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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 8, Issue 12, December 2017, pp. 1007–1019, Article ID: IJMET_08_12_109
Available online at http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=12
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication Scopus Indexed
DESIGN, ANALYSIS AND MEASUREMENT OF
TRASMISSION ERROR
Sourabh More, Kaustubh Ghadge
Keystone School of Engineering, SPPU, Pune, india
Shrenik Chillal
Trinity Academy Of Engineering, SPPU, Pune, india
ABSTRACT
The power transmission by the gears is mostly used in the industries such as
automobile gearbox, robotics office automation etc. This is possible mostly by the
gears. Gearing is one of the most critical components in mechanical power
transmission systems. Transmission error is the prime contributor which resulting in
poor power transmission and decrease in the efficiency of gear transmission drive.
Today’s generation is mostly focusing over maximum efficiency with low power loss.
The influence of transmission error (TE) cannot be determined by investigating the
gears only. The main aim of this paper is to survey the sources and mechanism for
gear noise and vibration. It has been brought to light that gear transmission error
widely occurs due to irregular shape, tool geometry, imperfect mounting and
misalignment of two gears. It is emphasised that TE has to be a system analysis rather
than just gears.
Keywords: Transmission error, Efficiency, Gear noise, Gear system, Vibration
Cite this Article: Sourabh More, Kaustubh Ghadge and Shrenik Chillal, Design,
Analysis and Measurement of Trasmission Error, International Journal of Mechanical
Engineering and Technology 8(12), 2017, pp. 1007–1019.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=12
1. INTRODUCTION
Chung et.al (1999) have analysed a Gear Noise Reduction through Transmission Error
Control & Gear Blank Dynamic Tuning, on the other hand Numerical methods to Calculate
Gear Transmission Noise was presented by Helinger et.al (1997). Some other references
pertaining to gear TE analysis and experiment have been also referred which were presented
by Choi M. and J. W. David (1990).
Gear transmission systems have a long history dating back since the time of the first
engineering systems. Their practical usage in the present day modern engineering system is
enormous. Techniques are growing requirements and working specifications in accordance
with a contemporary development of mechanical engineering. Different kinds of metallic
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gears are currently being manufactured for various industrial purposes. Seventy-four percent
of them are spur gears, fifteen percent helical, five percent worm, four percent bevel, and the
others are either epicyclical or internal gears. The main purpose of gear mechanisms is to
transmit rotation and torque between axes.
The gear is a machine element that has intrigued many engineers because of numerous
technological problems arises in a complete mesh cycle. If the gears were perfectly rigid and
no geometrical errors or modifications were present, the gears would result in a constant
speed at the output shaft. The assumption of no friction leads to that the gears would transmit
the torque perfectly, which means that a constant torque at the output shaft. No force
variations would exist and hence no vibrations and no noise could be created. Of course, in
reality, there are geometrical errors, deflections and friction present, and accordingly, gears
sometimes create noise to such an extent that it becomes a problem. Transmission error occurs
when a traditional non-modified gear drive is operated under assembly errors. Transmission
error is the rotation delay between driving and driven gear caused by the disturbances of
inevitable random noise factors such as elastic deformation, manufacturing error, alignment
error in assembly.
Gear noise control measures can be categorized into the classical areas of source - path –
receiver measures. Source treatment includes all design & manufacturing measures to
minimize the transmission error. Transmission error is the fundamental source of gear whine
& any reduction will result in lower perceived levels. Tooth contact analysis incorporating
meshes kinematics, assembly tolerances analysis & load deflections of the teeth gear blanks,
and shafting enables the engineer to minimize gear noise at the source.
Transmission error minimization was one of the highest weighted factors in the gear
design process for the gear set under study. Analytical modelling techniques and design
optimization are utilized to achieve the target design criteria. Gear tooth contact analysis
techniques were some of the fundamental tools which allowed the gear engineer to optimize
gear design & study gear stress, mesh stiffness, transmission error, load distribution & contact
pattern for differing conditions.
2. TRANSMISSION ERROR
“Transmission Error is defined as the deviation of a meshed gear pair or entire gear train from
constant position of ratio as defined by the tooth number ratio.”
The most frequently used type of gear profile is the involute. It is used for cylindrical spur
and helical gears as well as for conical gears like beveloid, hypoid and spiral bevel gears.
Some characteristics of involute (cylindrical) gears that have made them so common are:
Uniform transmission of rotational motion, independent of small error in centre
distance.
The sum of the contact forces is constant and the direction of the total contact force
always acts in the same direction.
An involute gear can work together with mating gears with different number of teeth.
Manufacturing is relatively easy and the same tools can be used to machine gears with
different numbers of teeth.
If the gears were perfectly rigid and no geometrical errors or modifications were present,
the gears would transmit the rotational motion perfectly, which means that a constant speed at
the input shaft would result in a constant speed at the output shaft. The assumption of no
friction leads to that the gears would transmit the torque perfectly, which means that a
constant torque at the input shaft would result in a constant torque at the output shaft. No
force variations would exist and hence no vibrations and no sound (noise) could be created.
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Of course, in reality, there are geometrical errors, deflections and friction present, and
accordingly, gears sometimes create noise to such an extent that it becomes a problem.
Figure 1 Example of typical transmission error signal and its component’s.
Transmission error is extension of position error. It will only refer non uniform output
motion when the input is uniform this may be expressed as angular displacement or as linear
displacement at the pitch point. In its simplest definition, transmission error is the deviation
from perfect motion transfer of a rotating gear pair.
There are many reasons for the presence of TE in gears. One is unavoidable: gears are
subject to torque, which causes forces on teeth, thus modifying their geometry by bending.
Another unavoidable effect, which would exist even if tooth deflections were negligible,
results from machining errors such as profile and pitch error, eccentricity, assembling errors,
which modify the ideal geometry of the gear. Therefore real teeth deformed under load,
affected by machining and mounting errors are subject to different working conditions from
the ideal ones. In particular, the different geometry of the teeth at the beginning of the mesh
causes impacts. Transmission error is the indicator of all these effects. Minimizing
transmission error has long been seen as the most important factor in minimizing gear noise.
It should be noted that one may cancel the effects of mesh stiffness variation by intentionally
providing tooth shapes with deviations from perfectly conjugate shapes. In doing so, it is
important to minimize transmission error in the torque range at which the gear noise is a
problem. Since stiffness variation changes with torque loading, the optimum profile
modification at one is likely not to be an optimum at another load. Following are the
transmission error results obtained from the analysis.
3. PROBLEM STATEMENT
We now discuss problem statement and analyse the TE results
To identify the type of transmission error and to measure the Transmission Errors in
Gears.
Validation of designed & analysed Transmission system with respect to experiment.
2.1. SOURCES OF TRANSMISSION ERROR
Following are the sources which contribute to the transmission error:
1. Position error in the individual gear –
Total composite error
i. Single cycle
ii. Eccentricity (Pitch line run out)
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iii. Side Wobble Error (Lateral run out)
High frequency tooth to tooth composite error
1. Profile error
2. Profile spacing error
3. Tooth thickness error
4. Lead error
Supplementary position error
2. Installation error –
a. Run out Sources
i. Clearance between gear bore & shaft
ii. Run out at point of gear mounting
iii. Ball bearing rotating-race eccentricity
iv. Miscellaneous run out
b. Miscellaneous error sources
i. Shaft coupling - Hook joint
ii. Shaft and bearing creepage
4. SELECTION OF VARIOUS COMPONENTS AND PARTS
4.1. SELECTION OF GEAR
We had selected a simple gear train having 58 no. of teeth’s on pinion and gear as it is a part
of low commercial vehicles (LCV). Therefore selecting standard gear dimensions. Standard
gear parameters are listed below.
a) No. of teeth on pinion- 58
b) No. of teeth on gear- 58
c) Face width- 15
d) Normal module- 2
e) Pressure angle- 20
f) Helix angle- 26
g) Centre distance- 128
h) Quality standard- ISO 7
4.2. SELECTION OF MOTOR
As readings at various speeds and loads are to be taken hence 3 Phase induction motor
(variable speed) is selected. Motor is connected to 3 phase AC supply which is driven through
Variable Frequency Drive (VFD) AC unit to run motor at different speeds.
4.3. SELECTION OF INDUCTIVE PROXIMITY SENSOR:
An inductive proximity sensor is a type of non-contact electronic proximity sensor that is used
to detect the position of metal objects. The sensing range of an inductive switch is dependent
on the type of material being sensed.
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Figure 2 Working principle of inductive proximity sensor
Table 1 denotations of proximity sensor setup
SR. NO. PART NAME
1 Sensor body/ casing
2 Input and output wiring
3 Internal circuit
4 Magnet
5 Sensing coil
6 Gear
Their operating principle is based on a coil and oscillator that creates an electromagnetic
field in the close surroundings of the sensing surface. The presence of a metallic object
(actuator) in the operating area causes a dampening of the oscillation amplitude. The rise or
fall of such oscillation is identified by a threshold circuit that changes the output of the sensor.
Fig.2 shows the working principle of inductive proximity. Operating distance of the
sensor depends on the actuator's shape and size and is strictly linked to the nature of the
material. Ferrous metals such as iron and steel, allow for a longer sensing range, while non-
ferrous metals, such as aluminum and copper, can reduce sensing range by upto 60%.
The sensitivity or operating distance for different types of metals.
Table 2 Sensitivity when different metals are present. Sn = operating distance
METAL SENSITIVITY
Fe37 (iron) 1.0 X Sn
Stainless steel 0.9 X Sn
Brass - bronze 0.5 X Sn
Aluminum 0.4 X Sn
Copper 0.4 X Sn
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4.4. SPECIFICATIONS OF INDUCTIVE PROXIMITY SENSOR:
Table 3 Specifications of inductive proximity sensor
PARAMETER RANGE
Diameter 18 mm
Operating distance (Sn) 8 mm
Supply voltage 10-30 V, DC
Load current 400 mA
Using the analytical method described above, the difference between modulation signals
gives the error in distribution of impulses. The error level corresponding to the tooth pitch
rotation determines the final accuracy of the TE measurements.
4.5. DESIGN OF THE TEST RIG:
The design process started with evaluation of different test rig principles. The test rig consists
of two identical gears meshing with each other.
Figure 3 Test rig for Transmission Error measurement
Fig.3. shows the model of photograph in Creo 2.0. One of the gears is mounted on main-
shaft which is coupled to the motor via jaw coupling and the other gear is mounted on
countershaft.
Fig.4.Shows the vertical plates to mount the shaft and bearing. The parellelity between
two plates is maintained by making right angle between vertical and horizontal flanges. Shaft
holes in both the plates are made by placing together at same the time to ensure the parellelity
between shafts. Vertical height between base plate and shaft is maintained by trial and error
method i.e. grinding the bas plate with surface grinder.
Figure 4 Vertical plates to mount the shaft and bearing
Fig.5. shows an arrangement is made to apply the load at the output shaft with pulley and
rope. The drive is given by means of electric motor of high horse power. The mechanical
principle was chosen to apply load at the output shafts because of the relatively low cost and
high performance. The torque is measured with a torque sensor placed at the loads on output
shaft.
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Figure 5 Position of inductive proximity sensor on input and output shafts along with the rope and
pulley arrangement
4.6. DATA ACQUISITION SYSTEM (DAQ SYSTEM)
DAQ system typically convert analog waveform into digital values for processing. DAQ is
the process of sampling signals that measure real world physical conditions and converting
the resulting samples into digital numeric values that can be manipulated by the computer.
Figure 6 Data acquisition system
5. ANALYSIS OF SINGLE GEAR PAIR IN ROMAX DESIGNER:
The torque input given is 3000 N.mm at the speed of 1440 rpm. The analysis of this pair is
done to find out the safety factor of gear in both contact and bending and the transmission
error. This gear pair is analysed for the duration of 3 hours with different loadings at the
output shaft end.
5.1. RESULTS:
5.1.1. GEAR PARAMETER DETAILS:
Table 4 Test gear parameters
PARAMETERS SYMBOL DRIVING DRIVEN
No. of teeth Z 58 58
Face width b 15 15
Normal module Mn 2
Pressure angle Phi 20
Helix angle B 26
Centre distance C 128
Quality standard - ISO 7
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From the above mentioned gear parameters the gears are modeled in Romax. These gears
mounted on two shafts namely driving and driven which are supported with bearing at the
both ends.
5.1.2. SAFETY FACTORS IN CONTACT AND BENDING:
From table.5 it has been found that the factor of safety of both driver and driven gear in both
contact and bending is large enough for the analyzed duty cycle. It can be said from the above
table the gears are safe.
Table 5 Factor of safety in contact and bending
Gear Contact stress (MPa) Bending stress (MPa) Safety factor
Left Right Left Right Contact Bending
Driver 0 518.0586 0 103.5476 3.627 5.817
Driven 0 518.0586 0 103.5476 3.627 5.817
5.1.3. ANALYSED MODEL OF TEST GEAR PAIR:
Figure 7 analysed model of test gear pair
5.1.4. LOAD DISTRIBUTION:
The maximum load per unit length without applying any micro geometry is 1177.9 N/mm.
Figure 8 Load distribution per unit length for the driver gear
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Fig 8 shows that, the load distribution per unit length of the face width has shifted from
the centre of the gear tooth to the edge of the tooth.
5.2. RESULT ANALYSIS
Following are the various results obtained from the analysis of test gear pair in Romax.
5.2.1. ROMAX RESULTS:
Following are the results of Transmission error at different speed and same (constant) load:
Table 6 Values of TE at different speed
At 2 kg At 4 kg At 6 kg At 10 kg
Speed
(RPM)
PTP TE
(um)
Speed
(RPM)
PTP TE
(um)
Speed
(RPM)
PTP TE
(um)
Speed
(RPM)
PTP TE
(um)
200 0.01853 200 0.00538 200 0.009547 200 0.01626
400 0.01853 400 0.00538 400 0.009547 400 0.01626
600 0.01853 600 0.00538 600 0.009547 600 0.01626
800 0.01853 800 0.00538 800 0.009547 800 0.01626
1000 0.01853 1000 0.00538 1000 0.009547 1000 0.01626
1200 0.01853 1200 0.00538 1200 0.009547 1200 0.01626
It seen from above observation that transmission error does not changes with speed.
5.3. TRANSMISSION ERROR IN TEST GEAR PAIR FOR VARIOUS LOADS
Figure 9 Transmission Error in test gear pair for constant load of 2kg & 4kg
Fig. 9 & 10. shows graph of speed Vs transmission error for load of 2 kg, 4 kg, 6 kg & 10
kg respectively. From all the above figures it has been observed that for specific load
transmission error does not changes as speed varies.
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Figure 10 Transmission Error in test gear pair for constant load of 6kg & 10kg
5.4. TRANSMISSION ERROR AT SAME SPEED AND DIFFERENT LOAD:
The transmission error at low torque is very low and it further decreases with increase in
torque around 5 N.mm. If the torque is increased beyond 5 N.mm, the transmission error
increases with increase in torque exponentially. Following are the results for the constant
speed with varying load.
Table 7 Values of TE at different load and same speed
At 200 RPM At 400 RPM
Load (Kg) TE (µm) Load TE (µm)
2 0.01853 2 0.01853
4 0.00538 4 0.00538
6 0.009547 6 0.009547
10 0.01626 10 0.01626
15 0.02492 15 0.02492
20 0.03371 20 0.03371
25 0.04244 25 0.04244
35 0.06019 35 0.06019
Table 7. shows the Transmission Error at constant speed but different operating loads.
And graph of torque Vs. Error Transmission. The figure shows the peak to peak transmission
error Vs. Torque obtained from Romax for the test gear pair. It is clear from the above graphs
that the transmission error is independent on the speed but it depends on the load applied.
Figure 11 Transmission Error in test gear pair for 200 rpm & 400 rpm
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5.5. EXPERIMENTAL RESULTS USING INDUCTIVE PROXIMITY
SENSOR:
Transmission error at different speed and NO (constant) load:
Table 8 Values of TE at different load and same speed
SPEED (RPM) TE (µm)
100 0.01625
200 0.01704
300 0.01648
400 0.01605
Transmission error at same speed and different load:
Table 9 Values of TE at different load and same speed
At 200 rpm At 400 rpm
Load TE (µm) Load TE (µm)
2 0.01496 2 0.0247
4 0.00347 4 0.0077
6 0.00650 6 0.0115
10 0.01998 10 0.0029
15 0.03502 15 0.0287
20 0.04565 20 0.0356
25 0.04540 25 0.0569
35 0.07017 35 0.0698
Figure 12 Transmission Error in test gear pair for 200 rpm & 400 rpm
From the fig. 12 and table 9 it is clear that the transmission error at no load is constant and
having very low value as compared to the values of transmission error at loaded condition. In
figure no. and no. it can be seen that the PTP transmission error is initially decreasing for
increasing torque and then it increases with increasing torque.
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5.6. COMPARISON OF ROMAX RESULTS WITH EXPERIMENTAL
RESULTS:
VALUES FOR 200 RPM & 400 RPM
Table 10 Deviation of Values of TE
LOAD (Kg)
TRANSMISSION ERROR
ROMAX (µm)
INDUCTIVE
PROXIMITY SENSOR
(µm)
PERCENTAGE
WITH RESPECT TO
ROMAX (%)
2 0.01853 0.01496
4 0.00538 0.00347
6 0.009547 0.00650
10 0.01626 0.01998
15 0.02492 0.03502
20 0.03371 0.04565
25 0.04244 0.04540
35 0.06019 0.07017
Table 11 Deviation of Values of TE
LOAD (Kg)
TRANSMISSION ERROR
ROMAX (µm)
INDUCTIVE
PROXIMITY SENSOR
(µm)
PERCENTAGE
WITH RESPECT TO
ROMAX (%)
2 0.01853 0.0247
4 0.00538 0.0077
6 0.009547 0.0115
10 0.01626 0.0029
15 0.02492 0.0287
20 0.03371 0.0356
25 0.04244 0.0569
35 0.06019 0.0698
It can be observed from the above graph and table for the 200 rpm, even though deviation
in the value of measured transmission error is considerably high, the trend obtained is similar
with theoretical values. The trend obtained in the graphs from the experimental analysis
results, almost following the same trend as that of the results obtained from the Romax
software, thus the results for the measurement of transmission error are validated.
5.7. USE OF TRANSMISSION ERROR RESULTS:
The calculation of transmission error is useful for several purposes, some examples are:
To choose appropriate gear geometry to minimize the variations in mesh stiffness, i.e.
determine module, helix angle and contact ratio.
Determine gear tooth modifications like crowning and tip relief (magnitude and
starting point) to minimize transmission error.
Investigate how different manufacturing errors influence gear noise and vibration
characteristics.
To obtain input to dynamic models of gear systems.
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6. CONCLUSIONS
In this work, a new approach for the tooth contact analysis (TCA) of gear
transmissions has been proposed. The TCA approach considers different positions of
the gear set along the gearing cycle.
Good co-relation was found between ROMAX analysis and experiment. As load
increases TE increases. This fact was found on both software and experiment.
ACKNOWLEDGEMENT
We would like to thank Prof. Sanjay S. Deshpande from College of Engineering, Pune for his
valuable guidance and continuous support during this work.
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