Structural dynamic analysis of the orbiting scroll wrap in the scroll compressor

Abstract

A deep analysis of orbiting scroll wraps was conducted in this paper by using ANSYS and SolidWorks. Through the modal analysis, the involute of the circle profile orbiting scroll wrap demonstrated a large span in natural frequencies, which led to more superiority in avoiding structural resonances. Based on the dynamic harmonic analysis, loads of frequency changes were gained and the stress and strain distribution of the orbiting scroll wrap in the most dangerous working conditions were obtained, which determined the segments with maximum stress and strain-displacement properties. Two paths defined to elucidate further the structural characteristics of the exhaust chamber provided evidence for the initial correction of orbiting wraps. The results of the present study offer a theoretical basis for the design and manufacture of scroll wraps, and providing a new way to evaluate different scroll wraps.

Keywords

scroll compressor / orbiting scroll wrap / model analysis / harmonic analysis

Introduction

The scroll compressor is a recently developed type of compressor widely used in the refrigeration and air conditioning industry. This compressor, consisting of only few components, is of a high efficiency and compact structure. In addition, it consumes little energy and works smoothly. The compression process in the scroll compressor is achieved through the pockets between the fixed scroll and the orbiting scroll [1,2].

The orbiting scroll wrap, as the main moving component in the scroll compressor system, is the key factor affecting the performance of the scroll compressor. The convective heat transfer inside the scroll compressor was previously studied experimentally by Oooi and Zhu [3]. Besides, simulation studies on the heat transfer and mechanism dynamic characteristics of the scroll compressor were reported [4-8]. Stress and deformation analyses of the orbiting scroll wrap were previously performed using the simulation function of PRO-E [9] and ANSYS [10]. A stress and deformation analysis of the fixed scroll wrap was also reported [11].

The aforementioned studies focused mainly on analyzing the stress and deformation of scroll wraps, but did not conduct further analysis on orbiting scroll wraps. Accordingly, the current paper established a circle involute orbiting scroll wrap using SolidWorks. Moreover, the structural dynamic characteristics of the scroll wrap were achieved using ANSYS. The top six natural frequencies were obtained, and the displacement transformation of orbiting scroll wraps in different vibration modes was united. Harmonic analysis of the circle involute orbiting scroll wrap and integrated displacement strain response curves were conducted. Load frequency changes were gained. The features of the orbiting wrap and the effect of different structural parameters on orbiting wrap characteristics were analyzed separately using the simulation results of the performance on dynamic characteristics to provide a new method to evaluate different scroll wraps.

Geometric description of orbiting scroll wrap and model construction

Geometric description of the orbiting scroll wrap

All continuous and derivable curves are potential scroll profiles. With the development of the scroll compressor industry, studies on the involute of circle profiles can help meet the demands of the growing industry. Such studies can also help provide a better theory in profile research in the developing traditional involute of circle profiles. The involute of circle scroll profile is simple and mature because of its processing technology. In addition, it has the most complete theoretical study and can meet the needs of industrial development to a large extent. Therefore, the involute of circle scroll profile occupies a major position in the scroll compressor field. In this paper, a circle scroll wrap involute with 3.45 mm base radius and

\mathrm{0.2}\text{π}

inner wall profile angle was constructed using SolidWorks. The parameter expression of the inner wall profile is

(1)\{\begin{array}{l}x=\mathrm{3.45}(\cos \phi +(\phi -\mathrm{0.2}\text{π})\sin \phi )\text{,}\\ y=\mathrm{3.45}(\sin \phi -(\phi -\mathrm{0.2}\text{π})\cos \phi )\text{,}\phi \in [\mathrm{0.2}\text{π},\mathrm{5.5}\text{π}].\end{array}

According to the symmetry of the inner and outer wall profiles, the parameter expression of the outer wall profile can be obtained as

(2)T\{\begin{array}{l}x=\mathrm{3.45}(\cos \phi +(\phi +\mathrm{0.2}\text{π})\sin \phi )\text{,}\\ y=\mathrm{3.45}(\sin \phi -(\phi +\mathrm{0.2}\text{π})\cos \phi )\text{,}\phi \in [-\mathrm{0.2}\text{π},\mathrm{5.5}\text{π}].\end{array}

Model construction

The orbiting scroll wrap is composed of carbon steel with a density of 7.85 g·cm^-3, an elastic modulus of 200 GPa, and a Poisson ratio of 0.3. The base circle radius of the scroll wrap is 3.45 mm, the height, 25 mm, and the back thickness, 10 mm. The orbiting scroll wrap was constructed using SolidWorks, and the initial form of this profile was modified using a pair of circulars arcs. The orbiting scroll wrap model was introduced into ANSYS by passing through the external connection of the ANSYS (Fig.β1). The scheme of the ANSYS mesh is shown in Fig.β2.

Structural dynamic analysis of orbiting wrap

Selection of calculation and constraint conditions

Selection of calculation conditions

Scroll compressors can be operated under different conditions. The gas pressure and gas force of every compression chamber differ with changing spindle angles. Consequently, the strength analysis of the orbiting wrap is very important to the scroll compressor. However, simple mechanical methods cannot be used to calculate the stress and strain. ANSYS simulation offers a better approach in analyzing and describing the stress and strain, or the high stress and strain areas in actual operation of scroll compressor, It seeks corresponding countermeasures to improve the structure of scroll wraps and the performance of scroll compressors.

Exhaust transient was selected as the calculation condition for the dynamic harmonic analysis. This condition is the most dangerous condition in the working process, wherein the pressure difference between the internal and external surfaces of the orbiting wrap is the largest. The symmetric compression chambers of the combination profile orbiting wraps are illustrated in Fig.β3. In engineering, the pressure of the suction, middle compression, and exhaust chambers could be obtained using the rough estimation method. After finding the discipline of the compression chamber change with different spindle rotation angles, the compression process can be viewed as adiabatic. The pressure i of the compression chamber, and the spindle rotation angle

\theta

can be expressed in Eq. (3) [12].

(3)p(\theta )=p_{}{\left[{\displaystyle \frac{V_{}}{V(\theta )}}\right]}^k,

where k (1.18) is the gas isentropic exponent and

p_{}

(0.1013 MPa), the suction pressure.

V_{}

and

V(\theta )

can be obtained using

(4)\begin{array}{l}V(\theta )=\text{2}h\left[{\displaystyle \frac{}{}}{R}_{}{}^{}{({\varphi }_{}\theta -\alpha )}^{\mathrm{3}}-{\displaystyle \frac{}{}}{R}_{}{}^{}{({\varphi }_{}-p-\theta +\alpha )}^{}\right]\\ \begin{array}{lll}& & \end{array}-\left[{\displaystyle \frac{}{}}{R}_{}{}^{}{({\varphi }_{}--\theta +\alpha )}^{}-{\displaystyle \frac{}{}}{R}_{}{}^{}{({\varphi }_{}--\theta +\alpha )}^{}\right]\text{,}\end{array}

(5)\begin{array}{l}{V}_{}=\mathrm{2}h\left[{\displaystyle \frac{\mathrm{1}}{\mathrm{6}}}{R}_{}{}^{\mathrm{2}}{({\varphi }_{}-\alpha )}^{\mathrm{3}}-{\displaystyle \frac{\mathrm{1}}{\mathrm{6}}}{R}_{}{}^{\mathrm{2}}{({\varphi }_{}--\alpha )}^{\mathrm{3}}\right]\\ \begin{array}{ll}& \end{array}-\left[{\displaystyle \frac{\mathrm{1}}{\mathrm{6}}}{R}_{}{}^{\mathrm{2}}{({\varphi }_{}-\mathrm{2}-\alpha )}^{\mathrm{3}}-{\displaystyle \frac{\mathrm{1}}{\mathrm{6}}}{R}_{}{}^{\mathrm{2}}{({\varphi }_{}-\mathrm{3}-\alpha )}^{\mathrm{3}}\right],\end{array}

where

{\varphi }_{}

is the final exhibition angle of the involutes;

\theta

, the spindle rotation angle; and

\alpha

, the occurrence angle of the involutes. However, based on the results of Eq. (4) and (5) and the rough estimation method, heat transfer and leakage exist in practical processes. The pressures in the suction, middle compression, and exhaust chambers were 0.3, 0.5, and 0.7 MPa, respectively.

Constraint conditions

The upper surface of the orbiting wrap can be regarded as being constrained by the undersurface of the fixed wrap in the z-direction because of the assembly relation of the scroll compressor. The undersurface of the orbiting wrap is restricted by the anti-rotation mechanism and follows an eccentric rotary translational trend. Therefore, the undersurface of the orbiting wrap can be viewed in the y-direction under the x-axis by the point constraint and in the x-direction by the y-axis point constraint.

Simulation analysis of orbiting wrap

Modal analysis

Conducting structural vibration analysis is one of the most important problems in structure analysis. The proper mass and stiffness determine the vibration characteristics of scrolls. These characteristics vary with different materials and the structural parameters of the orbiting scroll wraps. In designing dynamic scroll wraps, the proper adjustment of mass distribution and stiffness of the scroll wraps is important for avoiding the resonance caused by the external load and internal force.

In the present study, geometric stiffness was neglected in the modal analysis. The Block Lanczos method in ANSYS was used in the modal analysis. The top six orders of natural frequencies in the orbiting scroll wraps are listed in Table 1.

Two types of loads exist in the orbiting scroll wrap of a running scroll compressor. The first is temperature load, while the second includes inertial load, various gas forces, and contiguous load. The temperature distribution of internal and external scroll wraps is uniform because of the long stable operating time of the orbiting scroll wrap and the high thermal conductivity of the carbon steel. Thus, the temperature load can be neglected, and the gas forces on the orbiting scroll wrap are the only ones to be considered. The pressure of the gas absorbed from the external scroll wrap rises gradually when passing through the middle compression chamber. When the spindle rotation angle is

\theta

, the gas will exhaust at a set pressure of 0.7βMPa. The frequency changed in a certain range with the increase of gas pressure from 0.3 MPa to 0.7 MPa. The vibration modes and natural frequencies in a related range were analyzed based on the aforementioned analysis and simulation results. The vibration modes and the corresponding integrated displacements of each point at natural frequency from the first to the sixth orders of the different scroll profiles are depicted in Fig. 4.

From the modal analysis results, the uniting displacements of each point in different vibration modes were obtained, and the scroll wrap section with the maximum or minimum displacement deviation could also be determined. The vibration modal amplitude increased as the natural frequency of the orbiting scroll wrap increased. At the first order frequency, the integrated displacement of each point was smaller. The vibration modes of the orbiting scroll wrap was in a convex curve at 55.5 Hz or 1945.0 Hz natural frequency, whereas the concave curve was at the second to the sixth orders of the natural frequency. The span of the natural frequencies at the top six orders was larger. The operating frequencies should be different from the natural frequencies of the orbiting scroll wrap to avoid resonance. The resonance had a slight chance to occur for the involutes of the circle orbiting scroll wrap in the operating periodic of gas force. The modal analysis of orbiting scroll wraps could present an accurate node location and displacement of vibration modes, as well as a rapid analysis of the effect of structure size and material, among others, of the dynamic feature of scroll wraps. The modal analysis could also have a significant effect on the development and improvement of the scroll compressor, and provide a base for the evaluation of scroll profile and new profile theories.

Dynamic harmonic analysis

Sustained harmonic loads acting on the orbiting wrap can produce the same frequency steady state response. Harmonic response analysis of ANSYS was used to determine the discipline of orbiting wrap steady state dynamic response varying with frequency change. Through the dynamic harmonic analysis, the dynamic working characteristics of the orbiting wrap could be defined and the resonance be avoided.

Based on the modal analysis, harmonic analysis of the orbiting wrap can be conducted [13]. A natural frequency vibration mode of 3150 Hz was selected in accordance with the calculation conditions in applying load. That is, the exhaust transient of the scroll compressor, the most dangerous condition, was selected for the calculation conditions. The pressures applied on the internal surface of the suction, middle compression, and exhaust chambers were 0.3, 0.5, and 0.7βMPa, respectively. The Application of the pressure on the orbiting wrap is demonstrated in Fig. 5. The stress and strain distribution of the orbiting scroll wrap during the transient exhausting can be obtained via simulation (Figs. 6 and 7). As displayed in Fig. 6, the maximum stress was located at the center of the exhaust chamber, and the stress of the other orbiting wrap section gradually decreased from the inside to the outside. The simulation results show that the thickness of the exhaust chamber increased to sustain the high stress generated by the gas force. However, in the orbiting wrap sections with less stress, the casting materials in its range of allowable pressure, the thickness and weight of the orbiting wrap decreased for better heat transfer. As exhibited in Fig. 7, under the applying pressure loads, the maximum strain, whose value was 0.232βmm, was at the initial ends of the orbiting wrap,βconforming to theβdesignβspecifications of the orbiting wraps. The displacement strain gradually decreased as the orbiting wrap involutedly outward.

The following extraction points for the harmonic analysis were selected: point A at the internal of the exhaust chamber, point B at the internal of the middle compression chamber, and point C at the internal of the exhaust chamber. The displacement strain curves of the three points are presented in Figs. 8-10, wherein the reseda, purple, and red curves represent the displacement strains in the x-, y-, and z-directions, respectively.

The displacement strain curves were in the low frequency segment (Figs.β8-10). The strain in the axial direction gradually increased with the load frequency. The displacement strain response was the largest at the three points at 3150βHz load frequency, which verifies the results of the modal analysis. The orbiting wrap resonance occurred when the load frequency was similar to the natural frequency of the structure. The maximum displacement strain was at the center of the exhaust chamber in an axial direction. Consequently, a load near the structural natural frequencies should be avoided when the scroll compressor is running. The loads near the structural natural frequencies not only caused resonance but also increased the clearance between the orbiting wrap and the fixed wrap, which caused leakage and affected the volumetric efficiency of the compressor.

Two paths (i.e., paths 1 and 2) were defined to elucidate further the structural characteristics of the exhaust chamber. Path 1 is a series of points located along the internal surface of the exhaust chamber from the top to the bottom. Path 2 is a series of points located in the intermediate position from the inside to the outside of the internal surface of the exhaust chamber. The response curves of the displacement strain of these two paths are shown in Figs. 11 and 12.

As shown in Fig. 11, the strain of the axial path in x- and y-directions changed smoothly, whereas the change was more evident in the z-direction. The strain in the z-direction gradually increased, The maximum strains were found near the exhaust port. With the nodes getting away from the exhaust chamber, the displacement strain in the x-, y-, and z-directions gradually decreased, and the strain in the z-direction was larger than that in the x- and y-directions. From the strain response curves of the two paths, the variation of displacement strain response curves in the exhaust chamber internal surface in the axial and radial directions could be determined further, and a reference for the initial correction of orbiting wrap could be provided.

Conclusions

The present paper proposes a novel way to analyze the structural dynamic characteristics of the core-moving component of the orbiting wrap of the scroll compressor using a basic circle involute orbiting wrap to conduct modal and dynamic response analyses. The following conclusions are reached:

1) The top six natural frequency vibration modes were obtained through the Block Lanczos method of ANSYS for the modal analysis. The displacement transformation of the orbiting scroll wrap in different vibration modes was united. Through simulation, the main vibration of the basic circle involute scroll wrap was located in the inner concave bending. The bending angles increased with the increase in natural frequencies. The results show that the basic circle involute orbiting wrap has a large span in natural frequencies, which leads to more superiority in avoiding structural resonances.

2) Based on the model analysis, harmonic analysis was conducted of the orbiting scroll wrap and integrated displacement strain response curves. As a result, load frequency changes were gained. The stress and strain distribution of the orbiting scroll wrap in the most dangerous working conditions were obtained, which determined the segments with the maximum stress and the strain-displacement properties.

3) Two paths were defined in the internal surface of the exhaust chamber. The displacement strain was at its maximum near the exhaust port, whereas the strain away from the exhaust port of the exhaust chamber decreased. These results can provide evidence for the initial correction of orbiting wraps.

4) The structural parameters of the orbiting wrap can be changed by conducting a structural dynamic analysis of the orbiting wrap through the finite element software ANSYS, proceeding to topology optimization and obtaining a better dynamic performance. The results of the present study offer a theoretical basis for the design and manufacture of scroll wraps, and provide a new way to evaluate different scroll wraps.

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Higher Education Press and Springer-Verlag Berlin Heidelberg