Attività

The simplified theoretical and finite element model of the two kinds of two-stage mounting systems are analysed in the paper. The equation of two kinds of mounting systems’ isolation effectiveness expressed by transmissibility were deduced through four-pole parameter method. A comparison between the Single Pole Mounting System to ascertain the difference about vibration isolation efficiency at different specific frequency through FEM model analysis was made. A scale experimental platform was established to test the isolation efficiency of the two-stage mounting system having distributed intermediate mass.

The research results based on the calculation and analysing on the two kinds of mounting systems can provide a reference for engineer when designing mounting system for machinery equipment.

2. Mounting system theoretical model

2.1. Basic theory of four-pole parameters method

The behaviour of mounting systems is complicated and extremely hard to predict because of wave effects. To depict the behaviour of system’ dynamic performance is difficult so that to simplify practical mounting system is necessary .

Four–pole parameters method is an essentially simple idea and for this reason is helpful in providing a point of view . All of the pertinent properties of a system can be expressed in terms of four pole parameters which characterize only the system for which they are determined; their value is not influenced by the preceding or subsequent mechanical systems.

A linear mechanical system is shown schematically in Fig. 1. The system may be comprised one or more lumped or distributed elements, or be constructed from any combination of such elements. The input side of the system vibrates sinusoidally with a velocity  in response to an applied force . In turn, the output side of the system exerts a force  on the input side of some further system, sharing with it a common velocity . Thus the system shown is said to have input and output terminal pairs, a force  and velocity  at the input terminal pair giving rise to a force  and velocity  at the output terminal pair, the reaction of any subsequent mechanical system being accounted for. Forces are considered positive when directed to the right .

Isolators made of hard elastic material were used in the upper mount whose natural frequency were about 8 Hz and stiffness is 1.5×10e6 N/m, damping factor 0.09. Air spring was used in the lower mount whose natural frequency was about 4 Hz, stiffness is 10e6 N/m and damping factor 0.05. Intermediate mass amounts about 20 % of the total mass of the upper body including a vibration generator to simulate vibration source and rack to hold it. The vibration generator generates vibration at a precise frequency. The isolation effectiveness expressed by acceleration tested by PULSE exploited by Brüel&Kjær was shown in Table 1. All of the measurements summarized here were obtained after post-process using Pulse Reflex, driven by1/3 octave band filtered white noise, and by measuring 1/3 octave bands. Experimental results showed that satisfactory isolation effectiveness evaluated by vibration lever difference could be obtained by using distributed intermediate mass as frame structure intermediate mass does.

To compare the isolation effectiveness of two-stage mounting system having integral intermediate mass with distributed intermediate mass. FEMs of the two types of mounting system was designed based on the scale experimental prototype having distributed intermediate mass was set up through ABAQUS as is shown in Fig. 10 and Fig. 11. Q235 whose density  7800 kg/m3, elasticity modulus  200 GPa, Poisson’s ratio  0.3 was used as the material of foundation, intermediate mass and rack to install a vibration generator. The upper and lower isolators were simulated by spring with three dimensional stiffness and both ends of the spring were six degrees of freedom coupling constrained to the foundation, upper rack and intermediate mass with its actual contract area respectively. Data of isolators’ three dimensional stiffness was obtained through practical testing so that can be used as input parameters. The foundation was six degrees of freedom coupling constrained to the ground.

In this paper, four-pole parameter method and numerical calculation method were used to analyse the two types of two-stage mounting systems and a scale prototype was designed to test isolation effectiveness of two-stage mounting system having distributed intermediate mass. Results showed: