A Review on Dynamic CVT-IVT Transmissions

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of a conference paper (SAE 2014 World Congress & Exhibition) published by SAE International: Morales, F., and Benitez, F., "A Review of Dynamic CVT-IVT Transmissions," SAE Technical Paper 2014-01-1734, 2014, https://doi.org/10.4271/2014-01- 1734.. © SAE International. En idUS Licencia Creative Commons CC BY Page 1 of 11 14PFL-0225 A Review on Dynamic CVT-IVT Transmissions Author, co-author (Do NOT enter this information. It will be pulled from participant tab in MyTechZone) Affiliation (Do NOT enter this information. It will be pulled from participant tab in MyTechZone) Copyright © 2014 SAE International Abstract Currently continuously variable transmission (CVTs) is a topic of special interest as it allows the vehicle to have the engine working at its optimum regimen (either minimum or maximum power consumption as required) and keeping unaltered despite the changes in speed and torque required on the drive wheels during operation. There is a particular group of CVTs with special characteristics: the dynamic type CVTs. In these, in addition to act on a control element, as in the rest of kinematic type transmission, the gear ratio also depends on the external conditions to which the transmission is subjected, that is, the transmission ratio is also determined by other variables such as the angular velocity of the input shaft and the load torque exerted on the output shaft. This communication tackles a review of the most representative dynamic CVTs and torque converters (TCs) stating the basics of their functioning. The transmissions analyzed correspond to different patents, from one of the first one [1] to the most recent ones [2,3] In addition a brief description of each mechanism is carried out based on analytical and computational studies of the most interesting items, analyzing the advantages, disadvantages and deficiencies in the operation. Additionally, this review critically provides a warning regarding the pieces of information and working principles taken for granted. Introduction Fixed-ratio transmissions, whether manually operated or automatic, have a discrete number of speeds or transmission ratios. On the other hand, in a continuously variable transmission system (CVT) the transmission ratio between the input and output shafts can vary progressively within a determined range of possible ratios. A first classification of this family of transmission, according the regulation of the transmission ratio, groups them into kinematic or dynamic CVTs. Kinematic versus Dynamic CVT In a kinematic CVT, an external regulating element fixes the gear ratio. It is necessary to change the position of the regulation element to vary the transmission ratio. However, in an inertia-type CVT and apart from the ability to adjust the regulating element, the ratio also depends on the external conditions to which the transmission is subjected. In other words the ratio is determined by variables such as the speed of the input shaft or the resistive torque at the output driveshaft as well as by the mechanical characteristics of the system. This feature implies a self-regulation of the transmission. Torque Converter (TC) versus CVT A Torque Converter (TC) is a transmission system which can automatically regulate the transmission ratio between its input and output shafts depending on the speed and the torque applied to them. According to this definition, it might seem that the TC is actually a CVT. However this is misunderstood concept because the transmission ratio depend, solely and exclusively, on external conditions as the speed of the input shaft, the resistive torque, .et cetera. That is, the TCs do not have an external regulating system to change the speed of the vehicle without varying either the rotational speed of the internal combustion engine (ICE) or the resistive torque. An exercise to clarify the difference between TC and CVT would be to incorporate the two systems in a vehicle and tested under the same protocol. If a vehicle equipped with a torque converter and situated in a horizontal track is driven with a constant speed, the ICE angular velocity will be constant too. Then, if one wants to increase or decrease the speed of the vehicle, the unique alternative is to change the ICE speed due to the fact that the TC does not have any external regulating system. However, with a CVT it is possible to select a particular speed actuating on the external regulating system and without affecting the ICE rotational speed. Page 2 of 11 State of the Art on Dynamic CV The dynamic CVT is a very attractive concept because, as discussed above, it has the capability to self-adapt to the conditions regardless of possessing an external regulating system controllable by the driver. Next, the most representative transmissions of this type are analyzed so as to deeply understand their operation. TCs and CVTs with oscillating masses This kind of TCs and CVTs uses inertial forces generated by oscillating masses. There are very many systems of this type, however due to the similitude between them, only the most representative items will be shown. Examples of that are the systems patented by Wilfred Hunt [4, 5], by B. Borisoff [6], by Carter J. Ward [7] and by Frach [8]. Constantinesco's TC This is the first functional torque converter patented [1].The first Constantinesco's patent shows a simple sketch of the TC (Figure 1). Figure 1. Constantinesco's torque converter (GB 185,022). In this system, the input shaft drives the crank 1 which is attached via the rod 2 to bar 3. This bar 3 is connected to the output at point A and to the pendulum (bar 4) at point B. This pendulum is the inertial regulating element. The rod 3 provides an oscillating movement that has to be rectifier using freewheels or other kind of mechanical diodes. To analyze the operation of this system, we will use two extreme situations.In the first one, there is a high resistive torque at the output shaft causing the pendulum to swing between its two extreme positions due to the movement of the point A is near zero (figure 2a) (Figure 2 shows an equivalent construction of the converter). In this situation, the pendulum offers a high resistance to be moved due to its inertia. This resistance will be proportional to the inertia and the acceleration of the pendulum. Then, the resistance will be transmitted to the output shaft through the rod 3. As the pendulum movement is maximum in this situation, the transmitted torque will be maximum too. So we have a high torque and a low speed at the output shaft. In the second situation, for high speed at the input shaft and low resistive torque at the output, the amplitude of the oscillation of the pendulum is minimum, keeping the point C quasi immobile. This is so because the movement of the rod 3 is transmitted to the pendulum and the output shaft in an inversely proportional way to the resistance opposed by each element. In the situation of low torque at the output is easier to move the output shaft than the pendulum, therefore the bar 3 oscillates around the point B, which can be consider as a quasi-fixed point. Now, the system has a maximum transmission ratio (Figure 2b) because there is a low torque and a high speed at the output shaft. Usually the system will be at a situation between the two extreme cases exposed (figure 2c) Figure 2. Operating principle of the Constantinesco's torque converter (GB 185,022). As deduced from the operation of the torque converter, because of the additional degree of freedom, there are situations with rotations in the input shaft without motion of the output shaft. This makes possible the use of the transmission system without any clutch. To understand the self-regulation of the transmission ratio a comparative example between a manual transmission and the Constantinesco's torque converter can be conducted. Suppose that a vehicle with a transmission system as described herein is moving on a flat road. In this situation, the resistive torque is not excessively high (with low or moderates speeds) therefore the torque converter will be moving as shown in Figure 2c but closer to the case of Figure 2b than that of Figure 2a.If the gradient of the road is increased, the resistive torque increases as well, so the movement of the output shaft decreases. However, the pendulum motion will increases and the system will approach to the situation of Figure 2a. As the torque transmitted by the converter is proportional to the inertia and acceleration of the pendulum, the torque transmitted toward the output shaft will increase. This situation is equivalent to reduce a gear in a conventional gearbox, however the Constantinesco's TC regulates itself without the driver action. Based on the same operating principle as the preceding, Constantinesco improves his torque converter in a series of patents that complete the patent published in 1922. But it is not until the patent published in 1925 [9], when he shows a CVT based in the same principle as the torque converter. Page 3 of 11 There are at least two ways to transform a dynamic TC in a CVT: 1. Changing the inertia of the massive element. 2. Changing the length of any of the elements of the transmission. This is the simplest case if the torque converter has a driving mechanism that transforms a continuous movement in an oscillating one. Customarily this transformation can be achieved with a four-bar linkage driving mechanism comprising a crank, a connecting rod and a rocker arm so that, changing the length of the crank or the rocker, a variable amplitude oscillation is obtained. Constantinesco chose the first of the possibilities and transformed his torque converter into a CVT by changing the inertia of one of the elements of the transmission. This may seem simple, but it has a great complication because this modification of the inertia have to be performed with the transmission working and it must be reversible, that is, the driver should be able to increase and decrease the inertia when necessary. Constantinesco solves the modification of the inertia by replacing the mass of the converter by a variable-length column of fluid. Howard's TC This torque converter is described by R. P. Howard in his patent GB 2411932A in 2005 [10] (Figure 3). Figure 3. Howard's torque converter (GB 2411932A). The operating principle is based on continuous way of varying the angular velocity of the flywheels making them oscillate. A flywheel oscillates and the torque transmitted is proportional to the angular inertia of this flywheel. In this TC in particular, the engine is connected to the shaft 1. This shaft, through a pair of gears, transmits its motion to crankshafts 3.1 and 3.2, which are fixed to frame 2, output of the system. The crankshafts, links 4 and flywheels 5 form a four-bar mechanism. If the resistive torque is high, frame 2 has a small movement and the motion of shaft 1 is transmitted directly to the crankshafts. When these crankshafts gyrate, the flywheels are forced to oscillate. The inertial disks offer resistance to be moved due to their inertia, that’s why a torque is transmitted to the output and it is proportional to the resistance offered by the inertial disks. One can calculate the evolution of this torque using the equation of a 4-bar mechanism. As the inertia is constant, this evolution is similar to the evolution of the acceleration of the inertial disk and, as it is depicted in figure 4, the torque is oscillating making the use of a rectifier necessary. Figure 4. Evolution of the angular, velocity and acceleration of the flywheel. The resistive torque which opposes the movement of the flywheel is proportional to the angular acceleration of this disc with a value 𝐼 ∙ 𝑑𝜔 𝑑𝑡 , where I and 𝑑𝜔 𝑑𝑡 are the inertia and angular acceleration of the disk respectively. Due to the fact that the disk has constant inertia, the torque that opposes the motion will have exactly the same evolution as the angular acceleration of the disk multiplied by a constant (the inertia), and therefore it is an oscillating torque. The output torque of the TC is proportional to this torque, so the evolution will be similar (though the value is not the same, the shape is proportional) and a rectifier system will be needed to use the transmission. On the other hand, when the resistive torque at the output is low, frame 2 offers less resistance to be moved than the inertial disks. In this case, the crankshafts do not spin over themselves and the frame 2 oscillates with a large amplitude. Self-adaptive dynamic CVT In this transmission [11], the inertia element consists of an epicyclic reduction gear train with additional mass added to the ring gear. The gear train’s position in the CVT is reversed and therefore the input shaft is connected to the planet gear carrier and the output shaft to the sun gear (Figure 5). In this arrangement the epicyclic reduction gear train is, in fact, multiplying the input speed and so, from here on, it will be more appropriate to call it simply an epicyclic gear train. 0 5 10 15 20 25 30 -1 -0.5 0 0.5 Time (s) Angle (rad) 0 5 10 15 20 25 30 -1 -0.5 0 0.5 Time (s) w (rad/s) 0 5 10 15 20 25 30 -1 0 1 2 Time (s) dw/dt (rad/s2) Page 4 of 11 Figure 5. Reverse epicyclic gear train. The design of the dynamic CVT uses a particular property of epicyclic gear trains in this configuration as a principle of operation. If the sun gear is blocked and the planet carrier gear accelerates, the ring gear reacts by accelerating in a similar way (Figure 6a). (a) (b) Figure 6. (a) Reaction of the ring gear when the planet carrier accelerates and the sun gear is blocked. (b) Torque transmitted to the sun gear. As a result of this acceleration and while it lasts, torque is applied to the sun gear, which is blocked (Figure 6b). However, when the acceleration stops, the torque is null at the sun gear. As a result of the above it can be assumed that, if the input to this system is subjected to continuous periods of acceleration, the sun gear shaft will be able to overcome a resistive torque. For this purpose an oscillating angular motion is applied at the shaft of the planet carrier. This motion is generated by a driving mechanism that will be explained later. In the stated conditions, the output from the epicyclic train is also an oscillating movement. This property means the arrangement is an oscillating or ratcheting CVT. This factor is important because it implies the need for a mechanism that rectifies the output motions using mechanical diodes or unidirectional clutches (also known as free-wheel devices). The inclusion of a high-mass ring gear able to rotate contributes to an additional degree of freedom that categorizes this CVT as an inertia transmission system. As a consequence the transmission ratio is determined by external factors such as either the speed of the input shaft or the resistive torque at the output shaft. Therefore one can conclude that by adding mass to the ring gear with its additional degree of freedom, the system becomes an inertia mechanism that regulates power. The regulation in this case consists of cyclical accumulations and transfers of power, which is transferred to both the sun gear and the planets gear carrier. As explained so far, the complete transmission system consists of a driving mechanism; an epicyclic gear train that, with mass added to the ring gear, acts as an inertial mechanism; and a rectifying mechanism (Figure 7). Input DRIVE MECHANISM Oscillating movement Epicyclic Train INERTIAL MECHANISM Oscillating movement RECTIFIER MECHANISM Output Figure 7. Transmission scheme. The engine is connected to the drive mechanism, which transmits an oscillating movement to the epicyclic gear train, generating accelerations of the same type. The inertia mechanism regulates the torque transmitted to the output, in line with the operating conditions. Lastly, a rectifying mechanism converts the oscillating movement of the gear train output to a unidirectional angular velocity. Two extreme operating conditions will be now examined to illustrate the general manner in which the transmission works, although normal operating conditions will be somewhere between these two limits. The first situation is one in which the resistive torque at the output shaft is very low or zero. As the motor shaft rotates at a set velocity, the drive mechanism transmits an oscillating movement to the planet gear carrier. This will create the largest movement in the element (either ring gear or sun gear) that offers least resistance to movement. In this case the resistive torque at the sun gear of the epicyclic gear train is also very low or zero and therefore this gear offers little opposition to movement. On the other hand the ring gear, which is an element of considerable inertia, opposes greater resistance to movement than the sun gear. As a result the oscillation of the sun gear will be at maximum level. This implies maximum velocity of the output from the transmission for this motor speed. This case, of low torque resistance at the output shaft, results in high velocity output from the transmission and therefore a high transmission ratio. In the second situation the resistive torque at the output shaft is so high that the sun gear of the epicyclic gear train is blocked and therefore the shaft does not rotate. As the sun gear is blocked, movement is transmitted to the ring gear only, which is forced to oscillate at maximum amplitude. In this case, where a considerable mass is added to the ring gear, the ring opposes this movement with a torque proportional to its inertia and angular acceleration. As the oscillation of the ring gear is at maximum level for the given motor speed, the torque applied at the output shaft is also at maximum level. In this case a situation of high resistive torque and low velocity at the output shaft results in a low transmission ratio. Page 5 of 11 The transmission functions in a normal manner in situations that lie between the two extreme cases discussed above. Each situation is defined by the particular rotational speed of the engine and the current resistive torque at the output shaft. Changes in these variables lead to an adjustment of the transmission ratio. Due to the oscillations the high-mass ring gear acts as an inertial regulating mechanism for the transmission system. If the resistive torque increases, ie. when the vehicle is ascending a slope, the velocity of the output shaft diminishes, the oscillations of the ring gear increase and therefore the torque applied to the output also increases. This is equivalent to swift to a lower gear ratio. The variation of the transmission ratio occurs without affecting the speed of the internal combustion engine as seen in figure 8. In this figure it is shown how the transmission responds (at full throttle) to different road gradients. The results show that this type of vehicle transmission responds favourably to changes in gradient with the engine running at the same throttle level. Figure 8. Output velocity for different road gradients at full throttle. TCs and CVTs with eccentric masses This kind of TCs and CVTs uses inertial forces generated by eccentric masses. The most representative designs will be shown due to the similitude between them. Examples of them are the systems patented by Zhou Zhiming [12], by B. Osman [13], by Henry W. Wallace [14], and by Paul S. Moller [15]. Chalmer's TC In this TC [16], the engine is connected to the shaft 10 (Figure 9). This shaft rotates sun gear 11 that transmits its movement to planets 1. These planets have an eccentric mass 15. The inertial forces generated by the masses are transmitted to planets carrier 12 that it is linked to the output. Figure 9. Chalmers' TC (US 1,860,383). In the position shown in Figure 10a, centrifugal forces are all radial and pass through the center of rotation of the planet carrier. In this situation, all the centrifugal forces are balanced and there is no torque at the axis of rotation of the planet carrier. If the movement of the input shaft continues, the transmitted torque will increase until the eccentric masses reach the position shown in Figure 10b. In this case, the transmitted torque is maximum and positive. Figure 10. Operating principle of Chalmers' TC (US 1,860,383). After reaching the maximum torque value, if the movement continues, the torque begins to decrease until it becomes null when the position shown in Figure 10c is reached. After that, the torque generated will increase, but with the opposite sign. The Maximum negative torque will reach when the system is in the position shown in Figure10d, state at which the torque will decrease again, reaching zero in the initial position represented by Figure 10a. a) Zero torque b) Max. positive torque c) Zero torque d) Max. negativetorque Centrifugal force Centrifugal force Page 6 of 11 As proved so far, the torque will have an oscillatory nature and should be rectified in order to be of any use By analyzing a generic position of Chalmer’s TC (Figure 11), one can state the motion equations of the system as well as the torque transmitted. This torque will be at a maximum when the output speed is null. In what follows this maximum torque is quantified: Figure 11. Generic position of Chalmers’ TC. The rotating speeds of the masses are: 11 14 11 22 mass i RR RR     = =  =  (1) where: x  : angular speed of element x, 1 R : radio of gear 11, 2 R : radio of planet 14. The centrifugal force generated by a mass is given by 𝐹 𝑐= 𝑚 ∙ 𝑎𝑛 where m is the mass of the element (named as 15 in Figure 11), and 𝑎𝑛 is the normal acceleration of the mass. The acceleration 𝑎𝑛 is: 22 22 11 11 · · mass n mass D v aD DD  = = = (2) where 𝐷1stand for the distance between the center of gravity of the mass and its rotation axle and 𝑣 is the velocity of the mass. The tangential component generates a torque which causes the movement of the planet carrier 12, with the following value: · ( ) Tang c F F Sin  = (3) where: 𝐹𝑇𝑎𝑛𝑔: tangential component of the centrifugal force, 𝛼: angle between line connecting points 10 and 13 and the centrifugal force axis. The torque generated by the centrifugal forces has the value: ( ) ( ) 22 1 1 1 2 1 1 2 2 2 · · · · · ( )· Tang i R T F R R m D Sin R R R  = + = + (4) where 𝑇1 is the torque generated by just one mass. In this TC there are more than one mass, therefore the total torque will be: ( ) 22 11 1 2 2 2 · · · · · ( )· i R T nm D Sin R R R  =+ (5) being n the number of masses in the transmission. In this equation it is clear that the torque will be maximum (in absolute value) when 𝑆𝑖𝑛(𝛼)= ±1. This situation occurs when the angle α has a value of either 90° or 270°, which coincides with Figure 10b and Figure 10d respectively, corroborating the previous analysis. With this equation we can define the strategy to increase the torque. For example by increasing either the number of masses, the relation between R1 and R2 (this implies a modification of the angular velocity of the mass), the mass of the elements 15, the input speed or the eccentricity (distance 𝐷1).The equation also shows that the torque has an oscillatory nature (due to 𝑆𝑖𝑛(𝛼) has positives and negatives values). Because of this, a rectifier mechanism is required. Other authors also introduce the eccentric masses in the sun of an epicyclic train, using the same principle of operation, as is the case of Angel Fernandez [17] or Macintyre and Guy [18]. Tam's TC This TC was patented by Tam [19] and it has a drive mechanism composed by an input shaft 42 (Figure 12), which is linked to the engine, and the shaft 44. In this shaft 44 there are inserted the masses 46 that can move along the shaft 44. These masses 46 have the grooves 54 in which the ring 47 is inserted. Because of this, the movement of the masses is restricted to the shape of the ring (when this is blocked). As the ring is off-center respect to axle 55, the masses will have a displacement movement along the bar 44 and a rotational movement around the axle 55. Finally, the ring 47 is fixed to the shaft 48 which is the output of the transmission. 11 12 R2 R1 10 13 14 α Fuerza de inercia aplicada en el eje 13 Componente radial Componente tangencial D1 15 Par generado Radial component torque Tangential component Inertial force Page 7 of 11 47 42 55 44 45 46 a) b) Figure 12. a) Tam's TC (US 5,134,894) and b) front view of Tam's TC. This system is an example of the level of unreliability drawn from the registered description of the functioning of some of the systems patented. The author claims in his patent that a rectifier system is not needed. According to him, that is so because a free mass inserted in bar 31 has a trajectory as shown in Figure 13 and numbered as 34. But if the mass is required to describe a circular path, the effects of this mass on the two sides of the circular path (the left and right ones) are not symmetrical. The inertial mass has lower effects on the left side of the track that has it on the right side of the track, because the left side of the circular track substantially coincides with the natural trajectory of the free mass while the right side of the circular track substantially deviates from the natural trajectory. Then, there is a net reactive force exerted on the right half of the track by the mass. Figure 13. Operating principle of Tam's TC according to the author (US 5,134,894). In conclusion, the author claims that a unidirectional torque is generated and a rectifier system is not necessary. But one can easily check this is not right. This conception is true only the first time that the mass spins. The second time, the mass has a velocity and the trajectory is not like the trajectory numbered as 34. If the value of the inertial forces is obtained, one will be able to prove that they are symmetrical respect the vertical axle in a stationary situation and, therefore the net force is vertical. Because of this, the resultant torque is oscillating and a rectifier is needed. To obtain the transmitted torque Figure 14 helps showing an equivalent mechanism. Figure 14. Equivalent mechanism of Tam's TC. In the equivalent mechanism, the fixed length bar 47 forces the mass 46 to describe a circular path (which is equivalent to that of the ring 47 in Figure 12), so that the two mechanism are completely analogous. To obtain the inertial forces, it is necessary to calculate the angular velocity 𝜔2 as a function of the input speed 𝜔𝑖. From Figure 14, this relationship can be obtained: · ( )D Sin ArcSin R       = + = +   (6) where:  : angle rotated by the input bar 44,  : angle between bars 44 and 47,  : angle rotated by bar 47, R : radius of the circular path (length of bar 47), D : distance between the rotation centers of bars 44 and 47. If the angular input velocity (𝜔𝑖) is constant, the angle α varies as 𝛼 = 𝜔𝑖∙ 𝑡, where t stand for time. Substituting in expression (6) and deriving, the angular velocity 𝜔2 is obtained: 222 2 · · ( ) · ( ) ·1 ii i i D Cos t D Sin t RR    =+ −   (7) With this velocity, the centrifugal force can be obtained from 𝐹 𝑐= 𝑚 ∙ 𝑎𝑛, where m is the mass of the active elements (named 46 in Figure 14) and 𝑎𝑛 is the normal acceleration of the mass. As 𝑎𝑛= 𝜔2 2∙ 𝑅, the inertial force is: 47 42 55 44 45 46 ωi ω2 R α β 180-δ δ D L Page 8 of 11 2 22 2 · · ( ) ·· · ( ) ·1 i ci i i D Cos t F m R D Sin t RR      =+  −     (8) As can be seen in this equation and in its graphical representation (Figure 15), the forces are symmetrical respect to the vertical axis and so does the resultant net vertical force. As the inertial forces are symmetrical, the torque is oscillating with negative values when the mass is in the left half side of the circular track and positive values when the mass is in the right side of the track. Figure 15. Evolution of the centrifugal force. From equation 8 one derives that the force is minimum when 𝛼 = 𝜋 and maximum when 𝛼 = 0. So, the net force is vertical (maximum values when α=0) and not horizontal as Tam claims. The only component of the centrifugal force that generates torque is perpendicular to the axis that connects the rotation centers of the bars 44 and 47. Because of this, the torque transmitted is: ( ) ·· c T F Sin D  = (9) and from (8) and (9): ( ) 2 22 2 · · ( ) ·· · ( ) ·1 · ·· ii i i D Cos t Tm D Sin t RR D Sin R Sin ArcSin D R        =+  −    +     (10) which is represented in Figure 16. Figure 16. Torque transmitted. Corroborating that the torque is oscillating and a rectifier mechanism is needed. Lester's CVT In this section the continuously variable transmission patented by Lester in 2000 [2] is analyzed. Lester shows in his patent some different configuration. The following figure (Figure 17) represents the preferred embodiment of the patent. Figure 17. Lester's CVT. This CVT works in a similar way than the Chalmers' torque converter as it can be seen in Figure 18. Figure 18. Operating principle of Lester's CVT (US 6,044,718). 0 pi/2 pi 3pi/2 2pi -0.4 -0.2 0 0.2 0.4  T