Tire Energy Loss from Obstacle Impact3
Tires in actual service conditions operate on rough roads with a random distribution of obstacles. Rolling resistance, however, is typically measured on smooth surfaces. This paper considers the nature of tire energy loss when impacting obstacles. It is demonstrated by a simple example that translational energy can be “lost,” even in purely elastic impacts, by trapping energy in structural vibrations that cannot return the energy to translation during the restitution phase of the impact. Tire simulations and experiments demonstrate that this dynamic energy loss can be very large in tires if the impact times are short. Impact times indicating the potential for large energy loss are found to be in the range of normal highway speeds.Abstract
Uniform elastic rod schematic. The rod is considered attached to the rigid wall and given an initial velocity at time equal zero. This formulation produces the impact response from the rod without having to make any specific impact assumptions. The solution is continued until the contact force goes to zero. At that point the rod is assumed to lose contact.
Center of mass velocity and contact force versus time for a uniform elastic rod during impact with a rigid surface. The analytical solution and the FE solution are shown to agree. Note that the initial and final rod velocities are the same magnitude, with a change in sign indicating no loss of translational energy during the impact.
Schematic of a nonuniform rod formulated as two rods joined together. The nonuniformity can occur in the density, elastic modulus, and cross-sectional area of one of the rods compared to the other. Continuity of displacement and force are required at the position where the rods are joined together.
Center of mass velocity and contact force versus time for a nonuniform elastic rod during impact with a rigid surface. The nonuniformity consists of a difference of modulus in one-half of the rod. The part of the rod impacting the rigid surface is eight times the modulus of the remaining half of the rod. The analytical solution and the FE simulation are shown to agree. Note that the initial and final rod velocities are not the same magnitude, indicating a loss of translational energy during the impact. The calculated coefficient of restitution is 0.78 and the translational energy loss is 39%.
Schematic of ring impact problem. This problem involves analytical difficulties in solving the frequency equation. FE simulation will be used from this point.
Schematic of the process used to develop a two-dimensional elastic FE simulation of a 235/45R17 tire. The ring consists of a rubber layer representing the tread, belt layers of the correct extensional modulus, and a sidewall material. The sidewall material is given a modulus and initial thickness such that when it is stretched to the correct sidewall length it has the tension to match the sidewall membrane tension in the tire and the correct spring rate. The tire is then inflated and loaded. The sidewall material shear modulus is adjusted to give the correct load deflection, counter deflection, and contact pressure. Finally, the natural frequencies and mode shapes are checked and the mass adjusted to match the actual tire.
Simulation results of a rigid obstacle impacting the fixed tire at three inflation pressures. The data are fit to power law curves as a convenience and are not intended to show a functional relationship. The obstacle mass controls the impact time; heavy obstacles give long impact times. The velocity of the obstacle makes little difference in impact time. Long impacts have low-frequency content and do not excite much dynamic behavior in the tire; thus there is low energy loss. Short impacts have frequency content closer to the first natural frequencies of the tire and excite the lower modes of the tire, giving high energy loss.
Schematic of the drop rig used to measure energy loss in the actual tire. The obstacle has variable mass and can be dropped at up to 11 M/sec. The obstacle is assumed rigid. The loss of obstacle translational energy during the impact is attributed to the tire. The displacement of the obstacle is measured by a laser displacement gage and data are taken at 100 kHz.
Typical displacement data obtained from the drop test. The data are fitted with a fourth-order polynomial (the fit is included on this graph). This allows analytical differentiation of the polynomial to obtain velocity versus time curves. Direct differentiation of the displacement data is difficult because of noise in the measured data.
Typical velocity data obtained by differentiating the fourth-order polynomial fit of the displacement data. The minimum of the curve is considered the velocity just before impact. The maximum of the curve is considered the velocity just after impact. The time difference between the peaks is considered to be the time of impact.
Measured drop test data for various obstacle masses and impact velocities for a range of tire inflation pressures. The quasi-static hysteretic energy loss of the tire is shown in the lower curve. The quasi-static data were measured on a load deflection machine at a few millimeters per second. The data points represent different deflection cycles. The average value of the quasi-static loss at a given inflation pressure will be subtracted from the dynamic energy loss data in the subsequent graphs.
Comparison of the measured and simulated energy loss at
inflation pressure. Note that the measured data, corrected for the quasi-static hysteresis, are considerably greater than the simulation and do not increase as quickly as the impact time shortens. The simulation contains only the in-plane deformations from the in-plane modes.
Comparison of the measured and simulated energy loss at 2 bar inflation pressure. Note that the measured data, corrected for the quasi-static hysteresis, are closer to the simulation both in magnitude and change with impact time than is the
result. It is still above the simulation level as would be expected. The overall levels are lower than for the
case. These impact times have frequency content that is further from the tire natural frequencies because they increased with inflation pressure.
Comparison of the measured and simulated energy loss at 4 bar inflation pressure. Note that the measured data, corrected for the quasi-static hysteresis, are closest yet to the simulation both in magnitude and change with impact time. It is still above the simulation level as would be expected. The overall levels are lower than for the
and 2 bar cases. These impact times have frequency content that is further from the tire natural frequencies because they increased with inflation pressure.
The impact times can be converted to estimated vehicle speeds, if an obstacle height and contact patch length are assumed. Note that at highway speeds the simulation of tire energy loss is very high. This graph is not intended to predict energy loss from rolling over obstacles because the simulation is for impacts against static tires. The purpose is to indicate that the impact times for tires rolling over obstacles are short in terms of the simulations and measurements presented here.
Simulated energy loss from dropping two elastic tires with different wheel masses. The wheel mass determines the impact time. The heavy wheel results in a long contact time and thus low energy loss in one bounce, 4%. The light wheel shortens the impact time and results in a 10% energy loss in one bounce. The measured data on this graph indicate that an actual tire drop would have considerably higher dynamic losses.