Simulation and experiment research of vibration characteristic on star compressor

2.1. Structural characteristic

The common star compressor are three-star or four-star type. Their common characteristic is that there is only one crank. The piston is distributed around the vertical crankshaft. The original motor is integrated, which owns high speed and good operation economy. The compressor studied in this paper adopts a single-acting four-stage compression structure. Four connecting rods are arranged side by side on the vertical crankshaft. The piston is radially distributed around the crankshaft every 90 degree. Fig. 1 shows the schematic diagram of the structure. The arrangement greatly shorts the length of the crankshaft, which improves the natural frequency of the crankshaft to a certain extent, and makes the structure of the whole machine more compact. Inertia force of the piston gets a better balance by two pairs of connecting rods locating at both ends of the crank symmetrically [8].

Fig. 1Schematic diagram of star compressor structure

2.2. Dynamic modeling of crank-connecting mechanism

A compressor consists of many parts. In order to facilitate dynamic modeling and calculation, the piston assembly, connecting rod assembly and crankshaft assembly are simplified into three-dimensional assembly model by four pistons, four connecting rods and one crankshaft by Boolean operation. The three-dimensional model is saved as *.x_t file and imported into ADAMS/View. The piston and connecting rod, connecting rod and crankshaft, crankshaft and ground are connected by rotating pair, and the piston and ground are connected by moving pair. The rotation drive speed 1480 r/min is loaded on the rotational pair of crankshaft and ground. At the same time, gravity is applied to the whole system. Then the dynamic model of crank-connecting rod mechanism is obtained, as it is shown in Fig. 2. The mass of piston assembly is 4 kg, the mass of connecting rod assembly is 5 kg, the mass of crankshaft is 30 kg, and the mass of balance weight is 5.83 kg. Because the influence of flexible crankshaft on the moving pair is not so great compared with rigid crankshaft, the dynamic analysis of rigid crankshaft is adopted in this paper [9].

Fig. 2Dynamic model of crank-connecting rod mechanism

2.3. Modal analysis

The differential equation of crankshaft vibration is described as [4]:

where $\left[M\right]$, $\left[C\right]$ and $\left[K\right]$ are the mass matrix, damping matrix and stiffness matrix respectively, $\left\{\ddot{X}\right\}$, $\left\{\dot{X}\right\}$ and $\left\{X\right\}$ are the acceleration matrix vector, velocity matrix vector and displacement matrix vector respectively, $\left\{F\right\}$ is the load matrix vector.

The influence of damping $\left[C\right]$ on modal shapes and modal frequencies can be neglected. In a free vibration status, we ignore the external force in Eq.1, namely $\left\{F\right\}=\left\{0\right\}$. So, the Eq. (1) can be written as:

When the structure at free vibration status is under natural frequency, substituting $\left\{X\right\}=\left\{A\right\}\mathrm{s}\mathrm{i}\mathrm{n}(\omega t+\phi )$, we can get the basic equation of the modal analysis without damping as:

When the equation has nonzero solution, the condition $\left|\left[K\right]-{\omega }^2\left[M\right]\right|=0$ must be satisfied. Characteristic root ${\omega }_i$ is the natural frequency of the structure, characteristic vector $\left\{A_i\right\}$ is the corresponding mode. Because of the irregular shape of the crankshaft, it is difficult to solve the differential equation. Therefore, the finite element method is used to solve the problem, and the experiment is used to verify it.

5.1. Finite element modeling

Since the actual compressor block structure is complex, some structures need to be simplified in the process of establishing the finite element model. The simplification of solid three-dimensional model mainly includes the following steps. Firstly, remove structural external attachments, such as pipelines, condensers and oil-water separators, and adding them as a concentrated mass to the nodal located near the corresponding installation holes. Secondly, remove crank-connecting rod mechanism. The force acting on the body is loaded by the dynamic analysis of the crank and connecting rod. Thirdly, delete structural details. Remove oil holes, most bolt holes and air valves which have little influence on the whole structure. Fourthly, the structure is simplified. The motor is replaced by shell pulled out from cylinder, which only guarantees the mass is equal. The crankcase cover plate and the crankcase, the motor and the crankcase, the crankcase and the base are all integrated by boolean operation [11].

The three-dimensional model is imported into Abaqus, and the tetrahedron C3D10 element is used for meshing. In order to balance the calculation accuracy and time, the number of elements is 81555 and the number of nodes is 140691. The coupling between the motion pair and the cylinder sleeve is carried out by MPC. The four isolators between the base and the ground are replaced by springs with corresponding stiffness 1.52e6 N/m. The finite element model is obtained in Fig. 6. The body is made of material QT450, the base is made of QT235, and the spring between the body and the raft seat is replaced by 1e8N/m, which is closed to the stiffness of the material in order of magnitude.

Fig. 6Compressor finite element model and measuring point location

5.2. Result analysis

The experimental equipment are LMS acquisition card， notebook computer, and DYTRAN 3055B2T acceleration transducer. The location of acceleration point is shown in Fig. 7. Sampling frequency is set as 25.6 KHz.

Fig. 7Compressor finite element model and measuring point location

Generally, the experimental modal analysis of the main parts is needed, and then the results are compared with the finite element analysis to obtain a relatively accurate finite element model. Because the error of free modal analysis for a single part is not very large, it usually can be controlled below 5 %, but it is difficult to get relatively accurate results for modal analysis of composite structures. It is the boundary condition which makes it difficult for finite element analysis. Due to the limitation of experimental conditions and cost, the experimental modal analysis only get natural frequency and the finite element modal analysis is carried out. Through the transfer function, we can contrast the natural frequency between simulation and experiment in Table 1. Since the torsion stiffness of the isolator is not considered, the first three modes of the compressor are removed and the 4-9 modes are obtained in Fig. 8. It can be seen from the figure that the first two modes are body modes and the last four modes are base modes.

Fig. 8Modal analysis of compressor

Vibration acceleration of four measuring points on the base is shown in Fig. 9. The spectrum trend of the four experiment points are basically the same, only the amplitudes of some frequencies are slightly different. For simulation, crank-connecting rod mechanism and machine body interact with each other. The force of the motion pair is acquired in the previous section, which is loaded on the finite element body by MPC coupling. The force of 1-4# motion pair in the opposite direction, with 5# motion pair force in the previous direction, after 50 cycles of iteration, the force in time domain is obtained. Loaded the force on the machine body, simulation is carried out. Since the test acceleration of four points is nearly the same, only point 1 is compared with the simulation in Fig. 10. Due to the existence of the isolator, the acceleration response should have a resonance peak in the frequency band below 10 Hz. The experiment sensor cannot accurately measure the low frequency value, so there is no obvious resonance peak in the experiment value. If the low-frequency resonance peak needs to be measured accurately, a special low-frequency acceleration sensor is needed [12, 13].

By comparing the experiment with the simulation, it is obvious that the acceleration simulated is generally higher than experiment, because the compressor mass is large and the foundation is flexible. In the simulation process, the foundation is treated as a rigid body. Although the foundation strength is high, the vibration acceleration level is 109.4 dB in 10-10 kHz band during the test. From the vibration acceleration curve, it can be seen that there are several resonance modes near the frequency doubling of 3, 5 and 6, which should be avoid by design. From the above analysis, it can be concluded that the resonance below 150 Hz is mainly caused by insufficient body strength, and the resonance between 150 Hz and 200 Hz is mainly caused by insufficient rigid strength of the base.

Fig. 9Vibration acceleration of four measuring points on the base

Fig. 10Vibration acceleration comparison