Thermal Management of Open and Closed Circuit Hydraulic Hybrids A Comparison Study

Thermal Management of Open and Closed Circuit Hydraulic Hybrids A Comparison Study Hyukjoon Kwon*, Nathan Keller* and Monika Ivantysynova* Maha Fluid Power Research Center, 1500 Kepner Dr., Lafayette, IN, USA* E-Mail: hkwon12@purdue.edu This paper presents a comparison study of the required thermal management of the open and closed circuit hydraulic hybrid system. The hydraulic and thermal system behaviour of the open and closed circuit systems were successfully modelled using a lumped parameter approach. The temperature of both open and closed circuit systems have been compared using different cooling conditions based on the UDDS driving cycle. The simulation results show that the open circuit systems have the potential to require smaller heat exchangers as compared to closed circuit systems. In addition, the open circuit system consumes less power from the prime mover and incorporates a smaller charge pump. Keywords: Hydraulic Hybrids, Open and Closed Circuit Systems, System and Thermal Modelling Target audience: Mobile Hydraulics, Energy Management, Design Process 1 Introduction Unstable oil prices and environmental concerns are driving the automotive industry to develop more fuel-efficient vehicles. The Hybrid Electric Vehicle (HEV) has been highly publicized and is a well-funded area of research and development. However, negative environmental impacts, costs related to the mining of rare earth metals, the toxicity of batteries and the challenges of providing low-maintenance and long-life batteries create continuous stumbling blocks for HEVs. Hydraulic hybrid vehicles (HHV) are not as publicized but have several key advantages over HEVs. The HHV uses low cost materials, such as steel and no rare earth metals are used in their construction. They are easy to manufacture, require little maintenance, and are capable of recovering large amounts of kinetic energy during braking events, which can be used at a later time to improve efficiencies. Although the hydraulic oil is a petroleum product, it can be recycled and is not as toxic to the environment as the batteries used in HEVs. In addition, HHVs have been shown to be more fuel-efficient than HEVs in studies from industry and academic institutions. The open and closed circuit series hybrids have clear advantages and disadvantages /1/. The open circuit hydraulic hybrid requires a small charge pump to supply the hydraulic unit control systems but does not supply a lowpressure (LP) system. The open-circuit system also does not require a LP accumulator because of the absence of a LP system. However, the closed circuit system requires both a charge pump and a LP accumulator. This simplifies the architecture of the open circuit system, thus decreasing the cost and weight. On the other hand, the open circuit system requires a larger reservoir than the closed circuit system because all hydraulic units are directly connected to the reservoir. In this study, the thermal management of open and closed circuit systems of hydraulic series hybrids are compared using mathematical simulations. Open and a closed circuit hydraulic hybrid transmissions (HHTs) are successfully modelled using a lumped parameter approach in MATLAB/Simulink, which accurately demonstrated power consumption and transmission performance. High fidelity empirically derived loss models of axial piston machines were used in the mathematical models. These loss models were developed at the Maha Fluid Power Research Center from highly controlled tests of bent-axis machines. Scaling laws were used to account for the different pump sizes. In addition to the hydraulic model, an accurate thermal model is developed using a thermodynamic approach. This study shows the advantages and disadvantages of open and closed circuit hydraulic transmissions. This includes the differences in system cooling requirements, transmission power consumption, reservoir size and the required number of hydraulic components. To ensure a fair and accurate comparison of the two architecture designs, high efficiency bent-axis axial piston machines are used as the pump and motors, and the unit sizes are the same in the open circuit as in the closed circuit system. The two different architectures incorporate the same loading conditions and are applied to the same drive cycle, thus making a fair comparison between open and closed circuit hydraulic transmissions. The hydraulic and thermal models also allow for an accurate sizing of charge pumps and cooler sizes, which are essential in minimizing parasitic power losses to the prime mover. 2 Open and Closed Circuit Series HHTs In this study, an open and closed circuit series HHTs with identical hydraulic units and high-pressure accumulator are chosen for comparison. In both systems, Unit 1 is a 100 cc bent-axis unit driven by the engine shaft. Units 2 and Unit 3 are both 75 cc bent-axis units that are connected to the rear and front axles, respectively. A 32 L High- Pressure (HP) accumulator is chosen for both systems. This size is chosen to capture much of the braking energy of the vehicle. Other hydraulic components were designed based on the system architecture requirements. 2.1 Open Circuit Series HHT Figure 1 shows the hydraulic schematic of an open circuit series HHT. In the open circuit system, the unit control pressure is maintained at 20 bar by a 5 cc charge pump. For thermal management, a recirculation pump is incorporated in the reservoir to provide flow through the cooler. The size of the reservoir is 60 L, which has been selected based on simulation results. 2.2 Closed Circuit Series HHT Figure 1: Hydraulic circuit of an open circuit series HHT. Figure 2 shows the hydraulic schematic of a closed circuit series HHT. A 27 cc charge pump is selected for maintaining a stable pressure in the low-pressure line. A larger charge pump is needed in a closed circuit system to resupply the system with the lost flow from the hydraulic units. A 42 L accumulator is needed in the lowpressure line to exchange flow with the HP accumulator during braking and acceleration events. The flow through 15

the pressure relief valve from Line B is sent through the cooler to reduce oil temperature. A reservoir volume of 40 L is chosen. The hydraulic units are the heart of hydraulic systems. Two main equations exist for the units, effective flow rate and effect torque. The effective flow rate and torque take into consideration volumetric and torque losses, respectively, which is present in the unit. The losses are applied depending on whether the units are in pumping or motoring modes. The below equations show how the volumetric and torque losses are applied to Unit 1. The hyperbolic tangent is used to determine how the volumetric losses are applied. This is based on the sign of the differential pressure across the unit. It is used as a continuously switch to prevent numerical errors within the mathematical solver. In this architecture, Unit 1 never enters motoring mode. Therefore, Unit 1 will deliver less flow than theoretical, while requiring more torque to rotate. QQ 1AA = VV 1 nn eeeeee QQ ss1 (0.5 + 0.5 tanh pp AAAA ) (1) QQ 1BB = VV 1 nn eeeeee QQ ss1 (0.5 + 0.5 tanh pp AAAA ) (2) 3 Modelling Approach Figure 2: Hydraulic circuit of a closed circuit series HHT. Figure 3 shows a block diagram of the modelling approach for the hydraulic and thermal model. The hydraulic system model is simulated with a drive cycle, system control, and vehicle dynamics to generate the flow rate and pressure data for the thermal model. The thermal model then utilizes the flow rate and pressure as input parameters for calculating the system temperature. The methods used for the system control, hydraulic system model, and thermal model are described in the following subchapters. MM ee1 = VV 1 pp AAAA (3) + MM 2ππ ss1 The dynamic effects of the volumetric and torque losses on the hydraulic units are captured using a polynomial equation derived from extensive and reliable empirical data. The data was collected from carefully conducted steady-state measurements from many of operating conditions to create a high-fidelity polynomial loss model. Below, both the volumetric and torque loss equations are a function of unit displacement, pressure differential across the unit and unit rotational speed. QQ ss1 = ff QQ ( pp, nn, ββ) (4) MM ss1 = ff MM ( pp, nn, ββ) Units 2 and 3 are modeled very similar to Unit 1. However, the losses are applied differently. When Units 2 and 3 are in motoring mode, they consume more flow than theoretical, thus the volumetric losses must be added to the theoretical flow rate. The effective torque is lower than theoretical due to frictional losses, thus the torque losses are subtracted from the theoretical output torque of the units. (5) QQ 2AA = VV 2 nn 2 QQ ss2 (0.5 + 0.5 tanh pp AAAA ) QQ 2BB = VV 2 nn 2 QQ ss2 (0.5 + 0.5 tanh pp AAAA ) (6) (7) Figure 3: Block diagram of the modelling approach for the hydraulic system and thermal model 3.1 Hydraulic System Model The hydraulic model is developed using a lumped parameter approach in MATLAB/Simulink. Each hydraulic component is modelled separately and then combined into a larger model to create the completed hydraulic system model. The hydraulic system model mainly consists of hydraulic units, accumulators, check and relief valves, vehicle dynamics and, perhaps most importantly, the pressure build-up for each control volume. This section will discuss the equations needed to successfully model the closed circuit HHV, but the same governing equations can be applied to many different hydraulic system models. MM ee2 = VV 2 pp AAAA (8) MM 2ππ ss2 The charge pump is modeled in a similar manner as Unit 1. The only difference is how the losses of the unit are determined. Since high-fidelity loss models of fixed displacement gear pumps are not readily available, constant efficiencies are assumed. From those efficiencies, the losses of the charge pump can be determined. MM ss,cchaaaaaaaa = VV CChaaaaaaaa pp (1 ηη 2ππ hmm ) QQ ss,cchaaaaaaaa = VV CChaaaaaaaa nn eeeeee (1 ηη vv ) (10) Auxiliary valves, such as check and relief valves, are modeled using a flow orifice equation. The flow through the orifice is dependent on the pressure differential, oil density and a flow coefficient. The flow coefficient encompasses the effective area and flow losses of the valve. This coefficient can be found using valve data provided by the manufacturer. QQ vvvvvvvvvv = CC vv 2 pp Perhaps the most important equation in the hydraulic system model is the pressure build-up equation. Essentially, the pressure build-up is a function of the net flow rate and capacitance of the control volume. The capacitance is found by dividing the control volume by the bulk modulus of the oil. One must be careful on sign convention to (9) (11) 17

ensure the pressure build-up is modeled correctly. The equations below show the calculations required for the pressure build-up of. CC HH,AA = VV AA (12) KK pp AA = 1 (QQ CC 1AA + QQ 2AA + QQ 3AA + QQ CCCCCC + QQ AAAAAAAA,oooooo QQ AAAAAAAA,iiii QQ RRRRRR ) (13) HH,AA The capacitance in the High Pressure (HP) accumulator is slightly more complicated to calculate because of the changing volume. The changing volume is calculated from the equation below and is derived from the ideal gas law. The HP accumulator only has two flow components that must be considered because of the enabling valve connected to the accumulator outlet. CC HH,HHHHHHHHHHHH = ( VV 0,HHHHHHHHHHHH ) ( nn (pp HHHH,AAAAAAAA ) (1+nn)) (14) 1 pp HHHH,AAAAAAAA = (QQ CC AAAAAAAA,iiii QQ AAAAAAAA,oooooo ) (15) HH,HHHHHHHHHHHH The control volume for Line B has significantly more capacitance than because the Low Pressure (LP) accumulator is always connected to the line. This is different from because the HP accumulator is not always connected to due to the enabling valve. Therefore, the changing capacitance of the LP accumulator must be added to the line capacitance to accurately model Line B. The open circuit model does not contain Line B or a LP accumulator. Therefore, this portion of the model is omitted. pp 0 CC HH,BB = VV BB KK + CC HH,LLLLLLLLLLLL pp BB = 1 CC HH,BB (QQ 1BB + QQ 2BB + QQ 3BB + QQ CCCCCC + QQ RRRRRR QQ CCCCCCCCCCCCCC ) (17) pp LLLL = 1 CC HH,LLLL (QQ CChaaaaaaaa QQ CCCCCC QQ CCCCCC ) (18) Vehicle dynamics are essential to load the hydraulic system model. Without the vehicle dynamics model, the system will not be able to track measurements or simulate system performance. The vehicle dynamics used are based on Newton s 2nd Law to determine vehicle acceleration, as shown below. The resistive forces are subtracted from the tractive, or applied, forces. The tractive force is calculated from the combined effective torque produced by Units 2 and 3. The resistive forces include aerodynamic drag, grading and rolling forces. The grading forces are the forces applied to the vehicle on sloped or graded surfaces. Both the closed and open circuit models use the same vehicle kinematics model to provide the same loading conditions. The equations below represent the vehicle dynamics model. FF TTTTTTTTTTTTTTTT FF RRRRRRRRRRRRRRRRRRRR = mmmm aa = FF TTTTTTTTTTTTTTTT FF RRRRRRRRRRRRRRRRRRRR mm FF TTTTTTTTTTTTTTTT = MM ee,wwheeeeeeee rrrr MM ee,wwheeeeeeee = (MM ee2 + MM ee3 )ii aaaaaaaa 1 nn (16) (19) (20) (21) (22) FF RRRRRRRRRRRRRRRRRRRR = FF DDDDDDDD + FF GGGGGGGGGGGGGG + FF RRRRRRRRRRRRRR (23) 3.2 System Control A controller is needed for the hydraulic system to appropriately simulate system performance and accuracy. The controller must be implemented in the model, regardless of whether or not a controller is needed on the physical vehicle. Sequential and secondary controls are used in the hydraulic system model. The sequential controller is used when the vehicle is accelerating without the aid of the HP accumulator. During these operating conditions, the vehicle is in a hydrostatic driving mode. The secondary controller is used when the vehicle is braking or accelerating with the use of the HP accumulator. The controllers are identical in both the open and closed circuit hydraulic system models. The sequential controller is simply a ratio of the theoretical unit flow rates. This is a feed-forward controller that does not account for the losses in the units. If needed, it is possible to include a small proportional gain with a feedback loop to more accurately track velocity. However, the simple feed-forward controller is sufficient for this work. The sequential controller is used when the vehicle is in a hydrostatic driving mode, which is when the HP accumulator is not connected to. The equations used for the sequential controller are listed below. QQ 2 + QQ 3 ffffff QQ ββ 1 = { QQ 1 (QQ 2 + QQ 3 ) (27) 1 1 ffffff QQ 1 < (QQ 2 + QQ 3 ) 1 ffffff QQ 1 (QQ 2 + QQ 3 ) ββ 2 = ββ 3 = { QQ 2 + QQ 3 (28) ffffff QQ QQ 1 < (QQ 2 + QQ 3 ) 1 A secondary controller is used when the vehicle is accelerating with the assistance of the HP accumulator or during braking events. The displacements of Units 2 and 3 are synchronized together and are calculated from the PI controller that compares the commanded and actual vehicle speeds. During acceleration events, the discharge rate of the HP accumulator is regulated through the use of a supervisory control that controls the output flow of Unit 1. However, Unit 1 is sent to zero displacement during braking events. This is so all flow can enter the HP accumulator instead of running over Unit 1. Finally, a supervisory controller is needed to create switching conditions between the different control modes. This supervisory controller must be capable of providing smooth switching between the control modes. A simplified control diagram can be seen in Figure 4. Figure 4: Secondary control of hydraulic system when accelerating with the HP accumulator. 3.3 Thermal Model The thermal model is based on the first law of thermodynamics. Figure 5 shows the block diagram of the energy transfer rate for the open circuit system. The temperature rate can be derived as follows: = 1 VV(cc pp ββ 2 TT KKKK) [φφ WW CCCC + mm iih ii mm eeh ee + ( ββ TTKKKK The detailed derivation process can be found in reference /2, 3/. h) (mm ii mm ee) + (pp ββ TT KKKK) ] (29) FF DDDDDDDD = 1 2 aaaaaacc dd AA dd vv 2 (24) FF GGGGGGGGGGGGGG = mm vvvvh gg sin θθ (25) FF RRRRRRRRRRRRRR = μμ rrrr ggmm vvvvh cos θθ (26) 19

The heat transfer of each hydraulic component is calculated based on a lumped parameter heat transfer model as in reference /2, 4/. The thermal properties of the materials are taken from the reference /5/, and properties of the HLP 32 hydraulic oil are obtained from /6/. Temperature dependent coefficients are determined based on the temperature dependent equations, which is given by: cc pp = cc 0 + cc 1 TT (34) kk = kk 0 + kk 1 TT (35) KK = (pp + bb) [ 1 aa ln (1 + pp bb )] (36) where cc pp is the isobaric specific heat, kk is the thermal conductivity, subtitles 0 and 1 mean the constants for the constant part and temperature-dependent part, respectively, and KK is the bulk modulus and a and b are the constants based on empirical data. The constants for the given equations are listed in Table 3. Figure 5: Block diagram of the energy rate balance The governing equation can be simplified for each control volume. For the hydraulic units, the control volume can be assumed constant, and the temperature rate equation can be obtained as follows: = 1 VV(cc pp ββ 2 TT KKKK) [φφ WW CCCC + mm iih ii mm eeh ee + ( ββ TTKKKK h) (mm ii mm (30) ee)] The energy in the accumulator is stored in the compressed gas by volumetric work. In the governing equation, the volumetric work term is erased with one of the terms and the temperature rate equation becomes as follows. = 1 VV(cc pp ββ 2 TT KKKK) [φφ + mm iih ii mm eeh ee + ( ββ TTKKKK h) (mm ii mm ee) ββ TT KKKK ] (31) There is no work performed and no volumetric change in the hydraulic lines. Therefore, the temperature rate equation can be simplified as follows: = 1 VV(cc pp ββ 2 TT KKKK) [φφ + mm iih ii mm eeh ee + ( ββ TTKKKK (32) h) (mm ii mm ee)] Since the pressure does not change in the oil reservoir, the temperature rate equation can be simplified, as shown below. = 1 cc pp [φφ + mm (33) iih ii mm eeh ee h(mm ii mm ee)] The cooler is used for the management of the temperature within the system. The cooling performance of the cooler is based on empirical data given by manufacturers. The cooling performance curve is assumed as a log function of the flow rate through the cooler. Figure 6 shows the cooling performance of the coolers used in this study. The cooler is activated when the input temperature of the cooler is less than 50 C to prevent excessive cooling, which consumes unnecessary amounts of power. Description Parameter Value Specific heat cc 0 1807 [J kg -1 K -1 ] cc 1 4.21 [J Kg -1 K -2 ] Thermal conductivity kk 0 0.135 [W K -1 m -1 ] kk 1 7.35E-05 [W K - ² m -1 ] Bulk modulus aa 0.0733 bb 999.93 [bar] Table 1: Properties and constants for the hydraulic oil The thermal model is divided into several control volumes based on the main hydraulic components in the system. Figures 7 and 8 show the control volumes for the thermal modelling of the open and closed circuit HHTs. Thermal behaviours of each control volume are calculated based on the governing equation discussed previously. Figure 7: Control volumes for thermal modelling of the open circuit HHT Figure 6: Cooling performance curves of the coolers used in this study (ΔT=10 C) 21

Figure 8: Control volumes for thermal modelling of the closed circuit HHT 4 Results and Discussion 4.1 Hydraulic System Model The hydraulic system model behaves as expected. The simulated and commanded vehicle speeds match very well for both the open and closed circuit system architectures. The commanded vehicle speeds are taken from the Urban Dynamometer Driving Schedule (UDDS), which is a standardized drive cycle for on-highway vehicles to compare vehicle performance and efficiency. More information about the UDDS cycle can be found from reference /7/. The pressure differentials across the hydraulic units for both the open and closed circuit systems are nearly identical to one another. This is because both system models contain the exact same vehicle dynamics and the simulated speeds are similar. This can be seen in Figure 9. However, the open circuit system operates at slightly lower pressures due to the lack of a low-pressure system. Figure 9: Hydraulic system modelling results for the open and closed circuit hybrids It is important to note that when the vehicle is braking, the braking energy is being stored in the HP accumulator. That can be seen as the HP accumulator pressure increases during braking events. Equally important is using the power available in the HP accumulator when the vehicle is accelerating. That can be seen as the HP accumulator pressure drops as the vehicle accelerates. Since the control strategies of the open and closed circuit systems are identical, then the displacements of the units are also identical. The consumed power of the closed circuit system is only slightly higher than that of the open circuit system. This can be attributed to the larger charge pump required for the closed circuit system. Another interesting result to consider is the accumulator state of charge. Notice that the HP accumulator in the closed circuit system does not capture as much fluid as that in the open circuit system. This is caused by the lower differential pressure of the closed circuit system when using the same value for the maximum system pressure. Therefore, the open circuit system in this comparison study can recover slightly more energy than a closed circuit system. 4.2 Thermal Model In order to study the thermal behaviour of the systems under investigation, the UDDS cycle is repeated five times. Figure 10 shows the drive cycle with simulated velocities for the open and closed circuit systems. The hydraulic system results from this driving cycle are used as input parameters for the thermal model. Since the purpose of this study is the comparison of the thermal management of two different systems, we chose a representative driving cycle instead of extreme driving cycles. The cooling system should be chosen based on the different extreme driving conditions including high torque situation such as a going uphill situation and also high speed situation. In our study, we focus the comparison of two different hydraulic systems and we just compared the required cooler for the given same driving cycles. Since the driving cycle we used is not an extreme case, the cooling system need to be larger for other extreme driving conditions. 23

require a smaller cooler size than the closed circuit system. One comment that the coolers used in this study is chosen based on a representative driving cycle for the comparison of different systems, not for the cooling system optimization, and thus the cooling systems need to be sized based on extreme conditions for choosing an optimal cooler for the systems. Figure 10: Driving cycle and simulation results for the open and closed circuit systems In the thermal systems, the hydraulic units are the main sources of heating up the systems. A cooler is installed for cooling down the systems and also the system is naturally cooled down with natural heat transfer of each hydraulic component. Figure 11 shows the system temperature without cooling for the open and closed circuit systems. Since the systems do not use a cooler, the temperature for both systems rises to over 100 C. The open circuit system shows a slightly lower temperature distribution than that of the closed circuit system. In the open circuit system, large amounts of flow circulate through the reservoir and this results in relatively large amounts of heat transfer through natural convection. Figure 12: System temperature with different cooling conditions 5 Conclusion In this study, the thermal management of the open and closed circuit HHTs has been compared based on simulation results. Open-circuit systems have the potential of not only requiring smaller heat exchangers for cooling the systems but also reducing the power consumption from the prime mover with a downsized charge pump. The open circuit systems also contain fewer components than equivalently sized closed circuit systems. Figure 11: System temperature without cooling The temperature in the closed circuit system increases at a slower rate than the open circuit system because the capacitance of the closed circuit system is significantly larger than that of the open circuit system. The capacitance is larger because of the presence of a LP system and a LP accumulator. Figure 12 shows the system temperatures with the cooling conditions shown in Figure 6. For both circuits, the system temperatures are sufficiently reduced with Cooler-2. The systems are slightly too warm with Cooler-1, and the systems are over-cooled using Cooler-3. Without cooling, the open circuit system has a slightly lower temperature distribution compared to the closed circuit system. The open circuit consumes less power and would 25

Nomenclature Variable Description Unit AA dd Frontal Area [m 2 ] cc pp Isobaric Specific Heat [J/kg-K] h Specific Enthalpy [J/kg] KK Bulk Modulus [N/m 2 ] MM Torque [N-m] mm Mass Flow Rate [kg/s] nn Angular Speed [rpm] pp Pressure [bar] QQ Volumetric Flow Rate [lpm] rrrr Wheel Rolling Radius [m] TT Temperature [K] tt Time [s] VV Volume [m 3 ] ββ TT Volumetric Thermal Expansion Coefficient [1/K] ηη Efficiency [-] μμ rrrr Coefficient of Rolling Resistance [-] Density [kg/m 3 ] φφ Heat [J] References /1/ Cross, M., Ivantysynova, M., Practical Considerations for Pump / Motor Selection in Hydraulic Hybrid Vehicles, In: 52 nd National Conference on Fluid Power, Las Vegas, USA, March 23-25, 2011. /2/ Kwon, H., Sprengel, M., Ivantysynova, M., Thermal Modeling of a Hydraulic Hybrid Vehicle Transmission Based on Thermodynamic Analysis, In: Energy, Vol. 116, pp. 650-660, 2016. /3/ Busquets, E., Ivantysynova, M., Temperature Prediction of Displacement Controlled Multi-Actuator Machines, In: International Journal of Fluid Power, Vol. 14, No. 1, pp. 25-26, 2013. /4/ Kwon, H., Ivantysynova, M., System and Thermal Modeling for a Novel On-Road Hydraulic Hybrid Vehicle by Comparison with Measurements in The Vehicle, In: ASME/BATH 2017 Symposium on Fluid Power & Motion Control, Sarasota, USA, October 16-19, 2017. /5/ Incropera, F. P., DeWitt, D. P., Fundamentals of Heat and Mass Transfer, Wiley, 2001. /6/ Oppermann, M., A New Approach for Failure Prediction in Mobile Hydraulic Systems, VDI-Verlag, 2007. /7/ The United States Environmental Protection Agency, https://www.epa.gov/emission-standardsreference-guide/epa-urban-dynamometer-driving-schedule-udds, visited on November 16, 2017. 27