Electric machine sizing consideration for ePumps in mobile hydraulics

Environmental concerns have pushed toward electrified technologies for off‐road vehicle actuations that can lower greenhouse gas emissions and reduce energy consumption. Replacing a central diesel engine with a dedicated electric machine (EM) as a prime mover for the hydraulic supply offers several opportunities for so‐called ePumps (aka electric‐driven pumps) to maximize energy efficiency and limit the usage of electric materials. This paper discusses the impact of different choices for the ePumps architecture (i.e., fixed vs. variable displacement pump; variable speed vs. fixed speed electrical machine), and on their main design parameters in terms of size and efficiency. Although the procedure followed in the study could be extended to different types of electric and hydraulic units, the paper particularly considers ePumps based on permanent magnet synchronous machines combined with axial piston machines. The importance of properly considering the ePump drive cycle and its cooling requirements is taken into account while addressing energy efficiency, mass, and overall compactness of the solution. The results show that an ePump based on a variable displacement pump, when compared to fixed displacement ePumps, reduces the electrical machine size both in volume and mass up to 40%, when the high‐pressure demand is not combined with high flow rate demand, thus decreasing the cost of the EM. In all drive cycles, the variable speed EM–fixed displacement pump architecture has a higher efficiency, ranging from 1% to 5%, compared to the case of fixed speed EM–variable displacement pump. Finally, the paper compares the advantages and shortcomings of each ePump architecture presented, based on representative drive cycles.

Environmental concerns have been pushing toward solutions alternative to engines as prime movers for offroad vehicles.Abatement of CO 2 emissions and reduction in fuel consumption are the primary drivers for implementing electric vehicles in agriculture, construction, mining, and forestry applications.Combustion engines have energy efficiency limitations, topping 40% at best, as in real applications with highly variable power demand the engine often operates far from its best efficiency point.Additionally, combustion engines cannot recover energy from overrunning loads, which would be a great opportunity for several off-road applications handling gravitational loads.Electric prime movers can reduce greenhouse emissions as well as local air pollution.They can also reduce vehicle maintenance costs.However, the development of electric vehicles presents challenges such as initial cost, charge time, battery uptime, and machine weight.A study by Burke et al. estimated the cost of an electrified heavy-duty powertrain vehicle to be about 1.5 times higher than a similar one based on traditional engine technology. 1 The charging time of a battery currently ranges between 2.85 and 20 h, depending on the technology, while the refueling time of an internal combustion engine (ICE) can take between 6 and 12 min. 2A comparison between a hydraulic and an electric shovel of similar bucket size and load weight showed that the electric shovel weighs over two times the hydraulic shovel (1203 tons against 599 tons). 3lectric off-road vehicles are likely to continue utilizing hydraulic actuation, as hydraulic actuators offer advantages such as compactness, cost-effectiveness, resistance to shock, energy recovery in overrunning loads, and robustness.Therefore, electric-driven flow supply units (ePumps, aka electrohydraulic machines) are essential elements for such applications.An ePump is a device comprised of an electric machine (EM) connected to a hydraulic machine (HM) and designed for use in both hybrid-electric and all-electric mobile applications based on fluid power actuation.It is important to note that in an electrified application, ePumps will be key no matter the hydraulic system architecture of choice.Several hydraulic control architectures are available, each one having different features pertaining to actuator control and energy efficiency.The most general classification can be made by categorizing decentralized architectures, using one supply per actuator, and centralized ones, that group multiple actuators to a single supply.Decentralized architectures are the most convenient in terms of energy efficiency and capability of recovering energy from overrunning loads, 4 but centralized architectures are more conventional having advantages in terms of cost, installed power, and technical feasibility.In centralized hydraulic systems, ePumps can be viewed as a replacement of the pump connected to the ICE as shown in Gottberg et al., 5 or even integrated as a combination with a diesel engine as presented in Opgenoorth et al. 6 It is worth noting that engine-driven off-road vehicles often use multiple pumps, typically two or more, even in centralized architectures.However, ePumps are even more attractive to implement decentralized architectures in electric vehicles, where multiple EMs can be installed to promote energy efficiency.
With the above premise, it is clear that the possible utilization drive cycles (UCs) for ePumps can be very diverse, depending on both the application and the hydraulic system architecture.In fact, each vehicle must meet specific performance requirements (in terms of pulling force, vehicle and actuator velocities, inclination, etc.).Moreover, the need to reduce battery size and/or increase battery uptime is pushing for more applications where the ePump is required to operate in multiple quadrants.This paper tackles these important design aspects, and it studies the effect of different drive cycles on the best ePump architecture, in terms of cost and energy efficiency.
The selection of the most appropriate ePump architecture will not only depend on the specific application working cycle but also on the characteristics of both the EM and HM.Moreover, as it occurs in hydrostatic transmission for propulsion, 7 it is often convenient to avoid operation of the HM at its maximum power capacity (i.e., corner power point), as this usually implies a limitation on the power usage of the more expensive EM.Additionally, this paper will also consider the cases where both the EM and the HM do not reach operation at maximum power, which has practical relevance (i.e., selecting a larger size ePump for a given application due to technical availability).
In academia, a large focus was given to integrated ePumps, which combine the EM and the HM in a common housing.The literature shows examples of partial integration where the pump is not fully embedded inside the EM and therefore the HM is shaft driven.Relevant is the design by Gamez-Montero et al., 8 for an integrated nonshaft-driven gerotor pump with a permanent magnet motor.Voith designed a fully integrated ePump based on an internal gear pump and an alternating current (AC) induction motor, with the advantage of reducing the size by 50% as compared to nonintegrated units. 9Zhu et al. 10 have designed and experimentally validated the performance-integrated fixed displacement axial piston machine with a brushless direct current (DC) motor.Zappaterra al. 11 integrated a permanent magnet synchronous machine (PMSM) motor with an external gear pump based on an air-cooled solution.Pietrzyk et al. 12 designed a high-speed internal gear pump suitable for an electrohydraulic actuator.
Efficiency comparisons between the combination of a servomotor with different pump architectures (gear pump and piston pump) implemented on an electrohydraulic forklift were studied in Minav et al., 13 showing the potential to improve the system's overall efficiency when using a PMSM.Efficiency comparison between a variable displacement hydraulic pump and a variable speed electrical motors at different pressure levels are shown in Helduser 14 and is further extended to include a working drive cycle specific to an injection molding machine, demonstrating the potential of energy savings, specifically when idling is part of a drive cycle.A study for injection molding machines studied five different types of electrohydraulic supply units (ePumps), concluding that the servomotor coupled with a fixed displacement pump (FDP) shows the highest potential of energy savings. 15Mattos 16 showed that using a variable frequency drive with an AC motor or PM motor can increase the efficiency of the unit for various industrial applications but it comes with a higher initial cost.
The cited works confirm the interest in ePumps and can be divided into two parts.The first is focused on the design aspects to reduce its size and mass, 10,11 or by operating at higher speeds to achieve the same goal. 12he second are studies regarding right selection of the best ePump architecture for a given application, which is key toward effective electrification of current hydraulic systems.However, the state-of-the-art studies [13][14][15][16] prioritized the unit efficiency and cost and ignored the ability to reduce electrical materials when changing the HM type (fixed vs. variable displacement).No comprehensive study known by the authors has been conducted to address what is the best supply unit to use and how the pump type can affect the use of electric materials for mobile hydraulics.As a summary, the past work did not address the possibility of reducing the ePump mass and size by smartly choosing the ePump architecture and properly sizing the EM for a working drive cycle.
Despite the wide range of EMs available in the market, three-phase squirrel cage induction motors represent, by far, the vast majority of the market EMs. 178][19] However, their efficiency, especially for low-rated power, and their power density are significantly lower compared to permanent magnet motors. 18Permanent magnet motors are used in high-performance drives with a wide range of rotational speed regulations.They have the highest energy efficiency of all EMs, the highest rated and maximum torque values per unit of mass and volume, and high torque overload. 20,21Furthermore, they have high performance with the ability to operate at a higher torque than the rated torque for a small interval of time, and precision of the drive control, which makes them suitable for motion control applications such as mobile machines. 22he PMSM can be categorized into two different types, the surface-mounted permanent magnet motor (SPMSM) and the internal permanent magnet motor (IPM), depending on the mounting of the magnets on the rotor.IPM exhibits relatively lower material costs, 23 whereas SPMSM machines offer notable advantages in terms of overloading capability.With surface magnets, short-term peak torques can surge to four to six times the rated torque, attributed to their low d-axis inductances. 24Additionally, superior surface cooling mitigates the risk of demagnetization stemming from elevated temperatures. 24or off-road vehicles, this means that surface-magnet machines with lower rated power could be used because many duty cycles include only short-time high peak loads, which could be sufficiently covered by a smaller EM with high overloading capability, 25 which can offset the lower material costs offered by IPM.
Due to the aforementioned advantages of the PMSM, the type of EM selected in this study is an inverter-fed surface-mounted PMSM.
Axial piston machines dominate the high-pressure hydraulic pump markets owing to their high efficiency, high reliability, and power density. 26,27Additionally, their ability to vary displacement during operation also allows for an efficient flow control architecture.Such a displacement control base has been widely used in displacement-controlled systems to eliminate throttling losses.
The general trend toward a more demand-based pump control combined with electrification has made axial piston machines a good choice for an ePump.

| Paper scopes
This paper discusses and provides guidelines on sizing and selecting the optimal ePump architecture based on UCs.The considered UC differs in the features near corner power, therefore the effect of "how close and often the ePump operates near corner power" is addressed.Critical points from the UCs are selected as input to EM optimization.For each UC, the ePumps architecture is compared in terms of efficiency, EM mass, volume, and heat losses based on two domains the electrical and the hydraulics domain.
The remainder of this paper is divided into the following sections.The overall procedure to choose the optimal ePump is summarized in Section 2. An overview and classification of electrohydraulic units suitable for off-road mobile machines is presented in Section 3. The representative drive cycles considered for sizing the ePump are introduced in Section 4. The HM sizing, based on considerations on scaling laws and power losses are presented in Section 5.The EM design methodology and the model assumptions are covered in Section 6. Important considerations concerning heat generation from the EM and HM are described in Section 7. The results are presented in Section 8, while Section 9 includes a discussion on the results achieved from this work, before the final paper conclusions.

| OVERALL PROCEDURE DESCRIPTION
The methodology utilized to determine the optimal ePump size and architecture is outlined in Figure 1.First, few simplified UCs for the hydraulic supply are taken into consideration to reflect diverse case scenarios, which can be typical of different vehicles.These representative drive cycles consider only critical points of the UC that the ePump must meet.For instance, these critical points can be the most frequent points of operation, the highest flow demand, and the highest pressure demand.The selected representative drive cycles are further addressed in Section 4. Second, the flow and pressure requirements of the representative drive cycle are used to size the HM, ensuring it meets the working performance, including the ability to achieve the flow and pressure requirements of the system.
An EM optimization tool (explained in Section 6) is then utilized to design an appropriate EM for the given application.It uses the selected operating conditions of pressure and flow rate, which have been properly converted into EM torque and speed, as input.The torque is dependent on the pump displacement, pressure drop across the ePump, and hydromechanical efficiency, as illustrated in Equation (1).The EM speed is reliant on the desired flow rate, the pump displacement, and its volumetric efficiency (2).When adopting different ePump architectures, the speed and torque requirements of the EM clearly change, as a consequence of the torque and the speed equations.Consequently, the optimal solution of the EM design is affected by the chosen ePump architecture Finally, to compare the efficiency and the cooling requirements, the main losses for the ePump are identified.The key components that are contributing to losses are the inverter, the EM, and the HM, as displayed in Figure 2, which also indicates the energy flow from the battery up to the useful energy delivered by the ePump.The HM losses are described in Section 5.The portions related to the inverter and the EM are clarified in Section 6.

| OVERVIEW OF THE EPUMP ARCHITECTURE
There are three main ePump architectures to meet variable demand for the hydraulic flow.The pump can be either fixed or variable displacement and the EM can be fixed or variable speed.The four possible combinations are fixed motor variable pump (FMVP), variable motor fixed pump (VMFP), variable motor variable pump (VMVP), and fixed motor fixed pump (FMFP).However, it is important to note that the FMFP architecture is not of interest in this study as it requires inducing higher throttling losses to control the system compared to the F I G U R E 1 Electrohydraulic machine optimal architecture decision steps.EM, electrical machine.other architectures.The three ePump architectures considered in this study are shown in Figure 3.The input "i" represents the component that can be controlled to change the displacement (in the case of HM) or speed (in the case of EM).The first is the combination of a fixed-speed PMSM with a variable displacement pump (VDP), in which the flow rate can be controlled by varying the pump displacement.The second combines a variable-speed PMSM with an FDP, in which the control of the flow rate is done by varying the motor speed.The last architecture is achieved by combining a variable-speed PMSM with a variable pump, in which the desired flow rate is achieved by finding the optimal combination of EM speed and pump displacement to minimize the losses.
Each of the three ePump architectures introduced requires a specific control device as illustrated in Table 1.While an inverter is required to vary the speed of the EM, several solutions for varying the displacement of a VDP on the basis of electrohydraulic control exist, for t = M + 1, M + 2, …, T. 26 For the FMVP, an inverter that converts the DC to AC voltage is still required but the commanded speed is held constant.This means only the pump displacement shall be controlled, which is simpler than controlling the VMVP architecture.Another note is in the FMVP's ability to recover energy, which requires a pump with overcentering capabilities.
As the paper will show, the optimal ePump architecture in terms of efficiency and size, as well as its design, can vary for applications even with the same nominal power.

| REPRESENTATIVE DRIVE CYCLE
A simplified example of an actual pump usage for a commercial off-road vehicle is represented in Figure 4 (left), which shows measured supply flow (Q) and pressure (p) at the supply derived from in-machine measurements over a UC, as shown in the right of Figure 4.The time plots should be used to identify key characteristic points to simplify the representation of the overall cycle, from the energy usage point of view.When selecting the EM, points with high pressure but short duration can be usually disregarded as PMSM EMs can handle higher temporary overloaded torques, as long as they are within 150%-170% of the nominal torque. 28nstead, for PMSM importance should be given to points with the highest continuous pressure that lasts for a longer duration (typically more than 5 s) and points corresponding to the highest flow rates.Notably, the depiction of operating points on the left side of Figure 4, where the x-axis corresponds to flow rate and the y-axis signifies pressure, now incorporates the consideration of operating time to ascertain the size of each bubble.This refinement becomes evident when examining the two prominent points at 250 bar and 83 L/ min, and the subsequent point at 125 bar and 99 L/min.These two significantly larger bubbles correspond to the dominant time domain points, signifying their pivotal role in the operational profile.
Importantly, these points are also critical in terms of speed and torque, with one representing the highest continuous torque required by the EM, and the other representing the maximum flow or speed demanded for the EM.Consequently, these points are judiciously selected to optimize the EM, leading to simplifying the drive cycle into these points in Figure 5.
Three different representative drive cycles were chosen to analyze the ePump performance as illustrated in Figure 5.These representative drive cycles are simplified versions of possible scenarios for mobile applications.Obviously, there is a multitude of drive cycles spamming across the multitude of existing off-road vehicles.Therefore, the three cycles considered cannot be representative of the entire off-road sector, but still are sufficient to highlight different utilization scenarios for the hydraulic supply unit.
Drive cycles 1 and 2 are representative of a centralized hydraulic system in which a single pump supplies multiple actuators.Energy recovery during overrunning load is not performed as the pump always operates in pumping mode.In contrast, drive cycle 3 reflects a case that includes instances of energy recovery, which could be the case of a decentralized system that uses a dedicated pump for one actuator subject to both resistive and overrunning loads.Figure 5 shows the critical operating points for each drive cycle, with the blue lines in the y-axis representing the maximum pressure the pump can achieve, and the x-axis showing the maximum flow rate.The intersection of the two lines represents the hydraulic corner power of the pump, which displays its maximum pressure and flow rate capabilities.
Drive cycle 1 is classified under the category of intermediate power requirements represented by two operating points.The first point is the highest pressure in the drive cycle, while the next point is the uppermost request of flow rate.
It is important to consider the points at which the drive cycle frequently operates, as they can greatly impact the overall efficiency of the ePump.Therefore, drive cycle 2 characterizes an application where the pressure and flow demands span the entire operating envelope of flow and pressure and is therefore represented by four points instead of two previously.Unlike drive cycle 1, here the highest pressure in the system is combined with low flow rate demand.This implies that the pump does not operate near the corner power.Drive cycle 3 is separated into two parts: (1) resistive operating region and (2) overrunning operating region.The overrunning loads consist of negative flow and positive pressure taking place in conditions such as lowering the boom of an excavator.It occurs at low pressure accounting only for the gravitational forces that are dependent on the boom weight, and higher flow rate due to the area differential of a hydraulic cylinder.

| Drive cycle energy efficiency calculation
This subsection defines the equations used to estimate the ePump energy efficiency based on the considered drive cycles.When the load is resistive, input power 1 represents the power supplied by the battery, and output power 1 is the useful power delivered at the pump outlet.In the case of overrunning loads, input power 2 is the recoverable power at the pump port, and output power 2 represents the recovered power to the battery.The energy efficiency of a drive cycle consists of resistive loads and overrunning loads according to Equation (3).If the drive cycle consists of only resistive loads then the input and output power 2 are equal to zero η

Ouput power Output power Input power
Input power

| HM
This study considers as a reference three commercial variable displacement axial piston units available in the current market.They are referred to as Unit A, Unit B, and Unit C. The three units have different displacements therefore; their characteristics are scaled to a reference displacement of 25 cc/rev unit called Unit D based on the scaling laws explained in Ivantysyn and Ivantysynova. 27he reference displacement of 25 cc/rev (Unit D) and speed are chosen to be able to satisfy the flow requirements of the representative drive cycles presented in Section 4. This displacement can provide a sufficient flow rate for mid-size construction machines such as skid steers, and mini excavators if it is used as a centralized supply system, and the size is suitable for a decentralized system (supplying one function) in case of larger machines such as mining machines, wheel loaders, backhoes, and so forth.
It is worth mentioning that the three considered units (A, B, and C) are chosen among popular units used in today's mobile applications (market brands not reported to avoid commercialism).These three units well adhere to the scaling law, supporting that such law is well representative of today's technology.The motivation behind selecting three units to derive a fourth one to be used as a reference allows for avoiding possible biasing of the results due to a peculiar choice of the hydraulic unit.The units' maximum displacement, operating speed regime, and maximum pressure are summarized in Table 2.
The scaled unit called D has a minimum speed of 1000 rpm and a maximum speed of 4000 rpm.The minimum speed is selected from the highest minimum speed allowable between the three prementioned units.The maximum operating pressure of Unit D is 350 bar, again estimated using scaling laws.
For pump losses, this study focuses on volumetric and hydromechanical losses as they are the most | 799 dominant loss in a pump.Losses in the hydraulic unit are the volumetric loss and the torque loss, 27 which are often expressed in terms of volumetric efficiency, representative of the flow loss Q s (4) and hydromechanical efficiency, representative of the torque loss T s (5).These losses can be expressed as a function of the working conditions where n is the EM rotational speed, β is the commanded pump displacement, p ∆ is the pressure drop across the pump ports, and V p is the pump maximum displacement.
The POLYMOD tool developed at the author's lab 29 allows the evaluation of volumetric, mechanical, and total efficiency for different pressures, speeds, and displacements according to Equations ( 4) and ( 5).The program relies on experimentally measured data for the three commercial units (A, B, and C).Therefore, the efficiency of Unit D is the average efficiency of the three scaled units A, B, and C, and it is illustrated for maximum and partial displacement in Figure 6.It is important to note that the pump cannot operate at speeds below 1000 rpm; therefore, efficiencies at these points are not displayed.Additionally, the efficiency decreases at lower displacements compared to full displacements, which can be visualized in Figure 6.The right map of Figure 6 corresponds to 20% displacement.The maximum efficiency of the pump is generally achieved at intermediate pressures and higher speeds.Since the current commercial pumps are usually optimized for operation with combustion engines as prime movers, they are often optimized at a speed range of 1800 and 2200 rpm.

| EM
The permanent-magnet AC machine supplied from a controlled voltage or current source inverter is nowadays a popular choice.This is because of a relatively high torque density (torque/mass or torque/volume) and ease of control relative to alternative EM architectures.
The magnetic field for a synchronous machine may be provided by using permanent magnets made of neodymium-boron-iron, samarium-cobalt, or ferrite on the rotor.In some motors, these magnets are mounted with adhesive on the surface of the rotor core (known as the surface-mounted synchronous motor) such that the magnetic field is radially directed across the air gap.In other designs, the magnets are inset into the rotor core (known as the internal permanent magnet-mounted synchronous motor).
A surface-mounted PMSM EM type is adopted in this research where a cross-section is represented in Figure 7.The individual parts of the EM, namely, the shaft, rotor, stator, winding, and magnets are represented.The optimal design of the EM is a multidisciplinary problem depending on the operating demands, material properties, geometric constraints, winding configuration, inverter control, and battery voltage.These diverse aspects have individual design variables key to the design of the EM.In this paper, the design parameterization based on Sudhoff 30 is used to define the EM.A genetic algorithm 31 -based multiobjective optimization methodology is used to design the EMs.The optimization methodology relies on a PMSM machine model proposed by Sudhoff. 32An analytical lumped parameter magnet equivalent circuit capable of predicting key performance parameters for each EM design such as the efficiency, thermal losses, and material mass for each EM design.
The two objective functions considered in this optimization (i) minimize the electromagnetic material mass and (ii) minimize the power loss.The total mass is the summation of stator and rotor lamination, permanent magnets, and copper winding conductors.The losses accounted for in the optimization can be classified into four categories as listed in Table 3: (1) stator loss, (2) machine core losses, (3) airgap losses, (4) inverter conduction losses, and (5) inverter switching losses.Table 3 summarizes the evaluation of the loss, where more explanation of these and other losses is provided in Section 6.1 The PMSM also has additional losses, such as rotor losses generated by induced eddy current in the steel shaft and permanent magnets.Herein, a distributed winding with two slots per pole per phase was used, resulting in rotor losses that were not significant when compared with the total machine loss, and therefore magnetic rotor losses are neglected in the machine design process.Instead, the rotor loss may be calculated using two-dimensional finite element analysis time stepping analysis after a design is complete so that the assumption of negligible rotor loss can be validated.
The design model of the PMSM is similar to what was presented by Sudhoff. 32For the reader's convenience, Figure 8 summarizes and shows the major areas of the model.
T A B L E 3 Losses calculations in the optimization.

Losses Evaluation
Total power loss P ( ) l

P P P P P
Resistive loss P ( ) Core loss P ( ) c Ferromagnetic analysis 32 Airgap losses (P ) When optimizing an EM, the user makes design decisions by choosing parameters and setting constraints in the optimization.The constraint categories are geometrical, electrical, mechanical, and magnetic.For brevity, only the main constraints and design choices are listed and justified below.
1. Aspect ratio: The aspect ratio is calculated as the ratio between the EM diameter and the length.An aspect ratio of one is selected, as it can be considered suitable for mobile machine installation.2. Pole pairs: A higher pole pair allows for more compact EM designs, albeit with diminishing returns.However, it increases the impact of encoder-related nonidealities.Therefore, the authors assume a six-pole pair as a compromise between these opposing factors in this study.3. Voltage: Choosing a higher voltage can have a significant advantage for an electrified vehicle in terms of reducing cable requirements and reducing the size of connectors and terminations.On the other hand, as the voltage is increased suitable semiconductors must be used, and suitable insulating systems and creepage and clearance distances observed.As a compromise, this work proceeds with 800 V as the reference voltage.This is set as the upper DC supply voltage limit within the optimization where v (ll,max) is equal to the battery voltage minus twice the forward voltage drop across the inverter.v (ll,pk,o) is the line-to-line peak voltage required by the EM at the input operating condition.4. ePump design choice: It is important to note that the results obtained in this study do not consider any geometrical constraints linking the two units, which may limit their applicability in cases where an integrated design solution is desired.5. Current density: Increasing the current density in the winding of the EM is equivalent to increasing its power-to-weight ratio, which is crucial in terms of space and weight for onboard applications.But at the same time, it increases the losses in the winding due to more current flowing inside the conductors.That leads up to an increase in the heat generation and rising temperature of the EM.The maximum allowable current density is constrained to 15 A/mm 236 after assuming that it is based on a liquid cooling solution 6. Mass: A constraint is defined to limit the maximum electromagnetic mass of the EM.The electromagnetic includes the mass of the stator and rotor laminations, magnets, and copper windings 7. Torque: The core loss causes a drop in the outlet torque of the EM.Therefore, the outlet torque needs to be corrected and is given by Equation (15).The constraint (16) ensures that the target torque at the operating condition is met (the corrected torque is higher or equal to the target torque) 8. Power loss limit: A constraint is set on the maximum allowable power loss as below 9. Materials: The type of steel used for the rotor and stator laminations is M19 with a mass density equal to 7402 kg/m 3 .The conductor material is copper with a mass density, electric conductivity, and current density limit equal to 8890 kg/m 3 , 59.6 MS/m, and 7.6 MA/m 2 , respectively.The type of permanent magnet is NdFeB N35 with a mass density equal to 7500 kg/m 3 .
All the previously prementioned design parameters, constraints, and some other parameters are tabulated in Table 4.

| Operating condition
The aforementioned design assumptions and constraints are kept the same for all the EMs optimized in this study, except for the operating conditions as they are dependent on the drive cycle choice as well as on the ePump architecture.Therefore, for a total of three drive cycles and three ePump architectures, six optimal EM designs are formulated, and they are labeled with the code EM1-EM6 as in Table 5.
As the primary goal is to show the potential for downsizing the EM, the VMVP uses the same EM designed by FMVP as the FMVP is designed for maximum speed.This permits the VMVP architecture to have the full potential of lowering the torque demand at the PMSM shaft by changing the pump displacement.For example, EM1 refers to the EM optimized for FMVP and VMVP architectures for drive cycle 1, and EM2 for the one optimized for VMFP.Each EM is optimized based on two operating conditions that represent, respectively, the highest torque in the drive cycle (point 1) and the highest flow in the drive cycle (point 2) obtained from Figure 5.These two points for each EM are tabulated in Table 5.To illustrate the point, for EM1, point 1 is considered at a fixed motor speed of 4000 rpm.The pump displacement at this point is calculated by taking into account the desired flow rate and the volumetric losses.Using the known pressure value of 250 bar from Figure 5 and the calculated displacement, the torque value of 107 Nm is obtained.The total loss of the EM per operating condition is equally weighted.For FMVP architecture, the speed of the EM is always set at 4000 rpm as it corresponds to the maximum speed of the HM.
One can observe that for the VMFP architecture, the pump displacement is constant.Therefore, the highest torque is always determined by the maximum pressure during the drive cycle.Instead, with a VDP, the highest torque does not necessarily correspond to the maximum pressure since it is also dependent on the pump displacement at that specific point of operation.Table 5 shows that whenever a VDP is used, the torque required at the EM shaft is lower when compared to the FDP scenario.Each EM is optimized to meet the cycle requirements of torque and speed at points 1 and 2 as listed in Table 5.
For each study, starting from EM1 to EM6 a large number of PMSM designs are available and sorted in a Pareto front based on an increase in design mass, as illustrated in Figure 9.In this study, the most compact design (design 1 in Figure 9) is selected.For each ePump architecture, the most compact EM-corresponding to the highest current density-was selected to evaluate what is the potential of each architecture for achieving the minimum size EM while maximizing energy efficiency.

CALCULATIONS
This section compares the heat generation of different ePump architectures based on two domains (electrical and hydraulic domain) to provide guidelines on the cooling requirements of the ePump.The cooling requirements are considered to estimate the amount of heat that must be handled by an external cooling system.The hydraulic domain encapsulates losses stemming from pump inefficiencies, which were previously discussed in Section 5 as volumetric and torque losses, as outlined in Equations ( 4) and ( 5), respectively.The electrical domain pertains to losses originating from both the inverter and the EM components.An in-depth investigation of inverter losses encompasses conduction and switching losses, comprehensively detailed in Table 3 and expressed by Equations ( 11) and (12).
Correspondingly, EM losses, encompassing resistive, core, and airgap losses, are outlined in Table 3 as well.
In both the hydraulic and electrical domains, it is assumed that all losses manifest as heat.Within the hydraulic domain, this heat emission contributes to a rise in the working fluid's temperature.For the EM, the heat loss rises the temperature of the copper winding, the permanent magnets, stator yoke, stator teeth, rotor yoke, and the inverter, which is undesirable because electronic components are sensitive to temperature rise.These diverse sources of heat generation within both domains are succinctly summarized in Figure 10.
Currently, the majority of off-road vehicles have a cooler installed in the return line, taking advantage of the fact that oil is a good heat conductor.Therefore, the designer can favor the architecture that requires less cooling power in the electrical domain, as this minimizes the modifications needed to implement a cooler for the electric domain in the machine.Minimizing the losses of the electric domain can also make the air-cooled cooling strategy more feasible for the electric and electronic components, particularly when water piping is not desirable.For example, having the EMs on an implement of a tractor would require additional connectors and long pipelines that add extra cost to the system.

| RESULTS
This section is divided into three subsections.First, it compares the mass and volume of electromagnetic materials for the three ePump architectures, which are sized based on the considered representative drive cycles.Additionally, it provides details regarding the corresponding ePump efficiency, power losses, and heat generation, encompassing both hydraulic and electrical components.Second, the second subsection delves into a comparison of the raw material cost for the EM components, based on the selected ePump architecture.Finally, it discusses the outcomes of the results.

| Comparative analysis of ePump architecture and performance
Results for drive cycle 1 are given in Figure 11.As can be seen, the variable pump architecture (FMVP) results in a higher volume than the VMFP but a slightly lower mass.This can be explained by the operation of the drive cycle near the corner power of the HM.The EM is optimized for two points as shown earlier in Table 5.The points data (speed and torque in Table 5) indicate that the variable pump does not reduce the required torque significantly.Point 1 in Table 5 indicates a maximum torque of 107 Nm, combined with a higher speed of 4000 rpm, when compared to VMFP with 113 Nm and 3650 rpm.The difference in efficiency for this drive cycle is around 4%, in favor of both the VMFP and the VMVP architectures.These results suggest the use of VMFP when drive cycles are concentrated in proximity of the corner power of the HM, or when the high pressure in the system is combined with high flow rate demand.
The results for drive cycle 2 with multiple operating points are summarized in Figure 12.The efficiency for the VMFP is higher than for the FMVP, as the pump operates at regions of low displacement combined with low pressure.In such regions, the efficiency is low for a VDP pump.In this scenario, the VMVP is more efficient because of the flexibility of adjusting the pump displacement and speed to maximize energy efficiency.On the other hand, the mass of the EM with the variable pump option is reduced by 44% and the volume by 30%, which can be a cost-effective solution when looking at the EM cost separately.It can also be a preferred solution when the space available for the EM or ePump installation is limited.In reality, a VDP requires slightly more space than a fixed pump, as the pump adjustment system might not require significant additional space.A VMFP does not require any control element on the pump side, which can be viewed as a simpler solution with slightly lower efficiency than a fixed motor variable pump.
Drive cycle 3 represented in Figure 13 has a similar result to drive cycle 2.The EM mass drops from 10 kg with a VMFP architecture, to 7 kg with the other two architectures, a similar decrease is also observed in EM volume.The efficiency of the VMVP is still the best as compared to the other two architectures, but the difference is still small at less than 4%.The VMFP shows a higher efficiency when compared to FMVP architecture.
For all the drive cycle results (Figure 13), the HM heat generation is higher when looking at the FMVP architecture as compared to the other two architectures.Instead, the EM losses go down when compared to architectures with variable-speed motors.This distribution of the losses gives an insight into the consequences of the architecture choice for the ePump when considering the sizing of the cooling systems based on the architecture.As EM losses are lower in the FMVP architecture, this means that the current density of EM can be increased (i.e., more power density), or the cooling fluid flow rate can be decreased.By choosing the FMVP architecture, the designer can shift the power losses from the hydraulic domain to the electrical domain and vice versa.
To illustrate the variations in the chosen EM sizes, specifically their diameter and length, Figure 14 displays cross-sections of each EM.For instance, by comparing the cross-sections of EM3 and EM4 in Figure 14, one can easily visualize the differences in EM volume based on the chosen architecture presented in Figure 12.

| Architecture selection effect on EM raw material cost
A large number of variables contribute to the cost of an EM so it can only be approximated in this paper because it depends on the following factors 37 : (1) the number of EMs manufactured on a yearly basis of the same type, mass manufacturing allows for reducing the cost; (2) the cost of labor varies depending on the country; (3) quality of the used materials; (4) organization of production (overhead costs, company culture, productivity of employees, etc; (5) the manufacturing equipment, and the adoption of automation boosting the production capacity per year.
An acceptable approach is to identify the most important parts that contribute toward the total cost and express them as a function of the motor dimension, which can be expressed as the following equation: where K N ≤ 1 is the coefficient depending on the number of machines manufactured per annum, C w is the winding cost, C c is the cost ferromagnetic core and the auxiliary components such as the bearings, frame, end disk, and so forth.C PM is the cost of the permanent magnets, C sh is the cost of the shaft, Co represents the parts is the cost of the parts are independent of the size of the motor including the encoder, nameplate, and terminals lead can be neglected when comparing the different architectures assuming that these are essential, and their cost will not vary based on the motor size The cost of winding 18 is The cost of the PM and the shaft is, respectively, where k sp is the packing factor, k ii is the fabrication cost of coils including placing them in the stator slots and insulation materials, ρ cu is the specific mass density of copper, c Cu is the cost of the copper per kg, V sp is the space designed for the winding in the stator slots, V sh is the shaft volume, ρ steel is the specific mass density of steel, c steel is the cost of the steel bar, and k m is the coefficient accounting for the machining cost.Even though the equations to estimate the cost of the motor are stated in this study, to simplify the analysis, only the electromagnetic material cost is compared in this study.
The cost comparisons suggest that the use of FMVP architecture in cycles in which the pressure occurs at low flow rates has the potential to cut the electromagnetic raw material cost by up to 35%.This is the case for drive cycle 3 comparing the cost of EM5 and EM6.This cost reduction by the FMVP is nonexistent if the cycle is operating near the corner power point, as observed in drive cycle 1 when comparing the cost of EM1 and EM2.
Table 6 shows a comparison of raw costs for the different pre-designed EMs.The cost comparison results suggest that the use of FMVP architecture in cycles in which the pressure occurs at low flow rates has the potential to cut the electromagnetic raw material cost by up to 35%.This is the case for drive cycle 3 when comparing the cost of EM5 and EM6.This cost reduction by the FMVP is nonexistent if the cycle is operating near the corner power point, as observed in drive cycle 1 when comparing the cost of EM1 and EM2.
In Table 6, the cost comparison for electromagnetic materials is represented in unitless values to ensure currency independence and to account for potential changes in electromagnetic material prices over time.
The cost comparison results suggested that the use of FMVP architecture in cycles in which the pressure occurs at low flow rates has the potential to cut the electromagnetic raw material cost by up to 35%.This is the case for drive cycle 3 when comparing the cost of EM5 and EM6.This cost reduction by the FMVP is nonexistent if the cycle is operating near the corner power point, as observed in drive cycle 1 when comparing the cost of EM1 and EM2.

| Discussion
The primary outcomes of this study can be summarized as follows: 1.If operating continuously near the corner power as in drive cycle 1 shown in Figure 5, the VMFP is the best architecture of choice.This is because, in this case, the FMVP would not benefit from reducing the required torque to meet the operating condition as was listed in Table 5, and its efficiency is lower than the VMFP as illustrated in Figure 11.The comparison of the two motors, EM1 (182) and EM2 (179), as displayed in The cost comparison results, suggested that the use of FMVP architecture in cycles in which the pressure occurs at low flow rates has the potential to cut the electromagnetic raw material cost by up to 35%.This is the case for drive cycle 3 when comparing the cost of EM5 and EM6.This cost reduction by the FMVP is nonexistent if the cycle is operating near the corner power point, as observed in drive cycle 1 when comparing the cost of EM1 and EM2.Table 6 reveals that their costs are very closely matched.2. When instances of high pressure occur at low flow rates, as in drive cycles 2 and 3 (not operating near the corner power), a VDP (FMVP) can allow downsizing of the EM mass and volume up to 40% as be seen in both Figure 12 and Figure 13.Consequently, a reduction of cost for the electromagnetic material (up to 35%) can be achieved, for example, when comparing EM5 and EM6 costs in The cost comparison results suggested that the use of FMVP architecture in cycles in which the pressure occurs at low flow rates has the potential to cut the electromagnetic raw material cost by up to 35%.This is the case for drive cycle 3 when comparing the cost of EM5 and EM6.This cost reduction by the FMVP is nonexistent if the cycle is operating near the corner power point, as observed in drive cycle 1 when comparing the cost of EM1 and EM2 (Table 6).However, the drive cycle efficiency can suffer (up to 6% reduction) as compared to the VMFP configuration as observed in Figures 12 and Figure 13. 3. The VMVP architecture shows a marginal energy efficiency advantage (less than 4%), compared to the VMFP configuration.Consequently, considering its more complex control complexity, its adoption is not justified.This is particularly true for cycles like drive cycle 1, where it cannot even reduce the size of the EM. 4. Having a VMFP will result in higher losses in the electrical domain when compared to the FMVP and the VMVP architectures which is true for all types of | 807 drive cycles 1, 2, and 3 as the results of Figures 11, 12,  and 13.This is because the VMVP tends to have more hydraulic losses, as a VDP has lower energy efficiency at low displacements as depicted in Figure 6.

| CONCLUSIONS
The paper presents a study pertaining to the impact on losses and energy efficiency of different ePump architectures.The study considers a given design for the HM, carefully selected from commercial units that follow known scaling laws, and it optimizes the EM by considering the features of the duty cycle of the application.To this end, three simplified duty cycles are considered.The first two cycles represent a centralized hydraulic system where a single pump supplies multiple actuators without energy recovery during overrunning load.The third cycle represents a decentralized system with energy recovery, using a dedicated pump for one actuator subject to both resistive and overrunning loads.
The paper builds on a consolidated EM design methodology previously presented by one of the authors and introduces generic guidelines to select the appropriate ePump architecture for flow-on-demand applications.The original contribution is to provide a designed methodology that helps select the optimal architecture to meet application requirements.The study considers three architectures: FMVP, VMVP, and VMFP.The FMVP adjusts the pump displacement to achieve the desired flow, the VMVP optimizes both the pump displacement and motor speed to maximize unit efficiency, and the VMFP varies the motor speed to meet the required flow rate.The proposed methodology provides insights into the design of future ePumps for a range of applications.
In conclusion, the study highlights that the VMFP architecture proves advantageous when operating continuously near corner power, while the FMVP design offers significant downsizing potential and cost reduction for scenarios involving high-pressure occurrences at low flow rates.The VMVP architecture's minimal energy efficiency gains and increased complexity discourage its adoption.

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I G U R E 4 Mobile drive cycle based on measurements Q-p plot (left) and time measurements (right).F I G U R E 5 Representative drive cycles of mobile machines.

F I G U R E 6
Efficiency map of Unit D at full displacement (left) and efficiency map of Unit D at partial displacement of 20% (right).

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I G U R E 7 Cross-section of a sample permanent magnet synchronous machine.

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Electric motor design methodology.

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I G U R E 9 Permanent magnet synchronous machine optimization sample pareto-optimal front.F I G U R E 10 Heat losses flow diagram.

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I G U R E 11 Drive cycle 1 architecture comparison results.EM, electric machine; FMVP, fixed motor variable pump; HM, hydraulic machine; VMFP, variable motor fixed pump; VMVP, variable motor variable pump.F I G U R E 12 Drive cycle 2 architecture comparison results.EM, electric machine; FMVP, fixed motor variable pump; HM, hydraulic machine; VMFP, variable motor fixed pump; VMVP, variable motor variable pump.

F I G U R E 13
Drive cycle 3 architecture comparison results.EM, electric machine; FMVP, fixed motor variable pump; HM, hydraulic machine; VMFP, variable motor fixed pump; VMVP, variable motor variable pump.F I G U R E 14 Electric motor size comparison based on drive cycle.

T A B L E 6
Abbreviation: EM, electric machine.
Electrohydraulic machine architecture for mobile machines.FMVP, fixed motor variable pump; VMFP, variable motor fixed pump; VMVP, variable motor variable pump.