附 錄 A ABSTRACT High clamping force levels reduce the efficiency of the Continuously Variable Transmission (CVT). However, high clamping force levels are necessary to prevent slip between the belt and the pulleys. If a small amount of slip is allowed, the clamping force level can be reduced. To achieve this, slip in a CVT is investigated. From measurements on an experimental setup, Traction curve data and efficiency measurements are derived. A model describing slip in a CVT is verified using measurements with a belt with increased play. It is found that small amounts of slip can be controlled in a stable way on the setup. The traction curve was mostly dependent on the CVT ratio. Efficiency is found to be highest for 1 to 2% slip depending on the ratio. The model is in reasonable agreement with the measurements. 1. Introduction Applying a Continuously Variable Transmission (CVT) in an automotive driveline has several advantages. A CVT can operate at a wider range of transmission ratios, therefore the engine can be operated more efficiently than with a stepped transmission. Also, a CVT does not interrupt the torque transmission when shifting. This gives a more smooth ride than a stepped transmission does. A V-belt based Continuously Variable Transmission uses a belt or a chain to transmit torque from a driving side to a driven side by means of friction. The layout of the CVT and the V-belt are shown in figure 1. The variator consists of two pulleys which are wedge shaped. By changing the position of the pulleysheaves the ratio of the CVT can be adjusted. The V-belt consists of blocks which are held together by two rings that in turn exist of a set of bands. To achieve torque transmission sufficiently high clamping force levels are needed to prevent slip in the variator. Because the torque level is not exactly known at all times, since no torque sensor is used due to cost considerations, a safe clamping force level based on the maximum possible load is maintained at all times. This safety level is based upon assumed maximum shockload levels from the road, like bumps, and the engine torque. In order to maintain these safety levels higher clamping force levels are maintained then needed. Higher clamping force levels cause more losses in the CVT. These losses are caused by increases in power consumed by the hydraulic pump, by increases in the losses due to slip in the belt if a pushbelt is used, and by increases in deformation in the belt and in the pulleys. Furthermore wear is increased and fatigue life is reduced. In order to reduce these clamping force levels a method is needed to detect slip in the variator fast enough to prevent slip from reaching destructive levels. A method to detect and control slip is therefore needed. In this paper measurements are presented of the traction curve in a V-belt CVT. Figure 1. Layout of a CVT and a metal pushbelt 2. Traction curve The V-belt type CVT utilizes friction to transmit power from the primary pulley to the secondary pulley. The traction curve is the dimensionless relationship between transmitted torque and the slip. The maximum input torque that can be transmitted by the CVT is dependent on the applied clamping force. The traction coefficient is therefore chosen to be a dimensionless value. The traction coefficient is defined as: SSq RFT2 cos （ 1） In which qT represents the input torque, SR represents the secondary running radius of the belt on the pulley, SF represents the secondary clamping force and is the pulley wedge angle. Figure 2. CVT torque transmission scheme The second variable in the traction curve is the slip in the variator. Slip is defined as: 10 rPS （ 2） Where s is the angular speed of the secondary axle, p is the angular speed of the primary axle and 0r is the geometrical ratio, which is defined by: SPRRr 0 （ 3） PR is the running radius on the primary pulley. 2.1 Tangential slip Slip is defined in equation 2. When the CVT transmits power a certain amount of slip can be measured almost linear with the applied torque. This is called the microslip regime of the CVT, because traction is still increasing in this regime with increasing slip. The microslip is caused by gaps between the blocks on the idle part of the driving pulley as shown in figure 3. On the driving pulley an idle arc exists where no slip occurs. Also an active arc exists (see figure 2), where slip occurs relative to the total play in the belt and the active arc length. However, when the maximum torque capacity of the CVT is reached slip will increase dramatically. This situation, macroslip, is not stable during normal operation of the CVT, because the traction coefficient decreases with increased slipspeed. It is assumed that the total gap dt is evenly distributed along the idle arc of the driving pulley. The traction Figure 3. Gaps in the belt curve (figure 5) shows that torque transmission increases almost linearly with an increase in slip, until a certain maximum torque is reached. dt can be estimated by adding an initial gap do to the increase in belt length due to the internal stresses in the bands and a decrease in length of the blocks due to the compressive forces. dLt 0 （ 4） To calculate the slip caused by these gaps we can use the following equations: dRdtpstm （ 5） mmdv （ 6） In equation 5, a is the idle arc, d is the width of a belt element and dt is the total gap between the elements in the belt. To calculate the amount of slip the total gap dt has to be known. This effect has an influence on the traction coefficient in the macroslip regime. When macroslip occurs the traction will decrease with increasing slip. The Stribeck effect is modelled using equation 9. vcf 0 （ 7） 1210 vveaag （ 8） fgvv )sin( （ 9） Equation 7 gives a value for the friction caused by viscous friction component. Equation 8 gives a value for the coulomb friction component. a0,1, c0 and v1 are coefficients which can be chosen to match the measured values. With these equations we can derive slip and traction from measured data as shown in section 4. With Asayama 1995 we can obtain the tension and compression force distribution needed to calculate the lengthening of the belt. Also, we can calculate the idle arc from this model. From the idle arc, the length of the belt and the initial gap we can calculate an estimate for slip in the belt for a given load. 2.2 Radial slip Not only slip in tangential direction occurs, but also slip in radial direction. The first reason for radial slip is spiral running. When the belt runs along the arc of contact the radius at which it runs is not constant. This effect is caused by pulley deformation. One type of deformation is the bending of the axle between both pulley sheaves. The belt is not fully wrapped around the pulley, therefore the resulting normal force of the blocks on the pulley is not axial. This causes a bending moment in the axle. A second effect is the bending of the pulley itself. This effect is mostly dependent on the local normal force exerted on the pulley by the blocks. This effect is small when the belt is running on a small running radius, but on a large running radius this effect is significant. The second reason for slip in radial direction is due to shifting. When the CVT is shifted to a different transmission ratio, radial slip is forced. This is done by changing the clamping force ratio. The amount of radial slip that is forced depends on the shifting speed and the (primary) angular speed. 3. Experimental setup In the experiments the geometric cvt ratio is fixed and the clamping forces are constant, the traction coefficient then depends only on the slip in the system. The traction curve can be constructed from output torque and slip measurements. The test rig motors deliver a maximum torque of 298 Nm with a maximum speed of 525 rad/s. Both motors are equipped with a Heidenhain ERN1381 incremental rotary encoder with 2048 pulses/rev. The torque at both sides is measured using a HBM T20WN torque sensor. The maximum allowable torque is 200 Nm with speeds up to 1050 rad/s. A separate hydraulic unit is used to provide the required flow and pressure for the clamping forces. Figure 4 gives a schematic overview of the experimental setup. 4. Experimental results The geometric ratio of the CVT was fixed during the experiments using a so-called ratio ring and the limits of the primary pulley. This ratio ring limit the movement of the pulley. Primary and secondary pressure was held constant (clamping forces were held constant) during the experiments. Figure 4. Experimental setup 4.1 Traction coefficient The traction coefficient was measured at different ratios, at different primary speeds and at different pressures. In figure 6 and 7 can be seen that the traction coefficient depends little on primary speed or secondary clamping pressure, but mostly on the transmission ratio, as can be seen in figure 5. An increase in clamping force causes more slip (see figure 8). This is caused by an increase in tension in the bands and therefore in an increase in length of the belt. This causes the play to increase. Figure 5. Traction coefficient at 300rad/s, ratio low(0.4), Medium (1.1) and overdrive (2.26) 4.2 Efficiency The efficiency depends on pressure and on ratio. From figure 12 can be seen that an increase in pressure causes a decrease in efficiency. This effect is caused by the internal friction in the belt. Slip between the blocks and the bands also causes a strong dependency on ratio (see figure 9). Efficiency is clearly higher in medium than in overdrive or low. In medium no slip occurs between the blocks and the bands, but in overdrive or low the bands slip over the blocks. At high clamping levels this effect is greater, because the normal forces acting between the blocks and the bands increase linearly with an increase in clamping level. From figure 10 and 11 can be seen that input speed also has an influence on efficiency. Figure 6. Traction coefficient in overdrive, ws = 150,225,300 Figure 7. Traction coefficient in low, wp =150,225,300 Figure 8. Traction coefficient for resp. 5bar and 8bar secondary clamping pressure From figure 10 and 11 can be seen that input speed also has an influence on efficiency. 4.3 Play The microslip region is dependent on play in the belt. An experiment has been carried out with a belt with increased play. One block was taken out of the belt. The performance of the belt was measured with a total gap of 1.8mm. The cumulative gap in the belt was 0.3mm in the other experiments. A significant difference is measured in the LOW ratio of the CVT. In figure 4.3 the traction curve is shown for the low ratio of the CVT for the belt with increased play. Also the result of the numerical model is shown in figure 4.3. The results for overdrive show that in overdrive there is no significant change in the traction curve, see figure 4.3. However, the model is less consistent with the tractioncurve in overdrive than in low. Figure 9. Efficiency at 300rad/s, ratio low(0.4), Medium (1.1) and overdrive (2.26) Figure 10. Efficiency in overdrive, ws =150,225,300 Figure 11. Efficiency in low, PW = 150,225,300 Figure 12. Traction coefficient for resp. 5bar and 8bar secondary clamping pressure Figure 13. Effect of play in the belt, wp = 30rad/s, in low, with increased gap (1.8mm) Figure 14. Effect of play in the belt, wp = 30rad/s, in overdrive, with increased gap (1.8mm) 5. Conclusion The traction curve is mostly ratio dependent. This can be explained with the shown model as explained in section 4. Transmission efficiency is dependent on applied pressure, input speed and the CVT ratio. Gaps between the blocks of the belt cause at least part of the tangential slip of the belt. This was confirmed by the experiment with increased play in the belt. The consistency of the model is better in low than in overdrive. Future research will be directed at controlling slip in the CVT. This can enhance the efficiency of the CVT. 附 錄 B 各級(jí)高夾緊力降低了無(wú)級(jí)變速器（ CVT）的效率。然而，各級(jí)高夾緊力之間的必要措施，防止金屬帶和滑輪滑。如果滑少量是允許的，夾緊力水平可以降低。要做到這一點(diǎn)，在無(wú)級(jí)變速器滑動(dòng)進(jìn)行了研究。從上一個(gè)實(shí)驗(yàn)裝置測(cè)量，牽引效率測(cè)量數(shù)據(jù)和曲線推導(dǎo)。一個(gè)模型描述無(wú)級(jí)變速器滑動(dòng)驗(yàn)證使用具有增加播放帶測(cè)量。研究發(fā)現(xiàn)，少量的滑可在道路上設(shè)置穩(wěn)定控制。牽引曲線主要是依賴于CVT的比率。效率是發(fā)現(xiàn) 1至 2的最高比例滑倒而定，該模型與測(cè)量合理的協(xié)議。 1. 簡(jiǎn)介 應(yīng)用在汽車(chē)傳動(dòng)系統(tǒng)無(wú)級(jí)變速器（ CVT）有幾個(gè)優(yōu)點(diǎn)。無(wú)級(jí)變速器可以工作在更廣泛的傳動(dòng)比，因此該引擎可以使用，其傳輸效率比階梯。另外， CVT 的不中斷換擋時(shí)的扭矩傳遞。這給出了一個(gè)比一個(gè)更平穩(wěn)的傳輸并加強(qiáng)。阿 V 帶無(wú)級(jí)變速器的使用金屬帶或鏈條傳送通過(guò)摩擦意味著從驅(qū)動(dòng)側(cè)的扭矩到從動(dòng)側(cè)。該無(wú)級(jí)變速器和 V帶的布局見(jiàn)圖 1。該變速器由兩個(gè)滑輪是楔形。通過(guò)改變位置的 CVT的比例可以調(diào)整。 V型帶，其中包括分別由兩個(gè)環(huán)一起，在樂(lè)隊(duì)依次設(shè)置 存在的塊。為了實(shí)現(xiàn)足夠高的扭矩傳遞夾緊力水平是需要防止變速器滑。由于轉(zhuǎn)矩是不完全知道在任何時(shí)候，因?yàn)闆](méi)有采用扭矩傳感器由于成本的考慮，一個(gè)安全級(jí)別夾緊力最大的可能是維持負(fù)載為基礎(chǔ)在任何時(shí)候。這是基于安全等級(jí)最高的假定像顛簸道路上，和發(fā)動(dòng)機(jī)扭矩水平。為了保持這些安全級(jí)別較高的夾緊力水平維持不變，然后需要。夾緊力水平造成的 CVT 更多的損失。這些損失是由由液壓泵消耗功率提高造成的損失中帶滑，如果在一個(gè)帶使用的增加，并在帶變形和滑輪增加。此外磨損增大，疲勞壽命降低。為了減少這些夾緊力的方法檢測(cè)，需要足夠快的變速器， 防止破壞性的水平失誤達(dá)到的水平。一個(gè)方法來(lái)檢測(cè)和控制，因此需要滑。本文介紹了測(cè)量中的 V帶無(wú)級(jí)變速牽引曲線。 圖 1 金屬帶式無(wú)級(jí)變速器布置 2. 牽引曲線 V型帶式無(wú)級(jí)變速器采用了摩擦，從主滑輪傳送到輔助電源滑輪。牽引曲線之間傳遞扭矩和滑量綱關(guān)系。最大輸入扭矩，可以通過(guò)發(fā)送的 CVT 的夾緊力的應(yīng)用而定。牽引系數(shù)因此選擇是一個(gè)無(wú)量綱值。牽引系數(shù)的定義為： SSq RFT2 cos （ 1） 其中表示輸入扭矩，代表著對(duì)金屬帶輪二次運(yùn)行半徑，代表了二次夾緊力，是滑輪楔角。 圖 2 CVT的扭矩傳輸方案 牽引曲線中的第二個(gè)變量是在變速器滑移。 滑移的定義為： 10 rPS （ 2） s是次要軸角速度，p是主軸 角速度，0r是幾何比例，將其定義為： SPRRr 0 （ 3） PR 正在運(yùn)行的主滑輪半徑。 2.1 切向滑移 滑移是指在公式 2。當(dāng)無(wú)級(jí)變速器傳遞動(dòng)力滑移一定量的可測(cè)與施加的扭矩幾乎呈線性關(guān)系。這就是所謂的 CVT的 microslip政權(quán)，因?yàn)樵诖藸恳噪S滑移區(qū)增加。該 microslip 是由塊之間的間隙對(duì)傳動(dòng)滾筒閑置部分，如圖 3 所示。在主動(dòng)輪弧存在其中一個(gè)空閑無(wú)滑移發(fā)生。也是一個(gè)積極的弧存在（參見(jiàn)圖 2），其中發(fā)生相對(duì)滑移，在帶和總發(fā)揮積極的弧長(zhǎng)。然而，當(dāng) CVT 的最大扭矩達(dá)到防滑能力將顯著增加。這種情況， macroslip，是不是在本無(wú)級(jí)變速器的正常運(yùn)行穩(wěn)定，因?yàn)闋恳禂?shù)降低與增加滑移率。據(jù)推測(cè)，總差距是均勻分布在主動(dòng)輪的閑置弧線處。牽引曲線（圖 5）顯示，傳遞扭矩增大幾乎呈線性增加，在滑動(dòng)，直到達(dá)到一定的最大扭矩。t可以通過(guò)添加一個(gè)初始間隙做了帶長(zhǎng)度的增加，估 計(jì)由于內(nèi)部應(yīng)力的樂(lè)隊(duì)，并在適當(dāng)?shù)膲K長(zhǎng)度的壓縮力下降。 dLt 0 （ 4） 圖 3 空白帶 計(jì)算的滑動(dòng)造成這些差距的原因我們可以用以下的方程 : dRdtpstm （ 5） mmdv （ 6） 公式 5是一個(gè)空閑的弧線， D是一個(gè)帶元素的寬度和t是在金屬帶之間的元素的總差距。要計(jì)算總的差距滑t的金額為已知。這種效應(yīng)有一個(gè)關(guān)于在宏觀滑移政權(quán)牽引系數(shù)的影響。當(dāng)宏觀滑移發(fā)生的牽引滑移的增加會(huì)降低。效果是模仿的摩擦模型使用公式 9。 vcf 0 （ 7） 1210 vveaag （ 8） fgvv )sin( （ 9） 公式 7給出了由粘性摩擦元件所造成的摩擦系數(shù)。公式 8給出了庫(kù)倫摩擦組件的值。 0a 為 1， 0c 和 1 的是可以選擇匹配的測(cè)量值系數(shù)。有了這些方程，我們可以從測(cè)量數(shù)據(jù)下滑牽引，在圖 4所示，我們可以得到的張力和壓縮力分布計(jì)算所需的金屬帶延長(zhǎng)。另外，我們可以從這個(gè)模型計(jì)算出空閑的弧線。從閑置的弧線，金屬帶的長(zhǎng)度和初始差距，我們可以計(jì)算出在金屬帶承保給定負(fù)載的估計(jì)。 2.2 徑向滑動(dòng) 不僅在切線方向發(fā)生滑動(dòng)，而且滑徑向方向。對(duì)于第一個(gè)原因是徑向滑動(dòng)螺 旋運(yùn)行。當(dāng)沿帶的接觸半徑，在它運(yùn)行的弧線運(yùn)行的不是恒定的。這種效應(yīng)是由滑輪變形。一類是變 形的兩滑輪軸彎曲。金屬帶是不完全的滑輪包左右，因此導(dǎo)致正常的區(qū)塊隊(duì)在滑輪是不是軸向，這會(huì)導(dǎo)致軸彎矩。 第二個(gè)效應(yīng)是金屬帶輪本身彎曲。這種影響主要是對(duì)當(dāng)?shù)卣５挠?