# Model-Based Performance Analysis of a Hybrid Summation Drive Used in Off-Highway Vehicles

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## Abstract

High power density, wide speed range and overall good efficiency are the primary demands of a modern hydrostatic transmission used in heavy earth moving machineries (HEMM). Conventional hydrostatic drive consisting of a displacement controlled pump and motor is sometimes inadequate to meet such requirements. Therefore, there is a need for examining alternative concepts of drives for HEMM. This article studies one of such alternatives where the motors are connected in parallel. In another solution, one motor is permanently connected to the load and the other one is connected to the load through gear unit. The latter is used during high-torque, low-speed demand of the vehicle. The challenge with the concept is the reconnection procedure, where the disconnected motor is accelerated, synchronized to the main motor output speed and finally locked to the output shaft, all in fraction of a second. Two different principles for the reconnection are proposed: to control the connection using a disc-type clutch, or to control it from the fluid power system. The performances of the two systems are compared through bond graph model simulation with respect to pressure, speed and efficiency for the varying load demand usually catered by a HEMM.

## Keywords

Hydrostatic system Summation drive Single-motor mode Two-motor mode Bond graph Performance analysis## List of symbols

- \(a_\mathrm{dcv}\)
Port opening area of direction control valve

*C*Single-port energy storage capacitor element in bond graph model

- \(c_\mathrm{d}\)
The flow coefficient

- \(d_\mathrm{area}\)
The projected valve port opening distance

- \(D_\mathrm{p}\)
Main pump displacement

- \(D_\mathrm{m}\)
Motor displacement

- \(F_\mathrm{spl}\)
Solenoid force acting on the valve spindle

*I*Single-port energy storage inertial element in bond graph model

- \(J_\mathrm{ld}\)
Load inertia

- \(K_\mathrm{cl}\)
Bulk stiffness of the fluid at the clutch cylinder

- \(K_\mathrm{m}\)
Bulk stiffness of the fluid at the motor plenum

- \(K_\mathrm{p}\)
Bulk stiffness of the fluid at the pump plenum

- \(K_\mathrm{spl}\)
Spring stiffness of the solenoid valve spindle

- \(K_\mathrm{splh}\)
A high value of the spring stiffness of the solenoid spindle

- \(M_\mathrm{spl}\)
Mass of the solenoid valve spindle

- \(P_\mathrm{acml}\)
The constant pressure from the accumulator

- \(P_\mathrm{p}\)
The pump pressure

- \(P_\mathrm{ps}\)
The pump pressure corresponding to single-motor drive mode

- \(P_\mathrm{md}\)
Pump pressure of two-motor drive system

- \(P_\mathrm{ms}\)
Motor pressure of single-motor drive system

- \(P_\mathrm{md}\)
Motor pressure of two-motor drive system

- \(P_\mathrm{mp}\)
Motor pressure working as pump

- \(P_\mathrm{smp}\)
Sump pressure

- \(p_\mathrm{l}\)
Load momentum

*R*Single-port resistive element

- \(R_\mathrm{cv}\)
Clutch valve port resistance

- \(R_\mathrm{dcv}\)
Resistance of direction control valve

- \(R_\mathrm{lkgp}\)
Leakage resistance of the pump

- \(R_\mathrm{lkgm}\)
Leakage resistance of the motor

- \(R_\mathrm{lkgc}\)
Leakage resistance of the clutch

- \(R_\mathrm{ld}\)
Load resistance

- \(R_\mathrm{spl}\)
Viscous damping of the solenoid valve spindle

- \(R_\mathrm{low}\)
Resistance of the relief valve at low pressure

- \(\rho \)
Density of the working fluid

- SF
Single-port source of flow element in bond graph model

- SE
Single-port source of effort element in bond graph model

- \(\dot{V}_\mathrm{dcv}\)
Flow through the direction control valve

- \(\dot{V}_\mathrm{s}\)
Theoretical flow supplied by the pump

- \(\dot{V}_\mathrm{lkgp}\)
Leakage flow from the

*pump*plenum- \(\dot{V}_\mathrm{lkgm}\)
Leakage flow from the

*motor*plenum- \(\dot{V}_\mathrm{p}\)
Volume change rate of the fluid at

*pump*plenum- \(\dot{V}_\mathrm{m}\)
Volume change rate of the fluid at

*motor*plenum- \(\dot{V}_\mathrm{mi}\)
Flow supplied to the inlet port of hydro-motor

- \(\dot{V}_\mathrm{mo}\)
Outlet flow from the hydro-motor

- \(\omega _\mathrm{m}\)
Motor speed

- \(\omega _\mathrm{p}\)
Pump speed

- \(\omega _\mathrm{m1}\)
Speed of the motor \(\hbox {M}_{1}\)

- \(\omega _\mathrm{m2f}\)
Speed of the motor \(\hbox {M}_{2}\) during free running

- \(\omega _\mathrm{md}\)
Load speed of double-motor drive system

- \(\omega _\mathrm{th}\)
Threshold speed value

- \(x_\mathrm{clp}\)
Contemporary displacement of the clutch plate

- \(x_\mathrm{clpmx}\)
Maximum displacement of the clutch plate

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