04CVT-10 Development of 3-D simulation for power transmitting analysis of CVT driven by dry hybrid V-belt Masahide Fujita Hisayasu Murakami Power Train Research and Development Division, Daihatsu Motor CO., LTD. Shigeki Okuno Mitsuhiko Takahashi Power Transmission Technical Research Center, Bando Chemical Industries, LTD. Copyright © 2004 SAE International ABSTRACT A new CVT system driven by a dry hybrid V-belt having a higher transmitting capacity has been investigated for small cars. This paper reports dynamic FEM analysis of the CVT, simulating transmitting efficiency and dynamic strain acting on the belt running at high speeds. We constructed 3-dimensional models for both belt and pulley assembly. It is demonstrated that pulley rigidity and clearance between pulley shaft and movable pulley significantly affect the power transmitting efficiency of the system. Dimensional change of the belt due to permanent deformation of the rubber material also affects the efficiency at high-speed range at the end of belt life. The dynamic strain obtained by the FEM simulated life of the belt in a bench test successfully. INTRODUCTION Continuously variable transmissions (CVT) are increasingly utilized in automobiles aiming reduction in fuel consumption. In some CVT systems V-belts are used to transmit engine power. V-belts for CVT are roughly categorized into two types: metal V-belts in wet CVT and hybrid V-belts in dry CVT. Advantage of the metal V-belt is its large transmitting torque capacity. Recently, metal V-belts are used in large vehicles with engine volume of 3000 cm3 and more. 1) On the other hand, the dry hybrid V-belt has an advantageous feature of its excellent power transmitting efficiency in small cars, which results reduction of fuel consumption. Some disadvantages of the dry hybrid Vbelt include smaller torque capacity, reliability of the component polymeric materials and operating noise. A new CVT system overcoming the drawbacks has been investigated. The new system with improved torque capacity is equipped with a wider hybrid V-belt and an additional pulley that controlls the belt tension. This paper concerns simulations of dynamic behaviors of the new system such as transmitting efficiency, torque capacity and dynamic strain acting on the components of the belt running at high speeds. The dynamic strain can be used to predict belt life. For these purposes 3dimensional dynamic FEM analyses are performed. The chosen FEM code is PAM-MEDYSA(formerly PAMSHOCK), which has been used in analyses of metal Vbelts. 2) This software has some advanced features in dynamic CVT system simulation: 1. The effect of inertia of an object moving at high speeds can be considered. 2. Frictional contacts between belts and pulleys can be analyzed. 3. Dynamic movements of the belt components and pulleys can be visualized. The hybrid structure of the belt is carefully modeled, and the effect of dimensional change of the belt on its dynamic behaviors will be examined. Besides of the model of the hybrid belt, modeling of a movable pulley is very important. Many articles3)-5) have reported that pulley rigidity and clearance between a pulley shaft and a movable pulley greatly affect the system efficiency, belt strength and the variable-speed response. In this point of view, the rigidity and the clearance of the pulley shaft are also taken into account in the 3-D FE model. STRUCTURE OF A NEW CVT SYSTEM EQUIPPED WITH DRY HYBRID V-BELT . DRY HYBRID V-BELT Figure 1 shows a dry hybrid V-belt assembly. The belt has a structure of a pair of tension bands inserted in many H-shaped blocks. The core of the block is made of high strength aluminum alloys supporting a high transverse load from pulleys. The core aluminum alloy is covered with phenol resin giving the blocks a proper frictional coefficient with the pulleys. No lubrication is necessary because of a high frictional coefficient, which realizes an excellent transmitting efficiency in the CVT system. Aramid cords supporting belt tension lies at the center of the tension bands. Heat-resisting rubber material made of hydrogenated nitrile rubber (HNBR) surrounds the aramid cords. The surface of the tension band is reinforced by fabrics preventing crack initiation and enhancing abrasion resistance of the tension band. transmission. The contact angle of 172 degree for the new system at the driving pulley theoretically increases the torque capacity by 40% in comparison to the conventional system having the corresponding angle of 154 degree. The tension pulley, however, imposes additional reverse bending force to the belt. This reverse bending force may shorten the belt life. DYNAMIC SIMULATION OF POWER TRANSMISSION WITH FEM Block Tension band MODELING OF THE CVT SYSTEM Modeling of the dry hybrid V-belt Cord Rubber Inserted Fig.1 Structure of dry hybrid V-belt The FEM model of the belt is depicted in Figure 3. The H-shaped block was modeled as an aluminum core covered with resin. An assignment of the actual elastic moduli for the aluminum and the resin realizes the actual rigidities of the upper and the lower beam of the block in the model. The boundary between blocks and the tension bands defined as contacting surfaces at a properly assigned frictional coefficient. DRY CVT SYSTEM WITH A TENSION PULLEY Commercially available CVTs with dry hybrid V-belts include two V-pulleys, a driving and a driven pulley. Pulley thrust is applied by spring and torque cam at driven pulley. The applied thrust is converted to a belt tension ensuring power transmission without slippage. On the other hand, our new CVT system is equipped with an additional tension pulley at the slack side of the belt span, as shown in Figure2. Driving Pulley Tension Pulley Driven Pulley Pulley movement at shift down Fig. 2 Structure of a new CVT with a dry hybrid belt System The tension pulley control the belt tension directly to a desirable level, which improves transmitting efficiency of the system. Moreover, the rate of shifting ratio becomes faster since the axial movements of the driving and the driven pulley are linked by gears, accomplishing a better driving response. Another feature of the new system is a higher torque capacity over the commercially available systems. This is a simple consequence of larger contact angles of the belt with the driving and the driven pulley at the presence of the tension pulley. The increase in torque capacity with increasing contact angle can be theoretically calculated with Euler’s equation for power Block Resin Aluminum Rubber Upper beam Lower beam Cord (Membrane) Tension band Fig.3 FEM model of the belt The tension bands are modeled as a cord material surrounded by a rubber material. Both the cord and the rubber have anisotropic elastic moduli; the cord has a higher modulus in the longitudinal direction, whereas the short-fiber-reinforced rubber has a higher modulus in the direction of belt width. In order to express this anisotropy, membrane elements with proper elastic moduli were used for the cord and the rubber material. Modeling of pulleys Modeling of pulley as an elastic body As mentioned earlier, pulley rigidity greatly affects the dynamic behavior of the system. The pulley rigidity is related to the deformation of the pulley by an action of pulley thrust. The deformation of the pulley results in variation of V-angle and contact conditions with the belt. Such variation in the contact condition greatly affects the dynamic behavior of the belt. Experimental results confirmed that a difference in V-angle of the belt and pulley greatly influences the torque capacity and heat build-up in the belt. Therefore, as a first approximation, the pulleys are modeled as elastic bodies to simulate the deformation of the pulleys and the resultant variation in the contact condition with the belt. COMPARISON OF CALCULATIONS WITH EXPERIMENTAL RESULTS Modeling of the elastic pulley with shaft clearance In a bench test of the belt, a torque capacity was determined as a torque at the onset of belt slip. The onset of the belt slip was detected as a sudden variation in pulley ratio. Under the same condition, the calculation was performed, and the belt slip was detected in the same way. In Table 1 the results of calculations at different radii of driving pulleys at ratio of 1 were compared with the experimental results. Since the bench tests were performed with fixed V-pulley, the calculations were also performed with an elastic-body model of the pulleys without any shaft clearance. The calculation was consistent with the experimental results, confirming the calculated force balance in the transmission state successfully simulates the actual situation. In a scope that the clearance between the pulley shaft and movable pulley predominantly affects the rigidity of the pulley, the clearance was also taken into account in a modified model shown in Figure 4. Fixed pulley Movable pulley Movable pulley boss and sliding key TORQUE CAPACITY Table 1. Comparison of calculated torque capacities with experimental results (Shaft load: 3900N, Pulley ratio:1) Resin bush Fixed pulley shaft Fig. 4 Modified model for elastic pulley with shaft clearance Driving pulley radius(mm) 59.2 32.75 Experimental (Nm) 190 89 Calculated (Nm) 192 92 CALCULATION PROCEDURES TRANSMITTING EFFICIENCY The procedures of dynamic simulations with software “PAM-MEDYSA” were schematically shown in Figure 5. Calculations using elastic-body models of pulleys ③driven torque ①move the pulley center initial state belt set ②driving pulley rotation power transmitting Fig. 5 Calculation procedures First, the belt has a circular shape without any applied stress. Then, it was placed on the pulleys by moving the driving pulley outwards. Subsequently, a rotation of the driving pulley is applied, which was followed by imposing driven torque at the driven pulley. Balance of kinetic forces in power-transmission state was calculated with respect of time. Therefore, the calculations take a long time with the elastic-body models. In order to shorten the simulation time, the calculations were performed by using rigid-body models under transient conditions. The models were replaced with elastic models after reaching steady-state power transmission. Furthermore, calculations at different operating conditions were performed using “restart” function of the software for models with identical dimensions. In Figure 6, the calculated transmitting efficiencies at different belt velocities were compared with corresponding experimental results in the CVT unit having actual movable pulleys. The test conditions were a high ratio (0.407) and input torque of 80 Nm. In Figure 6 the belt velocity of 30 m/s corresponds to vehicle speed of 148 Km/h at the high ratio. The tendency of decreasing transmitting efficiency with increasing belt velocity was successfully simulated. The effect of inertia of running belt at high speed was examined correctly with the FEM model. However, the absolute values of calculated efficiencies were higher than those of experimental results by 2 percentage points. The calculated results seem to agree with the experimental results using fixed V-pulleys. movable pulley. It also causes tilting of the movable pulley. Transmitting efficiency(%) Ratio:High(0.407) Input torque:80Nm 100 99 98 97 96 95 94 2. Tilting of the movable pulley due to the clearance shifts the belt to a deeper position on the pulley. 3. The motion to the deeper position increases friction loss between the belt and the pulleys. 4. Transmitting efficiency decreases due to the friction loss at the pulley shafts and the increase in the friction loss between the belt and the pulleys. Calculated Measured 0 10 20 30 40 Belt velocity (m/s) Fig. 6 Transmitting efficiency for the model of elastic pulleys Calculations using models of elastic pulleys with clearance at pulley shaft In order to explain the reason for the 2 percentage point discrepancy in the previous section, the clearance between pulley shaft and movable pulley was considered in the elastic models of the pulleys. In Figure 7, the calculated transmitting efficiencies at different belt velocities were compared with corresponding experimental results in the CVT unit having actual movable pulleys. By the modification of the pulley model the calculated values agreed with the experimental results in magnitude. Ratio:High(0.407) Input torque:80Nm EFFECT OF PERMANENT DEFORMATION OF THE TENSION BAND ON TRANSMITTING EFFICIENCY PERMANENT DEFORMATION OF THE TENSION BAND DUE TO HEAT AGING Heat build-up of the belt upon running at high speeds causes permanent deformation of the rubber material. Consequently, the clearance between blocks and tension bands increases as heat aging of the rubber material proceeds as shown in Figure 8. In this section the influence of the dimensional change due to permanent deformation of the tension band on the transmitting efficiency is examined with the FEM model. Clearance between tension block band and block Clearance between Transmitting efficiency(%) tension band and 100 99 98 97 96 95 94 Calculated Measured 0 10 20 30 40 Belt velocity (m/s) Fig. 7 Transmitting efficiency for the pulley model with shaft clearance The decrease in the efficiency with pulleys having shaft clearance was elucidated by visualizing the movements of the belt running at high speed in the simulation. The observation demonstrated the following mechanism for the efficiency decrease: 1. The clearance at the pulley shafts results in increasing frictional loss between the shaft and the Fig. 8 Clearance between tension band and block for a fatigued belt First, the change in the clearance between the tension band and blocks was quantified in an accelerated bench test at belt temperature of 130deg C. The test conditions were shown in Figure 9. The measured clearance was plotted against duration of the test in Figure 10 Tensioner pitch diamater:81.4mm Drive pulley diamater:151.5mm Driven pulley diamater:61.5mm Fig. 11 Storage modulus of rubber material as a function of aging time at different temperatures. Test conditions Running speed of belt:30m/s Input torque:115Nm Belt temperature:130deg C Tensionner load:419N The aging time at a given aging temperature can be converted to the time at arbitrary reference temperature by using Arrehenius equation (Equation 1) with properly assigned activation energy. Fig. 9 Belt endurance test layout and conditions 250 0 .3 200 0 .1 150 0 .0 5 0 100 - 0 .0 5 - 0 .1 50 - 0 .1 5 - 0 .2 - 0 .2 5 3 0 .2 0 .1 5 d ista n c e (10 Km ) 0 .2 5 E stim a te d ve h ic le r u n n in g C le a ra n c e b e tw e en ten sion b a n d a n d b loc ks (m m ) t t 0 0 100 200 300 400 500 0 1 E 1 1 = exp − R T 0 T 1 (Equation 1) Where t0 is the aging time at a chosen reference temperature T0, t1 is the aging time at arbitrary aging temperature of T1, E is the activation energy in J/mol, and R is gas constant (8.31 Jmol-1K-1). The chosen reference temperature, T0 is 403.15 K (130deg C). Figure 12 shows a master curve at the reference temperature of 130deg C using an activation energy E of 96.3 kJ/mol. R u n n in g T im e a t 130 C (h ) Fig. 10 Clearance between tension band and blocks, and estimated vehicle running distance as a function of duration of accelerated test at 130℃. As mentioned above, this bench test is an accelerated test at the belt surface temperature of 130deg C. Therefore, the duration of the test needs to be converted to actual vehicle running distance. For this purpose, the aging test of rubber material was performed by measuring dynamic storage modulus of the rubber material at different aging temperatures. Figure 11 shows the results of the modulus as a function of aging time at different temperatures. Fig. 12 Master curve of elastic modulus as a function of aging time. (Reference temperature: 130℃) End of belt life 100 Transimitting efficiency (%) Next, Figure 13 shows a model distribution of vehicle speed and the relation between the vehicle speed and belt temperature. The distribution was expressed in percentage of time at each vehicle speed. The calculated averaged vehicle speed based on the distribution is 74 Km/h, meaning that the model distribution is the high-speed type, and it represents the severest condition for the belt. 99 98 97 96 95 Vehicle speed 60Km/h 94 123Km/h 93 92 148Km/h 91 173Km/h 90 0 0.05 0.1 0.15 0.2 0.25 0.3 Clearance between tension band and blocks (mm) Fig. 14 Transmitting efficiency as a function of tension band-block clearance at different vehicle speed Fig. 13 A model distribution of vehicle speed and relation between vehicle speed and belt temperature. (High-speed model) The distribution and belt temperature in Figure 13 and Equation 1 gives cumulative aging time at the reference temperature per unit vehicle running distance. The estimated vehicle distance was plotted against aging time at 130 deg C in Figure 10. Figure 10 indicated that the tension band-block clearance of 0.2 mm after 400 hour’s running at 130 deg C corresponds to vehicle distance of 200,000 km, assuming the severest condition of Figure 13. CALCULATION OF TRANSMITTING EFFICIENCY AT DIFFERENT CLEARANCE BETWEEN TENSION BAND AND BLOCKS The dimensional change of Figure 10 was considered in the calculation by creating the clearance in the belt model. Figure 14 shows the results, transmitting efficiency as a function of tension band-block clearance at different vehicle speeds (belt speeds). This result clearly demonstrates that the transmitting efficiency is lowered as the permanent deformation of the tension band proceeds. This deterioration is significant at high vehicle speed range at the end of belt life. Stated differently, the transmitting efficiency is kept at a high level if the vehicle speed is below 120 km/h. An accelerated endurance test of the belt reveals larger heat generation of the belt at the end of the belt life, supporting the calculated results of lower efficiency (higher loss). This energy loss attributes to an increase in frictional loss between the tension band and blocks at high speed range. ANALYSIS OF STRAIN ACTING ON THE TENSION BAND AND PREDICTION OF CRACK LIFE OF THE BELT CALCULATION OF THE DYNAMIC STRAIN ACTING ON THE TENSION BAND Figure 15 shows a crack at the tension band at the end of its life. The crack growth at the lower side of the band leads to rupture of the belt. Dynamic strain at the tension band is the cause of the crack initiation. Therefore, the dynamic strain at high belt speeds must be evaluated quantitatively using the dynamic FEM analyses. Fig. 15 Crack of tension band at the end of belt life In Figure 16 the calculated dynamic strain acting on the tension band was shown at belt speeds of 35 and 9.7 m/s. At the higher belt speed of 35 m/s a clear maximum of the strain was observed at the entrance of the tension pulley. In Figure 17 the maximum dynamic strain was plotted against belt speed. The result revealed that the dynamic strain increases by 20 % at the belt speed of 30 m/s. The increase in the dynamic strain was proportional to the square of the belt speed. position. In case of high belt speeds, the inertia pushes a block forwards, which causes collision of the blocks. This interference of neighboring blocks leads to momentum around the collision point. This momentum increases spacing between the blocks, which, in turn, leads to the maximum dynamic strain of the tension band. Velocity of belt Strain Peak in dynamic behavior Rotational direction ①Collision Ratio: High(0.407) Low(2.449) ① ②Reaction of Velocity of tension pulley surface the collision Strain Bending Strain ② Increase in the gap between block 0 Period of contact with tension Pulley Belt speed: 35m/s 9.7m/s Calculated strain S=0.00177V2+7.96 2 1 0 5 10 15 20 25 ベルト速度(m/s) 30 35 PREDICTION OF CRACK LIFE OF THE BELT The maximum strain in Figure 17 is used for the prediction of the crack life of the belt. For this purpose, S-N curves for the crack life of the tension band were drawn at different belt temperature in Figure 19. Each point is the result of experimental data evaluated by a flex test of a tension band itself (without blocks) with varying flex diameter and belt temperature. Bending strain 下コグ表面歪み(%) Tension band strain(%) Strain in dynamic behavior 0 Pitch circle of belt Fig. 18 Dynamic behavior of blocks at the entrance to the tension pulley Fig. 16 Strain in the tension band with respect to the relative position with tension pulley 12 11 10 9 8 7 6 5 4 3 Tension pulley 40 Belt speed(m/s) Fig. 17 Maximum strain in the tension band as a function of belt speed. The visualization of the belt demonstrated a larger pitch distance between the adjacent blocks at the entrance of tension pulley at the belt speed of 30 m/s. Additional static analysis confirmed that the larger pitch distance corresponds to the 20% increase of the strain due to tearing force imposed to the tension band by the blocks. Such dynamic behavior of the blocks at high speeds was depicted in Figure 18 schematically. The translation motion of the block changes to a rotational motion upon contacting with the tension pulley. The contact with the pulley decelerates the motion of the block at the contact Fig. 19 S-N curves of crack life of tension band at different belt temperature . The S-N curves in Figure 19 and the calculated maximum strain in Figure 17 predict crack life of the hybrid belt in bench tests at different belt velocity. Figure 20 shows the results of predicted crack life at belt temperature of 130deg C at high ratio. The predicted (calculated) life is consistent with the experimental results of bench tests. This consistency proves the accuracy of the maximum dynamic strains calculated in the proposed FEM analyses. 30m/s velocity of belt (m/s) Calculated Experiment value Calculated Experiment value Belt life (hr) Belt temperature: 130deg C 35m/s Fig. 20 Comparison of the prediction of crack life with the results of bench tests. IMPROVEMENT OF THE CVT SYSTEM The results in the previous section demonstrated that belt life is predominantly determined by operating belt temperature and dynamic strain acting on the belt. Therefore, lowering the belt temperature and strain is very important to achieve longer life of the belt. For this reason the following improvements was undertaken for the new CVT system: Cooling of the belt by increasing a ventilation flux rate by 100%. the movable. The transmitting efficiency decreases with increasing belt velocity. Permanent deformation of the tension bands creates clearance between the tension bands and the blocks in a fatigued belt. Dynamic simulations demonstrated that the clearance causes the decrease in the transmitting efficiency in a high belt speed range at the end of belt life. The decreased efficiency leads to heat build-up of the belt. The increase in belt temperature was confirmed in a bench test of the belt at the end of the belt life. Calculations of the dynamic strains acting on the tension band revealed a peak of the strain at the entrance to the tension pulley. The reason for the maximum strain was elucidated by the visualization of the dynamic motions of the blocks in the simulation. Crack life of the belt was predicted with the peak strain and S-N curves. The predicted life was consistent with the results of some bench tests at different belt speeds. Finally, improvements in the CVT system were explained. The improvements leading to the decrease of belt temperature and dynamic strain are the keys to achieve a longer belt life and higher transmitting efficiency of the system. REFERENCES 1. Yoshiaki Kato, Hiroshi Yamashita, Yoshihiro Kono :A Study on the Torque Capacity of Belt CVTs for 2.0-liter and 3.5-liter Front-Drive Cars JSAE Autumn Convention, No.65-03, p.1-4 (2003) 2. Hirofumi Shimizu, Daisuke Kobayashi, Junichi Kawashima, Yoshiaki Kato: Development of 3-D Simulation for Analyzing the Dynamic Behavior of a Metal Pushing V-Belt for CVTs JSAE Spring Congvention, No.8-99,p.9-12 (1999) 3. Masanori Shimizu, Kazuya Okubo, Toru Fujii, Mituhiko Takahashi, Ryuuichi Kido:Variations of Belt Pitch Line and Power Transmitting Efficiency due to Pulley-flange Tilting of CVT using a Dry Hybrid V-belt JSAE Autumn Convention, No.108-2, p.7-12 (2002). 4. Toshihiro Saito :Development of Metal Pushing Vbelt Stress Simulation for CVT JSAE Annual Congress, No.21-03,p.9-12 (2003) 5. [4]Hirokazu Uchiyama, Takeshi Yoneda, Hironaga Itou, Yasukazu Nobumoto :On the Shifting Mechanism of a Metal V-belt CVT JSAE Spring Congvention, No.8-99,p.21-24 (1999) Reduction of the maximum belt speed from 35m/s to 30m/s, which decreases heat generation due to higher transmitting efficiency, and decreasing dynamic strain acting on the belt. Optimization of the belt tension by controlling the tension pulley with a spring assisted by a hydraulic cylinder, which improve the transmitting efficiency, reducing the heat generation of the belt. CONCLUSION Dynamic FEM analyses of a new CVT system driven by a dry hybrid V-belt was performed with 3-dimensional models of the belt and pulley assembly. The calculated transmitting efficiency of the CVT as a function of belt speed was consistent with the experimental results with a modified elastic-body model of the driving and driven pulleys having actual clearance between pulley axis and