Mech Report

Embed Size (px)

DESCRIPTION

Continously variable transmission

Citation preview

ABSTRACTThis research shows that an existing rear wheel drive vehicle can be easily retrofitted with a continously variable transmission for the purpose of reducing the over all fuel consumption of the vehicle. This retrofit ability of this transmission is the primary advantage that it exhibits over other type of continously variable transmissions. By retrofitting this vehicle with the transmission components that are shown here, the existing vehicle transmission continoues to be used with the exception of the driveshaft which is replaced by the hydraulic continously variable transmission itself. Using a standard model for he vehiocle dynamics, this paper presents a detailed analysis for the speed ratios of all gears, and shows how to specify the size of the hydraulic pump and motor to insure a safe pressure level of operation. To illustrate the usefulness of this technology, an actual transmission designed for the 1997 ford ranger and the range of adjustability for the transmission is evaluated by seeking to hold the engine speed contant for the ramped speed output of the vehicle. In conclusion, this research shows that the design methodology is valid and that only minor errors in engine speed are observed during he low ground velocities for this vehicle.

INTRODUCTION

Continously variable transmission have been in use in the automotive industry for many years. The motivation for using a continously variable transmission in an automobile is to achieve a continously variable transmission of power, which allows the internal combustion engine to operate at its most efficient operating point for a given power requirement. Studieshave shown that these transmissions are able to reduce fuel consumption by upto 60%. Although continouly variable transmission have been in existence for many year and although they show tremendous promise for reducing fuel consumption, they are nevertheless too expensive to receive widespread acceptance in the market. Much of these is due to the facty that most conventional tecnologies use the elctric type of continously variable transmission and the components for these transmission are not affordable.In order to increase the penetration of continously variable technology into the automotive market, the environmental protection agency (EPA) has been sponsoring programs for the development of hydraulic hybrid vehicles. The EPA deems a hydraulic continously variable vehicle as being more cost effective than an electric continously variable vehicle. However the hydraulic designs have not proven themselves to be acceptable due to the high level of audible noisethat they genrate especially when operating at high pressures. In other words, he benefits of increased fuel efficiency and lower first-time buying costs have not been enough to persuade consumers to live with the noise that is associated with a hydraulic continously variable transmission vehicle. In this state of affairs only the electric continously variable-variable is sold for passenger use, and only a few of these are purchased by individuals who have enough wealth to put environmental concerns ahead of their pocketbook. In particular, the feasability of retrofitting an existing rear wheeldrive vehicle with a hydraulic continously variable transmission is explored to provide environmentally conscious individuals with an option to upgrade their vehicles without paying the high cost associated with an electric continously variable design. While this current solution does not address the noise issue associated with the hydraulic transmission, it does address the cost issue by using less expensive hydraulic components and by using less expensive hydraulic components and by using the existing mechanical transmission in the vehicle wih its associated differential gear at the final drive. The proposed transmission in this paper simply replaces the drive shaft in the vehicle with a hydraulic continously variable transmission, thus creating a continously variable transmission of power that is capable of significantly reducing the fuel consumption, thus, creating a continously variable transmissionof power that is capable of significantly reducing the fuel consumption of the automobile.In other words, if the end user is willing to endure the traditional noise levels that are associated with the hydraulic, the continously variable transmission, the continously variable transmission, the continously variable transmissionprposed here can significantly reduce fuel consum[ption cost for that individual while simultaneously serving to preserve the environment from the side effects of burning excess petroleum based fuels.

LITERATURE REVIEW

Automotive continuously variable-transmission research has been aimed operating the internal combustion engine at a point of maximum efficiency for a given power demand. This research has been roughly divided between electric continuously variable-technologies and hydraulic continuously variable-technologies. Examples of electric continuously variable. The application for this design is given by a rear-wheel drive automobile in which the existing transmission components research include work done by Pfiffner et al. in which a numerical method isused to model the transmission and to optimize the engine efficiency. This work does not model the transmission in detail but considers the efficiency characteristics of the engine. The efficiency of the transmission is assumed to be 100%. Pfiffner concludes that fuel consumption may be reduced by as much as 5% using the proposed method of control. Mapelli et al. have considered a transmission similar to that of Pfiffner; however, they have given greater attention to the losses in the transmission itself. This work does not present a comparison of the continuously variable vehicle with a more conventional design and so it is difficult to know whether or not any improvements have been made. Kessels et al provide more detail in the description of their electric continuously variable-vehicle which consists of two motor-generators with power electronics being used to regulate\ battery power input and output. By considering the efficiency of all components, Kessels and colleagues conclude that it may not always be best to operate the engine at its point of maximum efficiency for a given power demand since global optimal vehicle efficiency may not correspond with this operating point. Ehsani et al have provided a more comprehensive textbook for considering the fundamental building block of electric continuously variable vehicles. Hydraulic continuously variable-transmissions have been studied by Kumar and Ivantysynova in which a continuously variable pump and motor are used with an accumulator to provide a capacity for storing braking energy as well as optimizing the efficiency of the engine. This work concludes that the hydraulic continuously variable-design can reduce the fuel consumption of a comparable electric continuously variable-transmission by over 16%. A fair amount of work has also been done on hydraulic hybrid-technologies at the University of Missouri. Dirck has modeled a simple hydraulic hybrid which utilizes a parallel discrete-transmission to show that the fuel consumption of a typical automobile may be reduced by 37% for city driving and 14% for highway driving. Vermillion has modeled a more complex hydraulic continuously variable-transmission which utilizes a pressure compensated pump, and a variable displacement motor while considering the efficiency characteristics of the hydraulics. In his work, Vermillion has shown that fuel consumption may be reduced by just 1.28% in the city, and by over 22% for highway driving. Al-Ghrairi has shown that the transmission modeled by Vermillion can be designed within a compact space while ensuring that all transmission components, including complex gear arrangements, can satisfy the safety-factor requirements that are typical of modern machine design practice. All of this work, among others, has been very useful for considering barriers that may be encountered when implementing continuously variable-transmission-technology. Most of the work described in this literature has focused on the control of the continuously variable-transmission with an objective to eitheroptimize the engine efficiency or to optimize the overall vehicle efficiency. While this is the ultimate objective for these transmissions; this work has assumed that the transmission design is easily achieved and therefore the design of intermediate pumps, motors, and gearing is almost entirely neglected.

THEORY

Continously Variable Transmission:

Definition of Continous Variable Transmission:

A continuously variable transmission (CVT) is a transmission that can change seamlessly through an infinite number of effective gear ratios between maximum and minimum values. This contrasts with other mechanical transmissions that offer a fixed number of gear ratios. The flexibility of a CVT allows the input shaft to always maintain a constant angular velocity. CVT can provide better fuel economy than other transmissions by enabling the engine to run at its most efficient revolutions per minute (RPM) for a range of vehicle speeds. It can also be used to build a kinetic energy recovery system. Alternatively it can be used to maximize the performance of a vehicle by allowing the engine to turn at the RPM at which it produces peak power. This is typically higher than the RPM that achieves peak efficiency. Finally, a CVT does not strictly require the presence of a clutch, allowing its dismissal. In some vehicles though (e.g. motorcycles), a centrifugal clutch is nevertheless added, however this is only to provide a "neutral" stance on a motorcycle (useful when idling, or manually reversing into a parking space).

Uses and Application of Continously Variable Transmission:

Many small tractors for home and garden use have simple rubber belt CVTs. For example, the John Deere Gator line of small utility vehicles use a belt with a conical pulley system. They can deliver an abundance of power and can reach speeds of 1015mph (1624km/h), all without need for a clutch or shifting gears. Nearly all snowmobiles, old and new, and motorscooters use CVTs, typically the rubber belt/variable pulley variety. Some combine harvesters have CVTs. The CVT allows the forward speed of the combine to be adjusted independently of the engine speed. This allows the operator to slow or accelerate as needed to accommodate variations in thickness of the crop. CVTs have been used in aircraft electrical power generating systems since the 1950s and in Sports Car Club of America (SCCA) Formula 500 race cars since the early 1970s. CVTs were banned from Formula 1 in 1994 due to concerns that the best-funded teams would dominate if they managed to create a viable F1 CVT.[2] More recently, CVT systems have been developed for go-karts and have proven to increase performance and engine life expectancy. The Tomcar range of off-road vehicles also utilizes the CVT system. Some drill presses and milling machines contain a pulley-based CVT where the output shaft has a pair of manually adjustable conical pulley halves through which a wide drive belt from the motor loops. The pulley on the motor, however, is usually fixed in diameter, or may have a series of given-diameter steps to allow a selection of speed ranges. A handwheel on the drill press, marked with a scale corresponding to the desired machine speed, is mounted to a reduction gearing system for the operator to precisely control the width of the gap between the pulley halves. This gap width thus adjusts the gearing ratio between the motor's fixed pulley and the output shaft's variable pulley, changing speed of the chuck. A tensioner pulley is implemented in the belt transmission to take up or release the slack in the belt as the speed is altered. CVTs should be distinguished from Power Sharing Transmissions (PSTs), as used in newer hybrid cars, such as the Toyota Prius, Highlander and Camry, the Nissan Altima, and newer-model Ford Escape Hybrid SUVs. CVT technology uses only one input from a prime mover, and delivers variable output speeds and torque; whereas PST technology uses two prime mover inputs, and varies the ratio of their contributions to output speed and power. These transmissions are fundamentally different. However the Mitsubishi Lancer, Proton Inspira, Honda Insight, Honda Fit, and Honda CR-Z hybrids, the Nissan Tiida/Versa (only the SL model), Nissan Cube, Juke, Sentra, Altima, Maxima, 2013 1.2 Note, Rogue, X-Trail, Murano, Sunny, Micra, Honda Capa, Honda Civic HX, Jeep Patriot and Compass, and Subaru Impreza, Legacy and Outback, and Caliber offer CVT.

Types Of Continously Variable Transmission

Variable diameter pulley (VDP) or Reeves drive Torroidal or roller based CVT (Extroid CVT) Magnetic CVT Infiniely Variable Transmission (IVT) Racheting CVT Hydraulic CVT Naudic Incremental CVT (iCVT) Cone CVT Radial roller CVT Planetary CVT

Variable diameter pulley (VDP) or Reeves drive:

In this most common CVT system, there are two V-belt pulleys that are split perpendicular to their axes of rotation, with a V-belt running between them. The gear ratio is changed by moving the two sheaves of one pulley closer together and the two sheaves of the other pulley farther apart. Due to the V-shaped cross section of the belt, this causes the belt to ride higher on one pulley and lower on the other. Doing this changes the effective diameters of the pulleys, which in turn changes the overall gear ratio. The distance between the pulleys does not change, and neither does the length of the belt, so changing the gear ratio means both pulleys must be adjusted (one bigger, the other smaller) simultaneously in order to maintain the proper amount of tension on the belt.The V-belt needs to be very stiff in the pulley's axial direction in order to make only short radial movements while sliding in and out of the pulleys. This can be achieved by a chain and not by homogeneous rubber. To dive out of the pulleys one side of the belt must push. This again can be done only with a chain. Each element of the chain has conical sides, which perfectly fit to the pulley if the belt is running on the outermost radius. As the belt moves into the pulleys the contact area gets smaller. The contact area is proportional to the number of elements, thus the chain has lots of very small elements. The shape of the elements is governed by the static of a column. The pulley-radial thickness of the belt is a compromise between maximum gear ratio and torque. For the same reason the axis between the pulleys is as thin as possible. A film of lubricant is applied to the pulleys. It needs to be thick enough so that the pulley and the belt never touch and it must be thin in order not to waste power when each element dives into the lubrication film. Additionally, the chain elements stabilize about 12 steel bands. Each band is thin enough so that it bends easily. If bending, it has a perfect conical surface on its side. In the stack of bands each band corresponds to a slightly different gear ratio, and thus they slide over each other and need oil between them. Also the outer bands slide through the stabilizing chain, while the center band can be used as the chain linkage.

Torroidal or roller based CVT (Extroid CVT):

Toroidal CVTs are made up of discs and rollers that transmit power between the discs. The discs can be pictured as two almost conical parts, point to point, with the sides dished such that the two parts could fill the central hole of a torus. One disc is the input, and the other is the output. Between the discs are rollers which vary the ratio and which transfer power from one side to the other. When the roller's axis is perpendicular to the axis of the near-conical parts, it contacts the near-conical parts at same-diameter locations and thus gives a 1:1 gear ratio. The roller can be moved along the axis of the near-conical parts, changing angle as needed to maintain contact. This will cause the roller to contact the near-conical parts at varying and distinct diameters, giving a gear ratio of something other than 1:1. Systems may be partial or full toroidal. Full toroidal systems are the most efficient design while partial toroidals may still require a torque converter, and hence lose efficiency.Some toroidal systems are also infinitely variable, and the direction of thrust can be reversed within the CVT.

Magnetic CVT:

A magnetic continuous variable transmission system was developed at the University of Sheffield in 2006 and later commercialized. mCVT is a variable magnetic transmission which gives an electrically controllable gear ratio. It can act as a power split device and can match a fixed input speed from a prime-mover to a variable load by importing/exporting electrical power through a variator path. The mCVT is of particular interest as a highly efficient power-split device for blended parallel hybrid vehicles, but also has potential applications in renewable energy, marine propulsion and industrial drive sectors. The magnetic CVT cannot generate greater torque than an electric motor of the same size, so it is not a replacement for mechanical automobile transmission.

Infiniely Variable Transmission (IVT):

A subset of CVT designs are called infinitely variable transmissions (IVT or IVTs), in which the range of ratios of output shaft speed to input shaft speed includes a zero ratio that can be continuously approached from a defined "higher" ratio. A zero output speed (low gear) with a finite input speed implies an infinite input-to-output speed ratio, which can be continuously approached from a given finite input value with an IVT. Low gears are a reference to low ratios of output speed to input speed. This low ratio is taken to the extreme with IVTs, resulting in a "neutral", or non-driving "low" gear limit, in which the output speed is zero. Unlike neutral in a normal automotive transmission, IVT output rotation may be prevented because the backdriving (reverse IVT operation) ratio may be infinite, resulting in impossibly high backdriving torque; in a ratcheting IVT, however, the output may freely rotate in the forward direction. The ratcheting IVT dates back to before the 1930s; the original design converts rotary motion to oscillating motion and back to rotary motion using roller clutches. The stroke of the intermediate oscillations is adjustable, varying the output speed of the shaft. This original design is still manufactured today, and an example and animation of this IVT can be found here. Paul B. Pires created a more compact (radially symmetric) variation that employs a ratchet mechanism instead of roller clutches, so it doesn't have to rely on friction to drive the output.Many IVTs result from the combination of a CVT with a planetary gear system which enforces an IVT output shaft rotation speed which is equal to the difference between two other speeds within the IVT. This IVT configuration uses its CVT as a continuously variable regulator (CVR) of the rotation speed of any one of the three rotators of the planetary gear system (PGS). If two of the PGS rotator speeds are the input and output of the CVR, there is a setting of the CVR that results in the IVT output speed of zero. The maximum output/input ratio can be chosen from infinite practical possibilities through selection of additional input or output gear, pulley or sprocket sizes without affecting the zero output or the continuity of the whole system. The IVT is always engaged, even during its zero output adjustment.IVTs can in some implementations offer better efficiency when compared to other CVTs as in the preferred range of operation because most of the power flows through the planetary gear system and not the controlling CVR. Torque transmission capability can also be increased. There's also possibility to stage power splits for further increase in efficiency, torque transmission capability and better maintenance of efficiency over a wide gear ratio range.

Racheting CVT:

The ratcheting CVT is a transmission that relies on static friction and is based on a set of elements that successively become engaged and then disengaged between the driving system and the driven system, often using oscillating or indexing motion in conjunction with one-way clutches or ratchets that rectify and sum only "forward" motion. The transmission ratio is adjusted by changing linkage geometry within the oscillating elements, so that the summed maximum linkage speed is adjusted, even when the average linkage speed remains constant. Power is transferred from input to output only when the clutch or ratchet is engaged, and therefore when it is locked into a static friction mode where the driving & driven rotating surfaces momentarily rotate together without slippage.These CVTs can transfer substantial torque, because their static friction actually increases relative to torque throughput, so slippage is impossible in properly designed systems. Efficiency is generally high, because most of the dynamic friction is caused by very slight transitional clutch speed changes. The drawback to ratcheting CVTs is vibration caused by the successive transition in speed required to accelerate the element, which must supplant the previously operating and decelerating, power transmitting element.Ratcheting CVTs are distinguished from VDPs and roller-based CVTs by being static friction-based devices, as opposed to being dynamic friction-based devices that waste significant energy through slippage of twisting surfaces. An example of a ratcheting CVT is one prototyped as a bicycle transmission protected under U.S. Patent 5,516,132 in which strong pedalling torque causes this mechanism to react against the spring, moving the ring gear/chainwheel assembly toward a concentric, lower gear position. When the pedaling torque relaxes to lower levels, the transmission self-adjusts toward higher gears, accompanied by an increase in transmission vibration.

Hydraulic CVT:

Hydraulic transmissions use a variable displacement pump and a hydraulic motor. All power is transmitted by hydraulic fluid. These types can generally transmit more torque, but can be sensitive to contamination. Some designs are also very expensive. However, they have the advantage that the hydraulic motor can be mounted directly to the wheel hub, allowing a more flexible suspension system and eliminating efficiency losses from friction in the drive shaft and differential components. This type of transmission is relatively easy to use because all forward and reverse speeds can be accessed using a single lever.An integrated hydrostatic transaxle (IHT) uses a single housing for both hydraulic elements and gear-reducing elements. This type of transmission has been effectively applied to a variety of inexpensive and expensive versions of ridden lawn mowers and garden tractors.One class of riding lawn mower that has recently gained in popularity with consumers is zero turning radius mowers. These mowers have traditionally been powered with wheel hub mounted hydraulic motors driven by continuously variable pumps, but this design is relatively expensive.Some heavy equipment may also be propelled by a hydrostatic transmission; e.g. agricultural machinery including foragers, combines, and some tractors. A variety of heavy earth-moving equipment manufactured by Caterpillar Inc., e.g. compact and small wheel loaders, track type loaders and tractors, skid-steered loaders and asphalt compactors use hydrostatic transmission. Hydrostatic CVTs are usually not used for extended duration high torque applications due to the heat that is generated by the flowing oil. Although there are a variety of oil cooler designs to help counter this problem.The Honda DN-01 motorcycle is the first road-going consumer vehicle with hydrostatic drive that employs a variable displacement axial piston pump with a variable-angle swashplate.AGCO Corporation has employed the use of a hydrostatic CVT transmission for use in agricultural equipment. The transmission splits power between hydrostatic and mechanical transfer to the output shaft via a planetary gear in the forward direction of travel. In reverse the power transfer is fully hydrostatic.

Naudic Incremental CVT (iCVT):

The variator pulley of an iCVT is choked using two small choking pulleys. Here one choking pulley is positioned on the tense side of the chain of the iCVT. Hence there is a considerable load on that choking pulley, the magnitude of which is proportional to the tension in its chain. Each choking pulley is pulled up by two chain segments, one chain segment to the left and one to the right of the choking pulley; here if the two chain segments are parallel to each other, then the load on the choking pulley is twice the tension in the chain. But since the two chain segments are most likely not parallel to each other during operations of an iCVT, it is estimated that the load on a choking pulley is between 1 to 1.8 times of the tension of its chain.Also, a choking pulley is very small so that its moment arm is very small. A larger moment arm reduces the force needed to rotate a pulley. For example, using a long wrench, which has a large moment arm, to open a nut requires less force than using a short wrench, which has a small moment arm. Assuming that the diameter of a choking pulley is twice the diameter of its shaft, which is a generous estimate, then the frictional resistance force at the outer diameter of a choking pulley is half the frictional resistance force at the shaft of a choking pulley.The transmission ratio of an iCVT has to be changed one increment within less than one full rotation of its variator pulley. This means that the transmission diameter of the variator pulley, made generally from rubber, has to be changed from a diameter that has a circumferential length that is equal to an integer number of teeth to another diameter that has a circumferential length that is equal to an integer number of teeth; such as changing the transmission diameter of the variator pulley from a diameter that has a circumferential length of 7 teeth to a diameter that has a circumferential length of 8 teeth for example. This is because if the transmission diameter of the variator pulley does not have a circumferential length that is equal to an integer number of teeth, such as a circumferential length of 7 teeth for example, improper engagement between the teeth of the variator pulley and its chain will occur. For example, imagine having a bicycle pulley with 7 teeth; here improper engagement between the bicycle pulley and its chain will occur when the tooth behind the tooth space is about to engage with its chain, since it is positioned a distance of tooth too late relative to its chain.

Cone CVT:

A cone CVT varies the effective gear ratio using one or more conical rollers. The simplest type of cone CVT, the single-cone version, uses a wheel that moves along the slope of the cone, creating the variation between the narrow and wide diameters of the cone.In a CVT with oscillating cones, the torque is transmitted via friction from a variable number of cones (according to the torque to be transmitted) to a central, barrel-shaped hub. The side surface of the hub is convex with a specific radius of curvature which is smaller than the concavity radius of the cones. In this way, there will be only one (theoretical) contact point between each cone and the hub at any time.A new CVT using this technology, the Warko, was presented in Berlin during the 6th International CTI Symposium of Innovative Automotive Transmissions, on 37 December 2007.A particular characteristic of the Warko is the absence of a clutch: the engine is always connected to the wheels, and the rear drive is obtained by means of an epicyclic system in output.[15] This system, named power split,[16] allows the engine to have a "neutral gear": when the engine turns (connected to the sun gear of the epicyclic system), the variator (i.e., the planetary gears) will compensate for the engine rotation, so the outer ring gear (which provides output) remains stationary.

Radial roller CVT:

The working principle of this CVT is similar to that of conventional oil pumps, but, instead of pumping oil, common steel rollers are compressed.The motion transmission between rollers and rotors is assisted by an adapted traction fluid, which ensures the proper friction between the surfaces and slows down wearing thereof. Unlike other systems, the radial rollers do not show a tangential speed variation (delta) along the contact lines on the rotors. From this, a greater mechanical efficiency and working life are claimed.

Planetary CVT:

In a planetary CVT, the gear ratio is shifted by tilting the axes of spheres in a continuous fashion, to provide different contact radii, which in turn drive input and output discs. The system can have multiple "planets" to transfer torque through multiple fluid patches. One commercial implementation is the NuVinci Continuously Variable Transmission.

RETROFITTING OF THE CVT TO THE VEHICLE

Transmission Description:

Fig. 1 Schematic of the hydraulic continously variable transmission

Figure 1 shows a schematic of the hydraulic continuously variable-transmission as it is arranged within an automobile in a retrofitted configuration. In this schematic, four automobile tires are shown in each quadrant of the figure; however, only the rear tires are driven by the transmission. In other words, this vehicle is a rear-wheel-drive machine. The internal combustion engine is shown between the two front tires which is the traditional location for the engine. The standard automotive transmission is downstream of the engine and its discrete and shift-able speed ratio is symbolized by t. On the output shaft of the standard transmission, a spur gear is shown to split the power transmission between a mechanical path and a hydraulic path. This spur gear is shown in a simple configuration; however, it should be mentioned that a compound spur gear is likely to be used in order to achieve the needed speed ratios for this gear. The mechanical power path is shown in Fig. 1 to be a simple shaft that rotates at an angular velocity 1. The hydraulic power path is a standard hydrostatic transmission, which comprised variable displacement pump and a fixed displacement motor. The shaft speed of the pump is shown in Fig. 1 by 2 and the shaft speed of the motor is shown by h. As shown in Fig. 1, the mechanical and hydraulic power paths are reconnected by a planetary gear as indicated by the symbol in the figure. The output shaft of the planetary gear is then connected to a standard differential, which then transmits power to each rear-wheel axle. It is important to note that this transmission does not include an energy storage component and that it is not capable of regenerating brake energy. The transmission shown in Fig. 1 achieves its improved efficiency by operating the internal combustion engine at an optimal operating point and thereby increasing fuel efficiency by as much as 60%. If an energy storage device was included, additional improvements would be realized. The important feature of this transmission layout is that the continuously variable-transmission can serve as a retrofit design for the vehicle. In other words, the main drive shaft between the standard mechanical transmission and the differential can be dropped out of the vehicle, and replaced with the continuously variable-transmission comprised a spur gear, mechanical shaft, a hydraulic transmission, and a planetary gear. This paper will describe how this transmission can be designed to achieve the advantages of a continuously variable-transmission, without replacing other main power and power-transmitting components of the automobile.

Automobile Modeling:

Fig. 2 Automobile schematic

Figure 2 shows a schematic of an automobile that will be used as the basis for the analysis, design, and control of the hydraulic continuously variable-transmission. In this figure, the vehicle is shown to travel on a flat surface to the left at a velocity v. The mass of the vehicle is shown by the symbol m and a force F between the rear tire and the road is shown to move the vehicle forward. The torque and speed of the tire are shown by the symbols T and , and the tire radius is given by the symbol R. In the following paragraph, the dynamic motion of the vehicle will be modeled. Summing the forces acting on the vehicle in the horizontal direction, the following equation of motion may be written:

where the second term on the right represents the wind resistance which is proportional to the square of the velocity v, and the third term on the right represents the rolling resistance of the vehicle due to the vehicle weight. These terms are standard vehicle modeling terms that may be accessed in the literature. In the eqn. is the density of air, Cd is the dimensionless drag coefficient for the vehicle, A is the effective frontal areal of the vehicle, is the dimensionless rolling-resistance coefficient, and g is the gravitational constant. From a static analysis of the tires, it may be shown that the force exerted on the automobile in the horizontaldirection is given by

where the factor of 2 indicates that there are two tires, each being turned with a torque T. Similarly, if it is assumed that the tires do not slip, it may be shown that the vehicle velocity in the horizontal direction is give by

Where is the angular velocity of each tire. By substituting Eqs. the following equation of motion for the automobile may be written as follows:

The input to this equation is the torque, T which will be delivered from the vehicle engine to each tire through the vehicle transmission. The analysis and modeling of the transmission will becarried out in Transmission Analysis section of this paper.

Transmission Analysis:

This section will be used to analyze the transmissioncomponents for the hydraulic continuously variable-transmission shown in Fig.1. The objective of this analysis will be to identify the overall speed ratio between the engine and the tires of the vehicle and to illustrate how this speed ratio can be made into a continuously variable type through the adjustment of the swash plate angle for the pump. This analysis will be conducted by considering each transmission component in its turn and by assuming that all transmission components are 100% efficient.

1. Mechanical transmission

Figure 1 shows a mechanical transmission connected to the engine that is adjustable between adiscrete set of speed ratios. For a typical automotive application, there are five different speed ratios that may be selected. The conveyance of power through the mechanical transmission may be written as and t 3 + e = 0

where Te and e are the torque and speed from the engine, and T3 and 3 are the torque and speed delivered to the central gear on the spur gear set. The symbol t represents the adjustablespeed ratio for the mechanical transmission.

2. Spur Gear

Figure 1 also shows a spur gear connected to the mechanical transmission. As was mentioned earlier, this gear most likely needs to be of the compound gear type to achieve the needed speed ratios and therefore Figure 3 is presented to illustrate this gear in a more realistic arrangement. Figure 3 is drawn as viewed from the rear of the vehicle looking toward the engine where r1, r2, r31 , and r32 are the pitch radii for each gear. Note that the center distances between the hydraulic and mechanical paths of the gear train are shown by the symbols Ch and Cm, respectively. To satisfy kinetic equilibrium and kinematic relations, in may be shown that

, and

Fig. 3 Schematic of the compound spur gear

Where the speed ratios are given by1 = and 2 =

3. Hydraulic Transmission

Fig. 4 Schematic of the transmission

The hydraulic transmission is shown in Fig. 1, being comprised a displacement controlled pump, and fixed displacement motor. It may be shown that the input and output torque for the hydraulic transmission are given by

and

where P is the working pressure of the transmission,Vp is the maximum volumetric displacement for the pump, is the normalized swash-plate angle of the pump which ranges between and Vm is the volumetric displacement of the motor. Similarly, the speed of the pump and motor, respectively, may be written as follows:

and

where Q is the volumetric flow rate from the pump to the motor.By algebraically eliminating P and Q from Eqs. respectively, the conveyance of power through the hydraulic transmission may be written as

and

where the speed ratio for the hydraulic transmission is given by

h =

It is important to note that a pressure limitation exists within the hydraulic circuit due to stress limits in the design, and that Eq. (10) does not explicitly account for this limitation. Equation (8) will be used to account for this in the design section of this paper. Equation (11) shows that the speed ratio for the hydraulic transmission is controlled by altering the swash-plate angle of the pump. The intelligent control of this swash-plate angle is the mechanism by which the improved efficiency for the overallpower transmission is accomplished; therefore, optimal control for this parameter becomes a very important topic for achieving the transmission objective. The automatic control for this parameter is beyond the scope of this present research, however, this paper provides a mathematical description of the plant to be controlled.

4. Swash Plate

Fig. 5 Swashplate working

The rotating shaft and plate are shown in silver. The fixed plate is shown in gold and six shafts each take a reciprocating motion from points on the gold plate. The shafts might be connected to pistons in cylinders. Note the power may be coming from the shaft to drive the pistons as in a pump, or from the pistons to drive the shaft rotation as in an engine. A swashplate is a device used in mechanical engineering to translate the motion of a rotating shaft into reciprocating motion, or to translate a reciprocating motion into a rotating one to replace the crankshaft in engine designs.

Fig. 6 Construction of swashplate

Construction:

A swashplate consists of a disk attached to a shaft. If the disk were aligned perpendicular to the shaft, then rotating the shaft would merely turn the disk with no reciprocating (or swashplate) effect. But instead the disk is mounted at an oblique angle, which causes its edge to appear to describe a path that oscillates along the shaft's length as observed from a non-rotating point of view away from the shaft. The greater the disk's angle to the shaft, the more pronounced is this apparent linear motion. The apparent linear motion can be turned into an actual linear motion by means of a follower that does not turn with the swashplate but presses against one of the disk's two surfaces near its circumference. The device has many similarities to the cam.

The swashplate engine uses a swashplate in place of a crankshaft to translate the motion of a piston into rotary motion. Internal combustion engines and Stirling engines have been built using this mechanism. The axial piston pump drives a series of pistons aligned coaxially with a shaft through a swashplate to pump a fluid.

A helicopter swashplate is a pair of plates, one rotating and one fixed, that are centered on the main rotor shaft. The rotating plate is linked to the rotor head, and the fixed plate is linked to the operator controls. Displacement of the alignment of the fixed plate is transferred to the rotating plate, where it becomes reciprocal motion of the rotor blade linkages. This type of pitch control, known as cyclic pitch, allows the helicopter rotor to provide selective lift in any direction. Nutating flowmeters and pumps have similar motions to the wobble of a swashplate, but do not necessarily transform the motion to a reciprocating motion at any time. Active Electronically Scanned Array (AESA) radars are flat plates that can scan up to sixty degrees in any direction from directly ahead of them. By mounting an AESA radar on a swashplate, the swashplate angle is added to the electronic scan angle. The typical swashplate angle chosen for this application is 40 degrees so the radar can scan a total angle of 200 degrees out of 360

5. Planetary GearAs shown in Fig. 1, the planetary gear is used to reconnect the hydraulic and mechanical path of the continuously variable-transmission and to distribute the combined power to the differential. A schematic for the planetary gear is shown in Fig. 7 as observed from the back of the vehicle while looking toward the engine. This figure shows the hydraulic path on the left-hand side and the mechanical path on the right-hand side. The planetary gear is in the middle. The hydraulic path is connected to the planetary gear by meshing gears with the outside ring. The pitch radii for these two gears are shown in Fig. 7 by the dimensions rh and rR. The mechanical path is connected to the planetary gear by meshing gears with a less obvious gear that is attached to the arm of the planetary gear. The arm for the planetary gear is shown in Fig. 7 by four spokes which are pinned to four planet gears. The gear that is attached to the arm is shown in Fig. 4 by the dashed pitch-circle with a radius rA and is located behind the plant gear itself. The gear for the mechanical path is shown by the pitch-circle radius rm. As in Figs. 3 and 7 shows the center distances between the hydraulic and mechanical paths of the gear train using the symbols Ch and Cm, respectively. To model the power transmission though the planetary gear, a simplified schematic for this gearing unit is shown in Fig. 8. This schematic more clearly identifies the sun, arm, planet, and ring. For simplicity, only one spoke of the arm and only one planet are shown in this figure. In the bottom four quadrants of Fig. 8, partial free-body diagrams are shown for each component in the planetary gear set. The following analysis will evaluate the static equilibrium of each component. The first component to consider is the sun gear. Summing moments on the sun about the fixed point O and setting them equal to zero produces the following equation for the rotational equilibrium of this component

where Ts is the applied torque to the sun gear, Fs is the reaction force between the sun gear and the planet gear, and rs is the pitch radius for the sun gear. Similarly, for the partial free-body-diagram of the arm shown in Fig. 8, summing moments on the arm about the fixed point O and setting them equal to zero produces the following equation for the rotational equilibrium ofthe arm:

where Ta is the applied torque to the arm, Fa is the reaction force at the pin joint between the arm and the planet gear, and ra is the radial dimension shown in Fig. 8.

Fig. 7 Schematic of the planetary gear

Fig. 8 Parial free body diagrams for the components within the planetary gear

Continuing this analysis, Fig.8 shows a partial free-body-diagram for the planet gear. It is important to note that the planets do not convey power themselves and as such they undergo no rotational torque. They are idlers. In this case, summing forces on the planet in the vertical direction and setting them equal to zero produces the following equilibrium equation for the planet:

Finally, summing moments on the ring gear shown in Fig. 8, and setting them equal to zero, produces the following equation for the rotational equilibrium of the ring:

where Tr is the applied torque to the arm, Fs is the reaction force between the planet gear and the ring gear, and rr is the internal pitch radius for the ring gear. Assuming that the applied torque tothe sun gear is known, the following results may be obtained by a simultaneous solution for Eqs. (12)(15):

,

,

where the speed ratios for the arm and ring are given, respectively, as

Note that these speed ratios are also shown in Fig. 8. Throughout the remaining analysis, the forces Fa and Fs will not be referred to; however, the torque results in Eq. (17) are very important and will be used extensively. To conclude the analysis for the planetary gear, it is important to consider the net power that is being transferred by the gears. Assuming that the power is transferred without any losses due to friction, the conservation of power within the gear set may be written as

Substituting the torque from Eq. (17) into this result produces the following expression for the conservation of power in the planetary gear set:

In summary, these equations may be used to describe the kinetic and kinematic behavior of the planetary gear set. Figure 1 shows a mechanical path of power, which runs parallel to the hydraulic transmission and connects the spur gear to the arm gear of the planetary gear set. Considering the equations of static equilibrium between the mechanical-path gear and the arm gear, and the conservation of power, it may be shown that

where Ta and xa are the torque and speed of the arm gear of the planetary gear set and the speed ratio between the planetary gear set and the mechanical transmission is given by

and where the dimension rm and rA are shown in Fig. 7. Similarly Fig. 7 shows a hydraulic path of power, which is connected to the outer ring of the planetary gear set, using another gear with a pitch radius given by rh. Considering the equations of static equilibrium between these two gears, and the conservation of power, it may be shown that

where Th is the torque delivered by the hydraulic transmission, xh is the angular velocity of the output shaft of the hydraulic transmission, and the speed ratio between the planetary gear set andthe hydraulic transmission is given by

and where the dimension rh and rR are shown in Fig. 7. These equations may be used to describe the transmission of power from the planetary gear set to the mechanical and hydraulic power paths, respectively.

6. Differential Gear

The differential gearbox shown in Fig. 1 is used to distribute power from the planetary gear to the rear wheels of the vehicle. Satisfying the kinematic and conservation-of power requirements, it may be shown that torque and speed distribution through the differential gear is described as follows:

Where the speed ratio for the differential is given by d the angular velocity and torque at the wheels is given by and T respectively.

Transmission Design:

In designing the continuously variable-transmission that can be easily retrofitted to the rear-wheel drive automobile, it can be shown from the overall speed ratio in Eq. (26) that the unmodified transmission is described by a situation where h = 0 and

Furthermore, if we assume that the volumetric displacement of the pump and motor is identical, Eq. (11) may be used to show that the hydraulic transmission speed ratio is simply given by h = where is the normalized swash-plate angle for the pump which may vary between 1. In or-der to insure adequate adjustability of the overall speed ratio for the modified continuously varia-ble transmission, it would be desirable for a maximum pump swash-plate angle to produce a 25% adjustment for the overall speed ratio of the transmission. By inspecting Eq. (26), and assuming that Eq. (34) is satisfied, it may be shown that a proper amount of adjustment is achievable if the following design constraint is enforced:

In addition to these requirements, Eqs. (8) and (30) may be used to size the volumetric displacement of the motor based upon the maximum amount of torque that the motor will be required to generate during normal operation of the vehicle. This result is given by

where Tmax is the maximum torque that will be generated at the tire of the vehicle and Pmax is the maximum fluid pressure that can be safely generated within the hydraulic transmission without causing a machine failure. As previously stated, it assumed that the volumetric displacement of the pump Vp is equal to the volumetric displacement of the motor Vm. The maximum torque at the tire may be obtained using the vehicle model of Eq. (4). Normally, this torque is observed during high accelerations of the vehicle in which case wind and rolling resistance are negligible compared to the vehicle inertia. Finally, from a packaging point of view, the power transmission paths of the spur gear and the planetary gear must align. This is absolutely required for the mechanical power path, since a rigid shaft must be used to connect these two transmission points. Although, it is not as important to align the transmission points for the hydraulic power path since a fluid conduit is being used rather than rigid shaft; nevertheless, it is convenient to align these points and therefore the following design constraints will be enforced for the gear center distances:

For the purposes of illustrating a realistic design, a 1997 Ford Ranger was considered as a test bed and an effort was made to satisfy the design constraints of Eqs. (34) through (37). Figure 6 ispresented to show the design that was generated for the spur gear and the planetary gear based upon the vehicle and design information presented in the Appendix. Notice, these two gears looksubstantially different than their conceptual counterparts shown in Figs. 6 and 7; however, they are functionally identical. Although the hydraulic transmission is not shown in Fig. 6, it should be mentioned that a pump and motor with a displacement of 20 cc/rev can easily fit within the space limitations of the hydraulic path. Furthermore, the overall transmission size is relativelysmall and can easily fit within the existing space on the underside of the Ford Ranger. In other words, the design can easily be retrofitted to an existing vehicle.23 | Page