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The low-order vibration modes of a reciprocating compressor were studied by means of numerical simulation and experimental validation. A shell element model, a beam element model, and two solid element models were established to investigate the effects of bolted joints and element types on low-order vibration modes of the compressor. Three typical cases were compared to check the effect of locations of moving parts on the vibration modes of the compressor. A forced modal test with the MRIT (Multiple References Impact Test) technique was conducted to validate the simulation results. Among four numerical models, the solid element model with the bolt-pretension method showed the best accuracy compared with experimental data but the worst computational efficiency. The shell element model is recommended to predict the low-order vibration modes of the compressor with regard to effectiveness and usefulness. The sparsely distributed bolted joints with a small bonded region on the contact surface were key bolted joints that had greater impacts on the low-order vibration modes of the compressor than the densely distributed bolted joints. The positions of the moving parts had little effect on the low-order vibration modes of the compressor.

Reciprocating compressors are widely used in mechanical and petrochemical industries. Dynamic forces on reciprocating compressors such as unbalanced inertial forces, gas forces inside the cylinder, cross-head forces, and acoustic shaking forces can induce severe vibrations on compressor, pipes, vessels, small-bore appendages, and the skid [

The first step of the numerical simulation is to build the FEA model of the structure. A key point of numerical modelling is to choose the proper element type for the structure. Many studies have been conducted on the selection of element types for reciprocating compressors in order to simulate the dynamic characteristics of the compressor accurately and efficiently. The solid element model can simulate the actual geometric shape and physical morphology of the compressor, but its disadvantages include large memory cost and time-consuming operation. Benjamin [

Proper modelling of bolted joints is critical to estimating the dynamic characteristics of reciprocating compressors. The characteristics of bolted joints have drawn much attention in recent years [

During the operation, the compressor crankshaft was driven by the motor. The rotation of the crankshaft will be converted to the reciprocating motion of the piston through the crank-connecting rod mechanism, which consists of the crankshaft, connecting rod, cross-head, piston rod, and piston. The locations of the reciprocating moving parts vary between the TDC (top dead centre) and BDC (bottom dead centre) periodically as the crankshaft is rotated. The distance between TDC and BDC is defined as the stroke of the compressor. No research has been conducted on the influence of the locations of moving parts on the vibration modes of reciprocating compressors.

Modal analysis is widely used in many fields such as architecture, bridges, and vehicles to extract the vibration modes of structures [

In this paper, the low-order vibration modes of a processing reciprocating compressor were studied through finite element analysis and modal testing. Two solid element models using the bolt-pretension method and the surface-bonded method, a shell element model, and a beam element model were established to investigate the influence of element types and bolted joints on the low-order vibration modes of the compressor. The key bolted joints of the compressor were identified based on the analyses of contact statuses on the interfaces between bolted flanges. Three typical cases were compared to study the effect of the locations of moving parts on the low-order vibration modes of the compressor. A forced modal test with the MRIT (Multiple References Impact Test) technique was conducted to validate the numerical results.

The processing reciprocating compressor investigated in this paper is a balanced-opposed hydrogen compressor with a rated speed of 980 r·min^{−1}, rated shaft power of 73 kW, and total mass of 12500 kg. The compressor has two throws and four stages, as shown in Figure

The balanced-opposed reciprocating compressor.

The moving parts inside the compressor body were simplified as point masses by the equivalent principle of mass, as shown in Figure

The equivalence masses of moving parts.

The first throw of piston and piston rod

The second throw of piston and piston rod

The connection rod

The crankshaft

The crank-connecting rod mechanism

To assess the effect of element types and bolt joints on the accuracy and efficiency of the numerical simulation of vibration modes for the reciprocating compressor, two solid element models using the bolt-pretension method and the surface-bonded method, a shell element model, and a beam element model were established.

The solid element models were modelled using 3D (three-dimensional) solid elements, known as SOLID187 in ANSYS. This type of element is defined by 20 nodes, and each node has three translational DOFs (degrees of freedom). Two methods, namely, the bolt-pretension method and the surface-bonded method, were adopted to investigate the influence of bolted joints to the low-order vibration modes of the compressor.

The solid element method with the bolt-pretension method.

The solid element method with the surface-bonded method.

Some researchers [

Stress distribution region between bolted flanges.

In the shell element model, the compressor body was meshed with 3D shell elements, known as SHELL181 in ANSYS. This type of element is defined by 4 nodes, and each node has three translational DOFs and three rotational DOFs. There was no bolted joint included in this model except the connecting long bolts of the third- and fourth-stage cylinders. The pretension effect of the bolted joints was considered by the DOF coupling of nodes in the theoretical bonded region which was an annular region around the screw hole, as shown in Figure

The shell element model.

The beam element model as shown in Figure

The beam element model.

After building the FEA models, the bottom surfaces of the pedestal and the small fractions of the skid under the cylinder supports were fixed as constrained elements. For the solid element model with the bolt-pretension method, a nonlinear static analysis was first performed to evaluate the contact status of the interfaces between bolted flanges, and a pretension modal analysis was subsequently conducted to obtain the low-order MNFs and mode shapes of the compressor. For the other three FEA models, the modal analysis was conducted directly to extract the low-order vibration modes of the compressor.

A forced modal test with the MRIT (Multiple References Impact Test) technique was performed to identify the vibration modes of the compressor and validate the numerical results. The selection of the reference points is an important step in the modal test. The reference points should avoid the modal nodes of vibration modes of interest, and the modal shapes should be significant at the reference points to ensure that the FRF curves have significant peaks. As for this reciprocating compressor with two throws of cylinders, the excitations on one end of the compressor are difficult to arouse obvious vibrations on the other end, so we selected two reference points on each throw of cylinder based on pretests and numerical results. The four reference points, that is, the excitation points, are shown in Figure

Excitation and response points.

The experimental system is shown in Figure ^{−1}, measuring range of 22240 N, and hammer weight of 2.5 kg. The responses were acquired by a PCB 356B18 type three-axis acceleration sensor with a measuring range of ±5 g and frequency span of 0.5–3000 Hz. The sensitivities of the acceleration sensor in the ^{−1}, 1048 mV·N^{−1}, and 992 mV·N^{−1}, respectively. An NI 9234 data acquisition system with four channels was used to simultaneously record the force signal and accelerator signals in three directions. Signals obtained from the modal test were recorded and processed by the data analysis software Coinv DASP V10 developed by China Orient Institute of Noise and Vibration. During the modal test process, each point was gathered three times, and the measured data were linearly processed to reduce the error of the experiment.

The forced modal test process.

The modal parameters of the reciprocating compressor in the frequency range of 0–100 Hz were estimated by the ERA (Eigen Realization Algorithm) method which is one of the advanced time-domain modal identification methods. Figure

Stabilization diagram of the ERA method.

The MAC (modal assurance criterion) is a scalar constant used to denote the similarity between one mode vector and another, and lies in the range from 0 to 1. The higher the MAC, the better the orthogonality between the mode vectors. The MAC between the

MAC matrix of the extracted seven mode vectors in the frequency range of 0–100 Hz.

Figure

Experimental results of mode shapes in the frequency range of 0–100 Hz.

Figure

Comparison of computation time and storage space.

Solid element models | Shell element model | Beam element model | |||
---|---|---|---|---|---|

Bolt-pretension method | Surface-bonded method | ||||

74 bolted joints | 8 bolted joints | ||||

Computation time/h | 6.8 | 3.7 | 2.3 | 0.03 | 0.01 |

Storage space/GB | 8.95 | 3.24 | 2.76 | 1.74 | 0.40 |

Comparison of MNFs between numerical results of different element types and experimental results.

Low-order mode shapes of the solid element model with the bolt-pretension method.

Low-order mode shapes of the shell element model.

Low-order mode shapes of the beam element model.

The significant errors of the beam element model may be caused by two reasons. Firstly, the Beam188 elements in ANSYS are based on Timoshenko beam theory which assumes that the cross section of the element remains plane without distortion after deforming of the structure, so the ignorance of deformation on cross-sections of compressor cylinders will reduce simulation accuracy. Secondly, different components such as cylinders and cylinder supports were connected by rigid beam elements in the beam element model, which may lead to the increase of the overall stiffness and the overestimation of MNFs.

It was concluded that the solid element model with the bolt-pretension method showed the best accuracy compared with experimental results among the three numerical models discussed here. The deviations of the shell element model were within the engineering allowable range, and the shell element model saved 99.6% of computation time and 80.6% of storage space compared to the bolt-pretension method. In view of effectiveness and usefulness, the shell element model was recommended to predict the low-order vibration modes of the reciprocating compressor.

Figures

Comparison of MNFs between two kinds of solid element models and experimental results.

Low-order mode shapes of the solid element model with the surface-bonded method.

The contact statuses of frictional contact pairs in the solid element model with the bolt-pretension method were extracted from the static analysis results. There are five kinds of contact statuses in ANSYS, and among them the sticking and sliding statuses can be equivalent to the bonded contact [

Different contact statuses of different distribution densities of the bolted joints. The purple key represents that the contact surfaces are overconstrained and some contact constraints need to be removed. The yellow key indicates that there is a very small gap between the contact surfaces.

The sparsely distributed bolted joints

The densely distributed bolted joints

To study the influence of the distribution of bolted joints on the low-order vibration modes of the compressor and identify key bolted joints among these 74 bolted joints, we removed the bolted joints between interfaces whose contact status was similar to that shown in Figure

Comparison of MNFs between solid element models with different number of bolted joints and experimental results.

Using the above analyses, we can see that the characteristics of bolted joints will affect the low-order vibration modes of the compressor. The sparsely distributed bolted joints with a small bonded region on the contact surface were key bolted joints which had significant impacts on the low-order vibration modes of the compressor. Nevertheless, the characteristics of the densely distributed bolted joints can be ignored to improve the calculation efficiency. During numerical modelling for the assembly containing multiple bolted joints such as the compressor, the outer diameters of theoretical bonded regions on the interfaces between bolted flanges can be predicted using (

Figure

Comparison of MNFs between different positions of moving parts.

The effects of element types, bolted joints, and positions of moving parts on the low-order vibration modes of a reciprocating compressor were studied by numerical simulation and experimental validation. The following conclusions can be drawn from this study:

The shell element model was recommended for predicting the low-order vibration modes of assemblies such as the reciprocating compressor with regard to effectiveness and usefulness.

The sparsely distributed bolted joints with small bonded regions on the contact surface were the key bolted joints which had greater impacts on the low-order vibration modes of the assembly than the densely distributed bolted joints.

The positions of moving parts had little effect on low-order vibration modes of the reciprocating compressor.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by CNOOC (China National Offshore Oil Corporation) under Contract Z5TZENT089.