digital design of a prototype of an automatic transmission

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DIGITAL DESIGN OF A PROTOTYPE OF AN

AUTOMATIC TRANSMISSION

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LIST OF FIGURES

Figure 1 - The transmission ...................................................................................................................................... 5

Figure 2 - Three inputs AND ................................................................................................................................... 12

Figure 3 - Three inputs OR ..................................................................................................................................... 13

Figure 4 - The Logic Circuit for the 5 inputs ........................................................................................................... 13

Figure 5 - Simulation for row 5 .............................................................................................................................. 14

Figure 6 - Simulation for row 12 ............................................................................................................................ 15




Figure 10 - Simulation for row 28 .......................................................................................................................... 17



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SUMMARY

1 INTRODUCTION ......................................................................................................................... 4

2 DEVELOPMENT.......................................................................................................................... 5

2.1 VEHICLE’S TRANSMISSION .................................................................................................................. 5

2.2 CHANGE OF GEARS ........................................................................................................................... 6

2.3 SYSTEM DESCRIPTION ........................................................................................................................ 6

2.3.1 Digital circuit ..................................................................................................................... 6

2.3.2 Logic Gates ........................................................................................................................ 6

2.4 INPUTS ........................................................................................................................................... 7

2.4.1 Rotation speed .................................................................................................................. 7

2.4.2 Torque ............................................................................................................................... 7

2.4.3 Forward option .................................................................................................................. 7

2.4.4 Reverse option ................................................................................................................... 8

2.4.5 Acceleration/Brake ............................................................................................................ 8

2.5 OUTPUTS ........................................................................................................................................ 8

2.5.1 Accelerator ........................................................................................................................ 8

2.5.2 Change of gear .................................................................................................................. 8

2.6 TRUTH TABLE ................................................................................................................................... 9

2.7 BOOLEAN EXPRESSION ..................................................................................................................... 10

2.8 KARNAUGH MAP ............................................................................................................................ 12

2.9 BLOCK DIAGRAM ............................................................................................................................ 12

2.10 SIMULATION ON MULTISIM .......................................................................................................... 13

3 RESULTS AND DISCUSSION .......................................................................................................19

3.1 IMPROVEMENTS ....................................................................................................................... 19

3.1.1 Fuzzy logic ....................................................................................................................... 19

3.1.2 Increase the number of inputs or add more logic stages ................................................ 19

3.1.3 Input (sensor) for wheel’s position .................................................................................. 19

4 CONCLUSION ............................................................................................................................20

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1 INTRODUCTION

Transmissions are widely used in mechanical applications. They are present in

every car and several others transportation method, such as ships, helicopters, buses

bicycles and many others. Transmission can be defined as an assembly of parts including

the speed-changing gears and the propeller shaft by which the power is transmitted from

an engine to a live axle [1].

In motor vehicles, transmission adapts the output of the internal combustion

engine to the drive wheels. Since engines normally operate at a relatively high rotational

speed, a transmission is necessary to reduce the rotation to a value appropriate for

starting, stopping, and slower travel. By reducing the higher engine speed to the slower

wheel speed, the transmission also increase the torque, which is necessary for moments

when the vehicle is carrying larges loads or travelling in steep streets.

With the advance of technology, objects of every-day use are being modified to

provide a more intuitive and easy operation to the user. Since humans are error-prone,

engineers have been automating vehicles transmission in order to reduce fuel waste and

obtain a better efficiency. An automated transmission would, for instance, change gears

in a more accurate time, depending on the inputs of sensors.

To design an automatic transmission, engineers need to make use of

sensors that would measure torque, rotation velocity and temperature and by a logic

circuit, provide an output that activate a hydraulic system that would change the gears

in order to reduce or increase the speed of the vehicle. In this work, a digital circuit for

an automatic gear shift transmission will be designed to replace the manual one.

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2 DEVELOPMENT

2.1 VEHICLE’S TRANSMISSION

Within a vehicle, a transmission is composed by clutch, gearbox, prop shaft (for rear-

wheel drive), differential, and final drive shafts. Modern cars usually have five forward

and one reverse gear. The transmission is connected to the output shaft, which is

connected to the axles, which are connected to the wheels. When the transmission

rotates the output shaft this turns the axles, which in turn rotate the wheels [5].

The crankshaft only connects to the transmission when the car is in gear and the

clutch is engaged. If you press down on the clutch the crankshaft disconnects from the

transmission [5]. The image below shows the gears and the gear stick within a

transmission.

Figure 1 - The transmission ([5] March of 2015)

The procedure to change gears in a car can be described as follow [5]:

Release the accelerator pedal and at the same time press the clutch pedal down.

Remove your left hand from the steering wheel, cup it around the gear knob and

move the lever gently but positively from one position to another.

Return your left hand to the steering wheel.

Release the clutch pedal slowly and simultaneously apply power by pressing down

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on the accelerator pedal.

2.2 CHANGE OF GEARS

There are several relevant factors that should be considered by the driver in order to

make an optimal change of gears. The first factor is desired the speed for the vehicle, if

the car is in a stationary position and the driver desires to move forward, the first gear

should be selected. The driver must be constantly attentive to the car speed and

tachometer (instrument that measures the rotation speed of the shaft), to know

exactly when to change the gears, an experienced driver would know when to do it

by listening to the engine.

The first gear is also used when moving along in traffic queues at very slow speeds,

which is usually combined with clutch control [6]. Each car has an optimal speed for each

gear. A general guide for which gear should be used for the range of speed of the car is

presented below.

1st gear - From 0kph to 8kph

2nd gear - From 8kph to 24kph

3rd gear - From 24kph to 48kph

4th gear - From 48kph to 64kph

5th gear - 64kph upwards

2.3 SYSTEM DESCRIPTION

2.3.1 Digital circuit

In designing digital circuits, the designer often begins with a truth table describing what

the circuit should do. The design task is largely to determine what type of circuit will

perform the function described in the truth table.

2.3.2 Logic Gates

A digital circuit is often constructed from small electronic circuits called logic gates that

can be used to create combinational logic. Each logic gate represents a function

http://en.wikipedia.org/wiki/Logic_gate

http://en.wikipedia.org/wiki/Combinational_logic

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of Boolean logic. A logic gate is an arrangement of electrically controlled switches, better

known as transistors [2].

2.4 INPUTS

As shown in 2.2 the change of gears depends on several factors. To make a digital

circuit capable of change de gears, some simplification need to be made. The first

would be to consider all gears the same, the output would be then, just change the

gear but it does not specify to which gear the system will change. This allows to

simplify the circuit by eliminating all the gears in the input. If each gear would be

considered in the output all the six options (five forward and one reverse) should be

inserted in the inputs as well to enable to know which gear the output will go.

Since the circuit designed in this work will not distinguish for which gear the

system will change second stage will be necessary, this stage will not be presented,

but in section 3.1 more information about it will be presented and others

improvements will be discussed. The system will receive five inputs as follow:

2.4.1 Rotation speed

Instead of using the speed of the vehicle a more approach to change gears more

accurately is to use the rotation of the engine shaft. Since automatic transmission have

a larger number of gears if compared to the analogue transmissions, it is unviable to split

all gears as input, instead only one input will be used. As with the gear number, this is a

simplified system, and would require to have another digital circuit to inform whether

the rotation speed of the shaft has reached the right value for changing gears or not. In

this circuit it will only be considered that at some time the rotation variable will be high.

2.4.2 Torque

Torque in the transmission will work in parallel with the rotation speed, if either

one is indicating HIGH, then the gear will change depending on the other variables. An

OR gate will be used with these two variables (Rotation speed and Torque). Differently

from the rotation speed, the torque will only be set to HIGH when the car travelling on a

tilted

2.4.3 Forward option

Forward option will inform the system that the car should move forward. The gears will

http://en.wikipedia.org/wiki/Boolean_logic

http://en.wikipedia.org/wiki/Transistors

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change systematically from 0 to 8 and reduce as needed, depending on the desired speed

and torque required.

2.4.4 Reverse option

This option will not allow the car to move forward, therefore the gears will not change,

as there is only one gear responsible for reverse.

2.4.5 Acceleration/Brake

If the car suffers a quick change in acceleration, as when the driver presses the brake

pedal, the system needs to change gear very quickly (reduce) in order to help the

transmission to reduce the car speed. This means that when there is a large change in

acceleration the gear will change, depending only if the variable Forward is set to HIGH.

2.5 OUTPUTS

There are many outputs in a system that change gears, some of them are: accelerator,

change of gear itself and clutch pedal. Since all of them are inwardly connected to the

change of gear variable, they all happens as one output.

Due to the simplifications made in 2.4 then output for the change gear variable is

only HIGH or LOW, it cannot tell to which gear the transmission should change.

2.5.1 Accelerator

In an analogue transmission, the accelerator (throttle) would work as an input, that is,

the gears can only be changed if the throttle is not pressed. However, for a automatic

transmission, the accelerator changes to output, since the driver will press the

accelerator constantly, not removing it for the gears change, the accelerator will,

therefore, “stop working” (set to LOW) when the change of gear is set to HIGH.

2.5.2 Change of gear

The main output is the change of gears itself, it will be changed always the car is

moving forward and the speed or torque values are in the range specified. The change of

gears may be to increase the number, allowing the car to move faster, or reducing the

gear number, increasing the torque of the car and decreasing its speed, useful for curves

and tilted roads.

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2.6 TRUTH TABLE

A truth table is the second step for designing digital circuits. After determining the

inputs, a table with all variables and all possible values for the variables are created. The

number of possibilities depends exclusively on the number of variables, and respect the

following equation: 2nP , where n is the number of variables and P the total value of

possibilities. Since there are five variables, the total number of rows for the truth table

will be: 52 32P .

The truth table describes what the circuit should do. It is complicated to

determine the logic circuitry necessary for the system, however, there are procedural

techniques available to determine it, such as Boolean algebra that will be discussed in

the section 2.7. The table below is a truth table for the system and show all the 32

possibilities for the five variables of the system.

TRUTH TABLE

# Function Speed Torque Forward Reverse Break

0 0 0 0 0 0 0

1 0 0 0 0 0 1

2 0 0 0 0 1 0

3 0 0 0 0 1 1

4 0 0 0 1 0 0

5 1 0 0 1 0 1

6 0 0 0 1 1 0

7 0 0 0 1 1 1

8 0 0 1 0 0 0

9 0 0 1 0 0 1

10 0 0 1 0 1 0

11 0 0 1 0 1 1

12 1 0 1 1 0 0

13 1 0 1 1 0 1

14 0 0 1 1 1 0

15 0 0 1 1 1 1

16 0 1 0 0 0 0

17 0 1 0 0 0 1

18 0 1 0 0 1 0

19 0 1 0 0 1 1

20 1 1 0 1 0 0

21 1 1 0 1 0 1

22 0 1 0 1 1 0

23 0 1 0 1 1 1

24 0 1 1 0 0 0

25 0 1 1 0 0 1

10

26 0 1 1 0 1 0

27 0 1 1 0 1 1

28 1 1 1 1 0 0

29 1 1 1 1 0 1

30 0 1 1 1 1 0

31 0 1 1 1 1 1

Table 1 - Truth table for the system (Author)

In the above table, the column Function receive the value of 1 (HIGH) for all rows

that have the variables in the desired parameter. For instance the row five has the

variable Forward and Break set to HIGH, that are the parameter desired to have a change

in gears as explained in section 2.4. The same happens with the row 12, 13, 20, 21, 23,

24 and 25. These rows will receive a Boolean expression, which will help to determine

the logic circuitry necessary.

2.7 BOOLEAN EXPRESSION

Boolean consists of a mathematical system dealing with the relationship between

sets, used to solve problems in logic and engineering. Variables consist of 0 and 1 and

operations are expressed as AND, OR, and NOT.

Boolean algebra allow the designer to determine the circuitry necessary for a

system depending on the truth table. For each row in the truth table a Boolean

expression is written and then all the expressions are grouped by an OR operator, this

technique is known as Sum of Products, since the product represents the AND operator

and the Sum represents the OR operator. To simplify the function, the variables will be

used as appear in the table bellow:

Function f

Speed S

Torque T

Forward F

Reverse R Table 2 - Variables used in the Boolean Expression

(Author)

The table below shows the truth table and the Boolean expressions for the rows

that receive a HIGH value for the column Function:

Boolean Expressions

# Function Speed Torque Forward Reverse Breake Boolean

Expression

0 0 0 0 0 0 0

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1 0 0 0 0 0 1

2 0 0 0 0 1 0

3 0 0 0 0 1 1

4 0 0 0 1 0 0

5 1 0 0 1 0 1 S'T'FR'B

6 0 0 0 1 1 0

7 0 0 0 1 1 1

8 0 0 1 0 0 0

9 0 0 1 0 0 1

10 0 0 1 0 1 0

11 0 0 1 0 1 1

12 1 0 1 1 0 0 S'TFR'B'

13 1 0 1 1 0 1 S'TFR'B

14 0 0 1 1 1 0

15 0 0 1 1 1 1

16 0 1 0 0 0 0

17 0 1 0 0 0 1

18 0 1 0 0 1 0

19 0 1 0 0 1 1

20 1 1 0 1 0 0 ST'FR'B'

21 1 1 0 1 0 1 ST'FR'B

22 0 1 0 1 1 0

23 0 1 0 1 1 1

24 0 1 1 0 0 0

25 0 1 1 0 0 1

26 0 1 1 0 1 0

27 0 1 1 0 1 1

28 1 1 1 1 0 0 STFR'B'

29 1 1 1 1 0 1 STFR'B

30 0 1 1 1 1 0

31 0 1 1 1 1 1 Table 3 - Boolean Expressions

(Author)

According the table above, the Boolean expressions can be grouped by the Sum

of Products, as presented below:

( ) ( ) ( ) ( ) ( ) ( ) ( )f STFRB STFRB STFRB STFRB STFRB STFRB STFRB

The function generated by the truth table is rather complex. In the next section a

technique to simplify the expression and obtain a simpler circuitry for the system is

presented.

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2.8 KARNAUGH MAP

A Karnaugh map (most known as K-map) is a pictorial method used to minimize

Boolean expressions without having to use Boolean algebra theorems and equation

manipulations. A K-map can be thought of as a special version of a truth table [3]. For a

digital circuit with five variables, the procedure for a K-map is slightly different. One of

the five inputs is taken randomly out of the K-map and then two K-map are created one

is for when the input chosen is set HIGH and other for when the variable is set to LOW.

Karnaugh Map

RB/STF 000 001 011 010 100 101 111 110

00 0 0 1 0 0 1 1 0

01 0 1 1 0 0 1 1 0

11 0 0 0 0 0 0 0 0

10 0 0 0 0 0 0 0 0

Table 4 - Karnaugh table for five inputs (Author)

Once the K-map has been made, it is possible to group the cells which have the

number one in groups multiple of two. The Boolean expression, therefore, is reduced to

the following equation:

Once a reduced function is obtained, the circuit can be designed. The next section shows

the diagram and the operators necessary to implement the system.

2.9 BLOCK DIAGRAM

The function obtained in section 2.8 is a Sum of Products and uses three inputs

in each sum term, therefore, there will be needed to use 3-inputs AND operators, such

as the one shown below.

Figure 2 - Three inputs AND (Author)

A three inputs OR will also be necessary, since there are three Sum terms. Two 2-

( ) ( ) ( )f FRB TFR SFR

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inputs OR gates will be connected in series to represent a 3-inputs OR, as shown below.

Figure 3 - Three inputs OR (Author)

The circuit for the expression ( ) ( ) ( )f FRB TFR SFR is presented below.

Figure 4 - The Logic Circuit for the 5 inputs (Author)

2.10 SIMULATION ON MULTISIM

The last stage of designing a digital circuit is to simulate the circuit to verify if it

will work properly. There are several Software available for this task, the MULTISIM will

be used for the circuit presented in section 2.9. If all inputs were connected to a switch

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and subsequently to a VCC and Ground source, it is possible to connect a probe in the

Output and test the circuit by switching ON and OFF each Input according to the Truth

table and check if the Output is correct. The figures bellow show the simulation for all

seven lines of the truth table that have 1 in the Function column.

Figure 5 - Simulation for row 5 (Author)

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16



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It is important to notice that any other line on the truth table will turn off the blue

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probe as shown below.


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3 RESULTS AND DISCUSSION

Although the simulation shows that the circuit is correct, this prototype is too

basic for real implementation. All hypothesis made for simplifying the system should be

considered and a system with more than one stage of circuit should be designed. The

output acquired in the circuit should be used as an input of another circuit that would

use values of sensors and timers to effectively deactivate first the clutch and then

activating the hydraulic system, instead of activating all at the same time by using one

stage circuit. In the next stage some ideas for future improvements are discussed.

3.1 IMPROVEMENTS

3.1.1 Fuzzy logic

An automatic transmission analyse several factors before changing the gears.

However all these factors are analysed in Boolean form, if the value obtained by the

sensor lies in certain range than the value for the variable is set to HIGH or LOW,

depending on the variable. But this system is not the most efficient, there are some other

types of logic that allows to proximate the machine to a human manner of thinking. This

kind of logic is named fuzzy logic, which allows to consider variables not as 1 or 0 but as

functions (linear), a final system that uses fuzzy logic would change gears much more

efficiently enhance, therefore, the effectiveness of the vehicle.

3.1.2 Increase the number of inputs or add more logic stages

Although the clutch was treated in this work as an output, this is not entirely the

case, since the gears can only be changed when the clutch is depressed. Therefore the

clutch is a middle-term between the inputs and output (change of gear). As a future

improvement, the digital circuit should receive a time variable, which activate the

hydraulic system that changes the gears only a few moments after the clutch has been

depressed.

3.1.3 Input (sensor) for wheel’s position

Position of the wheel should also be considered as an improvement, a sensor that

tells whether the wheels is moving right or left is important in order to reduce the gear

to a more appropriate one. The change of position in wheels means the car is making a

curve and a more appropriate gear for curves is the second, which maintain the car in a

good speed and torque for the task.

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4 CONCLUSION

Digital circuits is quite useful for several applications in engineering, and

automation. Most of the electronics products used nowadays have some digital circuit in

its construction and the understanding of this subject is primordial for an engineer.

This work presented that a manual transmission can be transformed to automatic

by an arrangement composed of hydraulic (mechanical) system and a digital circuit.

There is a number of steps for designing a digital circuit. As shown, the designer must

begin by determining what will be the inputs and outputs, this might be the most

important step because if the number of inputs is wrong, the resulting system is useless.

Once the inputs are selected, it is important to make a truth table to determine what will

be the output results. After this some techniques are applied to implement the circuitry

necessary for the design, some of these techniques are: Boolean expressions and

Karnaugh map, together these techniques reduce the size of the expression and make

straightforward to obtain basically any digital circuitry.

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BIBLIOGRAPHY

[1] J. J. Uicker; G. R. Pennock; J. E. Shigley (2003). Theory of Machines and

Mechanisms (3rd ed.). New York: Oxford University Press

[2] Maini. A.K. (2007). Digital Electronics Principals, Devices and Applications.

Chichester, England.: Jonh Wiley & Sons Ltd.

[3] Simplifying Logic Circuits with Karnaugh Maps (2012). The University of

Texas at Dallas.

[4] Dwinger, Philip (1971). Introduction to Boolean algebras. Würzburg: Physica

Verlag.

[5] http://www.driving-test-success.com/gears/gearinfo.htm

[6] http://www.drivingtesttips.biz/

digital design of a prototype of an automatic transmission

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