Bending and torsional coupling study of rolling-piston compressor valves

In this paper, a model of a rolling compressor valve with one end fixed horizontally is presented and simulated using the flow-solid coupling (FSI) method for rolling rotor type compressors. Optimisation of the diagonally cut section can effectively reduce the pressure pulsation of the compressor. The results show that the valve blade generates coupled vibrations of bending and torsion, and the slant-cut structure improves the frequency of pressure pulsations, increases the stability of the compressor valve blade, optimises the compressor structure and reduces the pressure pulsations of the compressor.


Introduction
Rolling-piston compressor is one of the key components of the compression refrigeration system, in the compression system bears the important responsibility of compression and transport refrigerant.The physical diagram of the rolling rotor compressor is shown in Figure 1.Compressor valve is an important part of the compressor, the design of a reasonable high-quality valve can make the refrigeration mass energy loss to the compressor compression energy loss of 8% or less, while the design of the valve is not reasonable refrigeration mass energy loss of more than 15% of the compressor energy consumption or higher [1] .The performance of the valve is a serious constraint on the stability and reliability of compressor operation, and even affects the efficiency of the entire system.Such as the motor, rotor and piston cylinder and other large components in the premise of not failing, the fatigue failure of the valve is one of the main factors in the failure of the compressor [2] .Therefore, it is very important to study the law of motion of the valve for the optimisation and improvement of the valve to improve the energy efficiency of the compressor.
Pulsating airflow not only generates excitation forces that vibrate the casing and pipework, but is also a cause of damage to compressor valves [3] .Valve bending vibration and torsion vibration coupling relationship exists between the valve, and valve vibration damage often occurs in the bending and torsion coupling vibration of the results of the joint action, if a separate analysis of the bending or torsion vibration can not be analysed alone to give the valve damage to the accident to provide sufficient information, and the study of the valve bending and torsion coupling vibration characteristics of the valve can be analyzed from the process of obtaining more information on the failure of the useful and is conducive to optimizing the valve's structure to provide a better optimization of the direction of the valve, accurately grasp the valve's dynamical properties.Numerical analysis methods for airflow pressure pulsations in rolling-piston compressors include: frequency domain analysis based on plane wave theory [4] A time-domain analysis method for one-dimensional hydrodynamics [5] A threedimensional computational fluid dynamics analysis method based on multi-degree-of-freedom rigid body motion of the valve [6] and Numerical analysis method based on flow-solid coupling [7,8,9] .The numerical simulation and analysis method of flow-solid coupling is one of the most widely used methods in China to deal with compressors and pumps.The method can realise the coupling of structural, flow, temperature, electric and magnetic fields, and has the ability of solving the computational problems of complex multi-field coupling.The coupled flow-solid coupling method has made a significant contribution to the study of compressors, especially in the calculation of the intrinsic frequency of gas columns, airflow pulsation and pressure pulsation, and has successfully solved a number of practical problems.Rolling rotor compressor section shown in Figure 2, mainly by the rotor, stator, suction orifice, discharge orifice, cylindrical cylinder and so on.the working volume of the cylinder is composed between the inner wall of the cylinder and the outer circle of the rotor, as shown in Fig. 3, and the cylinder volume is the product of the crescent area AP and the rotor length L: ( ) When the compressor is working, the slide will divide the cylinder working volume into working volume into suction volume V S and compression volume V d two parts, compression volume and suction volume will change with the rotor rotation angle change.A ᵡ is the area occupied by the slide extending into the cylinder; τ is the ratio of rotor eccentricity to cylinder radius; θ is the ratio of rotor eccentricity to cylinder radius.The curve of compressed volume versus rotation angle is shown in Fig. 4.The radius of the rotor in the model r = 10.94mm;theradius of the cylinder R = 13.9mm;theheight L = 12.98mm.as shown in Figure 4, the angle of the rotor angle range between 210°~360°.For the application of rolling rotor compressors, the discharge mass flow rate is a key indicator for evaluating thermodynamic performance.Typically, refrigerant injection is used to increase the discharge mass flow rate, which can be expressed by the equation 4: q vt is Theoretical volumetric gas capacity，m 3 /h; n is rotation speed, r/min; Base element volume after compression volume is constantly decreasing, high-pressure gas exhaust through the valve, the flow rate after compression is constant.Therefore, the compressed volume equation 5 is shown as follows.
e is Eccentricity between rotor and cylinder.
valve seat valve plate restrictor

Analysis of the simulation results of the bending-torsion coupling of the valve sheet
The force sketch of the valve plate is shown in Fig. 6.the bolt restricts the valve disc between the valve seat and the lift limiter, so the contact surfaces between the valve and the valve seat, the valve and the limiter, and the valve and the bolt need to be restrained and fixed in the constraint setting of the valve.The thickness of the valve is 0.3mm, the total length of the cantilever section of the valve is L=46.52mmmm, the isotropic width is b=10.5mm,and the mass is m=0.014kg.In order to carry out the simulation test of the intrinsic frequency of the valve, 6 is selected as the maximum modal order as shown in Fig. 7.
First-order modal Second-order modal Third-order modal Fourth-order modal Fifth-order modal Sixth-order modal Figure 7 depicts the stress distribution and deformation of the valve sheet in different modes.From the valve sheet modal simulation bending and torsion coupling cloud diagrams, it can be seen that the first-order to the sixth-order deformation results show that in the frequency range of 0~1064.4Hz, the valve sheet only produces the bending results.In the frequency range of 1064.4~1258.8Hz, the valve sheet produces torsion results.It can be inferred from the results of the simulation cloud; the intrinsic frequency of the valve sheet will be much larger than the resonance range of the valve sheet and no resonance will occur.The valve sheet torsion occurs at the third order mode, from which it can be obtained that the action of pressure pulsation on the valve sheet produces bending vibration and bending and torsion vibration.

Fluid-solid coupling of compressor valves
This paper work is based on the method of flow-solid coupling as shown in Fig. 5, where the pressure chamber, valve seat, valve plate and limiter are modeled to create the transient compressor numerical simulation simulation model, Figures 8 and 9 show the comparisons carried out before and after the optimisation of the diagonal cut structure respectively.Transient calculations based on the finite volume method to obtain the change of pressure pulsation, double precision calculation, the model uses two K-Epsilon viscous turbulence equations, the use of scalable walls of the function of the application of the boundary wall of the solid part of the method of solving, the simulation process does not take into account the impact of fluid leakage, and the fluid material of the experimental leakage process of the stress performance has no significant impact, so the experimental The fluid material is simulated by applying air, the mass flow excitation is q t =5096(sin(60/t)+318sin(120/t)), and the boundary condition of pressure inlet is used at the outlet, and the outlet pressure is set to be 3.35MPa, and the turbulence method is applied to Intensity and Viscosity Ratio.The return turbulence intensity is 5% and the return turbulence viscosity ratio is 10.The pressure and mass flow coupling is done by SIMPLEC algorithm.
The real wall of the computational model adopts no-slip boundary conditions, and the number of time steps should not be set too much for the convenience of computation in the running computation, and the computational time step is set to 100, because the coupled flow-solid simulation is carried out by using a small time step of 1e-5s, and the end time of the step is 0.001 s.The type of the time advancement is Fixed, and the method of the time advancement is Used-Secified, and the maximum iteration time step is set to 50.The pressure change curve at different positions of the valve sheet is shown in Fig. 10.The maximum iterative time step of the calculation is set to 50.The pressure pulsation variation at different positions of the valve sheet is analyzed and the pressure variation curve at 0.001 time is shown in Fig. 10.In order to monitor the variation of pressure pulsation, monitoring points are inserted at the inlet and outlet of the fluid simulation model, and the coordinates of the three monitoring points are A (2.8mm, -5mm, -50mm) at the inlet, and the coordinates of the monitoring point B (2.8m, -5mm, 10mm), and a monitoring point is also placed around the valve sheet with the coordinates C (25mm, -2.5m, -10mm), and the monitoring point is convenient for monitoring the pressure in the chamber.The monitoring point facilitates the monitoring of pressure pulsations in the chamber.

Conclusion
In the work of this paper, numerical simulation experiments were carried out on the valve plate of a small rolling rotor compressor, and the pressure pulsation changes in the compression chamber were monitored using simulation, and the pressure change rule at different locations in the compressor chamber was analyzed and the frequency distribution at different locations in the compressor was analyzed.Frequency variation of compressor valves in different positions shown in Fig. 11.Based on this work, the following conclusions can be drawn: Taking the compressor valve sheet fixed at one end as the object of study, the computational model of the study is simplified, and the computational time is largely reduced in the calculation process.The pressure pulsation change of the valve sheet is analyzed by using the simulation and analysis method of flow-solid coupling.Optimization of the peak pulsation after the oblique cut attenuates the pressure pulsation by 0.01Mpa, and the amplitude of the pressure pulsation is reduced by 3.43%.A research idea is provided for the optimization of compressor pressure pulsation.
Optimize the compressor by adding a diagonal cut structure, and by comparing with and without the diagonal cut structure, it is found that the inclusion of the diagonal cut structure can effectively attenuate the pressure pulsation of the compressor, reduce the frequency amplitude of the compressor, and reduce the noise generated by the compressor.
Due to the simplification of the simulation model model, the muffler structure of the compressor valve plate is not put into the simulation experiment, which makes the simulation experiment high frequency noise is more, therefore, in the subsequent research will be further optimized by adjusting and matching the muffler, so as to make the compressor's frequency noise weakened.

Figure 2 .Figure 3 .
Figure 1.Diagram of a rolling compressor /mm.Figure 2. Simulation compressor model sectional drawing/mm.2.Cylinder volume change rule cylinder working volume

Figure 4 .
Figure 3. Cylinder working section/mm.Figure 4. Curves of suction volume and compression volume as a function of turning angle.

Figure 5 .
Figure 5. Three-dimensional model drawing of the valve piece/mm.

Figure 6 .
Figure 6.Simplified force diagram of the valve plate.

Figure 11 .
Figure 11.Frequency variation of compressor valves in different positions.