1. Introduction
To reduce ride vibration, existing tractors mainly use rubber mounts between the tractor body and the cabin in which the operator is seated. These rubber mounts have a large spring constant and a small damping coefficient, which makes them suitable for supporting weight but unsuitable for absorbing vibration transmitted to the cabin [
1]. Recently developed large tractors are increasingly equipped with cabin suspension instead of rubber mounts to reduce cabin vibration. Because the maximum driving speed of a 100 kW-class tractor recently developed in the Republic of Korea can reach 40 km/h, there has been increasing demand for cabin suspension that reduces the impact from the ground during high-speed driving. Studies have shown that vibration is reduced when rubber mounts are replaced with cabin suspension [
2]; however, there has been minimal research analyzing the characteristics of cabin suspension and the optimization of design factors.
Cabin suspension is functionally a combination of a spring that supports the weight by also acting as a low pass filter, and a damper that dissipates energy by reducing motion speed. Springs are divided into mechanical, pneumatic, and hydro-pneumatic types according to their operation method. In general, mechanical springs are used in systems with lighter weights, whereas pneumatic and hydro-pneumatic springs are used in systems with heavier weights. The damper reduces the speed by dissipating kinetic energy into heat energy through resistance generated when hydraulic oil passes through a narrow cross section. Dampers can be classified as passive, semi-active, and active depending on the damping force adjustment function and the presence or absence of an external energy source [
3]. Tractor cabin suspensions should be capable of level control in inclined operation environments; further, hydraulic springs are suitable for use in rough terrain because of the heavy load [
4].
Tractors perform a wide variety of tasks and can drive at a wide range of speeds, and thus experience varying types of vibrations coming from the ground. Therefore, a semi-active damper is considered suitable for adjusting the damping forces depending on the circumstances. Because of the wide variation in tasks and driving speeds, it is thought that adjusting the damping force according to the operation environment is suitable. In this study, a semi-active hydro-pneumatic suspension was selected as the suspension to be used for the tractor cabin, and the characteristics of the suspension were analyzed through a single unit test.
Zehsaz et al. [
5] measured acceleration data while driving a tractor with a passive cabin suspension system according to ISO 2631(1985), and developed a finite numerical analysis model based on the test results in order to perform parameter optimization. Sarami [
6] developed a system in which semi-active suspensions were mounted on a tractor’s seat, cabin, and axle in order to improve ride comfort. Virtual ground vibration was applied to the developed tractor using a road simulator, and the effectiveness of the suspension system was verified by measuring the rotational acceleration in the roll and pitch directions and the acceleration in the vertical direction. Recently, owing to the installation of proportional control valves in hydro-pneumatic suspensions, research has been conducted to develop optimal damping force control according to operating conditions. Sim [
3] modeled a semi-active hydro-pneumatic suspension system with a simulation program and verified the model by comparing it with actual vehicle test results. The ride comfort was analyzed by applying a suspension system and control logic to a tractor simulation model with 14 degrees of freedom. These previous studies on tractor cabin suspensions analyzed how these suspensions could improve ride comfort and reduce ride vibration, but did not analyze the characteristics of the tractor cabin suspension unit. In addition, the characteristics of a hydro-pneumatic suspension change according to current conditions, owing to the nonlinear characteristics of the hydraulic system. Thus, in order to improve the accuracy of the simulation model, it is necessary to accurately analyze the characteristics of the hydro-pneumatic suspension unit and to construct a model based on the characteristics of the suspension.
Various methods have been used to test the characteristics of suspensions. Omar et al. [
7] developed a device that can simultaneously test the performance of active and passive suspensions for automobiles. A suspension was installed on a vertically fixed guide, and sprung mass was added to the upper portion and a motor was installed on the lower portion. This test device made it possible to convert the rotational motion of a disk into vertical reciprocating motion. Konieczny et al. [
8] constructed a reciprocating test device by fixing one side of a suspension and then connecting the other side to a rotating crank in order to perform characteristic tests on semi-active suspensions in automobiles. However, using a disk and crank in this manner is problematic because even if the input is rotated at a constant frequency, the output appears as a trigonometric function that reflects the mechanical characteristics; thus, the displacement, velocity, and acceleration of the output must be converted. Giliomee and Els [
9] developed a test device equipped with a hydraulic cylinder that can control the displacement, velocity, and acceleration of a suspension. In their tests, the upper end of the suspension was fixed, the lower end was connected to the hydraulic cylinder, and the spring stiffness and damping coefficient were obtained by measuring the low-speed reciprocating motion and high-speed reciprocating motion, respectively. The above-mentioned suspension characteristic tests were mainly performed on automobile suspensions, such as those in passenger cars and commercial vehicles. Because agricultural tractors drive at relatively low speeds under completely different road conditions than automobiles, an automotive suspension cannot be used as a tractor cabin suspension. In addition, an automotive suspension is located between the wheels and the vehicle body, whereas the cabin suspension of an agricultural tractor is located between the tractor body and the cabin. Thus, the operating conditions of the suspension are different, and the results of characteristic tests of automotive suspensions cannot be applied to tractor cabin suspensions. Therefore, in this study, a characteristic test of a tractor cabin suspension was performed according to tractor operating conditions. A high-performance exciter equipped with a servo valve was used for testing; this approach simulated load conditions more accurately than the conventional disk and crank method.
To establish an accurate test method for deriving the spring constant and damping coefficient of a suspension, this study performed a characteristic test on a hydro-pneumatic, semi-active tractor cabin suspension under changing velocity and current conditions. The study also generated force-displacement and force-velocity diagrams of the suspension that can be input into a simulation model for control logic development. The test utilized an exciter with a servo valve for controlling the displacement and velocity of the hydraulic cylinder, and employed a method of fixing one side of the suspension and reciprocating the other side without sprung mass. In order to derive the spring constant of the suspension, a low-speed reciprocating motion test was performed to obtain the force-displacement diagram and to derive the damping coefficient; 48 tests were performed under 6 velocity conditions and 8 current conditions to obtain the force-velocity diagram for each result. The spring constant and damping coefficient derived from the characteristic test can be used as the cabin suspension characteristic values of the simulation model for evaluating the ride vibration of the tractor and developing the control logic of the suspension.
4. Conclusions
To establish an accurate test method for deriving the spring constant and damping coefficient of a suspension, this study performed a characteristic test on a semi-active hydro-pneumatic suspension under changing velocity and current conditions, and generated force-displacement and force-velocity curves representing suspension characteristics for input into a simulation model for control logic development. A semi-active hydro-pneumatic suspension combines a hydraulic spring whose performance is determined by the characteristics of the accumulator (nitrogen pressure, capacity) and a semi-active damper technology controlled by the flow rate inside the suspension. The test utilized an exciter capable of controlling the displacement and velocity of a hydraulic cylinder, and a method of fixing one side of the suspension and reciprocating the other side. The test was performed under six velocity conditions and eight current conditions.
In order to obtain the spring constant of the hydro-pneumatic suspension, the test configured the piston to move at a low speed to prevent the damping force from occurring and to ensure an accurate spring constant measurement. The reaction force according to the displacement was measured, and the spring constant was obtained. In order to obtain the damping coefficient of the hydro-pneumatic suspension, it had to be moved at a high speed to generate a large reaction force. The reaction force was measured at the point where the displacement was zero, and the damping coefficient was obtained using the force-velocity diagram. The test method used in this study could not fully implement the nonlinear characteristics with hysteresis of the hydro-pneumatic semi-active suspension. However, it was considered to be sufficient for the purpose of creating a simulation model for control logic development.
This study presented a method for accurately testing the dynamic characteristics of a semi-active hydro-pneumatic suspension that could change its performance according to the terrain or the needs of the operator. In future research, if the dynamic suspension characteristics obtained in this study can be applied to a tractor simulation model, the characteristics of tractor ride vibration could be more accurately predicted. Further, by employing the tractor ride vibration model, the findings of this study could be used in the development of control logic to minimize ride vibration.