Wheel slip formula

Original Poster. Search My Stuff What's New 3 12 24 Tyre Slip Ratio. FrazM Original Poster 20 posts months. Can anyone explain to me what tyre slip ratio is?

I read that it is defined as the difference in angular velocity of freely rotating tyre versus that of the same tyre whilst braking.

How can you compare the angular velocity of a freely rotating wheel with that of one that is continually slowing down??? Also I read this on Wikipedia which confuses me too: "When a vehicle is being driven along a road in a straight line its wheels rotate at virtually identical speeds.

When the driver applies the brakes in order to slow the vehicle, the speed of the wheels becomes slightly slower than the speed of the body, which is travelling along under its own inertia. The wheels slow down so therefore the rest of the car does too? Pretty sure I am just missing a simple point here so can anyone please point out the obvious for me! Cheers Fraz. This is going to test my descriptive abilities, to explain in words, but I'll give it a go.

Rubber stretches, right? So when you apply a force to a rotating tyre, be it braking, acceleration, or cornering, the rubber at the contact patch stretches in the direction of the force.

wheel slip formula

As the tyre rotates, the bit of rubber that is stretched is lifted away from the road surface and is allowed to relax again, to be replaced by the next bit of rubber. To take the case of a car that is braking, this continual stretching and relaxing of the rubber at the contact patch means that the amount of tarmac that passes under the tyre is more than the circumference of the tyre would roll over the road if the rubber wasn't stretching ie.

The difference between the distance the wheel should have covered if the rubber at the contact patch wasn't 'creeping' and the actual distance that the car has covered, expressed as a percentage, is the 'slip ratio'. There is always, in fact, some tyre slip occuring, even at a steady speed in a straight line This provides a nice comfort zone in low grip enviroments so no sudden loss of traction just a nice transition. However their peak loading is much less than a summer tyre.

The opposite to that would be a slick with a very narrow window of slip, but equally a very high loading ability on the right surface. Avocet posts months. I think the "Wackypedia" entry is a bit misleading. Obviously, the wheels need to be doing the same speed as the car - otherwise after a few seconds of heavy braking, you'd expect to see them in your rear view mirror!

The tyre surface will be sliding ever so slightly on the road surface.Documentation Help Center. The Tire-Road Interaction Magic Formula block models the interaction between the tire tread and road pavement. The longitudinal force arising from this interaction is given by the magic formula, an empirical equation based on four fitting coefficients. Tire properties such as compliance and inertia are ignored. The Magic Formula is a specific form for the tire characteristic function, characterized by four dimensionless coefficients, BCDand Eor stiffness, shape, peak, and curvature:.

A more general Magic Formula uses dimensionless coefficients that are functions of the tire load.

How Four-Wheel Drive Works

S Hx and S Vx represent offsets to the slip and longitudinal force in the force-slip function, or horizontal and vertical offsets if the function is plotted as a curve. The block uses a representative set of Magic Formula coefficients.

Numerical values are based on empirical tire data. These values are typical sets of constant Magic Formula coefficients for common road conditions. The Tire-Road Interaction Magic Formula block assumes longitudinal motion only and includes no camber, turning, or lateral motion. Physical signal input port associated with the normal force acting on the tire.

The normal force is positive if it acts downward on the tire, pressing it against the pavement. Physical signal input port associated with the Magic Formula coefficients. Port M is exposed only if the Parameterize by parameter is set to Physical signal Magic Formula coefficients.

For more information, see Parameter Dependencies.

wheel slip formula

Mechanical translational port associated with the wheel hub that transmits the thrust generated by the tire to the remainder of the vehicle. The table shows how the visibility of some Main parameters depends on the options that you choose for other parameters.

To learn how to read the table, see Parameter Dependencies. Parameterize by — Choose Peak longitudinal force and corresponding slipConstant Magic Formula coefficientsLoad-dependent Magic Formula coefficientsor Physical signal Magic Formula coefficients.The prediction of optimal slip ratio is crucial to vehicle control systems. Many studies have verified there is a definitive impact of tyre pressure change on the optimal slip ratio.

However, the existing method of optimal slip ratio prediction has not taken into account the influence of tyre pressure changes. By introducing a second-order factor, an improved optimal slip ratio prediction considering tyre inflation pressure is proposed in this paper. The simulation results show that the braking distances and braking time under different tyre pressures and initial braking speeds are effectively shortened with the improved prediction of optimal slip ratio.

When the tyre pressure is slightly lower than the nominal pressure, the difference of braking performances between original optimal slip ratio and improved optimal slip ratio is the most obvious. The longitudinal motion of a vehicle is governed by the forces generated between the tyres and the road surface.

Therefore, acquiring enough tyre friction is crucial to enhance vehicle dynamics. According to the friction principle, the magnitude of frictional force depends on two factors: normal pressure and friction coefficient. However, the relationship between the longitudinal friction coefficient and wheel slip ratio is complex. In the premise of constant normal pressure, when the wheel slip ratio is small, longitudinal force linearly increases with slip ratio.

With further increase of the slip ratio, longitudinal force increases and then decreases nonlinearly. When the longitudinal force reaches a maximum value, the corresponding slip ratio is called optimal slip ratio. Antilock braking system ABS is an automobile safety system that allows the vehicle wheels to maintain tractive contact with the road surface according to driver inputs during the braking process, preventing the wheels from both locking up and uncontrolled skidding.

The logic threshold control method is widely applied in commercial ABS products [ 1 ]. As an experience based control method, in the control process, wheel slip ratio is not maintained in optimal slip ratio but fluctuated near it which cannot acquire the best braking effect.

Meanwhile, if slip ratio is considered as the control target, ABS controller can maintain the practical slip ratio near the optimal slip ratio all the time during the braking process, so that vehicle controllability and stability are optimized and maximized. That is considered as the ideal braking method.

The research on ABS control, aiming at optimal slip ratio, has been carried out for many years. Most researchers put the emphasis on control strategy optimization and development of control methods based on the control theory of self-turning PID, fuzzy PID, artificial neural network, and so on [ 2 — 4 ]. Other researchers focused on identification of road surface and optimal slip ratio [ 5 — 7 ].

Up to now, most studies about optimal slip ratio control are based on an optimal slip ratio estimation expression, proposed by Liu [ 8 ] and Bian [ 9 ], which gives a quantification description of influence on optimal slip ratio due to changes of road adhesion coefficient, vehicle velocity, and tyre slip angle. The optimal slip ratio expression proposed by Liu et al.

In the early time, the influence of tyre inflation pressure changes was not considered into Magic Formula based on which the influence has not been put into existing optimal slip ratio expression. However, it is indicated in [ 11 — 13 ] that tyre inflation pressure changes can directly influence the relationship between tyre longitudinal force and slip ratio. That is, the value of optimal slip ratio is influenced by tyre inflation pressure changes.

Based on the existing optimal slip ratio expression and an improved Magic Formula model [ 14 ], a simulation is launched to make a study on relationship between tyre inflation pressure changes and tyre slip ratio.

A second-order factor, representing the influence of tyre inflation pressure changes on the value of optimal slip ratio, is acquired. In order to verify and evaluate the improved optimal slip ratio, an ABS controller with optimal slip ratio as the control target is established. Vehicle braking processes before and after improvement are simulated and compared. The paper is structured as follows.Wheel slipping occurs when tractive effort exceeds adhesive weight whereas sliding occurs when braking effort exceeds adhesive weight.

In both the situations, it is the adhesive weight playing the most important role. Adhesive weight is defined as the force that can be exerted by a wheel without slipping or sliding. Weight is limited by track structure and permissible axle loading which in the present context of Indian Railway is There is a plan to go for 25T axle load in heavy haul sections.

Maximum possible adhesion with advanced electronics possible had been 0. When Tractive effort is more than adhesive weight, difference in power accelerate the wheel which results into grinding action on the rail. In the similar manner, when braking effort exceeds the adhesive weight, extra braking force prevents its rotation but with continuation of linear motion which results rubbing of wheel at one location on the circumference and called development of wheel flat.

Both these conditions create unsafe situation. Weather and environmental conditions plays a vital role in reducing adhesion. There are always some impurities on rail table which when interact with moisture results drop in adhesion to as low as 0. The other conditions that has similar effect are. The condition keeps on varying from time to time in the same weather condition and is never constant. The churning effect of rolling of wheel and micro slip results in cleaning the deteriorated condition of the wheel continuously.

Experiencing wheel slip is more on circumstantial conditions of the prevailing conditions of adhesion and demand for tractive effort. Rail condition improves if a train requiring less adhesion is allowed to run in the section thus improving adhesion to benefit subsequent trains.

Statistical analysis plays an important role in identifying major causes for wheel slip based on section, weather condition at the time of wheel slip, load, type of stock, skill of the loco pilot etc.

Talking Wheel Slip

Protections towards wheel slip and slid lies with its early detection and reduction of tractive effort and braking effort respectively within least possible time.

The issue of protection towards wheel slip lies with traction wheels only i. Different methods are used for detection of wheel slip in different class of locomotive depending on the technology that was existing at that time.

With protection system invariable effective, damages on account of wheel slip is very less but may result in stalling of train if the need for tractive effort continuous to more than the adhesive weight. A slipping wheel will generate higher back emf thus less traction current and wheel slipping can be detected by comparing traction current. All Traction Motor works in parallel in the present configuration of Locomotives.

Three actions takes place simultaneously namely. This auto-regression may be 1 to 8 notches. Loco Pilot notches up slowly in readiness to regress notches manually and resort to manual regression, if there is tendency of wheel slip.

There is no protection towards sliding and there are many instances of wheel flat on locomotive. Preventive methods followed are. Detection, reduction and restoration of TE goes simultaneously thus making best utilisation of adhesion available. WAG9 class of locomotive is equipped with slide control also during regenerative braking. There is no protection for wheel slide on coaching and wagon stock. Therefore there are more chances of wheel skidding for any malfunctioning of braking system.

In recently introduced LHB coaching stock, slide control is provided and braking effort of the effected wheel is reduced on detection of wheel slide. Coefficient of adhesion varies with speed as per the empirical formula given below:.Slip ratio is a means of calculating and expressing the slipping behavior of the wheel of an automobile. It is of fundamental importance in the field of vehicle dynamics, as it allows to understand the relationship between the deformation of the tire and the longitudinal forces i.

Furthermore, it is essential to the effectiveness of any anti-lock braking system. When accelerating or braking a vehicle equipped with tires, the observed angular velocity of the tire does not match the expected velocity for pure rolling motion, which means there appears to be apparent sliding between outer surface of the rim and the road in addition to rolling due to deformation of the part of tire above the area in contact with the road.

When driving on dry pavement the fraction of slip that is caused by actual sliding taking place between road and tire contact patch is negligible in magnitude and thus does not in practice make slip ratio dependent on speed. It is only relevant in soft or slippery surfaces, like snow, mud, ice, etc and results constant speed difference in same road and load conditions independently of speed, and thus fraction of slip ratio due to that cause is inversely related to speed of the vehicle.

This slippage is caused by the forces at the contact patch of the tire, not the opposite way, and is thus of fundamental importance to determine the accelerations a vehicle can produce. There is no universally agreed upon definition of slip ratio. From Wikipedia, the free encyclopedia.

This article is about tire behavior in vehicle dynamics. For the phenomenon in fluid dynamics, see Slip ratio gas-liquid flow. Race Car Vehicle Dynamics. Society of Automotive Engineers. Categories : Vehicle braking technologies Engineering ratios.

Tire (Magic Formula)

Hidden categories: CS1 errors: missing periodical. Namespaces Article Talk. Views Read Edit View history. Languages Add links. By using this site, you agree to the Terms of Use and Privacy Policy.In automotive vehicle dynamicsslip is the relative motion between a tire and the road surface it is moving on.

This slip can be generated either by the tire 's rotational speed being greater or less than the free-rolling speed usually described as percent slipor by the tire 's plane of rotation being at an angle to its direction of motion referred to as slip angle. In rail vehicle dynamics, this overall slip of the wheel relative to the rail is called creepage. It is distinguished from the local sliding velocity of surface particles of wheel and rail, which is called micro-slip.

The longitudinal slip is generally given as a percentage of the difference between the surface speed of the wheel compared to the speed between axle and road surface, as:. A positive slip indicates that the wheels are spinning; [1] negative slip indicates that they are skidding. The lateral slip of a tire is the angle between the direction it is moving and the direction it is pointing.

This can occur, for instance, in cornering, and is enabled by deformation in the tire carcass and tread. Despite the name, no actual sliding is necessary for small slip angles.

Sliding may occur, starting at the rear of the contact patch, as slip angle increases. The slip angle can be defined as: [2]. From Wikipedia, the free encyclopedia. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources.

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wheel slip formula

Main article: Slip angle. Tyre and Vehicle Dynamics. Retrieved Besides areas of adhesion, areas of sliding may occur in the contact patch. The latter condition will arise when the deflection generated in the range of adhesion would have become too large to be maintained by the available frictional forces. Aquaplaning Groove wander Slip vehicle dynamics Tramlining. Outline of tires Category. Categories : Tires Motorcycle dynamics Classical mechanics stubs.

Hidden categories: Articles needing additional references from October All articles needing additional references All stub articles. Namespaces Article Talk. Views Read Edit View history. By using this site, you agree to the Terms of Use and Privacy Policy.Torque is the twisting force that the engine produces.

The torque from the engine is what moves your car. The various gears in the transmission and differential multiply the torque and split it up between the wheels. More torque can be sent to the wheels in first gear than in fifth gear because first gear has a larger gear-ratio by which to multiply the torque.

The bar graph below indicates the amount of torque that the engine is producing. The mark on the graph indicates the amount of torque that will cause wheel slip. The car that makes a good start never exceeds this torque, so the tires don't slip; the car that makes a bad start exceeds this torque, so the tires slip.

As soon as they start to slip, the torque drops down to almost zero. The interesting thing about torque is that in low-traction situations, the maximum amount of torque that can be created is determined by the amount of traction, not by the engine. Even if you have a NASCAR engine in your car, if the tires won't stick to the ground there is simply no way to harness that power. For the sake of this article, we'll define traction as the maximum amount of force the tire can apply against the ground or that the ground can apply against the tire -- they're the same thing.

These are the factors that affect traction:. The weight on the tire -- The more weight on a tire, the more traction it has. Weight can shift as a car drives.

wheel slip formula

For instance, when a car makes a turn, weight shifts to the outside wheels. When it accelerates, weight shifts to the rear wheels. See How Brakes Work for more details. The coefficient of friction -- This factor relates the amount of friction force between two surfaces to the force holding the two surfaces together. In our case, it relates the amount of traction between the tires and the road to the weight resting on each tire.

The coefficient of friction is mostly a function of the kind of tires on the vehicle and the type of surface the vehicle is driving on. The coefficient of friction for that same tire in mud would be almost zero. By contrast, huge, knobby, off-road tires wouldn't have as high a coefficient of friction on a dry track, but in the mud, their coefficient of friction is extremely high.

Wheel slip -- There are two kinds of contact that tires can make with the road: static and dynamic. Quite simply, wheel slip occurs when the force applied to a tire exceeds the traction available to that tire. Force is applied to the tire in two ways:.

Let's say you have a fairly powerful rear-wheel-drive car, and you are driving around a curve on a wet road.

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