## 1 Introduction
In short, motor is the main heat source of EHA, e.g., an experimental result shown in Figure 2. Under the condition of 4t with load and continuous working for seven minutes, the surface temperature of the motor rises from 29.5 \({}^{\circ}\)C to 51.6 \({}^{\circ}\)C, and the hydraulic-part temperature remained essentially unchanged. the problem of motor heating is the main reason affecting the EHA widespread application [13]. the energy loss of the motor is mostly dissipated through heat generation in the form of copper and iron losses. Meanwhile, the dynamic performance of the system at high temperatures will be affected to some extent. If the motor heating can be reduced, it is of great significance for EHA to improve the efficiency, dynamics and reliability, as well as increase continuous the working time and lifetime [14]. Figure 1: EHA structure &principle schematic. The idea of solving the problem of motor heating- is to popularly use high-speed motor and high-pressure system for the EHA-FPVM. For example, the EHA system designed by SAFRAN in France and UTC-Goodrich in the United States uses 20,000 rmp motors and 35 MPa hydraulic systems. the system achieved a level of 16,000 rpm and a peak pressure of 35 MPa. the method of high pressure and high speed can expand the speed regulation range of the motor and enable the motor to work in the high efficiency area [15]. This method is currently very popular because of its simple structure and control, but this fixed displacement architecture cannot achieve the optimal power matching of motor and pump, where the power of the selected motor is the larger, which is disadvantageous for high power density requirements. the EHA with variable pump displacement and variable motor speed (EHA-VPVM) has become a popular concern, because its two control variables can well achieve the motor-pump power matching and reduce the motor heating, as well as improve the EHA stiffness [16]. the general variable displacement mechanism requires an open valve-controlled cylinder with additional oil supply pressure to alter the pump displacement through varying the tilt angle of the swash plate [17]. the principle structure has fast response but increases the cost and complexity of the system. Reference [18] proposed a new type of electric variable mechanism composed of a direct current (DC) servo motor and related transmissions (gearbox + sector gear). the purpose is to simplify the structure of the variable mechanism, reduce hydraulic faults and improve maintainability. the meshing between gears inevitably has problems such as tooth-side clearance, inter-tooth lubrication media, and various transmission errors (including various manufacturing errors, installation errors, thermal deformation, wear, etc.). These coupling effects have a certain degree of influence on the performance of the electric variable mechanism. [PERSON] etc. designed a load-sensing pump based on a variable displacement architecture to reduce EHA heat generation in [19]. [PERSON] advanced the principle of direct load-sensitive EHA (DLS-EHA) based on load-sensing pumps [20]. the DLS-EHA automatically adjusts the pump displacement through the load pressure without the need for an additional power source, which can decrease the motor heating and achieve the motor-pump power matching to a certain extent. However, the back pressure spring of the variable mechanism must be selected according to the maximum load pressure to ensure that the variable mechanism is sufficiently rigid to stabilize the system. a large back pressure spring stiffness results in a low rate of change in displacement with load pressure. DLS-EHA does not give consideration to the dynamics and the efficiency of the system, and the variable characteristic is a constant value making it difficult to achieve optimal matching. Figure 2: EHA motor surface temperature before and after loading. Stiffness is an index to measure the effect on the system output when the load force changes. Dynamic stiffness describes the changing law of stiffness in the dynamic process.