2.3.3. Hydraulic Pump Model

The hydraulic pump model mainly presents its torque and power consumption and simplifies the hydraulic operation system, which is sufficient for researching the powertrain energy and control. The hydraulic pump model can be denoted by

$$T\_{\rm hp} = \frac{p\_{\rm hp} q\_{\rm hp}}{2\pi \eta\_{\rm hp}},$$

$$P\_{\rm hp} = \frac{50p\_{\rm hp}Q\_{\rm hp}}{3\eta\_{\rm hp}},$$

$$Q\_{\rm hp} = \frac{q\_{\rm hp} n\_{\rm hp}}{1000},$$

where *T*hp is the torque of the hydraulic pump, *n*hp is its speed, *p*hp is the outlet pressure, *q*hp is its displacement, ηhp is its efficiency, *P*hp is its power consumption, and *Q*hp is the flow.

### 2.3.4. Tracked Walking Mechanism Model

The tracked walking mechanism model is represented based on the kinematic relationship and takes the slip ratio as a major factor into consideration. The traction and speed of the tracks can be formulated as

$$F\_{\rm t} = \frac{T\_{\rm t}^{\rm in} \eta\_{\rm t}}{r\_{\rm dw}} \,\tag{22}$$

$$
\rho\_{\rm th} = \frac{\nu}{(1 - \varphi)r\_{\rm dw}},
\tag{23}
$$

where *F*<sup>t</sup> is the tangential traction of tracks, *T*in <sup>t</sup> is the input torque, η<sup>t</sup> is the track efficiency, *r*dw is the radius of the driving wheel, and ϕ is the track slip rate.

### *2.4. Dynamic Model*

The HEB has to overcome the resistance of bulldozing, climbing, ground deformation, acceleration, and air friction. The air friction is small and can be neglected due to the velocity of the bulldozer being very low. The dynamic model can be shown as

$$F\_{\rm t} = m\_{\rm veh, \rm g} g \mu \cos \alpha + m\_{\rm veh, \rm g} \sin \alpha + \xi m\_{\rm veh} \frac{dv}{dt} + F\_{\rm b} \tag{24}$$

where *m*veh is the HEB mass, *g* is the gravitational acceleration, α is the slope angle, ξ is the rotary mass coefficient, *v* is the velocity, μ is the ground deformation resistance coefficient, and *F*<sup>b</sup> is the bulldozing resistance.

In order to accurately calculate the resistance, the ξ was identified and the *F*<sup>b</sup> was extracted in our previous research [7].

Finally, the HEB model was built in the Simulink environment, as shown in Figure 5.

**Figure 5.** HEB model in Matlab/Simulink.
