降低變速器、車橋和轉(zhuǎn)向系統(tǒng)的功率損失（一）

Dr.F.－J.Joachim Dr.J.B?rner Dr.N.Kurz ZF Friedrichshafen AG

1 前言

目前整個汽車工業(yè)都在盡可能降低CO2排放。各種因素都會影響車輛降低CO2的排放，從發(fā)動機(jī)到空氣動力學(xué)、滾動阻力、輕量化設(shè)計(jì)、能量回收、熱管理以及混合動力和電動化。本文主要探討傳動系統(tǒng)和變速器機(jī)械系統(tǒng)優(yōu)化的可能性。傳動系統(tǒng)總機(jī)械效率建立在變矩器/離合器、主變速器和驅(qū)動橋的效率上，如圖1所示。

圓柱齒輪的99－99.8%效率已非常高。與之相比，由于存在更高的滑動摩擦圓錐齒輪和準(zhǔn)雙曲面齒輪的效率相對較低，圖2根據(jù)變速器的種類，其效率約為85－97%［1］。

1 Introduction

The entire motor vehicle industry is researching possibilities for the reduction of CO2emissions.Various factors are influencing the reduction of vehicle CO2emissions，from the engine to aerodynamics，rolling resistance，lightweight design，energy sources，and heat management，as well as hybridization and electrification.The following article mainly investigates the mechanical optimization possibilities of drivelines and transmissions.The overall mechanical efficiency of the driveline is made up of the efficiencies of the converter assem－bly/clutch，main transmission and axle drive，F(xiàn)ig.1.

圖1 車輛傳動系統(tǒng)效率Fig.1 Vehicle driveline efficiency

圖2 車輛變速器和車輛效率的參考值Fig.2 Reference values for the efficiencies of gears and vehicle transmissions

2 傳動系統(tǒng)的發(fā)展趨勢

根據(jù)文獻(xiàn)［2］所述，通過優(yōu)化傳動系統(tǒng)和底盤降低CO2排放的理論潛力約為60%。然而這是建立在一個幾乎沒有質(zhì)量和損失的傳動系統(tǒng)上。如圖3［2］所測試，在2011年的潛力約為30%。對變速器效率的影響在圖4中列出。這里必須在無負(fù)載和負(fù)載相關(guān)損失中作出選擇。目前主要關(guān)注于潤滑油優(yōu)化、降低攪油損失、優(yōu)化變矩器和油泵等。研究表明雙離合器變速器可采用干式離合器。

Spur gears alone already reach a very good efficiency of 99－99.8%.Bevel gears and，above all，hypoids in rear axle drives have a clearly lower efficiency，by contrast，because of their higher glide fractions，
Fig.2.According to the type of transmission，the efficiency is approx.85－97%［1］.

2 Development trends in drivelines

According to［2］，there is a theoretical potential for CO2emissions reduction by optimizing the driveline and chassis by approx.60%.This would，however，presume an unrealizable，nearly massless and loss－free driveline.With the measures in Fig.3 ，［2］demonstrates a potential for an increase of approx.30%by the year 2011.Influences on transmission efficiency are listed in Fig.4.It is necessary here to choose between noload and load－dependent losses.The activities currently concentrate on the optimization of lubricants，reduction of the churning losses，optimization of the torque converters and pumps.It is being investigated for dual clutch transmissions what torque values allow for a dry clutch.

圖3 傳動系統(tǒng)優(yōu)化的潛力和限制［2］Fig.3 Realizable potentials and limits of driveline optimization［2］

圖4 對變速器效率的影響Fig.4 Influencies on transmission efficiency

3 潤滑油的發(fā)展趨勢

近年來發(fā)動機(jī)和變速器技術(shù)發(fā)展迅速。新型變速器，例如DCT已投入批量生產(chǎn)?，F(xiàn)有種類的變速器在技術(shù)上也有改進(jìn)。集中在優(yōu)化換檔舒適性、效率和可靠性方面。這為用戶帶來效益：駕駛舒適性提高、油耗降低和車輛無需經(jīng)常維修。柴油機(jī)的發(fā)展對變速器影響深刻，因?yàn)檗D(zhuǎn)矩明顯增大。

圖5 ATF使用粘度對變速器牽引損失的影響Fig.5 Influence of the service viscosity（ATF）on the transmission drag losses

效率優(yōu)化的變速器潤滑油通常粘度低。在自動和手動變速器中使用該潤滑油可降低1%的油耗，見圖5.根據(jù)文獻(xiàn)［3］，在各種變速器中不同摩擦零部件的摩擦特性要求各異。自動變速器中的濕式多片離合器、DCT中的雙離合器、工程機(jī)械驅(qū)動橋中的濕式制動器以及手動變速器中的同步器等對變速器潤滑油的添加劑有著相當(dāng)離散的要求。例如對于濕式離合器而言，要求具有相當(dāng)高的靜態(tài)和準(zhǔn)靜態(tài)摩擦系數(shù)用于確保轉(zhuǎn)矩傳遞能力。這類要求通常與優(yōu)化動態(tài)摩擦系數(shù)相關(guān)，后者還與離合器和制動器降噪有關(guān)。因此對于濕式多片離合器，為降低尖叫聲，正摩擦系數(shù)在各種摩擦場合、變速器壽命周期和潤滑油全壽命中都必須盡可能的高?？篃幔趸芰κ亲兯倨鳚櫥偷囊粋€重要性能，并且由于能夠延長換油周期和密封變速器而變得更重要。未來粘度的降低受到限制，因?yàn)槟p和點(diǎn)蝕問題將顯現(xiàn)，同時還有油泵泄漏等問題。因此必須對所謂的“燃油效率潤滑油”的各種使用條件和影響因素進(jìn)行檢查。圖6顯示手動變速器采用低粘度潤滑油后抗點(diǎn)蝕性能有所下降。在今后該缺點(diǎn)可能通過合適的添加劑得以補(bǔ)償。

3 Trends in lubricant development

Engine and transmission technologies have developed rapidly in recent years.New transmission types，such as the dual clutch transmission，have gone into volume production.Existing transmission types were technically improved.Focus was placed on the optimization of shifting comfort，efficiency and reliability.This provided advantages for the customers：driving comfort improved，fuel consumption was reduced，and the vehicles did not have to go to the shop as frequently.Developments in engines have had the most influence on diesel engines in the capacity of the transmission，thanks to considerable increase in torque.

Efficiency－optimizing transmission oils mostly have lower viscosity.With automatic and manual transmissions，this reduces fuel consumption by up to 1%.，see Fig.5.According to［3］，demands on the friction performance in the various friction elements in the respective transmissions are very special.Thus wet multidisk clutches in automatic transmissions，dual clutches in DCTs，wet brakes in construction equipment axles，and synchronizations in manual transmissions have very defined demands placed on the additives in the transmission oil.The goals here are mostly high static and quasistatic friction coefficients for protecting the torque capacity of，for example，wet multidisk clutches.This demand is often in contrast to an optimal dynamic friction coefficient，which in turn is meant to help prevent noise when clutching and braking.Thus for wet multidisk clutches，in order to prevent squeaks a positive friction coefficient is required as much as possible for all conceivable states of friction and over the service life of the transmission，with lifetime lubrication.Thermo－oxidative ageing resistance is an important property of transmission oils，which are becoming increasingly important as a result of longer oil change intervals and sealed transmissions.Future viscosity reductions are limited because wear and pitting resistance became critical，also the leakage of pumps ect.so for so called”fuel efficiency lubricants”all criteria and influences have to be checked.Fig.6 shows that the pitting performance for low viscosity manual transmission fluids is reduced.Maybe this negative effect can be compensated by suitable additive systems in the future.

圖6 手動變速器采用低粘度潤滑油對齒輪點(diǎn)蝕耐久性的影響Fig.6 Gear pitting durability for a manual transmission oil with lower viscosity［3］

4 潤滑油性能試驗(yàn)

滲碳潤滑油的摩擦特性在潤滑油選擇和開發(fā)中扮演著一個重要角色。ZF公司開發(fā)了一項(xiàng)性能試驗(yàn)用于評估傳動系統(tǒng)的摩擦特性［7，11］。根據(jù)DIN 51354標(biāo)準(zhǔn)封閉式齒輪試驗(yàn)臺的中心距為91.5 mm。設(shè)計(jì)原理見圖7。與標(biāo)準(zhǔn)潤滑油試驗(yàn)相比，在效率試驗(yàn)中相同的試驗(yàn)齒輪被安裝在試驗(yàn)變速器和實(shí)際變速器中。高精度的動力測量組件安裝在驅(qū)動電機(jī)和變速器之間。這樣能夠在應(yīng)力循環(huán)中直接測量功率損失。該方法的測量精度遠(yuǎn)高于開式應(yīng)力循環(huán)試驗(yàn)（發(fā)動機(jī)－試驗(yàn)變速器－制動器）。

4 Lubricant efficiency testing

The frictional behavior of the carburized lubricants plays an important role in the selection of lubricant and the development of oil.A ZF efficiency test was developed for evaluating the frictional behavior of gearings［7，11］.A gear wheel foursquaretest rig in accordance with DIN 51354is used with a center distance of 91.5mm.The principle design is presented in Fig.7.In contrast to the standard oil test，in the efficiency test the same test gears are installed in the test transmission and the actual transmission.A highly precise power measurement hub is installed between the drive motor and the transmission.This makes it possible to directly measure the power loss introduced in the stress circuit.This approach is significantly more accurate than a measurement of performance difference in an open stress circuit（engine－test transmission－brake）.

圖7 有限功率損失和輪齒摩擦系數(shù)的車輛封閉試驗(yàn)臺（根據(jù)DIN 51354標(biāo)準(zhǔn)）Fig.7 Vehicle four－square test rig（in accordance with DIN 51354）for limiting the power loss and teeth friction coefficient

所使用的轉(zhuǎn)矩測量方法也適用于試驗(yàn)臺的不同中心距。這樣就能夠在實(shí)際運(yùn)行工況下研究批量生產(chǎn)的傳動裝置的摩擦特性。ZF效率試驗(yàn)采用標(biāo)準(zhǔn)的C型齒輪或者近似于批量生產(chǎn)的轎車變速器齒輪，見圖8。齒輪摩擦系數(shù)的測量在不同轉(zhuǎn)速和不同油底殼溫度下進(jìn)行。如果需要，試驗(yàn)條件包括圓周速度、表面應(yīng)力（轉(zhuǎn)矩）、潤滑油條件等均能直接調(diào)整以滿足特殊工況。在經(jīng)過一個低轉(zhuǎn)速和小轉(zhuǎn)矩運(yùn)行后，即可進(jìn)行實(shí)際功率損失PV和相應(yīng)的空載損失PW的測量。

Alternatively，the torque measurement method used can also be applied to a test rig with variable center distance.It is then possible to study the gearing friction behavior of volume－produced gearings under practical operating conditions.The ZF efficiency test employs the standard C gearing or，alternatively，apassenger car gearing that is close to volume production，F(xiàn)ig.8.The gear friction coefficients are determined at different rotation speeds and oil sump temperatures.If necessary，the test conditions－circumferential speed，surface stress（torque），lubrication conditions，etc.－can be adjusted directly to the values for each particular case.After phasing in with a low rotation speed and reduced torque，in the actual measuring run the total power loss PVand the corresponding idling power loss Pvoare determined.

圖8 ZF公司效率試驗(yàn)用試驗(yàn)齒輪Fig.8 Test gearings for the ZF efficiency test

總的功率損失包括以下各部分：

PV＝PVZP＋PVZ0＋PVLO＋PVLP＋PVD＋PVX

這里：

PV＝負(fù)載下的總功率損失，

PVZP＝與負(fù)載相關(guān)的傳動損失，

PVZ0＝與負(fù)載無關(guān)的傳動損失，

PVL0＝與負(fù)載無關(guān)的軸承損失，

PVLP＝與負(fù)載相關(guān)的軸承損失，

PVD＝密封損失，PVX＝其它損失。

與負(fù)載相關(guān)的軸承損失（PVLP）是根據(jù)軸承制造商所提供的手冊加以考慮的。在隨后進(jìn)行的齒輪摩擦系數(shù)計(jì)算中使用以下公式：

PVZP＝Pa＊μm＊HV，μm＝PVZP/Pa＊HV＝MVZP/T1＊HV

這里：

PVZP＝負(fù)載相關(guān)的傳動損失，

Pa＝輸入功率，

μm＝齒輪平均摩擦系數(shù)，

HV＝齒輪功耗因素＝f （齒輪形貌）［12，14］。

圖9顯示了在FZG試驗(yàn)臺上C型齒輪的功率損失測量值。從中可知，粘度低的潤滑油或同種潤滑油高油溫時的功率損失下降。圖10則顯示了一個潤滑油溫度影響的實(shí)例和潤滑油對齒輪摩擦系數(shù)的影響。摩擦系數(shù)隨油溫上升而下降。如果使用合成油，齒輪傳動的摩擦系數(shù)還能進(jìn)一步下降。圖11是齒側(cè)表面質(zhì)量對摩擦系數(shù)的影響。齒面摩擦隨表面精加工程度提高而降低。同樣，摩擦特性也受到齒側(cè)表面涂層的影響，見圖12。確定摩擦系數(shù)的方法源于大量的研究。由ZF齒輪效率試驗(yàn)確定的摩擦系數(shù)可精確地轉(zhuǎn)換為變速器的其它工況。

The total power loss is made up of the following components：

PV＝PVZP＋PVZ0＋PVLO＋PVLP＋PVD＋PVX

where

PV＝total power loss measured under load，

PVZP＝load－dependent gearing losses，

PVZ0＝load－independent gearing losses，

PVL0＝load－independent bearing losses，

PVLP＝load－dependent bearing losses，

PVD＝seal losses，PVX＝other losses.

The load－dependent bearing losses（PVLP）are accounted for according to the data provided by the bearing manufacturer in the relevant bearing catalogs.The back calculation of the gear friction coefficient is performed using the following equation：

PVZP＝Pa＊μm＊HV，μm＝PVZP/Pa＊HV＝MVZP/T1＊HV

where

PVZP＝load－dependent gearing loss，

Pa＝input power，

μm＝median gear friction coefficient，

圖9 在FZG試驗(yàn)臺上粘度和溫度對功率損失的影響Fig.9 Influence of viscosity and temperature on power losses in the FZG Test rig

圖10 潤滑油品種對齒輪摩擦的影響Fig.10 Influence of lubricant type on gearing friction

圖11 表面精加工對齒輪摩擦系數(shù)的影響（潤滑油：殼牌Spirax MA 80）Fig.11 Influence of surface finishing on gearing friction coefficient（oil：Shell Spirax MA 80）

HV＝gear loss factor＝f（gearing geometry）［12，14］.

圖12 表面涂層對齒輪摩擦系數(shù)的影響（潤滑油：半合成油GL4）Fig.12 Influence of a coating on the gearing friction coefficient（oil：semi－synthetic GL4）

Fig.9 shows the measured powerlosses in the FZG－test－rig with C－type gearing.You can see that powerlosses are reduced with lower viscosities of different lubricants or with higher oil temperatures of the same lubricants.Fig.10 shows an example of the influence of the oil temperature and the lubricant on the gearing friction coefficient.The friction coefficient tends to decrease with the oil temperature.With the use of synthetic lubricant，the gearing friction can be lowered as well.Fig.11 shows the influence of the surface quality of the gear flank on the friction coefficient.The gear friction can be reduced with surface finishing （super finishing）.The friction behavior can likewise be positively influenced by gear flank coating（here WC－C），F(xiàn)ig.12.The corresponding methods for determining the friction coefficient were derived on the basis of extensive investigations.It is thus possible to convert the friction coefficients determined in the ZF gearing efficiency test with good accuracy to other operating conditions in transmissions.

5 Calculation of gear losses

Simple formulations for the calculation of gearing power losses，such as the loss factor HV［12，14］，are based on an assumed load distribution dependent on the number of meshing teeth.The calculation of gearing power losses can be improved if load distribution in the area of contact is considered，which the LVR［13］program does.This load distribution is usually determined on the basis of deformation influencing variables with a system of equations for the sum of forces in the plane of action.Determination of losses also requires consideration of the frictional forces acting at right angles to the plane of action，for the purpose of which the system of equations for the balance of torques on the driving gear needs to be formed and resolved.The torque resulting on the output is determined on the basis of the calculated distribution of normal and frictional forces，and the torque loss follows from the difference compared to the nominal output torque.The lever arm of the friction－induced torque changes with the distance from the pitch point.The frictional forces are defined as a product of vertical force and coefficient of friction.The coefficient of friction changes via gear engagement as a result of changing sliding conditions and oil viscosities whose action depend on the oil temperature in the area of tooth contact.A constant average coefficient of friction can be used for a sufficiently precise solution because the coefficient of friction does not vary significantly.The relative torque balance loss Vcan be calculated for any point on the line of contact with the following equation［2］：

TV2—torque loss on driven gear 2；

TN2—nominal torque on driven gear 2；

rb—base－circle radius；

αw—service pressure angle；

βb—base helix angle；

μ—coefficient of friction；

ζ—distance from pitch point。

The losses increase with increasing helix angle because the torque－producing tangential force on the base circle grows smaller than the tooth normal force which produces the friction.Assuming constant values for center distance and transverse contact ratio，the losses decrease with increasing ratio because the frictional force torque on the driven gear grows smaller compared to the nominal torque as a result of the greater basecircle radius.If the number of teeth is increased，the same effect occurs on both gears.Fig.13 shows the relative losses as they depend on the distance from the pitch point per base－circle radius at various ratios i for a friction coefficientμ＝0.05and a base helix angleβb＝30°.Also shown are the limits of the transverse path of contact with a transverse contact ratio ＝1.5for z1＝12，24and 48.Reducing the distance of start and end of tooth contact from pitch point is the most effective measure to reduce power losses by changing tooth geometry.This goal can be achieved with reduced tooth height or increased operating pressure angle.A reduced tooth height is possible with lower tooth addendum as well as lower module with increased number of teeth.The use of lower module leads to larger overlap ratios which enable less noise excitation but root stresses increase simultaneously due to smaller cross sections.The potential of reducing losses by changing tooth geometry is shown in Fig.14.The way of reducing addendum and the option of increasing number of teeth is used with some examples starting from variant A.The operating pressure angle was increased additionally at some side steps.Increasing the number of teeth is most effective.Reduced addendum and increased operating pressure angle have less influence.Traces of noise excitation level versus load range of 10to 100%of nominal load are plotted in Fig.15 for some examples from Fig.14.Differences are clearly visible and they have to be considered in optimizing gears for low power loss.Improvements can be achieved with adjusted tooth modifications in doing so.Maximum stresses in case of nominal load are shown in Fig.16.Hertzian pressure is nearly constant for all variants.A distinctive increase of root stresses appears over decreasing loss factor from variant A to H.So an inadequate load－carrying capacity can be a result of minimizing power losses by changing tooth geometry.Finally the load distribution along the line of action is also influencing the level of power losses.Tooth loads at begin and end of contact can be reduced by increased tip relief，which decreases their large proportion to overall power loss as shown in Fig.17.Means of relieving start and end of contact for increased load－carrying capacity are also helpful for minimizing power losses of meshing gears.

5 計(jì)算齒輪損失

簡單計(jì)算傳動功率損失的公式如功耗因素HV［12，14］是建立在根據(jù)嚙合齒數(shù)決定載荷分布的基礎(chǔ)上。如果利用LVR［13］程序求出接觸區(qū)域內(nèi)的載荷分布，那么就能改進(jìn)傳動功率損失的計(jì)算方法。載荷分布通常由基礎(chǔ)變形所確定，該變形的各項(xiàng)變量由嚙合面上總作用力的方程給出。確定損失也需要考慮垂直作用在嚙合面上的摩擦力，因此為平衡主動齒輪的轉(zhuǎn)矩該方程必須可求解。輸出端的轉(zhuǎn)矩根據(jù)法向力和摩擦力計(jì)算得到，而轉(zhuǎn)矩?fù)p失則通過比較與額定輸出轉(zhuǎn)矩之間的差異而確定。生產(chǎn)摩擦轉(zhuǎn)矩的杠桿臂長隨嚙合點(diǎn)變化。摩擦力被定義成垂直力和摩擦系數(shù)的乘積。摩擦系數(shù)的變化取決于齒輪嚙合時的滑動狀況和潤滑油粘度，而后者則取決于嚙合區(qū)域的油溫。由于摩擦系數(shù)變化不大，因此可用一個常數(shù)均值表示，并且具有足夠高的精度。下式可用于計(jì)算轉(zhuǎn)矩?fù)p失［2］：

TV2—主動齒輪2上的轉(zhuǎn)矩?fù)p失；

TN2—作用在主動齒輪2上的名義轉(zhuǎn)矩；

rb—基圓直徑；

αw—壓力角；

βb—基圓螺旋角；

μ—摩擦系數(shù)；

ζ—距嚙合點(diǎn)的距離。

圖13 在接觸區(qū)輪齒摩擦造成的齒輪損失Fig.13 Relative gear loss resulting from tooth friction on the path of contact

損失隨螺旋角增大而增大，因?yàn)榛鶊A處轉(zhuǎn)矩所產(chǎn)生的切向力的增長小于產(chǎn)生摩擦力的輪齒所受的法向力。假設(shè)中心距和端面重合度不變，損失隨重合度增加而減小。因?yàn)樽饔迷趶膭虞喩系哪Σ赁D(zhuǎn)矩的增加小于額定轉(zhuǎn)矩的增加，這是由于基圓半徑更大的緣故。如果嚙合齒數(shù)增加，其效果相同。圖13表明不同速比、摩擦系數(shù)μ＝0.05和螺旋角βb＝30°的情況下，相對損失與基圓半徑到嚙合區(qū)距離相關(guān)。圖13還表明了在端面重合度為1.5和z1＝12、24、48時的端面嚙合線的限制值。

通過改變齒形以減少進(jìn)入和脫離嚙合距離能夠明顯降低功率損失。該方法可通過降低齒高或增大壓力角獲得。降低齒高的手段有降低齒頂高和采用小模數(shù)齒輪以增加齒數(shù)。減小模數(shù)將提高重迭程度，這能夠降低噪聲，但是齒根處應(yīng)力顯著增加，因?yàn)樵撎帣M截面變小。圖14給出了改變齒形降低損失的潛力。減小齒高和增加齒數(shù)的實(shí)例見變量A。增大壓力角也體現(xiàn)在該處。增加齒數(shù)非常有效。減小齒高和增大壓力角的效果較差。從10%到100%載荷時的噪聲水平線見圖15。其差別非常明顯，因此必須優(yōu)化齒輪副以降低功率損失。調(diào)整齒輪修型可實(shí)現(xiàn)該目標(biāo)。額定負(fù)荷下的最大應(yīng)力見圖16。接觸應(yīng)力在各種情況下基本保持恒定。齒根應(yīng)力隨著各種降低損失措施從變量A到變量H增加明顯。因此通過改變齒形以降低承載能力為代價是能夠?qū)⒐β蕮p失降至最小。最后，負(fù)荷沿嚙合線的分布狀況也影響功率損失的水平。增加齒端修緣能夠降低進(jìn)入嚙合和脫開嚙合時的輪齒載荷，齒端修緣能夠大幅降低功率損失，詳見圖17。緩解開始和退出嚙合以提高承載能力的措施引入有助于降低嚙合齒輪的功率損失。

圖14 不同齒輪副的Hv幾何參數(shù)Fig.14 Geometric loss factor Hvfor different gearings

圖15 圖14不同齒輪副的噪聲水平LAFig.15 Excitation Level LAfor different gear sets from Fig.14

圖16 計(jì)算圖14各齒輪副小齒輪的根部應(yīng)力和齒側(cè)壓力Fig.16 Calculated pinion root stresses and flank pressures for gear sets from Fig.14