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徐州工程學(xué)院
畢業(yè)設(shè)計(jì)（論文）任務(wù)書
機(jī)電工程學(xué)院 學(xué)院 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 專業(yè)
設(shè)計(jì)（論文）題目 臥式雙面十軸組合鉆床右主軸箱及
中間底座設(shè)計(jì)
學(xué) 生 姓 名 倪佳麗
班 級(jí) 04機(jī)本（4）
起 止 日 期 2008.2.25～2008.6.2
指 導(dǎo) 教 師 韓翔
教研室主任
發(fā)任務(wù)書日期 2008年2月25日
1.畢業(yè)設(shè)計(jì)的背景：
在實(shí)際生產(chǎn)活動(dòng)中，加工效率是否高，加工質(zhì)量是否穩(wěn)定是兩個(gè)重要的指標(biāo)。組
合機(jī)床的出現(xiàn)在一定程度上同時(shí)滿足了這兩個(gè)要求。
組合鉆床是指以系列化、標(biāo)準(zhǔn)化的通用部件為基礎(chǔ)，再配以少量專用部件而組成
的專用機(jī)床。這種機(jī)床既具有一般專用機(jī)床結(jié)構(gòu)簡(jiǎn)單，生產(chǎn)率及自動(dòng)化程度高，易保
證加工精度的特點(diǎn)，又能適應(yīng)工件的變化，具有一定的重新調(diào)整、重新組合的能力。
組和鉆床可以對(duì)工件采用多刀、多面及多工位加工。它特別適于在大批、大量生產(chǎn)中
對(duì)一種或幾種類似零件的一道或幾道工序進(jìn)行加工。它具有設(shè)計(jì)制造周期短、成本
低、加工效率高、加工質(zhì)量穩(wěn)定、可減輕工人的勞動(dòng)強(qiáng)度等優(yōu)點(diǎn)。在機(jī)械制造中，裝
備新企業(yè)或者對(duì)老企業(yè)進(jìn)行技術(shù)改造，采用組合機(jī)床及其自動(dòng)線，是發(fā)展生產(chǎn)、提高
質(zhì)量的有效途徑之一。
近年來，組合機(jī)床的產(chǎn)量迅速增長(zhǎng)，質(zhì)量不斷提高，新產(chǎn)品不斷涌現(xiàn)。組合機(jī)床
在制造工業(yè)中正獲得越來越廣泛的應(yīng)用。
2.畢業(yè)設(shè)計(jì)(論文)的內(nèi)容和要求：
根據(jù)工作量及設(shè)計(jì)時(shí)間要求，本設(shè)計(jì)的主要工作內(nèi)容為：組合鉆床的
右主軸箱及中間底座。該組合鉆床用于加工“汽車制動(dòng)室支架”。
要求：1.查詢相關(guān)文獻(xiàn)，收集資料。
2.右主軸箱設(shè)計(jì)并繪圖。
3.中間底座的設(shè)計(jì)。
4.撰寫畢業(yè)設(shè)計(jì)說明書。
5.翻譯約5000單詞量的相關(guān)英文文獻(xiàn)
3.主要參考文獻(xiàn)：
1.《組合機(jī)床設(shè)計(jì)簡(jiǎn)明手冊(cè)》
2.《組合機(jī)床圖冊(cè)》
3.《組合機(jī)床及其調(diào)整與使用》
4.《新編機(jī)械設(shè)計(jì)手冊(cè)》
4.畢業(yè)設(shè)計(jì)(論文)進(jìn)度計(jì)劃(以周為單位)：
起 止 日 期
工 作 內(nèi) 容
備 注
第1、2周
第3、4周
第5、6周
第7、8周
第9、10周
第11、12周
第13、14周
第15、16周
收集資料，查閱相關(guān)文獻(xiàn)，寫任務(wù)書，開題報(bào)告。
分析被加工零件，并畫零件圖。
對(duì)右主軸箱進(jìn)行分析、計(jì)算，確定主軸箱相關(guān)尺寸。
右主軸箱傳動(dòng)設(shè)計(jì)，確定各主軸的相關(guān)數(shù)據(jù)。
右主軸箱總體圖的繪制。
對(duì)中間底座進(jìn)行分析，中間底座零件圖的繪制。
撰寫畢業(yè)設(shè)計(jì)說明書。
翻譯約5000單詞量的相關(guān)英文文獻(xiàn)，完善所有圖和說明書，并仔細(xì)檢查及時(shí)改正。
教研室審查意見：
室主任
年 月 日
學(xué)院審查意見：
教學(xué)院長(zhǎng)
年 月 日
徐州工程學(xué)院
畢業(yè)設(shè)計(jì)（論文）開題報(bào)告
課 題 名 稱： 臥式雙面十軸組合鉆床右主軸箱及
中間底座設(shè)計(jì)
學(xué) 生 姓 名： 倪佳麗 學(xué)號(hào)： 20040601404
指 導(dǎo) 教 師： 韓翔 職稱： 講師
所 在 學(xué) 院： 機(jī)電工程學(xué)院
專 業(yè) 名 稱： 機(jī)械設(shè)計(jì)制造及其自動(dòng)化
徐州工程學(xué)院
2008年 3月 4日
說 明
1．根據(jù)《徐州工程學(xué)院畢業(yè)設(shè)計(jì)(論文)管理規(guī)定》，學(xué)生必須撰寫《畢業(yè)設(shè)計(jì)（論文）開題報(bào)告》，由指導(dǎo)教師簽署意見、教研室審查，學(xué)院教學(xué)院長(zhǎng)批準(zhǔn)后實(shí)施。
2．開題報(bào)告是畢業(yè)設(shè)計(jì)（論文）答辯委員會(huì)對(duì)學(xué)生答辯資格審查的依據(jù)材料之一。學(xué)生應(yīng)當(dāng)在畢業(yè)設(shè)計(jì)（論文）工作前期內(nèi)完成，開題報(bào)告不合格者不得參加答辯。
3．畢業(yè)設(shè)計(jì)開題報(bào)告各項(xiàng)內(nèi)容要實(shí)事求是，逐條認(rèn)真填寫。其中的文字表達(dá)要明確、嚴(yán)謹(jǐn)，語言通順，外來語要同時(shí)用原文和中文表達(dá)。第一次出現(xiàn)縮寫詞，須注出全稱。
4．本報(bào)告中，由學(xué)生本人撰寫的對(duì)課題和研究工作的分析及描述，沒有經(jīng)過整理歸納，缺乏個(gè)人見解僅僅從網(wǎng)上下載材料拼湊而成的開題報(bào)告按不合格論。
5. 課題類型填：工程設(shè)計(jì)類；理論研究類；應(yīng)用（實(shí)驗(yàn)）研究類；軟件設(shè)計(jì)類；其它。
6、課題來源填：教師科研；社會(huì)生產(chǎn)實(shí)踐；教學(xué)；其它
課題
名稱
臥式雙面十軸組合鉆床右主軸箱及中間底座設(shè)計(jì)
課題來源
工程實(shí)際
課題類型
設(shè)計(jì)制造類
選題的背景及意義
在實(shí)際生產(chǎn)活動(dòng)中，加工效率是否高，加工質(zhì)量是否穩(wěn)定是兩個(gè)重要的指標(biāo)。組合機(jī)床的出現(xiàn)在一定程度上同時(shí)滿足了這兩個(gè)要求。
組合鉆床是指以系列化、標(biāo)準(zhǔn)化的通用部件為基礎(chǔ)，再配以少量專用部件而組成的專用機(jī)床。這種機(jī)床既具有一般專用機(jī)床結(jié)構(gòu)簡(jiǎn)單，生產(chǎn)率及自動(dòng)化程度高，易保證加工精度的特點(diǎn)，又能適應(yīng)工件的變化，具有一定的重新調(diào)整、重新組合的能力。組和鉆床可以對(duì)工件采用多刀、多面及多工位加工。它特別適于在大批、大量生產(chǎn)中對(duì)一種或幾種類似零件的一道或幾道工序進(jìn)行加工。它具有設(shè)計(jì)制造周期短、成本低、加工效率高、加工質(zhì)量穩(wěn)定、可減輕工人的勞動(dòng)強(qiáng)度等優(yōu)點(diǎn)。在機(jī)械制造中，裝備新企業(yè)或者對(duì)老企業(yè)進(jìn)行技術(shù)改造，采用組合機(jī)床及其自動(dòng)線，是發(fā)展生產(chǎn)、提高質(zhì)量的有效途徑之一。
近年來，組合機(jī)床的產(chǎn)量迅速增長(zhǎng)，質(zhì)量不斷提高，新產(chǎn)品不斷涌現(xiàn)。組合機(jī)床在制造工業(yè)中正獲得越來越廣泛的應(yīng)用。
研究?jī)?nèi)容擬解決的主要問題
根據(jù)工件量及設(shè)計(jì)時(shí)間的要求，對(duì)組合鉆床的右主軸箱及中間底座進(jìn)行設(shè)計(jì)。該組合鉆床用于加工“汽車制動(dòng)室支架”。
課題的主要內(nèi)容如下：
1.任務(wù)書、開題報(bào)告；
2.正確設(shè)計(jì)被加工零件的零件圖，右主軸箱裝配圖，補(bǔ)充加工圖，中間底座零件圖等；
3.編寫說明書；
4.翻譯約5000單詞量的相關(guān)外文文獻(xiàn)。
研究方法技術(shù)路線
一、對(duì)被加工零件進(jìn)行分析，畫零件圖。
二、右主軸箱的設(shè)計(jì)
1.繪制多軸箱設(shè)計(jì)原始依據(jù)圖。
2.確定主軸結(jié)構(gòu)，齒輪模數(shù)。
3.擬定傳動(dòng)路線。
4.計(jì)算主軸，傳動(dòng)軸坐標(biāo)。
5.繪制右主軸箱總圖，零件圖及編制組件明細(xì)表。
三、對(duì)中間底座進(jìn)行分析，畫中間底座零件圖。
研究的總體安排和進(jìn)度計(jì)劃
在老師的指導(dǎo)和安排下，這次設(shè)計(jì)工作計(jì)劃及階段進(jìn)度如下：
第1、2周 收集資料，查閱相關(guān)文獻(xiàn)，寫任務(wù)書，開題報(bào)告。
第3、4周 分析被加工零件，并畫零件圖。
第5、6周 對(duì)右主軸箱進(jìn)行分析、計(jì)算，確定主軸箱相關(guān)尺寸。
第7、8周 右主軸箱傳動(dòng)設(shè)計(jì)，確定各主軸的相關(guān)數(shù)據(jù)。
第9、10周 右主軸箱總體圖的繪制。
第11、12周 對(duì)中間底座進(jìn)行分析，中間底座零件圖的繪制。
第13、14周 撰寫畢業(yè)設(shè)計(jì)說明書。
第15、16周 翻譯約5000單詞量的相關(guān)英文文獻(xiàn)，完善所有圖和
說明書，并仔細(xì)檢查及時(shí)改正。
主要參考
文獻(xiàn)
1.《組合機(jī)床設(shè)計(jì)簡(jiǎn)明手冊(cè)》
2.《組合機(jī)床圖冊(cè)》
3．《新編機(jī)械設(shè)計(jì)手冊(cè)》
4.《組合機(jī)床及其調(diào)整與使用》
指導(dǎo)教師
意 見
指導(dǎo)教師簽名：
年 月 日
教研室意見
學(xué)院意見
教研室主任簽名：
年 月 日
教學(xué)院長(zhǎng)簽名：
年 月 日
徐州工程學(xué)院畢業(yè)設(shè)計(jì)(論文)
摘要
組合機(jī)床是根據(jù)工件加工需要，以大量通用部件為基礎(chǔ)，配以少量專用部件組成的工序集中的一種高效專用機(jī)床。而且其生產(chǎn)效率高，加工精度穩(wěn)定，自動(dòng)化程度高，使工人勞動(dòng)強(qiáng)度降低。
本次設(shè)計(jì)的是一臺(tái)加工“汽車制動(dòng)室支架”的組合鉆床，主要用來一次性加工完成汽車制動(dòng)室支架的二個(gè)零件,共計(jì)10個(gè)孔，一次安裝兩個(gè)工件，左主軸箱鉆4孔，右主軸箱鉆6孔，我負(fù)責(zé)設(shè)計(jì)的是右主軸箱和中間底座的設(shè)計(jì)。
根據(jù)所加工孔的位置及速度要求，算出切削速度和主軸轉(zhuǎn)速，確定右主軸箱輪廓尺寸、主軸的型式和直徑。再根據(jù)驅(qū)動(dòng)軸位置和轉(zhuǎn)速、各主軸位置及其轉(zhuǎn)速要求，合理布置傳動(dòng)軸的位置，把驅(qū)動(dòng)軸和各主軸連接起來，使各主軸獲得所需轉(zhuǎn)速和轉(zhuǎn)向，完成鉆孔。
中間底座的結(jié)構(gòu)、尺寸則需要根據(jù)工件的大小、形狀以及組合鉆床的配置形式等來確定。
由于組合鉆床能夠進(jìn)行多工位加工，提高自動(dòng)化程度，縮短加工時(shí)間和輔助時(shí)間。而且組合鉆床大部分都是由通用部件組成，研制周期較短，便于設(shè)計(jì)、制造和使用維護(hù)，成本低。而且機(jī)床易于改造，產(chǎn)品和工藝變化時(shí)，通用部件還能重復(fù)利用，經(jīng)濟(jì)性較好。所以組合機(jī)床在大批量生產(chǎn)中的應(yīng)用十分廣泛。
關(guān)鍵詞：組合鉆床；主軸箱；中間底座
Abstract
Combination machine is based on the workpiece processing needs,take a large number of general part as the foundation, with a few of dedicated part which composes the focus on process of a efficient special machine.Moreover its production efficiency is high,machining accuracy is stable, degree of automation is high,cause the workers labor intensity to reduce.
This design is a combination drilling machine of processing "automobile brake room stent" , mainly uses for complete two parts of automobile brake room stent which processing a one-time, the total 10 holes, one-time installs two workpieces, the left spindle box drills 4 , the right spindle box drills 6 , what I am responsible to the design of the right spindle box and the middle base .
According to processes the hole the position and the speed request, calculated to cutting speed and the spindle speed ,determines the right spindle box outline of size, the spindle type and the diameter.Then according to drive shaft position and speed, various spindle position and rotational speed request, reasonable arrangement transmission shaft location, connects the drive shaft and various spindle ,causes various spindle to obtains needs the rotational speed and change direction , completes the drill hole.
The middle base’s structure , size has to be based on the workpiece size, the shape as well as the combination drilling machine configuration form and so on to determined.
Due to the combination drilling machine carries on the multi-location processing, improves the degree of automation, reduces processing time and auxiliary time. Moreover the combination drilling machine majority is composed of general part, the development cycle is short,and is advantageous for the design, the manufacture and use maintenance, the cost is low. Moreover the machine easy to transform, when product and process changes, the general part can also the reuse,the efficiency be good.So combination of machine tools is very widespread in production in enormous quantities application.
Keywords: combination drilling machine spindle box middle base
II
徐州工程學(xué)院畢業(yè)設(shè)計(jì)(論文)
目 錄
1 組合機(jī)床概述 1
1.1 引言 1
1.2 組合機(jī)床組成及特點(diǎn) 1
1.3 組合機(jī)床的工藝范圍及配置形式 2
1.3.1 組合機(jī)床的工藝范圍 2
1.3.2 組合機(jī)床的配置形式 3
1.4 組合機(jī)床的設(shè)計(jì)步驟 5
1.4.1 調(diào)查研究 5
1.4.2 總體方案設(shè)計(jì) 5
1.4.3 技術(shù)設(shè)計(jì) 6
1.4.4 工作設(shè)計(jì) 6
2 組合鉆床設(shè)計(jì) 7
2.1 零件分析 7
2.2 組合鉆床設(shè)計(jì)的組成及設(shè)計(jì)任務(wù) 7
2.2.1 組合鉆床設(shè)計(jì)的組成 7
2.2.2 本課題主要任務(wù) 7
2.3 工藝方案及基準(zhǔn)的選擇 8
2.3.1 確定組合鉆床工藝方案的機(jī)本原則 8
2.3.2 組合鉆床工藝方案的一般步驟 9
2.3.3確定切削力、切削轉(zhuǎn)矩、切削功率及刀具耐用度 10
2.4 組合鉆床主軸箱概況 10
2.4.1 組成 10
2.4.2主軸箱的通用零件 10
2.5 工序與計(jì)算 11
2.5.1 加工條件 11
2.5.2計(jì)算切削速度、主軸轉(zhuǎn)速 11
3多軸箱的設(shè)計(jì) 13
3.1 多軸箱的基本結(jié)構(gòu)和表達(dá)方法 13
3.1.1 多軸箱的簡(jiǎn)介 13
3.1.2多軸箱的組成 13
3.1.3多軸箱總圖繪制方法 13
3.2 多軸箱通用零件 13
3.2.1 通用箱體類零件 14
3.2.2 通用主軸 14
3.2.3 通用傳動(dòng)軸 14
3.2.4 通用齒輪和套 14
3.3通用多軸箱的設(shè)計(jì)分析 15
3.3.1 繪制多軸箱設(shè)計(jì)原始依據(jù)圖 15
3.3.2 確定多軸箱輪廓尺寸 16
3.3.3 主軸型式和直徑的確定 16
3.3.4主軸箱所需進(jìn)給力計(jì)算 18
3.3.5 主軸箱所需功率計(jì)算 18
3.3.6 動(dòng)力部件 19
3.3.7多軸箱傳動(dòng)設(shè)計(jì) 19
3.3.8 計(jì)算傳動(dòng)軸的坐標(biāo) 23
3.3.9 潤(rùn)滑油泵和手柄軸的安置 24
4 中間底座的設(shè)計(jì) 26
4.1 引言 26
4.2 中間底座的作用及基本要求 26
4.2.1 中間底座的作用 26
4.2.2 對(duì)于中間底座的基本要求 26
4.3 中間底座的設(shè)計(jì)原則 27
4.3.1 合理選擇截面形狀和尺寸 27
4.3.2 合理布置加強(qiáng)筋 27
4.4 中間底座壁厚、加強(qiáng)筋厚度的選擇 27
4.5 如何提高連接處的局部剛度和接觸剛度 28
4.6 中間底座結(jié)構(gòu)工藝性 28
結(jié)論 29
參考文獻(xiàn) 30
致謝 31
附錄 32
2
徐州工程學(xué)院畢業(yè)設(shè)計(jì)(論文)
附錄
英文原文
A GENERIC KINEMATIC ERROR MODEL FOR MACHINE TOOLS
Yizhen Lin, Yin-Lin Shen
Department of Mechanical and Aerospace Engineering
The George Washington University, Washington, DC 20052
ABSTRACT: A generic kinematic error model is proposed to characterize the geometric error of machine tools. Firstly, modeling was made on a moving bridge gantry machine, a moving table machine and a horizontal spindle machine respectively by means of the conventional homogeneous coordinate transformation. Then these models were generalized to derive the generic error model which is able to accommodate the different configurations and axis definitions in various kinds of 3-axis machine tools. Finally, the generic kinematic model is implemented in a virtual CNC computer program, which has rigorous procedures to interpret machine tool metrology data into 21 parametric errors. The effectiveness of the generic error model is tested by using the measurement data from a horizontal spindle machining center. The result of the diagonal displacement test is presented and compared with the model prediction. It is shown that the generic kinematic model is efficient and easy to implement, which can substantially reduce the modeling and implementation efforts.
INTRODUCTION
Global competition has imposed more and more stringent requirements on the levels of accuracy and productivity in the manufacturing industry.1 Since the accuracy of the manufactured workpieces is closely related to the accuracy of machine tools,2 a lot of research work has been carried out to enhance the machine tool accuracy and reduce the operational cost. Machine tools performance evaluation and real-time error compensation have provided an effective way to build up a highly precise manufacturing system.3-8
Currently, extensive research has been conducted to model the geometric and thermal errors of machine tools.3－11 These research works have proposed effective approaches in modeling the volumetric error of machine tools. However, these models are mostly developed for specific machines instead of generic machine tools They could not provide a universal and ready-to-implement model for various kinds of different machine tools. Here, the main challenge is how to develop a generic machine error model12 which could accommodate different machine configurations and axis definitions in the shop floor. For example, homogeneous coordinate transformation,13 the most extensively used technique in modeling the geometric error of machine tools, only provides a general approach and proves to be less efficient – for each new machine configuration and axis definition, people have to go through the same modeling procedures.
To this aim, we developed a generic error model for machine tools which can be used to characterize various kinds of 3-axis machine tools quickly and efficiently. The generic error model has been implemented in a virtual CNC computer program. The test results show that the generic model can predict the geometric error of machine tools well.
MACHINE ERRORS
Among the errors attributed to machine tools in the manufacturing systems, quasistatic errors, including geometric and thermal errors, are the major contributors to the positioning inaccuracies of machine tools. These errors, estimated to account for 70 percent of the errors of machines, have been observed to be as high as 70 to 120 μm for production class machine.11 For these errors, a variety of machine tool performance test systems have been developed.14 Among them, the parametric representation describes the machine error characteristics in a kinematic model that provides the position and orientation errors of the cutting tool in terms of the axis position, tool length, and machine axis characteristics (positioning accuracy, straightness, axis rotations and squareness). It is the most convenient format for characterizing the machine tool errors and has been shown to be very flexible and robust in the performance evaluation.15
The parametric errors are errors in the relative position and orientation between two successive axes in the kinematic chain from the workpiece to the tool. It has been well known that 21 parametric errors are enough to represent all the geometric error sources of a generic 3-axis machine. They are named as xTy, zRx, Sxy, etc., where R means rotation, T means translation and S means squareness.The left subscript means the moving slide and the right subscript means the error direction.15
The kinematic model relates errors in relative position and orientation of the tool to 21 parametric errors. In deriving the kinematic error model, we make the assumptions of rigid body kinematics and small error motions. Donmez9 developed a general methodology to derive the kinematic error model by using the homogeneous coordinate transformation, which represent the error motion as9，13
(1)
KINEMATIC MODELS
By means of the homogeneous coordinate transformation, we can derive kinematic error models for several specific machine types. Figure 1 shows a bridge type moving gantry machine which can be classified as FXYZ system, where F means the machine fixed base, X axis is the first slide stacked on the fixed base, Y axis is stacked on X axis and Z axis stacked on Y axis.
From Equation (1), we have
(2)
(3)
(4)
Here Hx, Hy and Hz are the transformation matrices for each axis. xRx, xTx, xRy,…, Sxz are the 21 parametric errors. The squareness error is interpreted as an angular error in the derivation.15 The positive direction of the squareness error is defined by the corresponding angular errors.
Figure 1.Bridge type moving gantry machine
Also we have the tool link offset vector:
(5)
According to the machine kinematic chain,
(6)
Apply Equations (2)-(5) to Equation (6), we have the kinematic equations for the FXYZ machine:
(7)
(8)
(9)
We further derive the model for machines with a moving table. A typical machine with a moving table (X axis) is shown in Figure 2. It can be classified into the XFYZ group. For XFYZ machine type,
(10)
The homogenous coordinate transformation also holds true for each axis so that Equations (2)-(5) are still valid here. Apply them to Equation (10), we have
(11)
Figure 2.Machine with a moving table-X axis Figure 3.Machine with moving tables(X,Y)
(12)
(13)
For the machines with two moving tables (X, Y axis), they can be classified into the XYFZ group,as
shown in Figure 3. For XYFZ machine type,
Therefore, we have
(14)
Apply Equations (2)-(5) to Equation (14), we have
(15)
(16)
(17)
We have discussed the kinematic models of FXYZ, XFYZ and XYFZ machines. All of them are vertical spindle machines. It is therefore of interest to study the case of the horizontal spindle machine. By convention, the spindle is defined as the Z axis.16 Figure 4 shows the kinematic chain of a FXZY-type horizontal spindle machine. Because Z axis, the spindle, is stacked on X slide now,Equations (3)-(4) will become
(18)
Figrue 4.Machine with horizontal spindle
(19)
Also, by the kinematic chain,
(20)
Applying Equations (2), (18) and (19) to Equation (20), we have
(21)
(22)
(23)
GENERIC KINEMATIC ERROR MODEL
Although the kinematic equations we have derived for different machines are different in mathematical forms, they hold the same structure in formulation because they have the similar physical kinematic chains. Therefore it is possible for us to generalize these specific models to develop a generic error model for 3-axis machine tools. In general, we have the following model:
(24)
(25)
(26)
I, II and III are the first, second and third physical axis of machine. I is the first axis directly related to the workpiece. III is the axis directly related to the tool link. II is the axis in between. δ123 is a multiplier,which will have:(1). δ123=1,when I, II, III form a right hand coordinate system; (2). δ123= -1, when I, II, III cannot form a right hand coordinate system.
By simply assigning I, II, III to X, Y, Z and setting δxyz=1 because XYZ form a right hand coordinate system in Figure 1, Equations (24)-(26) will change to Equations (7)-(9). Assigning I,II, III to X, Z,Y and setting δxzy = -1 because XZY form a left hand coordinate system in Figure 4, Equations (24)-(26) will change to Equations (21)-(23). For the other different axis naming conventions in the shop floor, by assigning the generic axes I, II, III to their respectively named axes, such as Y, X, Z, the specific error model can be obtained easily. It can be seen that the generic error model can handle different axis definitions well.
After assigning the axes to the generic model, we need to make the relevant change for moving table machines. As shown in Equations (27)-(29), we decompose the structure of the formulation in Equations (24)-(26) into three parts – zone-I, zone-II and zone-III respectively.
Equations (27)-(29) are the model for machines without a moving table. For machines with one moving table (such as XFYZ, YFXZ, etc.), the following changes will be made:
(1-1). zone-II and zone-III stay the same.
(1-2). All the terms in zone-I change signs.
(1-3). If Ip (excluding the one inside (Ip+I), where rule 1-4 applies) appears in zone-I, Ip should be changed to Ip-I.
(1-4). If (Ip+I) appears in zone-I, (Ip+I) should be changed to (Ip-I).
(27)
(28)
(29)
On basis of this, if one further considers machines with two moving tables (XYFZ or YXFZ etc.),the rules will be
(2-1). zone-III remains the same.
(2-2). All terms in zone-II change signs.
(2-3). For any IIp (excluding the one inside (II+IIp), where rule 2-4 applies) appears in zone-I or zone-II, IIp should be changed to IIp-II.
(2-4). For any (II+IIp) appears in zone-I or zone-II, (II+IIp) should be changed to (IIp-II).
These rules can be easily verified by comparing Equations (7)-(9) (FXYZ machine) with Equations (11)-(13) (XFYZ machine), then with Equations (15)-(17) (XYFZ machine). It can be seen that the generic error model also handles the moving table(s) machine well.
IMPLEMENTATION OF GENERIC ERROR MODEL
A virtual CNC computer program is developed to implement the generic error model. The program is capable of predicting the effects of machine error motions in the machine gauge point for the given XYZ nominal commanded movement of machines.
Figure 5 shows the inputs/outputs and functionality of the virtual CNC computer program. The program inputs include: (1). Machine type and axis assignment; (2). Machine tool metrology data, which consist of laser measurement data of machine axes, including positioning error, straightness errors, roll, pitch, yaw and the squareness measurement; (3). The commanded XYZ motion of the gauge point and moving directions of axes (to account for backlash). The program outputs will predict the actual XYZ position of the machine gauge point and IJK orientation of the cutting tool.
In the virtual CNC program, we use the machine tool metrology data to generate a lookup table for each of the 18 translation and angular errors for the 3-axis machine. The program also keeps three squareness numbers. The procedures to decode 21 parametric errors from the laser system measurement data are as follows:15
Figrue 5.Virtual CNC computer program implementing generic error model
(1). Construct an error lookup table of 6 parametric errors (linear displacement, 2 straightness,roll, pitch and yaw) for each axis. Initialize all the entries in the lookup table to zero.
(2). Read in the measurement data.
(3).Compensate the thermal expansion for the positioning error. If the metrology data have been compensated, advance to STEP 4.
(4). Shift the coordinates from the measurement coordinate system to the machine coordinate system.
(5). Extrapolate the measurement data to cover the whole range of axis in the machine working zone.
(6). Abbe Offset compensation for translation errors. Abbe Offset is the instantaneous value of the perpendicular distance between the displacement measuring system of a machine(scales) and the measurement line where displacement in that coordinate is being measured.14 Because of the Abbe Offset translation errors are often compounded by the effects of angular errors.
(7). For straightness data, calculate the best fit line through the compensated data and store the residuals.
(8). Calculate the squareness errors using the best fit lines obtained in STEP 7.
TEST ON A HORIZONTAL MACHINING CENTER AND DISCUSSION
We use the measurement data obtained by a 5-D laser system17 from a horizontal spindle machining center to verify our generic model. As shown in Figure 6, the horizontal spindle machine can be classified as the XFZY machine. Because the first axis is a moving table, applying the rule of the moving table to Equations (27)-(29), we have
(30)
(31)
(32)
Figure 6. Kinematic china of a horizontal spindle machining center
Finally, we substitute the general axes with the defined axes. In the XFZY machine, I = X, II = Z, III= Y, δ123= 1 (X, Z, Y form a right hand coordinate system). Therefore, the specific error model for the horizontal spindle machine center would be
(33)
(34)
(35)
We also try to derive the specific error model by the homogeneous coordinate transformation.
(36)
Apply Equations (2), (18) and (19) to Equation (36), we can verify that the specific model obtained from our generic model is exactly the same as that obtained by the homogeneous coordinate transformation. It can also be seen that the generic model is more direct and needs less calculation and modeling efforts. People without profound knowledge in the kinematics and the homogeneous coordinate transformation are still able to derive the machine error model from the generic model.
To further test the effectiveness of the generic model and the virtual CNC program, the diagonal measurement data from the machining center are used. The diagonal measurement14 is a simple linear measurement occurring along a diagonal of the machine working volume, which shows the combined effect of error motions of three axes. Figure 7 shows the diagonal test for the horizontal machining center which measured the linear displacement errors at 11 evenly distributed diagonal points back and forth. The prediction from the virtual CNC program was also shown. It can be seen that the virtual CNC program predicts the errors in the diagonal test well (within a few microns).
Figure 7.Diagonal test and model prediction
CONCLUSION
The generic kinematic error model can characterize the geometric errors of various kinds of the 3-axis machine tools. It can handle different machine configurations and axis definitions. Compared with the homogeneous coordinate transformation approach, the generic kinematic model is more efficient, easier to implement, substantially reducing the modeling and implementation efforts.
The virtual CNC program can implement the generic model and simulate the geometric errors of machine tools. It has rigorous procedures to decode 21 parametric errors from the machine tool metrology data and uses them in the generic model to predict the machine error motion and the tool orientation. The diagonal test result shows that the virtual CNC program can predict the machine errors and help reduce machine errors to a few microns.
The generic model will be tested with more data. Further research work on the generic model for machines with more axes is being carried out.
ACKNOWLEDGEMENT
This work was supported in part by the National Science Foundation under Grant No. DMII-9624966. The support is greatly appreciated. The authors would like to thank Dr. Johannes Soons of the National Institute of Standards and Technology, Mr. Richard Yang of Automated Precision,Inc., and Mr. Sungho Moon of the George Washington University for useful discussions.
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