Evaluation of Machining Errors of Scroll Profiles
Evaluation of Machining Errors of Scroll Profiles 1.2
2
Jianhong. Yang , Y. Arai and W. Gao2 1 2
Department of Mechanical and Electrical Engineering, Huaqiao University, Quanzhou, Fujian 362021, China
Nano-metrology and Control Laboratory, Department of Nanomechanics, Tohoku University. Aramaki Aza Aoba 6-6-01, Aoba-ku, Sendai, 980-8579, Japan E-mail: [email protected]
Abstract: The mounting error between the machining coordinate system and the workpiece coordinate system can lead to a larger profile error for scroll compressors. A rapid measuring system of scroll profile has been developed based on cylindricity measuring machine. First, measurement errors caused by measuring system are analyzed and compensated. The total rotational radial error and angle error are got by the best-fit of the measurement data. Second, the machining errors are got after compensating measuring system error. The total measurement time of machining error for involute scroll is about 200 seconds. The measurement error range is about µm.
±5
Keywords: Flank leakages, Scroll profile, Profile error, Machining error, Measurement time 1.
Introduction The scroll compressor is a device used for compressing air or refrigerant, which was originally invented in 1905 by a French engineer named Creux. The device consists of two nested identical scrolls constituted in the classical design by involutes of circle. One scroll is fixed scroll. The other scroll is orbit scroll. The two scrolls, whose axes of rotation do not meet each other, are assembled with a relative angle of π , so that they can touch themselves at different points and form a series of growing size chambers [1]. The main advantages of the scroll compressor are the small number of moving parts, a high efficiency and a low level of noise and vibrations [2]. Moreover, due to their low rotational speed, off-the-shelf electrical machines, like induction machines or brushless internal mounted permanent magnets machines, can be used in variable speed drives with high performance control strategies. However, the precision machining of the fixed scroll and the orbiting scroll plays a key role in improving their performance. The leakage clearances between the orbiting scroll and the fixed scroll can be influenced by machining accuracy of scroll wraps. There are two main leakage clearances, flank leakage and radial leakage, as shown in Fig.1. The flank leakage clearances are caused by machining error of the scroll profile. During the machining processing of the scroll profiles, there is a rotational radial error between workpiece and rotary stage. Moreover, there is a rotational angle error between the start point and the moving direction of the machine tool. Profiles are measured by coordinate measuring machines (CMMs), which are very time-consuming and expensive. To overcome the shortcomings of CMMs, a rapid measuring system of the scroll profile has been developed based on cylindrical coordinates [3]. The probe and rotary stage are controlled by PID controller. The probe scanned the flank profile of the scroll continually. The measurement errors caused by measurement system are analyzed and
compensated. The total rotational radial error and angle error are found by best-fit of measurement data. The radial error and angle error of the measurement system are compensated based on machining reference of workpiece. The rotational radial error and the angle error of machining system are measured accurately. The measurement results are compared with those of CMMs. The rapid measuring
Orbiting scroll
Radial leakage
Fixed scroll Flank leakage
Outside profile Inside profile
Fig1: The gearing leakages of scroll profile. system is better than CMMs on measurement time and measurement condition and can meet the on-machine requirement for scroll profiles. 2. Measurement system and method A rapid measuring system had been developed based on cylindricity measuring machine (RA-2000), as shown in
±
Fig.2. A ruby ball was employed as contact probe. The measurement range and resolution of the probe are 1 mm and 0.1 µm respectively. The outputs of XY direction for the probe were used to measure the profile and the output of Z direction is used to determine the position of end plate. The scroll workpiece were mounted on the precision rotary stage. First, the coordinate system was initialized. The rotational angle of stage and the encoder of X-axis were zero. Second, the probe was moved to the scroll profile and contacted the start point. Finally, the probe finished scanning of the scroll profile continually when the rotational speed of stage and the moving speed of probe were given [3-4]. Scroll profile error can be calculated by the Eq. (1).
±
∆r (i ) = r (θ i ) − ( Dr − Xd (i ) + xp (i )) ± rp
±40 .
y = a1 × Φ N + a 2 y p = b1 × α + b 2 θ = c1 × Φ N + c 2 ∆rw = r (ϕ + θ ) × cos(θ ) − r (ϕ )
(1)
where, θi is the rotational angle of the rotary stage, and r(θi) is the theoretical scroll radius of θi. The term Dr is the distance between the centre point of stage and the origin point of X-axis. The distance is a constant. Xd(i) is the encoder output of X-axis. xp(i) is the X directional output of the probe. The term rp is the radius of the probe ball. When inside profile error is considered, the term rp of the Eq. (1) is positive. Otherwise, it is negative.
Z
moving direction of the probe. Every contact point of scroll profile is not on situated the X-axis. Moreover, the Y-directional outputs of the probe are about µm The centre of the probe is not situated on the X-axis. The two kinds of error caused by the measurement system are shown in Fig.3. The term yout is the Y-directional output of the probe. The term yp is the offset of the contact point. The X-axis is theoretical reference axis. The X1-axis is the practical reference axis. Because the yp value is small, In the triangular ACD, there is a approximate linear relationship between y and ΦN. The same principle, a linear relationship of yp and α can be achieved. The error of measurement system can be calculated by the Eq. (2) and the Eq. (3).
Y
X
，
where, a1, a2, b1, b2, c1, c2 are some linear fitting coefficients. They can be calculated by assumed y, yp, ΦN α. ΦN is the slope of every contact point. θ is the scroll angle error of every contact point and can be calculated by the Eq. (2). In the Eq. (3), ϕ is rotational angle of rotary stage. The r is theoretical scroll radius of the rotational scroll angle. The term rw is scroll radius error by the reason of scroll angle error (θ). The term rp is radius error of the probe by the reason of scroll angle error. Moreover, in the Fig.3, there is another measurement
yp xp
probe
Measurement error/mm
zp
Xd
Dr Rotary stage Fig2: Rapid measuring system. 3.
Error analysis of measurement system Tangent line of every point for the scroll profile is different. The direction of tangent line is not vertical to the
error error
0.1
-0.1 -0.2
o
β
θ
Φ
αo y
p
N
D
2
yout probe
Scroll profile
Fig3: The error of measurement system.
X1 X
Measurement error/mm
o1
C (x, y)
D
△ rw △ rp
0
0
200
(a)
A
△
0.2
Y
c
(3)
∆rp = rp × (1 − cos(α ))
△
Scroll
(2)
400 600 800 1000 Rotational angle/degree
0.01
0
-0.01
-0.02
inside profile outside profile 0
200
400
(b)
600
800
1000
Rotational angle/degree
Fig 4: Measurement system error.
system error as a result of yout. The yout is the Y-directional outputs of the probe for every contact point. The measurement system error of yout can be calculated by the Eq. (4).
β = tan −1 ( yout / r (ϕ )) ∆rw1 = r (ϕ + β ) − r (ϕ )
(4)
2 ∆rp1 = rp − rp2 − yout
where, β is scroll angle error caused by the Y-directional output of the probe. r(ϕ) is theoretical scroll radius. rp is radius of the probe. rw1 is measurement error of workpiece by the reason of Y-directional output of the probe. rp1 is measurement error of probe by the reason of Y-directional output of the probe. The measurement system error in the Eq. (3) and Eq. (4) are shown in the Fig. (4). The Fig.4 (a) shows the measurement system error in the Eq. (3). The Fig.4 (b) shows rw1 of the measurement system error in the Eq. (4). rp1 is very small compared with measurement result and thus ignored. 4. Measurement results and comparing with CMMs In order to measure machining error accurately for scroll profile, a standard cylinder and centering table were employed, as shown in the Fig.5. The inside profile of the cylinder was measured by probe and measurement data was fitted into a circle. The centre point coordinate was found. The centre point coordinate is very small after adjusting centering table. The centering of the rotary stage was finished. Then orbiting scroll was mounted on the rotary stage. The rotary stage rotated as 20 degree/s. The moving speed of the probe can be calculated by Archimedean theory.
△
△
probe
y (i ) = ∆r (i ) × sin(ϕ (i )) a × x(i ) + b × y (i ) + c = −( x(i ) 2 + y (i ) 2 )
△
Y
Jig
x(i ) = ∆r (i ) × cos(ϕ (i ))
cylinder Centering table
dθ = (dx 2 + dy 2 − c) × 360 / 2 × π × rb where, x(i) and y(i) were calculated by profile error △r(i) in the Eq. (1). a, b, and c are the best-fit coefficient of circle. rb is basic circle radius of scroll profile. dx and dy are total radial error, dθ is total angle error. Finally, the scroll profile errors were calculated by the Eq. (6) as follows. -3
x 10
5 0 -5
-10 -15
Rotary stage Centre point
(5)
dx = − a / 2, dy = −b / 2
Profile error/mm
△
The moving speed of the probe is 0.793 mm/s. The probe scanned inside and outside profile for the orbiting scroll continually. The outputs of probe, X encoder, and rotary stage were sampled every 0.2 degree. The output of rotary stage was used to calculate theoretical scroll radius. The scroll profile errors were calculated by Eq. (1). The errors of measurement system were compensated by Eq. (3) and Eq. (4). The Eq. (5) is used to best-fit measurement data by least square method. The radial error and angle error that included machining error and measurement error were got [5]. The radial and angle errors are named as total error.
RMs CMMs 0
200 -3
X
5
x 10
400
600 800 1000 Rotational angle/degree
(a) Outside scroll profile
Measurement reference
Y
Orbiting scroll
X O
gauge block Centering hole
Profile error/mm
(a) Adjustment of the centre for rotary stage 0
-5
-10
RMs CMMs 0
200
400
600 800 1000 Rotational angle/degree (b) Inside scroll profile
(b) Measuring setup of orbiting scroll Fig 5: measuring setup of orbiting scroll.
Fig 6: Profile error by RMs and CMMs.
∆r1 (i) = ( x(i) − dx) 2 + ( y (i ) − dy ) 2 + 2 × dθ × π × rb / 360
△
(6)
where, r1(i) is the profile error of every point after compensating total radial error and angle error. The measurement results of inside and outside profile were shown in the Fig. 6. The measurement results of the rapid measuring system (RMs) are the same as those of CMMs. Required accuracy of involute profile measurement for orbiting scroll are 5 µm. Fig. 6 shows the rapid measuring system can meet the required accuracy. The orbiting scroll was mounted on rotary stage by the reference of centering hole and gauge block. The centre point of the centering hole had been adjusted by a standard cylinder in the Fig. 5(a). However, there is a measurement angle error between gauge blocks and X-axis. The measurement angle error was got by measuring the two gauge blocks. First, two measurement points were got from one side of gauge blocks. Measurement angle error was calculated by the line of the two measurement points. Second, another measurement angle error was calculated by the other side of the two gauge blocks. Finally, the mean measurement angle error was calculated by the two measurement angle errors. Machining angle error was got after removing measurement angle error. Machining radial error that is divided into X and Y directions are the same as dx and dy in the Eq. (5). The measurement results of machining error were showed in the Table.1. θ is the machining angle error. y and x are two components of machining radial error along X and Y directions. The measurement results of the rapid measuring system were compared with those of CMMs. The measurement results of machining angle error are proximately the same as those of CMMs. There are measurement errors of dx and dy between RMs and CMMs, which are caused by repeatability mounting error between standard cylinder and orbiting scroll. Machining time of each scroll workpiece is about 300 seconds. Measurement time of CMMs is 20 minutes, which can’t meet required measurement time. The scroll angle of inside and outside is 1600 degree. The rotational speed of RMs is 20 degree/s. The measurement time of involute profile is 80 seconds. Total measurement time of machining error is 200 seconds including the measurement time of the gauge block. The measurement time of RMs can meet requirement of on-machine. 5. Conclusion A rapid measuring system has been developed based on cylindricity measuring machine. Measurement method of RMs was studied. Different kinds of measurement system errors was analyzed and compensated to improve the measuring accuracy of scroll profile. In this study, the following conclusions were obtained: (1) The profile error of orbiting scroll measured by using RMs were ±5µm and compared with those of CMMs. RMs can meet required measurement accuracy. (2) Machining errors △x, △y, △θ were measured by RMs and compared with those of CMMs. Measurement results of machining errors were proximately the same as those of CMMs. (3) RMs can scan the involute profile for the scroll
continually and be used on-machine condition. The total measurement time of machining error for scroll is about 200 seconds. This improved machining efficiency and accuracy of scroll profile. Table1: machining error of scroll profile. Machining
△θ
△x
△y
error
(degree)
(um)
(um)
0.0379
3.8
5.7
Outside
0.0394
4.3
6.2
profile
0.0411
3.6
6.3
0.0435
4.7
6.1
0.0345
3.1
4.5
0.0543
4.4
6.5
0.0482
4.7
6.9
0.0509
4.4
7.1
0.0521
5.1
7.2
0.0493
3.7
6.1
0.0422
4.1
6.1
Inside and
0.0475
4.5
6.4
outside profile
0.0467
4.1
6.5
0.0453
4.9
6.7
0.0419
3.4
5.3
±
△
△
△
CMMs
Inside profile
CMMs
CMMs
References [1] B. Blunier, G. Cirrincione, Y. Herve et al. A new analytical and dynamical model of a scroll compressor with experimental validation, International Journal of Refrigeration, 2009, Vol.32, No.2, pp.874–891. [2] A. Inada, W. Gao. A high-speed profile measurement system for scroll compressors, Proc. of the 4th International conference on Leading Edge Manufacturing in 21st Century, Japan, 2007, pp.219-222. [3] J.H.Yang, Y. Arai, W.Gao. Rapid Measurement of Involute Profiles for Scroll Compressors, 7th international conference on measurement, Smolenice, Slovakia, 2009, pp.294-297. [4] Y. Arai, A. Inada, W. Gao. Precision measurement of scroll profiles Proc. of the 5th International Symposium on Instrumentation Science and Technology, Vol. 1, Shenyang, China, (2008), 120-125. [5] Wei Gao, Satoshi Kiyono, Takamitu Sugawara. High accuracy roundness measurement by a new error separation method, Precision Engineering, Journal of the ASPE, 1997, Vol.21, No.2, pp.123-133.
2
Jianhong. Yang , Y. Arai and W. Gao2 1 2
Department of Mechanical and Electrical Engineering, Huaqiao University, Quanzhou, Fujian 362021, China
Nano-metrology and Control Laboratory, Department of Nanomechanics, Tohoku University. Aramaki Aza Aoba 6-6-01, Aoba-ku, Sendai, 980-8579, Japan E-mail: [email protected]
Abstract: The mounting error between the machining coordinate system and the workpiece coordinate system can lead to a larger profile error for scroll compressors. A rapid measuring system of scroll profile has been developed based on cylindricity measuring machine. First, measurement errors caused by measuring system are analyzed and compensated. The total rotational radial error and angle error are got by the best-fit of the measurement data. Second, the machining errors are got after compensating measuring system error. The total measurement time of machining error for involute scroll is about 200 seconds. The measurement error range is about µm.
±5
Keywords: Flank leakages, Scroll profile, Profile error, Machining error, Measurement time 1.
Introduction The scroll compressor is a device used for compressing air or refrigerant, which was originally invented in 1905 by a French engineer named Creux. The device consists of two nested identical scrolls constituted in the classical design by involutes of circle. One scroll is fixed scroll. The other scroll is orbit scroll. The two scrolls, whose axes of rotation do not meet each other, are assembled with a relative angle of π , so that they can touch themselves at different points and form a series of growing size chambers [1]. The main advantages of the scroll compressor are the small number of moving parts, a high efficiency and a low level of noise and vibrations [2]. Moreover, due to their low rotational speed, off-the-shelf electrical machines, like induction machines or brushless internal mounted permanent magnets machines, can be used in variable speed drives with high performance control strategies. However, the precision machining of the fixed scroll and the orbiting scroll plays a key role in improving their performance. The leakage clearances between the orbiting scroll and the fixed scroll can be influenced by machining accuracy of scroll wraps. There are two main leakage clearances, flank leakage and radial leakage, as shown in Fig.1. The flank leakage clearances are caused by machining error of the scroll profile. During the machining processing of the scroll profiles, there is a rotational radial error between workpiece and rotary stage. Moreover, there is a rotational angle error between the start point and the moving direction of the machine tool. Profiles are measured by coordinate measuring machines (CMMs), which are very time-consuming and expensive. To overcome the shortcomings of CMMs, a rapid measuring system of the scroll profile has been developed based on cylindrical coordinates [3]. The probe and rotary stage are controlled by PID controller. The probe scanned the flank profile of the scroll continually. The measurement errors caused by measurement system are analyzed and
compensated. The total rotational radial error and angle error are found by best-fit of measurement data. The radial error and angle error of the measurement system are compensated based on machining reference of workpiece. The rotational radial error and the angle error of machining system are measured accurately. The measurement results are compared with those of CMMs. The rapid measuring
Orbiting scroll
Radial leakage
Fixed scroll Flank leakage
Outside profile Inside profile
Fig1: The gearing leakages of scroll profile. system is better than CMMs on measurement time and measurement condition and can meet the on-machine requirement for scroll profiles. 2. Measurement system and method A rapid measuring system had been developed based on cylindricity measuring machine (RA-2000), as shown in
±
Fig.2. A ruby ball was employed as contact probe. The measurement range and resolution of the probe are 1 mm and 0.1 µm respectively. The outputs of XY direction for the probe were used to measure the profile and the output of Z direction is used to determine the position of end plate. The scroll workpiece were mounted on the precision rotary stage. First, the coordinate system was initialized. The rotational angle of stage and the encoder of X-axis were zero. Second, the probe was moved to the scroll profile and contacted the start point. Finally, the probe finished scanning of the scroll profile continually when the rotational speed of stage and the moving speed of probe were given [3-4]. Scroll profile error can be calculated by the Eq. (1).
±
∆r (i ) = r (θ i ) − ( Dr − Xd (i ) + xp (i )) ± rp
±40 .
y = a1 × Φ N + a 2 y p = b1 × α + b 2 θ = c1 × Φ N + c 2 ∆rw = r (ϕ + θ ) × cos(θ ) − r (ϕ )
(1)
where, θi is the rotational angle of the rotary stage, and r(θi) is the theoretical scroll radius of θi. The term Dr is the distance between the centre point of stage and the origin point of X-axis. The distance is a constant. Xd(i) is the encoder output of X-axis. xp(i) is the X directional output of the probe. The term rp is the radius of the probe ball. When inside profile error is considered, the term rp of the Eq. (1) is positive. Otherwise, it is negative.
Z
moving direction of the probe. Every contact point of scroll profile is not on situated the X-axis. Moreover, the Y-directional outputs of the probe are about µm The centre of the probe is not situated on the X-axis. The two kinds of error caused by the measurement system are shown in Fig.3. The term yout is the Y-directional output of the probe. The term yp is the offset of the contact point. The X-axis is theoretical reference axis. The X1-axis is the practical reference axis. Because the yp value is small, In the triangular ACD, there is a approximate linear relationship between y and ΦN. The same principle, a linear relationship of yp and α can be achieved. The error of measurement system can be calculated by the Eq. (2) and the Eq. (3).
Y
X
，
where, a1, a2, b1, b2, c1, c2 are some linear fitting coefficients. They can be calculated by assumed y, yp, ΦN α. ΦN is the slope of every contact point. θ is the scroll angle error of every contact point and can be calculated by the Eq. (2). In the Eq. (3), ϕ is rotational angle of rotary stage. The r is theoretical scroll radius of the rotational scroll angle. The term rw is scroll radius error by the reason of scroll angle error (θ). The term rp is radius error of the probe by the reason of scroll angle error. Moreover, in the Fig.3, there is another measurement
yp xp
probe
Measurement error/mm
zp
Xd
Dr Rotary stage Fig2: Rapid measuring system. 3.
Error analysis of measurement system Tangent line of every point for the scroll profile is different. The direction of tangent line is not vertical to the
error error
0.1
-0.1 -0.2
o
β
θ
Φ
αo y
p
N
D
2
yout probe
Scroll profile
Fig3: The error of measurement system.
X1 X
Measurement error/mm
o1
C (x, y)
D
△ rw △ rp
0
0
200
(a)
A
△
0.2
Y
c
(3)
∆rp = rp × (1 − cos(α ))
△
Scroll
(2)
400 600 800 1000 Rotational angle/degree
0.01
0
-0.01
-0.02
inside profile outside profile 0
200
400
(b)
600
800
1000
Rotational angle/degree
Fig 4: Measurement system error.
system error as a result of yout. The yout is the Y-directional outputs of the probe for every contact point. The measurement system error of yout can be calculated by the Eq. (4).
β = tan −1 ( yout / r (ϕ )) ∆rw1 = r (ϕ + β ) − r (ϕ )
(4)
2 ∆rp1 = rp − rp2 − yout
where, β is scroll angle error caused by the Y-directional output of the probe. r(ϕ) is theoretical scroll radius. rp is radius of the probe. rw1 is measurement error of workpiece by the reason of Y-directional output of the probe. rp1 is measurement error of probe by the reason of Y-directional output of the probe. The measurement system error in the Eq. (3) and Eq. (4) are shown in the Fig. (4). The Fig.4 (a) shows the measurement system error in the Eq. (3). The Fig.4 (b) shows rw1 of the measurement system error in the Eq. (4). rp1 is very small compared with measurement result and thus ignored. 4. Measurement results and comparing with CMMs In order to measure machining error accurately for scroll profile, a standard cylinder and centering table were employed, as shown in the Fig.5. The inside profile of the cylinder was measured by probe and measurement data was fitted into a circle. The centre point coordinate was found. The centre point coordinate is very small after adjusting centering table. The centering of the rotary stage was finished. Then orbiting scroll was mounted on the rotary stage. The rotary stage rotated as 20 degree/s. The moving speed of the probe can be calculated by Archimedean theory.
△
△
probe
y (i ) = ∆r (i ) × sin(ϕ (i )) a × x(i ) + b × y (i ) + c = −( x(i ) 2 + y (i ) 2 )
△
Y
Jig
x(i ) = ∆r (i ) × cos(ϕ (i ))
cylinder Centering table
dθ = (dx 2 + dy 2 − c) × 360 / 2 × π × rb where, x(i) and y(i) were calculated by profile error △r(i) in the Eq. (1). a, b, and c are the best-fit coefficient of circle. rb is basic circle radius of scroll profile. dx and dy are total radial error, dθ is total angle error. Finally, the scroll profile errors were calculated by the Eq. (6) as follows. -3
x 10
5 0 -5
-10 -15
Rotary stage Centre point
(5)
dx = − a / 2, dy = −b / 2
Profile error/mm
△
The moving speed of the probe is 0.793 mm/s. The probe scanned inside and outside profile for the orbiting scroll continually. The outputs of probe, X encoder, and rotary stage were sampled every 0.2 degree. The output of rotary stage was used to calculate theoretical scroll radius. The scroll profile errors were calculated by Eq. (1). The errors of measurement system were compensated by Eq. (3) and Eq. (4). The Eq. (5) is used to best-fit measurement data by least square method. The radial error and angle error that included machining error and measurement error were got [5]. The radial and angle errors are named as total error.
RMs CMMs 0
200 -3
X
5
x 10
400
600 800 1000 Rotational angle/degree
(a) Outside scroll profile
Measurement reference
Y
Orbiting scroll
X O
gauge block Centering hole
Profile error/mm
(a) Adjustment of the centre for rotary stage 0
-5
-10
RMs CMMs 0
200
400
600 800 1000 Rotational angle/degree (b) Inside scroll profile
(b) Measuring setup of orbiting scroll Fig 5: measuring setup of orbiting scroll.
Fig 6: Profile error by RMs and CMMs.
∆r1 (i) = ( x(i) − dx) 2 + ( y (i ) − dy ) 2 + 2 × dθ × π × rb / 360
△
(6)
where, r1(i) is the profile error of every point after compensating total radial error and angle error. The measurement results of inside and outside profile were shown in the Fig. 6. The measurement results of the rapid measuring system (RMs) are the same as those of CMMs. Required accuracy of involute profile measurement for orbiting scroll are 5 µm. Fig. 6 shows the rapid measuring system can meet the required accuracy. The orbiting scroll was mounted on rotary stage by the reference of centering hole and gauge block. The centre point of the centering hole had been adjusted by a standard cylinder in the Fig. 5(a). However, there is a measurement angle error between gauge blocks and X-axis. The measurement angle error was got by measuring the two gauge blocks. First, two measurement points were got from one side of gauge blocks. Measurement angle error was calculated by the line of the two measurement points. Second, another measurement angle error was calculated by the other side of the two gauge blocks. Finally, the mean measurement angle error was calculated by the two measurement angle errors. Machining angle error was got after removing measurement angle error. Machining radial error that is divided into X and Y directions are the same as dx and dy in the Eq. (5). The measurement results of machining error were showed in the Table.1. θ is the machining angle error. y and x are two components of machining radial error along X and Y directions. The measurement results of the rapid measuring system were compared with those of CMMs. The measurement results of machining angle error are proximately the same as those of CMMs. There are measurement errors of dx and dy between RMs and CMMs, which are caused by repeatability mounting error between standard cylinder and orbiting scroll. Machining time of each scroll workpiece is about 300 seconds. Measurement time of CMMs is 20 minutes, which can’t meet required measurement time. The scroll angle of inside and outside is 1600 degree. The rotational speed of RMs is 20 degree/s. The measurement time of involute profile is 80 seconds. Total measurement time of machining error is 200 seconds including the measurement time of the gauge block. The measurement time of RMs can meet requirement of on-machine. 5. Conclusion A rapid measuring system has been developed based on cylindricity measuring machine. Measurement method of RMs was studied. Different kinds of measurement system errors was analyzed and compensated to improve the measuring accuracy of scroll profile. In this study, the following conclusions were obtained: (1) The profile error of orbiting scroll measured by using RMs were ±5µm and compared with those of CMMs. RMs can meet required measurement accuracy. (2) Machining errors △x, △y, △θ were measured by RMs and compared with those of CMMs. Measurement results of machining errors were proximately the same as those of CMMs. (3) RMs can scan the involute profile for the scroll
continually and be used on-machine condition. The total measurement time of machining error for scroll is about 200 seconds. This improved machining efficiency and accuracy of scroll profile. Table1: machining error of scroll profile. Machining
△θ
△x
△y
error
(degree)
(um)
(um)
0.0379
3.8
5.7
Outside
0.0394
4.3
6.2
profile
0.0411
3.6
6.3
0.0435
4.7
6.1
0.0345
3.1
4.5
0.0543
4.4
6.5
0.0482
4.7
6.9
0.0509
4.4
7.1
0.0521
5.1
7.2
0.0493
3.7
6.1
0.0422
4.1
6.1
Inside and
0.0475
4.5
6.4
outside profile
0.0467
4.1
6.5
0.0453
4.9
6.7
0.0419
3.4
5.3
±
△
△
△
CMMs
Inside profile
CMMs
CMMs
References [1] B. Blunier, G. Cirrincione, Y. Herve et al. A new analytical and dynamical model of a scroll compressor with experimental validation, International Journal of Refrigeration, 2009, Vol.32, No.2, pp.874–891. [2] A. Inada, W. Gao. A high-speed profile measurement system for scroll compressors, Proc. of the 4th International conference on Leading Edge Manufacturing in 21st Century, Japan, 2007, pp.219-222. [3] J.H.Yang, Y. Arai, W.Gao. Rapid Measurement of Involute Profiles for Scroll Compressors, 7th international conference on measurement, Smolenice, Slovakia, 2009, pp.294-297. [4] Y. Arai, A. Inada, W. Gao. Precision measurement of scroll profiles Proc. of the 5th International Symposium on Instrumentation Science and Technology, Vol. 1, Shenyang, China, (2008), 120-125. [5] Wei Gao, Satoshi Kiyono, Takamitu Sugawara. High accuracy roundness measurement by a new error separation method, Precision Engineering, Journal of the ASPE, 1997, Vol.21, No.2, pp.123-133.
