Patent ID: 8113048
Filing Date: 2012-02-14
Classification: G01M

Abstract:
1. A dynamic balancing method using a linear time-varying angular velocity model, comprising: rotating a rotational shaft, on which a rotational body having a rotating unbalanced mass is installed, at a linear time-varying angular velocity; measuring vibration generated by tangential force, centrifugal force, or the two forces generated by the rotating unbalanced mass of the rotational body from the support which supports the rotational shaft rotated at the linear time-varying angular velocity; estimating multiple frequency components of a measurement signal corresponding to the measured normal and centrifugal forces; and estimating the angular position, that is the angle, and the magnitude of the unbalanced mass of the rotational body using components of the measured tangential and centrifugal forces and characteristics of the frequency components (or Fourier coefficients) of the two forces, wherein the angular position and magnitude of the unbalanced mass of the rotational body is determined by the following equation: wherein F x (t) is the horizontal component of each of the tangential force F t and the centrifugal force F n acting on the support by the rotating unbalanced mass of the rotational body; F y (t) is the vertical component of each of the tangential force F t and the centrifugal force F n generated acting on the support by the rotating unbalanced mass of the rotational body; m[kg] is the rotating unbalanced mass of the rotational body; r[m] is a distance of the rotating unbalanced mass of the rotational body, which is spaced apart from the center of rotational shaft; a[radians/s] is an initial rotational velocity; b[radians/s 2 ] is a constant angular acceleration at the initial rotational velocity; θ(t) is an angular displacement of the rotational shaft; and θ 0 [radians] is an angular position from the rotation reference point of the rotational shaft wherein the angular position and magnitude of the unbalanced mass of the rotational body is determined by the following equation using the tangential and centrifugal forces, which are measured in the support and applied in the horizontal and vertical directions, wherein C Fx is the cosine component corresponding to Fourier coefficients of the horizontal component of the tangential force and the centrifugal force acting on the support by the rotating unbalanced mass of the rotational body, and S Fx is the sine component corresponding to Fourier coefficients of the horizontal component of the tangential and centrifugal forces acting on the support by the rotating unbalanced mass of the rotational body, and these components are determined by the following equation: and k is an integer indicating the order of Fourier coefficients, C Fy is the cosine component corresponding to Fourier coefficients of the vertical component of the tangential and centrifugal forces acting on the support by the rotating unbalanced mass of the rotational body, and S Fy is the sine component corresponding to Fourier coefficients of vertical components of the tangential and centrifugal forces acting on the support by the rotating unbalanced mass of the rotational body, and these components are determined by the following equation: and U cos is the cosine component of the unbalanced amount (U cos =mr·cos(θ 0 )) and U sin is the sine component of the unbalanced amount (U sin =mr·sin(θ 0 )), wherein the angular position and magnitude of the unbalanced mass of the rotational body is determined by the following equation using the tangential and centrifugal forces applied in the horizontal direction, wherein C Fx is the cosine component corresponding to Fourier coefficients of the horizontal component of the tangential and centrifugal forces acting on the support by the rotating unbalanced mass of the rotational body, and S Fx is the sine component corresponding to Fourier coefficients of the horizontal component of the tangential and centrifugal forces acting on the support by the rotating unbalanced mass of the rotational body, and these components are determined by the following equation: and k is an integer indicating the order of the Fourier coefficient, U cos is the cosine component of the unbalanced amount (U cos =mr·cos(θ 0 )) and U sin is the sine component of the unbalanced amount (U sin =mr·sin(θ 0 )), and wherein a measurement signal sampling method exploits a sampling pulse having a constant time width (Δt=constant) and then measures applied force signals of the support using the following equation: wherein C n and D n are a period of the reference pulse and a digital value used in measuring an observing time of a first sampling pulse after the reference pulse, ΔT is a period of a base clock used in measuring a period of the reference position pulse, T n is n-th revolution period, and d n is a fractional part of a sampling period, d n is a fractional part of a sampling period, and d n ·Δt is a time interval between an n-th reference position pulse and a sampling pulse, and M n is the number of signals sampled during one revolution, and C