A Virtual Laboratory for Understanding Hydraulic Hybrid Technology Introduction The rising price of gasoline and peaking of the world oil supply has led researchers to increased interest in hybrid vehicle technology. Hydraulic hybrid vehicle technology is an interesting alternative to the more ubiquitous electric hybrid. Hydraulic hybrids use an energy storage/power assist technology that is proving particularly promising for fuel economy improvement in delivery vehicles that make large numbers of starts and stops. The development of the hydraulic hybrid requires knowledge of engineering principles from a wide array of courses including fluid mechanics, thermodynamics, vibrations, and controls. The study of hydraulic hybrid technology can provide an engaging context for the understanding of these fundamental concepts. Several authors have presented simulations of hydraulic hybrid vehicles. Wu et al. developed a model for a series hybrid drivetrain and showed the potential for significant fuel economy improvements for an automobile following the Federal Urban Drive Cycle1. More recent work using the MATLAB/Simulink modeling tool has demonstrated the savings for both parallel2 and series3 hybrid technology incorporated into trucks. These simulations were based on model equations for hydraulic pumps and motors as presented by Pourmovahed et al.4 and Wilson5. A series of educational modules utilizing the MATLAB/Simulink platform was developed by Schumack et al. in order to reinforce principles of fluid mechanics and thermodynamics6. The heart of the hydraulic system is the pump/motor unit. The University of Toledo has developed a Hydraulic Hybrid Vehicle Laboratory and a set of undergraduate/graduate laboratory exercises centered on a hydraulic pump/motor test stand7. In order to provide students at institutions with similar learning experiences without the high hardware costs, a simulation has been created using the analytical and graphics capabilities of the data acquisition software LabVIEW. Developed at the University of Detroit Mercy, the simulation will be publicly available to interested academic users across the country. The remainder of this paper will describe the physical test stand setup, the governing equations, and the LabVIEW program and graphical user interface. Model validity will be demonstrated with actual lab data from a similar test stand. Finally, student lab handouts will be described along with expected results from the experiments performed in the virtual environment. Test Stand Description The hydraulic hybrid test stand is illustrated in Figure 1 using conventional hydraulics symbols. The pump and the motor are connected at far ends of the same shaft. An electric motor lies in the center of the shaft, and a torque sensor measuring the pump shaft input torque is situated between the electric motor and the pump. The simulation in LabVIEW simplifies the physical setup somewhat as shown in Figure 2. In the simulation the inlet to pump and the discharge of the motor are assumed to be connected to the sump; i.e., the low pressure side of the hydraulic circuit is at atmospheric pressure at all times in the simulation. The high pressure hydraulic line
from the pump to motor contains a high pressure relief valve, flow meter, and filter. These components are modeled with a single loss coefficient K as seen in Figure 2. For the pump tests described in this paper, the hydraulic motor essentially serves as the pump load.
Figure 1. Hydraulic circuit of the physical setup.
Figure 2. Schematic of the simulation model.
Both pump and the motor have the same configuration: bent axis, variable displacement, with axial tapered pistons designed for hydrostatic drives in open and closed circuits. The displacement is infinitely variable with a maximum displacement of 80 cm3/rev (4.88 in3/rev) and a maximum operating temperature of 115°C (240°F). The maximum operating speed drops at maximum displacement from 6150 rpm to 3900 rpm. The maximum torque that can be transmitted is 508.43 Nm (375 lb-ft). The temperature in the pump is maintained by supplying water to water jackets or by maintaining the temperature of the circulating hydraulic fluid. In order to record the inlet torque to the pump a rotary torque sensor is placed in the circuit with the help of an integral mounting base. It does not affect the torque or the speed of the shaft as it is contactless, having measuring capacities from 0.1 kNm to 1 kNm (0.85 to 8.85 klb-in). The sensor has a maximum speed of 7000 rpm with a maximum thrust load of 10 kNm (88.5 klb-in). The purpose of the electric motor is to augment the motor output torque. If all components in the system operated reversibly (without losses), the motor would operate the pump as a perpetual motion machine, provided both pump and motor had the same displacement. The electric motor thus serves to make up power losses and provide additional torque for the case where the motor displacement is less than the pump displacement (pump and motor displacements can be varied independently of one another). Even though the electric motor supplies the differential torque in steady state, it must be sized to run the system by itself during starting conditions when there is not enough pressure in the high pressure lines to drive the motor. The electric motor is a 3 phase AC motor with maximum rpm of 1780 rpm and a power rating of 112 kW (150 hp). The required electric supply is 440V at 60 Hz. The high-pressure fast response spring loaded relief valve is used to control the pressure in the high pressure line and protect components in the system. The maximum cutoff pressure of 41.368 N/mm2 (6000 psi) allows a maximum flow rate of 30 l/min (8 gpm).
Governing Equations and LabVIEW Programming The model described below assumes steady state operation. Pump equations: The volumetric flow rate – or discharge – through a pump is given by the following equation5:
Q p = ωD p − ΔQ p where ω is the shaft angular speed, Dp is the pump displacement, Qp is the pump discharge, and the leakage flowrate is given by Pp ΔQ p = Cs D p max μ where Cs is the discharge loss coefficient, Pp is the pump outlet pressure, Dpmax is the maximum pump displacement and μ is the viscosity of the fluid. The actual torque supplied to the pump is
T p =Pp D p +Cv μD p max ω where Tp is the actual pump torque and Cv is the torque loss coefficient. It is assumed that the terms Cs and Cv, both of which account for viscous losses5, are the dominant loss factors. Losses due to contact friction and pump inlet restrictions are ignored. Motor equations: Volumetric discharge of the motor is given by the equation
Qm = ωDm + ΔQm where Dm is motor displacement and Qm is motor discharge. The leakage flow is given by
ΔQm = C s
Pm Dm max μ
where Pm is the motor inlet pressure. The torque delivered by the hydraulic motor under a given pressure is given by:
Tm = Pm Dm − Cv μDmmax ω where Tm is the actual motor torque. Internal Pipe Losses:
Pressure drop and the velocity of the flow through the connecting lines are given as
Pp − Pm = V =
1 ρV 2 K 2
Qp A
where V is velocity of fluid in the hydraulic line connecting pump to motor, ρ is the density of the fluid, K is the total line friction loss coefficient and A is the line cross-section area.
Relief valve equation: The pressure drop across a spring loaded relief valve is given by the following equation:
Pm − Pc =
ksQr Cd π D A
2Pm ρ
where Pc is the relief valve cutoff pressure (set pressure), D is the pipe diameter, ks is the relief valve spring constant, Cd is an orifice coefficient (set equal to 0.61), and Qr is the discharge through the relief valve. There are two conditions that the system maintains at any given time in a steady state. The first is continuity of flowrate, and its form depends on whether the relief valve is discharging fluid. When Pm < Pc , Qp = Qm. This condition occurs when the motor inlet pressure is below the relief valve set point. On the other hand, when Pm ≥ Pc, Qp – Qr = Qm. The second condition is that at any given time the torque supplied to the pump is the sum of the electric motor and hydraulic motor torques: Τp = ∆Τ + Τm. LabVIEW programming: There are different ways to solve nonlinear simultaneous equations in LabVIEW, but the most effective way is to use the nonlinear Simultaneous Function Block in Zeros functions. The most important aspect in using this block is that it considers all numeric values in the equations as characters or strings. A major part of this programming is thus to convert the numeric values into strings and feed these strings in the equations sequentially using arrays and “for” loop nodes in LabVIEW similar to any other programming language. Some of the numeric values are variables and some are constants. The output from the Zeros functions is in the form of an array and is in the order of the array of unknowns. When the system pressure reaches the cutoff pressure the program displays the solution to a different set of equations which incorporates the relief valve equation. The program is also written to give the user the flexibility of using English or metric units. Figure 3 shows the front end of the LabVIEW interface.
Figure 3. Screen shot of the user interface in LabVIEW.
Validation of the simulation: The simulation is validated with the help of data obtained from the Environmental Protection Agency hydraulic system test laboratory in Ann Arbor, Michigan. Figure 4 shows the comparison of discharge at different pressures and a displacement of 1.306 in3/rev. Figure 5 shows the torque comparison at the same displacement. The generally good agreement between model and actual test results leads to confidence in the accuracy of the model. The constant values for Cv and Cs were determined from an analysis of EPA test results following the technique described by Wilson5. For the results shown below, values for Cv and Cs were 81741 and 4.06 × 10-9, respectively.
30
discharge (gpm)
25 lab@1000rpm
20
simulation@1000rpm lab@2000rpm simualtion@2000rm
15
lab@3000rpm simulation@3000rpm
10
5
0 0
1000
2000
3000
4000
5000
pressure (psi)
Figure 4. Pump discharge as a function of pressure rise across the pump for various angular speeds. The pump displacement is 1.959 in3/rev.
140 120
torque (ft-lbf)
100
lab@1000rpm simulation@1000rpm
80
lab@2000rpm simualtion@2000rpm
60
lab@3000rpm simulation@300rpm
40 20 0 0
1000
2000
3000
4000
5000
pressure (psi)
Figure 5. Pump torque as a function of pressure rise for various angular speeds. The pump displacement is 1.959 in3/rev.
Student Exercises The laboratory experience, which will be offered to fluid mechanics students for the first time during the summer of the 2008-09 school year, will be delivered in the form of a laboratory handout following the same format for experiments where students use physical lab equipment. The objectives for the lab are quoted below: A virtual laboratory computer simulation will be used to study positive displacement pumps. At the end of this lab, the student will have: •
Understood the fundamentals of positive displacement pump operation, including identification of significant dimensionless groupings.
•
Collected and analyzed data resulting in the generation of efficiency plots.
•
Explained the shortcomings of a virtual versus real laboratory experience.
The lab handout provides background covering the governing equations for positive displacement pumps, including a dimensional analysis showing that torque efficiency, ηT, and volumetric efficiency, ηV, are functions of the dimensionless term µω ∆p . Students are then given a test procedure to follow for the virtual test stand. The procedure consists mainly of having the students set the shaft speed and pump displacement, then adjust the motor displacement to collect pump torque and discharge data for various pump outlet pressures. After collecting the data from the virtual test stand and tabulating the results, students are required to perform some analysis, including plotting efficiency curves and discussing results. Finally, students are asked to give reasons why a computer simulation may differ from actual results. Figure 6 shows results from the simulation for a displacement of 1.959 in3/rev. To assess student learning, a set of quiz questions will be developed for the students to take after they hand in their lab reports. The lab handout and executable version of the simulation will be available to the general public at the Michigan-Ohio University Transportation Center website.
1 0.95 0.9
η
torque 0.85
volumetric total
0.8 0.75 0.7 0.0E+00
5.0E-09
1.0E-08
1.5E-08
2.0E-08
2.5E-08
µ ω / ∆p Figure 6. Laboratory exercise results: efficiency as a function of the nondimensional parameter µω/∆p at a displacement of 1.959 in3/rev.
Conclusion A computer simulation of a hydraulic test stand has been validated and will give mechanical engineering students the opportunity to learn about hydraulic pumps and motors in a virtual environment. Although the simulated laboratory apparatus was designed to mimic a particular setup, users have the capability to change other parameters that would be difficult if not impossible to change with a physical test stand given the limited time frame and resources typically allotted for an undergraduate lab course. Variables such as hydraulic line size, type of hydraulic oil, and pump/motor loss coefficients (to simulate other pump/motor models) can all be adjusted easily from the LabVIEW user interface. Future work will include comparison of the simulation with the actual test stand once it is operational and assessment of student learning after the initial offerings. The authors would like to thank Andrew Moskalik and Steve Mayotte of the EPA for their provision of test results and allowing us to witness tests in their facilities. We also are grateful for the Michigan-Ohio University Transportation Center for funding this work.
References 1.
2. 3. 4. 5. 6. 7.
Wu, P., Luo, N., and Fronczak, F.J., “Fuel Economy and Operating Characteristics of a Hydropneumatic Energy Storage Automobile,” SAE paper 851678, Society of Automotive Engineers, 1985. Wu, B., Lin, C-C., Filipi, Z., Peng, H., and Assanis, D., “Optimal Power Management for a Hydraulic Hybrid Delivery Truck,” Vehicle System Dynamics, 2004, vol. 42, nos. 1-2, pp. 23-40. Kim, Young Jae and Filipi, Zoran, “Simulation Study of a Series Hydraulic Hybrid Propulsion System for a Light Truck,” SAE paper 2007-01-4151, Society of Automotive Engineers, 2007. Pourmovahed, A., Beachley, N.H., and Fronczak, F.J., “Modeling of a Hydraulic Energy Regeneration System – Part I: Analytical Treatment,” J. of Dynamic Systems, Measurement, and Control, March 1992, vol. 114, pp. 155 – 159. Wilson, Warren E., Positive-Displacement Pumps and Fluid Motors, Pitman Publishing Corporation, 1950. Schumack, M.R., Schroeder, C., Elahinia, M., and Olson, W., “A Hydraulic Hybrid Vehicle Simulation Program to Enhance Understanding of Engineering Fundamentals,” 2008 ASEE Annual Conference Proceedings, 2008. Schroder, C., Elahinia, M.H., and Schumack, M., “Integrating Education and Research: Development of a Hydraulic Hybrid Vehicle Laboratory,” International Journal of Engineering Education, December 2008, 24(6): 1217-1228.