Tire design : Tire stiffness

The vertical tire force (Fz) can be calculated as a linear function of the normal tire deflection (z) measured at the tire center.

Fz = kz*z

the coefficient kz is call tire stiffness in the z direction. Similarly, the reaction of a tire to a lateral and longitudinal force can be approximated by

Fx = kx*x

Fy = ky*y

When kx , ky are called tire stiffness in the x and y directions.

The stiffness curve can be influenced by many parameter. The most effective one is the tire inflation pressure. Lateral and longitudinal force/deflection behavior is also determined experimentally by applying a force in the apporiate direction. The lateral and longitudinal force are limited by the sliding force when the tire is vertically loaded. The coefficient kx and ky are called tire stiffness . They are measured by the slope of the experimental stiffness curve. When the longitudinal and lateral force increases, part of the tire footprint creep and slide on the ground until the whole tire footprint starts sliding. At this point. the applied force saturates and reaches its maximum supportable value. Generally, a tire is most stiff in the longitudinal direction and least stiff in the lateral direction.

kx > kz > ky

Tire with a larger of plies have higher damping, because the plies’ internal friction generate the damping. Tire damping decreases by increasing speeds.

Polyurethane applied to Flexible Gaiters

Polyurethane is applied to automotive industry . The ball joints for steering linkages and front suspension mechanisms of cars have to be protected from wear otherwise play rapidly occurs, which is reflected back to the steering wheel with a resultant loss in steering control. The conventional method of protection is by packing the joint with grease and containing the grease with a flexible gaiter. These gaiters are subjected to the effect of the grease inside and the effect of moisture on the outside and have to operate over serveral years without deterioration. To operate satisfactority they also have to resist the damage caused by small stones thrown up by the tires. The high tear strength of polyurethane is an obvious advantage here, but another equally important advantage is that in the environment of grease, water, ozone and general exposure to weathering the polyurethane elastomers or nitriles. Initially these gaiters were made from millable types of polyurethanes and were two to three times the cost of similar gaiters made in neoprene. Even so the practical advantage gained dictated fairly widespread use, although it is considered that further material improvements are still required and injection-moulded gaiters are already replacing some millable types.

Tires : Effect of inflation pressure.

High inflation pressure increases stiffness, which reduces ride comfort and generates vibration. Tire footprint and traction are reduce when tires are over inflated. Over inflation causes the tires to transmit shock loads to the suspension, and reduces the tire ‘ s ability to support the required load for cornerability, breaking and acceleration. The rolling resistance friction coeficient decreases by increasing the inflation pressure. The effect of increasing pressure is equivalent to decreasing normal load.

Under inflation results in cracking and tire component separation. It also increases sidewall flexing and rolling resistance that causes heat and mechanical failure. A tire’s load capacity is largely determined by its inflation pressure. Therefore, under inflation results in an overloaded tire that operates at high deflection with a low fuel economy, and low handling. Proper inflation pressure is necessary for optimum tire performance, safety, and fuel economy (Energy Tires). Correct inflation is especially significant to the endurance and performance of radial tires because it may not be possible to find a 5 psi under inflation in a radial tire just by looking. However, under inflation of 5 psi can reduce up to 25% of the tire performance and life.

Polyurethane in Textile Machinery

The most importhant application to date in the textile field has been the use of polyurethane elastomers for loom pickers. Here the application is vary arduous, the shuttle weighing about 1 lb traversing a 4 ft loom approximately 150 to 200 times a minute. Previously the materials chiefly used were either raw hide or rubber-fabric composition. On the average polyurethane pickers outlast other types of pickers but they do exhibit a number of unexplained early faileres. The life of the picker is very dependent on the correct setting of the picker in relation to the shuttle, and if badly aligned, the picker will fail rapidly. The search for even better pickers is still proceeding, and the most recent design incorporate a wearing block of high density polyethylene inside a resilient body of a hard thermoplastic polyurethane.

Other application in the textile and allied field include falling bars for selector needles on the knitting machines, cot roller covering, and drive couplings for bobbins.

Polyurethane in Paper-making and Printing

Solid polyurethane are being used successfullyfor the top of vacuum boxed on paper-marking machinery. A gauze holding the paper fibers travels across the vacuum box and excess water is removed by vacuum. The polyurethane is less harsh to the guaze than other materials and is itself resistant to wear. This is an example where polyurethanes are used sucessfully in water at a temperature around 50 *C .

Special grades of very soft polyurethane elastomers have been used for many year for printing rollers. The hardness of these materials vary from around 10 to 30 Shore A and the physical properties are poor compared with what is normally expected from polyurethane elastomers. However, solid polyurethane around a hardness of 60 to 70 Shore A are being used for scraper blades on silk-screen printing due to their solvent resistance and low ink pick up.

Polyurethane properties : Coefficient of friction

The frictional properties of polyurethane elastomers are generally consistent with the established friction properties of rubber and vary from a coefficient of friction approximately 0.2 for the harder to around 2 to 3 for softest grades. The soft grades exhibit high values for coefficient of friction owing to the large true area of contact developed and the friction coefficients drop as the hardness increases. As with abrasion tests, however, values of friction obtained in the laboratory can be misleading and should only be taken as a rough guide as to actual service behavior. Such factors as surface cleanliness, lubrication by airborne dust or abrasion debris, and small traces of fluids can greatly influence the frictional charecteristics in practical applications.

The slip velocity has a small effect on the coefficient of friction, higher slip velocities giving slightly higher coefficient of friction. The coefficient of friction is higher on smooth moulded plastic surfaces than on the relatively rough surface of rough ground steel. The application of higher load increases the frictional force although there is a tendency for the coefficient of friction to fall with time. This effect is most probably due to lubrication of the interface by abrasion debris.

The coefficient of friction can be considerably reduced by lubrication, and when using polyurethanes for bearing applications it is generally beneficial to use oil or grease for this purpose. Where the provision of external lubrication is undesirable it has been claimed that additive can be incorporated into the polyurethane which makes them essentially self-lubricating. The additives generally employed are molybdenum disulphide, graphite and silicone oils. Caution must be observed when making use of these additives since in certain case it is known that their presence can have an adverse effect upon the ageing charecteristics of the polyurethane.

Polyurethane Properties : Effect of low temperature

Low temperature environments affect the properties of polyurethane elastomers, but no degradation occurs and effect is completely revesible. The major effect is an increase in Young’ s modulus below 0 *C with a corresponding increase in hardness, tensile strength, tear strength and torsional stiffness and a decrease in resilience.

The two properties that can have an important bearing on the use of polyurethane at low temperature are the decrease in resilience which has already been mentioned and the increase in stiffness. In the use of polyesterurethane at low temperatures another phenomenon can sometimes be observed. This is that of crystallization of the polyurethane when held at moderately low temperature foe some period of time. When crystallized the polymers are considerably harder and their stiffness charecteristics are similar to those normally observed at much lower temperatures. The effect is reversible and can be removed by the application of heat or by the generation of internal heat by flexing. The use of mixed polyesters reduces this tendency to crystallization.

Polyurethane in Shoes and Shoe Machinery

The use of solid polyurethane rubber for ladies’s shoe heel top pieces has been known for several year. Cast grades of medium to high hardness have generally been employed for this purpose, but more recently the thermoplastic polyurethane have been graining ground. The material cost of polyurethane are high compared with more conventional heeling materials and to be competitive the processing cost must be as low as possible. The high cost has so far prevented the use of solid polyurethanes for the soles of shoes but the development of the cellular varieties of the solid materials has reawakened interest in this outlet. By using cellular grades with a specific gravity of 0.4, material cost are reduce to a third of those of the solid. Provided the process can be refined sufficiently to keep the costs low, soles for hard-wearing applications are a distinct possibility. In this case closed cell matreial is necessary to prevent excessive uptake of water.

The process for shoe manufacture is becoming highly automated. The high hardness, toughness and flexibility of the solid polyurethanes make them excellent materials for many items in this application. Replacement of a natural rubber diaphragm by polyurethane increased the diaphragm life from two months to a yeas.

Tire footprint

The contact area between a tire and the road is called the tire footprint and is shown by Ap. At any point of a tire footprint , the normal and friction forces are transmitted between the road and tire. The effect of the contact force can be described by a resulting force system including force and torque vectors applied at the center of the tire footprint. The area of the tire footprint is inversely proportional to the tire pressure. Lowering the tire pressure is a technique used for off-road vehicle in sandy, muddy. or snowy areas, and for drag racing. Decreasing the tire pressure causes the tire to slump so more of the tire is in contact with the surface, giving better traction in low friction conditions. It also helps the tire grip small obstacles as the tire conform more to the shape of the obstacle, and makes contact with the object in more places. Low tire pressure increase fuel consumption, tire wear, and tire temperature. In most vehicles, the front and rear tires will wear at different rates. So, it is advised to swap the front and rear tires as they wear down to even out the wear patterns. This is called rotating the tires. Front tire, especially on front-wheel drive vehicles, wear out more quickly than rear tires.

Figure1 Tire footprint**

** Figure Ref. http://www.aircti.com

Tires behavior : Hydroplaning

Hydroplaning is sliding of a tire on a film of water . Hydroplaning can occur when a car drives through standing water and the water cannot totally escape out from under the tire. This causes the tire to lift off the ground and slide on the water. The hydroplaning tire will have little traction and there for, the vehicle will not obey the driver’s command.

Deep grooves running from the center front edge of the footprint to the corners of the back edges, along with a wide central channel help water to escape from under the tire.

There are three type of hydroplaning; dynamic, viscous, and rubber hydroplaning. Dynamic hydroplaning occurs when standing water on a wet road is not displace from under the tire fast enough to allow the tire to make pavement contact over the total footprint. The tire ride on a wedge of water and loses its contact with the road. The speed at which hydroplaning happens is called “Hydroplaning speed (VH) ” that is estimated in knots by equation 1

VH = 9*P^0.5 -------(1)

Where P is tire inflation pressure in psi

For a matric system would be

VH = 5.5753 x 10^-2*P^0.5

Where P is tire inflation pressure in Pa

VH is in m/s

Rubber hydroplaning is generated by superheated steam at high pressure in the tire footprint, which is causes by the friction generated heat in a hard braking.

Viscous hydroplaning occurs when the wet road is covered with a layer of oil, grease, or dust. Viscous hydroplaning happens with less water depth and at a lower speed than dynamic hydroplaning.

Ref. Vehicle Dynamics: Theory and Applications , Reza N. Jazar

Using polyurethane in mining and quarrying industries.

In the mining and quarrying industries, however, polyurethane is being used for many other applications with advantage and replacing rubber or even hard steel. In general these applications are connected with movement of very abrasive slurries of relatively small particle size such as in the ball and rod mills, flotation plant, hydrocyclones and piping.

Ball or rod mills have generally been lined with manganese steel replaceable linings, but in recent years the use of rubber replaceable linings has been developed. Dependent on the condition existing in a given mill these rubber linings can last several times longer than the manganese steel, and polyurethane linings can last considerably longer than the rubber linings. Further advantages are that the tooling cost with polyurethane are less and the fact that, due to the availability of the harder grades, the polyurethane can be used as a structural material and does not require reinforcement by metals.

Similarly in flotation plant the impellers, rotors, stator and scrapers are made of steel centers often covered in conventional elastomers. Polyurethane again can be used in certain cases and will generally outlive natural rubber. The main precaution to be observed are limitation in temperature and also extremes in acidity or alkalinity of the slurries.

Hydrocyclones used in the separation of ores and cray are also subjected to harsh abrasive condition, and polyurethane have been successfully used in these conditions.

In mines there is often a considerable fire risk, and comprehensive precaution are taken to avoid spark which can start a fire or explosion. For this reason the use of track laying vehicle with metal tracks is prohibited. Covering of the tracks with natural rubber goes only part of the way to solving the problem due to highly abrasive conditions causing relatively rapid breakdown. The polyurethane track pad do not wear so rapidly and are being used successfully. A further advantage of polyurethane as opposed to metal is the increase in traction obtained which enable the vehicle to climb steeper slopes.