外文翻譯--關(guān)于傳動(dòng)花鍵和平鍵的外形設(shè)計(jì)

1、<p>　　關(guān)于傳動(dòng)花鍵和平鍵的外形設(shè)計(jì)</p><p>　　Daniel Z.Li</p><p>　　摘要：花鍵和平鍵是安裝在軸和鍵槽間的傳輸動(dòng)力的機(jī)械零件?；ㄦI(或鍵)通常安裝在動(dòng)力傳動(dòng)副中的軸上，在軸上開(kāi)有相應(yīng)的鍵槽。本文分析了槽軸外形對(duì)動(dòng)力傳輸?shù)挠绊?。本文陳述了三種不同設(shè)計(jì)類(lèi)型的花鍵的外形設(shè)計(jì)。用微分的方法來(lái)計(jì)多算外形函數(shù)的最大值，可以成功地得到所要的數(shù)據(jù)。計(jì)算表明花鍵

2、以及斷開(kāi)線外形引起鍵槽的變形。此外，他們能承載最大的傳動(dòng)載荷。另外，輻形平直的外形能提高傳動(dòng)的效率。我們認(rèn)為該發(fā)現(xiàn)值得報(bào)道，該種方法同時(shí)也可用于其他花鍵的設(shè)計(jì)。</p><p><b>　　介紹</b></p><p>　　鍵是安裝在軸和鍵槽等動(dòng)力傳動(dòng)裝置如齒輪和扣練齒輪之間的零件。花鍵發(fā)揮著和鍵一樣的作用，將力矩從軸傳到配合零件上?；ㄦI和平鍵的主要區(qū)別是花鍵和平鍵連

3、為一體的，而鍵是安裝在鍵槽上的。與一個(gè)或兩個(gè)用來(lái)傳動(dòng)動(dòng)力的鍵相比，在軸上一般有四個(gè)或更多的花鍵。因此，傳輸?shù)牧馗愣?，每個(gè)花鍵上的所受的載荷較低。在傳輸力矩中，花鍵發(fā)揮著重要的作用，花鍵的外形對(duì)動(dòng)力傳輸?shù)挠绊懞艽?。與共軛外形不同，帶有花鍵和鍵槽的軸有同樣的轉(zhuǎn)動(dòng)軸，他們之間沒(méi)有相對(duì)運(yùn)動(dòng)，是緊密配合的。他們聯(lián)結(jié)在一起，有著相同的角速度。因此,它表明除軸外形之外的任何外形都可以用做花鍵的設(shè)計(jì)。然而，實(shí)際上花鍵和鍵槽間的載荷并不是分布在整個(gè)接

4、觸表面的。載荷通常集中在接觸表面的某小一部分和可變形的鍵表面。當(dāng)循環(huán)工作較久時(shí)，這就會(huì)引起軸和鍵槽之間不希望得到的空隙，并引起鍵槽表面的損壞。為了解決這些問(wèn)題，需要更進(jìn)一步分析花鍵的外形是怎樣影響力矩傳輸?shù)?，以便做出合適的花鍵外形設(shè)計(jì)。</p><p>　　目前使用中主要有兩種花鍵，分別為直線邊花鍵和漸進(jìn)線花鍵。漸進(jìn)線花鍵具有自動(dòng)調(diào)心的配合零件，可以用標(biāo)準(zhǔn)平頭釘切削器切除齒輪的齒。目前，相關(guān)的研究都著重于共軛外形

5、齒輪的設(shè)計(jì)以及彎曲外形的設(shè)計(jì)，以來(lái)減少配合表面的磨損。然而，由于不同的工作狀況，它們都不能直接應(yīng)用于花鍵的外形。在本論文中，建立了花鍵外形的基本公式，在不同設(shè)計(jì)對(duì)象中用來(lái)分析所要求的外形。三個(gè)設(shè)計(jì)對(duì)象，恒定變形，傳輸最大力矩和最佳傳動(dòng)效率，這三項(xiàng)被用來(lái)計(jì)算花鍵外形。成功地得到了分析方法。</p><p>　　2 陳述問(wèn)題并提出基本假設(shè)</p><p>　　如圖1所示，軸傳動(dòng)輪轂同時(shí)花鍵固定

6、在軸上。設(shè)計(jì)要求決定了軸半徑、花鍵高度、花鍵齒數(shù)，因此不能改動(dòng)。只能通過(guò)改變花鍵的輪廓來(lái)提高傳動(dòng)性能。為簡(jiǎn)化設(shè)計(jì)問(wèn)題以便于分析，做出以下幾點(diǎn)假設(shè)：</p><p><b>　　花鍵是剛體</b></p><p>　　相對(duì)輪轂，花鍵由剛性材料制成并假設(shè)它在承受負(fù)載后無(wú)變形。</p><p><b>　　輪轂屬?gòu)椥宰冃?lt;/b>

7、</p><p>　　輪轂表面變形在彈性變形范圍內(nèi)時(shí)，表面壓力與變形量成正比。</p><p><b>　　花鍵無(wú)軸向變形</b></p><p>　　通?；ㄦI的齒高相對(duì)于齒寬尺寸小很多。因此，我們假設(shè)鍵端無(wú)積累變形，只有輪轂面有變形。</p><p>　　花鍵與輪轂接觸處無(wú)間隙（面接觸）</p><

8、p>　　花鍵形狀與輪轂形狀不考慮制造誤差完全一致。它們屬于面接觸沒(méi)有間隙。</p><p><b>　　圖1 花鍵</b></p><p>　　3 花鍵變形跟輪轂變形一致</p><p>　　設(shè)計(jì)的第一目標(biāo)是使輪轂表面變形一致，那就要求輪轂上的壓力均布。這樣能保證表面承受的壓力均勻分布，以避免一些危險(xiǎn)點(diǎn)損壞材料。如圖2，表示軸半徑，表示花

9、鍵的小旋轉(zhuǎn)角。因?yàn)槲覀兗俣ɑㄦI為剛體，所以花鍵任兩點(diǎn)之間的變化就是輪轂的變形。花鍵聯(lián)接按照鍵的橫截面開(kāi)頭分為矩形花鍵聯(lián)接和漸開(kāi)線花鍵聯(lián)接。</p><p><b>　　圖2 花鍵小旋轉(zhuǎn)角</b></p><p>　　4 危險(xiǎn)截面確定簡(jiǎn)單</p><p>　　傳統(tǒng)設(shè)計(jì)方法考慮的前提是把影響零件工作狀態(tài)的設(shè)計(jì)變量，如應(yīng)力、強(qiáng)度、安全系數(shù)、載荷、環(huán)境

10、因素、材料性能、零件尺寸和結(jié)構(gòu)因素等，都處理成確定的單值變量。描述零件狀態(tài)的數(shù)學(xué)模型，即變量與變量的關(guān)系，是通過(guò)確定性的函數(shù)進(jìn)行單值變換獲得危險(xiǎn)截面。</p><p>　　常用的危險(xiǎn)截面的確定方法有以下幾種：</p><p>　　4．1 花鍵的最小直徑法</p><p>　　花鍵危險(xiǎn)截面的可靠度非常高(幾乎為 100％)，這是由于花鍵的直徑是按傳統(tǒng)的設(shè)計(jì)經(jīng)驗(yàn)確定的。

11、若要求適當(dāng)?shù)目煽慷戎?，則花鍵的直徑可選用較小的值。</p><p>　　4．2 可靠性安全系數(shù)法</p><p>　　采用可靠性安全系數(shù)法設(shè)計(jì)時(shí)，必須知道應(yīng)力和強(qiáng)度的分布類(lèi)型與分布參數(shù)估計(jì)值。而可靠性數(shù)據(jù)的積累又是一項(xiàng)長(zhǎng)期的工作，因而我們必須利用現(xiàn)有的數(shù)據(jù)資料，運(yùn)用有關(guān)定理與法則(如中心極限定理和“3 法則”等 )，來(lái)確定設(shè)計(jì)過(guò)程中所涉及的許多隨機(jī)變量的分布類(lèi)型與分布參數(shù)。在可靠性安全系數(shù)

12、計(jì)算 中，是把所涉及的設(shè)計(jì)參數(shù)都處理成隨機(jī)變量，將安全系數(shù)的概念與可靠性的概念聯(lián)系起來(lái)，從而建立相應(yīng)的概率模型。由于考慮到工程實(shí)際中發(fā)生的現(xiàn)象及表征參數(shù)的不確定性(隨機(jī)性)，因而更能揭示事物的本來(lái)面貌。理論分析與實(shí)踐表明，可靠性設(shè)計(jì)比傳統(tǒng)機(jī)械設(shè)計(jì)，能更有效地處理設(shè)計(jì)中一些問(wèn)題，提高產(chǎn)品質(zhì)量，減少零件尺寸，從而節(jié)約原材料，降低成本。</p><p><b>　　5 結(jié)束語(yǔ)</b></p&

13、gt;<p>　　機(jī)械可靠性設(shè)計(jì)是近幾十年來(lái)發(fā)展起來(lái)的一種現(xiàn)代設(shè)計(jì)理論和方法，它以提高產(chǎn)品質(zhì)量為核心 ，以概率論 、數(shù)理統(tǒng)計(jì)為基礎(chǔ) ，綜合運(yùn)用工程力學(xué) 、系統(tǒng)工程學(xué) 、運(yùn)籌學(xué)等多學(xué)科知識(shí)來(lái)研究機(jī)械工程最優(yōu)設(shè)計(jì)問(wèn)題。目前 ，可靠性設(shè)計(jì)的理論已趨于完善，但真正用于機(jī)械零件設(shè)計(jì)工程實(shí)際的卻很少。采用可靠性安全系數(shù)法設(shè)計(jì)時(shí)，必須知道應(yīng)力和強(qiáng)度的分布類(lèi)型與分布參數(shù)估計(jì)值。而可靠性數(shù)據(jù)的積累又是一項(xiàng)長(zhǎng)期的工作，因而我們必須利用現(xiàn)有的數(shù)

14、據(jù)資料，運(yùn)用有關(guān)定理與法則，來(lái)確定設(shè)計(jì)過(guò)程中所涉及的許多隨機(jī)變量的分布類(lèi)型與分布參數(shù)。</p><p>　　本文講述了三種花鍵（或平鍵）形狀最佳設(shè)計(jì)標(biāo)準(zhǔn)。用變量積分法來(lái)確定輪廓公式以及最大值，由此獲得分析結(jié)果。從結(jié)果可以看出，漸開(kāi)線花鍵導(dǎo)致輪轂變形一致，此外，能傳遞的載荷最大。另外，矩形花鍵傳動(dòng)最高效。相信如果要增加新的性能標(biāo)準(zhǔn)，別的形狀的花鍵很少會(huì)被用到。</p><p><b&g

15、t;　　參考文獻(xiàn)</b></p><p>　　[1] Robert L. Mott, Machine Elements in Mechanical Design, third ed., Prentice-Hall Inc., 1999.</p><p>　　[2] M.F. Spotts, Design of Machine Elements, third ed., Prent

16、ice-Hall Inc., 1961.</p><p>　　[3] Joseph E. Shigley, Larry D. Mitchell, Mechanical Engineering Design, fourth ed., McGraw-Hill Inc., 1983.</p><p>　　[4] D.C.H. Yang, S.H. Tong, J. Lin, Deviation-

17、function based pitch curve modification for conjugate pair design, Transaction of ASME Journal of Mechanical Design 121 (4) (1999) 579–586.</p><p>　　[5] S.H. Tong, New conjugate pair design—theory and applic

18、ation, PhD Dissertation, Mechanical and Aerospace Engineering Department, UCLA, 1998.</p><p>　　[6] F.L. Litvin, Gear Geometry and Applied Theory, Prentice-Hall Inc., 1994.</p><p>　　[7] D.B. Doon

19、er, A.A. Seireg, The Kinematic Geometry of Gearing, John Wiley & Sons Inc., 1995, pp. 56–63.</p><p>　　[8] Y. Ariga, S. Nagata, Load capacity of a new W–N gear with basic rack of combined circular and inv

20、olute profile, Transaction of ASME Journal of Mechanisms, Transmissions, and Automation in Design 107 (1985) 565–572.</p><p>　　[9] M.J. French, Gear conformity and load capacity, in: Proc Instn Mech Engrs, v

21、ol. 180(43), Pt 1, (1965–66), pp. 1013–1024.</p><p>　　[10] A.O. Lebeck, E.I. Radzimovsky, The synthesis of tooth profile shapes and spur gears of high load capacity, Transaction of ASME Journal of Engineerin

22、g for Industry (1970) 543–553.</p><p>　　[11] H. Iyoi, S. Ishimura, v-Theory in gear geometry, Transaction of ASME Journal of Mechanisms, Transmissions, and Automation in Design 105 (1983) 286–290.</p>

23、<p>　　[12] J.E. Beard, D.W. Yannitell, G.R. Pennock, The effects of the generating pin size and placement on the curvature and displacement of epitrochoidal gerotors, Mechanism and Machine Theory 27 (4) (1992) 373–

24、389.</p><p>　　[13] H.C. Liu, S.H. Tong, D.C.H. Yang, Trapping-free rotors for high sealing lobe pumps, Transaction of ASME Journal of Mechanical Design 122 (4) (2000) 536–542.</p><p>　　[14] Char

25、les Fox, Calculus of Variations, Oxford University Press, 1954.</p><p>　　ARTICLE IN PRESS</p><p>　　On the profile design of transmission splines and keys</p><p>　　Daniel Z.Li </p

26、><p>　　Abstract: Splines and keys are machinery components placed at the interface between shafts and hubs of power-transmitting elements. A spline (or key) is usually machined (or attached) onto the shaft of a

27、 power-transmitting pair, and the corresponding groove is cut into the hub. The influence of spline profiles on the performance of power transmission is investigated in this paper. The optimal design of spline profiles f

28、or three different design criteria is presented. The method of calculus of va</p><p>　　Introduction</p><p>　　A key is a machinery component placed at the interface between a shaft and the hub of

29、 a power-transmitting element such as gear and sprocket . A spline performs the same function as a key in transmitting torque from the shaft to the mating element . The main difference between splines and keys is that sp

30、lines are integral with the shaft but keys are inserted between shaft and hub. As compared with one or two keys used for load transmission, there are usually four or more splines on a shaft. Ther</p><p>　　Cu

31、rrently there are two main types of splines used, namely, straight-sided and involute splines. The involute splines provide the mating element with self-centering and can be machined with standard hob cutter used to cut

32、gear teeth. To date, the related research work focuses on conjugate profiles and gear design as well as the design of profile curvatures for reducing the wear of contact surfaces. However, none of them can be applied t

33、o the profiles of splines directly due to different workin</p><p>　　Problem description and basic assumptions</p><p>　　As shown in fig .1, The hub is driven by the shaft and the spline is fixed

34、on the shaft. The radius of the shaft, the height of the spline, and the number of spline teeth are determined by the design requirements and cannot be altered. Only the spline profile can be modified to improve the perf

35、ormance of transmission. To simplify the design problem for analysis, the following assumptions were made:</p><p>　　(1) The spline is a rigid body.</p><p>　　Compared with the hub, the spline is

36、made of hard material and assumed no deformation after applying the load.</p><p>　　(2) The hub is under elastic deformation</p><p>　　The surface deformation of the hub is within the range of ela

37、sticity and the surface stress is proportional to the normal deformation.</p><p>　　(3) There is no beam deformation on the spline.</p><p>　　For spline keys, usually the height of tooth shape is

38、small relative to its width. Therefore, we assume there is no accumulated deformation at the free end. The only deformation is the normal deformation on the hub surface.</p><p>　　(4) There is no clearance be

39、tween the spline and hub when they are in contact. (Surface contact)</p><p>　　The profile of the spline is exactly the same as that of the hub without considering manufacturing errors. They are in surface co

40、ntact without clearance.</p><p>　　3 Spline profile for uniform hub deformation</p><p>　　The first design objective is to have the uniform deformation on the surface of the hub, which also impli

41、es the uniform stress on the hub. This design can ensure the surface stress is evenly distributed and avoid the failure of material at some weak points. Referring to fig.2, Let denote the radius of shaft and denote a s

42、mall rotation angle of spline. Since we assume that the spline is a rigid body, the change between two spline positions will be the deformation of the hub. </p><p>　　4 It’s simply to confirmed the dangerous

43、 sections </p><p>　　Prerequisite that traditional design method considered whether pair influence part design variable of working state, for instance stress , intensity , safety coefficient , load , environm

44、ental factor , material performance , part size and structural factor ,etc., deal with the single value variable confirmed. Describe part mathematical model of state , i.e. variable and relation of variable , to go on si

45、ngle value vary and win the dangerous section through deterministic function.</p><p>　　There are several methods that usually the dangerous sections are determined: </p><p>　　Minimum diameter of

46、 the spline </p><p>　　Spline dangerous sectional reliability very getting high, this to confirm according to traditional design experience because of diameter of spline. If require appropriate reliability va

47、lue, then the diameter of the axle can select smaller value for use .</p><p>　　Safety coefficient law of dependability </p><p>　　While adopting the safety coefficient law design of dependability

48、 , must know the distribution types of stress and intensity and be distributed estimated value of the parameter . And the accumulation of dependability data is a long-term job, therefore we must utilize the existing data

49、 materials , it is (such as the terminal theorem in the centre and " 3 rules " to use relevant theorems and rule ), to confirm the distribution types of a lot of random variables involved of design process and

50、is di</p><p>　　5 Concluding remarks</p><p>　　The mechanical reliability design is one kind of modern design theory and the method which in the recent several dozens years develop, it take impro

51、ves the product quality as the core, take the theory of probability, the mathematical statistic as the foundation, synthesizes using the engineering mechanics, the system engineering, the operations research and so on th

52、e multi-disciplinary knowledge studies the mechanical engineering most superior design question. At present, the reliability design </p><p>　　References</p><p>　　[1] Robert L. Mott, Machine Elem

53、ents in Mechanical Design, third ed., Prentice-Hall Inc., 1999.</p><p>　　[2] M.F. Spotts, Design of Machine Elements, third ed., Prentice-Hall Inc., 1961.</p><p>　　[3] Joseph E. Shigley, Larry D

54、. Mitchell, Mechanical Engineering Design, fourth ed., McGraw-Hill Inc., 1983.</p><p>　　[4] D.C.H. Yang, S.H. Tong, J. Lin, Deviation-function based pitch curve modification for conjugate pair design, Transa

55、ction of ASME Journal of Mechanical Design 121 (4) (1999) 579–586.</p><p>　　[5] S.H. Tong, New conjugate pair design—theory and application, PhD Dissertation, Mechanical and Aerospace Engineering Department,

56、 UCLA, 1998.</p><p>　　[6] F.L. Litvin, Gear Geometry and Applied Theory, Prentice-Hall Inc., 1994.</p><p>　　[7] D.B. Dooner, A.A. Seireg, The Kinematic Geometry of Gearing, John Wiley & Sons

57、 Inc., 1995, pp. 56–63.</p><p>　　[8] Y. Ariga, S. Nagata, Load capacity of a new W–N gear with basic rack of combined circular and involute profile, Transaction of ASME Journal of Mechanisms, Transmissions,

58、and Automation in Design 107 (1985) 565–572.</p><p>　　[9] M.J. French, Gear conformity and load capacity, in: Proc Instn Mech Engrs, vol. 180(43), Pt 1, (1965–66), pp. 1013–1024.</p><p>　　[10] A

59、.O. Lebeck, E.I. Radzimovsky, The synthesis of tooth profile shapes and spur gears of high load capacity, Transaction of ASME Journal of Engineering for Industry (1970) 543–553.</p><p>　　[11] H. Iyoi, S. Ish

60、imura, v-Theory in gear geometry, Transaction of ASME Journal of Mechanisms, Transmissions, and Automation in Design 105 (1983) 286–290.</p><p>　　[12] J.E. Beard, D.W. Yannitell, G.R. Pennock, The effects of

61、 the generating pin size and placement on the curvature and displacement of epitrochoidal gerotors, Mechanism and Machine Theory 27 (4) (1992) 373–389.</p><p>　　[13] H.C. Liu, S.H. Tong, D.C.H. Yang, Trappin

62、g-free rotors for high sealing lobe pumps, Transaction of ASME Journal of Mechanical Design 122 (4) (2000) 536–542.</p><p>　　[14] Charles Fox, Calculus of Variations, Oxford University Press, 1954.</p>