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滾珠絲杠副設(shè)計(jì)及相關(guān)技術(shù)研究
摘要：滾珠絲杠是因其自身良好的可靠性，精度等級(jí)高，使用及維護(hù)成本都比較低的優(yōu)勢(shì)被廣泛應(yīng)用于多種場(chǎng)合，其中高精密機(jī)床上應(yīng)用甚多。所以研究和優(yōu)化滾珠絲杠具有巨大的前景。本設(shè)計(jì)中具體對(duì)滾珠絲杠進(jìn)行了多方面的學(xué)習(xí)，包括滾珠絲杠相關(guān)各種參數(shù)的計(jì)算及其校核。并對(duì)絲杠周圍部件進(jìn)行了了解。除此之外，本設(shè)計(jì)還對(duì)滾珠絲杠的高速化及其優(yōu)化方案也進(jìn)行了簡(jiǎn)述。
關(guān)鍵詞：滾珠絲杠 設(shè)計(jì)方案 高速化
II
中北大學(xué)信息商務(wù)學(xué)院2016屆畢業(yè)設(shè)計(jì)說明書
Abstract：Ball is due to its own good reliability, high level of accuracy, use, and maintenance costs are relatively high advantages are widely used in a variety of situations, many of which use high-precision machine tools. Therefore, research and optimization ball screw has great prospects. The specific design of the ball screw conducted extensive research, including the calculation of various parameters related to ball screws and check. And screw around parts of the inquiry. In addition, this design also on the high-speed ball screw and its optimization program has also been outlined.
Keywords: high-speed ball screw design
目 錄
摘要 ……………………………………………………………………………I
Abstract ……………………………………………………………………………II
目錄………………………………………………………………………………III
1.緒論 ……………………………………………………………………………1
1.1滾珠絲杠概述………………………………………………………………3
1.2本課題研究的意義…………………………………………………………8
2.滾珠絲杠的設(shè)計(jì) ………………………………………………………………8
2.1原始數(shù)據(jù)與技術(shù)條件………………………………………………………9
2.2滾珠絲杠的主體參數(shù)設(shè)計(jì)…………………………………………………9
2.2.1導(dǎo)程的選擇 ……………………………………………………10
2.2.2 絲杠軸長(zhǎng)度的選擇 ………………………………………………11
2.2.3絲杠軸直徑的選擇 ………………………………………………13
2.2.4絲杠軸支撐方式的選擇 …………………………………………12
2.2.5螺母的選擇 ………………………………………………………13
3.各零部件的校核………………………………………………………………14
3.1容許軸向負(fù)載的計(jì)算 ……………………………………………………14
3.2絲杠軸容許轉(zhuǎn)速的計(jì)算 …………………………………………………15
3.3螺母運(yùn)行距離的計(jì)算 ……………………………………………………15
3.4螺母軸向平均負(fù)荷及其壽命校核 ………………………………………16
4.定位精度的探討……………………………………………………………18
4.1導(dǎo)程精度的探討 …………………………………………………………18
4.2軸向間隙的校核 …………………………………………………………18
4.3軸向剛性的校核 …………………………………………………………18
4.4運(yùn)行姿態(tài)的探討 …………………………………………………………19
4.5旋轉(zhuǎn)扭矩的校核 …………………………………………………………19
5.電動(dòng)機(jī)的選擇 …………………………………………………………………20
5.1旋轉(zhuǎn)速度 …………………………………………………………………20
5.2最小進(jìn)給量 ………………………………………………………………20
5.3電動(dòng)機(jī)扭矩……………………………………………………………20
5.4扭矩的有效值 ……………………………………………………………21
6.滾珠絲杠高速化研究 ………………………………………………………21
1.精密滾珠絲杠副實(shí)現(xiàn)高速化要解決的主要矛盾 …………………………21
2.滾珠絲杠副高速化的技術(shù)對(duì)策 …………………………………………22
7.總結(jié) ……………………………………………………………………23
參考文獻(xiàn) ……………………………………………………………………24
致謝 …………………………………………………………………25
V
1．緒論
1.1滾珠絲杠的概述
滾珠絲桿是一種能在直線進(jìn)給和周轉(zhuǎn)運(yùn)動(dòng)之間互相轉(zhuǎn)換的理想的機(jī)械產(chǎn)品。因具有傳動(dòng)效率、運(yùn)動(dòng)平穩(wěn)、高精度、高耐磨性、高同步、高可靠性、無背隙和高剛性的諸多優(yōu)點(diǎn)，并被廣泛應(yīng)用于機(jī)械行業(yè)。
傳統(tǒng)的滾珠絲杠采用循環(huán)方式主要有三種。
第一，外循環(huán)，（管路式）其結(jié)構(gòu)簡(jiǎn)單易于使用。在滾珠滾道內(nèi)通過一根插管將進(jìn)口和出口相連接，從而達(dá)到無限循環(huán)。
圖1-5外循環(huán)
第二，內(nèi)循環(huán)，（哥德式）其結(jié)構(gòu)緊湊，也比較易于小型化，但制造成本較高。
圖1-6 內(nèi)循環(huán)
第三，端蓋式。（端面式）
1
圖1-7 端蓋式
滾珠絲杠至誕生以來，就得到了世人的許多關(guān)注，也進(jìn)行了比較大的改進(jìn)和融合。并發(fā)展出了許多不同用途，不同型號(hào)的滾珠絲杠產(chǎn)品。如在日本相關(guān)專利方面就有除了傳統(tǒng)內(nèi)外循環(huán)的滾珠絲杠外，還出現(xiàn)了不使用循環(huán)的滾珠方案，并且得到了諸多應(yīng)用。以下以舉例的形式表達(dá)一種非循環(huán)的滾珠絲杠方式：如圖，該發(fā)明滾珠絲杠螺母內(nèi)加入彈性元件，并使其能夠很方便放入滾道內(nèi)，使之隨著滾珠體一起進(jìn)行運(yùn)動(dòng)。在1-1、1-2圖中，當(dāng)滾珠體逆時(shí)針旋轉(zhuǎn)時(shí)，會(huì)壓迫彈性元件也向逆時(shí)針運(yùn)動(dòng)。當(dāng)該方向運(yùn)動(dòng)結(jié)束后，彈性元件便會(huì)將滾珠體再壓回原來位置。同理也有另外一個(gè)方向，如圖1-3所示。
2
圖1-1 一種非循環(huán)方式的滾珠絲杠裝置
循環(huán)軌道中的彈性元件能夠在運(yùn)動(dòng)的開始和結(jié)束狀態(tài)起到儲(chǔ)能的作用，也是實(shí)現(xiàn)非循環(huán)方式運(yùn)動(dòng)的關(guān)鍵。
3
圖1-2 一種非循環(huán)方式逆時(shí)針方向動(dòng)態(tài)圖解
圖1-3 一種非循環(huán)方式順時(shí)針方向動(dòng)態(tài)圖解
可以想象如此設(shè)計(jì)能夠最大限度地縮小螺母的徑向長(zhǎng)度，從而為滾珠絲杠的小型化開辟了道路。
圖1-4 一種非循環(huán)方式滾珠絲杠三維圖例
1.2本課題研究目的
CNC數(shù)控機(jī)床中，進(jìn)給系統(tǒng)的主體實(shí)現(xiàn)元件是滾珠絲杠副。雖然滾珠絲杠已經(jīng)出現(xiàn)了近百年的歷史，但其優(yōu)越性能仍然是現(xiàn)在許多元件無法替代的，并且具有很大的優(yōu)勢(shì)，啟動(dòng)力矩小，定位精度高，運(yùn)行可靠。并且隨著其他相關(guān)技術(shù)的成熟進(jìn)步，尤其是材料性能的改善和工藝技術(shù)的改進(jìn)優(yōu)化，滾珠絲杠副的優(yōu)勢(shì)將更加凸顯，所以我們很有必要將滾珠絲杠副的優(yōu)化設(shè)計(jì)放在自己的設(shè)計(jì)理念中，并將其優(yōu)點(diǎn)發(fā)揚(yáng)光大。
2.滾珠絲杠的設(shè)計(jì)
2.1原始數(shù)據(jù)與技術(shù)條件
表1.1滾珠絲杠的主體設(shè)計(jì)要求
工作臺(tái)重量W1
25kg
工作及夾具最大重量W2
80kg
工作臺(tái)最大行程 LK
1000mm
快速進(jìn)給速度Vmax
60m/min
動(dòng)摩擦系數(shù)
μ=0.003
定位精度
0.02mm/300mm
重復(fù)定位精度
0.01mm
全行程定位精度
0.025mm
要求壽命
30000 h
導(dǎo)向面阻力
15N
額定轉(zhuǎn)速
3000 r/min
驅(qū)動(dòng)電動(dòng)機(jī)
AC伺服電機(jī)
減速器A
1
電動(dòng)機(jī)的慣性扭矩
0.001
圖2-1 滾珠絲杠裝置整體受力圖
表1.2滾珠絲杠的主體參數(shù)
絲杠軸直徑
導(dǎo)程
螺母型號(hào)
精度
軸向間隙
絲杠軸支撐方式
電動(dòng)機(jī)功率
2.2.1導(dǎo)程的選擇
導(dǎo)程的選擇必須與所需要的最高速度相配合，本設(shè)計(jì)中的滾珠絲杠裝置最高速度選取1m/s，也即60000mm/min。電動(dòng)機(jī)擬采用AC伺服電機(jī)，其最大轉(zhuǎn)速為3000r/min。綜上，可計(jì)算出導(dǎo)程的許用最小值L為：
mm
在這里，根據(jù)機(jī)械手冊(cè)中查表數(shù)據(jù)可得滾珠絲杠的導(dǎo)程取L=20mm。
2.2.2絲杠軸長(zhǎng)度選擇
絲杠軸的選擇必須考慮到螺母的長(zhǎng)度,現(xiàn)在暫定其長(zhǎng)度為160mm，絲杠軸兩末端支撐長(zhǎng)度為160mm。
根據(jù)實(shí)際需求，絲杠長(zhǎng)度行程長(zhǎng)度選擇為1000mm。
則絲杠軸全長(zhǎng)為：
2.2.3絲杠軸直徑的選擇
本設(shè)計(jì)中絲杠軸擬采用一端固定，一端支撐的方式
（公式2.1）
當(dāng)安裝方式為固定，支撐時(shí)，查表：f=15.1
則Dr21.9mm
由機(jī)械設(shè)計(jì)手冊(cè)所示滾珠絲杠型號(hào)∶
絲杠軸直徑 導(dǎo)程
20mm —— 20mm
20mm —— 40mm
30mm —— 60mm
由上所述,根據(jù)機(jī)械手冊(cè)查表最終確定絲杠軸直徑40mm/導(dǎo)程20mm的設(shè)計(jì)方案。絲杠軸的設(shè)計(jì)到此為止，總體的設(shè)計(jì)圖例見下
圖4-1絲杠軸
2.2.4軸支撐方法的選擇
本設(shè)計(jì)中滾珠絲杠的最大行程為1000mm,屬于遠(yuǎn)跨距安裝;速度為1m/s，屬高速使用；而且考慮到升溫比較有可能會(huì)導(dǎo)致絲杠軸變形彎曲。故而確定該支撐方法采用固定-支撐的方式。
圖2-2 絲杠形變
上圖為固定-支撐安裝方式的絲杠允許最大變形量的安裝間距，從圖上可以看出，安裝間距為1000mm的該滾珠絲杠符合要求。
圖紙?jiān)O(shè)方案如圖：
圖2-3 絲杠軸左端支撐方式
圖2-4 絲杠軸右端支撐方式
絲杠軸被固定于四個(gè)軸承上，左邊的一端被緊固落螺母固定，從而達(dá)到固定的目的，如圖2-3右端為支撐端。如圖2-4所示為滾珠絲杠右端支撐方式，與左端不同之處在于這端并未采用緊固螺母，為自由端。兩端都采用角接觸球軸承和深溝球軸承疊加安裝，這樣既能夠使軸既能夠承受軸向載荷，又能夠承受徑向載荷，從而滿足滾珠絲杠正常工作時(shí)的實(shí)際要求。
2.2.5螺母的選擇
螺母旋轉(zhuǎn)型滾珠絲杠,是把滾珠絲杠螺母與支撐軸承一體的螺母旋轉(zhuǎn)式滾珠絲杠裝置。其螺母為使用外循環(huán)方式的鋼球循環(huán)結(jié)構(gòu)，鋼球沿著滾道從入口到出口完成不間斷的循環(huán)。而傳統(tǒng)螺母外周嵌套有一個(gè)套筒。套筒外徑與一個(gè)調(diào)心滾子軸承相連接，通過調(diào)心滾子軸承將傳統(tǒng)螺母的徑向旋轉(zhuǎn)運(yùn)動(dòng)，與軸向的進(jìn)給運(yùn)動(dòng)相互分離，從而達(dá)到螺母一邊旋轉(zhuǎn)，一邊軸向進(jìn)給，而不影響與之相連接的工作臺(tái)只有軸向進(jìn)給的需求。
圖3-1 螺母旋轉(zhuǎn)方式實(shí)現(xiàn)方案
兩臺(tái)電動(dòng)機(jī)允許和絲杠軸、滾珠絲杠的螺母進(jìn)行獨(dú)立聯(lián)接,并通過與螺母套筒相連接的齒輪將旋轉(zhuǎn)力矩傳遞給螺母和套筒，并可以使微量進(jìn)給控制在電動(dòng)機(jī)的穩(wěn)定旋轉(zhuǎn)范圍內(nèi)。因其獨(dú)立運(yùn)動(dòng)的特性，該設(shè)計(jì)方案可以使用兩個(gè)伺服電機(jī)驅(qū)動(dòng)，令兩臺(tái)電機(jī)同時(shí)驅(qū)動(dòng)的方案，將兩個(gè)速度進(jìn)行組合，可以擴(kuò)大整個(gè)運(yùn)動(dòng)副的速度控制范圍。
3.零件的初步校核
3.1容許軸向負(fù)載的計(jì)算
最大軸向負(fù)荷的計(jì)算
導(dǎo)向面的阻力 （無負(fù)荷時(shí)）
工作臺(tái)質(zhì)量
工件質(zhì)量
導(dǎo)向面上的摩擦系數(shù)
最大速度
重力加速度
加速時(shí)間
由此可知,所需數(shù)值如下。
加速度（公式3.1）
去路加速時(shí)
去路等速時(shí)
去路減速時(shí)
返程加速時(shí)
返程等速時(shí)
返程減速時(shí)
作用在滾珠絲杠上的最大軸向負(fù)荷如下所示∶
現(xiàn)在選定直徑為40mm的絲杠軸、導(dǎo)程為20mm（最小溝槽谷徑37.4mm）的絲杠軸進(jìn)行撓曲載荷和容許壓縮拉伸負(fù)荷的計(jì)算：
絲杠軸撓曲載荷：
與安裝方法相關(guān)的系數(shù)
絲杠軸溝槽谷徑
（公式3.2）
容許壓縮拉伸負(fù)荷：
由此可見, 絲杠軸的挫曲載荷和容許拉伸壓縮負(fù)荷至少等于最大軸向負(fù)，因此, 滿足這些條件的滾珠絲杠在使用上沒有問題。
3.2 絲杠軸容許轉(zhuǎn)速的計(jì)算
絲杠軸直徑：40mm； 導(dǎo)程：20mm；最大速度：60000mm/min
由絲杠軸的危險(xiǎn)速度所決定的容許轉(zhuǎn)速：
與安裝方法（安裝方法按固定－支撐）相關(guān)的系數(shù)
安裝間距（推算）
絲杠軸直徑∶40mm；導(dǎo)程∶20mm
則許用的絲杠軸的最大轉(zhuǎn)速為：
（公式3.3）
絲杠軸直徑∶40mm；導(dǎo)程∶20mm和40mm（大導(dǎo)程滾珠絲杠）
按絲杠軸的危險(xiǎn)速度計(jì)算可得選用絲杠軸直徑為40mm和導(dǎo)程為20mm的絲杠軸沒有問題。
3.3螺母運(yùn)行距離的計(jì)算
最大速度
加速時(shí)間
減速時(shí)間
加速時(shí)的運(yùn)行距離：
（公式3.4）
等加速時(shí)的運(yùn)行距離：
（公式3.5）
減速時(shí)的運(yùn)行距離：
（公式3.6）
3.4螺母軸向平均負(fù)荷及其壽命校核
正符號(hào)方向的軸向平均負(fù)荷
因載荷方向相異,取，計(jì)算軸向平均負(fù)荷：
（公式3.7）
負(fù)符號(hào)方向的軸向平均負(fù)荷
因載荷方向相異,取，計(jì)算軸向平均負(fù)荷：
（公式3.8）
因 ,所以軸向平均負(fù)荷為。
平均轉(zhuǎn)速
每分鐘往返次數(shù)
行程 LS ＝1000 mm
導(dǎo)程∶
（公式3.9）
工作額定壽命
額定壽命
每分鐘平均轉(zhuǎn)數(shù)
（公式3.10）
額定運(yùn)行距離壽命
額定壽命
導(dǎo)程∶
（公式3.11）
4.定位精度的探討
4.1軸向剛性的探討
對(duì)軸向剛度影響最大的是發(fā)熱變形，所以在此僅對(duì)熱變形進(jìn)行校核。
假設(shè)在滾珠絲杠在轉(zhuǎn)動(dòng)過程中,系統(tǒng)溫度升高5℃。這時(shí)引起的軸向定位誤差為：
（公式4.1）
4.2運(yùn)行中姿勢(shì)變化的探討
假設(shè)垂直公差在±10秒以下,絲杠L因垂直公差而引起的定位誤差為∶
Δa＝L×sinθ
＝150×sin（±10′′）
＝±0.007 mm （公式4.2）
由此可知,定位精度如下∶
（公式4.3）
4.3旋轉(zhuǎn)扭矩的探討
由外部負(fù)荷引起的摩擦扭矩如下∶
（公式4.4）
滾珠絲杠副加速時(shí)所需的慣性力矩為,則絲杠軸全長(zhǎng)1320mm的慣性力矩如下∶
＝ （公式4.5）
（公式4.6）
（公式4.7）
根據(jù)上述,加速所需要的扭矩如下∶
＝4.61× N·mm （公式4.8）
因此,所需扭矩如下∶
加速時(shí)，
等速時(shí)，
減速時(shí)，
5.電動(dòng)機(jī)的選擇
5.1旋轉(zhuǎn)速度
電動(dòng)機(jī)選擇使用AC伺服電機(jī)。最高使用轉(zhuǎn)速∶3000 r/min，電動(dòng)機(jī)額定轉(zhuǎn)速∶3000 rad/min
5.2電動(dòng)機(jī)扭矩
設(shè)計(jì)中選擇的AC伺服電機(jī)能產(chǎn)生的最大扭矩為
5.3扭矩的有效值
加速時(shí)
等速時(shí)
減速時(shí)
停止時(shí)∶
（公式5.1）
電動(dòng)機(jī)的額定扭矩通過以上計(jì)算必須為1305N·mm，而正常使用時(shí)電動(dòng)機(jī)產(chǎn)生的扭矩必須為此數(shù)值之上。市面上CA伺服電機(jī)的種類繁多，選擇余地也比較大，所以在這里我們的選擇只需滿足上述條件的精度和扭矩即可。
6.滾珠絲杠高速化研究方案
6.1 精密滾珠絲杠副實(shí)現(xiàn)高速化要解決的主要矛盾
高速化不僅僅只是將滾珠絲杠副所連接的電動(dòng)機(jī)的轉(zhuǎn)速提高了這一種實(shí)現(xiàn)方案，而應(yīng)該采用整體優(yōu)化的設(shè)計(jì)方案。
1）速度較高時(shí)，整個(gè)滾珠絲杠系統(tǒng)可能會(huì)出 現(xiàn)加大的震動(dòng)
系統(tǒng)共振時(shí)與臨界轉(zhuǎn)速的關(guān)系式為：
（公式6.1）
式中：
，支承系數(shù)；
L，支承間距，mm；
E，材料縱向彈性模量，；
I，小徑最小慣性矩，mm4；
g，重力加速度，mm/s2；
γ，材料密度，N/mm3；
A，小徑橫截面積，mm2。
從上式可以看出，滾珠絲杠速度的控制因素不止一種[3]。
2）滾珠受安全轉(zhuǎn)速的限制
滾珠絲杠副通常使用d0n值(此處d0為絲杠的名義直徑，n為絲杠的轉(zhuǎn)速)表示滾珠絲杠副的速度極限，也稱作DN值。滾珠絲杠系統(tǒng)中的DN值越大，表明其運(yùn)行的最高速度也最大，承載能力也最強(qiáng)。
3）溫升和熱變形的限制
高速轉(zhuǎn)動(dòng)下的滾珠絲杠螺母副會(huì)發(fā)熱變形，進(jìn)而降低滾珠絲杠的運(yùn)動(dòng)精度。
圖6-1 不同安裝方式下滾珠絲杠副的熱變形
從上圖可以看出，滾珠絲杠在不同安裝方式下，在正常工作狀態(tài)下，都會(huì)發(fā)熱變形，而不同的安裝方式下，其滾珠絲杠副的變形類型和性質(zhì)又不近相同，其中固定-支承方式下可以允許絲杠副有微小的軸向變形，但不能過大；而固定-固定形式的支承方式因?yàn)檩S向的變形不允許，其發(fā)生的彎曲變形較前者則大的多；而固定-自由型的安裝方法因其自身的類似懸臂梁的結(jié)構(gòu)，所以決定了它并不能承受過大的載荷而只能使用在很小的范圍內(nèi)。
4）噪聲較大，環(huán)保性差
任何機(jī)械在運(yùn)行過程中都會(huì)或多或少地發(fā)出噪聲，而滾珠絲杠也不例外，高速條件下，其本身會(huì)隨著速度的提高而發(fā)出過多的噪音。
6.2 滾珠絲杠副高速化的技術(shù)對(duì)策
上述面臨的問題是滾珠絲杠副高速化的優(yōu)化目的最大的障礙。本設(shè)計(jì)依據(jù)以上的分析有針對(duì)性地提出了以下的技術(shù)和對(duì)策：
1）增大絲杠的導(dǎo)程和螺紋頭數(shù)
絲杠方面的資料和實(shí)際經(jīng)驗(yàn)告訴我們提高滾珠絲杠轉(zhuǎn)速或是加大滾珠絲杠導(dǎo)程都能夠提高滾珠絲杠的運(yùn)行速度。
而導(dǎo)程的增加，會(huì)導(dǎo)致絲杠的運(yùn)行精度下降，而且絲杠系統(tǒng)啟動(dòng)力矩也會(huì)隨之升高，影響整體傳動(dòng)的平穩(wěn)性。所以我們必須在轉(zhuǎn)速和導(dǎo)程之間取得一個(gè)平衡點(diǎn)。從而達(dá)到滾珠絲杠副的最優(yōu)化設(shè)計(jì)。
有設(shè)計(jì)方案采用雙頭螺紋，這既能提高其剛度和承載能力，又能提高運(yùn)行中的平穩(wěn)性[5]。但也不是完全一味地增大。
2）采用強(qiáng)冷技術(shù)
圖6-2 螺母空心冷卻液強(qiáng)冷方式
如圖為滾珠絲杠的發(fā)明裝置。該裝置利用加在螺母上的空心孔，通過孔中流動(dòng)的冷卻液達(dá)到為滾珠絲杠副降溫的目的。
4）改進(jìn)滾珠循環(huán)返向裝置和滾珠的流暢性
5）優(yōu)化滾珠反向器的結(jié)構(gòu)
發(fā)熱和噪聲都是由摩擦造成的，所以依據(jù)此原理，可以將滾道內(nèi)的摩擦系數(shù)降到最低，從而達(dá)到最根本改善和優(yōu)化滾珠絲杠副。傳統(tǒng)的滾珠絲杠使用的都有一個(gè)反向器，而其精度也決定了滾珠在滾道內(nèi)的順利運(yùn)行。
6）無循環(huán)反向裝置
傳統(tǒng)循環(huán)方式中采用循環(huán)滾道的設(shè)計(jì)方案對(duì) DN值有極大的制約，所以有人提出了無返向裝置的滾珠絲杠副。而本設(shè)計(jì)說明中緒論部分也進(jìn)行過介紹，在此，將不再贅述。
圖6-3 行星滾柱絲杠副
上圖為一種新型的滾珠絲杠裝置，其使用非循環(huán)的滾柱絲杠形式，具有與滾珠絲杠不同的支撐部件，使用滾柱，加強(qiáng)了絲杠副的剛性和承載能力。使用壽命和正常使用速度也較普通滾珠絲杠有了很大的提升。
7）采用雙電動(dòng)機(jī)驅(qū)動(dòng)
兩臺(tái)獨(dú)立于絲杠軸和滾珠絲杠的螺母的電動(dòng)機(jī)分別連接,并通過與螺母套筒相連接的齒輪將旋轉(zhuǎn)力矩傳遞給螺母和套筒，這樣做擴(kuò)大了進(jìn)給控制系統(tǒng)的穩(wěn)定旋轉(zhuǎn)速度范圍。因其獨(dú)立運(yùn)動(dòng)的特性，該設(shè)計(jì)方案可以使用兩個(gè)伺服電機(jī)驅(qū)動(dòng)，令兩臺(tái)電機(jī)同時(shí)驅(qū)動(dòng)的方案，將兩個(gè)速度進(jìn)行組合，可以擴(kuò)大整個(gè)運(yùn)動(dòng)副的速度控制范圍。
所以本課題的研究方向是探究一種能夠?qū)崿F(xiàn)滾珠絲杠的高速運(yùn)行的創(chuàng)新裝置。能夠在保證精度和機(jī)械運(yùn)行的穩(wěn)定性的基礎(chǔ)上，達(dá)到高速，自鎖的優(yōu)化型滾珠絲杠。
總 結(jié)
經(jīng)過這段時(shí)間的系統(tǒng)性公關(guān)，對(duì)自己能力又是一次新的歷練。經(jīng)過這段時(shí)間，在老師的教導(dǎo)下，我也學(xué)會(huì)了許多新的知識(shí)和技能，畢業(yè)設(shè)計(jì)促進(jìn)了自己對(duì)所學(xué)知識(shí)的掌握，并且學(xué)到了許多實(shí)踐性的東西，對(duì)自己是很有意義的。其中，有老師的諄諄教誨，龐老師對(duì)我也很嚴(yán)格，自己的也在虛心接受老師的指導(dǎo)，我最應(yīng)該謝謝的人便是我的老師，他不僅僅是一個(gè)學(xué)術(shù)專業(yè)的教授，更是我在日后從事機(jī)械行業(yè)研究工作的人生導(dǎo)師。在此我也對(duì)我學(xué)到的東西進(jìn)行一下簡(jiǎn)單的總結(jié)：
1） 經(jīng)過了本次畢業(yè)設(shè)計(jì)，更加鞏固了我對(duì)CAD制圖技術(shù)的熟練程度，為我日后進(jìn)一步學(xué)習(xí)打下來堅(jiān)實(shí)的基礎(chǔ)。
2） 老師的學(xué)術(shù)品格深深把我折服，這將是我以后人生道路中又一個(gè)指路明燈，這里我應(yīng)該好好謝謝老師。
3） 嚴(yán)謹(jǐn)?shù)墓接?jì)算是從事機(jī)械研究的重要品行，小到微米級(jí)的計(jì)算單位大到米級(jí)的大型機(jī)械，每一個(gè)裝配尺寸都是嚴(yán)格有依據(jù)的，決不能憑空捏造，應(yīng)做到實(shí)事求是。
4） 機(jī)械工程是份神圣的行業(yè)，我們每一個(gè)中國(guó)人在現(xiàn)在嚴(yán)峻的技術(shù)革命形勢(shì)下，決不能無動(dòng)于衷，甘于沉浸在已經(jīng)取得的成就中，而應(yīng)該向前看，以不一樣的思維，開拓創(chuàng)新，為新機(jī)械制造業(yè)注入自己強(qiáng)大的動(dòng)力。
參 考 文 獻(xiàn)
［1］二宮瑞穗.マシニングセンタたあの高速高精度送リ技術(shù)1997(04).
［2］宮口和男.Ball screws for high speed drive[J] 2002(673).
［3］孫健利.滾珠絲杠副的高速化技術(shù)研究[J].制造技術(shù)與機(jī)床2010.
［4］Yamaguchi H;Ohkubo TDevelopment of "NSK S1 Seris" ball screuls and linear guides2008(671).
［5］郭慶鼎;王成元;周美文.高速化滾珠絲杠技術(shù)研究,2000.
［6］Bork B;Gao Hua;羅冬梅.直線電機(jī)應(yīng)用之經(jīng)濟(jì)性與應(yīng)用領(lǐng)域有關(guān),1999(04).
［7］王先逵;陳定績(jī);吳丹.精密滾珠絲杠綜述[J]制造技術(shù)與機(jī)床2001(08).
［8］寧立偉.滾珠絲杠副. 機(jī)床數(shù)控技術(shù),高等教育出版社.2010-1
［9］肖正義.滾珠絲杠副的發(fā)展趨勢(shì).制作技術(shù)與機(jī)床.2000-04
［10］黃祖堯.21世紀(jì)初海外滾動(dòng)功能部件發(fā)展動(dòng)態(tài).世界制作技術(shù)與裝備市場(chǎng).2003-2
［11］程光仁.施祖康.滾珠螺旋傳動(dòng)設(shè)計(jì)基礎(chǔ).北京.機(jī)械工業(yè)出版社.1987-08
［12］喻忠志.我國(guó)滾動(dòng)功能部件產(chǎn)業(yè)現(xiàn)狀分析.制造技術(shù)與機(jī)床.2004.04
［13］中國(guó)藝工滾動(dòng)功能部件產(chǎn)品綜合樣本及資料
［14］肖正義.焦?jié)?高速滾珠絲杠副的研發(fā)與測(cè)試技術(shù).制造技術(shù)與機(jī)床.2004-04
［15］滾珠絲杠譯文集.南京工藝裝備廠.1980-08
［16］THK綜合產(chǎn)品目錄.臺(tái)灣THK滾珠絲杠設(shè)計(jì)公司.互聯(lián)網(wǎng).2013-06/2016-05
［17］PMI產(chǎn)品目錄.PMI滾珠絲杠設(shè)計(jì)公司.互聯(lián)網(wǎng).2013-05/2016-05
［18］上銀產(chǎn)品目錄.上銀滾珠絲杠設(shè)計(jì)公司.互聯(lián)網(wǎng).2013-06/2016-05
致 謝
這次畢業(yè)設(shè)計(jì)中，我領(lǐng)悟了很多東西。要十分感謝我的導(dǎo)師的指導(dǎo)，還有他的理解與包容。沒有老師我很難完成這篇設(shè)計(jì)。從設(shè)計(jì)資料的搜集，到最后設(shè)計(jì)的修改的整個(gè)過程中，耗費(fèi)了老師很多心血和努力，我在這里表達(dá)我最真摯的感情。以后我一定以自己最大的努力，積極獻(xiàn)身新型機(jī)械制造業(yè)，為實(shí)現(xiàn)自己的人生價(jià)值和社會(huì)價(jià)值而奮斗。以報(bào)答您對(duì)我的恩情。
九層之臺(tái)，起于累土，沒有前面其他機(jī)械老師的努力培養(yǎng)，我也不可能學(xué)到如此有用的知識(shí)和能力，也非常感謝曾經(jīng)幫助過我的老師的悉心教導(dǎo)。設(shè)計(jì)過程中也有其他同學(xué)的幫助，在這里我也非常謝謝他們?cè)诖髮W(xué)四年最后時(shí)光的陪伴。
26
中 北 大 學(xué) 信 息 商 務(wù) 學(xué) 院
畢業(yè)設(shè)計(jì)任務(wù)書
學(xué) 院、系：
機(jī)械工程與自動(dòng)化系
專 業(yè)：
機(jī)械制造及其自動(dòng)化
學(xué) 生 姓 名：
張曉飛
學(xué) 號(hào)：
12020144X21
設(shè) 計(jì) 題 目：
滾珠絲杠設(shè)計(jì)及相關(guān)技術(shù)研究
起 迄 日 期:
2016年 2月29日~ 2016年6月5日
指 導(dǎo) 教 師:
龐學(xué)慧
系 主 任:
暴建剛
發(fā)任務(wù)書日期: 2016年 2月29日
畢 業(yè) 設(shè) 計(jì) 任 務(wù) 書
1．畢業(yè)設(shè)計(jì)的任務(wù)和要求：
掌握機(jī)床傳動(dòng)絲杠的基本知識(shí)；研究數(shù)控機(jī)床滾珠絲杠的關(guān)鍵技術(shù)，掌握其選型、應(yīng)用及設(shè)計(jì)方法等；完成一種滾珠絲杠的設(shè)計(jì)，滿足精密數(shù)控機(jī)床20m/min進(jìn)給速度的需求。
2．畢業(yè)設(shè)計(jì)的具體工作內(nèi)容：
1） 分析題目要求，查閱相關(guān)的國(guó)內(nèi)外文獻(xiàn)、設(shè)計(jì)資料、有關(guān)專利文獻(xiàn)等，在此基礎(chǔ)上，了解開題報(bào)告的撰寫方法、基本要求，完成開題報(bào)告；
2） 學(xué)習(xí)和掌握滾珠絲杠的有關(guān)知識(shí)，了解高速滾珠絲杠的關(guān)鍵技術(shù)及發(fā)展現(xiàn)狀；了解數(shù)控機(jī)床、加工中心對(duì)滾珠絲杠的要求；總結(jié)滾珠絲杠的設(shè)計(jì)要點(diǎn)、技術(shù)關(guān)鍵及發(fā)展方向；力爭(zhēng)提出滾珠絲杠設(shè)計(jì)的發(fā)展方向；
3） 按題目要求，設(shè)計(jì)一種滿足數(shù)控機(jī)床進(jìn)給運(yùn)動(dòng)需要的滾珠絲杠，完成結(jié)構(gòu)圖，給出必要的計(jì)算說明；
4） 編寫設(shè)計(jì)說明書；
5） 翻譯本專業(yè)外文科技文獻(xiàn)一份。
畢 業(yè) 設(shè) 計(jì) 任 務(wù) 書
3．對(duì)畢業(yè)設(shè)計(jì)成果的要求：
1）滾珠絲杠結(jié)構(gòu)圖；
2）滾珠絲杠的研究及設(shè)計(jì)說明書一份；
3）本專業(yè)外文科技文獻(xiàn)譯文一份。
4．畢業(yè)設(shè)計(jì)工作進(jìn)度計(jì)劃：
起 迄 日 期
工 作 內(nèi) 容
2016年
02月29日 ~03月21日
03月22日 ~04月30日
05月01日 ~05月20日
05月21日 ~05月31日
06月01日 ~06月05日
分析課題要求，查閱相關(guān)文獻(xiàn)資料，了解滾珠絲杠的國(guó)內(nèi)外現(xiàn)狀及發(fā)展趨勢(shì)，提出自己的設(shè)計(jì)思路，完成開題報(bào)告；
全面掌握滾珠絲杠的基本知識(shí)，了解高速機(jī)床對(duì)進(jìn)給導(dǎo)軌的要求，了解滾珠絲杠的設(shè)計(jì)特點(diǎn)；分析總結(jié)滾珠絲杠的發(fā)展方向；
完成滾珠絲杠結(jié)構(gòu)圖設(shè)計(jì)；
完成研究總結(jié)及設(shè)計(jì)說明書
撰寫答辯講稿，準(zhǔn)備答辯；
學(xué)生所在系審查意見：
同意開題
系主任： 暴建崗
2016年3月 3日
International Journal of Machine Tools fax 88656311500 E mail addresses jywe sunws nfu edu tw W Jywe table was rotated counterclockwise In general one rotary table calibration for a 3601 full circle requires 36 recording if the sampled period of measurement system is 101 Ifa 0890 6955 see front matter r 2007 Elsevier Ltd All rights reserved doi 10 1016 j ijmachtools 2007 02 004 pmc2 sunws nfu edu tw C J Chen allen nfu edu tw W H Hsieh pdlin mail ncku edu tw P D Lin schong nfu edu tw H H Jwo jeyang T Y Yang instruments are the rotary encoder the laser interferom eter the autocollimator and the precision level A rotary encoder 1 is commonly used in indexing measurement in a rotary machine e g a rotary table of the multi axis machine tool the joint of a robot the spindles of machine tools and the indexing of a ball screw However the rotary encoder is only suitable for the indexing error measure ment A laser interferometer 2 has often been used to measure a small angle but it can only obtain indexing error either one dimensional 1D error or 2D errors The complete calibration procedure of a rotary table requires 6 DOF measurement for a 3601 full circle but the measure ment range of most measurement systems is smaller than 101 Therefore the measurement range of the laser interferometer and autocollimator are not enough and in addition they are expensive The conventional calibration technique of the rotary table for a 3601 full circle requires one reference rotary table which must have high accuracy and high repeatability The error of the reference rotary C3 and the reference rotary table could be obtained The system calibration stability test system verification and full circle test were completed The angular stability of this system was less then 2arcsec while the displacement stability was less than 1 2mm r 2007 Elsevier Ltd All rights reserved Keywords Rotary table calibration Full circle test Grating Position sensing detector 4 Degree of freedom measurement Error separation 1 Introduction A rotary table is frequently used in industry in such things as machine tools CMM and assembly lines Therefore the calibration of the rotary table is very important The calibration of the rotary table requires an during an indexing test An autocollimator 3 is frequently used to measure small angles and it can be applied to two dimensional 2D angle measurement pitch error and yaw error but its measurement range is small and it require one standard polygon mirror A rotary table has 6 DOF errors 3 linear position errors and 3 angular position reference rotary table but with good repeatability is needed After two full circle tests the 4 DOF errors of both the target rotary table A novel simple and low cost 4 degree calibrating technique for W Jywe a C3 C J Chen b W H Hsieh a National Formosa University Department of Automation b National Cheng Kung University Department of Mechanical Received 30 October 2006 received in revised form Available online Abstract For calibrating an angular rotary table either a high precision standard employed at high cost This paper establishes a novel simple and low of a rotary table three angular position errors and one linear position one 1 dimensional 1D grating and two 2 dimensional 2D position sensing detectors ture 47 2007 1978 1987 of freedom angular indexing a precision rotary table P D Lin b H H Jwo a T Y Yang a g No 64 Wenhua Rd Huwei Taiwan ROC Engineering No 1 University Rd Tainan Taiwan ROC 1 February 2007 accepted 13 February 2007 February 2007 table or a laser interferometer and related optics are normally cost technique to calibrate the 4 degrees of freedom DOF errors error for a 3601full circle by employing one reference rotary table PSD With this technique no highly accurate ARTICLE IN PRESS more complete test is implemented the calibration process will takes a long time In general the rotary table includes the index error wobble error and eccentricity But conventional rotary table calibration techniques laser interferometer or auto collimator only calibrate the index error and the wobble error However the high precision rotary table must be calibrated in more details Through the complete rotary table calibration the errors of rotary table can be compensated In this paper the errors of rotary table were defined by 6 DOF i e three linear position errors d x d y d z and three angular position errors e x e y e z The index error was represented by e z the wobble error was represented by e x and e y the eccentricity was represented by d x and d y In recent years angular measuring techniques have focused on the interferometric methods In 1992 Huang et al 4 developed a small angle measurement system which was based on the internal reflection effect in a glass boundary and Fresnel s law In Huang s system the resolution was 0 2arcsec and the measuring range was 3arcsec In 1996 Xiaoli et al 5 established a 2D small rotation angle measurement system using two different parallel interference patterns PIP that were orthogonal to each other The standard deviation of Xiaoli s system was 0 6arcsec In the following year Xiaoli et al 6 improved their system so that its resolution was 0 2arcsec and measuring range was 730arcmin In 1997 Chiu et al 7 established a modified angle measurement technique with a resolution of 0 333arcsec and a measuring range of75 61 At its optimum performance the system s resolution was 0 288arcsec In 1998 Zhou and Cai 8 established an angle measurement technique which was based on the total internal reflection effect and heterodyne interferome try The system resolution was better than 0 3arcsec depending on the refractive index selected In 1998 Huang et al 9 established a method of angle measurement based on the internal reflection effects that used a single right angle prism They demonstrated that angle measurement with a range of 7500arcmin a nonlinearity error of 70 1 and a resolution of 0 1arcsec could be readily achieved In 1999 Guo et al 10 developed an optical method for small angle measurement based on surface plasma resonance SPR and a measurement resolution of 0 2arcsec was achieved experimentally In 2003 Ge and Makeda 11 developed an angle measurement tech nique based on fringe analysis for phase measuring profilometry The measurement range was 72160arcsec and the deviation from linearity was better than 70 02 arcsec In 2004 Chiu et al 12 developed an instru ment for measuring small angles using multiple total internal reflections in heterodyne interferometry and the angular resolution was better than 0 454arcsec over the measurement range C02 121pyp2 121 for 20 total internal reflections W Jywe et al International Journal of Machine Most angle measurement technique research focuses on 1D angle measurement and interferometric angle measurement and 2D measurement also focuses on interferometric techniques However interferometric systems are expensive and complex and cannot be used extensively in industry Therefore the low cost and multiple DOF measurement system is needed for rotary table calibration The position sensing detector PSD could be used to measure the rotary part error the speed of rotary part the rotation direction of rotary part the angular position and the indexing error 13 14 Jywe et al employed two PSDs and one reflective grating to test rotary table performance 15 but its measurement range was small o11 In 15 no full circle test was implemented and no analytic solution was provided However for the general rotary table calibra tion the 3601 full circle test is necessary This paper both describes the building of one 4 DOF measurement system and establishes a novel technique for rotary table full circle test The 4 DOF system presented in this paper comprises one 1D reflection grating one laser diode four PSDs and one reference rotary table The laser interferometer and the autocollimator were most used rotary table measurement system However in rotary table calibration process the laser interferometer and the autocollimator need a high accuracy reference rotary table and a polygon mirror respectively Therefore using the laser interferometer or autocollimator to calibrate rotary table is expensive Because the cost of 1D reflection grating PSD signal conditioning unit of PSD and laser diode and rotary table is about 1 5 of one laser interferometer system or 1 2 of one autocollimator system Moreover in the presented method no high accurate reference rotary table but with good repeatability is needed Even the indexing error and the geometric error of the reference rotary table is large they will be obtained by the presented method 2 The 4 DOF measurement system In this paper the 4 DOF measurement system includes one reference rotary table one 1D grating one laser diode two PSDs two PSD processors one A D card and one personal computer PC Fig 1 shows the schematic diagram The reference rotary table was placed on the target rotary table then the 1D grating was mounted on the rotary table by the fixture The laser diode and PSDs were placed near the 1D grating The laser beam from the laser diode was projected onto a 1D grating and then the 1D grating produced many diffraction light beams In this paper the 1 order and C01 order diffraction light beam are used and two PSDs were used to detect the diffraction light beam Generally six geometric errors are defined on a rotary table namely three linear position errors and three angular position errors pitch roll and yaw The three linear position errors are d x d y and d z and the three angular position errors are e x e y and e z respectively In addition there are eccentricity between the grating and the axis of the rotary table which are defined as D x and D y Tools d x d xt d xr C15 y C15 yt C15 yr d y d yt d yr C15 z C15 zt C0 C15 zr d z d zt d zr 13 where e z is the index difference between the target rotary table and the reference rotary table and it accumulatively varies during the calibration procedure The e x e y d x d y and d z are not accumulative Because one full circle test needs two tests the repeatability of the target rotary table and the reference rotary table must be good otherwise the measured results will not repeat The basic requirement of the calibrating technique is that the target rotary table under calibration can be rotated the same step size as the reference rotary table in different orientations say on for clockwise and the other counter clockwise Each sector of the table under test has been compared with every sector of the reference one in order to build the first set of data For example one rotary table was tested at 12 angular position points around 3601 i e at 01 301 601 y 3301 which were equally spaced segmented in the target rotary table and the reference rotary table At the start in 1000 C1C1C1 C010000C1C1C1 0 0100 C1C1C1 0 C010 00C1C1C1 0 0010 C1C1C1 00C0100C1C1C1 0 1000 C1C1C1 0 C010 00C1C1C1 0 0100 C1C1C1 00C0100C1C1C1 0 0010 C1C1C1 000C010C1C1C1 0 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 0 0 0 0 C1C1C11 C01 0 0 0 0 C1C1C1 0 C15 z1n C15 ztn C0 C15 zrn 14 where e z1n is the first set of angular readings and n is the number of increments over 3601 The subscript t of the symbol e zt1 means the error of the target rotary table and the subscript r means the error of the reference rotary table In the second test of full circle test the target rotary table and reference rotary table was set to 01 again and the reference rotary table was incremented by one nominal step ex 301 After the rotation of the reference rotary table the first set of sample was taken Then the target rotary table was rotated 301 clockwise and the reference rotary table was rotated 301 counter clock wise and the other sets of sample were taken From the above experiment process the results of second test were obtained Then the flowing relationship can be derived C15 z21 C15 zt1 C0 C15 zr2 C15 z22 C15 zt2 C0 C15 zr3 C15 z2n C15 ztn C0 C15 zr1 15 where e z2n is the second set of angular readings and n is the number of increments over 3601 The two sets of measured data can then be rearranged as follows C15 zt1 C15 zt2 C15 zt3 C15 zr1 C15 zr2 C15 zr3 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 C15 z11 C15 z12 C15 z13 C15 z21 C15 z22 C15 z23 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 16 C15 zrn C15 z2n and the original augmented matrix is shown as 1000 C1C1C1 C010000C1C1C1 C15 z11 0100 C1C1C1 0 C010 00C1C1C1 C15 z12 0010 C1C1C1 00C0100C1C1C1 C15 z13 1000 C1C1C1 0 C010 00C1C1C1 C15 z21 0100 C1C1C1 00C0100C1C1C1 C15 z22 0010 C1C1C1 000C010C1C1C1 C15 z23 0 0 0 0 C1C1C11 C01 0 0 0 0 C1C1C1 C15 z2n 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 17 An augmented matrix of the reduced system can then be derived as follows Since Eq 18 is linear dependent more equations are required An assumption is again made to presume that no closing error exists within the reference rotary table and consequently the following equation can be derived C15 zr1 C15 zr2 C15 zr3 C1C1C1 C15 zrnC01 C15 zrn 360 C14 20 ARTICLE IN PRESS Table 1 Components of the prototype 4 DOF measurement system PSD UDT SC 10D active area 100mm 2 PSD signal processor On Trak OT 301 PC Intel Pentium4 2 0G 256MB RAM 40G HD A D Card Advantech PCI 1716 16 bit sampling range 710V Max sampling frequency 250kHz Laser diode l 635nm 5mW 1D Grating Rolled diffraction grating 600grooves per mm Autocollimator NewPort LDS Vector measurement range 2000mrad W Jywe et al International Journal of Machine Tools Manufacture 47 2007 1978 19871982 1000C1C1C1 C010000C1C1C1 0 C15 z11 0100C1C1C1 0 C010 00C1C1C1 0 C15 z12 0010C1C1C1 00C0100C1C1C1 0 C15 z13 0000C1C1C1 1 C010 00C1C1C1 0 C15 z21 C0 C15 z11 0000C1C1C1 01C0100C1C1C1 0 C15 z22 C0 C15 z12 0000C1C1C1 001C010C1C1C1 0 C15 z23 C0 C15 z13 0000C1C1C1 10000C1C1C1 C01 P nC01 i 1 C15 z2i C0 C15 z1i 0000C1C1C1 C010000C1C1C1 1 C15 z2n C0 C15 z1n 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 18 From the last two rows in the reduced matrix it can be shown that C15 zr1 C0 C15 zrn X nC01 i 1 C15 z2i C0 C15 z1i C0 C15 z2n C0 C15 z1n 19 or X nC01 i 1 C15 z2i C0 C15 z1i 0 Fig 2 Photograph of the 4DOF measurement system with 4 PSD Fig 3 Calibration results b standard deviation Eq 20 is then incorporated into the augmented matrix in Eq 18 to give the following 1000 C1C1C1 C010 0 00C1C1C1 0 C15 z11 0100 C1C1C1 0 C010 00C1C1C1 0 C15 z12 0010 C1C1C1 00C0100C1C1C1 0 C15 z13 1000 C1C1C1 0 C010 00C1C1C1 0 C15 z21 0100 C1C1C1 00C0100C1C1C1 0 C15 z22 0010 C1C1C1 000C010C1C1C1 0 C15 z23 0000C1C1C11 C010 0 00C1C1C1 0 C15 z2n 0000C1C1C1011111C1C1C1 1 360 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 21 Finally using the Gaussian Elimination method the actual individual angle e zti and e zri at each target position can be calculated The calculation of e xti e xri e yti e yri d xti d xri d yti d yri d zti and d zri is different to e zti and e zri For instance C15 x11 C15 xt1 C15 xr1 C15 x12 C15 xt2 C15 xr2 C15 x1n C15 xtn C15 xrn 22 and C15 x21 C15 xt1 C0 C15 xr2 C15 x22 C15 xt2 C0 C15 xr3 C15 x2n C15 xtn C0 C15 xr1 23 The summation of e xri is C15 xr1 C15 xr2 C15 xr3 C1C1C1 C15 xrnC01 C15 xrn 0 C14 24 ARTICLE IN PRESS W Jywe et al International Journal of Machine Tools Manufacture 47 2007 1978 1987 1983 Fig 4 Stability test results a d 4 Experimental results and discussion In this paper the calibration of the 4 DOF measurement system system stability system verification and full circle test were accomplished The photograph of this system was shown in Fig 2 Components not shown in Fig 2 include a desktop PC connected to the PSD signal processor via an A D card The component specifications were listed in Table 1 4 1 System calibration System calibration was the first experiment In this experiment the NewPort autocollimator was used to provide the reference angular position Its measurement range was 7410arcsec resolution was 0 02arcsec and accuracy was 0 5arcsec Fig 3 a shows the calibration result and Fig 3 b gives the standard deviations for ARTICLE IN PRESS Tools Manufacture 47 2007 1978 1987 Therefore the matrix of e xti and e xri is 1000 C1C1C1 C010000C1C1C1 0 C15 x11 0100 C1C1C1 0 C010 00C1C1C1 0 C15 x12 0010 C1C1C1 00C0100C1C1C1 0 C15 x13 1000 C1C1C1 0 C010 00C1C1C1 0 C15 x21 0100 C1C1C1 00C0100C1C1C1 0 C15 x22 0010 C1C1C1 000C010C1C1C1 0 C15 x23 0000C1C1C11 C010000C1C1C1 0 C15 x2n 0000C1C1C1011111C1C1C1 10 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 25 Similarly 1000 C1C1C1 C010 0 00C1C1C1 0 C15 y11 0100 C1C1C1 0 C010 00C1C1C1 0 C15 y12 0010 C1C1C1 00C0100C1C1C1 0 C15 y13 1000 C1C1C1 0 C010 00C1C1C1 0 C15 y21 0100 C1C1C1 00C0100C1C1C1 0 C15 y22 0010 C1C1C1 000C010C1C1C1 0 C15 y23 0000C1C1C11 C010 0 00C1C1C1 0 C15 y2n 0000C1C1C1011111C1C1C1 10 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 26 1000 C1C1C1 C010000C1C1C1 0 d y11 0100 C1C1C1 0 C010 00C1C1C1 0 d y12 0010 C1C1C1 00C0100C1C1C1 0 d y13 1000 C1C1C1 0 C010 00C1C1C1 0 d y21 0100 C1C1C1 00C0100C1C1C1 0 d y22 0010 C1C1C1 000C010C1C1C1 0 d y23 0000C1C1C11 C010000C1C1C1 0 d y2n 0000C1C1C1011111C1C1C1 10 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 27 This technique can be used in the rotary table 6 DOF calibration but in this paper the measurement system could only measure 4 DOF errors so this paper lists only four equations Eqs 21 25 27 The recorded count was based on the measurement range of the system For example the measurement range of Lin s system laser interferometer 16 was about 101 W Jywe et al International Journal of Machine1984 Therefore one full circle test must record at least 36 points during the first and second tests respectively Fig 5 Verification result a and b ARTICLE IN PRESS W Jywe et al International Journal of Machine system uncertainty Throughout the calibration process it was clear that the linearity of e z was good and the uncertainty of e z was about 1 5arcsec The angular Fig 6 Full circle test Tools Manufacture 47 2007 1978 1987 1985 position e z measurement range of the 4 DOF measure ment system was about 11 because almost all measurement range of PSD was used results a h accurate reference rotary table but with good repeatability stability of this system was less then 2arcsec while the 1992 6047 6055 ARTICLE IN PRESS 4 2 System stability test System stability test was the second experiment System stability was evaluated by allowing the system to come to equilibrium under normal laboratory conditions i e no special temperature or vibrational isolation and then continuously recording the output signal for 4000s Fig 4 shows that the system stability of the basic prototype was reasonable i e with no special isolation or filtering the output of d y remained within 71 2mm and e x e y and e z remained within 71 5arcsec over 4000s 4 3 System verification System verification was the third experiment and the autocollimator was also used to verify the 4DOF measure ment system since it can measure the e x and e z simultaneously The autocollimator was set up at the back of the grating When the full circle test was implemented and error separation method was not used the autocolli mator recorded the error sum of the target rotary table and reference rotary table The autocollimator and the 4DOF measurement system recorded once when the target rotary table rotated one degree clockwise and once again when the reference rotary table rotated one degree counterclockwise Fig 5 shows the result of the system verification The result of 4DOF measurement system and autocollimator was similar so the mathematic model of 4DOF measurement system is correct 4 4 Full circle test The full circle test was the last experiment that was described in Section 3 The measurement range of the 4 D