EDP​​ SCIENCES徽标
O.P.en Access
yabo亚博问题
yabo亚博
体积22,2021
文章编号 33.
页数) 11
迪伊 HT.T.P.S.://doi.org/10.1051/meca/2021032
在线发布 2021年4月30日

© L. Geng et al., Published by EDP Sciences 2021

L.icence Creative Commons这是在Creative Commons归因许可证的条款下分发的开放式访问文章(HT.T.P.S.://creativecommons.org/licenses/by/4.0)提供任何介质中的不受限制使用,分发和再现,所以提供了正确的工作。

1介绍

螺旋锥齿轮广泛应用于航空,航空航天,船用和机床的优点,其优点是顺畅,传输效率高,负载能力优异等,因此,螺旋锥齿轮的制造一直是一个重要的话题。许多专家和学者都进行了深入研究。主要的螺旋锥齿轮加工方法是面部铣削和面部滚动。

For face milling, according to machine method of pinion can be divided into five-cut and two-cut. Generalized theory and methods of spiral bevel and hypoid gears manufactured by the five-cut method have been comprehensively presented by several gear scientists [1-3.]。Shtipelman [4.] introduced the generalized theory of the five-cut method and calculated machine settings parameters of spiral bevel and hypoid gears by the five-cut method in Gleason Works. Litvin [5.6.] proposed local synthesis and applied for tooth contact analysis (TCA), and determining the optimal machine settings parameters. For five-cut, the concave side and convex side adopts different machine setting parameters which the mesh performance can effectively control and correction.

在Gleason technology, two-cut method includes duplex spread blade method and duplex helical method. Traditionally, duplex spread blade method is used to process small module of spiral bevel gear. In book of spiral bevel gears published by Beijing gear factory proposed the calculation of machine setting parameters by duplex spread blade method, but its principle is not revealed [7.]。K. Kawasaki和H. Tamura [8.] proposed a method to manufacture gear with a large radius of curvature cutting edge and a modified tooth surface is obtained. Recently, Deng et al. [9.[提出了一种通过双工扩散叶片方法制造螺旋锥齿轮的方法,并通过齿面修饰优化网状性能。

Duplex Helix方法由Gleason提出[10.], but principle and calculation of machine setting parameters are not revealed. Tsay and Lin [11]开发了一种数学模型,可以应用于通过双工扩散刀片和双工螺旋方法模拟齿面几何形状。gonzalez-perez [12通过双面起伏方法接近给定发生器的特定机器设置参数的转换,通过双面起伏方法,并施加头切割器的叶片上的抛物线轮廓以调节接触图案。张等人。[13.14.[揭示了通过定义三个参考点的非生成齿轮的螺旋方法的广义理论,并通过定义三个参考点来计算基本机器设置参数。然而,通过双工螺旋方法计算机器设置参数复杂,并且机器的要求是苛刻的。难以控制和正确的网格性能对于凹面,凸面由相同的机器设置参数处理。

In this paper, a double–side milling method to machine spiral bevel gear is proposed which the calculation of machine setting parameters is simple. Through inclination of root line and considering cut parameters, geometrical parameters are designed by double–side milling method. In order to guarantee the normal tooth meshing, a modified mean point is selected, and machine setting parameters are calculated in modified mean point. Aiming at optimize the bias in contact caused by cut number; a helical motion is introduced to modify the pressure angle on the pitch line. Contact performance is controlled by adjusting coefficient of helical motion.

2几何参数设计

2.1牙齿锥度

T.He taper of tooth blank is different from single-side method to double-side method. Dedendum angle will affect tooth height in the direction of tooth length from toe to heel, and the influence of dedendum angle on tooth taper are analyzed as follow.

In single-side method, tooth height and tooth thickness are proportional to cone distance, as shown in图1一种。在平均点形成的切线角度P.一种两侧的牙齿空间P.一种1P.一种2可以表示为(1)

这里S.是T.He mean point arc tooth thickness of paired gear.

虽然对于双面方法,通过双侧切割同时处理牙齿表面的两侧。两侧的齿线是同心弧,如图所示图1B.。T.Hen the tangent angle formed at mean pointP.B.两侧的牙齿空间P.B.1P.B.2可以表示为(2)

这里O.是T.He center of cut, andR.是T.He nominal radius of cut,β是mean spiral angle.

Comparing图1,发生切角角度的差异,并且可以表示为(3)

这里R.m是平均锥距。

在制造期间,切口轴垂直于牙齿坯料的根锥。因此,牙齿坯料外部将比内部和在牙齿间隙两侧的平均点形成的切线切割,这将弥补Δψ1

为了研究Dependum角度对δ的影响ψ1那一种Nother pointP.'was taken near the tooth line, and the position of point was: ΔR.in the direction of cone distance, ΔHin the direction of tooth height, and ΔS.牙齿空间宽度的差异。两点之间的距离是δL.,如图所示图2。牙线上切的角度的增量可以表示为:(4)

这里α是标称压力角。

如果δ.ψ1 ≠ Δψ如图2所示,它可能导致使用双面方法造成异常齿锥,这将严重影响强度和切割寿命。所以应该避免这种情况。

T.Here are many factors affect Δψ1一种Nd Δψ2FR.om equations(3)一种Nd(4)。但确定后不应更改一些参数。所以专注角度θF改变以满足要求Δψ1 = Δψ2。最后,可以计算理想的专职角度(5)

T.He above analysis is suitable for pinion and gear. If both machined by double-side method, the following relationship can be obtained(6)

这里θF1θF2一种R.e dedendum angle of pinion and gear respectively;S.1S.2是平均点电弧齿厚度,并满足Z.0.S.1 + S.2) = 2Πr.mZ.0.是等价数量的牙齿。

T.Hen equation(6)可以表示为(7)

假设标准深度专用角度σθS.满足条件δψ1 = Δψ2,然后可以从方程获得标称切割半径(3)一种Nd(4)(8)

然后是一个标称半径R.C可以根据等式选择(8)那SubstitutingR.Cinto equation(7)那T.He corresponding sum of dedendum angle ∑θT.可以表示为(9)

名义半径R.Cwill affect sum of dedendum angle ∑θT.和侧翼锥度。为了避免在计算和选择之间的标称半径差异引起的过度齿坯,推荐的标称半径范围为1.1R.mβ ≤ R.C ≤ R.m

T.Humbnail Fig. 1

球场上的侧翼线。(a)单侧方法中的牙坯。(b)双面法中的牙坯。

T.Humbnail Fig. 2

专职角度对牙齿锥度的影响。

2。2几何参数设计

不同于通过鞋跟的外横跨模块计算几何参数的传统方法,螺旋锥齿轮的双面几何参数设计由平均正常模块完成。为了确保平均点的适当啮合深度,平均工作深度Hmw可以计算为(10)

这里H是工作牙齿高度因素,mN是Normal modulus of mean point,mT.是outer transverse module, andR.是outer cone distance.

根据平均点计算螺旋锥齿轮的间隙,并在齿长的方向上保持恒定。可以根据设计要求调整间隙并计算为(11)

这里C1是清关因素。

然后意味着整个深度可以表示为(12)

根据平均附录因素C火腿那T.He mean addendum and mean dedendum can be expressed as(13)

Dedendum angle is distributed according to the ratio of mean dedendum to mean whole depth(14)

T.Hen theoretical cut number can be calculated as(15)

由于截止数字已经标准化和序列化,因此接近截止数量N0.被选中。为了弥补真实和理论剪切数的差异,根线围绕平均点倾斜,倾斜量可以表示为(16)

Finally dedendum angle can be obtained according to equation(14)一种Nd(16)。附录角可以表示为(17.)

以上参数在平均点计算。为了便于生产测量,应将上述数据转换为脚跟。

面对锥角度δ一种1δ一种2可以表示为(18.)

根锥角δF1δF2可以表示为(19.)

然后外职职业和外表可以表达为(20)

O.uter working depth can be expressed as(21)

外部深度可以表示为(22)

外径可以表示为(23)

节锥顶皇冠可以表示为(24)

T.Hen geometric parameters of spiral bevel gear can be calculated

3计算机器设置参数

3.。1Initial machining setting parameters

设计后,标称压力角α那mean spiral angleβ那equivalent tooth numberZ.0.不可改变。随着根线倾斜的,专职角度的总和不会达到等式(7)。T.He spiral angle varies along the length of the tooth. So a pointm被选中以确保正常锥度和良好的啮合性能。该点命名为修改的平均点可以计算为(25)

分析equation(25)那T.He real cut numberN0.将影响修改平均点的位置,因此可以通过选择切割数来控制接触图案的近似位置。

T.He machine setting parameters are calculated in modified mean point. The installment of cut is shown in图3.。返回和垂直偏移的机器中心都是0.其他计算公式如下所示

T.He radial setting position is calculated as(26)

初始摇篮角度设置计算为(27)

根倾斜后,机器中心回来被改变。变化被确定为(28)

And other parameters are calculated as(29.)

T.Humbnail Fig. 3

分期付款。

3.2切割器数对压力角的影响

After real cutter number is determined, profile angle can be determined as(30)

T.He difference of pressure angle on concave side and convex side in modified mean point is(31)

仅考虑修改平均点处的螺旋角,沿齿长变化。因此,可以表达任何点中凹面和凸面侧的压力角的差异(32)

这里βyR.y是分别对应于该点的螺旋角和锥形距离。

T.He difference of pressure angle between modified mean point and any point can be expressed as(33)

T.Hen equation(33)C一种NB.e arranged as(34)

In modified mean point of tooth lineβ = βy那S.o Δ′α = 0. As far away from the modified mean point, the difference of pressure angle becomes large which will affect mesh performance and leads to bias in contact pattern.

3.3螺旋校正运动对压力角的影响

螺旋运动是一种改进的运动。除了在制造过程中产生运动之外,工件和切割还具有沿座椅轴方向的线性运动关系。螺旋运动对压力角的校正有影响;修改的基本原理如图所示图4.

产生由工件旋转和切割速度组成V.T.(沿着齿轮的切线方向)Asposition1所示,以及网点中的压力角m1α1; considering helical motion (position 2), then a radial motionV.R.是一种dded, resultant motion cut can be expressed asV.,如图所示图4.。T.He pressure angle in mesh pointm2α2那一种Ndα2 = α1+δ α

压力角的变化取决于径向速度的比率V.R.一种Nd tangential velocityV.T.(35)

这里,ω是T.He rotational angular velocity of cradle;P.是螺旋运动的铅。

压力角δ的变化αy一种T.一种NyP.oint in tooth line can be expressed as(36)

常压角的变化可以表示为(37)

T.Hen in modified mean point(38)

差异δ“αB.etween at any point and modified mean point in tooth line can be expressed as(39)

差异与从修改平均点的距离成比例。

如果设置δ.'α + Δα = 0, the bias in generated by cut number will be eliminated by the difference of pressure angle generated by helical motion. Then the helical motion coefficient can be expressed as(40)

While for some special working conditions, a bias in contact is more suitable. Then coefficient of helical motion can be adjusted to get an ideal contact pattern.

T.Humbnail Fig. 4

螺旋运动对压力角的影响。

4双侧铣削方法技术过程

根据本文提出的方法,流程图如图所示图5.

作为S.Hown in图5.根据基本参数,可以计算标准锥度的专职角度和理论标称半径的总和。然后可以获得双工锥度中的专职角度和理论切割数。由于实际切割数可能不等于理论,因此由根倾斜修改专职角度的总和。确定专职角度后,几何参数可以计数。选择修改的平均点,并在修改的平均点计算机器设置参数。仅保证修改平均点中的压力角。切割编号,压力角误差会导致齿长的方向。引入螺旋运动以在齿长方向上修改压力角。然后牙齿接触分析检查机器设置参数。调整螺旋运动系数和实际切割数以优化接触性能。

T.Humbnail Fig. 5

技术过程的流程图。

5.Numerical examples

A pair of spiral bevel gear was taken as an example for experimental verification. The geometric parameters were shown in表格1并且和机器设置参数显示在T.一种B.le 2

T.He helical motion coefficient of pinion was set as −1, 0, 1 respectively to calculate the tooth surface. The comparison of tooth surface is shown in图6.。蓝色对应于小齿轮理论齿表面,黑色是对应的P. =1, and red is the corresponding toP. = −1

WhenH = 1, for concave side, the correction is −0.10789 mm in toe of topland, −0.035967 mm in toe of root, 0.049979 mm in heel of top land, 0.13008 mm in heel of root; for convex side, the correction is 0.04147 mm in toe of topland, 0.10691 mm in toe of root, −0.15265 mm in heel of top land, −0.024998 mm in heel of root. Compared with theoretical tooth surface, for concave side, the pressure angle become small comparing to theory in toe of top land, and become large in heel of root, while the change of pressure angle are bigger comparing to the change in the direction from toe of root to heel of top land.

WhenH = −1, for concave side, the correction is 0.10929 mm in toe of topland, 0.038207 mm in toe of root, 0.038207 mm in heel of topland, 0.13002 mm in heel of root; for convex side, the correction is −0.04147 mm in toe of topland, −0.10775 mm in toe of root, 0.15276 mm in heel of topland, 0.024574 mm in heel of root. Compared with theoretical tooth surface, for concave side, the pressure angle become large comparing to theory in toe of topland, and become small in heel of root, while the change of pressure angle are bigger comparing to the change in the direction from toe of topland to heel of root.

分析图6.那T.He influence trend of helical motion coefficient on concave side and convex side are opposite, and helical motion coefficient has no effect on modified mean point. As far away from modified mean point, the change of pressure angle is large. Analysis results are consistent with equation(40)。So a well performance can be obtained by adjust helical motion coefficient.

综合考虑接触模式和传输错误曲线,呈螺旋运动系数P. = −0.3, and the corresponding results of tooth contact analysis (TCA) are shown in the图7.

有限元分析也是分析牙齿表面触点的有效方法[15.]。不仅可以直观地观察到在相应的负载下的齿面的接触时刻,也可以通过有限元分析来看接触应力。基于文献建立了一体的3D模型[9.]。T.Hen the finite element model was established by preprocess as shown in图8.。T.He results of finite element analysis by Abaqus with a load of 500N are shown in the图9.

作为图9.S.Hown, (a) is the stress distribution for gear convex side and (b) is the stress distribution for gear concave side. The biggest contact stress is 242.8 and 303.4 MPa under the load of 500N. The contact pattern is in the middle of tooth surface and there is no edge contact occurs, which is consistent with the results of TCA.

T.He contact performance is verified by tooth contact analysis and finite element analysis. The method proposed in this paper is proved to be effective in theory.

表格1

Geometric parameters.

T.一种B.le 2

机器设置参数。

T.Humbnail Fig. 6

螺旋运动对牙齿表面拓扑的影响。

T.Humbnail Fig. 7

R.esult of TCA. (a) Convex side. (b) Concave side.

T.Humbnail Fig. 8

Model of finite element analysis.

T.Humbnail Fig. 9

有限元分析结果。(a)齿轮的凸面。(b)凹陷的凹面。

5.。1Simulation

According to the parameters listed inT.一种B.le 2,剪切模型如图所示图10.。通过vericut进行模拟来检查和调试处理程序。模拟过程和小齿轮的产品显示在图11.。完成了具有理论的仿真产品的比较,结果显示在图12.。只有模拟小齿轮处理。

作为T.He results showed in图12.那T.He simulated product and established model are basically the same. In tooth surface, the biggest error in tooth surface is 0.02 mm for concave side and convex side. While the main error is in the root, the overcut and residue error is 0.05 mm. The tooth surface error comes from automatic approximated of parameters during model establishment for the precision of parameters are reserved to three decimal places or even more. The error in root mainly comes from the error caused by approximation of machine root angle. The comparison error meet engineering requirement. The correctness of parameters and machining procedures are verified.

T.Humbnail Fig. 10

刀具模型。

T.Humbnail Fig. 11

仿真过程和产品。

T.Humbnail Fig. 12

比较的结果。

5.2切割实验

牙齿切割实验是在YK2260X上进行的,是由洛阳Keda Yuege CNC Machinetool Co.,Ltd的五轴四连杆CNC铣床。工件安装在0.01毫米的直径跳动和面部跳动中。切割过程中没有颤抖。牙齿切割的场景显示在图13.

In order to check quality of process tooth surface, pinion and gear were measured after chamfering, burring and cleaning. The scenes of tooth surface measurement are shown in图14.。测量结果显示在图15.

作为S.Hown in图14.(a)是齿轮过程的场景,(b)是小齿轮过程的场景。图15.一种一种Nd b is the measurement results of gear and pinion, respectively. For gear measurement as displayed in图15.A,凸起侧和凹面的最大齿轮表面误差为0.004和0.006mm。用于小齿轮测量显示图15.B,凸形侧和凹面的最大齿面误差为0.006和0.004mm。误差符合工程要求,对齿面的啮合性能几乎没有影响。

Finally a rolling test was carried out. The workpieces were installed in 0.01 mm of diameter runout and face runout. The rolling ran smoothly without obvious vibration noise. The results were shown in图16.

作为图16.S.Hows, (a) is the scene of rolling test, (b) is tooth contact pattern of gear convex side, and (c) is tooth contact pattern of gear concave side. The contact pattern is located in the middle of the tooth surface and there is no edge contact and other bad contacts. The rolling test results are basically consistent with图7.一种Nd9.在位和形状。实验结果证明了本文提出的方法是有效可行的。

T.Humbnail Fig. 13

切割实验。(a)齿轮。(b)小齿轮。

T.Humbnail Fig. 14

测量场景。(a)齿轮。(b)小齿轮。

T.Humbnail Fig. 15

Measurement results of tooth surface. (a) Gear. (b) Pinion.

T.Humbnail Fig. 16

滚动测试和结果。(a)滚动试验。(b)齿轮的凸面。(c)凹陷的凹陷侧。

6.Conclusions

不同于通过横向模块计算几何参数的传统方法,螺旋锥齿轮的双侧几何参数设计由普通模块完成平均锥形距离与切割参数相结合。

根据双面方法的锥度,计算了一个名为改进的平均点的点满足啮合条件,并计算修改锥距离的加工设定参数。

分析了切割器数对齿长方向上的压力角的影响。研究了螺旋运动系数对牙齿表面的影响。结果表明,螺旋动作可以在齿长方向上校正压力角。实现了通过调整螺旋运动系数来优化接触性能。

T.He experimental results are consistent with the theoretical analysis results, which verify the effectiveness and feasibility of the double-side machining of spiral bevel gears proposed in this paper.

Acknowledgments

作者要感谢国家自然科学基金的经济援助和支持(授予第51975185号,授予第52005157号,并授予NO.51475141),河南省的主要科学和技术项目(授予号。191110213300-05)和国家重点研究和发展计划(授予NO。2020YFB1713505-4)。我们感谢审稿人和编辑的评价和建议。

R.eferences

  1. F.L.LITVIN,A. FIENTES,K. Hayasaka,设计,制造,应力分析和低噪声高耐久螺旋锥齿轮的实验测试,MECH。马赫。理论41.那8.3.-118.(20.0.6.)[Google Scholar]
  2. H。J. Stadtfeld, Tribology aspects in angular transmission systems part IV: spiral bevel gears, Gear Technology 66–72 (2011)[Google Scholar]
  3. F.L.Litvin,Y.张,M. Lundy,C。Heine,测定倾斜头切割器的设置,用于产生双瓦和螺旋锥齿轮,ASME J. MECH。传输。自动。des。110.那4.9.5.-5.0.0.(19.8.8.)[Google Scholar]
  4. B.A.Shtipelman,斜视齿轮,Wiley,纽约,1978年的设计和制造[Google Scholar]
  5. F.L.L.itvin, A. Fuentes, Gear Geometry and Applied Theory, 2nd edition, Cambridge University Press, New York, 2004[Google Scholar]
  6. F.L.L.itvin, Y. Zhang, Local synthesis and tooth contact analysis of face-milled spiral bevel gears, Technical Report National Aeronautics and Space Administration, Cleveland, 1991[Google Scholar]
  7. Beijing Gear Factory, Spiral Bevel Gear 1974, Science Press (in Chinese)[Google Scholar]
  8. K. Kawasaki,H.Tamura,双工散布叶片方法,用于切割双铁齿轮,改良齿表面,J. Mech。des。120.那4.41.-4.4.7.(19.9.8.)[Google Scholar]
  9. L.L.Geng,X.Z.邓,x.m。基于4轴CNC铣床,J.Adg,CAO等人。机械。des。系统。Manuf。,14.那1-16.(20.20.)[Google Scholar]
  10. Gleason Works, Calculation Instructions Generated Hypoid Gears Duplex Helical Method, The Gleason Works, New York, 1971[Google Scholar]
  11. C.B. Tsay,J.Y.林,一种用于牙齿齿轮齿几何的数学模型,Manuf。compu。模型。18.那23.-3.4.(19.9.3.)[Google Scholar]
  12. A. Gonzalez-Perez, A. Fuentes, K. Hayasaka, Computerized design and tooth contact analysis of spiral bevel gears generated by the duplex helical method, in: ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers, Washington, DC, United states, 2011, pp. 149–158[Google Scholar]
  13. Y.张,H.Z.Yan, New methodology for determining basic machine settings of spiral bevel and hypoid gears manufactured by duplex helical method, Mech. Mach. Theory10.0.,283-295(2016)[Google Scholar]
  14. Y.张,H.Z.作者:张莹莹,王莹,王莹,王莹,王莹,王莹,王莹,王莹,王莹,王莹,王莹,王莹,王莹,王莹,王莹,王莹,王莹,王玮eng。51.,15-23(2015)[Google Scholar]
  15. S. Bodzás, Designing and analysis of the TCA parameters of a bevel gear having circular tooth direction in the function of the moment, J. Appl. Polym. Sei. Eng.6.那3.10.-3.28.(20.19.)[Google Scholar]

Cite this article as: L. Geng, X. Deng, H. Zhang, S. Nie, C. Jiang, Theory and experimental research on spiral bevel gear by double-side milling method, Mechanics & Industry22.那33.(20.21)

All Tables

表格1

Geometric parameters.

T.一种B.le 2

机器设置参数。

所有数字

T.Humbnail Fig. 1

球场上的侧翼线。(a)单侧方法中的牙坯。(b)双面法中的牙坯。

在文中
T.Humbnail Fig. 2

专职角度对牙齿锥度的影响。

在文中
T.Humbnail Fig. 3

分期付款。

在文中
T.Humbnail Fig. 4

螺旋运动对压力角的影响。

在文中
T.Humbnail Fig. 5

技术过程的流程图。

在文中
T.Humbnail Fig. 6

螺旋运动对牙齿表面拓扑的影响。

在文中
T.Humbnail Fig. 7

R.esult of TCA. (a) Convex side. (b) Concave side.

在文中
T.Humbnail Fig. 8

Model of finite element analysis.

在文中
T.Humbnail Fig. 9

有限元分析结果。(a)齿轮的凸面。(b)凹陷的凹面。

在文中
T.Humbnail Fig. 10

刀具模型。

在文中
T.Humbnail Fig. 11

仿真过程和产品。

在文中
T.Humbnail Fig. 12

比较的结果。

在文中
T.Humbnail Fig. 13

切割实验。(a)齿轮。(b)小齿轮。

在文中
T.Humbnail Fig. 14

测量场景。(a)齿轮。(b)小齿轮。

在文中
T.Humbnail Fig. 15

Measurement results of tooth surface. (a) Gear. (b) Pinion.

在文中
T.Humbnail Fig. 16

滚动测试和结果。(a)滚动试验。(b)齿轮的凸面。(c)凹陷的凹陷侧。

在文中

当前的使用指标显示文章视图的累积计数(包括HTML视图,包括HTML视图,PDF和EPUB下载,根据可用数据)和Vision4press平台上的摘要视图。

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.