(采埃孚(中國)投資有限公司，上海 201615)

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基于有限元法的汽車變速器齒輪與軸承優(yōu)化

(采埃孚(中國)投資有限公司，上海 201615)

采埃孚集團(tuán)開發(fā)和生產(chǎn)了種類繁多的傳動齒輪。對于齒輪的優(yōu)化和可靠設(shè)計，有限元法是尤為適合的。而且，這種方法能容易集成于采埃孚的程序系統(tǒng)。本文展示了在開發(fā)過程中如何運用該方法進(jìn)行齒輪優(yōu)化。此外，文中多處演示了齒輪和軸承之間的相互作用。這也是采埃孚集團(tuán)致力于開發(fā)軸承計算的原因。文中實例展現(xiàn)了如何優(yōu)化滾動軸承以達(dá)到理想的齒輪接觸印痕。當(dāng)然，這些優(yōu)化方法也適用于傳動齒輪。

變速器 齒輪 軸承 有限元 優(yōu)化

1 采埃孚變速器的應(yīng)用范圍

采埃孚為多種發(fā)動機(jī)輸出及裝置開發(fā)相應(yīng)的變速器，應(yīng)用范圍涵蓋從乘用車如9檔自動變速器，到重型卡車變速器和風(fēng)力發(fā)電用變速器。同時，采埃孚也為飛機(jī)，客車和工程機(jī)械開發(fā)變速器產(chǎn)品。由于安全性要求、溫度范圍、扭矩及速度范圍、人員舒適性、驅(qū)動形式和傳動效率水平的差別，各應(yīng)用領(lǐng)域的設(shè)計要求也有所不同。下文采用了統(tǒng)一的有限元方法進(jìn)行優(yōu)化。

2 齒輪和軸承計算方法開發(fā)

在上文所提到的各個應(yīng)用領(lǐng)域中，需要大量不同形式的變速器。這些不同的變速器的設(shè)計結(jié)合了大量不同的齒輪、軸承、材料，并具有相互限制的設(shè)計要求。因此，精確和高效的計算十分關(guān)鍵。通常單個零件或整個變速器都必須滿足相當(dāng)高的舒適性或承載能力要求，所以也需要考慮所有零部件間的相互作用。按照采埃孚的觀點，有限元法能夠提供解決這類問題的基本條件。為了保證流程的高可靠度。

1 Application fields of ZF transmissions

ZF develops transmissions for a large range of engine outputs and applications. Application fields range from passenger car applications with 9-speed automatic transmissions, to heavy truck transmissions, and wind turbine gearboxes. ZF also develops transmissions for aircraft, buses and industrial engineering applications. Therefore, the requirements of the individual application fields result from different safety requirements, temperature ranges, torque and speed ranges, comfort, driveline types, and high degrees of efficiency. In the following paper a uniform method for optimization using FEM will be presented.

一套獨立的流程被用于齒輪和軸承的復(fù)雜網(wǎng)格劃分。根據(jù)齒輪和軸承的設(shè)計要求，單獨運行的軟件會生成網(wǎng)格化的齒輪和軸承模型。這套獨立流程的一個優(yōu)點是提供了可無縫調(diào)用的文檔，包含了所用到的齒輪和軸承參數(shù)。各項相關(guān)內(nèi)容都集成于這個總體模型之中。此外，我們使用了自有的標(biāo)準(zhǔn)化程序以系統(tǒng)地確定分析范圍，取代了對現(xiàn)有的前處理器的結(jié)果分析。

3 對有限元法的要求

現(xiàn)代的硬件平臺和求解器不僅能具有高可靠性和高可用性，也能求解相當(dāng)大型的有限元模型和復(fù)雜的接觸問題。在采埃孚集團(tuán)公司內(nèi)部各不同領(lǐng)域的變速器開發(fā)中都采用了有限元法。通過按實際任務(wù)調(diào)整原有的有限元模型，可以使流程得以簡化。除了產(chǎn)生剛度的宏觀幾何，在所有接觸問題中的一個重要因素是接觸區(qū)域的精確映射。要確保計算結(jié)果的質(zhì)量，零件或者接觸區(qū)域表面的網(wǎng)格劃分必須遵循特定的標(biāo)準(zhǔn)。例如，網(wǎng)格劃分不能造成明顯的結(jié)果偏差。為了達(dá)到噪聲和(或)應(yīng)力分析的目標(biāo)結(jié)果，接觸區(qū)域通常會被直接修正。作為一個可選項，對齒根剛度的優(yōu)化能夠附帶地滿足減重需求。因此，通過開發(fā)我們自己的有限元工具和分析方法，保證了更加高效的前處理和后處理。

使用有限元法并分析較大的工作區(qū)域使得我們能深入分析齒輪和軸承的噪聲水平和承載能力。這其中同時考慮了齒根剛度和接觸剛度。通常，實現(xiàn)承載能力和噪聲水平的平衡是最終的目標(biāo)。通過接觸分析能夠檢驗各不同影響變量之間的相互作用。

4 對齒輪和軸承計算的要求

只有確定了接觸幾何模型才能得到關(guān)于承載能力和噪聲水平的可靠描述。除了基本齒輪參數(shù)外，我們還需要修形和齒廓修形等參數(shù)。這些參數(shù)一般是來源于設(shè)計(或測量數(shù)據(jù))。

接觸定義是基于標(biāo)準(zhǔn)的面對面接觸和點對點接觸。網(wǎng)格劃分的精細(xì)程度是不受幾何尺寸的影響的，在需要時還能進(jìn)行調(diào)整。和齒輪本體的連接可以采用MPC(共節(jié)點約束)。

2 Method development for gearing and bearing calculation

These fields of application require a wide range of transmission types. This, combined with a large number of different gearings, bearing concepts, materials, and often contradictory requirements for use, makes an equally precise and efficient calculation method essential. Frequently, individual parts or transmission systems must meet very high standards of comfort or load-bearing capacity, therefore it is necessary to take into account the interaction of all components. In the view of ZF, FEM provides the basic conditions to ensure this. To guarantee high process reliability, the basic transmission is designed using a commercial pre-processor. A separate process chain is used for the complex meshing of the gearing and the bearing. Independent programs create the meshed gearings and bearings according to the requirements of the gearing and bearing design. The process chain described has the advantage of providing a seamless documentation of the gearing and bearing data used. The various items are precisely integrated in the overall model. Evaluation of the results with available post-processors is replaced by our own standardized routines that systematically access a certain evaluation area.

3 Requirements of the FE method

Apart from offering high process reliability and availability, modern hardware platforms and solvers are capable of solving very large FE models and complex contact problems. The Group-wide application of the FE method in various areas of transmission development makes it easier to adapt already existing FE models to our own tasks. An important factor in all contact analyses is not only the macro-geometry that creates rigidity, but also precise mapping of the contact areas. To ensure a comparable results quality it is necessary to follow standards when meshing parts/contact surfaces, i.e. the meshing must not have any significant effect on the results. To achieve the objective of a noise and/or stress analysis, the contact area is often di-

高效的接觸求解器能夠以通用的ASCII格式輸出結(jié)果。

4.1 前處理(圖1+圖2)

除了常用的圓柱齒輪(及有徑向跳動的軸體齒形)，變厚齒輪也能使用自動化的方式進(jìn)行網(wǎng)格劃分。需要使用的齒輪參數(shù)可以通過對外接口從設(shè)計環(huán)節(jié)中獲取，然后按照所要求的網(wǎng)格劃分精細(xì)程度，就可以生成齒輪模型。可供選擇的不僅有精細(xì)劃分的齒輪網(wǎng)格以用于嚙合工況仿真，也有較粗大的網(wǎng)格以用于剛度仿真。如果有需要，還可以使用混合密度的網(wǎng)格。對于更復(fù)雜的齒輪網(wǎng)格劃分(錐齒輪、花鍵、嚙合齒輪)，可以使用半自動化的方法。

rectly corrected, and the optimization of the surrounding rigidity is an option which additionally meets the demand for weight-saving solutions. Therefore, the development of our own FE tools and evaluation routines ensures more efficient pre and post-processing.

Using the FE method and evaluating a large operational area mean that we can analyze in depth the effects on the noise levels and load-bearing capacity of gearings and bearings. Both the surround-ing rigidity and the contact rigidity are taken into account here. The objective is very often finding a compromise between load-bearing capacity and noise. The contact analysis makes it possible to examine the interplay between individual influencing variables.

圖1 有限元結(jié)構(gòu)自動生成器的協(xié)作流程圖

圖2 采埃孚的齒輪和滾動軸承有限元模型

可作分析的軸承類型有圓柱滾子軸承、向心滾子軸承和球軸承。軸承的幾何參數(shù)來源于從軸承選型手冊或供應(yīng)商圖。軸承滾道形狀應(yīng)由供應(yīng)商提供或由測量得到。

4.2 后處理(圖3)

除齒根應(yīng)力外，還能對作用于嚙合作用線方向的齒面應(yīng)力進(jìn)行分析。這涉及到了在各個接觸位置下的所有應(yīng)力值。通過分析能夠確定在被分析區(qū)域的最大或最小應(yīng)力分布?？梢允褂玫团ぞ睾透吲ぞ貋淼玫讲煌膽?yīng)力分布結(jié)果。此外，除了局部應(yīng)力的分析， 同時也應(yīng)進(jìn)行壽命計算分析。

齒面方向的螺旋角修正也是用我們自有的分析軟件來確定的。在此之前定義了與已知接觸面和齒向相關(guān)連的節(jié)點，從其發(fā)生的變形可得到螺旋角修正的建議值。在一定的載荷范圍內(nèi)，可以得到螺旋角修正的變化梯度。而載荷變化時的齒面接觸應(yīng)力結(jié)果可以用螺旋角修正的梯度算出。

對軸承計算而言，從接觸力和已知的圓角和曲線可以計算得到壓應(yīng)力。再考慮到損壞發(fā)生的位置和應(yīng)力循環(huán)，就能確定軸向和徑向的最大損傷程度。通過調(diào)整軸承內(nèi)外圈的接觸間隙能夠有效地影響接觸壓應(yīng)力。無安裝間隙能夠避免軸承損傷或者能提高工作性能。除了上述的自有優(yōu)化方案，我們也采用有限元優(yōu)化的商業(yè)軟件來優(yōu)化剛度和重量。

4 Requirements of gearing and bearing calculations

Reliable statements on load-bearing capacity and noise emissions are only possible with precisely determined contact geometries. Apart from the general gearing data, we need corrections and modifications. Usually, these are available during the design (or otherwise from measurement data).

The contact definition is based on standardized contact values for both surface-to-surface contacts as well as node-to-node contacts. The meshing fineness is independent of size and can be modified if necessary. An MPC (multi-point constraint) can be used for connection to the gear body.

An efficient contact solver supplies the results in a usable Ascii format.

圖3 對齒輪和滾動軸承的有限元分析流程

5 應(yīng)用實例

在本節(jié)的應(yīng)用實例中，我們將通過一個滾動仿真實例和一個軸承計算實例來展示采埃孚軟件的能力。

在滾動仿真中(圖4)，軸和齒根的剛度都已確定。通過使用采埃孚的齒輪前處理器，可以由包括螺旋角修正的內(nèi)部加工參數(shù)得到有限元網(wǎng)格模型。齒輪模型被置于總體模型中的特定位置。因此，接觸對象、載荷和邊界條件都有待輸入。通過變換齒輪的節(jié)點坐標(biāo)，可以得到更多的計算模型。本例在一個徑節(jié)距上進(jìn)行了10點平均分布的滾動位置分析。計算結(jié)果是接觸寬度內(nèi)的齒面應(yīng)力分布和齒根應(yīng)力值。在這個簡單的圓柱齒輪傳動鏈模型中表明，在所選的載荷工況下螺旋角修正選用合理。為了正確記錄殼體和軸的變形對齒向修形的影響，滾動仿真都是使用整體模型，及/或使用轉(zhuǎn)化了邊界條件的簡化子模型。

對于行星齒輪組，齒輪周節(jié)誤差及公差對于軸承的影響更為復(fù)雜。下面以一個行星齒輪的軸承為例。

4.1 Pre-processing (Fig.1+2)

Apart from the spur gears mainly used (also shaft gearing with runout), beveloids can also be meshed in an automated way. The necessary gearing data is accessed from the design process via an interface and the gearing is generated with the required meshing fineness. Possible options are not only tightly meshed gears for simulating the meshing conditions but also loose meshing for simulating rigidity. If required, a mixture of degrees of mesh density can be used. Semi-automated processes are available for further gear cutting methods (bevel gears, drive gearing, meshing gears).

The bearing types available are cylindrical roller, taper roller, and ball bearings. The input data for the bearing geometry is taken from bearing catalogs or supplier drawings. Raceway profiles are either stated by the bearing supplier or derived from measurements.

4.2 Post-processing (Fig.3)

Apart from root stress, flank stress over the line of contact can be analyzed.

This involves evaluating any number of individual contact positions. The analysis then determines the distribution of the maximum/minimum stresses in the analyzed area. This allows a valua-tion of the stress distribution for both low and high torques. In addition to the local strain approach, a durability analysis can also be performed.

圖4 滾動仿真

圖5 計算流程與實例

這項研究的目的是在于確定考慮齒輪接觸下的行星齒輪軸承壽命。在研究中(圖5)，我們選擇了以下參數(shù)(圖6)：同軸度偏差S(行星軸中心線)，軸承間隙L(行星軸承)，接觸輪廓誤差P(行星軸承)，軸偏移Tx(行星軸水平方向)，軸偏移Ty(行星軸垂直方向)、軸座誤差B(與行星架的安裝)以及軸傾斜度N(行星軸徑向)。

為了確定其中的主要影響因素，需要對2197個不同組合進(jìn)行全因子分析。在DoE(試驗設(shè)計)的幫助下，這個數(shù)字能夠被縮減到36個。這意味著計算速度更快。在此例中，并未對齒輪作應(yīng)力相關(guān)的計算，而是使用了簡化的接觸模型。整體模型中的齒輪采用的是粗化的網(wǎng)格劃分。

The required corrections of flank direction of a gearing are also determined using our own evaluation program. The deformation of previously defined evaluation nodes in connection with the known contact surfaces and flank directions results in signed correction proposals. The gradient of the flank direction correction is determined over a load range, and the sensitivity of the observed tooth contact to load changes can be read off from the gradient of the correction curve.

圖6 影響軸承壽命目標(biāo)的因素圖示

圖7 負(fù)載相關(guān)的接觸印痕變化

盡管進(jìn)行了簡化，接觸的關(guān)鍵影響因素仍然計入了考慮范圍。因此，針對太陽輪/行星輪和行星輪/齒圈的接觸對，本例使用了點對點的接觸定義，并對帶鼓形量以及螺旋角修正(如果適用)的齒輪幾何進(jìn)行了仿真。

被測的螺旋角修正在小扭矩時傳遞的負(fù)載也較小。而增加到100%負(fù)載水平時，產(chǎn)生了偏向一端的接觸印痕。這明確表明齒輪的接觸印痕是和負(fù)載相關(guān)的，而且會不可避免地影響到軸承的接觸印痕變化。在這個實例的研究中，考慮了齒輪和軸承的接觸印痕相互作用。這意味著行星輪的周節(jié)誤差影響也在考慮范圍內(nèi)。

對于行星軸承(圖8)，滾子輪廓是測量得到的，為了排除不穩(wěn)定性對其形狀進(jìn)行了平滑處理。行星軸和軸承滾道是圓柱體，軸承間隙和滾子形狀的組合形成了有限元模形中軸承的初始接觸間隙。接觸輪廓和軸承數(shù)據(jù)(滾子直徑、滾子長度、滾子數(shù)量、內(nèi)圈直徑及位置參數(shù))是采用采埃孚的前處理器來生成有限元網(wǎng)格。

軸承反作用力是從有限元結(jié)果中提取出來按照已知的鼓形比例轉(zhuǎn)化到負(fù)載相關(guān)的壓應(yīng)力圖表中。在給定的負(fù)載循環(huán)下，行星軸和行星輪與接觸對象的相對滾動關(guān)系是不確定的。如果行星軸與行星架相固連，那么行星軸上損傷只發(fā)生于軸上滾道上的某一位置。 而當(dāng)行星輪轉(zhuǎn)動時，滾道會由轉(zhuǎn)動負(fù)載所損傷。這時齒輪相關(guān)的損傷或總合性的損傷就要由我們采埃孚的軸承S/N曲線來判定。

For the bearing calculation, the compressive stresses that occur are determined from the contact forces and the known radii of curvature. Taking into account the location of damage and the stress reversal cycle, the maximum occurring damage in the axial and circumferential directions is determined. It is possible to effectively influence the contact compressive stress by modifying the contact gap on the outer or inner ring. Bearing damage is avoided or an increase in performance can be achieved without additional installation space. Apart from these optimization options of our own, we also use commercial FE optimization programs (e.g. gear body optimization, housing) to optimize rigidity and weight.

5 Applications

In the current application, we will demonstrate possibilities of the ZF programs presented by means of a roll-off simulation and a bearing calculation.

For a roll-off simulation (Fig.4), the shafts and surrounding rigidities up to the interface to the gearing are prepared. Using the ZF pre-processor

圖8中標(biāo)出的最大損傷是行星輪上的傾覆力矩造成的。來自于法向力、徑向力和軸向力的部分傾覆力矩取決于行星輪和太陽輪及行星輪和齒圈嚙合的接觸印痕中心位置。在徑向分布圖中，可以看到滾子受接觸印痕的影響。

The test points were re-calculated for an accelerated test procedure and carried out on the test bench. The test transmission bearings were evaluated in the back-to-back test setup. The new calculation and test results were also included in the DoE analysis.

為了分析主要影響因素，新提出的試驗計劃被用于驗證計算結(jié)果。其他不受影響(滾子輪廓)或影響很小的(傾斜)的因素沒有被考慮在內(nèi)。為了加快試驗過程，試驗點被重新計算并運用在試驗臺架上。受測的變速器軸承在背靠背的試驗設(shè)置中得到了驗證。新的計算結(jié)果和試驗數(shù)據(jù)也列于DoE分析中。

6 計算過程的輸出結(jié)果及測試

量化地給出對軸承壽命的幾何影響因素已經(jīng)

for gearing, an FE meshing pattern is generated from internally provided manufacturing data for the gearing including corrections. The gearing model is integrated in a precise position in the overall model. Subsequently, the contact partners, loads and boundary conditions must be entered. The further calculation models are generated from this basic model by transforming the coordinates of the gearing nodes. In this case, 10 evenly distributed roll-off positions of a pitch module were evaluated. The result is the distribution of the load-sensitive contact and root stresses over the contact width. The example of a simple spur gear chain shows that the flank corrections for the selected load situation are well chosen. In order to correctly record the influences of housing and shaft deformations in connection with the flank corrections, the roll-off simulation is always carried out in the overall model and/or a reduced sub-model with corresponding shifting boundary conditions.

Recording the effects of pitch errors and tolerances on bearing behavior is more complex for planetary gearsets. This is shown in the following using the example of a planetary gear bearing.

The objective of the examination is to ascertain the service life in a planetary bearing taking into account the gearing contact. For the study (Fig.5), we selected the parameters (Fig.6) bolt misalignment S (of the bolt axis), bearing clearance L (of the planetary bearing), contact profile P (of the planetary bearing), bolt pitch Tx (of the planetary bolt in tangential direction), bolt pitch Ty (pitch of the planetary bolt in radial direction), bolt bearing B (fixing in planet carrier), and bolt inclination N (of the planetary bolt in radial direction).

實現(xiàn)。通過計算能夠確定軸承工作壽命中的主要影響因素。計算能確定損傷的位置和發(fā)生幾率。在加工公差范圍內(nèi)，選擇不利的參數(shù)時，工作壽命下降可達(dá)37%。而在有利參數(shù)下，可以期望工作壽命增長達(dá)74%。以上結(jié)果是在正向載荷下得到的。在相同位置的反向載荷會造成行星軸另一邊的損傷，但并不影響這些計算結(jié)果。

預(yù)測圖表(圖9)表現(xiàn)了各個參數(shù)的影響。使用垂直虛線，可以作出工作點位置。

預(yù)測數(shù)值如圖9中y軸所示，x軸列出了各因素數(shù)值的范圍。較大的斜率意味著影響也越大, 反之較小的斜率意味著影響也越小。但是，這些曲線只是簡單的概括，當(dāng)考慮交互作用時，斜率變化可能會非常明顯，甚至由正值變負(fù)值。在預(yù)測圖表中能清楚地看到相互作用的影響。行星軸位置和同軸度的實例表明行星軸位置的影響是和同軸度的影響相互作用的。在同軸度偏差較小時，軸的位置對壽命幾乎沒有影響。而同軸度偏差較大時，其影響要大的多。

To ascertain the influence of the main parameters, 2197 different variants would be necessary for a full-factorial analysis. With the help of the DoE (design of experiments), the number of necessary calculations can be reduced to 36. This means the calculations can be made much more quickly. In this case, the gearing is not tested in relation to stress, but a simplified contact model is used. The gearing was integrated into the model with coarse FE mesh.

圖9 使用DoE的結(jié)果分析

在帕累托圖中，包括了單一及交互影響的分析。圖中各影響變量以權(quán)重系數(shù)的形式表示。同軸度誤差和軸承間隙對壽命的影響最大。而軸偏移和軸傾斜度的影響最小。

7 總結(jié)

通過系統(tǒng)地使用自有程序，可以進(jìn)行更快速的有限元計算，所得結(jié)果也更有實際意義。使用我們的齒輪和軸承的網(wǎng)格劃分程序，能夠可靠地處理復(fù)雜幾何體如齒輪和軸承。在各個不同應(yīng)用領(lǐng)域，獨立于模型尺寸的網(wǎng)格劃分策略使有限元結(jié)構(gòu)對運算結(jié)果的影響實現(xiàn)了最小化。運算結(jié)果也按標(biāo)準(zhǔn)流程進(jìn)行了判定和解讀。這顯著提高了有實際意義的質(zhì)量水平和可再現(xiàn)性。必要的文件流程使得初始數(shù)據(jù)文件和結(jié)果文件易于處理。標(biāo)準(zhǔn)化的流程也改進(jìn)了結(jié)果的可再現(xiàn)性。

簡化的實現(xiàn)使其他流程如DoE更加易于操作。對于大批量數(shù)據(jù)的規(guī)劃、處理和評估也具有了可行性。同時，模型質(zhì)量和所用流程通過運算結(jié)果質(zhì)量得以驗證。

可以對多種因素(如制造誤差、微觀幾何和扭轉(zhuǎn)剛度)進(jìn)行系統(tǒng)地分析，以確定公差范圍并避免不必要的生產(chǎn)成本。

可以對傳動系統(tǒng)的穩(wěn)定性進(jìn)行確定，確認(rèn)影響大的因素并按合適的方法進(jìn)行處理。

可以確定最有效的方法來進(jìn)行優(yōu)化(如對現(xiàn)有安裝間隙)，以改進(jìn)安全性和可靠性。

Even with this simplification, the decisive influences on the contact finding are still taken into account. For this, the gear geometry with crowning and if applicable with flank direction corrections is simulated using node-to-node contacts for the contact pairs sun/planet and planet/ring gear. The contact pattern (Fig.7) shows the distribution of the contact forces over the ring gear contact area at 25% and 100% sun torque.

The tested flank correction leads to lower load transfers at low torques. An increase to 100% load level produces a one-directional contact pattern. This makes it clear that load-dependent contact patterns in the gearing inevitably lead to contact pattern alterations in the bearing. The interactions between the gearing and bearing contact patterns are taken into account in this study. This means the influence due to errors in the planet pitch can also be considered.

For the planetary bearing (Fig.8), the roller profile was measured and the profile shape smoothed in order to rule out unsteadiness. The planetary bolt and the planetary raceway are cylindrical. The combination of bearing clearance and roller profile create the initial contact gap of the bearing in the FE model. The contact profile and the bearing data (rolling-body diameter, rolling-body length, number of rolling bodies, inner bearing diameters, and position data) are processed by the ZF pre-processor to generate an FE mesh.

The bearing reaction forces are extracted from the FE calculation results and converted with the known crowning ratios into a load-dependent compression diagram. Using a given load duty cycle, the overrolling relationships of the contact partners on the bolt and the planet are ascertained. If the bolt is fixed to the planet carrier, a constant location of damage on the bolt raceway results. If the planet turns, its raceway is damaged by a rotating load. Then gear-related or aggregate damage is determined using our own ZF bearing S/N curve.

The damage peak marked (Fig.8) is attributable to the tilting moments that occur on the planetary gear. The proportional tilting moments that result from the tangential, radial, and axial forces depend on where the main focus of a contact pattern is in the sun and ring gear meshing. In the diagram of the circumferential distribution, the rolling bodies involved in the contact pattern can be seen.

To verify the calculations, a new test plan was drawn up for the main influencing factors. Factors which were not to be influenced (roller body profile) or only had a slight effect (tilt) were not taken into account. The test points were re-calculated for an accelerated test procedure and carried out on the test bench. The test transmission bearings were evaluated in the back-to-back test setup. The new calculation and test results were also included in the DoE analysis.

6 Results from the calculation process and the test

The objective of quantitatively proving the geometric influencing factors on the bearing life was achieved. The main influencing factors on the service life can be determined by calculation. The calculation process can be used to determine both the location of damage and the damage probability. Within the boundaries of the manufacturing tolerances we were able to determine a reduction in service life by 37% when very unfavorable parameters were selected. Under favorable conditions, an increase in service life of 74% can be expected. The results were determined for the load direction traction operation. At superposition of coast loads, the load reversal damages the opposite side of the bolt and does not influence these results.

The predictive graph (Fig.9) shows the influences of the parameters. Work points can be set with the help of the perpendicular dotted lines.

The predicted values are shown on the y-axis in Fig.9. The x-axis gives the factors with their value range. A large rising gradient indicates a large influence, a small rising gradient

indicates a smaller influence. However, these curves are only snapshots -when interactions are taken into account, the curve gradients can change dramatically, including from positive to negative. An interactive effect can clearly be seen in the predictive graph. The example of the parameters bolt position and misalignment shows that the influence of the bolt position is dependent on the factor misalignment. In the lower value range of the misalignment, the bolt position barely has an influence on the service life, while at the other end of the scale, the influence is much greater.

In the Pareto chart, the single and the interactive effects are evaluated. The influencing variables are shown as weighting factors on the target figure. The misalignment and the bearing clearance have the greatest influence on the service life. The inclination and the bolt pitch are shown to have little influence.

7 Summary

Calculation according to FEM can be carried out more quickly and with much more meaningful results by systematically using our own programs. Complex geometries such as gearings and bearings can be reliably processed using our own FE mesh programs for gearings and bearings. With the multitude of application fields, size-independent mesh strategies minimize the influences of the FE structure on the results. The results are also determined and interpreted according to standardized processes. This also significantly improves the meaningful quality and reproducibility. The necessary documentation chain facilitates the documentation of the initial data and results. Standardized processes also improve the reproducibility of provisions and results.

The simplifications achieved also make the use of other procedures such as DoE easier. The planning, procedure, and evaluation of large data volumes is possible. Simultaneously, the model quality and the procedures used are tested in terms of quality of results.

The influence of various factors (e.g. manufacturing deviations, micro-geometry, surrounding rigidity) can be systematically evaluated. Tolerance values can be determined and unnecessary production costs avoided.

The robustness of transmission systems can be determined. Factors with a high impact can be identified and influenced using suitable measures.

The most effective measures can be determined for optimizations (e.g. for an existing installationspace). That improves safety and reliability.

[1] PERMAS-User’s Reference Manual, INTES Publication #450, Rev. F, Stuttgart 2000.

[2] Heinz Linke: Stirnradverzahnung; Berechnung-Werkstoffe-Fertigung, Carl Hanser Verlag 2010.

[3] G. Niemann, H. Winter: Maschinenelemente Band 2; Getriebe allgemein, Zahnradgetriebe-Grundlagen, Stirnradgetriebe.

征稿啟事：

《傳動技術(shù)》是由上海交通大學(xué)和德國ZF集團(tuán)公司于1987年創(chuàng)刊合作創(chuàng)辦的一本技術(shù)性刊物。雜志主要面向有關(guān)航空、汽車、船舶、冶金礦山、石油、化工、農(nóng)機(jī)等從事傳動設(shè)備研究設(shè)計制造方面中、高級工程技術(shù)人員和有關(guān)大專院校師生。

為增加雜志的信息量，擬推出《市場動態(tài)》欄目，介紹傳動技術(shù)在上述領(lǐng)域中的發(fā)展趨勢、行業(yè)動態(tài)、市場預(yù)測、新產(chǎn)品介紹、新技術(shù)應(yīng)用等內(nèi)容，其中新產(chǎn)品介紹、新技術(shù)應(yīng)用等內(nèi)容的文章希望短小精干、圖文并茂。

Optimization of Gears and Bearings in Vehicle Transmissions by Means of FEMThomasMerath,JoachimNaas,Dr.FranzJoachim

ThomasMerath,JoachimNaas,Dr.FranzJoachimZF(China)InvestmentCo.,Ltd.

A large variety of gearings are developed and manufactured by the ZF Group. FEM is especially suitable for optimal, reliable gearing development. It can also easily be integrated into the ZF program landscape. This paper shows how the method can be used in the development process to optimize gearings. However, once again the strong interaction between gearing and bearing is repeatedly demonstrated. That is why ZF has also invested in the development of bearing calculations. We give an example of how rolling bearings can also be optimized for an ideal gearing contact pattern. Naturally, the methods can also be applied to running gears.

Transmission Gear Bearing FEM Optimization

1006-8244(2015)02-03-011

U463.212

A