**6. Experimental investigation**

The essential parameters, such as currents, voltage, pressure, flow and height, were measured from the DDH setup. The location of the utilized sensors is illustrated in Figure 4. The experimental efficiencies and energies of the DDH test setup system for lifting movements were calculated as shown below:

$$
\eta\_{\text{up\\_tot}} = \frac{E\_{\text{pot}}}{E\_{\text{mech}}} \,\,\,\,\tag{26}
$$

where *E*pot is the potential energy of the payload

The system pressure is illustrated in Figure 13, where *p*1 is the P1 pump/motor pressure, *p*3 is the P2 pump/motor pressure, and *p*2, *p*4 are the "tank" line pressures (line with accumulator A).

**Figure 13.** Simulation results of the pressure in the DDH system: *p*1 is the P1 pump/motor pressure, *p*3 is the P2 pump/

The pressure *p*<sup>3</sup> ranges between 0.93 MPa and 1 MPa during the whole lifting–lowering cycle with a maximum payload of 150 kg. The tank pressure (*p*2 and *p*4) varies between 0.38 MPa and 0.18 MPa. Thus, according to the simulation, Cases II, III and IV do not fulfill the require‐ ments of the leakage line where the maximum allowed constant pressure is 0.3 MPa and in the short term, it is 1 MPa. According to the results shown in Figure 13, from the proposed connection cases in Figure 7, only Case I can be used for the realization of the DDH setup,

The essential parameters, such as currents, voltage, pressure, flow and height, were measured from the DDH setup. The location of the utilized sensors is illustrated in Figure 4. The

where both external leakage lines are connected to line A (accumulator A).

motor pressure, and *p*2, *p*4 are the "tank" line pressures (accumulator A).

**6. Experimental investigation**

160 New Applications of Electric Drives

$$E\_{\rm pot} = mgH\_{\prime} \tag{27}$$

where *m* is the mass of the payload in kg and *g* is a gravitational constant in m/s2 . *H* is the position of the cylinder piston in m.

*E*mech is the energy of the shaft and is calculated as the integral of the power at the shaft (*P*shaft).

$$P\_{\text{shaft}} = T \Omega \,, \tag{28}$$

where *P*shaft is the output energy of the shaft in W, *T* is the motor torque in Nm and *Ω* is the angular speed in rad/s. A motor control algorithm was utilized to measure the angular speed and estimate the motor torque.

The output energy of the hydraulic part *E*hydr is calculated as the integral of the output hydraulic power:

$$P\_{\text{hydr}} = pv\_{c}A\_{\prime} \tag{29}$$

where *p* is the pressure in Pa, *v*c is the velocity of the cylinder piston in m/s and *A* is the cross area of the cylinder piston in m2 .

Depending on the operating point of a hydraulic pump/motor unit in its performance curve, the relationship between the flow and hydraulic losses in a system varies significantly. During the lifting, the hydraulic pump/motor unit operates as a pump. The input energy of the pump is mechanical energy and the output is hydraulic energy. Figure 14 presents an example of a Sankey diagram for the measured losses and efficiencies of the DDH system.

In Figure 14, hydro-mechanical losses equal 33.4%. Hydro-mechanical losses include shaft and hydraulic losses. Hydraulic losses in DDH systems are composed of pipe friction losses and other fittings, entrance and exit losses and losses from changes in the pipe size resulting from a reduction in the diameter, pump/motors and cylinder losses. The overall cylinder efficiency is mostly dependent on the frictional losses encountered by the piston and the rod during its stroke. Frictional losses depend on the pressure difference across the seal, sliding velocity, seal material, temperature, time, wear and direction of the movement. Measured electrical machine

**Figure 14.** Measured Sankey diagram of the DDH with a motor speed of 400 rpm and a payload of 150 kg (the efficien‐ cy of the frequency converter is not included) [19].

losses are 20.7%. Electrical machine losses are composed of the following elements: stator and rotor resistive losses, iron losses, additional losses and mechanical losses. Mechanical losses include friction in the motor bearings. Bearing losses depend on the shaft speed, bearing type, properties of the lubricants and the load. The converter losses take place mostly in the semiconductor switches and in the auxiliary power systems. In this study, the losses of the frequency converter are not included.

It was challenging to create the DDH test setup due to the asymmetrical double-acting cylinder used and the difficulty of finding matching displacements of the pump/motors in order to fulfill *R*Q = *R*A. Moreover, another challenge was the location of the hydraulic accumulators and external leakage pump/motor lines. The Sankey diagrams showed that electrical machine losses are in second place after the dominant hydro-mechanical losses. Taking pressure balancing into consideration, the hydro-mechanical losses in the system will be reduced in the second DDH prototype.
