Dynamic analysis and active vibration control of axially moving materials by wave propagation method

Belt and chain drives are commonly employed to transmit power in machinery and automobile accessories. Despite the many advantages of these drives, vibrations and noise generation associated with the drive motion have limited their use and are usually detrimental to their function, especially in high-speed operations and when lighter and higher quality components are required. For high speed and precision applications, it is thus necessary to introduce control methods to attenuate the vibration of the translating element. Although the focus of the proposed research is on vibration and control of belt and chain drive systems, our research findings may be useful for other industrial applications and may have important implications for the design of other high-speed, axially moving mechanical systems.; In this work, we present an exact solution for the linear, transverse response of an axially moving string with general boundary conditions. The solution is derived in the frequency domain and interpreted in terms of wave propagation functions. The boundary effects are included by the use of boundary reflection functions at the boundaries. The response in the time domain involves only several convolution integrals which can easily be obtained for many physical boundary conditions. The transient response of the translating string with a spring or a dashpot at a boundary is presented.; Active vibration control of an axially moving string using space feedforward and feedback controllers is presented. The space feedforward controller is established by employing the idea of wave cancellation. The proposed control law indicates that vibration in the region near to boundaries can be canceled. With the space feedforward control, the mode shapes of the axially moving string are changed such that the free response tends to zero in the region close to boundaries. An interesting physical interpretation is that the control force acts effectively as a holder (active support) which limits the vibration of the string to the upstream region and eliminates any vibration in the downstream region. Simulation results show that the response of the string to both sinusoidal and random excitations is suppressed by applying the space feedforward control. The feedback controller is introduced to attenuate the response of the string due to undesired disturbances in the downstream.; In order to achieve an effective real time control, the stability of the control law is discussed in this research. A modified control strategy leads to an implementable controller which is stable and robust. Experiments were performed on a laboratory belt/chain drive test stand. The experimental results demonstrate the effectiveness, stability and robustness of the proposed feedforward controller.