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yabo亚博问题
yabo亚博
体积20,数字6.,2019年
文章编号 626.
页数) 16.
DOI https://doi.org/10.1051/meca/2019064
在线发布 2019年12月0日

©G.Vouaillat等,由EDP Sciences发表2019

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1介绍

齿轮是航空传动箱的主要组成部分。飞机系统的正确功能直接依赖于其传输运行状态。然而,这些部件的概念或制造近似可能导致组件故障,微量速率是最复发的故障。在文献中,用于滚动滑动触点的微量工具,其特征在于典型的10μm长度和深度凹坑[1-5.]。

此外,油脂已经指出[6.]通过基于双盘的实验研究,7个因素影响这种特定失败。其中,压力,粗糙度,摩擦和滑移比是主要的。最近,rycerz [7.] has also identified slide-to-roll ratio as a major influencer in micropitting occurrence and particularly on the rough micro-contact stress cycles. This asperity stress history is highlighted as a potential basis for a micropitting criterion. Thus, the present study actually focuses on the influencing factors introduced above first, and on a shear stresses-based micropitting criterion then.

在所有先前引用的研究中,更通常被描述为润滑膜的组合结果和从粗糙表面光洁度的过度物质表面的结合结果更加描述。由于在本文中忽略了润滑以限制影响参数,因此需要对接触微曲线和材料微观结构进行准确描述,以便正确模拟故障现象。

R.egarding the material, SADEGHI's working team focuses on the granular description of some specific bearing or gear steels in [8.-10.]。T.he austenitic grain boundaries from typical bearing or gear steels are represented. The same concern for the microstructure representation is brought in this study.

关于联系人,Morales已审查[11.[文献中的不同方法考虑计算中的粗糙表面。他自己的贡献是基于格林伍德和约翰逊的工作[12.[由半分析方法组成,用于处理复杂的粗糙度轮廓。通过对瞬态解决方案的这些曲线的傅里叶分析,[13.-16.] a pressure field calculation for complex rough contacting surfaces. Applied to rolling element bearings or gears, these computed pressure fields are time-varying with the contact moving along the specific geometries. Such a model is used hereafter so as to completely simulate rough contacting gears. Thus, rolling contact fatigue estimations are made possible by criteria or stress analyses as presented in [17.]。

因此,本研究的最终目的是模拟和理解若干影响因素(压力,粗糙度,摩擦和滑辊比率)对接触正齿轮的微量核的个体和综合影响。基于文献的模型在第一方法中详细介绍了平稳接触。显着引入了由代表工业齿轮特异性的时间演化压力场计算的材料微观结构的主要贡献。然后,关于影响因素,考虑粗糙的触点,以最终模拟真正的接触式正齿轮。

2model description

2.1介绍

建立了一种数值方法,以答案对不同参数对齿轮表面寿命持续时间的实际影响的答案。该模型分为三个零件图1。首先,给出了分析分析内部的所有输入参数。然后对接触体中的宏观几何和微观一体进行压力场计算。这些字段被利用为有限元分析的边界条件。最后,通过诺埃尔最初开发的模型来操作压力和疲劳标准分析[18.19.]。T.he details of the model construction and computations are explained hereafter.

缩略图 F一世g. 1

模型的Organigram。

2。2B.一种S.一世cs of the model

A granular geometry is set as presented by NOYEL [19.]以表示在基本齿轮材料中观察到的大致典型的奥氏体晶界。这种特殊的几何形状呈现在图2。在该模型中数值产生晶粒(晶粒取向是随机设置的),选择它们的尺寸(25μm)以适合通常的工业齿轮芯粒度[20.]。T.he equivalent ASTM grain size [21.] is almostGASTM. = 7.

几何形状被复制地啮合以获取有限元模型(FEM)。晶界(GB)也用粘性元素啮合,以允许沿着这些GB的应力计算。平面应变假设用于FEM。该模型通过无摩擦的支持,在三个面上界定。

缩略图 F一世g. 2

一世llustration of the static Hertzian pressure field of simulation #0 and the dimensionless Tresca stress field associated.

2。3.S.T.你dy of a centered and static pressure field

When a basic contact between two surfaces is considered without any roughness, micro-geometry nor tangential effect, HERTZ's theory is applied [22.]。因此,方程式(1)一种N.d(2)用于干线接触。(1)(2)

然后,沿着方程中的表面计算正常压力场(3)并应用于网状几何形状图2(3)

获得该平面应变问题的Tresca等效剪切应力yabo亚博图2一种fter a Finite Element Analysis (FEA) with the numerical data from simulation #0 as presented in表格1。T.he equivalent stress is dimensionless (by the value of the Hertzian pressureP.0.)。此外,找到了在#0中模拟的线路触点的无量纲Tresca应力的文献古典0.3值(如tresca应力场颜色栏所示)F一世g. 2)。

从这些静态和居中的压力和应力场,只能施加基本的疲劳标准。例如,与来自Lamagnere的20μdef的塑性菌株的微产剪应力进行比较[23.](可以常用为100Cr6轴承钢的915MPa)。因此,计算Tresca最大剪切应力并与整个材料中的屈服应力极限进行比较。较高的值物理地对应于与塑料应变相关的位错创建。

表格1

T.一种B.le of simulations.

3对平滑接触的研究

Whether a more precise description of the damaging phenomena occurring inside the material is wanted, a computation of the load passing over the surface is needed. So, the previously mentioned model inspired from NOYEL is used. In a first approach a smooth contact is considered.

3.。1S.mooth contact passing over a surface

对于平滑的赫斯氏触点,由于方程式,每次时间的压力场再次计算(3)。B.你T.comparatively to the previous simulation, the pressure field is applied at different successive positions above the meshed geometry to simulate the load passage. At this step, no friction nor sliding is taken into account in the model.

然后沿着每个晶界(GB),计算平均剪切应力(或晶间剪切应力ISS)。GB由多个粘性元素组成。因此,ISS估计是沿着该GB的每个粘性元素的剪切应力的平均值。这样,对于每个GB的粒状几何形状,可以完整地模拟时间的演变。所有计算详细信息都在[19.]。

幅度δτ.然后计算ISS变化。该计算是疲劳标准估计的基础。对于每个GB获得该标准,孤立的最严重的标准,并且其值成为整个模拟的一般标准。δ.τ.一世S.estimated with the minimum-maximum method i.e. the detection of the two extrema of the shear stress. So, the GB presenting the largest value of Δτ.被隔离,它的位置和评估作为结果给出。

δ.τ.1for simulation #1 is given in图3.。一世T.corresponds to a smooth contact without any surface shear stress nor sliding effect. All the simulations results will be presented in this work relatively to the reference simulation #1.

疲劳标准基于文献中发现的实验结果[24.]并表示为S-N曲线图4.。通过直线建模该S-N曲线直接赋予剪切应力幅度与疲劳循环次数之间的关系(4)(4)

T.hese constants are expressed function of the variables and the material properties as given in(5)[24.]。(5)

然后,制定(6)comes directly from calculations so as to isolate the number of cycles to fatigueN.一世。无量纲版本是给出的(7)(6)(7)

所有材料参数(m一种N.dσ.R.)一种R.e found in RAJE's work [1]。和一种N.empiric point of view, this GB corresponds to the location of the first micro-crack in the material.

已经进行了另外两种模拟,以通过赫兹压力的变化来验证疲劳标准的正确演变P.0.。因此,模拟#1'具有最大压力P.m一种Xequals to 0.84 (lower than #1). Simulation #1′ has aP.m一种X3.63(高于#1)。似乎已选择这些值作为最大值(3.63)和最小值(0.84)值P.m一种X将在所有其他模拟中使用。所以,#1'和#1'被定义为δ中的极端边界τ.一种N.dN对于具有相同输入参数的模拟,即从#0到#10(CF.T.一种B.。1)。

因此到了P.m一种X在#1'中减少[分别在#1'中的增强],δτ.1'计算在图3.一世S.S.m一种ller than Δτ.1[和δτ.1'大于δτ.1]。T.his results in an increase for #1′ [respectively a decrease for #1′] in life duration to fatigue initiation. The micro-cracks initiate each time at the Hertzian depth in the material (CF.T.一种B.。1一种N.dF一世g. 7)。S.o concerning the maximum pressure evolution, the fatigue criterion evolution is consistent with the expectations.

缩略图 F一世g. 3

接触压力的影响和牵引系数变化在ISS,Δ上平滑接触的变化τ.一种N.dN结果。

缩略图 F一世g. 4

S-N.curve in complete reverse torsion [1]。

缩略图 F一世g. 7

一世llustration of micro-cracks nucleation location for smooth contacts.

3.2插入摩擦系数

下文调查了切向分量影响的插入。滑动和摩擦是需要在需要接触齿轮的完全模拟时考虑的两个主要参数。

For a smooth contact and among friction and sliding, only friction will impact the fatigue results. Sliding will actually be of no influence on the displacement of local microgeometries above the two contacting surfaces since none is present. Simulation #3 presents the lone influence of friction on a smooth contact. The details of those simulations parameters are shown in表格1

方产品表面剪切应力计算T.of the normal one for each step and a traction coefficientμ.。A maximum value of 0.1 is chosen for the traction coefficient. Such a value is high for a lubricated contact and rather corresponds to a typical boundary regime. It is also assumed that no micro-slip is present during sliding and only full slip occurs. A positive or a negative sign is attributed to the traction coefficient depending on the sliding direction. This formulation is detailed in equation(8.)(8.)

显示微裂纹成核的循环次数和次数图3.并与参考文献相比。最紧张的晶界(GB)位于材料深度的模拟#1和#3都是(Z. = 0.5 inF一世g. 7一种N.dT.一种B.。1)。

在结果方面,#1和#3曲线的比较给出了表面剪切应力对ISS的值的真正有限的影响:δ的全局价值T.几乎没有修改。#3 ISS的轻微左移与其受损GB的位置有关。与损坏的#1 GB相比,这一个位于左侧。因此,来自#3的GB在于#1的时间比GB在时间上强调。此外,底部的轻微偏移直接连接到表面剪切应力的插入。该组件向全球应力场引入了恒定的剪切贡献。

F一世N.一种lly, the number of cycles to fatigue initiation is almost not modified. So, no major change can be observed from the insertion of a surface shear stress with a constant traction coefficient on a smooth contact.

3.3表面上方的负载变化

喷齿轮理论的引入意味着两个接触表面之间的线接触。由于齿轮宏观 - 几何形状从圆形渐渐近实现,因此等效的曲率半径将沿齿轮作用线发展。同样的方式,啮合齿的数量正在演变齿轮参数的功能。因此,正常负载直接影响。牵引系数,速度和其他几个参数受到齿轮几何数据的演变的影响。

An example of those different variations for a smooth contact is illustrated in图5.for data given in表2.

值得注意的是,选择所有模拟齿轮参数(模拟#13除外),以模拟俯仰点围绕音高点的产生参数的对称行为。

在上图上孤立了三种不同的案例。对于该具体研究,它们对应于将分析的三个不同区域。先前引入的参数将进化研究区域的功能。在齿轮作用线上,已经选择这些区域以对应于啮合的特定点,并且损坏现象或动力学可能从区域发展到另一个区域。这些区域定义为:

  • T.he area around A: the approach contact point. This area analysis will be indexed in simulations as #i_A.

  • T.he area around一世: the rolling without sliding pitch point indexed as #i_I.

  • T.he area aroundB.:eCESS联系点索引为#i_b。

T.hese three sections are systematically kept to compare the results between the locations on the gear teeth. The global aim of these section identifications is to potentially identify for a complete gear simulation, a fatigue initiation difference between the tooth addendum, dedendum or pitch point.

根据分析区域的输入参数的修改将直接影响接触和前面提到的损坏参数作为滑动速率,负载或表面剪切应力。因此,特别是从正常载荷和等效曲率半径计算的赫兹压力正在沿齿轮作用线发展。

在模拟#6中研究了正常负载变化的影响。接触再次是平滑的接触,这里仅研究了正常的载荷演化。ISS变化呈现在图6.。B.oth results for the reference #1 simulation and those for the three areas are shown here. The stress and the number of cycles to fatigue initiation are also available on the figure.

Concerning the area around the pitch point, the ISS evolution and number of cycles are equivalent between #6_I and #1 as parameters from #1 have been chosen deliberately equal to those at the pitch of #6.

输入正常负载围绕接近和凹陷接触点,这些区域的最大赫兹压力也比在俯仰点处更小。因此,直接解释较低的ISS变化和对微裂纹成核的循环较高的循环。与上述相同的方式,围绕B]围绕一个[分别围绕B]施加的晶界(GB)位于左侧[右侧],但在比间距上的一个相同的无量纲深度。所以解释了ISS中的轻微转变。

因此,由于施加较低的正常压力,正常负载的变化导致寿命持续寿命持续时间增加。与#1中的孤立赫兹触点相比,我周围的等同寿命持续时间。还表明,对疲劳标准产生影响的负载变化分析是相关的,但是对于该特定齿轮几何形状的有限量。所有微裂纹位置都是如下所示图7.

缩略图 F一世g. 5

具有相应压力场通道的最大赫兹压力演化,牵引系数,三个研究区域的速度和识别的演变。

表2.

对称齿轮特性。

缩略图 F一世g. 6

牙齿啮合数量的影响及摩擦系数演化对ISS,δ的平滑接触τ.一种N.dN结果。

3.4完全平滑联系

为了模拟完整的齿轮平滑接触,设置了模拟#7。研究了对正常负载变化和非恒定牵引系数的组合影响。这种典型形状的牵引系数已从Diab的作品计算[25.] and is illustrated in图5.。一世T.一世S.一世N.cluded on the chosen sections in the following ranges:± [0.083; 0.1] (around the addendum and dedendum) and [–0.05; 0.05] (around pitch point). At the exact position of the pitch point, the value is null but increases rapidly around (CF.F一世g. 5)。它导致相当高的牵引系数接近点I.

所有的疲劳结果的ISS和数量都呈现为#7图6.图7.一世S.一世llustrating the micro-cracks nucleation locations in the material relatively to the reference one.

Around the approach and recess point, the respective ISS are shifted to the top [and the bottom] of the graph. This is the direct result of the signed traction coefficient introduction. However, the global Δτ.一种N.dN一世values are unchanged between simulations #6 and #7 around A and B. So, the traction coefficient and the normal load evolution combined aren't influencing the fatigue life of this simulated smooth contact. Compared to #1 results, only the load evolution is influencing the global stresses inside the material and its resulting fatigue life. In terms of initiation location, micro-cracks nucleate closer to the surface (CF.F一世g. 7)由于在相应的模拟中产生的正常负载的最小值。

在俯仰点周围,模拟#1,#6和#7的结果之间的非常低的差异确认了上面所描绘的结论。

3.5初步结论

FR.om all the previous simulations run for a smooth contact, both the influence of a surface shear stress and the variation of the normal load are tested. The amplitude of the load imposed is clearly shown to directly influence the stresses in the material and the number of cycles to fatigue initiation. The conclusion is not the same for the friction coefficient. It is indeed demonstrated above that fatigue results are just slightly or even not modified by the introduction of a surface shear stress.图8.总结所有模拟以进行平滑的联系人,并获得后续结果(疲劳和ISS的循环次数)。因此,参考#1周围的仿真组确认先前描绘的结论。

缩略图 F一世g. 8

结果几个参数对δ的影响τ.一种N.dNvalues with smooth contacts.

4研究粗略接触

当需要接触中的古典表面的更现实的表示时,需要引入粗糙的组件。在文献中确实突出显示了表面微曲测量[7.26.27.]作为一个主要参数,以便正确预测微米。所以,正弦粗糙度几何形状(一个频率1 /λ.)设置了[28.]。在粗糙度分布上进行的近似是在第一次接近结果的正确分析中。因此,方程式(9)使用AMP和λ分别描述该几何形状,分别是信号无量纲幅度和波长。(9)

从约翰逊的启发[29.],在[28.谢谢约翰逊的参数。(10)然后鉴定出两种不同的病例。

1。χ<1:连续压力场

压力场是连续的,并且可以直接从等式计算压力的粗糙分量(11)(11)

2。χ> 1:不连续压力场(CF.F一世g. 9

T.he pressure field is discontinuous and the rough component of pressure is also computed directly from equation(12)(12)

最终获得全局压力场作为每次步骤和计算的粗糙分量的赫兹压力场的直接叠加。

4.1基本粗糙联系

至于平稳接触,表面上的全球负载通道被分成几个步骤。对于粗糙接触的每个步骤,粗糙的部件被认为是固定的(对于纯轧制条件),并且只有赫兹组分正在移动(相对于参考坐标系)。然后单独计算所得到的全局压力场。

模拟#2已设置为表示基本粗糙的触点,而不会滑动也不是切向效应。相应的压力场段是表示的图9.。O.N.T.he figure, the roughness is indeed fixed relatively to the granular geometry and added to the Hertzian pressure to represent the global normal pressure.

在应力方面,同等的Tresca应力也显示在图9.。Compared to stresses in #0 and #1, the introduction of roughness to the geometry makes maximum stresses to move closer to the surface. The values ofZ.P.R.esented for both simulations in表格1和在图16.随着这个分析。使用此模拟,显着修改了ISS变化和疲劳成核的循环次数,如图所示图10.

因此,粗糙度的引入产生更多的损坏,并且在孤立的骑行接触和材料的近地下循环中产生更多损坏。在材料中的最大应力区域的位置解释了ISS形状。应力高度对应于全球压力刚刚在GB上的时刻。由于粗糙度不移动(这里没有滑动,因此该值保持相当恒定,直到粗糙的超压进一步比GB进一步。

缩略图 F一世g. 9

仿真#2粗糙接触的通过相关元件模型与TRESCA无量纲压力场相关联的有限元模型。

缩略图 图10.

一世N.fluence of the traction coefficient for a rough contact on ISS, Δτ.一种N.dN结果。

4.。2FR.一世ction in a rough contact

与平滑接触,摩擦和滑动的方式相同,是要考虑的两个主要和连接参数,以便完全模拟接触齿轮。在模拟#4中首先引入恒定的牵引系数。然后,模拟#8示出了可变牵引系数对不同档部分的影响。将研究滑动的影响。

O.N.ce again, the way the tangential component is computed is similar for a rough contact to the smooth one. Equation(8.)S.hows the formulation used. The ISS curves obtained for #4 and their number of cycles to fatigue initiation are presented in图10.

A small modification of ΔT.一世S.observed between #2 and #4. Because the damaged GB is almost the same in both simulations (position and orientation), the introduction of a surface shear stress with a constant traction coefficient creates a slight increase of shear stress for a rough contact. The number of cycles to fatigue initiation is directly influenced and the same diminution of life duration is obtained from #2 to #4. However the modifications are too small to conclude that a surface shear stress has an important influence on the initiation and the life duration.

当接触装置被认为是在一起一种T.一世on #8, it has already been shown that the contact parameters evolve function on the position on the gear action line. Thus, the three previously introduced gear sections (addendum, pitch point and dedendum) are used to describe the different fatigue behaviors function of the influencing parameters.

R.esults appear to be similar on the three gear sections (图10.)。首先,牵引系数值与具有相反标志的方法(点A)和凹陷点(点B)之间的部分之间等于。这解释了所观察到的类似结果。俯仰点周围的牵引系数很小。这解释说,ISS和疲劳循环次数的结果类似于#2中获得的结果(没有任何牵引系数)。此外,牵引系数从围绕A和B左右的牵引系数的降低值倾向于解释与模拟#4的结果的差异。

最后,关于启动位置,如图所示,在材料的近近表面上的微裂纹核心图16.。由于粗糙度导致的应力增加了这种结果和未改性的起始深度。因此,从这些模拟中,观察到牵引系数进化几乎没有影响疲劳微裂纹的粗糙接触的启动。

4.3滑动在粗糙接触中的影响

然后在模拟#5中引入滑动(没有任何切向效应)。在两个时间步骤之间,在压力场中设置滑动作为正弦粗糙度位置的换档(δS.defined in图11.)。T.he Hertzian component is still moving the same way as presented before.

T.he ISS computed by the numerical model presents a very different shape as the one observed for the previous simulations in图12.。观察到一些压力振荡。它们是由在发起的GB上通过连续粗糙度峰的通过。ISS形式的这种变化将直接影响疲劳标准,并应考虑其估计,因为Rycerz建议在[8.]。因此,方式δτ.计算被修改以考虑材料中的所有损伤现象。

S.o, a rainflow algorithm is set to fit these new ISS shapes. This algorithm is described in [30.]。T.he principle allows the detection of half and full cycles in a random signal. All the local extrema in cycle-shaped signal are isolated this way.

检测到的振荡的数量对应于受损GB所看到的粗糙峰的数量,并且可以分析计算。这样做,时间δT.对于材料表面的一个点,以看到整个接触通过滑动速度V.S.lide一世S.considered as described in equation(13.)。相应的距离是接触宽度(13.)

两个接触体分别在δ期间移动T.通过距离δS.1一种N.d ΔS.2在等式中描述(14.)在各自的速度下1一种N.d2(14.)

T.he relative dimensionless sliding shift ΔS.一世S.T.hen computed in(15.)一种N.d the number of oscillations seen by the considered point is deduced from(16.)(15.)(16.)

T.he speeds values directly depend on the slide-to-roll ratio. It is fixed in the first approach of simulation #5. So, all the linked parameters are constant and their variations will be studied later. The analytical data from equation(17.)(呈现了数值数据T.一种B.。1)confirm the number of rough peaks in simulation #5 found in the numerical simulation of six oscillations.(17.)

两个δτ.关于S.你lts are presented for simulation #5 in图12.。它们对应于从两种不同的极值检测方法获得的应力变化。δ.τ.5.那T.h由先前描述的最大 - 最小检测方法给出。将该值与δ进行比较τ.5.那R.e获得振荡IS的等效应力变化。δ.τ.5.那R.e一世S.computed from the following method:

  • 使用雨流程算法估计每个GB的振荡总数(每个极值被识别图12.通过一个完整的圆圈)

  • 对于每个GB中的每个振荡,局部Δτ.我,J.一世B.eing the index of simulation andj振荡1)估计最小最大方法

  • T.he global number of cyclesN一世,关于然后用方程计算(18.)

  • F一世N.一种lly, the equivalent Δτ.一世,关于一世S.obtained fromN一世,关于一种N.d equation(7)

(18.)

这些结果表明,通过雨流程方法进行了重要的修改。当考虑所有振荡时获得的ISS更高,但当考虑疲劳的循环次数时,差异更为重要。寿命持续时间确实显着降低(大约十次)。

滑动影响我粗糙的接触压力S.一世N.T.R.oduced through the shift explained before. On simulation #5, a constant slide-to-roll ratio is imposed. However, a contacting gear simulation requires the evolution of this parameter and of the resulting calculated shifts. Depending on the respective speed of each body and the sliding ratio, this shift can be positive or negative from a gear section to another. Thanks to the geometric relations in gears (CF.图13.)[31.], the shift can be calculated for each teeth in contact as:(19)

mm ′ the distance on the gear action line between two successive time steps,T.1m一种N.dT.2m分别在齿轮1和齿轮2上分别在齿轮1和齿轮2上的距离和所考虑的步骤M.的点之间的距离。R.B.1一种N.dR.B.2一种R.e the base circle radii of each gear. ΔS.1一种N.d ΔS.2一种R.e the shifts computed for a fixed value of毫米'for each gear. Those values are inserted inside the pressure computations to get the final sliding fields as described in图11.

因此,设置模拟#9以研究牵引系数的组合变化和滑动率比对材料疲劳寿命的影响。图12.呈现出疲劳的循环次数和循环次数的结果。

关于俯仰点周围的结果,δτ.9_I一世S.S.lightly lower than Δτ.2,模拟独特的粗糙接触。即使以小的速率也直接连接到存在滑动的情况。俯仰点的滑动速率的符号变化确实直接负责这种应力变化降低。因此,疲劳的循环次数受影响,并且比孤独的粗糙接触小一点。

围绕方法和凹陷点A和B,δτ.9_A一种N.d Δτ.9_B几乎类似于δτ.5.。因此,对疲劳寿命开始的结果非常接近这三种模拟。鉴于此,摩擦与平稳接触和滑动速率有相同的有限影响,明确指定为疲劳寿命的最大的一个参数。关于微裂缝位置,图16.S.hows that they also initiate at the near surface of the material.

缩略图 图11.

Details about the introduction of sliding inside the computed pressure fields.

缩略图 图12.

ISS,δ粗略接触滑动速率的影响τ.一种N.dN结果。

缩略图 图13.

一世llustration of the geometries of meshing gears.

4.。4.Complete symmetrical rough contact

最后与对称档位数据,使用所有影响参数(粗糙度,滑动率,牵引系数和正常负载演进)设置了仿真#10。

压力演变和终身持续时间的结果图14.。在俯仰点I周围,结果类似于在没有任何负载变化的情况下获得的结果。由于此变化非常有限,因此观察到应力的差异,并且严格的疲劳寿命是相同的。微裂纹位置保持不变。

Around points A and B, a difference is observed with the introduction of the normal load evolution. Less oscillations are indeed observed than on the lone rough sliding simulation #5. This phenomenon is explained by the number of teeth meshing. While only one tooth meshes in the pitch point section, two teeth mesh around the approach and the recess points. So, the normal load decreases and the contact semi-width is reduced function of the load and the equivalent curvature radius.

受损GB所见的全球步骤数直接减少,影响振荡的数量。具有方程数值数据(20)和理论方程式(13.)-(16.),发现3.4振荡用于模拟#10_A和#10_B(用于齿轮几何形状导致的变化参数的平均值)。(20)

因此,这两种模拟的ISS包括三到四个振荡,如图所示图14.。确切值取决于相对于触点内粗糙的过度放置峰位置的材料中的GB位置。

之间观察到的差异N10_A.一种N.dN10_B.comes from additional oscillation noticed on the ISS around the recess point B. Thus, the GB is more stressed at point B than at point A and the number of cycles influenced. This phenomenon is the result of the opposite direction of the combined sliding and friction coefficient around A and B. So, fatigue will potentially initiates earlier around B (which corresponds to the tooth dedendum) than at other sections. However the difference between the two sections results is small and is not representative of the slide-roll direction influence. This point is discussed in the conclusions.

缩略图 图14.

滑动速率的影响和牵引系数演进在ISS,Δ上粗略接触τ.一种N.dN结果。

4.5完全不对称粗糙齿轮几何形状

最后,在仿真#13中设置了不对称档。相关参数呈现表格1并受到FZG-C Gear的启发[32.]。数值结果应与实验结果进行比较。因此,模拟驱动齿轮的所有部分以进行研究和潜在地突出疲劳寿命差异。介绍了相关的ISS和循环循环次数图15.。在方程中的两个极端部分再次计算ISS振荡的数量(21)一种N.d(22)。由于齿轮几何形状产生的速度的局部变化在等式中呈现。(21)(22)

Around the pitch point, ISS shapes are similar to those obtained for a symmetrical gear. The limited sliding rate in this section only creates an increasing-decreasing behavior. The first respective micro-cracks initiate at the near surface and latter (in terms of number of cycles to fatigue) than at the approach and recess points.

At point A, the ISS presents a bit more than five oscillations when nine ones are observed around point B. This actually corresponds to the analytical results. This difference is linked to the velocity variation between the sections resulting from the gear geometry. Thus, the considered driving gear is at the dedendum around point A and at the addendum around point B. The velocity along the tooth profile being higher at the addendum, the shifting distance resulting from sliding is higher around the recess point B than around the approach point A for the same duration. So, according to equation(16.),在仿真#13_b中有更多的振荡。

moreover, the global ISS oscillations have a greater amplitude for #13_A than for #13_B. So, in spite of a greater number of oscillations around point B, the equivalent stresses variation Δτ.13._A一世S.higher than Δτ.13._B。由此产生的疲劳寿命引发给出齿轮牙齿专注时的早期微裂纹成核。图16.还表明,由于引入的粗糙度,微裂纹位置仍然靠近表面。

该数值结论与[32.]。作者确实研究了FZG-C型齿轮上的微点蚀发起,并且失败似乎在牙齿专用牙齿上优先发起。因此,在驱动齿轮Deatendum上方模拟的前方启动是在微裂纹传播后经验观察损坏的第一步

缩略图 图15.

S.T.你dy of a complete asymmetrical gear: influence of the number of teeth evolution, the sliding rate and the traction coefficient for a rough contact on ISS, Δτ.一种N.dN结果。

缩略图 图16

微裂缝的例证粗砺的接触者的成核位置。

5.Conclusions

因此,本研究介绍了针对疲劳分析的有限元模型。基于标准粒状钢微结构的耦合模拟,以及表示表面微造型物的时间演化接触压力场。还考虑了几个因素的个体和组合影响(在表面粗糙度,负载变化,牵引系数和滑动率之间)。材料疲劳寿命从晶界中的晶间剪切应力计算推导出。

概述了所呈现的所有粗略模拟及其结果(疲劳的循环次数)图17.

这项研究产生的最优先的结论是:

  • All the results around the pitch point section demonstrate similar stress and fatigue behaviors as those obtained for the simplest references. So, a classical calculation with a fixed Hertzian pressure field is appropriate for a smooth contact so as to study the fatigue analysis in this section in any case of influencing parameters (except roughness). The conclusion is the same for the rough contact with only a fixed rough pressure field.

  • 牵引系数甚至以高速速率也没有在疲劳微裂纹的成核中没有主要影响,既不是平滑也不是平滑的也没有粗糙的触点。

  • 材料疲劳寿命最大的因素是接触压力。在该研究中模拟的负载变化显示出直接改变计算的压力场,链接的应力和疲劳标准。需要在宏观尺度下考虑这种效果需要齿轮几何设计的控制。由微观几何参数产生的超压必须用表面光洁度改善调节。油脂通过经验研究获得了相同的结论[7.]。

  • 使用该模型实现了代表性齿轮损坏模拟。啮合齿轮的不同部分通过其不断的参数表示。该研究结果清楚地证明了牙齿Deentum的微裂纹成核和由两个部分中的齿轮几何特异性产生的分数之间的微裂纹成核之间的疲劳寿命差异(超过一个级别)。这些结果与Martins的结果相关[32.]。

  • T.he slide-to-roll ratio is also a major influencing factor in fatigue micro-cracks nucleation. When associated to a rough contact, the relative movement between the two contacting surfaces creates stresses oscillations. These additional local stress cycles worsen the material damage and significantly reduce its fatigue life. This study shows for example a decrease in the number of cycles to micro-cracks nucleation of two magnitude orders for a simple rough contact with and without a slide-to-roll ratio. It confirms RYCERZ's conclusions in [8.]。

rycerz突出的差异在[8.] which consists of a shorter fatigue life for contacts subjected to negative slide-to-roll ratios rather than positive ones is also observed here on a small scale. However, this phenomenon is actually described in the literature [33.34.] as part of the micro-crack propagation instead of their initiation. So the results obtained here cannot be an explanation to the previous conclusion. This point is a potential prospect of this study.

缩略图 图17.

结果几个参数对δ的影响τ.一种N.dNvalues with rough contacts.

命名法

一种:联系半宽[m]

放大器:粗糙度的幅度[m]

Amp: Dimensionless amplitude of roughness

B.:齿轮宽度[m]

δ.:最大变形[m]

E.一世: Young modulus of body一世[PA]

E. ′:相当于幼年模数[PA]

FN: Normal load [N]

L.model:有限元模型的负载通道长度(FEM)[M]

m0.:齿轮正常模块[M]

mσ.R.:材料参数表格S-N曲线[Ø]和[PA]

N.一世:疲劳的循环次数:第一个微裂纹成核

N.裁判: Number of cycles to fatigue for the reference simulation

N一世:模拟循环数#一世报告参考

Noscillations:晶间剪切应力图中的本地振荡数量

P.0.:Hertzian压力[PA]

P.m一种X:最大压力[PA]

P.m一种X:无量纲最大压力

P.N那T.ot: Dimensionless total normal pressure

P.T.那T.ot:无量纲总表面剪切应力

δ.P.: Rough peak of pressure [Pa]

δ.P.:无量纲粗糙的压力峰值

R.X一世:身体的曲率半径一世滚动方向X[m]

R.y一世:身体的曲率半径一世在齿轮宽度方向y[m]

R.X:等效曲率半径Xdirection [m]

R.y:等效曲率半径ydirection [m]

R.:等效曲率半径[m]

T.0.: Input torque [N m]

Z.一世:小齿轮的牙齿数量一世

Δs.一世:由身体滑动产生的微观位移一世

δ.S.: Global microscopic displacement resulting from sliding

ΔT.: Time for the contact to pass over a fixed point of the material [s]

Δτ.一世: Intergranular Shear Stress (ISS) variation of simulation #一世[PA]

Δτ.裁判: Reference ISS variation [Pa]

δ.T.一世:仿真的无量纲IS变化#一世

一世: Velocity of body一世[m/s]

V.S.lide:齿轮滑动速度[m / s]

X:联系人的位置(O.Xy)[m]

X: Dimensionless position in (O.Xy

Z.m一种X: Depth of the maximumτ.Xy[m]

Z.m一种X: Dimensionless depth ofτ.Xy最大

α.0.:齿轮压力角[°]

χ:约翰逊的参数

λ.: Sinusoidal roughness wavelength [m]

λ:无量纲粗糙度波长

ω.:齿轮输入旋转速度[RPM]

ν一世: Poisson's coefficient of body一世

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引用本文: G. Vouaillat, J.-P. Noyel, F. Ville, X. Kleber, S. Rathery, From Hertzian contact to spur gears: analyses of stresses and rolling contact fatigue, Mechanics & Industry20.,626(2019)

所有表格

表格1

T.一种B.le of simulations.

表2.

对称齿轮特性。

所有数字

缩略图 F一世g. 1

模型的Organigram。

在文中
缩略图 F一世g. 2

一世llustration of the static Hertzian pressure field of simulation #0 and the dimensionless Tresca stress field associated.

在文中
缩略图 F一世g. 3

接触压力的影响和牵引系数变化在ISS,Δ上平滑接触的变化τ.一种N.dN结果。

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缩略图 F一世g. 4

S-N.curve in complete reverse torsion [1]。

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缩略图 F一世g. 7

一世llustration of micro-cracks nucleation location for smooth contacts.

在文中
缩略图 F一世g. 5

具有相应压力场通道的最大赫兹压力演化,牵引系数,三个研究区域的速度和识别的演变。

在文中
缩略图 F一世g. 6

牙齿啮合数量的影响及摩擦系数演化对ISS,δ的平滑接触τ.一种N.dN结果。

在文中
缩略图 F一世g. 8

结果几个参数对δ的影响τ.一种N.dNvalues with smooth contacts.

在文中
缩略图 F一世g. 9

仿真#2粗糙接触的通过相关元件模型与TRESCA无量纲压力场相关联的有限元模型。

在文中
缩略图 图10.

一世N.fluence of the traction coefficient for a rough contact on ISS, Δτ.一种N.dN结果。

在文中
缩略图 图11.

Details about the introduction of sliding inside the computed pressure fields.

在文中
缩略图 图12.

ISS,δ粗略接触滑动速率的影响τ.一种N.dN结果。

在文中
缩略图 图13.

一世llustration of the geometries of meshing gears.

在文中
缩略图 图14.

滑动速率的影响和牵引系数演进在ISS,Δ上粗略接触τ.一种N.dN结果。

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缩略图 图15.

S.T.你dy of a complete asymmetrical gear: influence of the number of teeth evolution, the sliding rate and the traction coefficient for a rough contact on ISS, Δτ.一种N.dN结果。

在文中
缩略图 图16

微裂缝的例证粗砺的接触者的成核位置。

在文中
缩略图 图17.

结果几个参数对δ的影响τ.一种N.dNvalues with rough contacts.

在文中

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