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KOMISJA BUDOWY MASZYN PAN – ODDZIAŁ W POZNANIU
Vol. 27 nr 2
Archiwum Technologii Maszyn i Automatyzacji
2007
PIOTR KRAWIEC *
PROBLEMS OF DESIGNING AND SELECTING TOOLS
FOR EXPERIMENTAL RESEARCH
IN VARIABLE TRANSMISSION RATIO DRIVES
The article deals with the problems of selecting and designing tools for experimental research
in special belt transmission systems. A distinctive feature of transmission systems under consideration is a periodically changeable transmission ratio obtained thanks to the application of elliptical
pulleys and circular, eccentrically mounted pulleys. The article includes technical conditions of
designing measuring tools for conducting experiments regarding belt transmission systems with
variable kinematic and dynamic characteristics.
Key words: belt transmission system, measuring tools
1. INTRODUCTION
In recent years there has been a dynamic development of belt transmission
systems, where forces are transmitted through frictional contact and gear coupling thanks to the use timing belts. This development has occurred thanks to the
successful cooperation of science and technology which combined their efforts
to design, manufacture and test new experimental belt transmission systems. It
was also possible thanks to the scientific description of deformation processes
occurring in multi-molecule materials such as polymers and elastomers as well
as several physical phenomena occurring when belts and pulleys interact. The
use of new materials for toothed belts and designing their new geometrical characteristics have made it possible to use belt transmission systems in new drives.
Consequently, it was possible to develop new designs of toothed belt transmission systems, namely transmission systems with variable transmission ratios,
where a certain degree of speed variability is obtained by the use a belt transmission system with wheels having shapes of ellipses, ovals or non-circular disks [2,
3]. The problem of selecting their geometrical and kinematic characteristics was
*
Dr inż. – Chair of Basics of Machine Design, Poznan University of Technology.
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P. Krawiec
discussed by the author in paper [3]. In order to use such drives on a large scale
they must undergo a stage of experimental verification. That is why a need to
design and build a test stand appeared. The main objective of the research was to
find out, whether a toothed belt transmission system, having specific wheel
shapes, would work in accordance with the assumed kinematic and functional
criteria. It was also important to check whether drive’s cyclycity would be maintained. Moreover, test stand trials were to check calculated kinematic and dynamic characteristics of variable-speed transmission systems.
2. TORQUE METER DESIGN
Torque is one of basic qualities responsible for characteristics of power
transmission systems. As this statement is true, there is a need to create tools and
methods for precise and efficient measurements of instantaneous torque. Simultaneously, it should be remembered, that attaching a torque measuring apparatus
(torque meter) to the examined power transmission system introduces changes to
the way it operates. It is particularly important during dynamic measurements.
The inspiration to design and then construct the torque meter in question was
a need to conduct tests of classical and special belt transmission systems. Special
belt transmission systems shall be understood here as variable-ratio toothed belt
transmission systems. The basic rules of design and principle of operation of
transmission systems of that type are discussed in papers [2, 3].
Procedures concerning development of measuring methodology were started
with analysing the design solutions of torque meters available on the market.
The following assessment criteria were assumed:
− precision of measurements,
− possibility of adapting to different drive systems,
− price,
− measurement automation.
As a result of conducted comparative analysis of torque meters design characteristics, the solution suggested by Hottinger Baldwin Messtechnik has been
found quite interesting. However, that solution requires the so called “building
up”. Its price is also considerable. Hence an attempt to develop a new design and
build an improved torque meter.
For precise torque measurements in power transmission systems and equipment, torsion meters are most frequently employed, in which under influence of
a load, an elastic strain of a mechanical flexible converter occurs. Measuring
signals are shaped in torque meter’s electrical converter.
In rotation torque meters, the torsional element is directly a part of the rotating assembly. Hence, direct measuring of a torque transmitted by the power
Problems of designing and selecting tools….
105
transmission system’s shaft is possible. As a result of analysis of available
torque meters, their characteristics and prices a need appeared to design a set of
torsion torque meters, where signals would be transmitted to stationary coils
installed in torque meter housings without any actual physical contact (Figure 1).
Fig. 1. View of the universal torque meter on a special transmission system
Rys. 1. Widok uniwersalnego momentomierza przekładni specjalnej
The design of the torque meter is universal and makes it possible to use it for
measurements both in special transmission systems and other drive assemblies.
3. MEASURING ANGLES OF ROTATION OF WHEELS
IN A VARIABLE-SPEED TRANSMISSION SYSTEM
Another task which the designed test stand is to perform is measuring angles
of rotation (angular velocities) of the driving and driven shaft of a given variable-speed transmission system.
Instantaneous angles of rotation of shafts in a tested transmission system are
registered by rotation converters (Fig. 2) attached to shaft ends with bellow type
couplings. In order to determine initial angular position of a shaft, the converters
are equipped with sensors which make it possible to start the measuring process
of angles of rotation for shafts in the initial position at a 0 degree angle.
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P. Krawiec
Fig. 2. View of the encoding sensor for measuring shafts’ angle of rotation
Rys. 2. Widok czujnika obrotowo-kodowego do pomiaru kątów obrotu wałów przekładni specjalnej
4. TEST STAND FOR SPECIAL TRANSMISSION SYSTEMS
The test stand for testing non-classical toothed belt transmission systems is
presented in Figure 3, and the measuring diagram of a reducing/multiplying
transmission system is presented in Figure 4.
The test stand is used for conducting kinematic and dynamic tests of variable-speed two-wheel transmission systems with torque load transmitted or not
(then torque meters record only instantaneous moment of inertia).
The test stand consists of a basis 1. On the basis there is a driving shaft 4,
layshaft 5, driven shaft 6 and brake 9. On the basis a motor 2 is mounted which
is powered through a frequency converter 3. Shafts with attached torque meters
are placed in radial ball bearings on supports. The brake 9 is used to apply load
to a tested transmission system. The installed reducing gear 7 is directly coupled
with the multiplying gear 8. Signals from torque meters and encoding sensors
12, 13, 14 are transmitted to amplifier 10 and further on to computer 11. Control
unit 15 is used to adjust load applied by the brake.
Problems of designing and selecting tools….
107
Fig. 3. View of the special transmission system test stand
Rys. 3. Widok stanowiska badawczego przekładni specjalnej
Fig. 4. Measuring diagram of a variable speed belt transmission system (description of numbers is
in the text)
Rys. 4. Schemat układu pomiarowego nierównobieżnej przekładni pasowej (opis w tekście)
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P. Krawiec
The design of the magnetorheological brake requires constant cooling with
the liquid from tank 16.
The magnetorheological brake has been specifically developed for its intended
usage. The device uses changes in fluid’s viscosity under the influence of external
electrostatic or magnetic field, which is
a highly original solution. Fluid’s rheological properties are controlled in such a way
that their precise fine-tuning is possible,
thus allowing for changes in torque under
varying loads. Torque changes are effected
by means of electric control signals. Consequently, they can be transmitted to computers or PLC’s (Fig. 5).
The measuring procedure is presented
below. After starting the motor, a required
driving speed is set by means of the frequency converter. Then the brake is set to
apply a required load torque.
Having set the load and temperature,
angular movements and torques are measured.
Fig. 5. Magnetorheological brake
Signals from extensometric and encodRys. 5. Hamulec magnetoreologiczny
ing sensors are digitized by a multichannel A/C card and then directly transmitted via the DMA channel into computer's RAM memory.
Measurements are conducted automatically with a program written in C++
language. The program makes it possible to start measurements at a specific
angular position of the driving wheel, with a selected frequency and duration,
which in most cases is equal to one revolution of the driven wheel.
Results of the measurements are saved in a text file, which is then properly
processed with MS Excel and Statistica.
On the basis of conducted measurements the system calculates transmission
system wheels’ velocities and accelerations. Results of the calculations are presented in a graphical form in charts.
The test stand makes it possible to perform measurements of:
− torque within [−20÷20] Nm range (symbol “−” stands for load’s direction),
− angles of rotation of the driven and driving wheels (registered each 0.14°
revolution of the driving wheel).
It was assumed that the rate of rotation of the driving wheel shall be within
the range (0÷2000) rpm (for the specific test stand in question).
Problems of designing and selecting tools….
109
Any wheel of the transmission system can be the driving wheel in any configuration. The modular design of the test stand makes it possible to conduct
trials of belt transmission systems working in various configurations.
5. RESULTS OF RESEARCH ON A TWO-WHEEL TRANSMISSION SYSTEM
Tests of a two-wheel reduction gear were carried out for the average reduction ratio usr = 2. The driving wheel was a non-circular one, the driven wheel had
an elliptical envelope.
As a result of experimental research a table was produced stating angles of
rotation of pulleys and torques. Next a diagram showing relationship between
the characteristics of transmission ratio as a function of a degree of rotation of
wheel 1 was made (Figure 6). The following diagrams (Figure 7) illustrate the
character of changes of angular velocity ω of the driven wheel and characteristics of changing acceleration a of the driven wheel against the degree of rotation
of the driving wheel 1 (Figure 8). Figure 9 illustrates torque changes on each
shaft of the transmission system.
u 0,8
0,7
0,6
0,5
0,4
0,3
0
90
180
270
360
450
540
630
720
f (°)
Fig. 6. Transmission characteristics of a two-wheel transmission system with a given ω1 = 20 rad/s,
with a load torque Mh = 0 N⋅m, where: u – transmission ratio
Rys. 6. Charakterystyka przełożenia przekładni dwukołowej przy prędkości ω1 = 20 rad/s, moment
hamowania Mh = 0 N⋅m, u – przełożenie przekładni
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P. Krawiec
Fig. 7. Characteristics of angular velocity as a function of a degree of rotation of driving wheel of
a two-wheel transmission system with a given ω1 = 20 rad/s, with a load torque Mh = 0 N⋅m,
where: ω1 – angular velocity of shaft one, ω2 – angular velocity of shaft two, ω3 – angular velocity
of shaft three
Rys. 7. Charakterystyka prędkości kątowej w funkcji kąta obrotu wału czynnego dla przekładni
dwukołowej przy ω1 = 20 rad/s, przekładnia obciążona momentem Mh = 0 N⋅m, ω1 – prędkość
kątowa wału pierwszego, ω2 – prędkość kątowa wału drugiego, ω3 – prędkość kątowa wału trzeciego
a [rad/s^2]
0, 2
0,15
a2
0, 1
a1
0,05
0
-0,05 0
90
180
270
360
450
540
630
720
a3
-0, 1
-0,15
-0, 2
φ[ ]
Fig. 8. Acceleration characteristics of a two-wheel transmission system with a given ω1 = 20 rad/s,
with a load torque Mh = 0 N⋅m, where: a1 – acceleration of shat one, a2 – acceleration of shaft two,
a3 – acceleration of shaft three
Rys. 8. Charakterystyka przyspieszenia dla przekładni dwukołowej przy ω1 = 20 rad/s, przekładnia
obciążona momentem Mh = 0 N⋅m, gdzie: a1 – przyspieszenie wału pierwszego, a2 – przyspieszenie wału drugiego, a3 – przyspieszenie wału trzeciego
Problems of designing and selecting tools….
0,1
M [N⋅m]
M [Nm] 0,09
0,08
0,07
0,06
0,05
0,04
0,03
0,02
0,01
0
111
M2
M1
M3
0
90
180
270
360
450
540
630
720
φ[ ]
Fig. 9. Torque characteristics as a function of angle of rotation φ of a two-wheel transmission system
with a given ω1 = 20 rad/s, with a load torque Mh = 0 N⋅m, where: M1 – torque on shaft one,
M2 – torque on shaft two, M3 – torque on shaft three
Rys. 9. Charakterystyka momentów w funkcji kąta obrotu φ dla przekładni dwukołowej przy ω1 =
= 20 rad/s, przekładnia obciążona momentem Mh =0 N⋅m, M1 – moment na wale pierwszym,
M2 – moment na wale drugim, M3 – moment na wale trzecim
6. SUMMARY
On the basis of conducted experimental and theoretical research the following conclusions can be formulated:
− the conducted experimental research have justified the use of the designed
measuring equipment,
− the universal character of developed research methods and equipment
makes it possible to apply them in various configurations,
− variable-speed transmission systems are suitable for producing required
movement parameters with generally small useful loads. Nevertheless, measurements with an external torque applied were performed as well. The presented
results show that external loads are combined with the torques, in particular, at
higher speeds,
− on the basis of conducted experiments and calculations the range of permissible speeds of such transmission systems has been determined. The speed
should not exceed n ≤ 2000 rpm for a two-wheel transmission system working as
reduction gear and n ≤ 1000 rpm in case of a transmission system working as a
multiplying gear,
− the recorded torques of shafts with aluminum alloy wheels were comparable with their useful torques,
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P. Krawiec
− connecting several variable-speed transmission systems in a row makes it
possible to influence the final variability characteristics of the whole system.
REFERENCES
[1] Dudziak M., Przekładnie cięgnowe, Warszawa, PWN 1997.
[2] Dudziak M., Krawiec P., Meler F., Analiza nierównobieżnej przekładni cięgnowej, Special
Issue No 5 Computer Simulation in Machine Design, 1998. p. 79−85.
[3] Krawiec P., Nieklasyczna przekładnia cięgnowa z pasem zębatym, Przegląd Mechaniczny,
2005, vol. 4, p. 25−28.
[4] Krawiec P., Variable-speed toothed belt transmission systems with periodically variable
transmission ratios, Archives of Mechanical Technology and Automation, 2004, vol. 24, nr 2,
p. 115−121.
Praca wpłynęła do Redakcji 27.03.2007
Recenzent: prof. dr hab. inż. Bogdan Branowski
PROBLEMATYKA PROJEKTOWANIA I DOBORU NARZĘDZI
DO BADAŃ EKSPERYMENTALNYCH
NIERÓWNOBIEŻNYCH PRZEKŁADNI CIĘGNOWYCH
S u m m a r y
W artykule omówiono problematykę doboru i projektowania narzędzi do badań eksperymentalnych przekładni cięgnowych specjalnych. Charakterystyczną cechą tej przekładni jest okresowo
zmienne przełożenie uzyskane dzięki zastosowaniu kół o nieokrągłym zarysie wieńca oraz kół
okrągłych mocowanych mimośrodowo. Omówiono zaprojektowane i wykonane narzędzia oraz
zespoły pomiarowe. Wskazano uwarunkowania techniczne projektowania narzędzi pomiarowych
do badań przekładni cięgnowych o okresowo zmiennych cechach kinematycznych i dynamicznych.
Słowa kluczowe: przekładnia cięgnowa, narzędzia pomiarowe