Design Method of Offsetting the Orbiting Scroll and Its Influence on the Self-Rotation Characteristics of the Orbiting Scroll

In order to reduce the diameter of compressor casing of the automotive scroll compressor, the orbiting scroll is sometimes offset along a certain direction. This paper summarizes the method of offsetting the orbiting scroll, and analyses the influence of the offset amount on the self-rotation characteristics of the orbiting scroll. The theoretical calculation results show that a larger offset amount is beneficial to increase the stroke volume, however it is easy to make the orbiting scroll rotate around its driving center in the negative direction which would cause an impact on the scroll wrap and the anti-rotation mechanism. At last, this paper affords some advices in how to offset the orbiting scroll.

orbiting scroll was not further analyzed. In this paper, the general design method of offsetting the orbiting scroll for automotive scroll compressor is summarized, and the influence of the offset on the self-rotation characteristics of the orbiting scroll is discussed. Finally, a design method of offsetting the orbiting scroll is proposed to improve the self-rotational characteristics of the orbiting scroll.

General Design Method of Offsetting the Orbiting Scroll
In household air conditioning scroll compressor, the basic circle center of the orbiting scroll coincides with the driving center generally. However in automotive scroll compressor especially of the belt-driven type, the orbiting scroll is often offset to reduce the diameter of compressor casing due to the small installation space. The automotive scroll compressor can achieve the largest possible stroke volume under the same diameter of compressor casing by offsetting the orbiting scroll. For the scroll compressor, the stroke volume consists of two parts, one part is the closure volume of the suction chamber formed by the outer side of the orbiting scroll and the inner side of the fixed scroll, the other part is the closure volume of the suction chamber formed by the inner side of the orbiting scroll and the outer side of the fixed scroll. How the orbiting scroll is offset determines the number of scroll turns that can be arranged on the base plate, thus has a direct influence on the stroke volume.
In the following, the general method of offsetting the orbiting scroll will be introduced in detail. The influence of offset amount and offset angle on the scroll compressor's stroke volume will be discussed as well.
The planar view of the orbiting scroll profile with and without offset is shown in Figure 1, the two scroll profile share some basic parameters such as basic circle radius, orbiting radius and so on. In the figure, the coordinate s s s X O Y locates on the shaft center, the coordinate m m m X O Y locates on the basic circle center of the orbiting scroll, edge A is the inner edge of compressor casing and edge B is the outer edge of the base plate of the orbiting scroll, E is the point at the end of the inner side of the orbiting scroll, F is the point at the end of the outer side of the orbiting scroll, T is the tangent point at the basic circle of the orbiting scroll,  is the orbiting radius, e is the distance between the basic circle center of the orbiting scroll and the driving center, that is, the offset amount,  is phase angle of the vector from the basic circle center of the orbiting scroll to the driving center which is calculated from the positive direction of the m X axis, that is, the offset angle.  Figure 1(b). It is not difficult to find that the number of the orbiting scroll turns with offset is larger than that without offset when keeping other parameters the same.  . However point E is unknown in advance since it is associated with the number of the orbiting scroll turns which is also a parameter that needs to be determined. Therefore, it is necessary to determine the above parameters iteratively based on their underlying relationship.
Some basic parameters of the orbiting scroll are shown in Figure 2 The relationship between the offset angle  and the number of orbiting scroll turns orb N is as follows where E t is the local thickness of the scroll wrap at point E. It should be noticed that E t is not equal to the thickness of the scroll wrap t necessarily. In most cases, the outer involute profile of the orbiting scroll at end will be modified to increase the number of scroll turns further, leading to a smaller value of Since point F also locates on the outer edge of the base plate of the orbiting scroll, so the distance are solved simultaneously to obtain the number of orbiting scroll turns. The closure volume of suction chamber formed by the inner side of the orbiting scroll and the outer side of the fixed scroll at any orbiting angle can be calculated by following expression where h is the height of scroll wrap,  is the orbiting angle calculated from when the suction chamber formed by the inner side of the orbiting scroll and the outer side of the fixed scroll closes, b r is the basic circle radius, s V  is the correction of suction volume and can be calculated by following expression [4] It is assumed that E t equals to half of t after modification to the outer profile of the orbiting scroll in this paper. The parameters used in the calculation are shown in Table 1. As the offset amount of the orbiting scroll gradually increase from 0 to 2  , the closure volume of the suction chamber formed by the inner side of the orbiting scroll and the outer side of the fixed scroll is shown in Figure 3. It is obviously that increasing the offset amount helps bringing about a larger closure volume for the suction chamber formed by the inner side of the orbiting scroll and the outer side of the fixed scroll. This is because that more number of orbiting scroll turns can be arranged on the base plate of the orbiting scroll.  Table 2.  According to the calculation result in Table 2, the closure volume of suction chamber can be increased by 8.2% when the offset amount of the orbiting scroll reaches 2  compared with the case where the orbiting scroll is not offset ( 0 e  ). Generally speaking, the offset amount would not be chosen so large in the actual design since a large offset amount is likely to cause a sudden change in the self-rotation state of the orbiting scroll and makes the amplitude of driven torque larger. In the following, the influence of different offset design on the self-rotation characteristics will be discussed.

Judgment of Self-Rotation State of the Orbiting Scroll
In order to judge the self-rotation state of the orbiting scroll, it is necessary to perform force analysis on the orbiting scroll and the eccentric bushing system. For this reason, it can be assumed that the orbiting scroll does not rotate, and there are two meshing points between the fixed scroll and the orbiting scroll without considering the effect of anti-rotation mechanism on the orbiting scroll [1] [2].
Without considering the frictional force on the meshing point between two scrolls and the frictional moment between the orbiting scroll and the eccentric bush, the forces acting on the orbiting scroll are shown in Figure 4

Ys
Fc Figure 4 forces acting on the orbiting scroll The force balance equations of the orbiting scroll along the tangent and radial direction are as follows The forces acting on bushing system are shown in Figure 5, the frictional force between the eccentric shaft pin and the eccentric bush, and the frictional moment between the orbiting scroll and the eccentric bush are neglected here. In the figure, '

Influence of Offset Amount on the Self-Rotation State of the Orbiting Scroll
According to the method of judging the self-rotation state of the orbiting scroll, the self-rotation characteristic when the offset amount is 2  , 4  and 0 will be compared and analyzed in the following. The number of the orbiting scroll turns and the number of the fixed scroll turns of the scroll compressor studied in this paper are not equal, and the number of the fixed scroll turns is larger and fixed at 2.5. For the sake of discussion, it is assumed that the orbiting angle is zero when the end point of inner profile of the fixed scroll just contact with the outer profile of the orbiting scroll.
In the thermodynamic calculation, the refrigerant leakage between different chambers is not considered, and the compression process is assumed to be adiabatic compression [5]. The refrigerant used in automotive air conditioner is R134a and the operation condition used for calculation is shown in Table 3. When the offset amount is 2  , the maximal number of the orbiting scroll turns is 2.492 and the offset angle is -92.8° according to the calculation result in Table 2. The contact force on two meshing points and the corresponding self-rotation moment of the orbiting scroll during one orbiting cycle are shown in Figure  6. According to the value of 1 s F and 2 s F , the self-rotation state of the orbiting scroll can be divided into three cases: (1) When the orbiting angle varies in the interval  Figure 6. It is obvious that the self-rotation state of the orbiting scroll changed with the self-rotation moment. During most orbiting angle, the self-rotation moment s M varies between zero and the maximum peak. As the orbiting angle approaches 290°, the self-rotation moment s M decreases and the orbiting scroll tends to rotate in the reverse direction.
Likewise, when the offset amount is 4  and 0, the maximal number of the orbiting scroll turns is 2.426 and 2.359 respectively, the offset angle is -116.7° and -140.7° (the offset angle is meaningless for the case where the offset amount is 0) respectively according to the calculation result in Table 2. The contact force on two meshing points and the corresponding self-rotation moment of the orbiting scroll in both cases are shown in Figure 7 and Figure 8 respectively. Compare the above three cases and it can be found that as the offset amount decreases from 2  to 0, the variation amplitude of contact force and self-rotation moment decrease as well. It is not difficult to understand since the larger offset amount which corresponds to the larger compression force arm will lead to the larger self-rotation moment when the operation condition stays almost the same. The most important is that when the offset amount decreases, the probability that the orbiting scroll rotate in the negative direction becomes smaller. It can be seen from Figure 8 that when the offset amount is 0, the contact force 1 s F always varies above the abscissa, meaning that the orbiting scroll will never rotate in the negative direction.  Figure 8 the contact force and self-rotation moment of the orbiting scroll when the offset amount is 0 It should be noticed that in above calculation the leakage between different chambers and the friction on the meshing points are neglected and this would not cause too much error on the judgement of the orbiting scroll. According to previous paper [6], when only the leakage is considered, the orbiting angle span in which the orbiting scroll rotates in the positive direction is a little larger. This is because that leakage occurs in the meshing gaps owing to the self-rotation in the positive direction, leading to the increment of the pressure in the compression chamber formed by the inner side of the orbiting scroll and the outer side of the fixed scroll, thus enhancing the tendency of the self-rotation of the orbiting scroll in the positive direction further. Meanwhile the friction on the meshing points is one of obstruction factors that prevent the self-rotation of the orbiting scroll, the influence of the leakage on the self-rotation of the orbiting scroll can be offset by the friction. Therefore calculation results in this paper are quite acceptable though neglecting the leakage and the friction at the same time.
Generally speaking the orbiting scroll without offset will never rotate in the negative direction under normal operation condition, however the case is different when the orbiting scroll is offset. When the orbiting scroll is offset, the orbiting scroll would frequently rotate in the negative direction especially for the larger offset amount according to above analysis. When the orbiting scroll rotates in the negative direction even for a while during one orbiting cycle, the reliability of scroll compressor would encounter some problems. The sudden change of the self-rotation direction would cause an impact to the two scroll wraps and the anti-rotation mechanism and generate noise and vibration especially when the compressor operates at high speed. Therefore, when designing a scroll compressor, especially an automotive scroll compressor, care must be taken to avoid reverse self-rotation of the orbiting scroll.

Some Suggestion on Offsetting the Orbiting Scroll
According to the previous analysis results, given the inner diameter of compressor casing and the orbiting radius, the larger the offset amount, the more orbiting scroll wraps can be arranged on the base plate of the orbiting scroll. However, the orbiting scroll with a larger offset amount is more likely to rotate in the negative direction during the operation of the compressor, resulting in a decrease in compressor performance and reliability.
Therefore, it is necessary to reasonably select the offset amount so that it can achieve the effect of increasing the stroke volume without making the orbiting scroll rotate reversely. There is no need to follow the one-to-one correspondence relationship between the offset amount and the offset angle to maximize the stroke volume. By adjusting the offset angle while keeping the offset amount unchanged, the effect of increasing the stroke volume and improving the self-rotation characteristics of the orbiting scroll can both be achieved.
It may be a laborious work to determine the limiting offset amount for various sizes of automotive scroll compressors since the self-rotation state of the orbiting scroll depends on not only the offset design but also the compressor operation condition. Just as mentioned in previous paper [3], the optimum value of the offset depends on the individual scroll design. One general rule should be followed to offset the orbiting scroll is that the orbiting scroll will not rotate in the negative direction under most operation conditions, the specific design process is as follow: (1) According to the required stroke volume, determine the minimum number of orbiting scroll turns which meets the requirement, then determine the minimum offset amount min e and optimal offset angle opt  that matches the minimum number of orbiting scroll turns by resolving equations (2) -(9) simultaneously; (2) Resolve equations (10) -(15) simultaneously and analyze the self-rotation characteristics of the orbiting scroll according to the method mentioned in this paper. If the orbiting scroll does not rotate reversely under most operation conditions, the minimum offset amount min e determined in previous step is suitable, otherwise enter the next step; (3) Increase the offset mount to min ee  ( 0 e  ) on the basis of minimum offset amount but assure it is not more than 2  , and adjust the offset angle to opt   or opt   ( 0   ) accordingly. Resolve equations (10) -(15) simultaneously and analyze the self-rotation characteristics of the orbiting scroll according to the method mentioned in this paper. Repeat this step repeatedly until the orbiting scroll does not rotate reversely under most operation conditions.

Conclusion
This paper summarizes the method of offsetting the orbiting scroll, and analyses the influence of the offset on the self-rotation characteristics of the orbiting scroll. The theoretical calculation results show that a larger offset amount is beneficial to increase the stroke volume, however, a larger offset is likely to make the orbiting scroll rotate around its driving center in the negative direction which would cause an impact on the two scroll wraps and the anti-rotation mechanism. When there is no offset ( 0 e  ), the orbiting scroll will not rotate in the negative direction, getting rid of the sudden change of the self-rotation state. At the end, this paper gives some suggestion on offsetting the orbiting scroll.