Related work on vertical properties
Vibration tests on non-rolling tyres have been published by Lehtonen et al (2006). A hydraulic test rig was used as the excitation source and three types of off-road tyres were investigated: a 14R20 military off-road tyre, a 710/45R26.5 forest machine tyre and a 16R25 heavy steel-belted tyre used by container handling vehicles and cranes. Compression tests showed that the quasistatic force-deflection behaviour was nearly linear, with the stiffness increasing with the tyre pressure. The tyre stiffness was largely independent of excitation frequency.
The vertical damping was estimated from the frequency response of the tyres. It was seen that the damping decreased considerably with increasing frequency, for all the tyres tested. One example is seen in figure 10, which depicts the damping of the military off-road tyre at two different inflation pressures: 4.5 bar (a) and 1.7 bar (b). Similar trends were observed for the other tyres. It can also be seen that the damping for this tyre has a peak at 1 Hz when inflated to 4.5 bar. This peak in the damping was not seen at a lower tyre pressure.
Besides the tendency of the damping to decrease with increasing frequency, the tyres also showed great variety in the magnitude of the damping. The forest machine tyre was seen to have a damping that was about three times higher than that of the military offroad tyre, resulting in higher relative damping at the load applied. The damping coefficient of the container handler tyre was comparable to that of the military tyre, although the stiffness was higher, which would result in lower relative damping at the tested load. Hence, tyres of comparable size but different structural design can be expected to exhibit different dynamic behaviour. The tyre damping was also affected by the dynamic and static loads applied, as indicated in figure 10. Data on rolling agricultural tyres of the dimension 13.6R38 has been published by Lines and Murphy (1991a; 1991b), based on experiments using a trailing single wheel tester that is described in detail in an earlier report (Lines and Young, 1989). The tyre stiffness and damping were computed from the dynamic response when excited by a hydraulic shaker. The results (figure 11) show that the vertical stiffness, examined at 1.38 bar inflation pressure, was almost constant irrespective of the velocity and frequency. However, the static stiffness was typically 10-20% higher than the stiffness of the rolling tyre. It was also found that the stiffness increases with the tyre age due to rubber stiffening, but also that excessive wear of the tyre tread may decrease the stiffness because of less material in the lugs. Hence, the combined effect of old age and wear may be difficult to predict. Another noteworthy observation was that the tyre stiffness was independent of the applied driving torque.
The damping of the rolling agricultural tyres, determined at 1.38 bar inflation pressure, was found to decrease with increasing excitation frequency and velocity in the same manner as the damping of the tyres tested by Lehtonen et al (2006), see figure 12. As in the case of stiffness, the damping is also higher for older tyres.
Tyre data from the measurements cited above have been used in ride vibration predictions using a multibody dynamics model on a corrugated wood track (Lines, Peachey and Collins, 1992). A point contact model was used for the tyre-to-ground interaction. Simulations with frequency- and velocity-dependent tyre properties proved more accurate with respect to the frequency response, but did not improve predictions of RMS accelerations. This indicates that the actual acceleration of the vehicle is also dependent on local deformations of the tyre footprint. This could be an explanation as to why off-road ride predictions have historically been less successful (Crolla, 1981). The combination of large radius and low speed also means that the radial run-out of off-road tyres may excite vibrations at relatively low frequencies. Tyre run-out is therefore important for large off-road tyres (Brinkmann and Schlotter, 2004). Tyre pattern excitation has also been seen to cause low frequency excitation in off-road tyres (Brinkmann and Schlotter, 2004). While pattern excitation mainly affects noise, it may be relevant to ride vibrations as well at low velocities, particularly when driving on hard surfaces.