# 1. For dummies

##### a. The driving force of a wheel

Newton’s Law

1st law: An object on which no resulting force acts is at rest or moves linearly at constant speed.
2nd law: The change in speed is directly proportional to the resulting force and follows the straight line in which the force operates.
3rd law: Action is reaction.

Drive force

• The driving force is obtained by applying the torque of a motor via a drive train to the axle of the wheel.
• This driving force must now also be transferred to the “track”. This can be, for example, the bottom, a rail or a drum.
• In order to be able to transfer the driving force, we need grip.
##### b. Grip & Frictional force

Friction

• In order for an object to slide, force must be built up. As soon as there is movement, less force will be needed to maintain the movement.
• It is the friction between the ground and the object that causes this phenomenon. As long as a maximum is not exceeded, the object remains in place and there is static friction. As soon as there is movement, we speak of dynamic friction.
• The ratio between the tensile force and the normal force is the coefficient of friction.
• The types of materials (PUR, metal, concrete, …) that slide over each other and their condition (smooth, rough, ground, blasted, temperature…), determine how much friction occurs. Moisture, oil, grease, dust or sand will change the friction.

Grip

• Grip is the reaction force we generate by accelerating, braking or steering. This action causes slip in the contact surface. Grip is the frictional force (reaction) that prevents slipping (action). Without slip there is no grip ! Maximum grip is created at about 10 slips.

# 2. For experts

##### Grip and slip scientifically substantiated

The speed in the contact surface of a wheel is equal to zero, as long as there is no acceleration, braking or steering. This action creates a speed difference between the circumferential speed of the wheel and the speed of the vehicle. This is slip.

As a result of slip grip is created.

The grip is determined by 2 phenomena in which the viscoelastic properties of an elastomer play a major role. These viscoelastic properties are translated into a parallel circuit of a spring and a damper, where the spring is responsible for the elasticity and the damper for the hysteresis losses. As a result, force and deformation do not work in phase.

##### a. Mechanical grip

When the elastomer glides over a bulge in the “roadway”, due to the viscoelastic properties of elastomers, this deformation to the left and right of the bulge will be different. This creates a resulting force. The tangential component of this force provides grip. It is important to know that this force is generated by the sliding movement in the contact surface!

The roughness of the “roadway” varies from micrometer to centimeter level. The roughness is the reason why the elastomer is locally deformed.

The phenomenon of grip is maximized by choosing a material with high hysteresis losses (or a low % rebound).

Molecular adhesion is a phenomenon that works on a nanometre level and can generate a substantial part of the grip.

When the elastomer touches the ‘track’, connections are made as a result of the Vander Waals forces. When the elastomer slips across the surface, these connections are stretched and broken again to make new connections further along. Due to the viscoelastic behaviour of the elastomer a resulting force is generated. The tangential component of this resulting force generates grip.

Again, it is important to note that this force is generated by the slippage in the contact surface. The type of elastomer, temperature and the speed of slippage influence the molecular adhesion. To obtain adhesion there has to be contact. A higher load on the wheel ensures more contact and therefore influences the grip. The influence of water in the contact surface is substantial on this phenomenon, while the roughness continues to provide grip.

However, when all the roughness is submerged, contact and deformation are no longer possible and all the grip is lost. This is called aquaplaning.
By now we understand that there has to be (micro)slippage in the contact surface if we want to generate grip. Only a wheel that is driven, braked or steered has this slippage!

In a wheel of a vehicle moving at a constant speed, we see that the instantaneous speed at the contact point is zero. The distance travelled by the vehicle equals the distance rolled off by the wheel.

When we start braking, the wheel starts to turn slower which reduces the rolled off distance and a bit of slippage occurs. This slippage generates grip, creating a counteracting force which slows down the vehicle. When accelerating, the rolled-off distance increases and slippage occurs again, generating a reaction force that accelerates the vehicle. Steering also generates such reaction forces due to (micro)slippage. The functioning of a wheel therefore has 2 paradoxes: 1. to avoid skidding there has to be slippage 2. at a constant speed of a vehicle, the speed in the contact surface is zero.

##### c. Slip
• The grip is not a constant value.
• It depends on, among other things, the wheel slip. The maximum coefficient of friction is reached with a slip between 5 and 15 %.
• When we brake hard, the grip builds up to the maximum.
• Let’s block the wheel, then the grip drops to a lower level and we start to slip.
• When accelerating hard, we also first build up grip until we reach the maximum at approx. 10% slip.

# 3. In practice

Now that we better understand the complexity of driving, braking and steering, we can apply this to the composition of the wheel that delivers the necessary performances. We are also confronted with some contradictions here, which makes compromises inevitable.

We have learned that an elastomer with high hysteresis losses generates a good grip. On the other hand, these same hysteresis losses generate an increase in temperature and rolling resistance of the wheel, which has a direct influence on the performance, the wear and the life span.

1. Vulkollan©, however, offers a perfect compromise between rolling resistance and sufficient grip. The soft qualities of Vulkollan© (VK75 and VK80) also offer sufficient grip in damp conditions because these versions better adopt the roughness of the ground.
2. However, when there is aquaplaning, only profiled tyres can offer a reliable solution. The increase in the contact pressure can offer a solution in some cases if the water film is pushed away and is breached.
3. Usually rubber wheels give higher grip values than polyurethane. The reasons for this are the lower hardness levels with which rubbers are used and the naturally higher molecular adhesion forces. The disadvantages of rubber wheels are the significantly lower load capacities and thus the need to make the wheel a lot bigger to reach the same load capacity as for wheels made out of polyurethane.
##### b. Friction coefficient
###### Determination friction coefficient

In practice the necessary driving force is usually known. To determine the right kind of wheel, only the friction coefficient still needs to be calculated. Keep in mind the speed and the deployment time of the appliance as well. For a comparison of the friction coefficient of Vulkollan© with other materials, Vulkoprin has experimentally established the following guideline values:

 Friction coefficient µmax Track Vulkollan© Steel, dry, polished 0.50 – 0.65 Steel, humid, polished 0.20 – 0.30 Steel, dry, sandblasted 0.50 – 0.65 Steel, wet, sandblasted 0.30 – 0.50 Industrial floor, smooth concrete, dry 0.60 – 0.80 Industrial floor, smooth concrete, wet 0.30 – 0.50

For example

• If a driving force of 20 kN is to be transferred onto a dry concrete floor, the table above shows µmax = 0.6-0.8. It is always advisable to include a safety margin, so the wheel does not have too much of a tendency to slip. So, we choose µmax = 0.6 or lower to make sure we can generate the necessary driving force, but also to limit the slip and wear and thus lengthen the life span.
• To produce the necessary driving force, we need a minimal load on the wheel: 20 kN/0.6 = 33.3 kN
• The load capacity of the chosen wheel must meet these minimum requirements.

##### c. Transfer of driving force

To transfer the driving force of the motor onto the wheel, the wheel may not be able to rotate on the driving axle. The following common assembling options are used:

1. Keyway connection:
– Axles with h6 or h9 tolerance are fitted with a sunk key DIN 6885.
– The bore of the wheel with a tolerance of H7 is fitted with a keyway. When the driving direction is in the same direction, a JS9 tolerance is chosen. When the driving direction changes frequently a P9 tolerance is chosen.
2. Clamping bush connection:
The wheel is fixed to the axle by means of clamp bushing. This connection provides both axial locking and the transmission of driving forces. The purchase of a clamping bush is more expensive, but it offers a lot of advantages especially in assembly and disassembly.
3. Flange connection:
The wheel is fixed to the driving axle by means of a flange with bolt holes. This connection is commonly used when the wheel is fixed on a shaft end of a vehicle. This application can be found in drive wheels of forklifts.
##### d. Other elements
• A thin layer of elastomer increases the load capacity of the wheel but it is detrimental to the drive applications. A thick layer of elastomer results in more contact surface and thus more grip.
• The maximal friction coefficient is relatively independent of the hardness of a type of elastomer.
• An elastomer with high hysteresis losses is favourable for a good grip, but very detrimental to the rolling resistance and the increase in temperature of the wheel. However, Vulkollan© offers a very good compromise.
• Materials used for roller coaster applications are generally less good in drive applications than standard Vulkollan©, because their hysteresis losses are much lower.
• Generally the state of the ‘track’ has the most influence on the grip.
• Condensation, grease and dirt decrease the grip substantially.
• flat tread pattern is more favourable than a gently contoured tread.
• When a rail is used, it has to be at least 10% wider than the tread of the wheel.
• Soft starters can solve many drive problems and prolong the life span of wheels.

It is the manufacturer’s responsibility to configure the right wheel, considering the above-mentioned factors. Vulkoprin has a lot of experience and is equipped with a modern drum tester to carry out simulations and tests. Consult the Vulkoprin Wheel team for an accurate analysis.