Design and analyse of a front suspension system of motorcycle

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CHAPTER 1: INTRODUCTION

1.1 AIMS

The main aim of this project is to Design and analyse of a front suspension system of motorcycle. The designing and modelling of the fork is done using Pro-Engineer (wildfire-4) and Stress analysis is undertaken by Ansys 11 software's.

1.2 OBJECTIVES

  • To get aware of deformations caused due to application of brakes to the fork of the front suspension system;
  • To demonstrate detailed view of functioning of fork ;
  • To show existence of various kind of front suspension systems used in motorcycles;
  • Evolution of front suspension systems;
  • To verify the benefits and the flaws of different front suspension systems, used right from the old age to modern age;
  • To illustrate how the motorcycle keeps its balance and analyzing the factors that come into play while riding;
  • Application of vibration modes, on suspension system of a motorcycle while riding.

1.3 INTRODUCTION TO MOTORCYCLE FRONT SUSPENSION SYSTEM

A Motorcycle front fork connects a wheel and axle to its frame, by way of a pair of triple trees. The bike is steered by handle bars which are attached to the triple tree and also brake is provided to retard or stop the acceleration of the bike. There are loads of critical geometric parameters such as ‘Rake' and ‘Trail' which are establish by the fork and its attachment points on the frame, which usually play for handling and riding and dives as well during braking.

Telescopic forks

The term ‘Telescopic forks' is defined because the tubes slide in and out of the body they are ‘Telescoping'. The upper portion generally called as ‘Fork tubes' (Male tubes) slides inside the fork bodies (Female tubes), which are lower part of the forks. Over more than century years of motorcycle improvement, different variety of front form arrangements have been attempted but some of them are still remain available nowadays. The most common form of front suspension for motorcycle now days are the ‘Telescopic fork' Nimbus was the first manufacturer to produce a motorcycle with hydraulically damped telescopic forks in 1934.Early front suspension designs were used frames with springs. Greeves, a British manufacturer used a version of swinging arm for front suspension on their motocross design and also a single sided version suspension system is used in motor scooters such as the Vespa.

Suspension system is equipped with large hydraulic shock absorbers with internal coil springs. The main work of the shock absorbers is to allow the front wheel to react to imperfections in the road while isolating the rest of the motorcycle from that motion. The Upper part (Top yoke) of the forks is connected to the motorcycle's frame in triple tree clamp, which allows the forks to be turned while steering the bike. The Lower part (Bottom yoke) is fixed to the front axle around which front wheel rotates. The fork tubes should be smooth and mirrored finish, so as to seal the fork oil. Some fork tubes found on the off-road motorcycles are covered with plastic protective sleeves called as ‘Gaiters'. The forks are constructed either of the conventional ‘right-side-up' or sliding -female configuration, or the ‘Upside-down' or Sliding -male configuration. In Both the cases, a cylindrical tube or piston sided axially within the cylindrical cylinder.

Trail and Rake:

‘Trail' is the measurement, on the ground, from a point which is projected through steering axis to the centre of the tyre's contact patch below the axle. Trail determines the self centring stability of the steering as well. The triple clamps provide good lateral offset that the forks clear the sides of the front tyre. Usually Triple clamps are introduced to provide some measure of longitudinal offset as well, to alter the trail. Trail impacts directly on the steering stability of the motorcycle and its ‘return-to-center' force. The trail is much affected by rake .Rake is defined as the angle between the vertical and steering axis. The steeper rake reduces the trail and trail itself is also affected by the longitudinal fork offset. More offset decreases the trail. The trail is also affected by axle offset. The trail increases in the case if the axle is coupled to the forks in front of their centre.

Ride height:

Sometimes rider desires to increase or decrease trail to change the steering feel so as to improve steering swiftness, or to eliminate high-speed shake, or to reduce a front end push. Ride height is simply defined as the forks extending up through the triple clamp. Decreasing the ride height by raising the forks farther through triple clamps in reality steepens the rake, which results in decreasing the trail. Alter in trail causes the effects to the rider to his ride height adjustments.

CHAPTER 2: LITERATURE REVIEW

Motorcycles were first developed out of the bicycle frame, which certainly is rigid. Suspension systems were progressed over the years after critical researchers to filter out ground disturbances in more efficient ways.

CHAPTER 3:

3.2 FORK FUNCTIONING:

The weights are transmitted from inner tube to the outer tube or vice versa through the slider bushes which are placed between the two tubes. The bushes used for the good fork are critical because it should have a very low coefficient of friction as well as mounting tolerance.

The system smoothness is totally dependent upon the friction forces developed during sliding movements as well as on the amount of stiction.The stiction is at maximum at “Moto incipiente “,,When the initiation of the movement occurs between the surfaces. This stage is called as static friction. In Designing and fabrication of the slider bushes, the problem of sliding friction always stand for a weak point in the front fork of the vehicle.

If we compare it, for example, to the rear suspension in which there is practically no sliding due to the displacements consists of rotations around the bearings. The suspension settings can be achieved by the stiffness of the spring, as well as the damping provided by the hydraulic part, to which is added the resistance given by the sliding friction. It is difficult to predict what the suspension behaviour operates and its proper functioning is taking cared by the availability of friction.

In the design stage, limiting friction forces require that the loads on the bushes be minimized, boosting movement of the unit. When the fork is extended fully, only a small segment of the slider tube enters inside the sleeve. Hence at this stage its overlap is reduced to a minimum. This is also constitutes the least rigid configuration of the whole system. At the end of the travel, as a substitute of the fork tube overlap extreme therefore maintaining the stiffness.

3.3 FORK STRESSES AND DEFORMATIONS:

Certain forces acts on the fork leg while the vehicle is in motion. Two cases can be considered which helps us to derive fork stresses as well as deformation. They are

(i) Fork flexure due to vertical loads:

The flexure due to vertical loads involves the stresses which act on by weight of the motorcycle plus rider. Also stresses tend to develop due to road surface irregularities such as through potholes, steps ridges, etc. Actually these stresses are considered negligible for example, If we travel in the city at <50 km/h and heading towards a step that rises 4 to 5 cm's from the profile of the road, thus 100 % front overloading can be easily achieved.

The ‘Moment of flexure' or ‘Bending moment' is generated when the vertical load is finally applied to the wheel. The moment of flexure or bending moment gradually increases as the fork is inclined. When with the same force applied, the bending moment will reach to the maximum in the case of fork extended fully and vice versa the bending moment will be minimum with the maximum compression. Therefore the values vary as the changes occur in the arm of the force applied. The stresses are less when the slider bushes are closer to the wheel spindle and are expected to function better.

When the rider passing over dip holes in the ground in the road surface, the vertical loads can attempt very high values, hence the frame structure has to be stiff enough to avoid excessive deformation and simultaneously it should have the capability to absorb all the immediate bumps whenever the suspension bottoms out. At the front end the area, steering head tube receives the heavy stress .whereas, at the rear end connecting rods as well as the shock mounting come under the greater stress.

When the motorcycle is stationary, the load values that appear during normal use are two to three times as big as static loads which are normally acting on the wheels.

If we consider a medium powered street bike which is kindly moving on a bumpy road with a high speed and if the wheel bounce on hole then the stress exerted on the structure may be hundred of kilos or more. Maximum load values can take place when the off-street bikes jumps and cross over the obstacles.

(ii) Fork flexure due to braking force:

As it is the known fact that when braking force is applied to the wheel, then it is obvious to the wheel, experiencing the deformations upon different circumstances of road. In this case, Bending will greater as the length of the fork is high. The highly noticeable point of interest is that the deformation due to vertical forces is opposite to the deformation due to the braking force.

In the previous case we observed that, during braking, because of the weight transfer effect, the front load increases; i.e. there can't be a braking force without an increase in vertical load.

When the brakes are applied to the bike then some strong longitudinal forces are created, giving rise to bending moment that gets stronger as it rises from the ground to the steering head tube, finally transmitted to the whole frame. The steering head tube experiences the strongest moment. The steering head tube is the point with the least depth of section, which is the major plane of stress. Due to this considerations observed, detailed research and study has undergone to give the actual design dimensions of the whole steering tube. On this part of flexure happens during the big thrust of acceleration would definitely cause trail variation. When the braking stress dies out for example; when entering a corner, there would be an annoying elastic rebound action in response. Meanwhile the rear fork doesn't experience much stress during braking as front fork does.

The above two effects (i) Flexure due to vertical load as well as (ii) Flexure due to braking force will certainly oppose each other and within the deceleration range of characteristics of motorcycle, depending upon Cg height, wheel base and fork inclination. In general fork flexing during braking is not as severe as one might think.

Deformation due to torsional forces:

The twisting forces which derived are as follows

  • The alignment is poor between the fork axis and equilibrium forces;
  • The components of equilibrium forces perpendicular to the fork axis and out of alignment with it;
  • The couple which applied by the rider to the steering head.

The resultant deformation is said to be very harmful for handling because the wheel does not respond properly according to the direction of control set by the rider of the vehicle.

Effect of deformation on functionality:

It is clear straight away that the presence of fork deformation makes the proper sliding inside one another more complex to the point of potentially impeding it. When the bike is in motion, the deformation is at highest at most critical circumstances such as brake application and corner entry.

3.4 DIFFERENT DESIGN TYPES OF FRONT SUSPENSION SYSTEM

Telescopic forks are mainly classified into two kinds which are used in practical applications in daily routine life. They are

  • Traditional or standard which is equipped with an internal tube, the one with smaller diameter in the upper postion, fixed to the frame.
  • Upside Down or Inverted which is equipped with internal tube in the lower position, which is fixed to the frame.

The hydraulic as well as elastic fundamentals of these kinds can be simply comparable in order to know the different responses of the same motorcycle equipped with two distinct types of forks. There are some manufacturers whom have created a ‘Cartridge' containing the hydraulic part which can be easily mounted onto each of the applications being tested.

The first telescopic fork prototypes was designed right after the Second World War, were laid out with little attention as to whether they were in traditional or upside down form. In the sixties, the majority of the forks produced was traditional type whereas Upside down design came into the existence at the beginning of the eighties. The upside down design was popularised back into circulation of sport bike applications.

Contrast between Traditional and Upside Down form of telescopic forks:

Benefits of Tradional form:

  • Less number of components, given that the wheel attachments and axle lug derive directly out of lower stanchion which also keeps weight down;
  • Unsprung mass weight is slightly reduced;
  • Tubes slides in areas that are more protected from bumps and dirt.
  • Benefits of Upside down form:
  • It has superior torsional stiffness with the same weight, where the tube has larger diameter and is positioned in upper area, which deals with greater stress from the bending moment;
  • Strong attachment between the tubes and the triple clamps which have large tube diameters.

The above comparison between the two applications says that one is absolutely better than other. So, in this case upside down layout presents more advantages in the terms of stiffness which makes ideal for some sport-oriented applications.

Both the applications Traditional as well as Upside down forks are characterized by

  • Different stiffness's;
  • Different weight distribution;
  • Different values of unsprung weight;
  • Different center of gravity heights between the steering and the ground;
  • Different values of inertia around the steering head axis.

There are some other types of unconventional fork types and can be classified into the groups. They are

  • Swinging front fork or Pivoted;
  • Parallelogram linkage or Girders;
  • Straight line slider guides;
  • Paralever linkage.

a) Swinging front fork :

This type of fork was especially used on the earliest bike models and it is a very simple construction solution. In practical, it reproduces the geometry of the rear fork, along with a n arm that usually rests on a fulcrum which is placed on the steering column, making the fork rotate in one piece along with the steering head. Depending upon whether the arm is compressed or extended during braking, leading link or trailing link front forks are discovered. In both the cases of the forks, the layout may be seen to be symmetrical to the head angle with two arms or it may consist of only one arm. For scooter models, Pivoted front fork suspension is adopted, but they are almost rare when coming to high performance vehicles.

The main characteristics of swinging front fork suspension system are as follows.

  • In Smoothness ,They are very smooth when the rotations are assured by rolling bearings eliminating stiction;
  • When the matter comes to design construction, the stiffness may be better or sometimes worst.
  • The connecting rod linkage systems have never been used to gain progressive rates; it is easy enough to obtain progressive spring rather.
  • The inertia is high around the steering axis and the unsprung masses have moderate weights which are totally dependent upon the type of construction used for the forks

If we compare both leading link as well as trailing link, it will be the great point of interest.

Leading link:

In mid 1950s, the world champion Moto Guzzis which are the best handling racing machines of their period, were installed with leading link. The leading link consist of a tubular or pressed steel structure which connects the steering column in the link pivots and slot in for the suspension struts. The links appear to be independent or formed by a single U-shaped loop around the back of the wheel. In the case of the links separation, their resistance to independent movement as in the type of telescopic fork, depends upon the rigidity if their attachment to the wheel. If the wheel has large- diameter spindle then it also haves large wheel bearing and the most convenient and efficient method is a loop behind the wheel and a smaller -diameter spindle.

Benefits of leading fork are as follows

  • Quality of detail design
  • Possibility of greater rigidity.
  • Greater stability on the fork
  • Precise control over the steering.

The lack of stiction enhances the sensitivity to the small undulations and also any degree of anti -dive under heavy braking. The wheel has precise path which usually depends on the relative heights of the wheel spindle and link pivots. Because of the curve shaped, these forks are highly unsuited for the large movements which are usually used on modern off road machines.

In the leading link during braking the anti-dive behaviour can be seen. The anti dive behaviour tries to extend the suspension, in the case of application of braking force that is applied to the fork .The Anti -dive behaviour can be prevented by fixing brake calliper to a torque arm which is connected to the steering. In this case, spontaneous center of rotation may be positioned so as to create anti-dive behaviour.

Trailing link:

The trailing link differs from that of leading link in many ways like the link pivots of the wheel spindle are ahead, not behind. The demerit of this kind of fork is higher steering inertia, since the bulk of the mass is relatively far from the steering axis, which has an effect that partially offset by the smaller amount of material required to reach the pivots.

In the trailing link during braking, the pro-dive effect occurs which is quite similar to the traditional fork .In this case as well brake torque arm will be introduced along with fixing brake callipers in order to get the proper effect when braking.

b) Parallelogram linkage or Girders:

Girder forks are widely used now a day's which is also considered for their excellent steering. Due to friction dampers, the performance was generally limited and very crude by current hydraulic standards. The links which operates the suspension system were short and due to this kind of forks are very much suitable for small amount of suspension movement.

One of the forks namely Vincent “Girdaulic” was most sophisticated. It consists of light -alloy blades and one-piece upper as well as lower link assemblies. The trail for this fork was readily adjustable. Springs were adjusted in the long telescopic tubes, behind the uprights, but the hydraulic damper was separate, mounted in front of the head stock. The lateral stiffness was boosted by a plate which will bridge the front of the blades. Hydraulic damping is employed against suspension movement and also to damp out steering excursions, a damper was used.

The most recently released linkage designs comes under this category. The main characteristics of the parallelogram linkage are as follows

  • The smoothness of the fork is outstanding, since sliding friction is substituted by rolling friction i.e. Sliding movements are kindly replaced by rotations around the roller bearings;
  • It has got adequate amount of stiffness enhanced by the design construction;
  • The progressive rate of the suspension can be incorporated;
  • The trajectory control is excellent which is highly dependent on type of fork used. It is possible to have different types of wheel trajectories with the help of parallelogram linkage system. The trajectory can be considered perpendicular to the ground, maintaining the same wheel base, or to obtain certain degree of anti-dive it may be inclined forward, in the beginning phrase.
  • The trail control is good. In this case, it is highly possible to create constant trail geometry with varying travel .It can be increased or decreased according to riding behaviour of the vehicle.
  • Depending upon the fork design, the unsprung weigh could be less but the net weight of the suspension remains constant.
  • The most popular design solutions used in automotive industry are as follows

Solution (a):

In this type of solution, the fork legs are allowed longer along with mounting brake callipers. Like single sided rear fork, the links that hold the wheel can also be asymmetrical. The steering is controlled by positioned links.

Solution (b):

It is rarely employed and characterized by high steering masses and substantial inertia, less bulk and steering control is high.

Section (c):

This type is rarely employed. The leg length is reduced to make large wheel travel. Kinematic loads will be large with such a short fork legs.

Solution (d):

This kind of solution is generally employed for light motorcycles and has been introduced right after the Second World War. The steering control is good but it imposes limits on the steering mass size and on trajectories available to the wheel. Because the links are located at certain altitude, the stresses on the links due ot the forces are very tough.

Solution (e):

This kind of solution has been introduced in most advanced applications. In general, it unites all the advantages offered by girder solutions. When it comes to design of the fork, it experiences some drawbacks in the terms of the looks. The horizontal arms have to be long enough to allow the wheel to be steered. Due to this factor, it could be a strong limit the maximum steering angle value, which usually restricting the use of this solution to the street bikes.

The links controls the steering; offering the possibility to position the shock absorber in areas that make the mountings powerful and fabrication is easy. Through connecting rod system, the steering control may be easily constructed.

Solution (f):

This solution is quite similar to the solution (e), but it does not allow offset of the wheel with respect to the steering head axis or zero offset. Due to the large diameter bearings in order to house the steering kingpin, the wheel hub center becomes complicated.

(c) Straight -line slider guides:

Straight-line slider guides are especially regarded by the same geometry as the rear fork when speaking about the controlling the trajectory of the point O point and trail are concerned. Practically, the cylindrical slider is replaced by a straight line slider but of rolling type. The classic shock absorber is represented as the damping element in this case, while rolling guide bearings are similar to ones used for highly developed mechanical machining work.

The Advantages of Straight-line slider guides are as follows

  • ü It enhances better smoothness;
  • ü It hails limited play as well as has got good stiffness;

The limitations of straight-line slide guides are as follows

  • The main problem is difficulty in positioning the two disc brakes
  • Asymmetry-it gives rise to bothersome moment around the steering axis.

(d) Paralever linkage

This type of solution is generally considered as a corrupted parallelogram linkage system because, the upper linking bar is missing and also the suspension function is done by a slider derived from intermediary part that becomes a sort of fork.

Advantages of paralever linkage system are as follows:

  • The sliding motion in this case is simpler when compare it to standard fork
  • The transmission ratio is 1:1 in this case as the steering is directly connected to the tubes.

Limitations of Paralever linkage are as follows:

It is more mechanically complex than a traditional fork and generally bulky due to the presence of horizontal arm.

(e) Mechanical anti-dive system:

In the field of racing, mechanical anti-dive type fork systems have been introduced to limit their tendency to front end dive. In this case, By means of a series of links, the braking force sustained by the brake calliper is transferred to the chasis, opposing its tendency to dive.

The mechanical anti-dive system has been not recognised universally because of the following problems incurred.

  • Making of brake callipers is difficult in this case which mounts rigid enough, with possible braking power loss and aswell as formation of micro-vibrations.
  • The system's weight is high
  • Moment of inertia is increased over the steering masses
  • Less amount of effort have made in vehicle's handling.

(f) Hydraulic anti-dive system:

Mechanical anti dive system has been replaced by hydraulic-anti system. Hence they are increasingly rare. The hydraulic anti-system is totally based on the hydraulic braking usually when the brakes are applied, by blocking the passages.

When the hydraulic brakes are made too strong thus it becomes difficult to absorb small irregularities in the road surface, especially during the complex way of entering the corner of the road.

CHAPTER 4: STRAIGHT LINE MOTION

The topic straight line motions deals with How the motorcycle keeps its balance analyzing the factors that come into play which can simply help the rider to maintain the motorcycle in a vertical and stable position while travelling. The factors that are responsible for maintaining the straight line motion path are

  • Inertia effects
  • Gyroscopic effects
  • Righting effects.

4.1 INERTIA EFFECTS

The product if mass multiplied by the velocity of a body gives the quantity of motion of the body. Due to greater value of this is, the less influence external forces will have on trajectory.

For example, let's assume that a motorcycle is travelling at high speed such as 100km/h then the vehicle also attains a velocity of 10 km/h perpendicular to the original trajectory as shown in fig a. If the motorcycle moves at slower speed of 10km/h, then the same component velocity influenced by the gust of wind brings variation in the direction of travel as shown in fig b. Hence as the velocity increases, small directional variations orthogonal to original direction will bring smaller angular variation. Therefore, now we can state that the greater the forward velocity, the more difficult is to move the vehicle from its initial straight-line trajectory. The same concept can be applied to mass like heavier a body is; the more it resists changes to its speed and direction.

In the figure, Vint = initial velocity

Vres = resultant velocity

dV = variation in velocity

α = angular variation in velocity.

4.2 GYROSCOPIC EFFECTS:

When every time a body spins rapidly on its axis and simultaneously is to set into rapid spin around a second axis is referred as gyroscopic effects or a moment that eventually acts around a third axis perpendicular to the other two. In routine life, gyroscopic effects can be seen for example, a spinning of bicycle wheel in between one's hands illustrates gyroscopic effect. If the wheel is set to keep axially parallel to it and raise and lower the wheel straight up and down then we can notice no opposing action on our hands. Hence it can be said that the opposing vertical force is needed to perform the action will never be more than the weight of the wheel itself.

Now in the next trial if the axis of the wheel is turned in clockwise motion around vertical axis, as if we were holding the steering handlebars. In this case, we will notice that our arms are affected by a couple that tends to rotate them around the longitudinal axis. From the following experiment, certain conclusions can be drawn

Gyroscopic effects will be more when the wheel rotates faster

The intensity of the reaction will differ obviously, if the axis is tilted faster or slower.

4.3 RIGHTING EFFECTS:

The parameter righting effects is profoundly influenced by the geometrical characteristics of the steering unit of the motorcycle. The correct combination of these factors gives positive results for the awareness of stability. Righting effects can be depend upon the following phenomenon's

  • Steering axis
  • Rake angle (Castor)
  • Trail

4.3.1 Steering axis:

Regardless of structure of motorcycle suspension they are characterized by a front wheel suspension by a front wheel steering, because front wheel is free to rotate around the axis which is called as steering axis. In general, the steering axis in the bicycles is referred as Head angle and is measured clockwise from the horizontal when viewed from right hand side. A 90° head angle would be vertical. For example a 2007 Filmore, which was designed for the track with a head angle, varies right from 72.5 ° to 74 °, depending upon frame structure and size.

4.3.2 Rake angle:

In the case of front suspension, it is very easy to identify steering axis especially in the telescopic fork because the steering axis coincides with the axis of the guide bearings inside the slider around which the fork rotates. This steering axis is present in all automotive type suspensions is inclined with respect to the vertical angle known as Rake angle. Rake angle is measured usually in degrees from zero.

Inclination of rake angle (ε):

If we increase the angle of the steering axis then we should also increase the value of trail. Usually the steeper the inclination of the rake angle, the motorcycle tends to be more stable directionally. Some grand prix bikes meant for competitive or sports oriented uses smaller rake angles such as little as 21° rake angle. custom made bikes have modified a steeper rake angle beginning from 28° and reaching 40°.

4.3.3 Trail:

The Trail of the front suspension system is defined as the distance between the point of intersection of the axis with the ground and the contact point of the front wheel with the ground (Contact patch).Trail is denoted as ‘t'. The phenomenon trail is cited as an important determinant of the motorcycle handling characteristics. The trail is a function of head angle, fork offset or rakes, and wheel size. Trail can be increased by either increasing the wheel size, or decreasing or slackening the head angle.

A trail is said to be positive when the suspension system is aligned straight on the road surface whereas the trail can be negative, when the steering axis meets the ground behind the point of contact and the moment acting on the steering will be inverted due to which the rotation of the front end towards the direction steering .hence this type of consequences can lead to disaster in spite of experienced riders.

The trail for the motorcycle front suspension can be expressed mathematically as If all the parameters kept constant then increase of radius of the wheel increases the trail. Substitution of front wheel rim with different wheel diameter can pull out large difference4s in the behaviour of the vehicle.

4.3.4 Fork Offset:

Fork offset is defined as the perpendicular distance from the steering axis to the center of the front wheel. Generally the steering axis does not lie on wheel axis, rather it lies at certain distance of measurement called as Offset and is denoted by‘d'. In bicycles, fork offset is also known as ‘fork rake'. In motorcycles with telescopic fork tubes, fork offset can be developed by either an offset in the triple tree, adding rake angle to the fork tubes which is mounted into fork tubes. The length of a fork is measured parallel to the steer tube from lower fork crown bearing to axle centred.

The amount of trail can be determined by varying combinations of offset and rake angle. There is a possibility to obtain the same amount of trail using different combinations of rake angle and offset. In the routine every day applications, the offset values ranges from 25 to 40 mm. The desired trail can be achieved in combination with right rake angle. Let us consider different offset as shown.

CHAPTER 5: DAMPER CHARACTERISTICS

5.1 ELASTIC COMPONENT

The Elasticity is the property of a component or material which causes is to be restored to its original shape after distortion. The substance is said to be more elastic if it restores itself more precisely to its original configuration. According to Hooke's law, when a spring is stretched, it exerts a restoring force which tends to bring back its original length. This restoring force is directly proportional to the amount of stretch. For wires or columns, the elasticity is described in the terms of the strain (Amount of deformation) resulting from a given stress (Young's modulus).

In the figure, one of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That linear dependence of displacement upon stretching force is called Hooke's law.

The most widely Elastic component used is a coil spring with ‘Round cross -sectioned wire which is almost universally adopted. The elastic component makes sure that the possibility of obtaining varying stiffness responses to varying demands, with moderate cost, restricted bulk as well as 100 percent consistency.

Every spring experiences elasticity, because of elastic potential energy .The energy which is stored by the change in its shape is known as elastic potential energy. Elastic potential energy can be elaborated with the ease using three cases. (a) Static (b) Compressed and (c) Stretched. If the spring is pressed down, it expands to its original shape when it allows let go. The thing happens to be the same if we pull its ends in opposite directions. This is mainly because of elastic potential energy acted by the spring itself. When we pull one end of a spring, it stores elastic potential energy until we let go. The potential energy converts to kinetic energy, the energy of movement which normally allowing the spring to resume its normal shape and sometimes to bounce around as shown in the figure below.

Coil springs can furthermore have progressive rates in which when spring is pressed down stiffness increases gradually. If the diameter of the wire is constant, then the spacing between the coils is known as ‘Pitch' .A spring is said to be progressive if the placing springs with different stiffness end to end in series. Now-a-days, in the automobile industry for the production of bikes, based on the other elastic systems like torsion bars for automobiles or leaf springs are rarely applied.

5.2 FUNCTIONS OF SUSPENSION

The main functions of the suspension are as follows

  • To endow with ‘Riding comfort' for both rider and passenger.
  • To ‘Control' the dynamics of the bike's motion or attitude.
  • To guarantee ‘Grip' or wheel to ground contact.

5.2.1 RIDING COMFORT:

The best way to express riding comfort is the amount of movement that is transmitted to the rider. The derivation of acceleration in quantifiable terms is called as Jerk. Ideal level of riding comfort can be achieved best if the chassis is perfectly stationary and with unsprung masses moving when it hits bump. The acceleration forces on the rider in this case would be nil.But, this is not possible .The most effective way for the riding comfort is to minimise the movement of the sprung weight, its speed, its acceleration as well as derivative action.

For example: Let us take a ratio between sprung and unsprung masses for different kind of motorcycles: If we take a bike weighing 140 kg and a big touring cruises weighing 230 kg then the ration between their sprung masses is about 2 and the unsprung masses only come to 1.3.

Hence we can conclude that it is much easier to obtain high riding comfort from heavily cruisers than from light transport bikes. However, how much one tries to optimize the suspension settings, a heavier motorcycle will probably have an advantage of riding comfort.

Riding comfort can be enhanced by the following ways

  • Low stiffness suspension for the bikes.
  • Compression Damping should be limited.
  • Unsprung masses should be very lightweight.
  • Huge sprung masses which are certainly not conductive to easy handling.

5.2.2 CONTROL OF ATTITUDE:

The attitude of the motorcycle under various conditions is determined by the suspension stiffness, spring's modulus of elasticity and its initial preload. A motorcycle having very soft suspension will sink just when it is released from main stand. When the rider mounts the bike it may tend to sink further more and will press down even more when it moves around the corners because of centrifugal force.

Certain factors effects varying attitude with respect to initial conditions. They are center of gravity height from the ground and rake angle. These conditions explain why a sport type bike must be equipped with stiff suspension so as not to effect the significant variation in attitude. Depending upon the hydraulic settings, if a steady attitude is determined by stiffness, the time and means used to achieve it. For the typical sport bikes, strong damping's have to minimize transitions between a series of differing attitudes, while touring bikes can get much softer settings.

When the brakes are applied, a very strong hydraulic braking suspension will help the bike reach the steady attitude in a more controlled way than is possible with weak braking suspension. In this case, the front end of the motorcycle will obviously sink quickly but after sometime it will oscillate before stabilizing itself around its position of equilibrium. In the bumpy roads or dug up road surface, the hydraulic system works well.

The attitude of the bike will be slighter in the case when it is travelling in a straight line over a series of hollows, first with standard settings and then with stronger compression braking. The Motocross enthusiasts are aware of the influence of hydraulic suspension on the motorcycle attitude in the presence of deep holes and ridges across their path are the average both in straight-line motion as well as in corners.

To optimize the control of attitude, following ways must be adopted

  • Should keep ‘high stiffness' on the suspension
  • The dampers should be Strong.

5.2.3 GRIP:

To transmit driving force to the ground both under acceleration and under braking there must be good adhesion between the tire and the ground.

The parameter which defines adhesion is

Adhesion index = F (∆N/N)

Where, ∆N is the relation between variations in dynamics load on the wheel

N is the static load bearing on its axle.

If there is a increase in the static weight bearing on a wheel, then it can enhance the adhesion index .Shifting our own body on the top of the rear wheel when it's slipping on a surface with low coefficient of friction will not succeed in transmitting the driving force.

The settings which are best for the grip depends upon the type of road surface and the kind of motorcycle. In general terms, damping required for the good adhesion is higher than the damping needed for a comfortable ride. In this case, too, lighter unsprung masses improve the condition because the weight transfer (Ntrans) is reduced and is allowed to work well up to high frequency ranges.

CHAPTER 7: VIBRATION MODES

If motorcycle is assumed to run straight on a flat surface with certain velocity and the rider is thought to be a rigid body sitting on the rear frame, which can exert no control on the motorcycle. If the motorcycle is said to have rigid suspension; from a kinematic point of view then it looks like a spatial system whose motion can be derived using four coordinates:

  • Steering angle;
  • Roll angle;
  • Yaw angle;
  • Lateral displacement of the mass center.

The motorcycle body system consists of two parts divided

  • The Front frame which includes the forks,the handle bars and front wheel
  • The Rear frame which includes the rider,the engine,the fuel tank ,seat as well as rear wheel

The front frame and the rear frame are hinged together at the steering axis by means of a revolutionary pair.During the motion the tires are sideslip so that they produce lateral forces which areee a linear function of the sideslip angles and the camber angle. From the practical point of view, it may be considered to be restoring forces like those produced by the springs.

In the above figure, the steering axis is constrained so that it can't move laterally. so motorcycle has two decoupled systems each having only one degree of freedom.

  • The front frame oscillates around the steering axis on which the lateral front tire force with the normal trail as lever acts as a restoring force.
  • The rear frame which oscillates around the steering axis on which lateral rear tire force with a lever proportional to the wheel base acts as a restoring force.

Routine use of motorcycles is conditioned by the presence of the oscillatory motions. This problem can be easily tackled by the mathematical analysis .If we would like to make gross generalisation that is mathematically incorrect, the three vibration modes can be linked with three fundamental requirements of the vehicle.

  • Wobble-Steering handling stability
  • Weave-Rear end handling stability
  • Falling motion-Ease of entry into corners.

The oscillatory modes ,Wobble and Weave in reality are completely different phenomenon to dealt with and often occur together in day to day life with the vehicle riders, which often occurs or both of them may not always disassociated.

Whenever there is occurrence of weave there is almost always a steering oscillation, that is, a component of wobble that makes it difficult to judge whether the problem is due to one or the other. An exact analysis of vibration modes requires the use of a very complex calculating instruments, while creating mathematical models take place ad hoc during the development of the manufacturer's model,which is hidden from public.

7.1 WOBBLE:

The oscillation of the front frame around the steering axis is known as Wobble mode.

The wobble phenomenon can be better explained by a dessert tray or a shopping cart with front turning wheels. When cart is pushed then we can observe that one of the wheels will suddenly start to oscillate with a twitching movement around the steering axis. When the cart reaches certain speed, it passes over irregularities. This phenomenon is known as ‘Shimmy'. The wobble mode is usually a steering oscillation of the front forks. This type of fork doesn't involve the rear frame. The typical wobble frequencies which can be expected from light weight motorcycles are 4 Hz whereas heavy motorcycles can reaches up to 9Hz.

Wobble generally occurs at front wheel and handle bars of the vehicle. Due to the wobble, the vehicle suddenly experience shaking from side to side while riding.

For example; the front wheel shimmy is generated by external stressors such as a small deep hole or any other type of unevenness on the road surface which pushes against tire, including lateral pressures. The eccentricities and wheel imbalance due to rim deformation or tire, repeated with the same frequency that the wheel rotates, which can also provoke dynamic imbalance that generate wobble. While travelling, the oscillations are likely appearing, for example the tires smoothed down by braking or with a rim that has static imbalance or is deformed due to impact of collision.

The frequency of the wobble is given by

an is the normal trail

If is the moment of inertia of the front frame around the steering axis;

klf is the front tire stiffness;

e is the steering head angle.

Certain instructions to be followed to prevent from wobbling. They are

  • Do not try to accelerate out of a wobble, it will simply make the cycle more unstable. Instead of that firmly grip or hold the handlebars.
  • Don't use the brakes harshly while wobbling. Braking could be responsible for the wobble worse.
  • Adjusting the riders weight as far forward and as low as possible
  • Pull off the vehicle aside, as soon as worst wobble starts and try to fix it.

7.1.1 FACTORS RESPONSIBLE FOR GENERATION OF WOBBLE

The parameters that influence the wobble are as follows. They are

Trail:

Motorcycle which has high rake angle and trail believed to be stable up to high speeds, but head shake condition occurs it will be violent and hence it is difficult to control.

Inertia at front end around steering axis:

The steering axis which has high moments of inertia reduces the frequency, give rise to slower and milder oscillations.

Front tire of vehicle:

If we vary the type of the tire, its stiffness and damping characteristics, the behaviour of the motorcycle can be significantly altered. The tire products which are made in the latest generation make use of recent developments in this field, proving improved riding safety of the driver.

Lateral Flexibility of the fork:

When the external shocks are experienced, such as a series of hollows or wheel imbalance, the high rigidity of the latest generation of fork makes it harder to dampen the wobble than with more elastic and shock absorbing forks. A steering damper is said to be effective damping for the wobble movements. It dissipates the energy around the steering axis, making the motorcycle more stable.

The bikes which race with very stiff forks, low moment of inertia around the steering and very small trail and rake angles, must be designed with a steering damper system. These bikes exit a corner they still exhibit a very visible steering headshaking.

7.2 WEAVE:

An oscillation of the rear frame around the steering axis is known as weave mode. Weave is considered as the most complex of the vibration modes, because the vehicle oscillates in a rolling motion around the axis of the ground, additionally to a rotating motion around the vertical axis called yaw.

Honestly speaking this is a distinct vibration from that of the wobble. According to the mathematical description from the literature taken confirms that this vibration mode does not oscillate at low speeds and its natural frequency is found to be nil, when the motorcycle is stopped. Again when the speed picks up, even though the oscillation frequency can reach up to 2 to 3 hertz's, with little damping, which makes it potentially dangerous. At greater speeds, the weave frequency can become so high that the rider is unable to get involve effectively, causing practical difficulties in bike control.

The frequency of the weave mode is given by

l is the lever of the rear tire force with respect to the steering axis;

Ir is the moment of inertia of the rear frame around the steering axis;

klr is the rear tire slip stiffness.

The parameters that cause the weave mode to occur are same as we observed for wobble. They are as follows

  • Center of gravity height (Cg):
  • It tends to stabilize weave mode which is oscillatory, by raising the Cg with respect to the ground. When the motorcycle rolls, the inertia increases thus, those oscillations will be slower.

  • Vehicle's Wheel base:
  • The oscillatory mode will be stable as long as the wheel base is longer i.e. Center to center distance.

  • Heavy weight:
  • The luggage, which is heavy weight on the vehicle, which is rebound onto the rear, affects the weave mode. For example if the loads are not rigidity attached to the body of the bike then modifies the rear end inertia, amplifying the oscillatory weave effect.

  • Bodyworks:
  • Motorcycle which has correct body can diminish front end lift owing to the rider's sail effect, but are stable at higher speeds. For example, a rider travelling on a endure bike in a straight -up sitting position, producing a sail effect, which eventually lifts front end and makes it easier for weave response to effect.

    Modifying the aerodynamic drag and simply by crouching down lower, the rider can significantly reduce the weave phenomenon. In order to rectify problem in the modern endure bikes with high speed potential the compact dome shaped windscreens were installed. As many motorcycles are considered with geometrical characteristics that, at the speed of 60 km/h should bring on weave oscillations and yet few rides experience this kind of problem.

7.3 SIDE FALL MOTION:

This mode is totally different from the wobble and weaves modes. The ‘Side fall motion' is not vibrational and it does not repeat overtime. In practical terms, this falling motion can be perceived as the effect of ‘falling into the corner' that the motorcycles will have some degree at low speeds when going around the tight corner like a U-turn.

The falling mode becomes stable when the speed is raised or atleast, it becomes almost stable allowing the rider to pass into automatic pilot and instinctively control the motorcycle.

The parameters which influence the stability in falling mode are as follows

  • The speed at which rider travel's.
  • Wheel inertia.
  • Inertia of the motorcycle with respect to the roll axis of the ground.
  • Mass of the motorcycle.
  • Position of the center of the gravity.
  • Rake angle of the front suspension system
  • Trail of the front suspension system
  • Tire dimensions.

The sideways fall phenomenon is described according to falling time. In this case, the shorter the duration, the mode will be more stable. The instability of the vehicle does not inevitably have to be interpreted as a drawback.

For example, Let us consider a situation that exists when setting a bike at the corner:The agility necessary for a racing bike to complete a circuit with rapid changes in the direction will certainly take advantage of constant, short falling time; thus a bike will eventually ‘enters' or ‘falls' without effort by itself into corners. When Skilled riders are allowed to do so then they act swiftly and are able to exploit the characteristic of the unstable vehicle, effectively achieving optimum results on their times at the circuit. If we consider a touring bike, the user will probably prefer more solid, slow and manageable control over the bike when leaning into the corner. Therefore touring bikes are specially designed to have ‘longer falling time constants'.

REFERENCES

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