HIGH-SPEED 4-WAY ROTARY ON/OFF VALVE FOR VIRTUALLY VARIABLE DISPLACEMENT PUMP/MOTOR APPLICATIONS

Transcription

1 HIGH-SPEED 4-WAY ROTARY ON/OFF VALVE FOR VIRTUALLY VARIABLE DISPLACEMENT PUMP/MOTOR APPLICATIONS Haink C. Tu Center for Compact and Efficient Fluid Power Department of Mechanical Engineering University of Minnesota Minneapolis, Minnesota Michael B. Rannow Meng Wang Perry Y. Li Thomas R. Chase Kai Loon Cheong ABSTRACT The application of switched mode control to hydraulic systems has the potential of decreasing component complexity, size, and cost. This is accomplished by enabling variable pump or motor functionality using a single on/off valve paired with a compact, inexpensive fixed displacement machine. A 4-way tandem rotary on/off valve is presented in this paper that extends a novel rotary valve concept (experimentally validated for pump applications) to hydraulic pump/motors. The pump/valve system is referred to as a Virtually Variable Displacement Pump/Motor (VVDPM) since the effective displacement of the system is variable and not the physical displacement of the pump itself. This paper investigates the design and efficiency of the proposed rotary valve when utilizing the VVDPM on a light weight powersplit hydraulic hybrid passenger vehicle that is driven over a standard federal drive cycle. Simulated VVDPM efficiency maps are presented for motoring and pumping and the cycle efficiency of an optimized VVDPM is compared to that of a typical bent axis unit. Vehicle fuel economy is also explored through simulation. INTRODUCTION Virtually variable displacement pump/motors (VVDPM) based on switched-mode control have the potential of approaching variable displacement pump/motor (P/M) efficiency using compact, inexpensive fixed displacement units paired with a single on/off valve. Assuming efficiency is acceptable, the reduction in size and cost of VVDPMs over traditional variable units increases the viability of low margin consumer products such as hydraulic hybrid passenger vehicles (HHPV). One such hybrid Address all correspondence to this author. Figure 1. Input coupled power-split HHPV. The proposed VVDPM will be designed for implementation as the speeder pump/motor. vehicle, shown in Fig. 1, is an input coupled power-split that is currently being developed by the Center for Compact and Efficient Fluid Power (CCEFP) at the University of Minnesota [1 3]. The two hydraulic P/Ms on the vehicle, labeled speeder and torquer, enable full engine management. The speeder, connected to the engine and wheels via a planetary gearset, is used to decouple the engine speed from the wheel speed. The torquer, in contrast, is connected to the engine via a fixed ratio and is used to manipulate the engine torque. This paper will study the impact of replacing a bent axis speeder P/M with a VVDPM when driving the HHPV over the combined EPA Urban and Highway drive cycles. For brevity, the torquer case is not presented here. A schematic of the proposed 4-quadrant VVDPM based on a 4-way tandem on/off control valve is presented in Fig. 2. The VVDPM has two modes of operation: 1) in the ON mode the

2 Figure 2. 4-quadrant 4-way tandem on/off valve controlled VVDPM. Bold lines (solid for volume A, dotted for volume B) indicate sections of the circuit that contribute to switched volume. on/off valve is in Position I and the VVDPM is operating at full displacement since the full P/M flow is transmitted to the system, and 2) in the OFF mode the valve is in Position II and the VVDPM is effectively operating at zero displacement since the inlet and outlet ports of the P/M are connected and no flow is transmitted to the system. If the on/off valve is pulse-widthmodulated (PWM) between its two positions, the effective displacement of the VVDPM can be controlled by the PWM duty ratio, i.e. the ratio of time per period that the valve is in Position I and the VVDPM is ON. The proposed VVDPM can be extended to 4-quadrant operation, defined as the ability to pump or motor bidirectionally, with the addition of a directional control valve (DCV in Fig. 2). Check valves A and B are included to limit pressure spikes at the outlet port of the P/M during valve transition while valves a and b are included to prevent cavitation. The 4-way valve based VVDPM offers several advantages in comparison to systems based on 3-way valves [4, 5]. The tandem position of the 4-way valve decreases compressibility losses by porting decompressing fluid to the inlet of the P/M during each cycle as the valve transitions from Position I to II. The 4-way valve also relocates the directional valve outside of the switched volume (volume between the P/M and on/off valve, see Fig. 2) so that the internal volume of the directional valve does not contribute to compressibility losses. This paper presents a new 4-way tandem rotary valve that extends the experimentally validated 3-way valve concept [6, 7] to the control of motors and P/Ms. Like its 3-way predecessor, the continuous rotary motion of the 4-way valve reduces actuation power compared to a conventional linear valve from a frequency cubed dependence (due to inertial forces) to a frequency squared dependence (due to viscous friction). With the reduction in actuation power, switching frequency and flow area can be increased simultaneously, thus increasing system bandwidth while reducing losses. An updated valve optimization procedure is presented that optimizes the rotary valve based on pump torque and speed trajectories taken from a vehicle optimization that minimizes the total drive train losses over the combined EPA Figure 3. Helical land rotary valve consisting of stationary valve sleeve and rotating/translating valve spool. Urban/Highway drive cycles [8]. The optimized valve parameters are then simulated using a dynamic model that extends the 3-way valve model [7] to the 4-way valve by modeling the pressure dynamics in the inlet and outlet ports of the P/M. Simulated VVDPM efficiency maps for motoring and pumping are presented and overall drive cycle efficiencies are compared with a typical bent axis unit. Vehicle fuel economy is also simulated. Concluding remarks are given at the end of the paper. 4-WAY TANDEM ROTARY VALVE DESIGN The helical land based rotary valve concept is presented in Fig. 3. The rotary valve consists of a two degree-of-freedom valve spool that rotates and translates inside of a stationary valve sleeve. The sleeve is integrated with a custom housing that replaces the stock housing of any fixed displacement P/M of interest. This is to reduce the internal volume of the valve and the associated losses due to fluid compressibility. The valve spool consists of two section types that are connected internally via an axial channel. The first type, labeled End section in Fig. 3, is typically used at the ends of the spool for axial pressure balancing. This reduces the axial positioning power requirements. These end sections are connected to ports on the sleeve at all times. The second type, labeled PWM section, features helical lands that perform the on/off switching as the spool rotates. The helical land partitions the spool into two flow paths that linearly vary in proportion with respect to its axis of rotation (see Fig. 4). As the spool translates inside of the sleeve with respect to the rhombic ports (Port A in Fig. 3), the fraction per revolution that the valve is connected to one flow path versus the other changes. This controls the valve s duty ratio. The rotary motion of the spool alternately switches the con-

3 Figure 5. Schematic of rotary valve external driving mechanism. R indicates rotating components and T indicates translating components. Figure 4. Top: 4-way tandem rotary on/off valve concept. Bottom: Open area profiles illustrating when Port D is connected to Port B or blocked and when Port A is connected to Port C or B. A r is the flow area of a single rhombic port and N is the total number of ports. nection of the sleeve s rhombic ports (Port A) between the two flow paths created by the helical land. This switches the rotary valve between its two positions at a PWM frequency that is proportional to the spool s angular velocity. To keep the spool intrinsically balanced, the sleeve contains N = 3 rhombic ports. Thus, N on/off cycles occur per revolution of the spool. An embodiment of the rotary valve that achieves the desired 4-way tandem functionality is illustrated in Fig. 4. Like-colored sections of the valve (dark gray, light gray) are internally connected via through holes. The spool contains two synchronized PWM sections that connect to Ports A and D on the sleeve. Two end sections connect to Ports B and C. In Position I (refer to Fig. 4), the spool connects Port D to Port B via the dark gray flow path. Similarly, Port A is connected to Port C by the light gray flow path. In Position II, Port D becomes blocked by the solid section of the spool (labeled black in Fig. 4). Port A becomes connected with Port B by the dark gray flow path while Port C, having been disconnected from Port A, remains unconnected. Rotary Actuation Method Several methods of actuating the rotational motion of the valve spool have been proposed. The simplest method, implemented successfully on a 3-way valve [6,7], is to fix the direction of flow through the spool and design the PWM and end sections as turbines. This approach, termed self-spinning, has several advantages: 1) the spool can be mechanically decoupled from the sleeve, thus eliminating force imbalances, and 2) actuation power is scavenged from the fluid stream, therefore eliminating the need for an additional actuator. For applications where the P/M shaft speed (and flow rate through the valve) is constant, self-spinning is attractive since the turbines can be optimized for a specific flow rate. However, for applications such as the HHPV where the flow rate through the valve varies, research has shown that selfspinning overly constrains the valve design and severely limits the valve efficiency [9]. An additional consequence of variable flow rate is that it causes the PWM frequency of the valve to fluctuate according to the flow rate squared. For the HHPV, this translates to a variable torque ripple on the vehicle. An alternative is to rotate the valve using an external actuator. Besides the efficiency and constant frequency benefits of external actuation, one additional benefit is bidirectional flow capability. For applications that require 4-quadrant operation, this eliminates the need for an additional rectifying directional valve and its added pressure drop, internal volume, and cost. A hydraulically actuated driving mechanism that decouples the rotary and translational sealing functions is presented in Fig. 5 [9]. The mechanism uses a rotating intermediate shaft that is fixed to translate with a sliding piston to separate the seals. The axial position of the mechanism is actuated hydraulically against a return spring based on the area difference between the spool and translating piston (D > D piston ). The rotary motion is actuated using an electric motor through the various couplings of the device. Primary Valve Losses Analysis developed for a 3-way rotary valve [6, 1] has shown that the majority of loss in the valve can be attributed to five sources: full-open throttling, transition throttling, compressibility, leakage, and friction. A diagram illustrating the sources and parameters affecting the losses is presented in Fig. 6. This section will provide a brief overview of the losses. For more details, please refer to earlier papers by the authors [6, 1]. Full-open throttling is due to pressure drops across the valve when it is fully open to Position I or II and subject to a flow rate

4 The leakage flow is modeled as laminar pressure driven parallel plate flow mapped to concentric cylinders [12] that is scaled by a CFD determined correction factor of 2.5. Friction due to the viscosity of the lubricating fluid in the clearance between the spool and sleeve is modeled using Petroff s Law [13]. Petroff s Law describes Newtonian shear stress between concentric cylinders with relative rotary motion. Valve Optimization The prototype valve is optimized to work with a donated 9.8cc fixed displacement bent axis P/M. The objective of the optimization, similar to the previous approach proposed by Rannow et al. [1], is to determine the VVDPM valve geometry that minimizes the total valve losses when implementing the unit as the speeder P/M in the HHPV transmission shown in Fig. 1: min{ [π open (x) + π trans (x) + π comp (x) + π leak (x) + π f (x)]dt} x cycle Figure 6. Primary externally actuated rotary valve power losses and their functional dependence on geometric and system parameters. Brackets indicate dependence of physical quantities on optimization variables. Q. The pressure drop across the torus pressure rail (P rail ) with cross sectional diameter D rail (see Fig. 3) is modeled as a minor loss that is proportional to Q 2 with a loss coefficient of 6. The pressure drops across the rhombic ports (P open ) and end sections (P end ) are modeled as orifices, and the pressure drops across the PWM sections (P PWM ) are modeled using a CFD generated semiempirical formula [11]. Transition throttling occurs when the rhombic ports become partially restricted when the valve is switching position. The energy loss per switch is estimated by integrating the instantaneous hydraulic power loss based on pressure drop and flow trajectories modeled using the orifice equation with a linear flow area profile. Compressibility losses are derived from the energy required to pressurize the fluid in the dead volumes of the valve (V A,V B ) from low to high pressure every cycle. A portion of this energy is lost when the fluid decompresses. Compressibility can be significant depending on the system pressure and PWM frequency due to the reduced bulk modulus of oil in the presence of air entrainment. A pressure dependent bulk modulus model with air entrainment (but no dissolved air) is used to model this loss. Leakage through the clearance between the spool and sleeve is a result of the pressure differentials across the sealing lands. x = [D,R w,r h,l s,l end,a out,c r,d rail ] is the optimization variable vector where D is the spool diameter, R w and R h are the rhombic port width and height, L s is the spool length, L end is the end section land width, A out is the end section flow area, c r is the radial clearance, and D rail is the cross sectional diameter of the torus pressure rail (refer to Fig. 6 for definitions). The speeder VVDPM speed (ω pm ) and torque (τ pm ) trajectories were chosen to match the optimal points for a typical bent axis P/M for a vehicle driving over the EPA Urban and Highway cycles with a working pressure differential of 21MPa. The optimal points were chosen based on an energy management and vehicle optimization strategy proposed by Cheong et al. [8] that assumes a generalized transmission from which optimal component sizes (gear ratios, pump displacement, etc.) are chosen to minimize total power train losses. Pump displacement is scaled assuming a fixed efficiency map based on normalized torque and flow. The valve optimization is subject to several constraints: 2R w R h = πd LN (1) κ = 4NR w πd 1 (2) x min x x max (3) f PWM Nω 2π (4) The first constraint, Eq. (1), forces the edges of the rhombic ports to be parallel with the helical lands where L is the spool s axial travel. This maximizes the orifice area gradient and minimizes transition losses. The second constraint, Eq. (2), states that the valve transition cannot exceed one cycle where κ is defined as the fraction per revolution that the valve is in transition. The third constraint, Eq. (3), is the result of lower and upper parameter

5 1 Speeder VVDPM overall cycle efficiency η h Cycle Energy (kj) Breakdown of speeder valve cycle losses Open Trans Comp Leak Fric f (Hz) PWM Figure 7. Top: Optimized VVDPM overall efficiency, defined as η h = cycle τ pm ω pm dt, plotted with respect to PWM frequency for 21MPa cycle (τ pm ω pm +π tot )dt vehicle working pressure differential. Bottom: Breakdown of losses. Table 1. Optimized speeder valve parameters for 4Hz PWM frequency and 21MPa vehicle working pressure differential. L s = 12mm, A out = 1mm 2, and c r =.13mm were driven to their respective parameter bounds in both cases. All lengths in mm and volumes in cc. D R w R h L end V A V B η h Optimal D Bound bounds. The final constraint, Eq. (4), is a frequency bound on the PWM frequency assuming the valve will be externally rotated. The valve optimization results for different PWM frequencies are presented in Fig. 7. The reported cycle efficiency includes P/M losses. Figure 7 reveals a linear drop off in efficiency as the PWM frequency is increased from 1Hz to 1Hz due to the dramatic increase in transition losses. While low PWM frequency is beneficial from an efficiency standpoint, high frequency is desirable to reduce torque ripple on the vehicle. Since the effects of PWM frequency on vehicle ripple is still under study, a PWM frequency of 4Hz will be considered for the remainder of this paper. Optimized valve parameters and efficiency at 4Hz are presented in Table 1. The true optimal valve is compared to one with an upper bound on the diameter. Since the efficiency difference is minor (1%), the 3mm OD spool will be analyzed due to its compactness an ease of manufacture. DYNAMIC SIMULATION AND EFFICIENCY STUDY This section provides an overview of the dynamic model used for simulating the proposed VVDPM. Pressure profiles, efficiency maps, and comparisons to a bent axis P/M are presented. Figure 8. Flow diagram of model including pump/motor and on/off valve. Arrowheads indicate positive flow directions. Solid dots indicate flow junctions or pressure connections. Inset illustrates leakage paths. Model Overview The proposed dynamic model is based on the pressure dynamics within the two internal volumes of the P/M (V A,V B ). Included in the model are the effects of fluid compressibility, the rhombic port and helical land geometry, and leakage across the major sealing interfaces. The simulation uses the same loss models described in the Primary Valve Loss section of this paper. Losses due to the fixed displacement P/M are included based on manufacturer provided efficiency maps. Simplifying assumptions include constant accumulator and tank pressures (P and P t ), no line losses, and no check valve dynamics (instant open/close). Figure 8 presents a flow diagram representing the VVDPM model. Flow subscripts indicate positive flow directions, i.e. Q AB is positive for fluid flow from Port A to Port B. Solid dots indicate flow junctions or pressure connections. Q cav,a and Q cav,b refer to the flows through the cavitation preventing check valves a and b in Fig. 2 while Q by,a and Q by,b refer to the bypass flows through check valves A and B that reduce pressure spikes during valve transition. Using Fig. 8, the pressure dynamics are: Ṗ A = β(p A) V A [ Q QAC Q AB Q by,a + + Q cav,a Q leak,ac Q leak,ab ] (5) Ṗ B = β(p B) V B [ QDB + Q AB Q Q by,b + + Q cav,b + Q leak,ab Q leak,b ] (6) The model is simulated in the Matlab/Simulink environment using a fixed step size of.2µs using the ODE3 (Bogacki-Shampine) solver. System parameters used in the simulation correspond to

6 5 Pressure (MPa) Pressure (MPa) Motor Figure 9. Pump 2 P P A 15 fw P B 1 P 5 P t Time (s) Speeder VVDPM pressure profiles for motoring and pumping (one cycle). VVDPM is operating at 4rpm and 5% axial travel. the HHPV and include accumulator pressure of P = 22.1MPa, tank/low pressure accumulator of P t = 1.4MPa, cavitation prevention check valve cracking pressure of.28mpa, and bypass check valve cracking pressure of P ck =.76MPa. The hydraulic oil properties used in the simulation include a density of 876kg/m 3, dynamic viscosity of.387pa s, and 5% air entrainment by volume and no dissolved air. VVDPM Pressure Profiles Simulated pressure profiles for the speeder VVDPM are presented in Fig. 9. During the time interval from.4s to.15s, the on/off valve is in Position II and the VVDPM is idling. Notice that the freewheel pressure (P f w ) decreases during motoring but increases during pumping. This is due to whether Port C or D is connected to the accumulator. During motoring for the shaft direction simulated in Fig. 9, the accumulator is connected to Port D while Port C is connected to tank. Since Port D is blocked in Position II, it is assumed that no leakage occurs. In contrast, there is leakage across the helical land from Port A (at the freewheel pressure) to Port C (connected to tank). When the VVDPM is pumping, the accumulator and tank connections become switched and there is now leakage from Port C into Port A, which raises the freewheel pressure. Another interesting feature of the pressure profiles is the relatively complex transition during motoring. This is because P B > P A when the VVDPM is acting as a motor and P A > P B when acting as a pump. When the VVDPM is freewheeling, it is acting as a pump: power is required at the shaft to force flow across the full open pressure drop of the valve. Therefore, when the VVDPM is motoring, P A and P B must change relative magnitude (i.e. P A P B changes sign) during every transition. This switch causes the additional transition effects seen in the top of Fig. 9. P/M Torque (normalized) P/M Torque (normalized) P/M Speed (rpm) (a) Motor valve efficiency P/M Speed (rpm) Figure (b) Motor overall efficiency 5 5 Speeder VVDPM efficiency maps for motoring. VVDPM Efficiency Maps The efficiency maps presented in this section correspond to a valve PWM frequency of 4Hz and an operating pressure differential of 21MPa. The mean efficiency for each point of the map is determined by dividing the total VVDPM output energy by the input energy over a time interval T avg. An interval of T avg =.25s (1 cycles at 4Hz) was used. The overall efficiency at each combination of speed and valve axial position is: η m = η p = T avg τ pm ω pm dt [ ] T avg (P Pt )(Q DB Q by,a Q by,b ) + π cav + π pm + π f dt T avg (P P t )(Q AC + Q by,a + Q by,b )dt T avg [τ pm ω pm + π pm + π f ]dt (7) (8)

7 P/M Torque (normalized) P/M Speed (rpm) (a) Pump valve efficiency Table 2. EPA combined Urban/Highway speeder cycle efficiency. Bent axis VVDPM (valve) VVDPM (overall) Table 3. HHPV cycle fuel economy over combined EPA Urban/Highway cycle. B indicates bent axis while V indicates VVDPM. In all cases, both speeder and torquer sizes are optimized. Baseline Speeder VVDPM Both VVDPM Torquer 12cc B 13.1cc B 15.3cc V Speeder 15.1cc B 22.4cc V 19.9cc V Mpg P/M Torque (normalized) P/M Speed (rpm) (b) Pump overall efficiency Figure 11. Speeder VVDPM efficiency maps for pumping. imately 5% (i.e. 9% to 85%) across the entire map for both pumping and motoring. When comparing the motor efficiency maps (Fig. 1) with the pump maps (Fig. 11), motor efficiency is typically 5% lower across all operating points with an additional drop off in efficiency at higher speeds. The lower motor efficiency is a consequence of transition losses. The bypass and cavitation preventing check valves, which reduce transition losses during pumping, are seldom active during motoring. This is because the intake side of the motor, initially at high pressure, must transition to tank pressure before the cavitation prevention check valves will open. Similarly, the outlet side, initially at tank pressure, must transition to the accumulator pressure before the bypass check valves will open. In contrast, during pumping the outlet side is already at high pressure, which triggers the bypass check valves at the onset of transition (likewise for the inlet side). These effects can be observed in the pressure profiles shown in Fig. 9. π cav = [(P t P B )Q cav,b + (P t P A )Q cav,a ] is the input power due to the cavitation preventing check valves. η m and η p represent overall motor and pump efficiency respectively. Valve efficiency can be calculated by simply omitting π pm, the power loss due to the fixed displacement P/M, from Eqs. (7) and (8). Efficiency maps comparing valve efficiency with overall VVDPM efficiency for the speeder are presented in Figs. 1 (motoring) and 11 (pumping). The efficiency maps are plotted with respect to the mean shaft torque averaged over the interval T avg normalized with respect to the maximum P/M torque τ pm,max = D pm (P P t ) 2π (where D pm is the fixed P/M displacement). This represents the corrected displacement fraction of the VVDPM. In comparing the valve efficiency to overall efficiency, the losses contributed by the fixed displacement P/M (a bent axis unit in this study) lead to a reduction in VVDPM efficiency of approx- Efficiency Comparison with Bent Axis This section compares the speeder cycle efficiency between bent axis P/Ms and VVDPMs. Overall vehicle fuel economy over the EPA combined drive cycle for a HHPV using different combinations of the two technologies is also compared. For the cycle efficiency comparison, the VVDPM will be compared to the bent axis P/M using the optimal bent axis speed and torque operating points that were used to optimize the VVDPM in the Valve Optimization section of this paper. The cycle efficiency is calculated by determining the losses from the overall VVDPM (or bent axis) efficiency map (π tot ) and dividing the total cycle output energy by the cycle input energy: η cycle = cycle,m (τ pmω pm )dt + cycle,p (τ pmω pm π tot )dt cycle,m (τ pmω pm + π tot )dt + cycle,p (τ pmω pm )dt (9)

8 cycle,m refers to operating points where the unit is motoring and cycle, p refers to operating points where the unit is pumping. The speeder cycle efficiencies calculated using Eq. (9) are presented in Table 2. The results show that losses from the fixed displacement P/M decrease VVDPM efficiency by 6% over the cycle. The bent axis P/M achieves 11% higher cycle efficiency, likely due to the chosen operating points (optimal for bent axis) as well as the additive nature of the rotary valve losses to the P/M losses. The impact of lower VVDPM cycle efficiency on vehicle fuel economy is investigated to assess the viability of implementation on a HHPV. To provide a comprehensive comparison, the VVDPM efficiency maps presented in this paper were input into the vehicle optimization code by Cheong et al. [8], which previously used bent axis maps, to determine the optimal drive train sizing. The HHPV cycle fuel economy is calculated by converting the total input energy required by the vehicle (losses plus cycle work) into fuel consumed using the heating value of diesel ( J/L). Full regenerative braking was assumed (i.e. no friction braking). The fuel economy for the baseline case plus cases where one or both P/Ms are replaced by VVDPMs is presented in Table 3. In all cases the P/M displacements are optimally sized. Results show that replacing only the speeder P/M with a VVDPM reduces fuel economy negligibly by.4mpg (.6%). However, when VVDPMs are used for both the speeder and torquer, the fuel economy decreases by 3.3mpg ( 5%) from the baseline case. CONCLUSIONS A novel 4-way tandem rotary on/off valve designed for use in virtually variable displacement pump/motors has been presented. This valve is an extension of a 3-way design that was limited to the control of hydraulic pumps. In addition to the valve concept, this paper has presented a case study of implementing the rotary valve VVDPM as the speeder pump/motor on a light weight input coupled power-split hydraulic hybrid vehicle. Simulated efficiency maps based on optimized rotary valve geometries have been presented that show that reducing transition losses is a key to enhancing VVDPM efficiency. For pumping, bypass check valves connected in parallel with the on/off valve to the system accumulator can provide significant improvements in efficiency. In contrast, there is currently no analogous technique for reducing transition losses during motoring. This void must be researched in order to increase the competitiveness of VVDPMs with competing variable P/M technologies. For the hybrid vehicle application explored in this paper where the P/M operating points were optimized for a typical variable bent axis unit, the VVDPM was not able to match the drive cycle efficiency of the bent axis machine. However, despite the lower cycle efficiency, replacing the speeder P/M with a VVDPM only results in a decrease in fuel economy of.4mpg (.6%). Replacing both P/Ms results in a slightly larger decrease of 3.3mpg ( 5%). Therefore, from an efficiency standpoint, VVDPMs are a viable alternative with the added benefits of potential cost and size savings. A prototype VVDPM is currently under development that will be used to validate the analysis presented in this paper. ACKNOWLEDGMENT This work is supported by the NSF funded Center for Compact and Efficient Fluid Power under grant EEC REFERENCES [1] Van de Ven, J., Olson, M., and Li, P., 28. Development of a hydro-mechanical hydraulic hybrid drive train with independent wheel torque control for an urban passenger vehicle. Proceedings of the 51st National Conference on Fluid Power, National Fluid Power Association, Milwaukee, WI [2] Sim, T., and Li, P. Analysis and control design of a hydromechanical hydraulic hybrid passenger vehicle. 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