# Design and Lateral Stability Analysis of an Attitude Adjustment Tractor for Moving on Side Slopes
## 5 Case Study and Experiment Variation
### Manufacture and Test of a Prototype
#### 5.2.2 Bench Tests  
Some interesting tests are carried out to check the practical performances of this tractor. The tractor can achieve basic functions, such as move forward, back, and turn. It not only can adjust its attitude, but also can level itself on side slope angles in the range of 0-15\({}^{\circ}\). The previous model is solved using MATLAB software. In this section, we use bench tests to verify the lateral stability of the designed tractor. As shown in Figure 9, the test equipment is the roll test bench. This test bench is equipped with a slope-measuring instrument connected to the computer. The computer can read the slope angle data in real time. While ensuring the safety of this prototype, this tractor is braked on this test bench. In the initial state, the prototype is leveled. Then, with the increase in the slope angle, the contact force between the wheel and slope changes. The overturning of the prototype with the test bench can be observed. When the contact force between the wheel and slope is less than or equal to zero, this tractor overturns. As shown in Figure 9, the working conditions can be divided into initial state and attitude adjustment, respectively. The designed tractor can actively adjust its posture on side slopes with the mechanisms installed on the rear axle. (1) First, a tractor in its initial state is braked on the bench, with the increase in slope angle, the contact force between the wheel and slope changes. When the slope angle is 30.91\({}^{\circ}\), the uphill rear wheel leaves the ground, then the tractor overturns. (2) Then, the test tractor equipped with an adjusted attitude function is braked on the bench, as increasing lateral slope angle, the contact force between the wheel and slope changes. When the slope angle is 40.74\({}^{\circ}\), the uphill rear wheel leaves the ground, then the tractor overturns. Results show that by actively adjusting the roll angle of the tractor, the limit instability angle increases from 30.91\({}^{\circ}\) to 40.74\({}^{\circ}\). The mathematical model is presented in Section 4, representing the relationship between a tractor's posture change/configuration and stability evaluation index on transverse slopes. First, the force model on side slopes is built to obtain the limit instability angle (\(\theta_{lim}\)). Then, taking the proposed tractor, for example, the effects of attitude/configuration on tractor lateral stability are studied in Section 5.1. Theoretical analysis shows that the lateral stability can be enhanced by adjusting the tractor's attitude. The limit instability angle (\(\theta_{lim}\)) can be increased by increasing the active input (rotation angle of the rear axle, \(\alpha\)). In the initial state, \(\theta_{lim}\) is 33.42\({}^{\circ}\); when the rotation angle of the rear axle (\(\alpha\)) is 90\({}^{\circ}\), \(\theta_{lim}\) turns 44.87\({}^{\circ}\) (increased 34.26%). As shown in Figure 10, the lateral stability solutions with the mathematical model in Section 4 are compared with the results of bench tests in this section. The working conditions are divided into initial state and attitude adjustment. In the initial state, the difference between theory (33.42\({}^{\circ}\)) and test results (30.91\({}^{\circ}\)) is 8.12%. After attitude adjustment, the difference between theory (44.87\({}^{\circ}\)) and test results (40.74\({}^{\circ}\)) is 10.14%. Figure 9: Bench tests: (**a**) Initial state; (**b**) Attitude adjustment. There are two possible reasons for the difference (10%) between the theory model in Section 4 and bench tests in Section 5.2.2: (1) In the theory model, the wheel is assumed as a rigid model, and the wheel's deformation is not considered. On the other hand, the wheels in the tests are low-pressure tires, and they will become deformed; (2) The uphill/downhill sides tires are considered as a whole to establish the mechanical model. Meanwhile, the rear wheel on the uphill side loses contact with the ground in the test.