Calculation of oil free scroll compressor

Scroll compressor was created at the beginning of 1900s. Due to the limitation of processing technology, there are no product before the 1970s. Now the scroll compressor is the major compressor used by air conditioning. However, there are still many  technology shortages of oil-free scroll compressor. I find it hard to get the right equations for calculation of oil free scroll compressor during me trial on designing a oil-free scroll compressor as my graduation thesis. Here, I want to share my experiences on oil-free scroll compressor. This result is a combination of books and research papers. I reconfigured each step in order to get a right result in shorter time.

中文用户可以查看中文版：无油润滑涡旋压缩机设计计算步骤

Disclaimer:

This calculation method is suit for designing a compressor that you know the compressor displacement Q_d (V³/min) and suction pressure p_s as well as the exhaust pressure p_d (MPa). And according to a Chinese paper “Choice of Bask Geometric Parameters and Structure Parameter,λ=h/Pt , on a Scroll Compressor” by Gu Zhaolin, published on “Compressor Technology”, 1996, we choose Pt、t and h as bask geometric parameters. So I modified the calculate steps to this method:

1. Calculate the indicated power of electromotor. P_i (Kw)

You can find this equation in document [2] at page 62. In this book, it use  kgf/cm² as unit of pressure. So I made a small change in order to change the pressure unit to IU MPa.

2. Compute motor power P_e (Kw)

The leakage and friction factors concerned, shaft power Pz can be counted through this equation:

P_z=1.12P_e

Make sure there are about 5%～15% power reserve, the motor power Pe should be:

P_e=(1.05～1.15)P_z

3. Select motor speed n_w, it should be between 1000 and 4000r/min

4. Calculate the exhaust volume V_d (m³/r)

V_d=Q_d/(i*nw)

‘i’ in this equation is a parameter defined by the amount of compression chamber. If there is just one orbiting scroll and one fixed scroll, i should be 2. For compressor with Z orbiting scrolls and fixed scrolls, i should be 2*Z.

5. Calculate the suction volume V_s (m³/r)

Use a ideal gas model to simplify the calculation and assume the cycle as adiabatic. So:

pV^k=C

k is the adiabatic exponent of working medium or refrigerant. The adiabatic exponent is 1.4. The suction volume can be defined:

6. Geometric interior volume specific ratio ε_v

ε_v=V_s/V_d

7. Select  scroll pitch P_t(mm), scroll width t (mm). t should be 2～6mm

8. The angle that the involute beginning α (rad)

α=pi*t/P_t

pi=3.1415926535 897932

9. The maximum angle of involute Φ_e(rad) and the exhaust angle θ_d(rad)

ε_v=(2*Φ_e-3pi)/[2(Φ_e-θ_d)-3pi]

You will get the answer by combine the three equation. You may need tools like Matlab to get the  result. https://www.zhangpeng.info/

10. Scroll height h (mm)

V_s*1000000=P_t(P_t/2-t)h(2Φ_e-3pi)

You should adjust your parameters to use unit of ‘m’ other than ‘mm’. But I defined all the distance use the unit of ‘mm’, so I plus a 1000000 to make the change.

11. Check λ=h/P_t if it appropriate

Some paper said λ should between 1.5 and 2.5. If the λ you gained exceed the limit, duplicate step 7-11.

12. Radius of basic circle R_b (mm)

R_b=P_t/2pi

13. Radius of shaft circle R_or (mm)

R_or=(P_t-2t)/2

14. Balanced design of orbiting scroll.

15. Choose a oil-free format and the self-lubricatingmaterial

References:

1、刘振国.涡旋式流体机械与涡旋压缩机[M].机械工业出版社. 2009

2、编写组.活塞式压缩机设计[M].机械工业出版社. 1974

3、Gu Zhaolin, Yu Yongzhang. 涡旋压缩机设计计算研究[J].流体机械. 1996.2

4、Gu Zhaolin. Investigation of Scroll Compressor Design[J].低温工程. 1996.1

All these references are written in Chinese, you ask me if you have any question during reading these references.