dDrive Transmission Report

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

*A division of Gilmore Engineers Pty Ltd Research and Development

BTP Technology and Conference Centre Tel : +61 7 3853 5250 Brisbane Technology Park Fx : +61 7 3853 5258 1 Clunies Ross Court Email : [email protected] PO Box 4037, EIGHT MILE PLAINS 4113 Web : www.e3k.com Brisbane, Queensland, Australia ABN : 12 060 559 480

TM*

Our Ref: Your Ref:

2 of 23

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.

TM

3 of 23

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

TM

4 of 23

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

TM

5 of 23

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.

TM

6 of 23

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

7 of 23

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.

TM

8 of 23

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.

TM

9 of 23

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

10 of 23

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).

TM

11 of 23

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.

TM

12 of 23

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).

TM

13 of 23

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

TM

14 of 23

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:

InputControlIOutput ×−×= 125.0375.0 .....................................(Eq 1)

InputControlIIOutput ×+×= 125.075.0 .....................................(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.

TM

15 of 23

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)

Gea

r R

atio

(O

utpu

t/In

pu

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

16 of 23

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)

Gea

r R

atio

(Ou

tpu

t/In

pu

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

1st G

ear

2nd G

ear

3rd G

ear

4th G

ear

Reverse

TM

17 of 23

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)

Gea

r R

atio

(Ou

tpu

t/In

pu

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

18 of 23

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

TM

19 of 23

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)

TM

20 of 23

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

21 of 23

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-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

TM

22 of 23

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.

TM

23 of 23

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.

TM

APPENDIX 1

• 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

Class I epicyclic gearset Class III epicyclic gearset

APPENDIX 2

Int. J. o f Vehicle Design, vol. 9. no. 6, 1988. Printed i n UK.

Fuel economy goals for future powertrain and engine options

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.

Copyright O 1988 Inderseience Enterprises Ltd, U.K.

Powertrain und engine fuel economy goals 617

2 Automotive powertrain developments

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 hi l l 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 (kwh

This specification is typical of the average vehicle produced for the worldwide automobile market.

618 D.B. Gilmore

3.2 Internal combustion engine

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 of 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 95% (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 or 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 97%, 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

Ratio 3.71 2.16 1.37 1 .O 3.73

Powertrain and engine fie1 economy goals

3.4 Injnitely variable transmission (I VT)

An infinitely variable transmission (IVT) attached to the 2-litre engine was simulated. This transmission could adjust to any sped 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

D.B. Gilmore

cell veloc~ty and acceleration, was able to predict the aggregate fuel consumption of a veh~cle to an accuracy better than 2% of that determined volumetrically on the road or 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, i t 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 lop4 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 ful l 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.

Powertrain and engine fuel economy goals 62 1

4.2 Infinitely variable transmission (IVT)

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.

622 D.B. Gilmore

5 Results achieved

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 95%, 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@@ 148R 1600 18BP 2 0 8 8

MINIMUM E N C l H E SPECD CRPIT)

Powertruin and engine fuel economy goals 623

Figure 3 Fuel consumption ADR27C city cycle: unrestricted cut ratio with efficiency o f gearbox 95%

IB?

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 SPEED ( R P n )

D l F F RBTlO 3 . 3 5 7 1 + D l F F RBT10 3 . 7 3 ' ' DIFF RdTIO 4.103 --

i

Figure 4 Fuel consumption ADR27C city cycle: restricted ~.atio cut 3.71: 1 with gearhox cl ' l ic ie~~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 IVT. 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 CVT 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 the performance at a differential ratio o f 3.73: 1.

624 D.B. Gilmore

Figure 5 Fuel consumption ADR27C city cycle: variable displacement engine, efficiency 95%

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 B0i !

t I 1 . CUT EFF 85% I I 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 2808

MINIMUM PNCINE SPEED (RPM?

The VDE data of Figure 8 shows that i t 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

Powertrain and engine fuel economy goals 62 5

Figure 7 Fuel consumption ADR27C city cycle: restricted ratio 3.71:l cut, differential ratio = 3.73:l

I .'- CUT EFT 7B/. / I i * CUT EFF 75% i , ' CUT EFT 8Bz

I :~ CUT EFF 85% ' i 1 - 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

626 D.B. Gilmore

Figure 9 Fuel consumption at constant speed: manual transm~ssion

18 T

U T RES

3 . 3 5 7 : 1

, DlFF RfiTIO 4 . 1 0 R : l

@I+---+ ------- -.+-+..-+-- i ---l--- ----+--- 1 2 3 4 5 6 7 e 9 1 0 1 1 1 2 1 3 I 4 1 5 16

VEHICLE SPEED ! KM/H/I@)

Figure 10 Fuel conwmpt~on at con\tanl \peed unltmttcd ratto cut

I @L-r + - . . +d - -+ - - -b -~ - -++ ! 8 a *

1 2 3 4 5 6 7 e 9 1 0 1 1 1 i 1 ' 3 1 i i 5 1 b VEHICLE SPEED ( I(M/H/10)

and 90 kmlh. In that region, fuel consumption is between 10 and 20% lower than that for the MAN powertrain with a 3.357:l ratio. This reduction is a little more than that ! found with the urban drive cycle. The CVT resuit of Figure I 1 shows that the fuel con- sumption is as low as that of the IVT between 50-60 krnlh, but 8% higher at 100 kmlh.

'

Dependency on the differential ratio is generally small and negligible below 50 kmlh, and '

above 120 krn/h. I

Powertrain and engine fuel economy goals

Figure 11 Fuel consu~nption a1 constant speed: restricted ratio 3.71: 1 cut

I + DIFF R O T 1 0 1 3 . 7 3 : 1

I I DIFF R h T I O , 4 . 1 8 3 1

0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6

VEHICLE SPEED (KM/H / l0 )

Figure 12 Fuel consumption a1 constant speed: variable displacemenr engine, efficiency = 958

oC-+-- -+ +---+--- ------ +-+--.i---+ ---* 8

1 2 3 4 5 6 7 8 9 1 0 1 1 1 Z 1 3 1 4 1 ' 5 1 ~ UFHICLE SPFED ( K H / H / l 8 )

Figure 12 shows that the VDE has a broad 20 to 85 kmlh speed band where fuel con- sumption is less than 6 litres1100 km. The VDE uses 33% less fuel than the MAN drivetrain at 40 kmlh, 25% less at 50 km/h, and the same at 120 km/h. At speeds greater than 120 km/h the drag power requirement would demand the 2-litre displacen~ent engine, which has been specified as having a 95% relative efficiency compared with the 2-litre fixed displacement engine. Hence, the fuel consumption of the VDE fuel below that of the MAN powertrain.

628 D.B. Gilmore

Figure 13 Fuel consumption at constant speed unl~m~ted la110 cut

i + REL ENGEFF : 7 5 %

1 ' REL ENGEFF = 8B%

. REL ENCETF : 85% I

i REL ENCEFF = 96/: 1 1 '

- REL ENGEFF = 9 5 % , ,

@ k 2 ~ 4 > - - ~ ~ ~ ? 4 = 6 VEHICLE SPEED (EW/H/l@)

Figure 14 Fuel consumption at constant speed: restricted ratio 3.71: 1 cut

Figures 13 to 15 depict for the IVT, CVT and VDE, the constant speed fuel con- sumption dependency on relative mechanical efficiency with a differential ratio of 3.73: 1. Figure 13 shows that the IVT cannot achieve ankfficiency higher than the MAN power- train (Figure 9) at constant speeds below 40 kmlh. At 80 kmlh, a relative efficiency of 70% is required, but this rises to 95% at 130 kmlh. At higher speeds, the manual trans- mission is superior.

The CVT (Figure 14) is similar to the IVT below 50 krnlh and above 120 krnlh. The

Powerrrain and engine fuel economy goals

Figure 15 Fuel consumption at constant speed: variable displacement engine

I I I

28-

15 --

KM , REL E ~ C E F F 85% j I - REL ENCEFF 98% I - REL ENCEFF 95X

1 REL ENCEFF 188% -- 1

1 2 3 4 5 6 7 8 9 1 8 1 1 12 13 14 15 16

VEHICLE SPEED (KM/H/IO)

relative efficiency to match the MAN powertrain must be higher than the IVT in the inter- mediate range and typically is 82% at 80 kmlh.

Figure 15 depicts that a VDE would require a relative efficiency of less than 70% to achieve the constant speed fuel consumption of the MAN powertrain below 40 knilh: rising to 80% at 80 kmlh and greater than 100% at faster than 130 knilh.

6 Conclusions

The following points can be made in summary: As a general conclusion fuel consumption is lowered as minimum engine speed with open throttle is reduced, regardless of the transmission design or the type of engine (fixed or variable displacement).

However. for the three transmissions considered, between 6 and 12% less fuel is consumed with a minimum engine speed of 600 rpm versus 1300 rpm. (If the engine efficiency contours are unchanged).

The VDE does not however need low engine speed development to achieve fuel savings.

Very important Iniporlanl - Not iniporrilnt

Manual IVT CVT VDE

'The importance of a variation in differential ratio can be summarised in Table 2. If an IVT, CVT, or VDE could be made with the same relative efficiency as a con- ventional fixed displacement internal combustion engine and manual gearbox, then i t is clear that major fuel savings would be achicved.

Typically these will be 6-12% for the IVT, and 6- 15% for the CVT. The VDE will achieve 13-24% savings. However, the following conclusions can be drawn: (i) an IVT or a CVT needs

to have > 82% mechanical efficiency on average to be better than a manual gear- box; (ii) a VDE needs to have > 80% relative mechanical efficiency on average to be better than a Manual gearbox with a fixed displacement engine. Table 3 summarises average mechanical efficiencies required to achieve benchmark 5% and 10% fuel savings under urban and constant 100 kmlh conditions. For the IVT and CVT. lower engine-speed capabilities down to 600 rpm and 800 rpm, respectively, would increase the possible savings.

TABI,B 3 Mechanical efficiencies required for benchmark heel savings

Average mechanical efficiency (%) required :

Drive Gain in fuel Minimum I V T CVT VDE cyclc ctficiency (%) enginc (relative

speed(rpm) (efficiency)

Urban 5 1300 90 90 80 Constant 100 kmlh 5 - 87 95 93 Urban 10 1300 Scc GI) See (b) 85 Constant 100 kmlh 10 - 90 See (c ) l 00

No~es: (a) Impossiblc: minimunl cngine speed musr be 700 rpm. (b) Impossiblc: minimum engine speed must be 1600 rpm (c) Impossiblc.

If there exists the probability of achieving efficiencies of greater than 90% relative to the fixed displacement engine, on average, then the VDE engine is worthy of ' further development. There would then be the opportunity to achieve urban drivc I cycle savings of 15% but no change in the highway cruising fuel consumption at 100 kmlh. Thcre is no advantage in reducing the minimum engine speed below 1300 rpm. 1 If a 90% average mechanical efficiency can be achieved with the IVT, CVT and VDE, the lowest possible fuel consulnption which is indicated by this paper is given in Table 4.

In terms of a fuel economy performance index alone, this paper highlights the develop- ment of IVT technology in conjunction with the lowering of the stable operating speed in fixed displacement engines to 600 rpm at high torque levels, as the most fruitful area for further reductions in passenger vehicle fuel consumption.

Pow~~rtrair~ und engine fie1 economy goals

/ TAHI.C: 4 Summary of fuel consumption rebults

Engine typc

Gearbox type

Gearbox ~nechan~cal efficiency

Minimum engine speed (city) rpm (open throttle)

Differential ratio

Fuel consumption urban cycle (litres1100 km)

Fuel consumption highway-conslant speed I00 kmlh. (litres1100 km)

Minimum engine speed (highway) rpm

Fixcd FD displacement (FD)

Manual IVT

FL) FD Variable displacement (VDE)

IVT CVT Manual

907; 90%' 90 2 (engine)

600 600 1300

i"'

References b,

" ' A~nann, C.A. (1986) .The poucrtrain. fuel ecsnoniy and the eiivironnic~~t'. Irri J . I * Vc,/ri~/~, Oc .~ i l~ i , vol. 7. F l., nos. 112, pp. 1-34. :I

Austrdlian Design Rule No. 27C (1982) l i~ r vehicle e~iiission control. Dcparrnient of Tranhpc111 Austrdli;~. C;~riherra. f!

Australia. 1,. Gilmore. D.B. and Bullock. K.J. (1982) 'An on-road evaluation ot'd 1500 kg ~iiulti-purpose hyhrid vehicle with

{: triniodal energy storage'. XIX International FISITA Congress. SAE Australasia. Melbourne. Paper no. p, 82053.

'tselikc, M. (1981) 'Improving fuel econolny through changes in engine and trans~~~ission design'. Irrr. J . 01' Vc~hic,lc D~,si,q!r, vol. 2 , no. I , pp. 19-28.

st, K . er (11. (198 I ) 'Fuel economy and cn~issions rescarcli ;lnnl~al rcporr'. Charles Kollins Rcscarcli Lahora~ory Technical Note ER-36. Department of Mechanical Engineering. Universily of Sydney.

: Post, K o ul (1983) 'Motor veh~cle tuel econolny - veh~clc mapr, power deniand niodelr and un\teddy rtate engine maps report'. Charles Kolling Research Laboratory Technic;ll Note ER-42. Dcpartment nl' Mechanical Engineering, University of Sydney.

Izo. J. (1986) Article puhlishetl in Err,qirr~~e~,:s Au.srrolitr. Inslilut~on 01' Engineers Aust~elia. Canhcrra. July I I . pp. 24-25.

Siegl~, D.C., Sicwcl-I. R.M. (1979) 'The variahle strokc engine - problc.~~i\ and pro~l~ibc\'. SOCICIY (~IAuto~iiotivc Engineers Inc. (USA), Papcr no. 780700.

Stieg. R.F.. Worlcy. W.S. (1983) 'A ruhbcl bell CVT for liont-whecl drivc cars'. Society ol' Automotive Engineers Inc. (USA), Papel- no. 820746.

Slubbs, P.W.R. (19x1) 'The developmenr o i a Perhury traction transmission for motor ~ ; I I - applicat~ons'. Jour- rrcll of Mrc./rurlic.tr/ Dc,.si,y~r. vol. 103. pp. 29-40,

ang, D. and Frank. A.A. (1985) 'An optiniisalion technique for the design o f a conlinuously variahle transniission control system for automobiles', /!if. J. (~/ 'V~~liic~lu D(,.sip~, vol. 6 . no. I. pp. 41-54. i, Van Dongen, L.A.M. (1983) 'Efliciency characteristics ol' manual and automatic passenger car tranwxles', Society

$' of Autn~notive Engineers Inc.. (USA). Paper no. 820741.