3.2. Numerical Model

A mathematical description of a physical (or other) behavior based on pertinent hypotheses and simplified assumptions is known as numerical modeling. The proposed concept requires an acceleration force to lift the patient, which is generated using a hydraulic actuator. The hydraulic lifting model, as shown in Figure 10, is composed of:

Schematic diagram of hydraulic lift.

The hydraulic oil from the hydraulic pump enters through the directional control valve and returns to the oil reservoir in the first motion condition, which is when directional valve 3 is at the mean position. As there is less energy use, the system is unloading. Plunger-type cylinder’s hydraulic feed and return lines are disconnected. Stretcher assembly remains still. When the directional valve goes to the right, the stretcher assembly and plunger-type cylinder move downwards. While the hydraulic pump is not functioning, the hydraulic oil runs in via a plunger-type cylinder, an explosion-proof valve, and a directional valve and returns to the oil reservoir. The hydraulic fluid flowing through the directional valve and explosion-proof valve causes the stretcher assembly to be lifted upward when the directional valve moves to the left.

The model of the proposed system is extended from [42]. The flow rate of the hydraulic pump is given by

where Qp is the flow rate of the hydraulic pump, v is the speed of the hydraulic pump, d is the displacement of the hydraulic pump, Cp is the internal leakage coefficient of the hydraulic pump, and Pp is the outlet pressure of the hydraulic pump.

The flow rate through the relief valve is given by

where Qr shows the flow rate through the relief valve and Kc represents the flow pressure coefficient of the relief valve.

The flow rate through a plunger-type cylinder is given by

where Qi shows the flow rate through the plunger-type cylinder, A is the area of the plunger-type cylinder, and d˙ shows the displacement of the plunger-type cylinder.

The outlet pressure of the hydraulic pump can be calculated as

where E shows the bulk modulus of the fluid, and VT is the volume occupied between the plunger-type cylinder and pump.

The accelerational force required to lift the patient is given as

where m is the mass of the load (stretcher assembly and patient), g shows the acceleration due to gravity, and f shows the friction of the plunger-type cylinder.

The friction inside the cylinder is comprised of viscous friction and Coulomb friction. A linear model is used to showcase the friction effects on the force. Thus, the friction model can be described as:

where f shows column friction, fc is the static friction, and fv is the viscous friction coefficient.