## 1 Introduction
VFDs allow applications to use a much higher starting torque and reduced energy consumption once the application is operating. This feature is crucial, due to the low starting torque of high-efficiency systems. Research has been focused on the study of the interaction between the electric motor and the variable frequency driver and between the electric motor and the operated device. [PERSON] et al. [7] reported that VFD systems can save about 15-40% energy and extend equipment lifespans by enabling gentle start-up and shutdown. [PERSON] et al. [8] reported that in their experiments, VFDs significantly reduced system input power by 85% at a 50% rated frequency and increased the power factor to 0.95 at a 95% rated frequency, with a voltage total harmonic distortion (THD) always less than 1%. [PERSON] et al. [9] investigated a variable-speed compressor refrigerator in both on/off and variable-speed modes, finding a 10% increase in exergy efficiency and a 14% increase in the coefficient of performance (COP) due to variable-speed operation. [PERSON] et al. [10] demonstrated that VFD saved 15% energy compared to the on/off mode in tests with household refrigeration systems using a variable-speed compressor. [PERSON] et al. [11] reported that in tests on VFDs in compressors for ship cold storage refrigeration, the COP improved by 13.9% as the compressor frequency decreased. [PERSON] et al. [12] evaluated the electric energy consumption of small to medium-sized Tuscan olive oil mills, taking into account all equipment and process steps, including pumps and fans. Centrifugal extractors and crushers are examples of process equipment driven by electrical motors, and their energy consumption during the production campaign can be substantial, particularly when the decanter centrifuges operate for extended periods of time. In this case, to ensure rapid decanter operation, the electrical motors are sometimes oversized, resulting in suboptimal efficiency. [PERSON] et al. [13] proposed a model to study the energy consumption of a decanter equipped with an electromechanical recovery system (i.e., regenerative braking), also reporting how the use of the installed power varied from 20% to 40%, resulting in a sub-utilization of the installed power and in a not-efficient energy utilization. [PERSON] et al. [14] created a model to study the energy requirement of a decanter centrifuge driven by VFDs and equipped with a regenerative braking recovery; the aim was to identify the energetic optimal conditions and their relation to the quality of the product. Therefore, it is very difficult to operate the motor at its maximum efficiency, because different restraints have to be considered (e.g., the time to bring the device to the operating speed, different and variable motor loads, and the behavior of the load with regard to the shaft speed); furthermore, a study analyzing the operating efficiency of a motor, while also taking into account the possibility of operating the motor at different speed using a gearbox and a variable-frequency driver, is lacking. Some researchers demonstrated how variable-frequency drivers using the \(\mathrm{V/F}\) operation reach a good efficiency when the motor is operated near the full load region [15], and, for this reason, the idea was to investigate the use of a gearbox to adapt the load to the motor's optimal torque, thus also adapting the efficiency curve of the three-phase electric motor. Through simulations and experimental measurements, this study seeks to determine the existing relationship between the system's overall efficiency and an electronic-driven motor connected to a horizontal centrifuge, demonstrating, in addition, the applicability of simulation programs in engineering problems related to electric motors [16; 17]. The simulation made it possible to test the system without the high cost of purchasing electric motors and variable-frequency drivers.