MODELLING OF SERVO DRIVE SYSTEM WITH HYDRAULIC ���MULTI PISTON��� MOTOR
MODELLING OF SERVO-DRIVE SYSTEM WITH
HYDRAULIC “MULTI-PISTON” MOTOR
Jan Szlagowski,
Tomasz Miroslaw
M.Sc., Ph.D., D.Sc, Professor
M.Sc., Ph.D.
Warsaw University of Technology
BUMAR Ltd
Faculty of Automotive and Construction
11 Jan Pawel II avenue
Machinery
00-828 Waszawa, Poland
Institute OE Construction Machinery Engineering
tmiroslaw@bumar.com
84 Narbutta Str.
02-524 Warszawa, Poland
jan.szlagowski@simr.pw.edu.pl
Zbigniew ebrowski
M.Sc., Ph.D., Assistant Professor
Warsaw University of Technology
Faculty of Automotive and Construction Machinery
Institute OE Construction Machinery Engineering
84 Narbutta Str.
02-524 Warszawa, Poland
zbigniew.zebrowski@simr.pw.edu.pl
ABSTRACT
The great progress in computer hardware and software technique and technology changed the way of new product
designing. It concern not only new designing tools like CAD/CAM programs but also a new approach to creation process.
Additional stage of work appeared - the computer modelling. It helps us to find out mistakes at the very beginning. The
computer modelling helps to understand real physical process in machinery and verify the construction.
The complexity of computer models depends on destination and programs possibility. It is possible to base model on
physical equation and law, which are written in classical form of differential equation. Nevertheless, it is not easy to find
model of hydraulic motor which presents the conversion of oil pressure to torque.
In paper authors present their experience in modelling of servo-drive system with hydraulic piston motor with
MATLAB/SIMULING software use. The result of simulation and real tests are compared and discussed.
KEYWORDS
Computer modelling, hydraulic system, hydraulic piston motor
238
presented. This model was built with the use of
1.
INTRODUCTION
MATLAB/SIMULING. This software is very
The great progress in computer hardware and
common and it is often used for students teaching
software technique changed a way of new product
and training. In this paper the special attention is
designing. It concerns not only new designing tools
paid to the basic relation between torque, pressure
like CAD/CAM programs but also a new approach
and liquid flow especially in the hydraulic piston
to creation process. Additional stage of work
motor and servo-valve. The phenomenon of friction
appeared – the computer modelling. Before real
in valve and piston are taken under consideration
scaled model could be prepared for investigation the
and its influence on simulated system behaviour is
computer model should be built and tested.
presented. The result of simulation and real tests are
Preparing such model, we have to systematize and
compared and discussed.
verify our knowledge on system and understanding
2.
HYDRAULIC CIRCUIT MODEL
it [1]. It helps us to find out mistakes at very
beginning and therefore save a lot of time and
The well known and quite common hydraulic circuit
money. The computer modelling helps us to
what can be found in many basic books is presented
understand real physical processes in machinery and
in Fig. 1.
to verify used equation and relations. This can be
It consists of tank with oil, pump, valve and motor
used in designing control systems, especially
which are connected with pipe. For technical-
automatic ones. The modelling is particularly
hydraulic description of running process we use
important for designing heavy machineries, which
values like pressure and flow in special points
are rather expensive. There are many special devices
(especially on the input /inlet/ and output /outlet/ of
which are designed only for one application. The
these elements) [1–3].
special sensors net and feedback controlled
subsystems and systems are needed for them. The
computer model allows us to simulate and
investigate the future machinery behaviour under
various work, load and surrounding conditions. For
this reason the computer simulation is the most
efficient way to gain some experience.
motor
valve
The complexity of computer models depends
purpose and programs capability.
pump
Many computer programmes not only calculate
tank
values of equations but they can solve differential
equations. It is possible to use the equation and law
of classical physics, which are written in differential
Figure 1. Typical hydraulic circuit
form in time domain.
When we start to build computer model we would
There are many computer models of hydraulic plants
like to have a such model which mirror the shape
with actuators description in various literature. They
and connection of physical object. But in real object
allow to analyse oil pressure and flow. However it is
we have one pipe and at least two important values
not so easy to find model of hydraulic motor which
inside, which are pressure and flow for our first
concentrate on conversion of oil pressure to torque.
approach. For some others purpose we can add
Most of models are too simplified with omitting
temperature, density etc.
some important phenomena like for instance the
In modelling we can treat those values as a signals
friction problem or motor movement instability.
which pass through elements and parts of circuit.
In the next parts of this paper the model of
Some methods of modelling enable us to show the
hydraulic system with piston motor will be
transformation of signals. An example of such
239
model is presented in Fig. 2. We have three blocks
(semi-actual) input value. For short time interval the
and three signals. Two signals: F (force from Load)
difference between values in the following cycles
and p (oil pressure form pressure supplier) enter into
should be small, so the mistake coming from this
the Actuator and they are transformed into signal
method is negligible, and the equitation is much
“v” speed of piston movement.
easier to be solved. So the eq.1. can be replaced
with:
F
Load
un = f(an,cn,u n–1)
(2)
a, v
Actuator
The usage of such method allows replacing
complicated relation with quite simple one. It is
Pressure
supplier
possible to build a model of full hydraulic drive
p
basing on simple physic laws and equations.
In the Fig. 3 we can see that the pipe is represented
by block, which has two inputs and one output.
Figure 2. Simplified model of hydraulic system with
However if we need the value of flow in the pipe,
signal transformation
we will need another output from this block.
It is a very simple model, but the mathematical
So, the (natural) ‘one input – one output‘ block
description for real system can not be so simple. The
which represents the pipe (in Fig. 1), should be
“v” (speed) is the result of “a” (acceleration)
replaced with ‘two input – two output’ block: one
integration. This acceleration depends on F (load)
pair: input/output for pressure and another pair for
and p (oil pressure) on the actuator input (inlet). But
flow.
this pressure in turn, depends on pressure losses in
the pipes. These losses are connected with oil flow,
The example of the inner of such block is presented
which is proportional (roughly) to piston movement
in Fig. 4.
speed – “v”.
Therefore, if want to find the speed we have to use
pI
pO
+
quite complicated implicit function like [4]:
1
-
u = f(a,c,u)
(1)
* K
qI
qO
Its means that value of u depends on itself
This problem can be solved by the usage of more
sophisticated model (presented in Fig. 3) with some
Figure 4. Exemplary inner of pipe modeling block
kind of feedback signal [4].
In the similar manner we can model each hydraulic
Load
F
block with adding some inputs and outputs for other
a, v
kind of values (signals) like: mechanical – speed and
Actuator
torque (for motor), electrical – current (for electri-
Supplier
p1
Pipe
p2
cally controlled valves).
This approach to each element of the system gives
v
us following advantages:
– makes the modelling much more simple,
Figure 3. Model with back-loop structure
– results with homogenous model of system,
Additionally in computer simulation the calculation
– makes available all required values in their
is made in discrete time domain. It allows to use the
pure forms,
just calculated values (in the previous cycle) as the
– enables usage of basic laws and rules for model
building.
240
There are many programs which can help us to
pressure which appears on hydraulic supplier output
design and model systems. Some of engineers prefer
depends on oil flow resistance. When this resistance
to write simulating program themselves using such
decreases, the flow rises but it is limited by pump’s
common use software as C (Builder), Pascal
features. The kinetic parameters like position speed
(Delphi).
and acceleration, are related to dynamic parameters
(forces and torques). Of course some simplifying
3.
SUBJECT OF MODELLING
assumptions can be done, for instance:
3.1. Modelling matter
– constant output power of hydraulic supplier,
Described model is a shortened version of hydraulic
– linear relation between pressure drop and oil
drive of mini-excavator. This excavator was
flow through the hydraulic pipes (for expected
prepared for special use and very low stable speed
flow rate).
rotary was needed [5]. The idea was to use typical
driving system with slow rate radial piston motor
3.3. Model of System
which was supplied with oil though electronically
In this paper the model built in Matlab environment
controlled servo-valve. The encoder – (the senor of
is presented. It is quite common software which is
rotation angle) was the only sensor that could be
very often used by students and engineers. The
used as a feedback signal source [6].
MATLAB environment with SIMULINK graphic
As it was said at the beginning the analysis of
interface is a quite efficient tool for such challenge
system
behaviour
was
required
for
better
[7–9].
understanding and modelling. Model was used for
The general scheme of proposed model is shown in
control system design and algorithm analyses. This
Fig. 5.
methodology was much more effective and cheaper
than starting with real tests.
There are following blocks which represent main
functional elements of hydraulic drive system:
3.2. Task Analyses
position and speed regulators, hydraulic supplier,
The aim of this modelling was to build regulator
hydraulic drive, gear (coupler), load, position
which increase speed rate (rate the maximum to
sensors for motor and load. The structure of this
minimum stable speed) and makes this drive system
model can be changed with switches’ set-up. All this
more accurate. It was assumed that this widening of
blocks can be developed deeper – to a more detailed
stable speed range would be achieved by lowering
structure, right down to the simple mathematic
lowest stable speed given by producer. The lower
function, like relation between pressure drop and
stable speed should affect higher positioning
flow, piston position in relation to motor shaft angle,
accuracy. For this reason, a model which includes all
etc. This structure enables modification of model in
necessary elements (such as: regulators, supplier,
details of particular blocks, without any needs of
pipes, motors and load, which shows motor running
changes in other parts. All dynamic relations are
at slow movement speed) was needed.
modelled (described) with use of the differential
equations in time domain. This way was chosen
There are few important problems to be solved
because it is most natural for average engineers and
before modelling begins. The first one is to choose
it is also easier to analyse and to make direct
parameters which would be treated as the primary
comparison with results of real experiment.
and parameters which would be treated as derivate.
In real device all parameters influence each anthers.
It is one more of advantages of this software. If good
And changes stop when the device reaches the state
methodology is taken you can develop elements
of balance. It means that all load forces and torque
separately replacing them with more sophisticated
are balanced with forces produced by oil pressure.
version.
The flow of oil affects on pressure drop. The
241
Figure 5. Hydraulic driver system
Figure 6. Drive block “inside”
242
Figure 7. Model of radial piston rotary hydraulic motor
The most important part of this model is hydraulic
3.4. Model of piston motor
drive. The revealed driver block is shown in Fig. 6.
The main element of hydraulic drive is a hydraulic
The inlet and outlet pressure, and load torque are the
motor. The main problem in piston motor modelling
inputs signal, and the position (angular) of motor’s
is a coexistence and co-operation of linear and
shaft and flows of inlet and leakage are the output
rotation movement. The linear movement is
signals. The motor rotation angle is given to gear
converted to rotation and vice versa.
block, from where it gets input signal of motor load.
For instance the force created by pressure in one
In simplification the difference between motor load
cylinder, affects on movement all pistons and the
and propelling piston forces (and torques) cause
shaft of this motor. So it has to overcome friction
acceleration of pistons and shaft. Their speeds
forces which appear there. Of course motor rotation
changes, and changes motor flows.
can be also caused by external torque.
243
Another problem is lack of multiple valued function
The difference between simulation and real tests
which defines shaft position in relation to piston
arise from different time interval-simulation time
displacement. There are two shaft angular positions
was much shorten than real tests, so, we can notice
for almost all piston positions. But a such relation
the stroke movement instability.
exists in opposite direction. It is very easy to
calculate piston position basing on shaft rotation
angle.
The model of motor which considers these inter-
actions is presented in Fig. 7.
This model consists of identical blocks of motor's
cylinders. Inputs of these blocks are: shaft angle,
supplying pressure, propelling torque. Outputs are:
flows, torque generated in this cylinder and
propelling torque. All torques created in cylinders
are summed with external load, and result the torque
which propels all piston and shaft. So this torque is
given to the input of first cylinder. It is passing
through this cylinder but it is decreased by value of
piston movement resistance and inertia forces.
Result of this is passed to next cylinder input and so
Figure 8. Simulation result for control current linear
on to the last cylinder and farther to the shaft. The
changes from 0mA up to 10mA, next down to –10mA and
remaining
torque
affects
shaft
acceleration.
back to 0mA
Integration of it gives speed and again shaft angle.
Pętla histerezy charakterystyki w=f(u)
The shaft position is one of motor output signals. It
is given to gear block where the position of load is
1600
1400
given as well. The outputs of this block are: load
1200
1000
torque (which is given to motor input) and
800
600
propelling torque (passed to load input). This model
]
/
s
400
z
considers backlash between cogs. When difference
200
[
D
w
0
ć
ś
of motor and load position exceeds backlash the
o -350
-250
-150
-5 -2
0 00
50
150
250
350
k
d
-400
r
ę
cogs are strained and reaction forces appear. The
p
-600
created torques is proportional to radius of cog-
-800
-1000
wheels. Motor’s and load’s torques are in relation
-1200
-1400
which corresponds to gear rate.
-1600
sterowanie [dz]
4.
SIMULATION RESULTS VERSUS REAL
TESTS
Figure 9. Real tests result for control current linear
changes from 0mA up to 10mA, next down to –10mA and
The proposed way of modelling appears very
back to 0mA
effective. The results of simulation are in high
accordance with real test findings. An example of
The next picture (Fig. 10, 11) shows result of
simulation and real test for changes of servo-valve
simulation and real tests for stable movement with
coil current for both directions is shown in Fig. 8.
constant valve control current.
The result of simulation and real test for constant
We can observe high similarity between them. The
servo-valve current is shown in Fig. 9. We can see
difference is connected with gear fault (non centric)
that the characters of both registrations are similar.
which was simulated in the next step.
244
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[1]
Backe W. (2000). „What Will be the Future of Fluid
Power” Developments In Fluid Power Control of
Machinery and Manipulators, Fluid Power Net
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[2]
Guillon M. (1961). „Etude et Determination des
Systemes Hydrauliques” Dunod, Paris.
[3]
Kretz D. (1989). “Einfluss der Dynamik des
Servoventils auf den Regelkreis” Der Hydraulik
Trainer Band 2, Proportional- und Servoventil-
Technik, Mannesmann Rexroth GmbH, Lohr am
Main.
[4]
Ivantysynova M. (2000). “Pump Controlled Actuator
– a Realistic Alternative for Heavy Duty
Manipulators and Robots” Developments In Fluid
Power Control of Machinery and Manipulators,
Figure 10. results of simulation for constant value of
Fluid Power Net Publication, Cracow.
valve’s coil current
[5]
Mirosław T., Szlagowski J., . ebrowski Z. (2001).
„Problems of manipulator rotation control, based on
speed for constant servo-valve current
automation of miniexcavator”, ISARC 2001
[6] Mirosław T. (1999). Control And Position Control-
350
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250
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/
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[
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d
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Figure 11. Results of real tests for constant value of valve
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245
