外文翻譯--選擇固定參數(shù)研究齒輪牙側(cè)面的設(shè)計規(guī)則英文版

1、DOI 10.1007/s00170-003-1741-8OR I GI NAL AR T I C LEInt J Adv Manuf Technol (2004) 24: 789–793Feng Xianying · Wang Aiqun · Linda LeeStudy on the design principle of the LogiX gear tooth profile and the selectio

2、n of its inherent basic parametersReceived: 2 January 2003 / Accepted: 3 March 2003 / Published online: 3 November 2004 ? Springer-Verlag London Limited 2004Abstract The development of scientific technology and pro- duct

3、ivity has called for increasingly higher requirements of gear transmission performance. The key factor influencing dynamic gear performance is the form of the meshed gear tooth profile. To improve a gear’s transmission p

4、erformance, a new type of gear called the LogiX gear was developed in the early 1990s. How- ever, for this special kind of gear there remain many unknown theoretical and practical problems to be solved. In this paper, th

5、e design principle of this new type of gear is further studied and the mathematical module of its tooth profile deduced. The in- fluence on the form of this type of tooth profile and its mesh performance by its inherent

6、basic parameters is discussed, and reasonable selections for LogiX gear parameters are provided. Thus the theoretical system information about the LogiX gear are developed and enriched. This study impacts most significan

7、tly the improvement of load capacity, miniaturisation and durability of modern kinetic transmission products.Keywords Basic parameter · Design principle · LogiX gear · Minute involute · Tooth profile1

8、 IntroductionIn order to improve gear transmission performance and satisfy some special requirements, a new type of gear [1] was put for- ward; it was named “LogiX” in order to improve some demerits of W-N (Wildhaver-Nov

9、ikov) and involute gears. Besides having the advantages of both kinds of gears men- tioned above, the new type of gear has some other excellentF. Xianying (u) · W. Aiqun School of Mechanical Engineering, Shandong Un

10、iversity, P.R. China E-mail: FXYing@sdu.edu.cn Tel.: +86-531-8395852(0)L. Lee School of Mechanical & Manufacturing Engineering, Singapore Polytechnic, Singaporecharacteristics. On this new tooth profile, the continuo

11、us con- cave/convex contact is carried out from its dedendum to its ad- dendum, where the engagements with a relative curvature of zero are assured at many points. Here, this kind of point is called the null-point (N-P).

12、 The presence of many N-Ps during the mesh process of LogiX gears can result in a smaller sliding coeffi- cient, and the mesh transmission performance becomes almost rolling friction accordingly. Thus this new type of ge

13、ar has many advantages such as higher contact intensity, longer life and a larger transmission-ratio power transfer than the standard in- volute gear. Experimental results showed that, given a certain number of N-Ps betw

14、een two meshed LogiX gears, the contact fatigue strength is 3 times and the bend fatigue strength 2.5 times larger than those of the standard involute gear. Moreover, the minimum tooth number can also be decreased to 3,

15、much smaller than that of the standard involute gear. The LogiX gear, regarded as a new type of gear, still presents some unsolved problems. The development of computer numer- ical controlling (CNC) technology must also

16、be taken into con- sideration new high-efficiency methods to cut this new type of gear. Therefore, further study of this new type of gear most significantly impacts the acceleration of its broad and practical application

17、. This paper has the potential to usher in a new era in the history of gear mesh theory and application.2 Design principle of LogiX tooth profileAccording to gear mesh and manufacturing theories, in order to simplify pro

18、blem analysis, generally a gear’s basic rack is begun with some studies [2]. So here let us discuss the basic rack of the LogiX gear first. Figure 1 shows the design principle of di- vided involute curves of the LogiX ra

19、ck. In Fig. 1, P.L represents a pitch line of the LogiX rack. One point O1 is selected to form the angle ?n0O1N1 = α0, P.L ? O1N1. The points of intersection by two radials O1n0 and O1N1 and the pitch line P.L are N1 and

20、 n0. Let O1n0 = G1, extend O1n0 to O ? 1, and make two tan- gent basic circles whose centres are O1, O? 1 and radii are equal to G1.. The point of intersection between circle O1 and pitch line791Here: n0n? 0 ? O1O? 1, n1

21、n? 1 ? O1O? 1, n1n1 ?n0n? 0, and the pa- rameters α0, δ, G1 and ρm0 are given as initial conditions. The curvature radius of the involute curve at point s1 is ρs1 = G1δ, or ρs1 = ρm1 + G1δ1. Thus the curvature radius and

22、 pressure angle of the minute involute curve at point m1 are as follows:ρm1 = ρs1 ? G1δ1 = G1(δ ?δ1) (1)α1 = α0 +δ +δ1 . (2)According to the geometrical relationship, we can deduce:tg(α0 +δ) = 2G1 ? G1 cos δ ? G1 cos δ1G

23、1 sin δ ? G1 sin δ1= 2?(cos δ +cos δ1)sin δ ?sinδ1 . (3)Based on Eqs. 1, 2 and 3 and the forming process of the LogiX rack profile, the curvature radius formula of an arbitrary point on the profile is deduced: ρmi = ρmi?

24、1 +Gi(δ?δi). When i = k and ρm0 = 0?, it is expressed as follows:ρmk = G1(δ ?δ1)+ G2(δ ?δ2)+···+ Gk(δ ?δk)=k ?i=1 Gi(δ ?δi) . (4)Similarly, the pressure angle on an arbitrary k point of the tooth profile c

25、an be deduced as follows:αk = α0 +(δ +δ1)+(δ +δ2)+···(δ +δk)= α0 +k ?i=1 (δ +δi) = α0 +kδ +k ?i=1 δi . (5)By ni?1ni = Gi(sin δ ? sin δi)/ cos(αi?1 + δ), Eq. 5 can be obtained:n0nk =k ?i=1 ni?1ni =k ?i=1Gi(

26、sin δ ?sinδi)cos(αi?1 +δ) . (6)Thus the mathematical model of the No. 2 portion for the LogiX rack profile is as follows:?x1 = n0nk ?ρmk cos αk y1 = ρmk sin αk (No. 2) . (7)Similarly, the mathematical models of the other

27、 three segments can also be obtained as follows:?x1 = ?(n0nk ?ρmk cos αk) y1 = ?ρmk sin αk (No.1) (8)?x1 = s ?(n0nk ?ρmk cos αk) y1 = ρmk sin αk (No.3) (9)?x1 = s +n0nk ?ρmk cos αk y1 = ?ρmk sin αk (No.4) . (10)Fig. 6. M

28、esh coordinates of LogiX gear and its ba- sic rack3.2 Mathematical module of the LogiX gearThe coordinates O1X1Y1, O2X2Y2 and PXY are set up as shown in Fig. 6 to express the mesh relationship between the LogiX rack and

29、the LogiX gear. Here, O1X1Y1 is fixed on the rack, and O1 is the point of intersection between the rack tooth profile and its pitch line. O2X2Y2 is fixed on the meshed gear, and O2 is the gear’s centre. PXY is an absolut

30、e coordinate, and P is the point of intersection of the rack’s pitch line and the gear’s pitch circle. In accordance with gear meshing theories [3], if the above model of the LogiX rack tooth profile is changed from coor

31、dinate O1X1Y1 to OXY, and then again to O2X2Y2, a new type of gear profile model can be deduced as follows:?x2 = ?ρmk cos αk cos ?2 ?(ρmk sin αk ?r2) sin ?2 y2 = ?ρmk cos αk sin ?2 +(ρmk sin αk ?r2) cos ?2 . (11)Here the

32、 positive direction of ?2 is clockwise, and only the model of the LogiX gear tooth profile in the first quadrant of the coordi- nates is given.4 Effect on the performance of the LogiX gear by its inherent parameters and

33、their reasonable selectionBesides the basic parameters of the standard involute rack, the LogiX tooth profile has inherent basic parameters such as initial pressure angle α0, relative pressure angle δ, initial basic circ

34、le radius G0, etc. The selection of these parameters has a great in- fluence on the form of the LogiX tooth profile, and the form directly influences gear transmission performance. Thus the rea- sonable selection of thes

35、e basic parameters is very important.4.1 Influence and selection of initial pressure angle α0Considering the higher transmission efficiency in practical de- sign, the initial pressure angle α0 should be selected as 0?. B

36、ut the final calculation result showed that the LogiX gear tooth pro- file cut by the rack tool whose initial pressure angle was equal to zero would be overcut on the pitch circle generally. Thus the initial pressure ang