tailieunhanh - The balancing of rotating machinery as nonlinear system

In this paper a method for dynamical balancing of rotating machines as nonlinear system is proposed. After analysing and identifying the nonlifiear system, procedure of dynamical balance including measurement and processing of vibration signals, for calculating magnitude and location of imbalance mass is presented. An example or simulation and calculation is investigated for illustration of the method. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. 21, 1999, No 3 {165 - 172) THE BALANCING OF ROTATING MACHINERY AS NONLINEAR SYSTEM NGUYEN CAO MENH Institute of Mechanics, Hanoi j. ABSTRACT. In this paper a method for dynamical balancing of rotating machines a nonlinear system is proposed. After analysing and identifying the nonlifiear system, procedure of dynamical balance including measurement and processing of vibration signals, for calculating magnitude and location of imbalance mass is presented. An example simulation and calculation is investigated for illustration of the method. or 1. Introduction One of the main causes of machinery vibration is imbalance of rotational parts. The dynamical balancing of rotat ing machines has been developing for new kinds of machines with high speed and improving balancing results more exactlx and quickly. The system of machines with its rotational part is usually regarde AO - - - - 3. Balancing rotational part on non-linear system . Equation of motion Let us investigate the system in Fig. 2 If the system has imbalance mass m4 with distance r from shaft line and the stiffness of the system is described by function f (x) then the differential equation of motion in the direction of axis X is governed as follows •. + ht± + /(~) Denoting f(x) ma we have hl ma = m4rwi cos w1t () = 2hwo, = w5x + g(x), m4r ma = P, Fig. 2 x + 2hwo± + w5x + g(x) = Pwi cosw1t. 166 () In practice the function f(x) and therefore the function g(x) is symmetric for two sides of vibratioP with respect to axis X, therefore in matheiiiaticaLexpression · the function f (x) is odd, that means f( -x) = - f(x) Then the expand of g( x) is of the form () Since the vibration of the system is supposed to be small, then we restrict ourself by first term and the equation (2) becomes ( where h, wo, Wt are given constants and b3 is to be determined below. . Identification of the system by measurement .