壓縮包內(nèi)含有CAD圖紙和說明書,均可直接下載獲得文件，所見所得，電腦查看更方便。Q 197216396 或 11970985
畢業(yè)設(shè)計（論文）指導(dǎo)情況記錄表
（本表由學(xué)生和指導(dǎo)教師按指導(dǎo)情況分別如實填寫） 第11周
教師指導(dǎo)意見及指導(dǎo)方式（教師填寫）：（指導(dǎo)學(xué)生開題、查閱文獻(xiàn)資料、綜合運用知識、方案設(shè)計、論文寫作、外文應(yīng)用、實驗、指出存在問題及解決辦法等簡況）
1、布置學(xué)生按規(guī)定的格式編寫論文，注意重點及論文的要求。
指導(dǎo)教師簽名： 20**年5月5日
學(xué)生意見（任務(wù)完成情況及需要解決的問題）：
1、隨時與指導(dǎo)老師在網(wǎng)上交流。
2、多查閱文獻(xiàn)。
學(xué)生簽名： 20**年5月6日
注：此頁可根據(jù)需要自行復(fù)制，每指導(dǎo)一次，填寫一次，不受頁數(shù)限制。
1
畢業(yè)設(shè)計（論文）指導(dǎo)情況記錄表
（本表由學(xué)生和指導(dǎo)教師按指導(dǎo)情況分別如實填寫）
教師指導(dǎo)意見及指導(dǎo)方式（教師填寫）：（指導(dǎo)學(xué)生開題、查閱文獻(xiàn)資料、綜合運用知識、方案設(shè)計、論文寫作、外文應(yīng)用、實驗、指出存在問題及解決辦法等簡況）
1、開題報告格式按照有關(guān)規(guī)定進(jìn)行調(diào)整。
2、下達(dá)畢業(yè)設(shè)計任務(wù)書。
3、初步檢查開題報告編寫進(jìn)度。
指導(dǎo)教師簽名： 20**年 2 月 29日
學(xué)生意見（任務(wù)完成情況及需要解決的問題）：
1、完成開題報告，并對其格式進(jìn)行修改。
2、向?qū)焻R報進(jìn)度，了解整體安排。
3、對課題內(nèi)容準(zhǔn)備資料。
學(xué)生簽名： 年 月 日
注：此頁可根據(jù)需要自行復(fù)制，每指導(dǎo)一次，填寫一次，不受頁數(shù)限制。
1
畢業(yè)設(shè)計（論文）指導(dǎo)情況記錄表
（本表由學(xué)生和指導(dǎo)教師按指導(dǎo)情況分別如實填寫）
教師指導(dǎo)意見及指導(dǎo)方式（教師填寫）：（指導(dǎo)學(xué)生開題、查閱文獻(xiàn)資料、綜合運用知識、方案設(shè)計、論文寫作、外文應(yīng)用、實驗、指出存在問題及解決辦法等簡況）
1、本次采用的方式：網(wǎng)上指導(dǎo)。
2、譯文格式，字體、段落要重新處理一下。
3、開題報告內(nèi)容的大框架還可以，有的地方需細(xì)化。
指導(dǎo)教師簽名： 20**年3 月7 日
學(xué)生意見（任務(wù)完成情況及需要解決的問題）：
1、對外文翻譯的格式進(jìn)行重新編排。
2、完成開題報告，修改細(xì)節(jié)內(nèi)容。
3、準(zhǔn)備繪制圖紙，進(jìn)行設(shè)計。
學(xué)生簽名： 年 月 日
注：此頁可根據(jù)需要自行復(fù)制，每指導(dǎo)一次，填寫一次，不受頁數(shù)限制。
1
畢業(yè)設(shè)計（論文）指導(dǎo)情況記錄表
（本表由學(xué)生和指導(dǎo)教師按指導(dǎo)情況分別如實填寫）
教師指導(dǎo)意見及指導(dǎo)方式（教師填寫）：（指導(dǎo)學(xué)生開題、查閱文獻(xiàn)資料、綜合運用知識、方案設(shè)計、論文寫作、外文應(yīng)用、實驗、指出存在問題及解決辦法等簡況）
本次現(xiàn)場統(tǒng)一布置和講解：
1、主要講解每位所設(shè)計的題目，如何開始進(jìn)行設(shè)計和構(gòu)思。
2、統(tǒng)一設(shè)計時使用的圖紙標(biāo)題欄要求。
3、設(shè)計時使用CAD軟件繪圖，除cad繪圖外必須有手工繪制的一張3號圖。
指導(dǎo)教師簽名： 20**年3月14日
學(xué)生意見（任務(wù)完成情況及需要解決的問題）：
1、了解設(shè)計題目的設(shè)計思路，了解其結(jié)構(gòu)及運動過程。
2、對圖紙所用的標(biāo)題欄格式進(jìn)行統(tǒng)一。
3、準(zhǔn)備設(shè)計資料，并查詢繪制基準(zhǔn)。
學(xué)生簽名： 年 月 日
注：此頁可根據(jù)需要自行復(fù)制，每指導(dǎo)一次，填寫一次，不受頁數(shù)限制。
1
畢業(yè)設(shè)計（論文）指導(dǎo)情況記錄表
（本表由學(xué)生和指導(dǎo)教師按指導(dǎo)情況分別如實填寫）
教師指導(dǎo)意見及指導(dǎo)方式（教師填寫）：（指導(dǎo)學(xué)生開題、查閱文獻(xiàn)資料、綜合運用知識、方案設(shè)計、論文寫作、外文應(yīng)用、實驗、指出存在問題及解決辦法等簡況）
1、查閱資料，參考同類產(chǎn)品的基礎(chǔ)上構(gòu)思自己所設(shè)計結(jié)構(gòu)。
2、齒輪箱的設(shè)計中涉及到的齒輪傳動、傳動軸設(shè)計等內(nèi)容都是機械專業(yè)的基礎(chǔ)知識，復(fù)習(xí)機械設(shè)計課程中的相關(guān)內(nèi)容。
3、去圖書館查閱相關(guān)資料，啟發(fā)設(shè)計思路。
4、認(rèn)真閱讀所提供參考書的相關(guān)章節(jié)，了解齒輪箱原理。
指導(dǎo)教師簽名： 20** 年3 月 21 日
學(xué)生意見（任務(wù)完成情況及需要解決的問題）：
1、閱讀相關(guān)資料，了解其他同類產(chǎn)品在其結(jié)構(gòu)設(shè)計的理念。
2、對設(shè)計中用到的齒輪知識，進(jìn)行相關(guān)的了解，查閱以前設(shè)計的內(nèi)容。
3、了解相關(guān)知識，對齒輪箱結(jié)構(gòu)原理有一定的了解。
學(xué)生簽名： 年 月 日
注：此頁可根據(jù)需要自行復(fù)制，每指導(dǎo)一次，填寫一次，不受頁數(shù)限制。
1
畢業(yè)設(shè)計（論文）指導(dǎo)情況記錄表
（本表由學(xué)生和指導(dǎo)教師按指導(dǎo)情況分別如實填寫）
教師指導(dǎo)意見及指導(dǎo)方式（教師填寫）：（指導(dǎo)學(xué)生開題、查閱文獻(xiàn)資料、綜合運用知識、方案設(shè)計、論文寫作、外文應(yīng)用、實驗、指出存在問題及解決辦法等簡況）
該生因工作缺席指導(dǎo)，但提交了電子文檔，其完成總裝圖的設(shè)計，能按進(jìn)度完成要求，圖紙中有小部分結(jié)構(gòu)設(shè)計錯誤，經(jīng)修改后達(dá)到要求。另外要按新國標(biāo)進(jìn)行圖紙的繪制。
指導(dǎo)教師簽名： 20** 年3 月28 日
學(xué)生意見（任務(wù)完成情況及需要解決的問題）：
1、繪制好總裝配圖及部分零件圖，并修改部分錯誤。
2、修改尺寸、技術(shù)要求等方面問題。
3、將新國標(biāo)進(jìn)行了解，運用到繪圖過程中。
學(xué)生簽名： 年 月 日
注：此頁可根據(jù)需要自行復(fù)制，每指導(dǎo)一次，填寫一次，不受頁數(shù)限制。
1
畢業(yè)設(shè)計（論文）指導(dǎo)情況記錄表
（本表由學(xué)生和指導(dǎo)教師按指導(dǎo)情況分別如實填寫）
教師指導(dǎo)意見及指導(dǎo)方式（教師填寫）：（指導(dǎo)學(xué)生開題、查閱文獻(xiàn)資料、綜合運用知識、方案設(shè)計、論文寫作、外文應(yīng)用、實驗、指出存在問題及解決辦法等簡況）
網(wǎng)上指導(dǎo)：
1、總裝圖總體布置合理，視圖選擇正確，表達(dá)方法正確，投影規(guī)律正確，但一些細(xì)節(jié)結(jié)構(gòu)表達(dá)有問題或未表達(dá)。
2、標(biāo)注上有一些問題。
3、貫徹國標(biāo)要加強。
指導(dǎo)教師簽名： 20**年4月4 日
學(xué)生意見（任務(wù)完成情況及需要解決的問題）：
1、對總裝配圖進(jìn)行修改，完成所有圖紙的繪制。
2、標(biāo)注部分出現(xiàn)差錯，進(jìn)行修改。
3、對國標(biāo)進(jìn)一步的了解。
學(xué)生簽名： 年 月 日
注：此頁可根據(jù)需要自行復(fù)制，每指導(dǎo)一次，填寫一次，不受頁數(shù)限制。
1
任務(wù)書
題 目
花生聯(lián)合收割機齒輪箱設(shè)計
論文時間
20**年2月20日至 20**年6月1日
課題的主要內(nèi)容及要求(含技術(shù)要求、圖表要求等)
隨著我國經(jīng)濟(jì)的不斷發(fā)展，農(nóng)戶對農(nóng)機具的需求日益高漲，尤其需要基本形農(nóng)機具，其成本低，適用于一個農(nóng)戶家庭的收割作業(yè)。需要設(shè)計一個精密型花生聯(lián)合收割機于12馬力手扶拖拉機向配套，有效利用拖拉機動機，設(shè)計相應(yīng)的齒輪箱，成本控制在1萬元左右。
設(shè)計一種花生聯(lián)合收割機齒輪箱，完成總裝圖及零件。編寫設(shè)計說明書；完成專業(yè)外文資料翻譯1份。
課題的實施的方法、步驟及工作量要求
設(shè)計方法：學(xué)生在指導(dǎo)教師的指導(dǎo)下，利用所學(xué)的課程并自學(xué)有關(guān)知識，掌握機械設(shè)計的特點、方法，借助《機械設(shè)計手冊》等技術(shù)資料，完成本機設(shè)計。
設(shè)計步驟：調(diào)研收集設(shè)計資料——根據(jù)所給定的參數(shù)制定總體設(shè)計方案——完成總裝圖及部裝圖——完成零件圖——編寫設(shè)計說明書。
工作量要求：設(shè)計圖紙工作量合計3張零號圖紙（A03張、A10張、A23張、A31張、A40張）；畢業(yè)設(shè)計說明書不少于8000漢字；外文資料原文(與課題相關(guān)的1萬印刷符號左右)，外文資料翻譯譯文（約3000漢字）。
指定參考文獻(xiàn)
[1] 濮良貴.《機械設(shè)計》（第七版）[M]. 北京：北京高等教育出版社， 2001
[2] 吳相憲.《實用機械設(shè)計手冊》[M]. 北京： 機械工業(yè)出版社，1994
[3] 李天無.《簡明機械工程師手冊》[M].云南：云南科技出版社，1988年。
[4] 候鎮(zhèn)冰.《機械設(shè)計制圖手冊》 [M]. 上海：同濟(jì)大學(xué)出版社,1991
[5] 北京農(nóng)業(yè)機械化學(xué)院.《農(nóng)業(yè)機械學(xué)》[M].北京：農(nóng)業(yè)出版社，1986年
[6] 王樹人.《機械設(shè)計便覽》（參編）[M].天津：天津科技出版社，1988
畢業(yè)設(shè)計(論文)進(jìn)度計劃(以周為單位)
第 1 周（20**年 2月20日----20**年 2 月 26 日）：
下達(dá)設(shè)計任務(wù)書，明確任務(wù)，熟悉課題，收集資料，上交外文翻譯、參考文獻(xiàn)和開題報告。
第2周——第8周（20**年 2 月 27 日----20**年4 月 15 日）：
制定總體方案，繪制總裝圖草圖。
第 9 周——第14周（20**年4月16 日----20**年 5月 27日）：
修改并完成總裝圖及部裝圖，完成有關(guān)零件圖的設(shè)計。
第15 周——第 16 周（20**年 5 月28日----20**年 6 月5 日）：
編寫設(shè)計說明書
第 16 周（20**年 6月 6日----20**年6 月 8 日）：
準(zhǔn)備答辯
備注
注：表格欄高不夠可自行增加。此表由指導(dǎo)教師在畢業(yè)設(shè)計（論文）工作開始前填寫，每位畢業(yè)生兩份，一份發(fā)給學(xué)生，一份交院（系）留存。
ORIGINAL ARTICLE Optimal mechanical spindle speeder gearbox design for high speed machining D R Salgado and the turning pair is the link between the arm member 3 and the planet In the present work the expression simple planet will be used for a planet constructed with a single gear such as the planet of Fig 2a b and double planet for one constructed with two gears such as the planets of Fig 2c f A more detailed explanation of the structure of PGTs may be found in 9 11 2 1 Efficiency considerations It is possible to prove that the efficiency of the multiplier based on the four member PGT is higher if it is designed with an input by the arm member 3 This is the reason why all mechanical spindle speeders are designed as multiplier four member PGTs with an input by the arm member 2 2 Economic and operating considerations Of the solutions with a double planet configuration Fig 2c f that of Fig 2d is more interesting from an economic point of view since it offers the advantage of not using a ring gear The reason for this is that spindle speeder gears must be hardened tempered and ground to avoid high heating and a ground ring gear is more expensive than a ground non ring gear Also if the ring gear is not ground heat buildup will occur in a shorter period of time and this heating limits and reduces the input speed and torque The constructional solution of Fig 2a presents the advantage over the other solution constructed with simple a bcdef Fig 2 The six constructional solutions of the four member PGT Fig 1 a Members of a plane tary gear train PGT b A mechanical spindle speeder Int J Adv Manuf Technol 2009 40 637 647 639 planets Fig 2b in that the ring gear is the fixed member For this reason the constructional solution of Fig 2b is not used for mechanical spindle speeder design since it increases the kinetic energy of the spindle speeder considerably Following this same reasoning the construc tional solutions of Fig 2e f are not appropriate config urations from the solutions constructed with double planets for mechanical spindle speeder design 2 3 Planet member considerations In spindle speeder design it is quite important to choose an optimal number of planets for the required power and speed ratio The number of planet members N p can vary from two to three four or even more depending on the application for which it is designed For example the mechanical spindle speeder of Fig 1a has three planet members N p 3 This number must be as small as possible in order to reduce the weight and the kinetic energy of the transmission while ensuring a good distribution of the load to each of the planet gears Whichever the case the planets must always be arranged concentrically around the PGT s principal axis to balance the mass distribution In short for mechanical spindle speeders only the constructional solutions of Fig 2a c d must be considered for an optimal spindle speeder design In particular these constructional solutions are the ones that are most often used by manufacturers 3 Constraints on mechanical spindle speeder design In this section the constraints for the mechanical spindle speeder design are described They are grouped into three sets according to the type of constraint These are Constraints involving gear size and geometry PGT meshing requirements Contact and bending stresses 3 1 Constraints involving gear size and geometry The first constraint is a practical limitation of the range for the acceptable face width b This constraint is as follows 9m C20 b C20 14m 1 where m is the module The module indicates the tooth size and is the ratio of the pitch diameter to the number of teeth in the gear For gears to mesh their modules must be equal Gear ISO standards and design methods are based on the module All of the kinematic and dynamic parameters of the transmission depend on the values of the tooth ratios Z nl where Z nl is the tooth ratio of the gear pair formed by the linking members n and l In particular Z nl is defined as Z nl Z n Z l 2 For the definition of the tooth ratios to satisfy the Willis equations Z nl must be positive if the gear is external meshing gear gear and negative if it is internal meshing ring gear gear 10 11 For the train of Fig 2a one would have to take Z 14 0 and Z 24 0 In theory the tooth ratios can take any value but in practice they are limited mainly for technical reasons because of the difficulty in assembling gears outside of a certain range of tooth ratios In this work the tooth ratio for the design of mechanical spindle speeders are quite close to the recommendations of M ller 12 and the American Gear Manufacturers Association AGMA norm 13 and are 0 2 Z nl 5 3 C07 Z nl C02 2 4 with the constraint given by Eq 3 being for external gears and that by Eq 4 for internal gears It is important to note that these constraints are valid for designs with different numbers of planets N p In respecting these values one achieves mechanical spindle speeder designs that are smaller lighter and cheaper Another constraint that will be imposed on the design of spindle speeders with double planets is that the ratio of the diameters of the gears constituting a double planet is 1 3 d 4 d 0 4 3 5 where d 0 4 is the diameter of the planet gear that meshes with member 2 and d 4 is the diameter of the planet gear that meshes with member 1 see Fig 2 In the constructional mechanical spindle speeders based on the PGT of Fig 2c d the tooth ratios Z 14 and Z 24 0 are related to the radii of the gears constituting the planet In particular the following geometric relationship must be satisfied in the spindle speeder configuration of Fig 2c 1 2 d 1 d 4 1 2 d 2 C0 d 0 4 C0C1 6 Expressing the above equation in terms of the module of the gears it is straightforward to find that the ratio of the diameters of gears 4 and 4 conditions the value of Z 14 and Z 24 0 This ratio is d 0 4 d 4 Z 14 1 Z 24 0jjC0 1 7 640 Int J Adv Manuf Technol 2009 40 637 647 Likewise one obtains for the case of the configuration in Fig 2d the expression d 0 4 d 4 Z 14 1 Z 24 0 1 8 Lastly one assumes a minimum pinion tooth number of Z min C21 18 9 3 2 Planetary gear train meshing requirements The meshing requirements are given by the AGMA norm 13 The following constraint Eq 10 is for the design of Fig 2a Z 2 C6 Z 1 N p an integer 10 where Z 1 is the number of teeth on the sun gear member 1 and Z 2 is the number of teeth on the ring gear member 2 The sign in Eq 10 depends on the turning direction of the sun and ring gear with the arm fixed The negative sign must be used when the sun and ring gear turn in the same direction with the arm member fixed Planetary systems with double planets must either of which factorise with the number of planets in the sense of Eq 11 below see AGMA norm 13 Z 2 P 2 C6 Z 1 P 1 N p an integer 11 where P 1 and P 2 are the numerator and denominator of the irreducible fraction equivalent to the fraction Z 0 4 Z 4 where Z 0 4 is the number of teeth of the planet gear that meshes with member 2 and Z 4 is the number of teeth of the planet gear that meshes with member 1 see Fig 2 Z 0 4 Z 4 P 1 P 2 3 3 Contact and bending stresses The torques on each gear of the proposed spindle speeder designs were calculated taking power losses into account This aspect allows one to really optimise the mechanical spindle speeder design unlike the optimisation studies in which these losses are not considered 14 15 The procedure for obtaining torques and the overall efficiency of the spindle speeder is that described by Castillo 11 For each of the gears of the spindle speeder configura tion the following constraints relative to the Hertz contact and bending stresses must be satisfied s H s HP 12 s F s FP 13 For the calculation of the gears the ISO norm was followed The values of the stresses of Eqs 12 and 13 are defined by this norm as H K A C1 K V C1 K H C1 K H p C1 Z H C1 Z E C1 Z C1 Z F t b C1 d C1 u 1 u r 14 F K A C1 K V C1 K F C1 K F C1 F t b C1 m C1 Y F C1 Y S C1 Y C1 Y 15 The values of HP and FP are given by s HP s Hlim C1 Z N C1 Z L C1 Z R C1 Z V C1 Z W C1 Z X 16 s FP s Flim C1 Y ST C1 Y NT C1 Y drelT C1 Y RrelT C1 Y X 17 It is important to emphasise that the tangential force F t was obtained from the calculation of the torques taking the power losses into account To include power losses in the overall efficiency calculation we used the concept of ordinary efficiency 10 11 which is what the efficiency of the gear pair would be if the arm linked to the planet were fixed By means of this efficiency one introduces into the overall efficiency calculation of the PGT the friction losses that take place in each gear pair For this we took a value of 0 0 98 for the ordinary efficiencies i e 2 of the power passing through each gear pair is lost by friction between these gears In studies that do not take this power loss into account the value of the tangential forces is only approximate and may be quite different in the case of PGTs because of the possibility of power recirculation 10 Given the start up characteristics of machine tools in general we took an application factor of K A 1 The pressure angle is 20 The material chosen for the gears is a steel with Hlim 1 360 N C14 mm 2 and Flim 350 N C14 mm 2 Lastly the distribution of the loads to which each of the planet gears is subjected was determined using the distribution factors recommended in the AGMA 6123 A 88 norm 13 as a function of the number of planets N p Int J Adv Manuf Technol 2009 40 637 647 641 4 Objective functions and design variables Various works have presented methods for the optimisation of a conventional transmission 14 23 but only a few studies have proposed optimisation techniques for the design of PGTs 20 21 In addition none of these studies on PGTs 24 25 calculate exactly the torques to which each of the gears is subjected since they do not consider the power losses in the different gear pairs of the PGT Nevertheless it is known that power losses in these transmissions may be considerably greater than in an ordinary gear train 10 11 and therefore an optimal design must take this factor into account Indeed not considering power losses as well as not ensuring an optimal mechanical spindle speeder design impedes one from knowing its overall efficiency with certainty In this section we describe the objective functions and the design variables The objective functions are the volume function and the kinetic energy function It is important to bear in mind that these functions have different expressions depending on the constructional solution adopted for the spindle speeder design In particular the volume function for the constructional solution with simple planets Fig 2a is expressed as follows V a p 4 b 14 d 1 2d 4 2 18 where V a represents the total volume of the gears The same objective function for the constructional solution of Fig 2c takes another form and is expressed as follows V c p 4 b 14 b 24 0 C1max d 1 2d 4 d 2 2d 4 0 2 19 and for the constructional solution of Fig 2d it is expressed as V d p 4 b 14 b 24 0 C1max d 1 2d 4 d 2 2 20 where b 14 is the face width of gears 1 and 4 and b 24 0 is the face width of gears 2 and 4 The kinetic energy function is also different for the constructional solutions with simple and double planets as can easily be deduced The function for the constructional solution of Fig 2a is expressed in the following form KE a 1 2 I 1 w 2 1 N p 1 2 m 4 v 2 4 1 2 I 4 w 2 4 C18C19 21 where I 4 w 4 and m 4 are the moment of inertia the rotational speed and the mass of the planet gear respectively and v 4 is the translation speed of the centre of the planet gear In the above expression I 1 is the moment of inertia of the sun member and N p is the number of planet gears Table 1 Optimal designs of spindle speeders based on the constructional solution of Fig 2a Spindle design P in kW n rpm m mm b mm mm Vol mm 3 KE 2 10 C06 mm 5 s 2 C16C17 KE 3 10 C06 mm 5 s 2 C16C17 T mm 1 3 5 Z 1 24 Z 4 18 Z 2 60 10 kW 1 25 14 84 14 69 850 860 905 1 057 741 77 30 8 000 rpm 1 25 11 91 25 64 285 908 152 1 115 791 82 75 16 kW 1 25 17 03 18 83 448 1 672 529 2 054 933 78 86 10 000 rpm 1 25 15 23 25 82 142 1 812 970 2 227 485 82 75 1 4 Z 1 18 Z 4 18 Z 2 54 20 kW 2 5 30 75 15 471 718 1 754 273 2 280 555 139 76 3 000 rpm 2 5 25 32 25 441 278 1 864 076 2 423 300 148 96 30 kW 2 5 26 22 16 406 100 4 235 937 5 506 718 140 44 5 000 rpm 2 5 23 62 21 387 891 4 289 504 5 576 355 144 60 45 kW 2 5 32 4 0 463 769 11 443 060 14 875 978 135 00 8 000 rpm 2 5 22 71 18 359 411 9 804 361 12 745 669 141 95 1 5 Z 1 18 Z 4 27 Z 2 72 1 7 kW 0 6 6 26 0 9 181 166 090 230 173 43 20 24 000 rpm 0 6 5 45 8 8 150 104 760 145 181 43 62 2 kW 0 7 9 75 17 21 270 69 271 95 988 52 70 10 000 rpm 0 7 8 48 25 20 598 74 688 103 506 55 61 3 5 kW 0 7 9 65 15 20 640 213 482 295 851 52 18 18 000 rpm 0 7 7 77 27 19 545 237 579 329 244 56 56 5 kW 0 9 11 68 14 40 934 361 818 501 420 66 78 13 000 rpm 0 9 9 65 25 38 754 392 580 544 051 71 50 6 4 kW 1 11 92 15 52 045 573 010 794 095 74 54 13 000 rpm 1 9 93 25 49 223 615 591 853 106 79 44 7 kW 1 13 92 17 62 011 593 508 822 503 75 30 12 000 rpm 1 11 21 28 58 557 657 453 911 120 81 54 8 kW 1 25 12 00 11 87 770 865 087 1 198 865 91 68 10 000 rpm 1 25 11 25 20 81 077 872 034 1 208 492 95 78 642 Int J Adv Manuf Technol 2009 40 637 647 The same objective function for the constructional solutions of Fig 2c d is expressed as follows KE cd 1 2 I 1 w 2 1 N p 2 m 4 m 4 0 v 2 4 N p 2 I 4 I 4 0 w 2 4 22 In Eqs 21 and 22 the energy of the arm has been neglected because this member can be designed in different and variable forms and because it is considerably less than that of the planetary system The design variables are of the constructional solution chosen from those of Fig 2a c d the number of planet gears N p the module of the gears m i the number of teeth on each gear Z i the face width b i and the helix angle i When these design parameters are determined by minimising the above objective functions the PGT is perfectly defined Table 2 Optimal designs of spindle speeders based on the constructional solution of Fig 2a cont Spindle design P in kW n rpm m mm b mm Vol mm 3 KE 2 10 C06 mm 5 s 2 C16C17 KE 3 10 C06 mm 5 s 2 C16C17 T mm 1 6 Z 1 18 Z 4 36 Z 2 90 2 5 kW 0 7 6 30 20 22 247 248 709 355 298 67 04 18 000 rpm 0 6 8 50 22 22 653 191 109 273 013 58 24 5 3 kW 0 9 10 57 15 58 355 708 768 1 012 526 83 86 15 000 rpm 0 9 8 76 25 54 946 758 054 1 082 934 89 37 7 kW 1 5 12 21 25 212 852 667 212 953 160 148 95 5 000 rpm 1 25 17 67 27 221 326 498 477 712 111 126 26 7 kW 1 25 12 11 15 129 047 798 786 1 141 124 116 47 9 000 rpm 1 25 11 25 20 126 682 828 543 1 183 633 119 72 9 3 kW 1 25 12 29 14 129 760 1 928 215 2 754 593 115 94 12 000 rpm 1 25 11 25 19 126 682 2 007 100 2 867 285 119 72 10 kW 1 25 15 77 14 166 484 1 718 698 2 455 284 115 94 10 000 rpm 1 25 11 43 30 151 508 1 963 409 2 804 871 129 90 1 7 Z 1 18 Z 4 45 Z 2 108 3 kW 1 13 70 19 140 453 251 865 365 659 114 22 5 000 rpm 1 10 60 30 129 475 276 759 401 801 124 70 5 kW 0 8 11 11 23 76 852 835 980 1 213 682 93 86 15 000 rpm 0 8 9 31 30 72 790 894 546 1 298 709 99 76 7 kW 0 8 10 83 14 67 466 1 834 027 2 662 653 89 05 25 000 rpm 0 8 7 65 30 59 792 2 040 360 2 962 218 99 76 1 8 Z 1 18 Z 4 54 Z 2 126 3 kW 0 6 8 24 14 39 271 615 788 902 415 77 91 25 000 rpm 0 6 6 67 25 36 468 655 435 960 516 83 42 4 kW 0 6 8 06 18 40 012 1 069 958 1 567 985 79 49 32 000 rpm 0 6 6 91 25 37 770 1 112 217 1 629 914 83 42 1 10 Z 1 18 Z 4 72 Z 2 162 3 kW 0 6 5 71 19 47 403 1 339 693 1 982 746 102 80 32 000 rpm 0 6 5 43 21 46 279 1 341 915 1 986 034 104 12 4 kW 0 6 6 25 18 51 238 2 236 335 3 309 776 102 20 40 000 rpm 0 6 5 48 25 49 520 2 380 045 3 522 466 107 25 Table 3 Optimal designs of spindle speeders based on the constructional solution of Fig 2c Spindle design 14 24 0 m 14 m 24 0 mm b 14 b 24 0 mm d 1 d 4 mm d 1 d 4 0 mm Vol mm 3 KE 2 10 C06 mm 5 s 2 C16C17 T mm 1 5 5 kW 13 000 rpm 24 0 9 11 08 19 75 64 64 78 475 668 153 69 13 8 0 8 9 98 24 69 20 20 Z 1 20 Z 2 80 Z 4 25 Z 4 0 25 1 6 5 3 kW 15 000 rpm 26 0 9 10 12 18 02 72 17 89488 865 896 78 10 4 0 8 8 56 30 04 24 05 Z 1 18 Z 2 90 Z 4 30 Z 4 0 30 1 8 3 kW 25 000 rpm 4 0 6 7 36 12 03 65 53 58 743 719 211 72 17 16 0 9 7 00 30 07 23 40 Z 1 20 Z 2 70 Z 4 50 Z 4 0 25 1 10 4 kW 40 000 rpm 13 0 6 6 14 12 30 59 58 49 422 1 271 833 73 78 25 0 6 5 42 30 74 16 55 Z 1 20 Z 2 90 Z 4 50 Z 4 0 25 Int J Adv Manuf Technol 2009 40 637 647 643 5 Results and discussion The optimisation problem of mechanical spindle speeders described in this paper was applied to a set of different designs of spindle speeders i e different speed ratios and powers covering the entire marketed range Tables 1 and 2 summarise all of the cases studied for the design based on the constructional solution of Fig 2a and show the optimal designs In these tables the first and second columns list the speed ratio the input power and the maximum output speed for each design The first column also indicates the tooth number of each member for the minimum volume and Table 4 Optimal designs of spindle speeders based on the constructional solution of Fig 2d Spindle design 14 24 0 m 14 m 24 0 mm b 14 b 24 0 wmm d 1 d 4 mm d 1 d 4 0 mm Vol mm 3 KE 2 10 C06 mm 5 s 2 C16C17 T mm 1 5 5 kW 13 000 rpm 17 1 125 10 15 21 17 47 66 182 947 4 964 871 105 85 24 5 0 8 10 64 42 34 15 88 Z 1 18 Z 2 54 Z 4 36 Z 4 0 18 1 6 5 3 kW 15 000 rpm 28 3 1 125 10 15 22 99 53 63 221 436 8 157 084 114 97 20 0 8 11 18 45 99 15 32 Z 1 18 Z 2 63 Z 4 36 Z 4 0 18 1 8 3 kW 25 000 rpm 30 0 6 7 35 12 47 39 31 104 920 4 136 545 95 59 17 0 7 7 27 41 56 14 55 Z 1 18 Z 2 54 Z 4 60 Z 4 0 20 1 10 4 kW 40 000 rpm 26 0 6 6 62 12 01 39 98 91 889 6 682 166 92 11 8 0 6 7 17 40 05 12 11 Z 1 18 Z 2 66 Z 4 60 Z 4 0 20 1 5 1 6 1 7 1 8 1 9 1 10 2 4 6 8 10 12 14 Speed ratio Ratio between the volume and kinetic energy of the spindle speeder gearbox based on the constructional solucion of Fig 2 c and Fig 2 d and the volume and kinetic energy of that based on the constructional solution of Fig 2 a V c V a KE c KE a V d V a KE d KE a volume kinetic energy Fig 3 Ratio between the volume and kinetic energy of the optimal spindle speeder gearbox designs based on the constructional solutions of Fig 2c and Fig 2d and the corresponding gearbox designs based on the constructional solution of Fig 2a for different speed ratios The dots represent the ratio between the volumes and the open diamonds show the ratio between the kinetic energies The dashed line represents the comparison between the design based on the construc tional solutions of Fig 2c a and the continuous line for the comparison between Fig 2d a 644 Int J Adv Manuf Technol 2009 40 637 647 minimum kinetic energy solutions For example for the case of speed ratio 1 3 5 we chose two multiplier designs one for a power of 10 kW and another for 16 kW with different maximum output speeds which are 8 000 rpm and 10 000 rpm respectively For this design the optimal number of teeth according to the objective functions are for the output member Z 1 24 for the planet gear Z 4 18 and for the ring gear Z 2 60 The two rows corresponding to the same power and maximum output speed correspond to the minimum volume and minimum kinetic energy solutions The third fourth and fifth columns give the module the face width and the helix angle respectively The sixth column lists the volume occupied by the gears and the seventh and eighth columns are the kinetic energies of the gear system when it is designed with two KE 2 or with three KE 3 planet gears The kinetic energy is expressed independently of the specific value of the density of the steel used in the gears The units are therefore mm 5 s 2 Finally the ninth column gives the total diameter of the planetary transmission Continuing with the case of speed ratio 1 3 5 and in particular for 10 kW and 8 000 rpm it can be seen that for both the minimum volume and minimum kinetic energy designs the module of the gears is 1 25 For the minimum volume desig