Modeling of Compressor Vibration for Improved Dynamic Design

The two main sources contributing to scroll compressor vibration at running frequency are the residual rotational unbalance in the crank-rotor assembly and the reciprocating force due to the Oldham ring. The intent of this paper is to develop a rigid body model of the compressor vibrating on resilient grommets. This model is a design tool capable of identifying the sensitivity, of the steady-state vibration levels, to manufacturing process tolerances of counterweight and crank-rotor parts. Other capabilities of the model include prediction of transient start-up vibration thus identifying key parameters for its control. Also using this model one can predict any potential resonances that could occur with new compressor design supported on standard grommets; this enables us to modify the existing grommet designs to tune away the resonances and also provide the vibration isolation desired. INTRODUCTION The two main mechanical components contributing to the scroll compressor vibration are the residual rotational unbalance in the crank-rotor assembly and the reciprocating force due to the Oldham ring. It has been observed that the compressor vibration at the running frequency is primarily a rigid body mode. Hence the intent of this analysis is to develop a simple model based on the concept of a rigid body (entire compressor) vibrating on resilient supports or grommets. In order to simplify the analysis symmetry is assumed leading to the uncoupling of some of the modes of vibration. The periodic excitation sources for this model are the residual rotating unbalance which can be obtained from measurements on a balancing machine or from an estimation of the process tolerances in the assembly of the crank-rotor and counterweight parts, as well as a residual reciprocating force due to the Oldham ring. VIBRATION MODEL Figure la shows a schematic of the compressor mounted on grommets and Figure lb shows the relevant dimensions used in the vibration model as well as the gronunet shear ( Ks )and compression stiffnesses ( K v ). The governing equations for a rigid body on resilient supports can be derived from using a Lagrangian approach and is given below in matrix differential equation form (neglecting damping) as: Mii+Ku=F (1) M=diag[me 4 u={ux e zf (2a-c) me me fx ly Iz]; K= l:rJsri; Uy Uz ex By I= I rj=[~ 0 0 0 -LG -rf sin(a j] [Ks 0 ~ l aj =a0 +U-1)~ 1 0 LG 0 r1 cos( a) ; S = 0 Ks (3a-c) 0 1 r1 sin(a i) -r1 cos(a) 0 0 0 Kv