Design and Performance of an Exponential Roller Gear Continuously Variable Transmission with Band Clutches

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1 4CVT-18 Design and Performance of an Exponential Roller Gear Continuously Variable Transmission with Band Clutches Copyright 24 SAE International James G. Nugent GearClear Technology ABSTRACT Many applications will benefit from a higher efficiency continuously variable transmission. This paper presents the design, performance, and measured efficiency of a linear low-slip continuously variable transmission prototype. It discusses the chosen design approach with an emphasis on efficiency and presents improvements on previous designs that make it practical. The ratio variability comes from exponential roller gear and cam gear pairs that function as noncircular gears. The roller/cam pairs are located on three centers of rotation, two fixed and one translating to provide the varying ratio. Two power paths are used and the power from the appropriate path is fed into the output by a band clutch that is synchronized to the output by the exponential gears and tightened by an internal cam. The cam is made up of telescoping segments driven in a nonlinear fashion by the location of the translating axle. Power crosses four gear meshes between the inline input and output shafts. The prototype has a ratio range of 5.85:1. A method of using internal torque to shift the transmission is presented. INTRODUCTION Many applications benefit from a continuously variable transmission (CVT). There are numerous historic and ongoing efforts to solve this problem. While many of these efforts are yet impractical, several have reached a level of design maturity that is sufficiently reliable, inexpensive, and efficient to be mass-produced. However, for some possible applications, the efficiency of currently available CVTs is not sufficient to provide enough of an increase in performance to make it cost effective to replace a fixed ratio transmission with a CVT. This paper presents an effort to provide an improved CVT. MAIN SECTION This paper presents the design, performance, and measured efficiency of an exponential roller gear CVT with band clutches. It will be referred to as the presented CVT below. The presented CVT exists as an operating prototype. The paper discusses the chosen design approach with an emphasis on efficiency and presents improvements on previous designs that make it practical. DESIGN GOALS The presented CVT was designed with a goal of being truly continuously variable, highly efficient, and able to transmit high torque levels. To broaden its possible applications, it was designed to not require computer control to operate. Although it depends on friction within the clutches to operate, it avoids the slip and spin of traction CVTs such as variable pulley and toroidal designs. Only clutches that would be synchronized during all clutching and declutching actions were considered acceptable. A further constraint on the design was a requirement that it transmit torque both forward and backward. This caused the solution to avoid the use of one-way clutches. It was determined that the presented CVT was to be purely mechanical, not requiring hydraulic pumps or electrical motors. BACKGROUND Continuously variable transmissions (CVTs) can be grouped into electrical, hydraulic, traction, and ratcheting categories. Electrical CVTs convert mechanical energy to electrical energy and then back to mechanical energy. Hydraulic CVTs convert mechanical energy to fluid pressure and flow and then back to mechanical energy. Substantial energy is dissipated in each of these conversions. It is desirable to have a purely mechanical device that would avoid such power loss. Many efforts have been made in this regard. CVTs other than electrical or hydraulic can be grouped into two main categories: traction drive or ratcheting. TRACTION CVTS One example of a traction drive uses a belt and variable pulleys. Another uses a split toroid and tilting rollers. All traction CVTs depend on shear friction on a contact patch. The ratio changes as the contact patch is moved. As the drive member always has some finite width, it will be driving a range of values across the contact patch. This is known as spin. There is also slip that occurs

2 when the driven member falls behind the driving member due to the torque it is transmitting. Slip dissipates additional energy. Traction CVTs may have a pump to control clamping forces on the friction surfaces. More energy is consumed by the pump and does not get to the transmission output. RATCHETING CVTS CVTs that have multiple power paths commonly use ratchets, sprags, or one-way clutches to combine the appropriate path into the output. The Zero-Max Adjustable Speed Drive is an example of the basic concept. Moving the pivot such that a rotary input drives an oscillation in multiple power paths, with varying phases, varies the throw of connecting arm geometry. Combining these multiple paths with one-way ratchets generates the output. This class of CVTs has become known as ratcheting CVTs. The two basic functions of ratcheting CVTs are generating multiple oscillations, or stroke variation, and selecting the proper portion of each to drive the output, or clutching. Stroke Variation A simple crank with a variable throw or variable pivot is a well-known method of generating variable oscillations. The output of an eccentric ratcheting CVT is not smooth; rather it has an uneven ratio across a rotational cycle. Approximating Linearity Although the output is desired to be linearly related to the input, the speed of the output is modulated by the underlying nonlinear relationship that causes the varying ratio. This is apparent in U.S. Patent 5,4,115. This is only partially solved by increasing the number of parallel power paths. Additional parallel power paths also lead to increased parts counts with higher weight and costs. A transmission design that provides a linear relationship on each power path will lead to fewer power paths with lower cost and higher efficiency. True Linearity Many ratcheting CVT designs approximate linear motion by selecting the best portions of curves such as the peaks of sinusoidal motion. They require a large number of power paths to keep the variation in the output to an acceptable level. However, several ratcheting CVTs are designed to achieve linear motion directly within each power path. Examples include the Barloworld Varibox Joint based CVT with 4 power paths, Company Ex IVPD with 6 power paths, and Infinity Drives CVT with 6 power paths. The presented CVT is also linear with two power paths. Clutching Ratcheting CVTs use eccentric motion and multiple power paths that are combined into the output. Each of these separate paths has a portion its motion that it is at the appropriate ratio to be locked to the output. For the portion of the motion for which the ratio is not matched, that path must be disconnected while another path carries the load. One-way Clutch Problems Many ratcheting CVTs use one-way clutch mechanisms to recombine the power prior to output. The one-way clutches that are used in CVTs described above and many other designs have several drawbacks. Unidirectional The first is that the transmission can only transmit power in one direction. A one-way clutch overruns and is not able to provide functions such as engine braking. Benefits such as recovering energy during braking, or regenerative braking, cannot be realized. A reverse gear requires additional hardware. Wear A second drawback is that the friction that makes most one-way clutches work also causes wear. The clutches are used with a high frequency and have a small contact area. The clutches lock while under load. They are not synchronized. This causes slippage and additional wear. Ratchets also lock while under load, adding shock loads to the transmission. They only lock at discrete locations, thus keeping the transmission from being truly continuously variable. Only the Fastest Power Path A third less obvious, but important drawback is that oneway clutches can only choose the power path that is turning the fastest. In order to make use of the full range of ratios, some transmission designs require that the slower path be used for a range of ratios. In the case of the presented CVT, being able to use the slower moving of the multiple power paths of the transmission gives it a much greater ratio range than an equivalent transmission with one way clutches. Previous Efforts Another CVT that uses separated power paths is shown in U.S. Patent 4,765,195. Exponential gears that are varied in phase relative to each other provide portions of a revolution of a shaft with the desired output speed. Here, one-way clutches are used to combine the power onto the output shaft and to disengage the shafts at the times they are not turning at the right speed. Other Alternatives Several efforts are designing away from the limitations of one-way clutches. The Luk Crank-CVT has a one-way clutch that can be selected to go either direction. This can provide a reverse gear but not regenerative braking. Epilogics patented a commutator in order to perform the

3 power combining function. The design of the Infinity Drives CVT includes two-way actuated gripping devices to provide engine braking. The presented CVT uses band clutches that are synchronized to the linear portion of each power path. THE PRESENTED CVT Figure 1: Overall view of the presented CVT The presented CVT is patented, with other patents pending. The solution presented here uses roller gears that vary ratio within one rotation in an exponential relationship. By combining an increasing exponential with a decreasing exponential in series, a constant ratio or sweet spot is obtained over a portion of the cycle. Two power paths are used in order to cover the portion of the cycle that is not within the sweet spot. The ratio is determined by the phasing of the gear meshes. One moving axis of rotation changes the phase of the gear meshes. Clutches select the correct power path. The clutching action is controlled by the position of the clutch and the angle of the moving axis of rotation. The presented CVT synchronizes the driving and driven members prior to clutch engagement and ensures synchronization until the clutch is completely disengaged, thus increasing durability and decreasing unnecessary friction and heat generation. It provides two way mechanical communication while allowing both overrunning and under running of unused power paths. The clutch mechanism is self powered and does not require external power, such as hydraulic or pneumatic pressure from a pump, nor electric energy. chosen. The presented CVT is among these linear ratcheting CVTs. Exponential Relationship Ratio (Speed of Roller Gear/Speed of Cam Gear) Angle of Cam Gear (radians) Figure 2: Exponential Ratio Figure 2 shows the ratio of the roller gear/cam gear combination as a function of the angular position of the cam gear. The base of this function in each of the regions is chosen so that there is one revolution of the cam gear for each revolution of the roller gear. The ratio falls exponentially for the first and larger portion of revolution, known as the synchronized portion, and rises exponentially for the smaller portion known as the return portion. The angle describing the larger portion is known as. Angle of Roller Gear (radians) Angle of Cam Gear (radians) Figure : Angular Motion Figure shows the angle of the roller gear as a function of the cam gear rotation. Exponential CVT Designs Exponential CVTs make use of exponential variations in rotation. They may be considered to be ratcheting CVTs in that they have multiple power paths, one of which is

4 Figure 4: Simplified Exponential Gear Figure 4 is a simplified representation of the exponential roller gear and cam gear combination. The circle on the left represents the cam gear and the circle on the right represents the roller gear. Both are divided into larger synchronized and smaller return regions. The larger region on the left circle is a region with decreasing effective radius as it turns counterclockwise. The smaller region has an increasing effective radius as it turns counterclockwise. Likewise, the larger region on the right circle has an increasing effective radius as it turns clockwise and the smaller region has a decreasing effective radius as it turns clockwise. Figure 5: Exponential Cam Gear and Roller Gear Profiles Moving from the simplified circular representations of the gears to the physical manifestation, Figure 5 is the twodimensional profile of an exponential roller gear/cam gear pair. A cam gear interacting with a roller gear provides the exponential ratio. Figure 6 is the threedimensional view as fabricated in the prototype. Figure 6: Physical Cam Gear and Roller Gear Two Exponential Gear Meshes give a fixed ratio U.S. Patent 4,685,48 describes the use of noncircular gears to affect a CVT. Three noncircular gears with two spur gear meshes are used. The first gear mesh has exponentially increasing ratio that is dependent on the angle of the second gear. The angle of the second gear mesh relative to the first gear mesh can be varied. As the second gear turns a specified amount, for each increase in the ratio of the first mesh, there is a comparable decrease in the ratio of the second gear mesh. The ratio of the first gear to the third gear thus remains constant for a fixed angle between the meshes. I define a basic exponential gear set as a three-gear set made up of a center gear and two gears that have ratios that vary as the exponential of the rotation of the center gear. The center gear and one of the other gears are on fixed axes and the axis of the third gear translates about the center gear. The center gear in the presented CVT is made up of two gears. They are offset so that the first and third gears do not overlap. The offset is also chosen so that the maximum shift and minimum shift are symmetric about the plane through the fixed axles. The Sweet Spot A set of gears is operating in its sweet spot if each of its roller gear/cam gear pairs is operating in the synchronized region. The motion of the input shaft is related linearly to the output shaft in the sweet spot. This is the portion of the revolution that can be used to transmit power. At a 1:1 ratio, the sweet spot covers the entire synchronized region of all the meshes. As the angle between the meshes moves away from this, the

5 sweet spot is reduced. Of course, there is a limit to the linear behavior. As the first gear passes from synchronized region to the return region, the ratios of both meshes are increasing and thus the overall ratio is as well. Also, when the second gear mesh passes from synchronized region to the return region, the overall ratio is decreasing. Figure 9: Simplified gears in the most positive shift position Figure 7 is a simplified representation of the full gear train on both the left and right sides of the presented transmission. The left side is above the right side. The small index marks on the fixed gears show the allowance for clutch engagement. During this part of the rotation, the gear train is in the sweet spot and the drum and both clutches are moving at the same speed. The clutch in the non-active power path clutches fully prior to it becoming the active power path. The clutch in what had been the active power path releases fully before the drum speed relative to the clutch changes. 12 Translating Gear (radians) Figure 7: Simplified gears in the most negative shift position Figure 9 is also a simplified representation of the full gear train on both the left and right sides of the presented transmission, but this time it is in the most positive shift position. Again, the left side is above the right side and the small index marks on the fixed gears show the allowance for clutch engagement. 9 6 Right Side Left Side Translating Gear (radians) Fixed Gear (radians) Figure 1: Motion of Left and Right Power Paths Right Side 6 Left Side Figure 1 is the angular position of the fixed gears relative to the angular position of the translating gear for the positive shift position. The more shallow sloped regions are in the sweet spot and are used to transfer power. 6 9 Fixed Gear (radians) 12 There are steeper slope and shallower slope regions on Figures 8 and 1. Each of these is in the sweet spot of the rotation. Both are used in the presented CVT, one for positive shift positions and the other for negative shift positions. Figure 8: Motion of Left and Right Power Paths Figure 8 is the angular position of the fixed gears relative to the angular position of the translating gear. The more steeply sloped regions are in the sweet spot and are used to transfer power. At the extreme shifting positions, the sweet spot of one power path is just long enough to cover the portion of the other path that is not in the sweet spot. The position of the gear is described by the angular position of the reference line. The ratio is the cam effective radius divided by the roller assembly effective radius. Figure 11: Top view of main power handling parts

6 The roller/cam pairs are located on three centers of rotation, two fixed and one translating to provide the varying ratio. Power crosses four gear meshes between the inline input and output shafts. Clutch Control The distance of the rollers from the axis of rotation of the roller gear varies. The distance on a specific roller generally matches the size of a circular gear radius at closest crossing. Band Clutch Description Two power paths are used and the power from the appropriate path is fed into the output by a band clutch that is synchronized to the output by the exponential gears and tightened by an internal cam. The cam is made up of telescoping segments driven in a nonlinear fashion by the location of the translating axle. The exponential ratios control the motion of the roller gears with clutches. Any overload that would cause clutch slippage would not affect the timing of the gear train as the drum on the output is the point at which the left and right power paths come together. Roller Gear/Cam Gear Description The roller gear is made of two plates with rollers mounted between them on bearings. The rollers act as gear teeth. In interacting with the cams, at least one roller is pushing forward and at least one is holding back. Figure 14: Band Clutch on Drum, One Side Removed

7 The output shaft is fastened to a drum that is alternatively driven by right and left clutches. The clutches are bands that are tightened by an arm with a wheel that is rolling inside the clutch control loops. Raised sections on the control loops press the arm in as it passes, thus tightening the band and locking the roller gear to the drum and output shaft. Forces on the Translating Gear The variation in ratio of the translating gears relative to the fixed ratio idler gear causes torque on the support beam. By choosing an appropriately sized idler gear, this torque can be made to cycle through positive and negative values within one revolution of the input shaft. This torque can be used to shift the CVT. In the presented CVT, pawls control the motion of the support beam. They are released in the direction of desired movement. Accelerating Parts The roller gear that drives the clutches moves at a constant speed, goes through a transition and then moves at another constant speed. It does not have to reverse direction; rather it speeds up and slows down. Many of the parts of the presented CVT turn at speeds that are proportional to the speed of the input. The parts that do not are the cam gear that varies exponentially and the roller gear that drives the clutches. This moves in a stepwise linear fashion. TEST RESULTS Basic efficiency testing was performed to assess the efficiency of the prototype. Test Setup The source of power for the testing was a 2 Toyota Prius with a front wheel removed and an adapter plate installed. A drum brake provided the load. Torque sensors and tachometers measured the power in at the input shaft and out at the output shaft. Data was gathered via RS-22 into a laptop computer. Efficiency Initial testing at the 1:1 shift position demonstrated approximately 87% efficiency at 2 rpm and 6 Nm torque. Additional testing across the full range of ratios is ongoing. CONCLUSION The presented CVT provides a mechanical continuously variable transmission that provides two way mechanical communication. It has linear ratios throughout the power cycle and transfers power without slip or spin. Shifting can be self-powered. It does not require outside control such as computer control or active operator control. It has low frictional losses and supports high torque loads. ACKNOWLEDGMENTS I would like to acknowledge the skill of the people at OMW Corporation, Novato, CA, who performed the machining and shared in the assembly of the prototype. I would also like to acknowledge the expert assistance of Cooper Instruments and Systems, Warrenton, VA, who supplied instrumentation for testing. REFERENCES 1. US Patent 4,685,48 2. US Patent 4,765,195. US Patent 5,4, US Patent 6,212, CONTACT I can be contacted by phone at or at Jim.Nugent@GearClearTech.com. DEFINITIONS, ACRONYMS, ABBREVIATIONS Active power path: a power path that is providing torque between input and output. Synchronous region: a portion of the revolution of a gear pair that is used when the power path is active. Return region: a portion of the revolution of a gear pair used to return the gears to the desired ratio in the synchronized region. Roller gear: a set of rollers held in a supporting frame that rotate individually and are held in a frame that rotates as a unit. Cam gear: a cam that interacts with a roller gear as a gear set to provide arbitrary gear ratios. Basic exponential gear set: A three gear set made up of a center gear and two gears that have ratios that vary as the exponential of the rotation of the center gear. The center gear and one of the other gears are on fixed axes and the axis of the third gear translates about the center gear. Exponential fixed gear: the fixed gear in a basic exponential gear set. Exponential center gear: the center gear in a basic exponential gear set. Exponential translating gear: the gear that moves around in a basic exponential gear set.

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