【機械類畢業(yè)論文中英文對照文獻翻譯】渦旋壓縮機漸開線齒形的快速測量
【機械類畢業(yè)論文中英文對照文獻翻譯】渦旋壓縮機漸開線齒形的快速測量,機械類畢業(yè)論文中英文對照文獻翻譯,機械類,畢業(yè)論文,中英文,對照,對比,比照,文獻,翻譯,渦旋,壓縮機,漸開線,齒形,快速,測量,丈量
附錄1：外文翻譯
渦旋壓縮機漸開線齒形的快速測量
渦旋壓縮機廣泛應用于空調(diào)、真空泵等。渦旋壓縮機齒形的快速測量對提高壓縮機的壓縮效率和降低噪聲具有重要意義。用紅寶石接觸探針測量齒廓。探頭沿著X軸以勻速直線滑動。渦旋工件固定在精密旋轉(zhuǎn)臺上。舞臺的旋轉(zhuǎn)速度與X軸移動速度符合阿基米德曲線之間的關系。分析了快速測量系統(tǒng)的測量數(shù)據(jù)，通過補償回轉(zhuǎn)中心與工件中心坐標之間的偏移量，消除了測量誤差。將測量結(jié)果與商業(yè)坐標測量機（CMM）測量結(jié)果進行了比較。利用研制的快速測量系統(tǒng)，在測量精度保持不變的情況下，利用CMM 10分鐘測量時間，將渦旋漸開線輪廓的測量時間縮短到153秒。
關鍵詞：渦旋型線、誤差分離、漸開線齒廓，渦旋壓縮機，快速測量
1引言
渦旋壓縮機通過滾動滾動的運動來壓縮空氣。高氣壓的空氣通過軌道滾動從放電口排出。渦旋壓縮機具有扭矩變化小、振動小、噪聲小等優(yōu)點。由于抽吸和排出口之間沒有直接的流體通路也可以實現(xiàn)高效率。
（一）主要表現(xiàn)為兩種泄漏和傳動原理兩卷軸。圖1（b）給出了包括內(nèi)漸開線輪廓、外漸開線輪廓和非漸開線齒廓在內(nèi)的齒廓測量。其中的泄漏是由這兩種渦旋葉片的側(cè)面之間的間隙引起的側(cè)漏。另一個是由端板和卷軸的渦旋葉片之間的間隙引起的葉尖泄漏。這些泄漏的增加能使制造精度?？焖贉y量高度和側(cè)面輪廓對減少制造誤差非常重要。傳統(tǒng)上，用坐標測量機（CMM）測量渦旋齒廓，費時費力。三坐標測量機的測量時間不能滿足在線加工測量要求[ 3 ]。本文研制了一種快速、準確的內(nèi)、外漸開線渦旋型線輪廓測量系統(tǒng)。通過仿真分析測量誤差。將快速測量系統(tǒng)的測量結(jié)果與三坐標測量機的測量結(jié)果進行了比較。經(jīng)驗證，開發(fā)的快速測量系統(tǒng)能滿足要求的測量精度（±3μm）和測量時間（每件300秒/）。
2、測量系統(tǒng)和測量方法
圖2顯示固定滾動平臺的開發(fā)的快速測量系統(tǒng)。測量系統(tǒng)由圖-è階段和接觸式掃描探針。由于滾動在線加工測量的空間非常有限，因此基于圓度測量系統(tǒng)開發(fā)了快速測量系統(tǒng)。測量系統(tǒng)的尺寸非常小。固定的卷軸用兩個錐形銷固定在旋轉(zhuǎn)臺上。舞臺旋轉(zhuǎn)角度分辨率為0.0025度。這個x軸可以由精密控制板移動。在測量渦旋型線時，采用PID控制器（4）控制旋轉(zhuǎn)軸的運動速度和轉(zhuǎn)速。因此，該測量系統(tǒng)可以實現(xiàn)精確定位。定位誤差小到可以忽略。每個編碼器的位置由每個編碼器測量，并通過多軸控制板進入個人計算機。
考慮到切削油和切屑的影響，在研制的測量系統(tǒng)中采用了以球型紅寶石制成的接觸式位移探頭。在X軸端固定探頭用于掃描安裝在旋轉(zhuǎn)臺上的側(cè)面漸開線齒形。
[ 5 ]一個直徑為5毫米的紅寶石球附著在探測軸的末端。掃描探針球在XYZ方向上有三個刻度。x和y方向的輸出被用來測量漸開線輪廓，Z方向的輸出用來確定z軸的摩擦。探頭的電壓輸出通過A/D轉(zhuǎn)換器傳輸?shù)絺€人計算機中[ 6, 7, 8 ]。的分辨率和探測范圍為0.1μM和±1毫米，分別。測量力約為0.12 N。根據(jù)所需的測量時間，旋轉(zhuǎn)臺的轉(zhuǎn)速設定為20度/秒。滾動半徑的增量可以用下面的等式來描述。
R 1 R 2θ?θ=一×（θ2?θ1）×π/ 180（1）
根據(jù)方程（1），可以計算X軸的運動速度。
x軸運動速度為0.7923毫米/秒。
基本圓的漸開線螺旋線可以用下面的方程來描述（2）。
X=一[ COS（?+α）+?×（?+α）]（2）
Y=一[罪（?+α）??×COS（?+α）]
其中，一個是基圓半徑，φ是漸開線渦旋角，α是出發(fā)點的角度為漸開線齒廓。渦旋極角與渦旋角的關系可用以下方程描述：（3）。
?=θ+（?）（3）
在那里，φ是每個測點和θ滾動角是每個測點的極角。每個測量點的理論漸開線滾動半徑可以用
方程（2）和方程（3）。測量的滾動半徑可以通過探頭編碼器和X軸編碼器輸出得到。輪廓誤差可以用下面的公式來描述（4）。
rerror=RTH?rmea（4）
在那里，rerror是漸開線齒形誤差，在理論滾動極半徑；rmea卷軸極半徑測量。同樣的滾動樣品也被測量以比較由商業(yè)CMM，它安裝在一個溫度控制計量室。CMM的探測精度為0.6μM.
3、測量結(jié)果和誤差分析
無誤差分離的測量結(jié)果
利用研制的快速測量系統(tǒng)測量了固定渦卷的漸開線輪廓誤差。測量的結(jié)果在圖外輪廓測量的誤差范圍約為20米±顯示μ測量誤差范圍內(nèi)的配置文件是±40
μM.可以看出有非常大的快速測量系統(tǒng)的測量誤差。測量精度無法達到要求的測量精度（±3μm）。
通過計算機模擬B.測量誤差分析
測量誤差的原因進行分析。有工件和旋轉(zhuǎn)舞臺的中心坐標之間的偏移量。偏移值有顯著的效果的測量結(jié)果。接觸點的Y Y方向的偏移量是由接觸探頭和齒廓之間的摩擦引起的。Y對測量結(jié)果的影響也。
確定坐標系統(tǒng)誤差的影響，模擬對偏移量的影響進行了分析。圖4顯示仿真結(jié)果接觸點在固定渦卷偏移的情況下。水平軸和垂直軸表示固定滾動顯示仿真波形誤差的旋轉(zhuǎn)角度。圖4（a）顯示的影響
接觸點的Y方向的偏移量。在這里，Y的定義
通過接觸測量點的Y方向的偏移量。計算輪廓誤差，whenconsidered y = 0.5毫米和1毫米?？梢钥闯?，在剖面結(jié)果大影響Y。的影響變得更加顯著增加Y。為了實現(xiàn)
所需的漸開線齒廓測量精度，它被證實，Y方向的偏移誤差必須從測量齒形誤差的消除。圖4（b）對工件和旋轉(zhuǎn)舞臺坐標之間的偏移中心顯示的影響。測試中心坐標偏移的影響，計算機模擬是基于理想的外部和內(nèi)部進行involulte漸開線齒廓。在這里，xn和yn的中心定義的坐標和工件旋轉(zhuǎn)階段之間的偏移量。如圖所示，xn和yn，即使中心坐標的偏移很小，產(chǎn)生一個非常大的周期測量誤差的影響。圖3周期輪廓誤差是由于Xn
YN。有必要單獨的中心坐標的偏移
偏移精度要求在y方向為。
誤差分離后的測量結(jié)果
圖3測量輪廓度誤差由中心坐標和接觸點的Y方向的偏移量。接觸點的Y方向的偏移量可以通過編碼器的輸出測量探頭。探頭的y方向的輸出約為0.1mm。Y方向的偏移，使探頭的中心偏離X軸。探頭接觸點與x軸之間有傾斜角度。測量接觸點的實際渦旋極角可以通過方程（5）顯示出來。
θ房=θMEA+潭?1（?Y / R）（5）
在那里，θ房是真正的卷軸極角的測量點。θMEA是旋轉(zhuǎn)編碼器的輸出階段。Y是探針的Y方向偏移。r是每個測量點的理論滾動半徑。探頭中心的Y方向的偏移補償由方程（5）。
為了獲得中心坐標和工件測量系統(tǒng)偏移，測量輪廓度誤差，如圖3所示裝入圈由以下公式（6）。
一個×X+B×Y+C=?（X2+Y 2）（6）
在那里，一=?2xc，B=?2yc，C=XC2+YC2?R 2。
XC YC可以通過A和B的x和y的計算通過測量齒形誤差的計算。測量輪廓誤差
如圖3所示為補償?shù)腦C，YC和△Y.
測量結(jié)果顯示在圖5。圖5（a）表示外輪廓誤差補償后。外部輪廓誤差約為5米±μ圖（b）表示的內(nèi)輪廓誤差補償后。內(nèi)輪廓誤差大約
±6μM.測量誤差快速測量系統(tǒng)基本滿足精度要求。
為了測試快速測量系統(tǒng)的測量結(jié)果，在恒溫室中用商用坐標測量機測量了固定渦旋的內(nèi)外輪廓誤差。分別從內(nèi)、外側(cè)面獲得約1560個測量點。內(nèi)、外輪廓測量時間約為20分鐘。由快速測量系統(tǒng)分別從內(nèi)、外輪廓測量得到約4090個測量點。用快速測量系統(tǒng)測量內(nèi)外輪廓約150秒。的內(nèi)外輪廓如圖6所示測量結(jié)果。從圖中可以看出，外輪廓和內(nèi)輪廓的快速測量系統(tǒng)的測量結(jié)果是相同的。
三坐標測量機。但快速測量系統(tǒng)的測量時間比CMM的測量時間要短得多。渦旋工件的加工時間約為300秒[ 9 ]?？焖贉y量系統(tǒng)能滿足在線加工測量要求。
5總論
研制了一種基于精密三坐標探頭的渦旋壓縮機快速測量系統(tǒng)。通過仿真分析了兩種補償方式的測量誤差。快速測量系統(tǒng)的測量結(jié)果與三坐標測量機的測量結(jié)果相同，但快速測量系統(tǒng)的測量時間比三坐標測量機的測量時間短得多。所開發(fā)的快速測量系統(tǒng)能夠滿足渦旋壓縮機在線加工測量的要求。非漸開線齒形的快速測量是今后的工作方向。
附錄2：外文原文
Rapid Measurement of Involute Profiles for Scroll Compressors
Jianhong. Yang*1, Y. Arai1, W. Gao1
1Nano-metrology and control laboratory, Department of Nanomechanics, Tohoku University, Aramaki Aza Aoba 6-6-01, Aoba-ku, Sendai, 980-8579, JAPAN *e-mail: Jianhong@nano.mech.tohoku.ac.jp
Scroll compressors are widely used in air conditioners, vacuum pumps and so on. Rapid measurement of flank profile of a scroll compressor is important to improve the compression efficiency and decrease noises. A contact probe made of ruby was used for measurement of flank profile. The probe was moved by a linear slide along the X axis at a constant speed. The scroll workpiece was fixed on a precision rotary stage. The relationship between the stage rotational speed and the X axis moving speed complies with the Archimedean curve. The measurement data of the rapid measurement system were analyzed and measurement errors were removed by compensation of the offset between the coordinates of the rotary stage center and those of workpiece center. The measurement results were compared with those measured by a commercial coordinate measuring machine (CMM). The measurement time for the involute profile of the scroll is shortened to 153 seconds by the developed rapid measurement system from the 10 minutes measurement time by the CMM while the measurement accuracy is kept the same.
Keywords: scroll profile, error separation, involutes profile, scroll compressor, rapid measurement
1. INTRODUCTION
SCROLL COMPRESSORS compress air by orbiting motions of scrolls. The air with a high pressure is taken out from a discharge opening by orbiting scroll. The scroll compressor has a lot of advantages, including small variations of torque, low vibrations and noises. High efficiency can also be achieved because there is no direct fluid path between the suction and the discharge opening [1], [2].
Orbit scroll
Flank
leakage
Fixed scroll
Bottom
(a)
leakage
40
Inside volute
Y/mm
Outside volute
Non-involute
20
0
-20
-40
-40-20
0
20X/mm40
(b)
Fig.1 Leakages of scroll compressor and measurement profile
67
In order to further improve the efficiency of the scroll compressor, it is very important to reduce the leakages. Fig.1
(a) shows mainly two kinds of leakages and gearing principle of the two scrolls. Fig.1 (b) shows flank profile measurement including the inside involute profile, the outside involute profile and the non-involute profile. One of the leakages is flank leakage caused by a gap between the flanks of the two scroll blades. The other is tip leakage caused by a gap between the end plate and the scroll blade of the scrolls. These leakages can be decreased by increasing manufacturing accuracy. Rapid measurements of height and flank profile are important to decrease manufacturing errors. Conventionally, scroll flank profiles were measured by coordinate measuring machine (CMM), which is very time-consuming and expensive. Measurement time of CMM for scroll profiles cannot meet the on-line machining measurement requirement [3]. The paper develops a rapid and accuracy profile measurement system for inside and outside involute scroll profile. Measurement errors are analyzed by simulations. Measurement results of rapid measurement system are compared with those of the CMM. It is verified that the developed rapid measurement system can satisfy required measurement accuracy ( ± 3 μm) and measurement time (300 seconds/per workpiece).
2. MEASUREMENT SYSTEM AND MEASUREMENT METHOD
Fig.2 shows a platform of the developed rapid measurement system for the fixed scroll. The measurement system consists of X-Z-θ stages and a contact type scanning probe. Because there is very limited room for the on-line machining measurement of the scroll, the rapid measurement system was developed based on roundness measurement system. The size of the measurement system is very small. The fixed scroll was fixed on a rotary stage by two taper pins. The rotational angle resolution of the stage is 0.0025 degrees. The
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X axis could be moved by a precision control board. When involute profiles for scroll were measured, the moving speed of X axis and rotational speed of the rotary stage were controlled by a PID controller [4]. So the measurement system can realize precision positioning. The positioning error was small enough to be ignored. The positions of each stage were measured by each encoder and taken into a personal computer via multi axis control board.
Z axis
Rotation stage
Y axis
X axis
θ axis
Fig.2 Measurement system of scroll profile
Taking into consideration the influence of cutting oil and chips, a contact-type displacement probe made of ruby in the form of a ball was employed in the developed measurement system. The probe fixed on the end of X axis was used for scanning the flank involute profile mounted on the rotary stage
[5]. A ruby ball with a diameter of 5 mm was attached to the end of the probe axis. The scanning probe ball had three scales in the direction of XYZ. The outputs of the X and Y direction were used for measuring the involute profiles and the output of the Z direction was used for determining friction of the Z axis. The voltage outputs of the probe were transferred into a personal computer via an A/D converter [6, 7, 8]. The resolution and measuring range of the probe were 0.1 μm and ±1 mm, respectively. Measuring force was about 0.12 N. According to the required measurement time, rotational speed of the rotary stage was set to 20 degrees/second. The increment of scroll radius can be described by the following equation.
rθ1 ? rθ 2 = a × (θ 2 ? θ1) × π /180
(1)
From the equation (1), X axis moving speed can be calculated.
X axis moving speed is set for 0.7923 mm/s.
The involute spiral of base circle can be described by the following equation (2).
x = a[cos(? + α ) + ? × sin(? + α )]
(2)
y = a[sin(? + α ) ? ? × cos(? + α )]
Where, a is base circle radius, φ is involute scroll angle, α is the angle of start point for involute profile. The relationship of scroll polar angle and scroll angle can be described by the following equation (3).
? = θ + tan(?)
(3)
Where, φ is scroll angle of each measurement point and θ is the polar angle of each measurement point. Theoretical involute scroll radius of each measurement point can be calculated by
equation (2) and equation (3). Measurement scroll radius can be obtained by outputs of probe encoder and X axis encoder. Profile error can be described by the following equation (4).
rerror = rth ? rmea
(4)
Where, rerror is involute profile error, rth is theoretical scroll polar radius; rmea is measurement scroll polar radius. The same scroll sample was also measured for comparison by a commercial CMM, which was installed in a temperature controlled metrology room. Probing accuracy of CMM was 0.6 μm.
3. MEASUREMENT RESULTS AND ERROR ANALYSIS
A. Measurement results without error separation
The involute profile errors of the fixed scroll were measured by developed rapid measurement system. Measurement results are shown in Fig.3 The measurement error range of the outside profile was about ±20 μm. The measurement error range of the inside profile was about ±40
μm. It can be seen that there were very large measurement errors in the rapid measurement system. The measurement accuracy could not meet the required measurement accuracy (±3 μm).
0.06
outside profile
error/mm
0.04
inside profile
Profile
0.02
0
-0.02
-0.04
-0.060 200 400 600 800
Rotation angle/degree
Fig.3 Measurement result without error separation
B. Measurement error analysis by computer simulation
The reasons for measurement error must be analyzed. There are the centre offset of coordinates between the workpiece and the rotary stage. The offset value had significant effect on measurement results. The Y-directional offset of contact point y was caused by the friction between the contact probe and the flank profile. y has significant influence on measurement results too.
To confirm the influence of coordinate system error, simulations were carried out for analysis of the influence of the offset. Fig.4 shows the simulation results of contact point offset in the case of fixed scroll. The horizontal axis indicates rotational angle of fixed scroll and vertical axis shows simulation profile error. Fig.4 (a) shows the influence of
Y-directional offset of the contact point. Here, y was defined
by Y-directional offset displacement of the contact measurement point. Profile errors were calculated, when
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considered y=0.5 mm and 1 mm. It can be seen that y has large influence on the profile results. Influence becomes more significant with an increasing y. In order to achieve the
required measurement accuracy of involutes profile, it had been confirmed that Y-direction offset error must be removed from the measurement profile error. Fig.4 (b) shows influence of the centre offset of coordinates between the workpiece and the rotary stage. To test the influence of centre coordinate offset, computer simulations were conducted based on the ideal outside involulte and inside involute profile. Here, xn and yn are defined by the centre coordinate offset between the workpiece and the rotary stage. As can be seen in the figure, xn and yn generate a very large periodic measurement error influence even if the centre coordinate offset is very small. The periodic profile error of Fig.3 was caused by xn and
yn. It is
necessary to
separate the centre coordinate offset
and y-direction offset under the required
accuracy order.
error/mm
0
-0.1
Simulation
y=1.0mm
-0.2
-0.3
y=0.5mm
0
200
400
600
800
Rotation angle/degree
error/mm
(a) Y-direction offset
x0=5μm,y0=5μm
0.01
x1=10μm,y1=10μm
Simulation
0.005
0
-0.005
-0.01
-0.0150
200
400
600
800
Rotation angle/degree
(b) Xn and yn offset
Fig.4
Simulation analysis of impacting measurement result
4. MEASUREMENT RESULTS AND COMPARISON WITH CMM
Where, θreal is the real scroll polar angle of measurement point. θmea is the outputs of rotary stage encoder. The y is the Y-directional offset of probe. The r is the theoretical scroll radius of every measurement point. The Y-directional offset of probe centre is compensated by the equation (5).
In order to obtain the centre coordinate offset of workpiece and measurement system, measurement profile error that is shown in Fig.3 is fitted into circle by the following equation (6).
a × x + b × y + c = ?(x2 + y 2 )
(6)
Where, a = ?2xc ， b = ?2yc ， c = xc2 + yc2 ? r 2 .
xc and yc can be calculated by a and b. x and y are calculated by measurement profile error. Measurement profile error that
is shown in Fig.3 was compensated by xc, yc and △y.
Measurement results are shown in Fig.5. Fig.5 (a) represents the outside profile error after compensation. The outside profile error is about ±5 μm. Fig.5 (b) represents the inside profile error after compensation. Inside profile error is about
±6 μm. Measurement error of rapid measurement system basically meets the required accuracy.
ì m
10
5
error/
0
Profile
-5
-10
0
200
400
600
-200
Rotation angle/degree
m
10
(a) Outside profile error
ì
5
error/
0
Profile
-5
-10
0
200
400
600
-200
Rotation angle/degree
(b) Inside profile error
Fig.5
Measurement result after error separation
B. Measurement result compared with that of the CMM
AFTER ERROR SEPARATION
A. Measurement results after error separation
The measurement profile error of Fig.3 consists of centre coordinate offset and Y-directional offset of contact point. The Y-directional offset of contact point can be measured by the outputs of the probe encoder. The Y-directional outputs of the probe are about 0.1mm. The Y-directional offsets make probe centre deviate from the X axis. There are leaning angles between probe contact point and X axis. The actual scroll polar angle of the measurement contact point can be showed by the equation (5).
θreal = θmea + tan?1 (?y / r)
(5)
69
In order to test the measurement result of the rapid measurement system, the outside and inside profile errors for the fixed scroll were measured by a commercial CMM in constant temperature room. About 1560 measurement points were obtained from the inside and outside profiles respectively. The measurement time was about 20 minutes for the inside and outside profile. About 4090 measurement points were obtained from the inside and the outside profiles respectively by the rapid measurement system. The measurement time was about 150 seconds for the inside and outside profile by the rapid measurement system. The measurement results of the outside and inside profile are shown in Fig.6. As can be seen in the figure, the measurement results of rapid measurement system for the outside and inside profile were the same as
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those of the CMM. But the measurement time of the rapid measurement system was much shorter than that of the CMM. The machining time for a scroll workpiece was about 300 seconds [9]. The rapid measurement system can meet the on -line machining measurement requirement.
ProfileProfileerror:error:20μmì m
Protype
Y/mm
40
Theoretical
CMM
20
0
-20
-40
-40 -20 0 20 40
X/mm
Fig.6 Measurement results for involutes profile of scroll
5. CONCLUSIONS
A rapid measurement system for scroll compressors has been developed based on a precision three-coordinate probe. The measurement errors of two kinds of offsets were analyzed by simulations. The measurement results of the rapid measurement system were the same as those of the CMM, but the measurement time of rapid measurement system was much shorter than that of the CMM. The developed rapid measurement system can meet the on-line machining measurement requirement of scroll compressors. The rapid measurement of non - involute profile is the future work.
MEASUREMENT SCIENCE REVIEW, Volume 9, No. 3, 2009
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