjected to external excitation force. This system represents many applications in machine tools, ultrasonic cutting process, etc. Optimum working conditions for the absorber are by the same frequencies ω = ω2 [1] of the action force F =F0 sinω t and main mass m1. The effects of different parameters of the system are studied numerically with Matlab.

Optimization of mounting of a machine and its parts

Vondrich J., Havlicek R.

Journal of Machine Engineering

2008

Vol. 8, No. 1

123--129

Frequency dependence values of input or mutual mechanical impedances of vibrating machines and their parts can be measured using an impedance hammer and a two-channel frequence analyzer. The knowledge of the frequency response of mechanical impedance provides for the determination of properties of vibration energy transmission in the structure of the machine based on which it is possible to adjust the mounting arrangement of the machine and its parts in order to attenuate vibrations. The obtained data concerning the dynamicbehaviour of the machine then serve as a basic for a proper design and implementation of elastic mounting of the machine and its parts on damping elements which attenuate unwanted vibrations to the minimum. The design consists in assembling a model of the machine assuming that elastic mounting has been provided for, describing the model using equations of montion and elaborating their numerical solution. An efficient damping arrangement is achieved by mounting the vibrating parts of the machine using air springs. The air pressure in the air springs can be regulated according to deflections of the individual machine parts measured by accelerometers using a control element. The numeric solution provides for determination of values of stiffness coefficients k and damping coefficient c which would be optimal for the specified machine parameters in order to minimise the defections of the individual machine parts.