DBG:BM:208320 21st August 2008 REPORT TO Mr Stephen Durnin 40 Raby Esplanade ORMISTON QLD 4160
RE: DURNIN TRANSMISSION
ON
STAGE 1 – ENGINEERING ASSESSMENT OF IVT CONCEPT
Prepared by: Authorised By:
Dr Ben McGarry Dr Duncan Gilmore
Principal Engineer, e3k Think Director and President, e3k
BTP Technology and Conference Centre Tel : +61 7 3853 5250
Brisbane Technology Park Fx : +61 7 3853 5258
1 Clunies Ross Court Email : info@e3k.com
PO Box 4037, EIGHT MILE PLAINS 4113 Web : www.e3k.com
Brisbane, Queensland, Australia ABN : 12 060 559 480
1. INTRODUCTION
Mechanical transmission devices allow energy and power to be transmitted through physical space and enable matching between differing characteristics of energy sources and loads. A lever, for example, converts a small force applied over a long distance to a large force applied over a small distance, or a gearbox converts a small torque over a large angle to a large torque over a small angle.
e3k have been approached to assess the engineering feasibility of a particular mechanical transmission – a proposed infinitely variable transmission (IVT) concept embodied in a prototype designed and developed by Mr Durnin. This report describes an inspection of the prototype, offers a kinematic analysis describing the mechanical workings of the transmission, and discusses the feasibility of using the transmission concept for IVT applications.
2. INITIAL INSPECTION OF PROTOTYPE
I have inspected the prototype that was provided by Mr Stephen Durnin on 3rd July 2008. The prototype
is very well constructed from milled nylon, and stock shafts, gears and bearings. Integrated into the front ‘input’ end and driving the input shaft is a small DC motor with an integral reduction gearset. This allows the input shaft of the prototype to be driven at effectively constant speed over a range of loads, making it easy to investigate and demonstrate different operating regimes of the transmission.
A ‘stack’ of stages exist between input and output, with the stages affixed and spaced out on four corner posts. The output is a small hand wheel. Two control wheels protrude from the top of the prototype, with each control wheel mechanically connected to its own intermediate shaft in the transmission via right-angle bevel gears. Both Control I and Control II wheels are depicted schematically in Figure 7 of this report, with Control I being attached to planetary gear, and Control II being attached to sun gears.
A DC motor controller box is also provided, and I understand the control wheels are able to be driven with electric motors rather than via hand wheels as currently embodied.
When the input motor is activated, the internal workings of the mechanism can be seen to move. The control handles rotate at a common speed, but the output shaft does not move. In the absence of any external control action, this can be called the ‘natural’ regime in which the transmission operates. The output shaft can be freely rotated by hand (with the input shaft operating), and in doing this, both controls deviate from their original rotational speeds. However, with one hand forcing Control I to rotate at its ‘natural’ speed, the output shaft is stationary and can no longer be freely rotated by hand. This is a demonstration of the output shaft producing torque at zero output speed (‘geared neutral’).
When the handle of Control I is braked (held fixed), the output shaft rotates in a direction opposite to that of the input shaft, and at a slower speed than the input shaft. When the handle of Control I is driven slightly faster than its ‘natural’ speed, the output shaft rotates in the same direction as the input shaft. As the driven speed of Control I is varied, the output shaft speed varies, with the input speed constant. These operating regimes are demonstrations of variable negative and positive output/input gear ratios.
The same is true using Control II, though the rotational direction of the output is reversed and the speed ratios are different from those achieved by varying Control I.
Empirically, then, the transmission prototype can be seen to effect a continuous range of output/input ratios, from negative, through zero, to positive, depending on how the controls are actuated. The transmission can be used to provide torque on the output shaft at zero shaft speed, by driving the controls at a particular speed while the input shaft is being driven i.e. the transmission does behave in a similar sense to an IVT, notwithstanding constraints which are discussed further in this report.
3. OVERVIEW OF VARIABLE-RATIO MECHANICAL POWER TRANSMISSION SYSTEMS
A power transmission is a device which transfers energy between a power source and a load. In mechanical power transmission systems, which include the majority of automotive gearboxes, for example, the purpose is to match the torque and speed characteristics of the Input power source (engine) to the torque and speed characteristics of a Output load (vehicle moving on road).
In a conventional pair of mating gears, the ratio between the speeds of the two gears is fixed. Calling one shaft speed ‘Input’ and the other ‘Output’, the ratio of Output to Input is fixed (and is determined by the ratio of the gear diameters). This relationship is depicted schematically in Figure 1. For a given Input, there is only one possible Output.
Figure 1. Schematic showing the fixed speed ratio Output to Input relationship for a Gearset. In automotive applications, mechanical transmissions can be classified into three basic groups.
- Manual Gearboxes
- Conventional Automatic Gearboxes incorporating discrete planetary gearsets
- Continuously Variable Transmissions (CVT), or Infinitely Variable Transmissions (IVTs)
3.1 Geared Mechanical Transmissions
A manual gearbox consists of a number of helical gears running on parallel shafts. Different gear sets are engaged ‘manually’ (by hand via a gear shifter) to suit the load conditions, such as driving at high speed, driving up a hill, or towing a large load. Since each gear set (eg ‘second gear’) creates a specific ratio between the engine speed and wheel speed, the engine speed must be varied as the vehicle’s road speed changes, up to the limit of the engine’s useful operating range, at which point a different gear is selected. Adding more gears to a manual gearbox allows the engine to operate within a narrower band of torque and speed conditions (which can increase efficiency), and/or it increases the top speed of a vehicle.
Gearset
Input Output
An automatic gearbox is essentially the same device as a manual gearbox but with automatic instead of manual gear changes, and using epicyclic (‘planetary’) gear sets instead of helical gears running on parallel shafts. This output/input relationship holds for common manual and automatic automotive transmissions – for a given ‘gear’ such as ‘2nd gear’ (selected manually or automatically), the engine
speed has a fixed ratio to the wheel speed.
The gear ratio characteristics of the ZF 6 HP-26 automatic automotive transmission are shown in Table 1 as an example. This table illustrates the stepwise changes in Output/Input ratio as the selected gear is varied. Note that the speed ratio range of this transmission (ratio of the highest to lowest gear ratio) is approximately 6, which is common for a 6-speed automatic gearbox.
Gear Input/Output Ratio Output/Input Ratio
1 4.171 0.240 2 2.340 0.427 3 1.521 0.657 4 1.143 0.875 5 0.867 1.153 6 0.691 1.447 R -3.403 -0.294
Table 1. ZF 6 HP-26 Transmission Characteristics (adapted from Bosch (2004) p746)
Note that 5th and 6th gears in this transmission are ‘overdrive’ – the transmission output is rotating faster
than the engine (if the torque converter locks up). Note also that as the vehicle launches (i.e. takes off from a standstill) a torque-converter provides an additional degree of gearing as well as neutral gearing (providing wheel torque when stationary). A launch device such as a torque converter or clutch is typically required for all geared transmissions.
3.2 CVTs and IVTs
Allowing an engine to operate within its high-efficiency or high-power range maximises fuel economy or performance, and in a geared manual or automatic transmission this is best achieved by having a large number of gears. Transmissions with 7-speeds and even 8-speeds are becoming available in passenger-car market, for example, to maximise efficiency and/or performance over a wide range of vehicle speeds.
An alternative strategy to having a large number of discrete gears is to use a transmission that enables a continuously-variable (as opposed to stepwise-variable) transmission ratio. A continuously variable transmission or CVT can achieve an optimum matching between engine and load conditions without having to ‘change gears’ through discrete steps. From standstill to vehicle top speed, a CVT continuously transmits power from the engine to the wheels, even though the engine can be operating at a fixed speed. Use of a CVT allows an engine to run at optimum power or efficiency over a vehicle’s entire range of load conditions. This can improve economy, comfort, emissions and durability. It also provides improved performance by avoiding gear changes, which interrupt the flow of energy from the engine to the wheels. A launch device such as a torque converter or clutch is typically required for
CVTs, as the variable-speed element cannot typically generate torque at zero or very low wheel speeds.
As Leopold Mikulic, VP of Mercedes’ Powertrain Development, stated, “The theoretical ideal, in terms of both acceleration and consumption, would, after all, be the continuously variable adjustment of transmission ratios to the engine’s operative conditions. However, a further increase in the number of gears would make little sense from today’s point of view. Instead, a continuously variable automatic transmission would be the next logical step” (Jost, 2004).
An infinitely variable transmission (IVT) is similar in operation to a CVT, with the added feature of providing inherent ‘neutral gearing’ without a launch device (providing torque at zero road speed) and inherent reverse gearing. Gilmore (1988) recommended that IVT technology be further developed as a means to reduce fuel consumption of passenger vehicles (attached as Appendix 2).
Strictly, many purely electrical and hydrostatic power transmission arrangements can also be described as CVTs, although these are rarely used in automotive applications due to efficiency, cost and reliability considerations. Pure electric vehicles appear to be re-entering the automotive market (eg Tesla Motors) after a false start with GM’s EV1 in the 1990s.
There are several classes of mechanical CVT which have been developed:
- Friction (including “Belt and V-Pulley” and “Toroidal” types)
- Hydrostatic
- Ratcheting
- Positive Drive
The most common class of mechanical CVT, particularly in automotive applications, is the friction-based CVT, with the most common and well-known forms being the “belt and v-pulley” system and the “toroidal” system.
3.3 Belt and V-Pulley System
The belt and v-pulley CVT system consists of a strong belt acting between pulleys on the input and output shafts. One or both of the pulleys is able to be varied in such a way that the effective radius of the pulley increases or decreases, providing different speed ratios between the two shafts. In modern systems, this is commonly achieved by having v-shaped pulleys, with the gap between the two pulley halves being made wider or narrower, which forces the belt to change the radius at which it operates.
3.4 Toroidal System
The toroidal CVT system consists of two curved discs fixed to the input and output shafts respectively. Rollers acting between the input and output discs serve to transmit torque from one to the other, with the speed ratio being controlled by the angle of the rollers, as depicted in Figure 2.
Figure 2. Toroidal CVT System. Adapted from NSK (2008).
4. HISTORY OF CONTINUOUSLY VARIABLE TRANSMISSIONS 4.1 Late 19th Century – Early 20th Century
In 1877, Charles Hunt patented a friction-based toroidal CVT, a concept improved by Frank Hayes in the 1920s and used in the Austin 600 ‘York’ motor vehicle around 1930. The materials and lubrication technology of the time meant that the concept was beset by problems with reliability and power capacity.
In 1886, Daimler and Benz developed a friction-based belt CVT for their early engine prototypes, based on a rubber v-belt acting between variable diameter conical pulleys.
These two concepts, the toroidal and belt CVTs, remain the principal categories of modern CVTs at the current time.
4.2 1950s-1970s
The first widely produced CVT transmission was by Hub van Doorne, inventor of the van Doorne belt transmission and co-founder of Dutch truck company DAF (“van Doorne's Automobiel Fabriek”). In 1958, DAF produced the first mass-produced passenger car (the ‘600’) with a continuously variable transmission, called the ‘Variomatic’. DAF sold its passenger car division to Volvo, Sweden in the 1970s, who continued to use the DAF Variomatic transmission in their 300- and 400-series automobiles until 1995. The Variomatic transmission used two parallel steel belts with integrated steel ‘push blocks’ acting between variable diameter pulleys, making it an advanced version of the belt CVT concept. As for the toroidal CVT, Perbury Engineering Limited (UK), took up the concept for their own research and development in the 1950s, testing prototypes on small vehicles.
In the 1960s, Charles Kraus (USA), a U.S. Inventor, developed and tested a toroid-based CVT for military applications, noting that they could also be used for automotive applications. It is understood
Output Shaft Input Shaft Power-Transmitting Rollers TM
that his technology has been licensed to a number of companies around the world, including Transmission Technologies Corporation (TTC), USA, which is understood to be commercialising a modified Kraus Transmission.
In 1978, bearing manufacturer NSK Ltd, Japan started research and development on their own toroid-based CVT.
4.3 1980s-1990s
Van Doorne continued to be associated with VDT (Van Doorne’s Transmissie), who continued to develop the critical steel belt component for CVTs. This development effort was first seen in the CVT-equipped subcompact Subaru Justy, which was introduced in 1987 and was in production until the mid 1990s. They also supplied their CVT to Fiat and Nissan during this period. At the time, maintenance costs and reliability were cited as problems, but Subaru continued to refine their CVT, with the most recent iteration emerging in the Japanese-market Subaru Pleo in 1998.
Bosch Automotive Systems Corporation issued a press release in 1991 stating that at that time, CVTs had been installed in 3 million vehicles.
Nissan released a belt-based CVT version of their Micra into the Japanese market in 1992.
In 1993, VDT tested the feasibility of an experimental CVT (the ‘Transmatic’) in a prototype V10, 800 horsepower Williams F1 racing car. David Coulthard produced impressive results in this vehicle, but the FIA subsequently banned CVTs and other “driver aids” from single-seater racing in 1994.
4.4 2000 onwards.
VDT was bought by Bosch in 1995, and continued to improve the power-handling capability of their steel push-belt, demonstrating their CVT for a 5.4L V8 SUV (Sports Utility Vehicle) at the Detroit Motor Show in 2001. VDT now produces the Van Doorne push-belt component used in many CVT transmissions, including the European Ford Focus C-Max. The other major supplier of belt-CVT components is LUK, who produce the belt/chain for Audi’s (Germany) transmission. Audi’s chain-based CVT transmission utilizes the same principle as the VDT concept, but uses a different belt/chain design. By 2004, according to the Bosch Group which now own Van Doorne’s Transmissie (VDT), 5 million VDT transmissions were in use worldwide, with an annual production of approximately 1.2 million units (Pennings et al., (2004)). Sales of Nissan CVTs topped 1 million in the 2007 fiscal year, a quadrupling of CVT sales since 2004, and representing 28.6% of its global transmission sales (Nissan (2008)). NSK's research led to the development of the Powertoros Unit, the half-toroidal CVT depicted conceptually in Figure 2. Central to this design is NSK's development of the 'EP steel' (Extremely Pure) used for the metal surfaces. A special EHD (elastohydrodynamic) fluid is used between the steel traction surfaces to transmit torque with low losses. These two technologies are at the core of the Jatco (Japan) Extroid CVT transmission, used in the Japanese-released 3-litre Nissan Cedric and Gloria models since 1999.
The Extroid CVT has an impressive torque capacity of 390Nm, and Nissan (Japan) claim an approximate 10% improvement in fuel economy over a conventional automatic. The toroidal Extroid CVT transmission in the Nissan Gloria and Cedric has the highest torque capability of all CVTs currently in production, and is the world's first application of a CVT to large-displacement rear wheel drive vehicles. In a clear display of confidence in the transmission, Nissan use in their high-end Skyline model, featuring a 200kW turbocharged 3.5L V6 engine.
Torotrak is a UK-based spin-off of Rover/Leyland/BTG, who have taken up the mantle of UK toroidal CVT development from Perbury. Torotrak have developed a full-toroidal IVT (infinitely variable transmission) using an elastohydrodynamic fluid between rolling metal-to-metal surfaces in the Variator (see Figure 3). They claim a 20% improvement in fuel economy over a standard 4 speed automatic. The Torotrak transmission works by splitting the power from the engine into two paths, where one of the paths traverses through a toroidal-based ‘variator’, which changes the ratio of that power flow. The two power paths are re-integrated in an epicyclic gearbox, which can operate in two regimes depending on which of the epicyclic gearbox elements is being driven by the ‘unmodified’ power path.
Figure 3. Torotrak full-toroidal IVT schematic.
From http://www.infrastructures.com/0503/torotrak.htm, last accessed 15th August 2008.
Carraro of Italy have signed a licence enabling them to develop the IVT for medium-sized off-highway (agriculture and construction) and on-highway (bus and truck) applications. Torotrak have also demonstrated the transmission in a 5.4L Ford Explorer SUV (Sports Utility Vehicle), attracting further interest from a number of Tier 1 automotive manufacturers. Ford also field tested the Torotrak transmission in their Ford Mondeo with positive results, according to Torotrak.
5. KINEMATIC ANALYSIS OF DURNIN TRANSMISSION
A kinematic analysis of the mechanism was undertaken using hand calculations and 3D CAD software (Solidworks™). Kinematic analysis provides a description (mathematical or otherwise) of how machine elements move relative to each other and through space – that is, the operational behaviour of a machine.
The Durnin transmission uses multiple epicyclic (or ‘planetary’) gearsets. Relative to simple spur gears, epicyclic gearsets often have the advantages of high power density (high power-to-volume ratio), and simultaneous, concentric, bidirectional outputs from a single unidirectional input (Norton (2003)). Figure 4 is a sketch of a single epicyclic gearset showing the main elements, together with its schematic representation. Directions of rotation are shown assuming the large ‘ring’ gear is fixed in space. Traditional nomenclature also describes the central gear as the ‘sun’ gear, the small peripheral gears as ‘planet’ gears, and the member carrying the planet gears as the ‘carrier’.
Figure 4. The simplest epicyclic gearset. With the ring gear fixed, the planet gears are forced to rotate as the sun gear rotates, which also rotates the planet carrier.
The epicyclic gearset depicted in Figure 4 has a single degree of freedom. That means that for a given Input Speed (eg sun gear), the Output Speed (eg carrier) is only determined by a third element or parameter (eg ring gear). This third parameter is named the ‘Control’ in this report. This relationship is depicted schematically in Figure 5.
Figure 5. Schematic showing the variable speed ratio Output to Input relationship for an Epicyclic Gearset, determined by a third Control parameter.
Ring Planet Carrier Sun Epicyclic Gearset Control Input Output TM
Lévai (1966) enumerated the 12 basic configurations of epicyclic gearsets as shown below in Figure 6. All compound epicyclic gearsets (including automatic automotive transmissions) are built from these elements or kinematic analogues of them.
Figure 6. The twelve simple and complex epicyclic gearset configurations described by Lévai (1966).
Using this same notation, a conventional transmission diagram of the full Durnin transmission mechanism is shown in Figure 7. Note the Controls are driving intermediate shafts in the transmission via right-angle bevel gears.
Figure 7. Durnin transmission mechanism rendered in functional schematic notation.
The kinematic analysis of the Durnin transmission reveals a kinematic relationship between Input and Output with a single degree of freedom, as found in a single epicyclic gearset. In the Durnin transmission, for a given Input, each value of the Control produces a particular Output value. That is, for a given Input, varying the Control varies the Output.
5.1 ‘Black Box’ Distillation of Mechanism
Keeping the same range of speed ratios between the Input, Output and Control elements, it appears that the Durnin transmission can be rendered in a simpler form, without some of the intermediate elements present in its current embodiment. This is because many of the components are ‘mirrored’, or doubled up, with elements in one half of the machine kinematically constrained such that they move identically to a matching element elsewhere in the machine. Figure 8 depicts a schematic of the transmission, with colours indicating elements that are kinematically linked (constrained to move identically).
Figure 8. Durnin transmission schematic with kinematically linked elements indicated.
Appendix 1 depicts the progression of steps that may be taken to eliminate components and decompose or distill the Durnin transmission into a simpler form, while retaining the desired output/input ratio and using either Control I or Control II. In other words, treating the device as a ‘black box’, the same functionality can be achieved with a device with fewer elements. This kinematic distillation gives rise to a single mechanism with input, output and two controls. When distilled even further, though, it is equivalent to the two simpler mechanisms shown in Figure 9, each of which is driven by one control. Note that these two mechanisms are kinematically equivalent to (i.e. correspond to) the Class I and Class III epicyclic mechanisms described by Lévai (see Figure 6).
Figure 9. Mechanisms that are kinematically equivalent to the Durnin transmission, and corresponding epicyclic gearset configurations as described by Lévai.
Each of these two mechanisms can achieve the same kinematic functionality as the Durnin transmission – each is able to achieve the same range of Output/Input ratios given the same range of Control speeds. The mechanisms can also be combined as in the second-last step of the distillation shown in Appendix 1. The diameter ratios (gear ratios) between components must remain the same in these kinematic equivalents in order to achieve the same ratios as the original Durnin transmission. For example, the diameter of the Input sun gear in the modified version must remain as 1/3 the diameter of the mating planet gear. Control I must be geared onto the ring gear in the modified version, retaining the same 3:1 ratio between Control I and the ring gear as in the original.
5.2 Speed Ratio Range using Control I or Control II
The Durnin transmission has a single degree of freedom, meaning that the relationship between Input and Output (i.e. the gear ratio) is determined by the value of this additional ‘Control’ parameter. The Durnin transmission is built with two controls, Control I and Control II, but either of these alone would suffice to control the transmission. In order to effect an Output speed that is one-quarter of the Input speed, for example, either Control I could be driven at the Input speed or Control II could be held stationary. The relationship between the two controls is fixed such that a given Output/Input ratio can
Class I epicyclic gearset Class III epicyclic gearset
be achieved either by driving one control at a particular speed or by driving the other control at a (different) particular speed.
The kinematic analysis of the mechanism has provided two equations enabling the Output speed to be calculated based on the Input speed and the Control speed. The form of the equations shows that whether Control I or Control II is used, the Output is the weighted sum of the Input and the Control. This highlights the ‘summing’ characteristic of epicyclic gearsets:
Input ControlI Output=0.375× −0.125× ...(Eq 1) Input ControlII Output=0.75× +0.125× ...(Eq 2)
Table 2 outlines some of the possible kinematic states of the transmission, achieved by driving Control I or Control II at speeds between –Input and +Input. The values shown indicate the number of revolutions achieved by the transmission element for a single revolution of the Input shaft, or correspondingly, the speed of the transmission element if the Input shaft has a speed of 1. The results of the table apply whether the Durnin transmission is used in the form embodied in the prototype, or in the kinematic equivalents identified in Figure 9. Each of the kinematic scenarios (a) to (e) has a different Control speed. The speed of the Ring Gear element is also shown in the table.
Scenario Input Speed Control I Speed Control II Speed Ring Gear Speed Output Speed Output/Input Ratio (a) 1 -1 -1 -0.333 -0.5 -0.5 (b) 1 0 -0.5 0 -0.125 -0.125 (c) 1 0.333 -0.333 0.111 0 0 (d) 1 1 0 0.333 0.25 0.25 (e) 1 ∗ 1 1 1 1
Table 2. Example kinematic states of Durnin transmission showing relationships between Input, Control and Output speeds. Column shading colours correspond to element colours used in Figures 8 and 9. The same information is depicted graphically in Figure 10. Each line captures the set of possible Output/Input ratios achievable using either Control I or Control II. Note that each of the scenarios in the table appears twice on the graph, as any given Output/Input ratio (i.e. any given y-value on the graph) is achievable either with Control I or Control II.
∗ Note that to achieve this scenario, Control I would need to be driven at a speed of 3. While this is certainly achievable, the analysis in this report assumes each of the Controls can only be driven up to the Input speed, for mechanical simplicity.
Gear Ratio vs Control Multiplier -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20 -1 -0.5 0 0.5 1
Control Multiplier (Control/Input)
G ea r R at io ( O u tp u t/ In p u t)
Figure 10. Plot of relationships between Durnin transmission Gear Ratio and Control multipliers. A number of noteworthy features are evident in Table 2 and Figure 10.
Firstly, all of the scenarios except (c) are achievable by driving a Control at a speed of 0 or ±1. These scenarios can be achieved mechanically by physically braking the Control onto the gearbox chassis so it is a fixed stationary element (for a Control speed of 0) or by coupling the Control directly (via clutch) to the Input or to a counter-rotating Input (for Control values of ±1). This strategy is used to achieve multiple transmission ratios in a conventional automatic transmission, albeit with more rotating elements and more brakes and clutches.
The ZF gearbox described in Table 1, for example, uses 3 clutches and 2 brakes to achieve its 6 discrete transmission ratios. For comparison, Figure 11 shows the Output/Input ratios achieved in the ZF 6 HP-26 gearbox overlaid on the Output/Input ratios using Control II of the Durnin transmission. The first four gear ratios of the ZF gearbox lie within the ratio range of the Durnin transmission with Control II driven between speeds of 0 and 1. If the Durnin transmission were coupled to a device able to vary the Control speed between 0 and 1 (i.e. from stationary up to the Input speed), the Durnin transmission would provide a variable range of speed ratios spanning a very similar range to that offered by conventional automatic automotive transmissions.
(a) (b) (b) (c) (c) (d) (d) (e) Control I Control II TM
Gear Ratio vs Control Multiplier -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20 -1.000 -0.500 0.000 0.500 1.000
Control Multiplier (Control/Input)
G e a r R a ti o ( O u tp u t/ In p u t)
Figure 11. Plot of relationship between Durnin transmission Gear Ratio and Control II multipliers with ZF 6 HP-26 gearbox Gear Ratios overlaid.
5.3 Speed Ratio Changes using a single Control or multiple Controls
The second notable feature is that using Control I, a range of negative to positive Output/Input ratios (including 0) is possible simply by varying the Control from 0 to 1. In other words, using Control I, the transmission can provide both ‘forward’ and ‘reverse’ Output with a positive Control speed. This would make Control I easier to implement that Control II, which requires both negative and positive Control speeds to achieve negative and positive Output speeds.
The disadvantage of using Control I only is that the speed ratio range is limited – that is, assuming the Control is only able to be driven between the nominated speeds of –Input to +Input, the range of Output speeds is limited to less than that achievable using Control II (see Figure 10).
The best features of Control I and Control II are ‘one-sided operation’ and ‘wide range’ respectively, and these could conceivably be combined in a multi-Control strategy. Referring to Figure 12, assume now that each Control can only be driven between speeds of 0 and +Input (as opposed to between -Input and +Input). In this case, Control I could be used to achieve Reverse, Neutral Gearing and Low Ratios, and Control II could be used to achieve Low to High Ratios. This could be implemented mechanically with a clutch that was designed to selectively couple some external variable-speed device such as a CVT to either Control I or Control II. The simplest CVTs do not allow both negative and positive ratios, so using this multi-Control strategy would eliminate the requirement for the external variable-speed device (eg CVT) to produce both negative and positive ratios. This could allow for a simpler mechanical product (through enabling the use of a simpler CVT) than would be possible using Control I or Control II alone.
(a) (b) (c) (d) (e) Control II 1 st G ea r 2 nd G ea r 3 rd G ea r 4 th G ea r R eve rse TM
Gear Ratio vs Control Multiplier -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20 -1 -0.5 0 0.5 1
Control Multiplier (Control/Input)
G e a r R a ti o ( O u tp u t/ In p u t)
Figure 12. Plot of relationships between Durnin transmission Gear Ratio and Control multipliers greater than zero only.
It would appear, then, that the Durnin transmission could be used to achieve a range of transmission ratios comparable to a conventional automotive automatic transmission in two ways:
1) The Durnin transmission could be combined with an external speed-varying element such as a CVT able to produce speeds between -Input and +Input speeds, with that speed-varying element driving Control II, or
2) The Durnin transmission could be combined with an external speed-varying element such as a CVT able to produce speeds between 0 and +Input speed, with that speed-varying element driving Control I and Control II selectively.
These two potential embodiments are shown schematically in Figure 13.
Figure 13. Potential configurations of a transmission system comparable to a conventional automatic transmission using the Durnin transmission as an element.
(b) (c) (d) (d) (e) Control I Control II Durnin Transmission Control II Input Output CVT - to + Durnin Transmission Control I Input Output CVT 0 to + Control II TM
5.4 Dependence of Speed Ratio on sizing of gear elements
The speed ratios available using Control I or Control II (as shown in Figure 10) are dependent on the selection of gear ratios between the various elements of the transmission. The relationship between Input, Output and Control could be ‘designed’ to target a specific behaviour of the mechanism, and implemented via particular choices of gear ratios between elements. In its current embodiment, for example, all mating gear elements are built on a 3:1 ratio, but different ratios would give rise to different Input/Output/Control relationships. Referring to Figure 10, changing the fundamental ratios between mating gear elements and/or the basic layout of the mechanism would change the slope and/or the point where the line crosses the x-axis.
It could well be considered favourable, for example, to have neutral gearing achieved by setting the Control to a speed of 0 (though this is not possible with the current embodiment). To achieve this target, the topology of the transmission (‘what connects to what’) would need to be changed such that the operating line (Figure 10) would now pass through the origin – here, a Control of 0 gives an Output of 0.
5.5 Torque requirement of Control shaft
A three-shaft epicyclic drivetrain such as the Durnin transmission has at any time either one input and two output shafts, or two input and one output shafts, depending on how the power is flowing through the machine. The lowercase terms ‘input’ and ‘output’ here are according to the convention where ‘input’ designates ‘power flowing in’ (i.e. torque is in the same direction as rotation) and ‘output’ designates ‘power flowing out’ (i.e. torque is in the opposite direction as rotation). The designation of ‘input’ and ‘output’ shafts can in general be confusing, as it is possible for a shaft which is designated the ‘Output’ shaft (eg. the shaft from the transmission to the wheels) to become an ‘input’ (for example when the vehicle is being braked with the engine).
Our designation of ‘Input’ and ‘Control’ shafts in this report is arbitrary in that both would conventionally be used to provide power. There is no inherent character of the mechanism that requires the Input to be the dominant power-providing element. The torque provided by the Control shaft will typically be of the same magnitude as the torque provided by the Input shaft. Kinematic analysis shows, for example, that at operating point (e) (see Figure 10), the torque on the Control shaft is equal to the torque on the Input shaft. The speeds of these shafts is also equal, so the power delivered to the transmission via these shafts must also be equal. In other words, 50% of the Output power comes from the Input, the other 50% comes from the Control.
The Control shaft (and associated mechanical elements) should be sized to this torque requirement accordingly – the Input and Control should be considered as parallel power paths rather than as ‘power’ and a ‘control’ elements respectively.
6. POTENTIAL APPLICATIONS
The Durnin transmission is operating as a conventional epicyclic gear set, combining power flows from three shafts in various combinations. It can be embodied as one of the twelve general epicyclic gearset
classes described by Lévai (1966), (i.e. as a Class I or Class III epicyclic gearset) or as a combination of these two gearsets.
The Durnin transmission is strictly an element of an Infinitely Variable Transmission. In general terms, it can be used to achieve a range of speed ratios between two shafts (Input and Output) by varying the speed of a third shaft (Control). The Durnin transmission requires some external means of varying the speed of the Control shaft (and providing power through that shaft) to serve as a true IVT.
This variable-speed Control shaft could be powered by an additional ‘variator’ component (a component capable of a continuously varying transmission ratio), for example a CVT. A combination of the epicyclic transmission described by Durnin and a variator component would produce a true IVT, for example, as demonstrated by Torotrak. This transmission has found use in on-road and off-road wheeled vehicles, but IVTs could be used in any application requiring power delivered by a rotating shaft in both ‘forward’ and ‘reverse’ directions and including geared neutral.
Alternatively, the epicyclic transmission described by Durnin could be used as an element of a hybrid drivetrain. In this case, the Control would conceivably be driven by an electric motor/generator, enabling various modes of operation.
Epicyclic gearsets are indeed currently used widely in hybrid transmissions because of their flexibility in summing and splitting mechanical power flows. Epicyclic gearsets can be used either to combine (‘sum’) the power flows from the engine and electric motor to a single output (the wheels), or to separate (‘split’) the power flow from the engine to drive both a generator and the wheels. A schematic of the Toyota Prius hybrid drivetrain (Figure 14) shows how the planetary gear set is used to relate the power flows between engine, two motor/generators and the wheels. Note that two motor/generators are used in this vehicle specifically to enable series/parallel hybrid operation, whereas the simplest hybrid configurations use a single motor/generator.
Figure 14. Schematics of the Toyota Prius parallel hybrid drivetrain. From The Clean Green Car Company (2008)
If the Durnin transmission were used in this application, the ‘Control’ would be an electric motor/generator (or other auxiliary power system such as hydraulic motor/pump etc) connected to an energy storage device such as a battery. The most obvious configuration (parallel hybrid) is depicted in Figure 15.
Figure 15. Potential configuration of a parallel hybrid drivetrain using the Durnin transmission as an element.
In ‘direct drive’ mode, the Durnin transmission would effectively be ‘transparent’, serving only to drive the Output (wheels) at a fixed ratio relative to the Input (eg petrol engine). A separate ‘direct drive’ mode would enable the Output to be driven simply at a fixed ratio relative to the Control (eg electric motor).
In a ‘power summing’ mode, the Durnin transmission would serve to combine the Input and Control power (for example, combining the power of the petrol engine and the electric motor) to drive the Output, which would be wheels in the case of a road vehicle.
In ‘power split’ mode, the Durnin transmission would serve to split the Input power into ‘Control’ power (i.e. the Control would be an output, driving the electric generator to recharge the batteries) and the Output wheels.
In a ‘regenerative’ mode, power would flow from the wheels (and optionally also from the Input engine) to the Control, driving the generator to recharge the batteries as the vehicle braked.
Other applications include wherever epicyclic gearboxes are currently used. Durnin Transmission Control Input Output Motor/ Generator Battery TM
7. CONCLUSIONS AND RECOMMENDATIONS
a) I have inspected the well-executed prototype gearbox provided by Mr Durnin and I confirm that it operates as a form of conventional three-shaft epicyclic gearset, albeit with an additional fourth shaft providing an optional substitute for one of the three shafts. The gearbox can definitely act as the primary and key element of an innovative and valuable Infinitely Variable Transmission (IVT) system.
b) The examined prototype includes an input shaft, output shaft and two intermediate control shafts (designated Control I and Control II for the purposes of this report). Either of the control shafts alone would be sufficient to effect a range of operational regimes, in combination with the input and output shafts.
c) If Control I on the examined prototype is driven between speeds of –Input to +Input (including zero), a continuous range of Output/Input ratios from -0.5 to 0.25 (including 0) is achieved. This includes a ‘geared neutral’ operating point where the output shaft produces torque at zero speed.
d) If Control II on the examined prototype is driven between speeds of –Input to +Input (including zero), a continuous range of Output/Input ratios from -0.5 to 1.0 (including 0) is achieved. This includes a ‘geared neutral’ operating point where the output shaft produces torque at zero speed. This range of speed ratios is importantly very similar to the range of speed ratios achieved by a conventional 4- or 5-speed automatic automotive transmission (since the automotive industry is a prime potential application for IVT systems).
e) A multi-control strategy has also been identified wherein Control I and Control II are able to be used at different times to achieve different Output/Input ratios.
f) At any time, the transmission can operate as a Class I or Class III epicyclic gearset (Lévai (1966)) depending on whether Control I or Control II is being used.
g) The forces and torques encountered in this transmission are of the same magnitudes as those found in conventional planetary transmissions (eg automotive automatic transmissions) of comparable size and subject to comparable loading. This is important from a practical manufacturing and cost viewpoint.
h) To execute true IVT operation in a single power source application (eg a petrol-engined automobile), the transmission would be required to be integrated with an external speed-varying device such as a CVT. This speed-speed-varying device would connect the power source to the Control of the transmission, enabling the Control to be different at varying speeds relative to the Input. The power from the power source, having been split into two parallel paths, would be recombined in the transmission to drive a single Output shaft. The Torotrak IVT transmission offers an example of how this could be achieved.
i) The transmission could potentially form the valuable ‘power splitting’ or ‘power summing’ element of a broader hybrid-drive mechanism utilising two power sources (eg petrol engine and electric drive). Existing hybrid-vehicle drives such as that of the Toyota Prius offer examples of how this could be achieved.
j) In our opinion, the Durnin transmission engineering concept as inspected, is sound. We have however identified that it could be beneficially simplified to an even more compact transmission
having fewer components while executing the same function. A means to achieve the functionality of the Durnin transmission with a simpler epicyclic transmission has been described in this report. The level of further development required is regarded as being relatively minor compared to the innovative development which has already occurred to produce the existing prototype ie. an incremental step. Such further development is seen, and recommended, as a means of optimising the existing concept, thereby further increasing the value of any inherent Intellectual Property.
k) IVTs enable improved performance and/or efficiency of vehicle systems by enabling the power plant (eg internal combustion engine) to operate continuously at peak power or peak efficiency. The Durnin transmission concept, when paired with external speed-varying elements (such as a CVT or electric motor/generator), enables true and valuable IVT operation.
l) Additional development work, aimed at further increasing the value of any Intellectual Property, would include developing a speed varying control element able to transmit power comparable to the rating of the device, and then integrating this element into the simplified Durnin concept. Significant market potential exists for a compact, low-cost, efficient IVT transmission, and with further research and development as identified, the Durnin transmission concept could secure a place in that market.
8. REFERENCES
Bosch (2004) Bosch Automotive Handbook, 6th ed., Plochingen, Germany.
Gilmore, D.B., (1988) Fuel economy goals for future powertrain and engine options. International
Journal of Vehicle Design, Vol. 9, no. 6, pp. 616-631. UK.
Jost, K. (2004) ‘The need for speeds’, Automotive Engineering International, SAE International vol.112, no. 7, pp. 24.
Lévai, Z. (1966) Theory of epicyclic gears and epicyclic change-speed gears. Doctoral Dissertation, Technical University of Building, Civil and Transport Engineering. Budapest, Hungary.
Machida, H & Murakami, Y., (2000) ‘Development of POWERTOROS UNIT half toroidal CVT’, Motion
and Control, October, no. 9, pp. 15 – 26.
Nissan (2008) http://www.nissan-global.com/EN/NEWS/2008/_STORY/080422-02-e.html, last accessed 15th August 2008.
Norton, R.L., (2003) Design of machinery: An introduction to the synthesis and analysis of mechanisms
and machines. McGraw-Hill Professional.
NSK (2008) http://www.nsk-singapore.com.sg/products_automotive.asp, last accessed 15th August
2008.
Pennings et al. (2004) New Push-Belt Design to Increase Power Density of CVTs Featuring a New Maraging Steel, SAE International, 04CVT-2
The Clean Green Car Company (2008) http://www.cleangreencar.co.nz/page/toyota-prius-iii-hybrid-car-technical-information, last accessed 15th August 2008.
• Remove duplicated elements • Relocate Output
• Remove Right-Angle Bevel Gears • Replace large internal planet gear with
smaller external planet gear to achieve same ratio (note sense of rotation is reversed).
• Invert Mechanism
• Gear Control I to Ring Gear
D.B. Gilmore
Department o f Mechanical Engineering, University o f Queensland. Brisbane. Australia
Abstract: Efficiency goals represent one o f the key factors governing powertrain choice. These goals are specified for three novel developments in automotive technology which would enable them to compete on this single basis with the conventional four-speed manual or automatic transmission (with torque converter lock-up) coupled with a fixed displacement spark-ignition engine. The fuel consumption tigures o f continuously variable ratio and infinitely variable ratio automobile transmissions are presented using a simulation model o f a vehicle in both urban (EPA cycle) and constant-speed operation. A powertrain utilising a variable displace- ment engine is also simulated.
Reference to this article should be made as follows: Gillnore, D.B. (1988) 'Fuel economy goals for future powertrain and engine options', Inr. J . of Vehicle Design, vol. 9 , no. 6, pp. 616-63 1 .
Keywords: Automobile powertrain, engine design, fuel economy, continuously variable. in- finitely variable, variable displacement transmission, vehicle design.
1 Introduction
Several powertrain options currently exist for future automobiles which offer variable gear ratios and engine capacities (Amann, 1986).
Numerous designs of continuously variable ratio transmissions (CVT), and variable displacement reciprocating internal combustion engines (VDE) have been proposed, and some have been taken to the stage of mass production. Whilst each design has its own advantages and disadvantages, there is a requirement to review the specifications that are necessary for such new equipment to enable them to compete successfully with conven- tional manual and automatic gearboxes, as well as fixed displacement reciprocating inter- nal combustion engines. The goals are often a moving target because methods have been made available as a result of recent research and development to improve the performance of current powertrains without changing the basic design concept. The performance in- dices must include fuel consumption, driveability, exhaust emissions, reliability, as well as initial and operating costs.
This paper directs attention to one of these major performance goals - vehicle fuel consumption calculated over a road cycle and at constant speed.
It is intended that these results should, in isolation, give an indication of the desired fuel economy goals to be achieved before the novel powertrains are likely to be considered as competitors.
Whilst fuel economy does not rate as the most important performance index in the 1980s, it will inevitably play a major role in the longer-term development of the personal automobile. Finite petroleum reserves and the predicted 'greenhouse' effect are two fac- tors which should discourage complacency.
The continuously variable transmission concept has been studied by numerous authors (Mitschke, 1981; Stubbs, 1981; Stieg and Worley, 1982; Yang and Frank, 1985). In ad- dition, the efficiency of manual and automatic powertrains has been examined by Van Dongen (1982). The infinitely variable transmission (IVT) is a CVT with an unlimited gear ratio range, i.e. the engine can be operating and torque produced on stationary wheels, with an effective gear reduction of infinity. One successful prototype of such a transn~ission using a split-path electromechanical arrangement was reported by Gilmore and Bullock (1982).
Many automobiles are still produced with manual transmission and most are now four- speed. The four-speed automatic with lock-up of the torque converter in every gear is established in the market-place and represents commercially viable technology. The effi- ciency in each gear will then closely approach that of a manual transmission.
Reciprocating internal combustion engines of fixed displacenient dominate the automotive market-place. Variable displacement engines utilising a variable stroke capability have been proposed since the 1890s and recently investigated by Siegla and Siewert (1978) and Scalzo (1986). Such designs could be regarded as competitors to continuously'variable transmissions, as they are also able to increase the brake thermal efficiency of the power- train at partial load and at any road speed. The CVT does this by allowing continuous selection of a gear ratio between engine and road wheels which will optirnise the engine efficency, normally at a relatively low engine speed, and high torque.
The variable displacement engine is able to de-stroke on partial load. thereby creating a fractional size displacement and a higher efficiency at a given torque and speed. The fully stroked engine is still available for peak acceleration and hill climbing capabilities.
3 Scope of investigation
This paper gives the results of calculations performed to evaluate the fuel consun~ption of a standard vehicle when operated with a variety of powertrains over two types of driv- ing styles.
3.1 Road power losses
Post et 01. (1983) report that the Australian tleet averaged vehicle has a mass of 1 160 kg, and that the total drag power (kW) absorbed by the vehicle can be represented by equation ( 1 ):
Z ,,,,,, = Z,,,,
+
MV(a13.6+
9.8lsinL9)13600 (1)Z
,,,,
= (0.036V+
0.45 x lo3v'+
0 . 8 ~ lo-"' (2) where M is the vehicle's mass (kilograms), V is the vehicle's velocity (kn~lh), a is the vehicle's acceleration (krnlhls), L9 is the road gradient (degrees), and Z is the drag power (kwhThis specification is typical of the average vehicle produced for the worldwide automobile market.
A nominal 2-litre reciprocating spark-ignition engine was chosen as the typical power plant for the purposes of this analysis. This size is also representative of the power plant which is commonly installed in a 1160 kg vehicle. T h e total brake thermal efficiency contours of such an engine were measured, and are depicted in Figure 1.
Figure 1 2-litre spark-ignition engine brake thermal efficiency contours as measured Cross Cslorific Value o f Fuel 47.2 W l k g
The baseline fuel consumption was calculated for a manual transmission with the gear and differential ratios listed in Table I .
Variations in ratios for a range of vehicles have been accounted for by calculating the variation in fuel consumption which would arise from a & 10% variation in the dif-
ferential, and therefore thc overall, transmission gear ratio.
Limited data available on the efficiency of manual transmissions (Van Dongen, 1982) suggests that the overall mechanical efficiency in any gear at greater than 20% of rated torque will be 9 5 % (tolerance +O%,-2%) at the operating temperature. All transmissions will suffer a drop in mechanical efficiency at part load, whether they are manual, C V T o r IVT. T o avoid another variable in this analysis, the mechanical efficiency of a manual transmission in any gear at any load was fixed at 9 5 % .
Similarly, the efficiency of a final-drive differential has been taken at 9 7 % , bascd on the data given by Van Dongen (1982) and this author's research.
'I'ABI.E 1 Ratios for manual gearbox
Gear I 2 3 4 D~ll'erent~al
An infinitely variable transmission (IVT) attached to the 2-litre engine was simulated. This transmission could adjust to any s p e d ratio between the input and output shafts that suited the operation of the engine for maximisation of efficiency.
The ratio could be anywhere between A infinity:l. The part load efficiency characteristics of such transmissions will depend on their design. The intention of this paper is to evaluate the worth of different gearbox ratio options rather than their individual efficiency characteristics. However, the overall average efficiency of such a transmission is very important, and so an 'average' efficiency has been adopted. Calculations have been performed for average efficiency of the IVT's of between 70% and 95%. It is argued that it is most unlikely that an IVT would achieve an average greater than that of a manual transmission.
3.5 Continuously vuriable transmission
The CVT adopted in this paper is an IVT with a restricted overall speed.ratio. The maxi- mum ratio allowed in the CVT in these calculations is 3.71: 1 (equal to the IstAgear ratio in the manual transmission) and the minimum ratio is 0.742. This gives an overall speed ratio range of 5 : l . Predictions of the likely consequences of increasing this speed ratio range can be gained from interpolation of the CVT and IVT results. Slip and losses in the clutch which will be necessary between the engine and the CVT are both assumed to be negligible.
3.6 Variable displacement engine (VDE)
The variable displacement engine modelled in this paper is able to destroke from a capa- city of 2 litres down to I litre. This 2: 1 ratio appears to be representative of likely future developments in this technology. The engine is attached to a manual gearbox of similar specification to that described in Section 3.3.
Such an engine would most probably be attached to an advanced automatic gearbox with lockup in each gear, and the transmission is therefore well modelled by the manual gearbox for the purposes of this paper.
3.7 Urban driving cycle
The Australian design rule 27C (1982) for vehicle emission control specifies the 1372 second duration EPA (USA) urban driving schedule for test purposes. This cycle has been used for an evaluation of fuel consunlption in stop-go urban conditions at speeds between 0 and 92 kmlh.
Post er al. (1981 ; 1983), have derived a fuel consumption matrix for the ADR 27C cycle. Each matrix cell entry represents the number of one-second observations that a vehicle is within the boundaries of a particular acceleration and velocity cell, when i t is driven over that cycle on a dynamometer. Their work extended to mapping other road cycles in a similar manner, based on measurements from instrumentation attached to vehicles as they were driven on the road. They reported that the instantaneous power demand model which considered a complete driving cycle to be a series of short trip cells at the specific
dynamometer.
This model has been used to calculate the urban drive cycle fuel consumption by calculating the engine torque and speed necessary to achieve the velocity and acceleration
in each cell, with each of the transmission options and their control logic. Fuel consump-
tion is determined by evaluating the efficiency of the engine at that torque and speed from Figure 1. The total engine power required is given by equation (1) with the grade angle
9 set to zero. At some negative levels of acceleration, it is possible that Z,,,,, is zero. In
that case the engine will be operating in a high-speed idle condition, and the fuel con-
sumption rate is obtained by linear regression of experimental data on the engine type 1
selected.
Normal idle in the drive cycle at zero velocity, zero acceleration is accounted for by a 212 second cell entry at a velocity of 2.5 kmlh. Each cell entry encompasses a 2.5 kmlh speed range and a +0.5 krnlhls acceleration range. -Fuel ccnsumption as measured at
specified idle speed was 3.36 x l o p 4 litresls. This idle consumption was also assumed
for conditions demanding a negative total engine power (retardation).
3.8 Constant speed operation
Whilst the majority of automobiles consume fuel in conditions represented by the many urban drive cycles available, constant speed operation provides information at the opposite extreme and is more indicative of freeway or open highway driving.
4 Powertrain control strategy
Each powertrain considered requires a control logic to govern its operation.
4.1 Manual trunsmission
At any particular velocity and acceleration the software attempts to operate the gearbox in its highest gear (4th). This would produce the highest possible torque and lowest speed operation which is the general criteria accepted for economical driving. The driver, however, will override this requirement if the resultant engine speed is below what he regards as an acceptable minimum, depending greatly on the engine design, its mounting construction, and the presence of unwanted resonances. Commonly, this is about 1300 prm, but recent designs allow minimum engine speeds well below 1000 rpm. Generally, the fuel supply systems are not designed for extra-low speeds, but operation down to 600 rpm at full throttle might be considered by manufacturers in the near future.
The strategy for gearbox operation was to operate in the highest gear possible, whilst ensuring that engine speed did not fall below a set minimum. The engine torque was also prohibited from rising above 126.9 N m (70% of the maximum engine torque of 141 N m) which is the torque producing the generally highest efficiency of the engine. Efficiency falls at higher torques which are reserved for peak power demands. Most manufacturers recommend a change to a lower gear (higher gear ratio) as correct driving practice, and this procedure was adopted in these control algorithms.
Attempts are made to maintain torque at an optimum level for maximum engine effici- ency through the use of the IVT. A level of 126.9 N m (70% of maximum torque) is main- tained up to a speed of 2500 rpm. Engine speed is calculated to provide the power required by the driving cycle. Should the speed fall below the set minimum chosen, that set speed is selected by the software and the torque recalculated to a level below the optimum. Should the engine need to exceed 2500 rpm the torque will be set at a level given by equation (4).
One iteration is performed to calculate the engine speed as follows. Torque is set at 126.9 N m and engine speed N is calculated to provide the power required by the driving cycle. If N is greater than 2500 rpm, T is calculated using equation (4), and N subsequently recalculated. If N exceeds a practical limit of 5000 rpm, that speed is selected and the torque is recalculated to a level above the optimum.
The maximum gearbox ratio achieved is calculated but not restricted in any way.
4.3 Continuously variable transmission (CVT,',
The control of the CVT is identical to the IVT except that the gearbox ratio between engine and driveshaft speeds is restricted as discussed in Section 3.5. If the software of the IVT demands a ratio greater than 3.7 1 or less than 0.742, then the ratio is fixed at those limits, and the engine torque re-calculated.
4.4 Variable displacement engine (VDE)
The control software for the transmission follows that of the manual gearbox to select initially an appropriately high gear (low ratio). If the torque required, based on the 2-litre engine, is below the optimum torque specified for IVT operation (Section 4.2). the engine is destroked in an attempt to locate a smaller engine capacity which will have that torque as optimum, assuming that the normalised shape of the efficiency contours does not alter. At the upper and lower limits of engine displacement, the capacity is fixed at either I litre or 2 litres, and the appropriate overall efficiency calculated.
As the average efficiency of a VDE will undoubtedly be somewhat less than that of a fixed displacement engine because of compromises necessary in the combustion chamber surface/volume ratio, location of spark plugs, and the mechanism used to alter the stroke, calculations have been performed in this paper with relative mechanical efficiencies be- tween 70% and loo%, compared with a fixed displacement engine.
4.5 Range of modelling for aggregate fuel consumption
Each powertrain has been modelled over the urban drive cycle with specified minimum engine operating speeds of between 600 and 2000 rpm as an input variable.
Constant speed operation has been modelled between 10 and 160 km/h. For these latter calculations, the minimum engine speed was set at 1300 rpm to remove it as a variable.
Vehicle aggregate fuel consumption was calculated for each of the powertrain options over the urban driving cycle and at cunstant speed. Results are given in Figures 2 to 15.
Figures 2 to 5 depict the dependency on both the minimum engine speed desired and the differential ratio over the urban drive cycle. The IVT and CVT are specified as having a mechanical efficiency of 9 5 % , whilst the VDE has an efficiency of 95% relative to the manual powertrain. Essentially, lower differential ratios yield lower fuel consumption, as would be expected, except for the IVT which is able to optimise the engine efficiency independently of the drivetrain gear ratios. The manual powertrain fuel consumption can vary by & 3 % at minimum engine speeds below 1000 rpm, whereas at 1300 rpm minimum
there is no advantage in selecting a differential ratio below 3.73:l.
The IVT is able to produce a 6- 12 % reduction in fuel consumption compared with the manual (MAN) transmission (Figure 3). The 12 % reduction occurs at a minimum engine speed of 1800 rpm. The CVT and IVT are essentially identical with minimum speeds be- tween 1000 rpm and 1600. Above 1600 rpm, the CVT uses approximately 3 % less fuel as the restricted ratio enforces lower engine speeds than the desired minimum and higher engine efficiencies (Figure 4). Below 1000 rpm, the IVT use's up to 4 % less fuel than the CVT as it is able to take advantage of these extra low speeds over the total driving cycle. At a relative efficiency level of 95 %, the VDE with manual transmission (Figure 5) achieves between 13% and 24% lower fuel consumption than the MAN powertrain. This result is largely independent of minimum engine speed, up to approximately 1400 rpm. Figures 6 to 8 depict the dependency on both the minimum engine speed desired and the relative efficiency of the powertrain over the urban drive cycle with a differential ratio of 3.73: 1. Figure 6 shows that the mechanical efficiency of the IVT can fall to an average of 70% before fuel consumption equals that of the MAN drivetrain. However, the MAN powertrain fuel consumption can be lowered by reducing the differential ratio whereas
Figure 2 Fuel consumption ADR27C city cycle: manual transmission
@ --- +--- +---+-.--+--+----t---+
6 8 8 X0B lei30 la@@ 1 4 8 R 1 6 0 0 18BP 2 0 8 8
3 1
I
I
:i
.L-+--
-.--- + ----6ea see lee8 lzee 1 4 0 ~ ~ s e e ~ s e e zeee
n I N I n u n E N G I N E S P E E D ( R P n )
D l F F RBTlO 3 . 3 5 7 1
+ D l F F RBT10 3 . 7 3
'
' D I F F RdTIO 4.103--
i
Figure 4 Fuel consumption ADR27C city cycle: restricted ~.atio cut 3.71: 1 with gearhox cl'licie~~cy 95'Z
I
1 ... D l F F RdTIO 3 . 3 5 7
i
1 + D I F F R O T I O 3 . 7 3 1
/ ' b l F F RdTlO 1.183
1
i t has no effect on the I V T . Therefore, the mechanical efficiency o f the I V T can only
fall to an average of 82% before fuel consumption equals thal o f the M A N powertrain
with a differential ratio o f 3.357: 1 and a minimum engine speed o f between 1000 and
1300 rpm.
Figure 7 shows that the C V T must also achieve an average o f 82% mechanical effi-
ciency to equal the best performance o f the M A N powertrain, and at least 80% to equal
LITRES/I00 KM 4 ? + DIFF RdTlO 3.73
* DIFF RbTIO 4.103 1
? k ~ ' 0 - - ~ 7 & - 7 i & 1 6 b e 0 ~ ~ ; : ~ 0
MINIMUM ENGINE SPEED (RPM)
Figure 6 Fuel consumption ADR27C city cycle: unrestricted cut ratio, differential ratio = 3.73:l
T I
r
I I j + CVT EFF 75% , /I===''-
1
' CVT EFF B 0 i!
t
I 1 . CUT EFF 85% II
I - - CUT EFF 904 i I,
- CUT EFT 95,1
I @ .b b---l---- 4 J i __t 6RR ~ Q Q l@@B 1290 140% 1 6 0 ~ 1 1808 2808MINIMUM PNCINE SPEED (RPM?
The VDE data of Figure 8 shows that it must achieve an average efficiency of at least 75% relative to the fixed displacement engine to allow it to equal the performance of the MAN powertrain with a differential ratio of 3.73: 1 or 80% with a differential ratio of 3.357: 1 and minimum engine speeds below 1000 rpm.
Figures 9 to 12 depict for all powertrains the dependency of fuel consumption on con- stant driving speed and differential ratio. Again the IVT and CVT arc specified as having
I .'- CUT EFT 7B/. / I i * CUT EFF 75% i , ' CUT EFT 8Bz I :~ CUT EFF 85%
'
i1
- CUT m 9a.A I - CUT EFF 95% 1'
u
I
@.L i i--t---- 6 0 8 8 0 8 l @ 0 A 1 2 6 0 1 4 0 0 1 6 8 0 1 0 0 0 2 0 0 0 MI I l l HllH ENC! YE S!'EFT) (RP1(>F i r e 8 Fuel consumption ADR27C city cycle: variable displacement engine. diffel.entinl ratio = 3.73: 1
1 P -7
I /-
LlTRES/100 Kt! 5 -r I I ? XEL ENCEFF 85%
I
RE?. EnCEFF 98%
i
I
a mechanical efficiency of 95% whilst the VDE has an efficiency of 95% relative to the manual powertrain. Minimum desired engine speed was set at 1300 rpm in all powertrains. The MAN powertrain achieves minimum fuel consumption at between 40 and 60 kmlh with variations of k 12% depending on the differential ratio.
As anticipated, the IVT fuel consumption (Figure 10) is not dependent on differential ratio and has a broad low consumption region of less than 6 litres1100 km between 40
