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Design of precision angular indexing system for calibration of rotary tables?
Mechatronics & Manufacturing Center, Samsung Electronics Co. LTD., Suwon-city, 443-742, Korea
Abstract
The indexing table was developed for angle measurements on machine tools. The measuring techniques, which have been reviewed in this paper, are currently available in manufacturing engineering to calibrate the angle measurement. The measuring principles of each equipment are outlined and their capabilities are also discussed. The new indexing table using 6 points kinematic concept and employing ball and vee grooves location was designed and manufactured to calibrate angle errors of rotary tables using a laser interferometer. The manufacturing method was evaluated to manufacture the accurate vee grooves. A special cam was designed and manufactured to trans-late rotation movement into lift-up and rotation movement. A CNC machining centre and indexing head were used to manufacture the cam. All parts of the new indexing table were manufactured with a manufacturing tolerance according to drawings, squareness and paral-lelism checked to obey the 6 points kinematic concept. Also these factors controlled the repeatability of the new indexing table. After installing the new indexing table, the performance was evaluated using rotary table operating in both the horizontal and vertical orienta-tions.
1. Introduction
Many types of indexing tables appear in industry. These in-dexing tables have recently become an increasing necessity for improving the precision and accuracy of angle measure-ment, and circle dividing in various fields of science and tech-nology. Most indexing tables use a HIRTH coupling, worm and wormwheel, or a grating disc. The manufacturing process together with the requirements for precision is very difficult. Consequently these indexing tables are expensive and usually used for manufacturing purpose of rotating.
To calibrate these indexing tables, a polygon and autocolli-mator, or the serrated type indexing table which is usually ±1 second accuracy, are usually used and the calibration accuracy of the polygon and autocollimator is about ±1 second. Many mathematical models have been developed to calibrate rotary tables using polygon and autocollimator . These mathe-matical models usually use a matrix form and calibration takes a long time.
Subsequently a calibration method using a laser interfer-ometer was developed by Lin . To accomplish his calibra-tion method, the indexing table requires good repeatability, so an automatic indexing table using a ball and pin was devel-oped [2]. Although this performed very well in a laboratory situation, it was not considered robust enough to reproduce as a commercial design. The problem with this automatic index-ing table is the balls which are located on the circumference of the body could move when the top plate was located, or any force was applied to the top plate. Consequently a new mechanism should be considered for the indexing table. Thus a 6 point contact kinematic design concept of ball and vee groove was used, because the ball and vee groove system can attain 0.1 μm repeatability [3] and has good rigidity.
The aim of this research is to consider the design and manu-facturing of an automatic indexing table using this kinematic design concept.
2. Techniques for the calibration of rotary indexing tables
All measuring instruments possess finite accuracy. The er-ror which arises from instrument limitations is usually not of a magnitude which could significantly affect the accepted accu-racy of specific measurement. Nevertheless, for assuring the reliability of measurements, it is necessary to determine the operating accuracy of circular dividing instruments by means of a dependable calibration process.
Fig. 1. Calibration of rotary table with 1440 indexing table and mirror.
Fig. 2. Reading the change of angular optics due to a changing angle.
2.1 Calibration of indexing table by polygon and autocolli-mator
For the calibration of an indexing table, the most generally used method is based on the use of a polygon and autocolli-mator. Calibration of the rotary table is readily performed by means of a precision polygon mounted on a table and read by a single fixed autocollimator. Several methods to calibrate a rotary indexing table were developed by N.P.L. [1].
The fixed autocollimator is null on the centre of the first face of polygon. Next the rotary table is rotated through the prescribed angle, corresponding to the increments (number of faces) of the polygon. Angular deviation shown by the auto-collimator is recorded when returning to its original setting face. A correction factor (error of each polygon face from nominal) furnished by the manufacturer is applied to the read-ing to find the actual error of the rotary table at the sectors calibrated or measured.
2.2 Rotary table calibration with serrated tooth type indexing table
Fig. 1 shows a 1440 indexing table which has 1440 serrated tooth and 0.1 second accuracy. It is mounted on a rotary table for calibration. A single shield reflecting mirror and autocol-limator, much the same as that employed for self-calibration of the 1440 indexing table are used. The arrangement is typi-cal of that already supplied by the rotary table manufacturers.
Errors of the rotary table are read directly on the autocolli-mator, requiring no ‘closing of the circle’, nor use of calibra-tion factors. Errors of the 1440 indexing table in this applica-tion may be considered negligible. The advantages compared to the other method of calibration with the polygon, can be summarized as follows:
(1) One self - contained unit is the equivalent of several types of polygons
(2) The polygon can only be relied on to 1 or 2 seconds, compared to the 0.1 second accuracy of the 1440 indexing table.
Only one mirror is used. The importance of the single mir-ror cannot be over emphasized; a large flat mirror may be perfected for maximum reflectivity. Effort need only be ex-pended to assure that it is absolutely flat without having to consider simultaneously its angular position. The same spot in the mirror is always used, instead of shifting mirror to mirror.
2.3 Calibration of indexing table by laser interferometer and ball type automatic indexing table
A researcher [2] developed the laser calibration of the rotary table with an automatic indexing table and a laser interferome-ter. The calibration method usually uses a mathematical model with a matrix and off line system. Also the autocollimator is dependant on air currents therefore the calibration data is reli-able only when the air condition is stable. When the laser in-terferometer is used for calibration, air currents can be com-pensated for by the compensator of the laser interferometer.
As this system is used for calibration, the most important thing is that automatic indexing table should give good repeat-ability. To accomplish repeatability the automatic indexing table employs the ball and pin using a kinematic design prin-ciple. The balls are in contact with the circumference of the body and outer ring holding the balls fixed on the circumfer-ence of the body. The pins are fixed in the top disc. The top disc can be moved 6 degrees each step by a camshaft and mo-tor. Also the pins are kinematically located at every target position [2].
This system incorporates an indexing table and laser inter-ferometer with angular optics. As mentioned above with this system the table only needs to be repeatable. The principle of angular measurement using the laser interferometer is shown Fig. 2. The range of angular optics is normally restricted to ±10° but by using the indexing table to repeatedly reset of the angular optics to a nominal zero position, it becomes feasible to undertake a 360° full scale test. The indexing table is driven by a camshaft and motor assembly. This allows indexing by one single step of 6° during angular measurement. The angu-lar optics is mounted on the automatic indexing table under calibration.
This reading is accomplished by stepping the table under test forward one step and then indexing backward through the same nominal angular increments. This measuring technique contains two sets of laser readings which are needed to cali-brate errors for both tables.
From the Fig. 3
Fig. 3. Mathematic modeling for angle analysis. Fig. 5. Kinematic location of balls in radial vee.
Fig. 4. Kinematic couplings.
CSin (γ + θ i ) = CSinγ + Ri
CSin (γ + β i ) = CSinγ + γ i
θi = β i + αi .
From the above equations, γ , β i , θ i ,αi are calculated [2]. It is so called a self-calibration technique that requires no pre - calibration of the indexing table.
3. Design of new indexing table
3.1 Concept of kinematic design
Kinematic design is widely recognized as one of the fore-most design concepts in precision engineering. Most objects in space have three degrees of translators and three degrees of rotational freedom [6, 7]. Two different philosophies for me-chanical design exist - kinematic and elastic.
While being quite different in approach they can be com-bined in a design. In the kinematic design philosophy, the aim is to locate all parts relative to each other, while allowing a degree of freedom as needed, by connecting points together without significant elastic deformation. Fig. 4 shows three examples of kinematic couplings.
A simple theorem that allows calculation of the number of points of contact was enunciated by Strong [4]. He defined:
“Kinematic design is correct when a body in contact with another has at least 6-n points of contact where n is the number of degrees of freedom existing. If the system has more than 6-n points of contact it has mechanical redundancy” [4].
In Fig. 4(a), three rotations are possible for the ball, whereas in Fig. 4(b) and (c) no freedom of movement is provided.
3.2 Feature of new indexing table
As mentioned in previous section, the automatic indexing table which was developed by Lin [2] employs pins and balls. The balls are in contact with the circumference of the body and the outer rings hold the balls fixed on the circumference of the body. The ball is moved by applying high speed rota-tion of camshaft. Consequently the automatic indexing table cannot give good repeatability.
3.2.1 Detailed consideration of new indexing table
The basic principle of this new indexing table employs a vee and balls kinematic location system. Each ball is contact with both side of vee surface so each ball has 2 contact points on the vee. Therefore three balls have 6 kinematics contact points. The chosen incremental indexing angle is 5 degree because 5 degree incremental angle is considered to be the smallest increment used for the practical calibration of 360° indexing tables.
The detailed specification of this new table is as follows:
（1）An incremental angle indexing device which is small and light weight thus does not influence the machine on which it is being used.
（2）The size of the device compatible with the angle reflec-tor optics of the laser interferometer. The size of this angle reflector is 40×40×72.6 (mm).
（3） The table should be capable of operating in any attitude. (i.e. vertical, horizontal and up-side down)
（4）Automatically indexed from a program command on a P.C.
（5）Step angle of 5 degrees.
（6）Accuracy of step angle of about ±1 second of arc but it is not essential using the calibration technique employed.
（7）Repeatability of indexing ±0.2 seconds of arc.
（8）Table can be easily manufactured and does not require high precision technique.
（9）Low cost.
Fig. 6. Mechanism of indexing table.
3.2.2 Mechanism of new indexing table
Generally, commercially available indexing tables contain two step operations for indexing (i.e. lift up and rotate), but this new type of indexing table employs one step operation, lifting up and rotating simultaneously by using a camshaft and motor. Fig. 6 shows the mechanism of the indexing table.
To hold the top disc on the body and lock the top disc on the vee, the indexing table employs a compression spring be-tween the body and pindisc which is connected to the shaft by screws. A needle bearing is fitted between the spring and pin disc to prevent torsion and minimize friction.
The vee and ball type of indexing table is designed to mi-nimize the working space and gives good repeatability be-cause the vee and ball contact with 6 points kinematic concept (i.e. each ball contact with vee surface with 2 contact points). Spur gears are employed to translate motor motion into the camshaft and to increase rotation force (i.e. torque).
The indexing table employed a pindisc to transform the ro-tation motion into lift-up and rotation motion of the top disc. The pindisc which is assembled with main shaft and top disc, had 36 equally spaced pins giving a 10 degree incremental angle around the circular disc. Pins are designed to guide, lift-up and rotate during camshaft rotation. The pindisc follows the groove of the camshaft during camshaft rotation. The rota-tion of the camshaft is controlled by an opto-disc which is fixed to the camshaft end. Two slots in the opto-disc trigger an opto-switch when rotation takes place.
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轉(zhuǎn)臺校準用精密角度分度系統(tǒng)設(shè)計
摘要
分度臺是為機床上的角度測量而開發(fā)的。本文所述的測量技術(shù)目前在制造工程中可用于校準角度測量。概述了每種設(shè)備的測量原理，并討論了其功能。設(shè)計并制造了使用6點運動學(xué)概念和使用球和V形槽位置的新分度臺，以使用激光干涉儀校準旋轉(zhuǎn)臺的角度誤差。評估制造方法以制造精確的V形槽。設(shè)計和制造了一個特殊的凸輪，以便將旋轉(zhuǎn)運動轉(zhuǎn)換成提升和旋轉(zhuǎn)運動。CNC加工中心和分度頭用于制造凸輪。新的分度臺的所有部件均按制造公差制造，按照圖紙，方形和平行度檢查，以遵守6點運動學(xué)概念。而且這些因素控制著新分度臺的可重復(fù)性。在安裝新的分度臺之后，使用在水平和垂直方向操作的旋轉(zhuǎn)工作臺來評估性能。
目錄
1緒論 14
2旋轉(zhuǎn)分度臺校準技術(shù) 15
2.1用多邊形和自準直儀校準分度臺 15
2.2鋸齒形分度臺轉(zhuǎn)臺校準 15
2.3用激光干涉儀和球型自動分度臺校準分度臺 16
3.新的分度臺的設(shè)計 18
3.1運動設(shè)計的概念 18
3.2新分度臺的功能 18
3.2.1詳細考慮新的分度臺 18
3.2.2新分度臺的機制 19
參考文獻 20
1緒論
行業(yè)中出現(xiàn)了許多類型的分度臺。這些分度臺最近已成為提高角度測量的精度和精度以及科學(xué)和技術(shù)各個領(lǐng)域的分界的必要條件。大多數(shù)分度臺使用HIRTH耦合器，蝸桿和蝸輪，或者光柵盤。制造過程和精度要求是非常困難的。因此這些分度臺是昂貴的，通常用于制造旋轉(zhuǎn)的目的。
為了校準這些分度臺，通常使用多邊形和自準直儀，或通常使用精度為±1秒的鋸齒形分度臺，多邊形和自準直儀的校準精度約為±1秒。許多數(shù)學(xué)模型已經(jīng)被開發(fā)來使用多邊形和自準直儀來校準旋轉(zhuǎn)臺。這些數(shù)學(xué)模型通常使用矩陣形式，校準需要很長時間。
隨后，Lin 開發(fā)了一種使用激光干涉儀的校準方法。為了完成他的校準方法，分度臺需要很好的重復(fù)性，所以一個使用球和針的自動分度臺已經(jīng)開發(fā)出來。雖然這在實驗室中表現(xiàn)得非常好，但它不足以作為商業(yè)設(shè)計再現(xiàn)。這個自動分度臺的問題是當頂板位于主體圓周上的球可能移動，或者任何力施加到頂板。因此，分度臺應(yīng)該考慮一個新的機制。因此采用了球和V形槽的六點接觸運動學(xué)設(shè)計理念，因為球和V形槽系統(tǒng)可以達到0.1μm的可重復(fù)性，并具有良好的剛性。
這項研究的目的是考慮使用這種運動學(xué)設(shè)計理念的自動分度臺的設(shè)計和制造。
2旋轉(zhuǎn)分度臺校準技術(shù)
所有測量儀器都具有有限的精度，儀器限制引起的誤差通常不會顯著影響公認的具體測量精度。盡管如此，為了確保測量的可靠性，有必要通過可靠的校準過程來確定圓形分割儀器的操作精度。
圖2-1使用1440分度臺和反射鏡校準轉(zhuǎn)盤。
圖2-2讀取角度變化引起的角度變化。
2.1用多邊形和自準直儀校準分度臺
對于分度臺的校準，最常用的方法是基于使用多邊形和自準直儀。旋轉(zhuǎn)臺的校準通過安裝在桌子上的精密多邊形容易地執(zhí)行，并由單個固定的自準直儀讀取。NPL開發(fā)了幾種校準旋轉(zhuǎn)分度臺的方法。
固定的自準直儀在多邊形的第一個面的中心為零。接下來，旋轉(zhuǎn)臺旋轉(zhuǎn)規(guī)定的角度，對應(yīng)于多邊形的增量（面數(shù)）。自動準直器顯示的角度偏差在返回到其原始設(shè)置面時記錄。由制造商提供的校正因子（每個多邊形面的誤差來自標稱）被應(yīng)用于讀取以查找校準或測量的扇區(qū)處的旋轉(zhuǎn)臺的實際誤差。
2.2鋸齒形分度臺轉(zhuǎn)臺校準
圖2-1顯示了一個1440分度臺，其中有1440個鋸齒，精度為0.1秒。它安裝在旋轉(zhuǎn)臺上進行校準。一個單一的屏蔽反射鏡和自動準直儀，與1440分度臺的自校準使用的相同。這種裝置的典型特點是由轉(zhuǎn)臺制造商提供。
直接在自準直儀上讀取轉(zhuǎn)盤的誤差，不需要“關(guān)閉圓”，也不需要使用校準因子。 在這個應(yīng)用程序中的1440分度臺的錯誤可能被認為是微不足道的。 與用多邊形校準的其他方法相比，其優(yōu)點可總結(jié)如下：
(3) 一個自包含單元相當于幾種類型的多邊形。
(4) 多邊形只能依靠1秒或2秒，而1440分度表的精度為0.1秒。
只使用一面鏡子。單反的重要性不能過分強調(diào), 一個大的平面反射鏡可以完美的最大反射率。只需要付出努力，以確保它絕對平坦無需同時考慮它的角度位置。總是使用鏡子中的相同點，而不是將鏡子移動到鏡子。
2.3用激光干涉儀和球型自動分度臺校準分度臺
研究人員利用自動分度臺和激光干涉儀開發(fā)了旋轉(zhuǎn)臺的激光校準。校準方法通常使用帶有矩陣和離線系統(tǒng)的數(shù)學(xué)模型。自準直儀也依賴于空氣流量，因此只有在空調(diào)狀態(tài)穩(wěn)定的情況下，校準數(shù)據(jù)才是可靠的。當使用激光干涉儀校準時，氣流可以通過激光干涉儀的補償器來補償。
由于該系統(tǒng)用于校準，最重要的是自動分度表應(yīng)該具有良好的重復(fù)性。為了實現(xiàn)可重復(fù)性，自動分度臺采用運動學(xué)設(shè)計原理采用球和銷。球體與球體的外周接觸，外球體將球體固定在球體的圓周上。引腳固定在頂部光盤中。 頂盤可以通過凸輪軸和電機每步移動6度。 此外，這些針腳在運動學(xué)上位于每個目標位置。
該系統(tǒng)包含一個分度臺和帶角度光學(xué)元件的激光干涉儀。正如上面提到的這個系統(tǒng)，表格只需要是可重復(fù)的。使用激光干涉儀的角度測量的原理如圖2所示。角度光學(xué)器件的范圍通常限制在±10°，但是通過使用分度臺將角度光學(xué)器件重復(fù)復(fù)位到標稱零點位置，進行360°全面測試。分度臺由凸輪軸和電機組件驅(qū)動。 這允許在角度測量期間通過一個6°的單個分度進行分度。校準時，角度光學(xué)元件安裝在自動分度臺上。
這個讀數(shù)是通過將被測表格向前推進一步，然后通過相同的標稱角度增量向后分度來完成的。 這種測量技術(shù)包含兩套激光讀數(shù)，這兩種激光讀數(shù)需要校準兩個表的誤差。見圖2-3。
圖2-3角度分析的數(shù)學(xué)建模 圖2-4球在徑向三角的運動位置
圖2-5運動聯(lián)軸器
CSin（γ+θi）=CSinγ+Ri
CSin（γ+βi）=CSinγ+γi
θi=βiαi。
從上式可以計算出γ，βi，θi，αi。 這就是所謂的自校準技術(shù)，不需要
預(yù)先校準分度臺。
3.新的分度臺的設(shè)計
3.1運動設(shè)計的概念
運動設(shè)計被廣泛認為是精密工程中最前沿的設(shè)計理念之一。大多數(shù)空間物體都有三個譯者和三個旋轉(zhuǎn)自由度。存在兩種不同的機械設(shè)計理念 - 運動學(xué)和彈性。
雖然在方法上有很大的不同，但可以在設(shè)計中結(jié)合使用。在運動學(xué)設(shè)計理念中，目標是通過將點連接在一起，而不會產(chǎn)生顯著的彈性變形，從而使所有零件相對于彼此定位，同時允許一定程度的自由度。圖4顯示了三個運動學(xué)耦合的例子。
一個簡單的定理，允許計算的接觸點的數(shù)量由Strong 闡明。他定義：
“當一個身體與另一個身體接觸時，運動學(xué)設(shè)計是正確的，至少有6-n個接觸點，其中n是數(shù)字，現(xiàn)有的自由度。如果系統(tǒng)具有超過6-n個接觸點，則具有機械冗余。
在圖2-5（a）中，對于球可以進行三次旋轉(zhuǎn)，而在圖2-5（b）和（c）中沒有提供運動的自由度。
3.2新分度臺的功能
正如前面提到的那樣，Lin [2]開發(fā)的自動分度表使用了針和球。球體與球體的周圍接觸，外球體將球體固定在球體的周圍。通過凸輪軸的高速旋轉(zhuǎn)使球移動。因此自動分度表不能提供良好的重復(fù)性。
3.2.1詳細考慮新的分度臺
這個新的分度臺的基本原理采用了一個VE和球運動定位系統(tǒng)。每個球都與V形表面的兩側(cè)接觸，所以每個球在V形上有兩個接觸點。 因此三個球有6個運動學(xué)接觸點。所選擇的增量分度角是5度，因為5度增量角被認為是用于360°分度表的實際校準的最小增量。
這個新表的詳細說明如下：
(1)增量式角度分度裝置由于體積小而重量輕，因此不會影響正在使用的機器。
(2)該設(shè)備的尺寸與激光干涉儀的角反射器光學(xué)元件兼容。這個角度反射器的大小是40×40×72.6（mm）。
(3)桌子應(yīng)該能夠以任何姿態(tài)進行操作。 （即垂直，水平和正面向下）
(4)從PC上的程序命令自動編入分度
(5)步角5度。
(6)使用所使用的校準技術(shù)，步進角精度約為±1秒。
(7)分度重復(fù)性,0.2秒的電弧。
(8)表可以很容易地制造，不需要高精度的技術(shù)。
(9)低成本。
圖3-1分度臺的機制
3.2.2新分度臺的機制
一般來說，商業(yè)化的分度臺包括分度（即抬起和旋轉(zhuǎn)）的兩步操作，但這種新型分度臺采用一步操作，通過使用凸輪軸和電機同時抬起和旋轉(zhuǎn)。圖3-1顯示了分度臺的機制。
為了將頂盤固定在主體上并將頂盤鎖定在V形上，分度臺在主體和小圓柱體之間使用壓縮彈簧，該小彈簧通過螺釘連接到軸。彈簧和銷盤之間裝有一個滾針軸承，以防止扭轉(zhuǎn)和減少摩擦。
V型和V型球的分度臺被設(shè)計成使工作空間最小化并且具有良好的可重復(fù)性，因為V型和V型球與6點運動學(xué)概念（即每個球與V型接觸點接觸）接觸。采用正齒輪將電機運動轉(zhuǎn)換成凸輪軸并增加旋轉(zhuǎn)力（即扭矩）。
分度臺采用小圓柱來將旋轉(zhuǎn)運動轉(zhuǎn)換成頂盤的提升和旋轉(zhuǎn)運動。與主軸和頂部圓盤組裝在一起的圓柱體，有36個等距的銷釘，圓盤周圍有10度的增量角度。凸輪軸旋轉(zhuǎn)過程中，引腳設(shè)計用于引導(dǎo)，提升和旋轉(zhuǎn)。在凸輪軸轉(zhuǎn)動過程中，小圓柱跟隨凸輪軸的凹槽。凸輪軸的旋轉(zhuǎn)由固定在凸輪軸端的光盤控制。旋轉(zhuǎn)時，光盤中的兩個插槽會觸發(fā)一個光電開關(guān)。
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