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Simulation for Vertical Dynamic Loading Forces on Track Rollers of the Half-tracked Tractor Based on Nonlinear Voigt’s Model

M. A. Rabbani
JSAM Student Member, Department of Bioresources and Bioenvironmental Sciences, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan

Susumu Takeoka
JSAM Student Member, Department of Bioresources and Bioenvironmental Sciences, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan

Muneshi Mitsuoka
JSAM Member, Faculty of Agriculture, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan

Eiji Inoue
JSAM Member, Faculty of Agriculture, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan

Takeshi Fukushima
JSAM Member, Faculty of Bioresources, Mie University, 1577 Kurimamachi, Higashi, Tsu-city 514-8507, Japan

Takeshi Okayasu
JSAM Member, Faculty of Agriculture, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan

Abstract/ Executive Summary:

Experiments to measure the vertical dynamic loading forces acting on the track rollers of a half-tracked tractor were conducted by using strain gauges. In addition, a driving simulation model was constructed to predict the vertical dynamic loading forces acting on the track rollers as the tractor ran on an asphalt road surface. A twodimensional model to evaluate the vibration characteristics of the half-tracked tractor is discussed. It was modified and improved by considering the linear and nonlinear interactions of the rubber crawler with the track roller as well as the roller’s location arrangement.

Keywords: Half-tracked Tactor, Strain Gauge, Dynamic Loading Force, Track Roller

Location: Department of Bioresources and Bioenvironmental Sciences, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan

Start Date:

End Date:

Program Area: Farm Mechanization

Commodity: Manipulation

Objectives:

To measure the vertical dynamic loading forces acting on the track rollers of a half-tracked tractor were conducted by using strain gauges.

Methodology:

The dynamic two-dimensional model of a half-tracked tractor driven over a rigid horizontal surface. In this model, the track rollers are fixed onto the track frame and mounted at the hitch point of the tractor. The following assumptions were also introduced for simplification. The model parameters k₁(t), k₃(t), and c(t) are the proper linear dynamic spring constant, nonlinear dynamic spring constant, and viscous damping coefficient beneath the track rollers under actual driving conditions, respectively. For this model, the track rollers can be assumed to run on the upper surface of the rubber crawler. The flowchart below indicates the solving of the vertical dynamic loading forces on the track rollers. Based on the mathematical model designed for the prediction of the vertical dynamic loading force of the half-tracked tractor by using the Runge-Kutta method, a computer simulation program was developed using Microsoft Visual Basic 6. The experimental system was composed of a half-tracked tractor that was driven by an oscillating crawler system. To determine the effect of the dynamic loading force on the track rollers of the half-tracked tractor, strain gauges (KYOWA, KFG-3-120-C1-11L1M2R) were used on each track roller. Since the track rollers were of the double-track type, the position of the dynamic loading force should also be determined. Thus, two strain gauges were set 50 mm apart in the shaft of the track roller at positions A and B, and the moment at point A for the vertical dynamic loading force P can be determined as M_A= P.X. Three similar track roller arrangements were selected for simulation to compare the measured and simulated results. Using the main gear, sub gear, and number of rotations of the engine shaft, we varied the running speed through four different values—0.144, 0.253, 0.771, and 1.29 m/s—that were equivalent to frequencies of 1.714, 3.012, 9.179, and 15.357 Hz, respectively. These frequencies indicate the number of lug pitches that a track roller passes per second. An asphalt road surface with little unevenness was selected to carry out test drives, and data were measured when the road surface was dry and with no-man drive. The measured voltage signals from the strain gauges were amplified by a strain amplifier (KYOWA, YA-506B, 500 με-2 V). The results were filtered for signals above 100 Hz and recorded in a data recorder (GRAPHTECH GL1000). The analysis was carried out on a notebook computer using DADiSP-Pro 4.1 data analyzing software. Measurements were carried out three times for each speed and track roller arrangement.

Source of Information: Engineering Agriculture Environment and Food 3(4) 119-126, 2010

Article Link (Online Journal):

Funding Source:

Total Budget (Tk.) :

Achievement/Findings:

In this study, numerical simulation was used to predict the vertical dynamic loading force acting on the track rollers of a half-tracked tractor. The model and methodology of the analysis used for predicting the vertical dynamic loading force were presented. A two-dimensional model for predicting the vibration characteristics of the half-tracked tractor was discussed. It was further improved by introducing the vertical dynamic loading force acting on the track rollers on the oscillating rubber crawler system. The following conclusions were drawn from this study:

- Inclusion of the vertical reaction force in the model considerably improves the prediction of the vertical dynamic loading force on the track roller.

- For the entire range of speeds used to predict the vertical dynamic loading force, the simulated and measured results are closest to each other when the standard arrangement is used

- Based on the PSD, the simulated value of the vertical dynamic loading force reaches its peak at the same frequency as the measured value. However, quantitative variations exist because of the nonlinear behavior of the semi-crawler during interaction with the track roller. The several peaks that were observed for the measured value at about half the frequency of the lug passing at 1.29 m/s may have occurred because of the high speed of the crawler, when the effect of the nonlinearity of the rubber crawler is very high. The model needs to be further improved to overcome this dissimilarity.

The introduction of the nonlinear relationship between the vertical dynamic loading force and track roller of the rubber crawler in the model improved the simulated results both qualitatively and quantitatively. However, it was difficult to correctly identify the model parameters when the displacement due to the loading force on a track roller varied over a wide range because of the increased machine vibrations. Hence, in order to understand the actual vibration characteristics and build an accurate simulation model of the half-tracked tractor, it is necessary to extend the present model from a two-dimensional form to a three-dimensional form by considering the loading forces as well as the movement of the center of gravity and the lug phase difference of the left and right rubber crawlers.

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