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Modelling of vibration with absorber

Vondřich J., Thöndel E., Jirku S.

Journal of Machine Engineering

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2010

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Vol. 10, No. 4

100--105

EN

Machine vibration occurs as a result of unbalanced revolving masses, loading forces and moments, starting and coasting of driving motors and other effects. We try to eliminate these undesirable vibrations by suitable mounting of the mechanical system. Another possibility of suppression of the vibration machine is to use an absorber. A model of a vibration mechanical system with a vibration absorber is presented in the paper. The model consists of a fixed-end vibrating beam with primary vibrating mass M and with stiffness K and damping B. The harmonic force F with frequency ? and amplitude A acts on the primary mass M as well as on the beam with stiffness k and damping b, where the secondary mass m of the absorber is mounted. The task of the absorber is to minimize the movement of the mass M. A model (Fig. 1) has two degrees of freedom X and x. Two equations describe the movement of the primary mass M and the secondary mass m of the absorber. The model is solved first numerically by using Simulink. In numerical solution it is possible to set up parameters of the mechanical system with respect to the vibration reduction. According to the mechanical requirements for the mechanical system (output trajectory, velocity, forces and torques acting on the individual parts of the system), it is also possible to design input parameters (driving torques and other parameters of the mechanical system). A experimental model will be designed in order to verify results, where a voice-coil will be used as the actuator of the force F Numerical and experimental model allows changing parameters i.e. masses M and m, length L and l of the beams and frequency ? of the excitation force F. The results from the numerical solution are then possible to compare with the measured values of the experimental model. It is assumed that the experimental model will be equipped with accelerometers enabling the measuring of vibration, which will be placed on the masses M and m.

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Modelling suppression of non-linear machine vibration

Vondrich J., Thöndel E.

Journal of Machine Engineering

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2009

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Vol. 9, No. 2

45--50

EN

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.

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Machine vibrations with more degrees of freedom

Vondřich J., Thöndel E.

Journal of Machine Engineering

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2008

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Vol. 8, No. 4

80--87

EN

Rigid mounting of machines to a solid base is one of the requirements for high performance and quality of production. Machine vibrations occur as a result of unbalanced revolving masses, loading forces and moments, starting and coasting of driving motors and other effects. We try to eliminate these undesirable vibrations by suitable mounting of the machine and its parts as much as possible. Suitable mounting of the machine is possible using components such as torsion springs, pneumatic springs, rubber pads or other components. The article describes numerical calculation of optimal displacements the machine for the given his parameters.