The Experts below are selected from a list of 5793 Experts worldwide ranked by ideXlab platform

I Y Shen - One of the best experts on this subject based on the ideXlab platform.

  • closed form vibration response of a special class of spinning cyclic symmetric rotor Bearing Housing systems
    Journal of Vibration and Acoustics, 2015
    Co-Authors: Weiche Tai, I Y Shen
    Abstract:

    Vibration of a spinning, cyclic symmetric rotor supported by flexible Bearings and Housing is governed by a set of ordinary differential equations with periodic coefficients. As a result, analytical solutions of such systems are generally not available. This paper is to prove that closed-form solutions are available for such systems if the following two conditions are met. First, the rotor has a rigid hub and the rest of the rotor is flexible. Second, elastic mode shapes of the rotor's flexible part only present axial displacement. Under these two conditions, the periodic coefficients will only appear between repeated modes of the spinning rotor and vibration modes of the stationary Housing. This unique structure enables a coordinate transformation to convert the governing ordinary differential equations with periodic coefficients into a set of ordinary differential equations with constant coefficients, whose closed-form solution is readily available. Moreover, the coordinate transformation can be derived explicitly. Finally, we demonstrate the closed-form solution through a benchmark numerical model that consists of a spinning rotor, a stationary Housing, and two elastic Bearings. In particular, the rotor is a circular disk with four evenly spaced radial slots and a central rigid hub. The Housing is a square plate with a central rigid shaft and is fixed at four corners. The two elastic Bearings connect the rotor and the Housing between the hub and shaft. Numerical results confirm that the original equation of motion with periodic coefficients and the closed-form solutions predict the same vibration response.

  • ground based response of a spinning cyclic symmetric rotor assembled to a flexible stationary Housing via multiple Bearings
    ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC CIE 2013, 2013
    Co-Authors: Weiche Tai, I Y Shen
    Abstract:

    This paper is to study free response of a spinning, cyclic symmetric rotor assembled to a flexible Housing via multiple Bearings. In particular, the rotor spins at a constant speed ω3, and the Housing is excited via a set of initial displacements. The focus is to study ground-based response of the rotor through theoretical and numerical analyses. The paper consists of three parts. The first part is to briefly summarize an equation of motion of the coupled rotor-Bearing-Housing systems for the subsequent analyses. The equation of motion, obtained from prior research [1], employs a ground-based and a rotor-based coordinate system to the Housing and the rotor, respectively. As a result, the equation of motion takes the form of a set of ordinary differential equations with periodic coefficients of frequency ω3. To better understand its solutions, a numerical model is introduced as an example. In this example, the rotor is a disk with four radial slots and the Housing is a square plate with a central shaft. The rotor and Housing are connected via two ball Bearings. The second part of the paper is to analyze the rotor’s response in the rotor-based coordinate system theoretically. When the rotor is at rest, let ωH be the natural frequency of a coupled rotor-Bearing-Housing mode whose response is dominated by the Housing. The theoretical analysis then indicates that response of the spinning rotor will possess frequency components ωH ± ω3 demonstrating the interaction of the spinning rotor and the Housing. The theoretical analysis further shows that this splitting phenomenon results from the periodic coefficients in the equation of motion. The numerical example also confirms this splitting phenomenon. The last part of the paper is to analyze the rotor’s response in the ground-based coordinate system. A coordinate transformation shows that the ground-based response of the spinning rotor consists of two major frequency branches ωH − (k + 1) ω3 and ωH − (k − 1) ω3, where k is an integer determined by the cyclic symmetry and vibration modes of interest. The numerical example also confirms this derivation.Copyright © 2013 by ASME

  • parametric resonances of a spinning cyclic symmetric rotor assembled to a flexible stationary Housing via multiple Bearings
    ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC CIE 2012, 2012
    Co-Authors: Weiche Tai, I Y Shen
    Abstract:

    This paper is to present findings from a theoretical study on free vibration and stability of a rotor-Bearing-Housing system. The rotor is cyclic symmetric and spinning at constant speed, while the Housing is stationary and flexible. Moreover, the rotor and Housing are assembled via multiple, linear, elastic Bearings. For the rotor and the Housing, their mode shapes are first obtained in rotor-based and ground-based coordinate systems, respectively. By discretizing the kinetic and potential energies of the rotor-Bearing-Housing system through use of the mode shapes, a set of equations of motion appears in the form of ordinary differential equations with periodic coefficients. Analyses of the equations of motion indicate that instabilities could appear at certain spin speed in the form of combination resonances of the sum type. To demonstrate the validity of the formulation, two numerical examples are studied. For the first example, the spinning rotor is an axisymmetric disk and the Housing is a square plate with a central shaft. Moreover, the rotor and the Housing are connected via two linear elastic Bearings. Instability appears in the form of coupled vibration between the stationary Housing and spinning rotor through three different formats: rigid-body rotor translation, rigid-body rotor rocking, and elastic rotor modes that present unbalanced inertia forces or moments. For the second example, the rotor is cyclic symmetric in the form of a disk with four evenly spaced slots. The Housing and Bearings remain the same. When the rotor is stationary, natural frequencies and mode shapes predicted from the formulation agree well with those predicted from a finite element analysis, which further ensures the validity of the formulation. When the cyclic symmetric rotor spins, instability appears in the same three formats as in the case of axisymmetric rotor. Number of instability zones, however, increases because the cyclic symmetric rotor has more elastic rotor modes that present unbalanced inertia forces or moments.Copyright © 2012 by ASME

Weiche Tai - One of the best experts on this subject based on the ideXlab platform.

  • closed form vibration response of a special class of spinning cyclic symmetric rotor Bearing Housing systems
    Journal of Vibration and Acoustics, 2015
    Co-Authors: Weiche Tai, I Y Shen
    Abstract:

    Vibration of a spinning, cyclic symmetric rotor supported by flexible Bearings and Housing is governed by a set of ordinary differential equations with periodic coefficients. As a result, analytical solutions of such systems are generally not available. This paper is to prove that closed-form solutions are available for such systems if the following two conditions are met. First, the rotor has a rigid hub and the rest of the rotor is flexible. Second, elastic mode shapes of the rotor's flexible part only present axial displacement. Under these two conditions, the periodic coefficients will only appear between repeated modes of the spinning rotor and vibration modes of the stationary Housing. This unique structure enables a coordinate transformation to convert the governing ordinary differential equations with periodic coefficients into a set of ordinary differential equations with constant coefficients, whose closed-form solution is readily available. Moreover, the coordinate transformation can be derived explicitly. Finally, we demonstrate the closed-form solution through a benchmark numerical model that consists of a spinning rotor, a stationary Housing, and two elastic Bearings. In particular, the rotor is a circular disk with four evenly spaced radial slots and a central rigid hub. The Housing is a square plate with a central rigid shaft and is fixed at four corners. The two elastic Bearings connect the rotor and the Housing between the hub and shaft. Numerical results confirm that the original equation of motion with periodic coefficients and the closed-form solutions predict the same vibration response.

  • ground based response of a spinning cyclic symmetric rotor assembled to a flexible stationary Housing via multiple Bearings
    ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC CIE 2013, 2013
    Co-Authors: Weiche Tai, I Y Shen
    Abstract:

    This paper is to study free response of a spinning, cyclic symmetric rotor assembled to a flexible Housing via multiple Bearings. In particular, the rotor spins at a constant speed ω3, and the Housing is excited via a set of initial displacements. The focus is to study ground-based response of the rotor through theoretical and numerical analyses. The paper consists of three parts. The first part is to briefly summarize an equation of motion of the coupled rotor-Bearing-Housing systems for the subsequent analyses. The equation of motion, obtained from prior research [1], employs a ground-based and a rotor-based coordinate system to the Housing and the rotor, respectively. As a result, the equation of motion takes the form of a set of ordinary differential equations with periodic coefficients of frequency ω3. To better understand its solutions, a numerical model is introduced as an example. In this example, the rotor is a disk with four radial slots and the Housing is a square plate with a central shaft. The rotor and Housing are connected via two ball Bearings. The second part of the paper is to analyze the rotor’s response in the rotor-based coordinate system theoretically. When the rotor is at rest, let ωH be the natural frequency of a coupled rotor-Bearing-Housing mode whose response is dominated by the Housing. The theoretical analysis then indicates that response of the spinning rotor will possess frequency components ωH ± ω3 demonstrating the interaction of the spinning rotor and the Housing. The theoretical analysis further shows that this splitting phenomenon results from the periodic coefficients in the equation of motion. The numerical example also confirms this splitting phenomenon. The last part of the paper is to analyze the rotor’s response in the ground-based coordinate system. A coordinate transformation shows that the ground-based response of the spinning rotor consists of two major frequency branches ωH − (k + 1) ω3 and ωH − (k − 1) ω3, where k is an integer determined by the cyclic symmetry and vibration modes of interest. The numerical example also confirms this derivation.Copyright © 2013 by ASME

  • parametric resonances of a spinning cyclic symmetric rotor assembled to a flexible stationary Housing via multiple Bearings
    ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC CIE 2012, 2012
    Co-Authors: Weiche Tai, I Y Shen
    Abstract:

    This paper is to present findings from a theoretical study on free vibration and stability of a rotor-Bearing-Housing system. The rotor is cyclic symmetric and spinning at constant speed, while the Housing is stationary and flexible. Moreover, the rotor and Housing are assembled via multiple, linear, elastic Bearings. For the rotor and the Housing, their mode shapes are first obtained in rotor-based and ground-based coordinate systems, respectively. By discretizing the kinetic and potential energies of the rotor-Bearing-Housing system through use of the mode shapes, a set of equations of motion appears in the form of ordinary differential equations with periodic coefficients. Analyses of the equations of motion indicate that instabilities could appear at certain spin speed in the form of combination resonances of the sum type. To demonstrate the validity of the formulation, two numerical examples are studied. For the first example, the spinning rotor is an axisymmetric disk and the Housing is a square plate with a central shaft. Moreover, the rotor and the Housing are connected via two linear elastic Bearings. Instability appears in the form of coupled vibration between the stationary Housing and spinning rotor through three different formats: rigid-body rotor translation, rigid-body rotor rocking, and elastic rotor modes that present unbalanced inertia forces or moments. For the second example, the rotor is cyclic symmetric in the form of a disk with four evenly spaced slots. The Housing and Bearings remain the same. When the rotor is stationary, natural frequencies and mode shapes predicted from the formulation agree well with those predicted from a finite element analysis, which further ensures the validity of the formulation. When the cyclic symmetric rotor spins, instability appears in the same three formats as in the case of axisymmetric rotor. Number of instability zones, however, increases because the cyclic symmetric rotor has more elastic rotor modes that present unbalanced inertia forces or moments.Copyright © 2012 by ASME

Wengang Chen - One of the best experts on this subject based on the ideXlab platform.

  • Direct load monitoring of rolling Bearing contacts using ultrasonic time of flight
    Proceedings of the Royal Society A: Mathematical Physical and Engineering Science, 2015
    Co-Authors: R Mills, Wengang Chen, Rob S Dwyer-joyce
    Abstract:

    The load applied by each rolling element on a Bearing raceway controls friction, wear and service life. It is possible to infer Bearing load from load cells or strain gauges on the shaft or Bearing Housing. However, this is not always simply and uniquely related to the real load transmitted by rolling elements directly to the raceway. Firstly, the load sharing between rolling elements in the raceway is statically indeterminate, and secondly, in a machine with non-steady loading, the load path is complex and highly transient being subject to the dynamic behaviour of the transmission system. This study describes a method to measure the load transmitted directly by a rolling element to the raceway by using the time of flight (ToF) of a reflected ultrasonic pulse. A piezoelectric sensor was permanently bonded onto the bore surface of the inner raceway of a cylindrical roller Bearing. The ToF of an ultrasonic pulse from the sensor to the roller–raceway contact was measured. This ToF depends on the speed of the wave and the thickness of the raceway. The speed of an ultrasonic wave changes with the state of the stress, known as the acoustoelastic effect. The thickness of the material varies when deflection occurs as the contacting surfaces are subjected to load. In addition, the contact stiffness changes the phase of the reflected signal and in simple peak-to-peak measurement, this appears as a change in the ToF. In this work, the Hilbert transform was used to remove this contact dependent phase shift. Experiments have been performed on both a model line contact and a single row cylindrical roller Bearing from the planet gear of a wind turbine epicyclic gearbox. The change in ToF under different Bearing loads was recorded and used to determine the deflection of the raceway. This was then related to the Bearing load using a simple elastic contact model. Measured load from the ultrasonic reflection was compared with the applied Bearing load with good agreement. The technique shows promise as an effective method for load monitoring in real-world Bearing applications.

Rob S Dwyer-joyce - One of the best experts on this subject based on the ideXlab platform.

  • Direct load monitoring of rolling Bearing contacts using ultrasonic time of flight
    Proceedings of the Royal Society A: Mathematical Physical and Engineering Science, 2015
    Co-Authors: R Mills, Wengang Chen, Rob S Dwyer-joyce
    Abstract:

    The load applied by each rolling element on a Bearing raceway controls friction, wear and service life. It is possible to infer Bearing load from load cells or strain gauges on the shaft or Bearing Housing. However, this is not always simply and uniquely related to the real load transmitted by rolling elements directly to the raceway. Firstly, the load sharing between rolling elements in the raceway is statically indeterminate, and secondly, in a machine with non-steady loading, the load path is complex and highly transient being subject to the dynamic behaviour of the transmission system. This study describes a method to measure the load transmitted directly by a rolling element to the raceway by using the time of flight (ToF) of a reflected ultrasonic pulse. A piezoelectric sensor was permanently bonded onto the bore surface of the inner raceway of a cylindrical roller Bearing. The ToF of an ultrasonic pulse from the sensor to the roller–raceway contact was measured. This ToF depends on the speed of the wave and the thickness of the raceway. The speed of an ultrasonic wave changes with the state of the stress, known as the acoustoelastic effect. The thickness of the material varies when deflection occurs as the contacting surfaces are subjected to load. In addition, the contact stiffness changes the phase of the reflected signal and in simple peak-to-peak measurement, this appears as a change in the ToF. In this work, the Hilbert transform was used to remove this contact dependent phase shift. Experiments have been performed on both a model line contact and a single row cylindrical roller Bearing from the planet gear of a wind turbine epicyclic gearbox. The change in ToF under different Bearing loads was recorded and used to determine the deflection of the raceway. This was then related to the Bearing load using a simple elastic contact model. Measured load from the ultrasonic reflection was compared with the applied Bearing load with good agreement. The technique shows promise as an effective method for load monitoring in real-world Bearing applications.

Kwonhee Kim - One of the best experts on this subject based on the ideXlab platform.

  • electrical monitoring of mechanical looseness for induction motors with sleeve Bearings
    IEEE Transactions on Energy Conversion, 2016
    Co-Authors: Junyeong Jung, Sang Bin Lee, Chaewoong Lim, Chang Hee Cho, Kwonhee Kim
    Abstract:

    Mechanical looseness in induction motors is a common problem caused by loose bolts, structural damage, improper fit, or increased clearance between components, and results in increased vibration and wear. Detection of mechanical looseness in the sleeve Bearing of industrial motors mainly relies on vibration analysis. However, there are many motor applications in the field where vibration analysis cannot be applied due to cost, environmental, and/or sensitivity limitations. The feasibility of using existing voltage/current measurements available in the motor control center for remote, low-cost monitoring of mechanical looseness due to improper fit between the Bearing-Housing and Bearing-shaft is evaluated in this paper. It is shown through experimental testing on a custom built sleeve Bearing test setup and on a 6.6 kV, 2250 hp motor that monitoring of the one-half and one-third subsynchronous components in the instantaneous power spectrum can serve as a reliable indicator of mechanical looseness.