Lateral natural frequency modeling and verification for vibration systems of wheeled tractors

Abstract: In China, operators of off-road vehicles such as agricultural vehicles and mining vehicles are exposed to excessively high levels of vibrations in all of 3 translational modes - vertical, longitudinal and lateral mode, which can pose health risks to the drivers. According to international organization for standardization 2631-1:1997, the lateral vibration can be more hazardous to operators' work performance, comfort and health than the vertical vibration when the vibration frequency is below 3 Hz, and meanwhile, some vibration systems of off-road vehicles can resonate in this frequency range. But seldom research was conducted on the lateral vibration characteristics of off-road vehicles. In this paper, a new theoretical vibration model including the lateral and roll directions of ride vibration in space was constructed for the unsuspended tractor with 2 degrees of freedom, and the theoretical formula was presented for calculating the lateral natural frequency of domestic tractors. In this lateral vibration model, the radical and lateral stiffness of tires was taken into account. By the use of a CF700 tractor without suspensions from Changfa Group in Jiangsu Province, the accuracy of the theoretical values of the lateral vibration model was improved according to the measured radial stiffness of the tire on the test rig, which was independently developed in light of free vibration logarithmic decrement method for measuring the radial stiffness and damping of tractor tires. And the lateral stiffness of tires was calculated by the mathematic formulas. Subsequently, the rolling moment of inertia of the CF700 tractor's body was obtained on another test rig, which was independently developed based on simple pendulum with edge and spring method for measuring the moments of inertia of both pitch and roll. The experiments were repeated 3 times. Then, the theoretical and experimental methods were combined to calculate the theoretical values of the lateral natural frequency of the CF700 tractor. Driving experiments were conducted on an ISO-5008 standard track to investigate the lateral vibration characteristics and to verify the validity of the theoretical values of the lateral natural frequency for the CF700 tractor. The lateral vibrations of the CF700 tractor were measured approximately at 5 forward speeds of 5, 9, 11, 13 and 15 km/h. The measurement was repeated 5 times for each speed. The experimental values were obtained mainly with the LMS test system and the on-board strain-gage-based transducers and triaxial accelerometers. The discrete time series of the measured data were resolved and reconstructed by wavelet and Fourier analysis. The results showed that the experimental values of the lateral natural frequency of the CF700 tractor were 1.975, 1.953, 1.904, 1.902 and 1.901 Hz respectively at 5 forward speeds. And the peak values of lateral vibration acceleration power spectral density were respectively 0.52, 2.84, 3.43, 4.08 and 4.95 (m·s2)2/Hz. And the theoretical calculated values of the lateral natural frequency of the CF700 tractor were respectively 1.9603, 1.9314, 1.8996, 1.8996 and 1.8996 Hz. Compared with the measured lateral natural frequency, the maximum relative error was 1.11% for the theoretical calculated value. Therefore, it verified the accuracy of the theoretical formula of the lateral natural frequency. And it further indicated that the lateral natural frequency decreased to a constant with the increase of the travelling speed of the CF700 tractor. Also, it showed that higher travelling speed produced higher peak level of lateral vibration acceleration power spectral density, which made drivers feel the more lateral vibration intensity of off-road vehicles. Therefore, the lateral vibration of off-road vehicles needs to be isolated. The work provides an important reference for the design of the lateral vibration reduction system of seat suspension of agricultural tractors or other off-road vehicles.