斜盘式轴向柱塞泵马达的负载和压力分析

1.

外文原文（复印件）

Load and Stress Analysis for the Swash

Plate of an Axial Piston Pump/Motor

M. Z. Norhirni

M. Hamdi

S. Nurmaya Musa

N. Hilman

Abstract

In an axial piston pump design, the swash plate plays an important role in controlling the

displacement of the pump, especially in a closed loop system. In this paper, the axial piston pump

is incorporated into the design of a hydraulic regenerative braking system for hybrid vehicles.

The pump in this configuration should function in dual mode, as a pump and as a motor. For this

to occur, the swash plate should swing in two opposite directions. The swash plate presented

in this paper is designed for stability and ease of control. Analytical analysis of torque and forces

were conducted using MATLAB software to verify the motion of the swash plate. Furthermore,

finite element analysis was also carried out to evaluate the rigidity and stress in the system. The

analytical evaluation has shown that as the swash plate angle increases, the required control force

and

torque increase almost linearly. However, the change of the plate angle was found to have no

effect on the force exerted on the X-axis and the torque exerted on the Z-axis.

Keywords

: swash plate, axial piston pump, finite element analysis,

hydraulic regenerative braking, hybrid vehicle

Introduction

The

hydraulic

regenerative

braking

system

(HRBS)

is

a

mechanism

that

reduces

vehicle

speed

by

converting

some

of

the

kinetic

energy

into

potential

energy

by

storing

it

inside

a

hydro- pneumatic accumulator for future use [1]. The system is made up of four main components:

working fluid, reservoir,

pump/motor (variable-displacement, axial-piston type pump), and accumulator, to power a

vehicle at low speeds and to augment the gasoline engine [2]. Normally, when the driver presses

the brake pedal, friction force is applied on the disc brakes. In this situation, the

vehicle’s kinetic

energy is transferred as heat energy and wasted into the air. During braking, the hydraulic axial

piston pump installed in the system operates as a pump, extracting kinetic energy and storing it in

the accumulator. Supposing that the accumulator reaches maximum capacity before the vehicle

has stopped, conventional brakes are used to bring the vehicle to a stop. Whenever the vehicle

accelerates from stationary mode, pressurized working fluid discharges from the accumulator,

which in turn converts potential energy into kinetic energy directly to the driveshaft to move the

2

vehicle .

In order to make the system work and capture the kinetic energy, the hydraulic axial piston

pump has to store more energy and work in dual mode. However, most hydraulic axial piston

pumps available on the shelf are made with fixed displacementstatic control with small flow rate,

which are not suitable for installation in heavy vehicles. Furthermore, conventionally, axial piston

pumps work only in single mode

—

either as a pump or as a motor. Previous research conducted

on bent-axis piston pump showed that it is capable of operating in dual function. The bentaxis

piston pump=motor has been designed for hydraulic hybrid vehicles by the US Environmental

Protection Agency (EPA), Abuhaiba et al. [5]. Analysis and results have provided a useful guide

for design improvement. In an axial piston, the major part is the swash plate angle because it

determines the mode of the pump [6]. Variable displacements of the axial piston pump were

controlled by its swash plate angle; therefore, by varying swash plate angle, the flow and pressure

of an axial piston can be controlled.

In addition to the structural design of the swash plate, another important consideration is the

dynamic control of the system. The ability to dynamically control the swash plate angle would

increase

the

efficiency

in

supplying

variable

flow

rate

and

pressure

required

for

the

hydraulic

circuit. Zeiger and Akers

explain that it is necessary to have a mathematical model representing the equation of motion of

the swash plate in order to study the behavior of the swash plate actuation and control system.

The most important factor in the model is the torque on the swash plate about its pivot. Several

studies have been conducted to determine the control torque of the swash plate, mainly by

empirical test data or

numerical methods .

The numerical method of analysis is in the form of mathematical description of the torque

components, which enables the effects of different designs, tolerance variations, and varying

operating conditions on the torque characteristics . Based on the mathematical description, the

equation of swash plate motion can be written in a linearized form, thus the system for

controlling the pump output variables can be designed. The geometrical features of the pump and

the operating conditions both have significant effects on the torque load .

In addition,

Manring reported that bearing and actuator forces for the swash plate control

depend on the swash plate design. The forces and torque, which act upon the swash plate in three

dimensions, were considered for adequate control and containment of the swash plate during

machine operation. Likewise, the cradle-mounted design and the related applied forces on the

swash plate by the control devices have been the topic of study by past researchers .

This

study

presents

a

new

design

for

a

dual-mode

axial

piston

pump

which

can

be

3

specifically

used

in

HRBS

applications.

A

new

concept

for

a

dual

mode

axial

piston

pump

is

presented. This dual mode system can be incorporated into the design of a HRBS which requires

the capture and the subsequent release of the stored energy. For the dual mode system to function,

the

swash

plate

should

be

designed

to

angularly

turn

for

switching

between

pump

and

motor

mode. The general equations for the control and containment forces exerted on the swash plate

are

derived

through

the

general

equations

from

previous

studies

of

Manring .Additionally,

the

equations

for

the

actuator

forces

applied

on

the

swash

plate

design

are

also

derived.

These

equations could be used to obtain the control and containment requirements for any steady-state

operating condition

of any

pump

with

similar swash

plate design to

ensure the proper position

and

motion

of

the

swash

plate.

The

steady

state

and

mechanical

analysis

produced

by

the

MATLAB software are graphically presented. Finite element analysis was carried out to ensure

the design has high stability and durability to withstand the very high working forces within the

piston.

HRBS Principles

The regenerative braking system operation is straightforward. It receives input from the

throttle pedal and activates the operation through the intelligent control system.

In deceleration, when the driver steps on the brake pedal (slowing the vehicle), the braking

unit will be activated in pump mode. The vehicle then operates the braking unit and hydraulic

fluids from the reservoir will be transferred into a high-pressure accumulator and compresses the

Nitrogen gas inside. The braking unit provides normal braking and stores the waste energy.

During acceleration, when a driver presses the throttle pedal to accelerate the vehicle, the braking

unit will be activated in motor mode. The previously stored energy during braking is released

back to the vehicle. Pressurized hydraulic fluid will be transferred back into the reservoir through

the braking unit. Total energy needed from the engine is reduced. Hence, fuel consumption and

harmful emissions are also reduced.

Hydraulic Axial Piston Pump Design

Displacements for the variable-displacement axial piston pump were controlled by its swash

plate angle; therefore, by varying swash plate angle, the flow and pressure of an axial piston can

be controlled. The proper swash plate motion is related to the forces and movements acting along

the parts. However, during operation, reaction torque always acts on the swash plate about the

titling

shaft; it tends to rotate the swash plate to a position perpendicular to the drive shaft. This reaction

is directly proportional to the swash plate angle and is substantially independent of the drive shaft

rotational

speed

[6].

Therefore,

in

order

to

change

the

swash

plate

angle

during

operation,

the

plate must be moved

2

against the reaction force and torque.

Concept generation is based on the swash plate shape, volumetric shape, and its support

structure. All three concepts have stability and rotation feasibility. However, the support and

control structure located at one side for Concept 1 and Concept 2 will cause it to easily lose

control; thus, a weak support is created

which increases the possibility of it turning over. Concept 3 in Fig. 2 is chosen since it has a

hemisphere shaped body and a through-hole with an ellipse open-end for coupling with the shaft

to constrain the possibility of the swash plate revolving more than 20 deg. Prominent geometrical

features such as elliptical open ends with 20-deg ascent at both sides function as additional safety

regions in the event of failure in the revolving mechanism of the swash plate. The semicylindrical

support structure increases the swash plate stability and

functions as a guide for the rotational motion. The swash plate is mounted to the pump using a

circular supporting structure and is generally allowed to rotate about the Y-axis. A total of four

control pistons arranged symmetrically reduces the needed actuator forces. The piston is used to

control the turning angle of the plate, which determines the angular pump displacement.

Fig. 1 Third angle projection of swash plate design (a) hemisphere

shaped body (b) ellipse open-end

Mechanical Analysis

Load description

. The free- body diagram of the swash plate design is shown in Fig. 2. It shows

that forces and torque exerted by the piston control on the swash plate and the primed and

unprimed axes are spatially identical. The primed Cartesian coordinate system is attached to the

swash plate system. The only force exerted on the swash plate was from the piston reaction force

Fx acting along the X-primed axis. In addition, there are two torques, Ty and Tz, acting on the

swash plate. Friction is neglected in the analysis, and it is assumed that contact surfaces are well

lubricated. Therefore, no forces are exerted on the swash plate in the Y-primed and Z-primed

axes and no torque is exerted on the X-primed axis.

There are four applied forces to the swash plate by the control pistons, denoted as Fs1, Fs2,

Fs3, and Fs4. The control devices will exert a force on the swash plate in the direction parallel to

3

the pump shaft axis, which means that the control forces will act along the unprimed X-axis and

are generally located at a distance of L1 and L2 away from the X-axis. As the swash plate rotates

about the Y-primed axis, the control forces exerted on the swash plate at the X-primed and

Z-primed axes will also change. These forces and geometric relationships are shown in Fig. 2.

For the containment of the swash plate there are two forces, Fb1 and Fb2, exerted on the

swash plate supporting structure, located symmetrically on both sides of the Z-primed axis by the

dimensions L10 and L11. These forces are considered positive if they point toward the Y-primed

axis and considered negative if they point away from the Y-primed axis. The radial locations of

these

applied forces on the supporting structure are given by the dimensions ?

1 and ?

2, respectively,

and these angular dimensions can be either positive or negative.

Free-Body Diagram Analysis

Fig. 2 Free-body diagram of the swash plate

From Fig. 2, by only considering the steady state characteristics of the control and

containment, the total reaction force acting on the X-primed (Eq. (1)) and Z-primed (Eq. (2)) axes

is described in the following equations:

?

F

b

2

cos(

?

2

)< /p>

?

2

F

s

1

,

2

cos

?

?

2

F

3

,

4

cos

?

?

F

x

?

0

X _ primed:

F

b

1

cos(

?

）

2