Road Vehicle Dynamics: Fundamentals Of Modeling And Simulation

Fundamentals of Modeling and Simulation

Giancarlo Genta, Alessandro Genta

• Publisher: WSPC
• ISBN:
  9789814713450
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

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Road Vehicle Dynamics supplies students and technicians working in industry with both the theoretical background of mechanical and automotive engineering, and the know-how needed to perform numerical simulations. Bringing together the foundations of the discipline and its recent developments in a single text, the book is structured in three parts: it begins with a historical overview of road vehicles; then deals with the forces exchanged between the vehicle and the road, and the vehicle and the air; and finally, deals with the dynamic behavior of the vehicle in normal driving conditions with some extensions towards conditions encountered in high-speed racing. Coverage of contemporary automatic controls is included in this edition.

-->0 Readership: Students & Professionals dealing with Mechanical engineers.
-->Motor Vehicle, Dynamics, Modeling, Numerical Simulation, Ground Vehicles

• The book has been updated, including the background and the mathematical models needed to deal with those control systems which are increasingly applied in the automotive field (ABS, vehicle dynamics control, active suspensions, 4WS, etc.)

Chapter 1

SHORT HISTORICAL NOTES ON MOTOR VEHICLES

Road vehicles with mechanical propulsion are a recent achievement of technology, dating back to less than one and a half century. In this short time, however, they have deeply changed our lives, giving human beings a freedom of movement which was unheard of. In the 20^th century the production of automobiles became a leading industry in many countries, contributing substantially to their wealth. Contrary to many pessimistic statements heard in recent years, its importance is bound to last well into the 21^st century and beyond.

1.1Ground vehicles with mechanical propulsion

Ground vehicles with mechanical propulsion appeared only quite recently in the history of human civilization. They can be said to be one of the main consequences of the industrial revolution.

To allow their construction, a prime mover able to move itself, together with the vehicle structure and payload, was needed. Remembering that the power P needed to move the mass m at the speed V on a level surface with coefficient of friction (sliding or rolling) f is equal to

it is easy to conclude that the minimum value of the power/mass ratio of a prime mover that is able to move itself is

where α is the ratio between the mass of the engine and the total mass of the vehicle and η is the total efficiency of the mechanism which transfers the power and propels the vehicle.

From Eq. (1.2) it may seem that the required power/mass ratio tends to zero when V tends to zero, i.e., that it is very easy to move at low speed. This is however misleading, since the efficiency η tends to zero in these conditions.

Remark 1.1. Prime movers with an adequate power/mass ratio were practically not available until the 19^th century, and this consideration is sufficient to explain the above mentioned delay.

The development of a suitable prime mover is however not sufficient for the construction of a successful automotive vehicle. The problems related to the construction of suitable transmission, propulsion, control and guidance systems must be successfully solved as well. The development of automotive vehicles is based consequently on that of vehicles propelled by animals and on the development of the wheel, in its two aspects of supporting and propelling device.

1.2Vehicles on wheels from prehistory to the end of the Roman Empire

1.2.1The supporting wheel

For hundreds of thousands years humans lived without using any particular means of transportation. When they had to move an object, they simply lifted and carried it if they were strong enough. If the object was too heavy, they arranged to drag it along. It is possible that occasionally, branches or other round objects were slipped under the load to reduce friction, but no evidence of this practice remains from prehistoric times.

With the neolithic revolution, the need for transportation greatly increased and, on the other hand, the practice of taming animals opened new perspectives. With the development of agriculture there was a need to transport seeds to the field and crops back to the homestead. The number of objects which were considered important and which humans needed to carry with them increased as a result.

Sleighs were used in northern Europe before 5000 B.C., and their use at that time in other places can be inferred. Sleighs and drags can actually be used for transportation not only on snow and ice, but also on grassland — American Indians used the travois well in the 19^th century — and even in deserts and sometimes on rocks.

Remark 1.2. It is not possible to state when a drag was mounted on a pair of wheels for the first time or who operated this technical revolution. Ancient wheels were made mainly of wood, but there was little archeological evidence.

About 3500 B.C. the potter’s wheel was introduced to produce pots with axial symmetry. The use of the potter’s wheel can be inferred from the marks left on pots made with it. The supporting wheel for vehicles is thought to have originated at about the same time.

The most ancient evidence of a wheeled vehicle is from a pictogram on a tablet from Inanna temple in Erech, Mesopotamia. Such document dates back to slightly later than 3500 B.C. and includes a small sketch of a cart with four wheels, together with that of a drag (Fig. 1.1a).

The vehicle shown in Fig. 1.1b has two features typical of all vehicles at that times: The wheels are discs made from three planks of wood and the animals are harnessed to a central shaft. This uniformity of the types of wheels and driving systems, particularly if compared with the great variety of vehicle has led to the opinion that the wheel was “invented”, or developed, in a certain place, followed by a slow diffusion in all of the ancient world. In the various places where it was introduced, the local type of sleigh was adapted to the new vehicle using the standard wheels and harness.

The place where the wheel was first developed is not known, but it can be inferred that it was in Southern Mesopotamia, where the wheel was used around 3500 B.C. The introduction of the wheel was quite slow. Evidence of its use dates from 3000 B.C. in Elam and Assyria, around 2500 B.C. in Central Asia and Indus Valley, 2250 B.C. in northern Mesopotamia, 2000 B.C. in southern Russia and Crete, 1800 B.C. in Anatolia, 1600 B.C. in Egypt and Palestine, 1500 B.C. in Greece and Georgia, 1300 B.C. in China and about 1000 B.C. in northern Italy. Some centuries later it reached northern Europe.

Figure 1.1. (a) Pictograms representing a sleigh and a wagon from a tablet from about 3500 B.C. found at Erech, Mesopotamia (b) Copper model of a war chariot with 4 onagers harnessed. It was found in a tomb at Tell Agrab in Mesopotamia (third millenium B.C.).

It is difficult to infer from ancient pictures whether the axle did turn together with the wheels or whether it was stationary. The central hole of the wheel disc was round because it was easier to construct. It is likely that both these designs were used as there are still people who use those primitive technologies nowadays (Fig. 1.2).

It is likely that the wheel did not derive from the roller; the types of wheels used would rule that out. More likely from the viewpoint of the ancient wheelmaker, the wheel and the roller had little in common.

Remark 1.3. In reality, the wheel and roller have nothing in common. In the former the radius of the surface rolling on the ground is much larger than the radius of the surface supporting the load in the bearing (the axle), while the latter does not have an axle and the radius of the surface rolling on the ground is the same as that in contact with the object to be supported.

Figure 1.2. Cart axle with two wheels dating back to the mid-twentieth century. Except for the iron tire, the structure with a disc made of three planks is the same as that of prehistorical wheels. The axle turns together with the wheels (picture taken in Urchisar, Turkey, in 2011).

The need to build lighter wheels for war chariots probably led to the development of the spoked wheel. The wheel with spokes was first used probably in about 2000 B.C., and by 1600 B.C., it reached its fully developed form in Egypt. The central part of a wheel of that type (with 8 spokes) is shown in Fig. 1.3a. It is a part of a chariot dating back to 1350 B.C. found in a tomb near Thebes. The spokes are fitted in the hub; the felloe is usually built in various parts but some examples of felloes in one piece, bent in a circular shape, were found as well.

A wheel which develops from the disc and the spoked wheel is shown in Fig. 1.3b. This wheel seems to be built from a design of the spoked wheel by a wheelwright used to disc wheels. However wheels of the same type are represented in more ancient Greek paintings.

During those ancient times, wheels had a hoop or tire or at least some device to strengthen the rim. Some disc wheels have a wooden rim in one or more pieces. Sometimes the rim of the wheel is inlaid with copper nails to reduce wear or to keep a leather tire in position. Certainly, many Egyptian war chariots had wheels covered with leather. In some ancient pictures, something which looked like a metal tire could be seen. The evidence of such practice is much more recent, dating back to about 1000 B.C. These metal tires were built in various parts, welded together and then shrink-fit to the wheel.

Figure 1.3. (a) View and cross section of the central part of a wheel of an Egyptian war chariot (1350 B.C.), found in a tomb near Thebes (b) Wheel found in Mercurago, northern Italy (about 1000 B.C.).

1.2.2Animal traction

As it was already stated, only after animals were tamed could wheeled vehicles be propelled in a proper way. In Mesopotamia both transportation vehicles and war chariots were pulled by onagers, a sort of wild donkeys. Also, oxen were used for transportation.

The spoked wheel that appeared about 2000 B.C. was accompanied by the use of horses to drive war chariots. It is not known where horses were first tamed and used for that purpose. The archeological evidence indicated that it could have happened in north-east Persia, and then from there the use of horses spread to the whole of the ancient world, from China to Egypt and Europe.

The lack of a proper knowledge of the anatomy of animals led to the harnessing of onagers and horses in the same way as oxen. A collar was added to the yoke, as horses could not exert much force directly with their shoulders unlike oxen.

The collar however pressing on the windpipe of the animal, caused a decrease in physical efficiency when a strong tractive force was applied. Horses could not exert on the harness with all their force, a situation prevalent until the end of the Middle Ages. In Roman times horses were reputed to provide a maximum tractive force of about 620 N. The advantage of using horses instead of men was thus marginal: A horse exerted about the same power as four slaves, but needed a correspondingly greater amount of food. Hence the trade-off was influenced by their availability and other circumstances.

Remark 1.4. The failure to understand this simple fact had severe consequences on the development of ground transportation, and in general, on all mechanisms driven by animals.

Ancient people were not used to shoe horses. Horses, camels and mules were fitted with provisional shoes of metal, leather or straw when they had to walk over slippery or very hard surfaces. The use of adequate horse shoes is thought to have been introduced in the Roman Empire from the East around 2^nd century A.D., becoming widespread only in the 8^th century.

In the ancient world, the only source of power available to humans for general use was their own muscular power and that of tamed animals, since wind power was exploited only for sailing.

Mechanical prime movers were introduced at the beginning of the Christian Era, in the form of the water wheel. It could not be used directly for transportation and there is no evidence of its application to pull loads with ropes (like cable cars). There was little application even in cases where it was suitable, e.g. grinding wheat, pumping water or operating static machinery, because animals and slaves were available. Although windmills were introduced later, there was little application of these as there were no attempt to build sail vehicles on wheels.

1.2.3Vehicles

The possibility that carts originated as sleighs on wheels has already been mentioned. Ancient evidence of both two-wheel carts and four-wheel wagons is available. It is likely that the axle-load had to be limited due to the lack of roads and the small width of the wheels. It was then necessary to use wagons with four wheels for transportation. War chariots which had to be light and easily maneuverable, always had two wheels.

The front axles of all wagons were not articulated on the body of the vehicle, at least until the beginning of the Christian era, and no suspensions were used.

Remark 1.5. Wagons were consequently scarcely maneuverable and could be forced on a curved trajectory only due to the very low “cornering power” of the wheels. At any rate, changing the direction of motion of a wagon with no steering on soft soil required a considerable muscular strain.

The lack of suspen...

Table of contents

• Cover
• Halftitle
• Title Page
• Copyright
• Preface
• Contents
• Symbols
• Acronyms
• 1 Short Historical Notes on Motor Vehicles
• I FORCES ACTING ON THE VEHICLE
• II DYNAMICS OF A RIGID VEHICLE
• III DYNAMICS OF A VEHICLE ON ELASTIC SUSPENSIONS
• References
• Index
• Series on Advances in Mathematics for Applied Sciences
• About the Authors