design, analysis and measurement of trasmission error · others are either epicyclical or internal...

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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

Design, Analysis and Measurement of Trasmission Error


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.

Sourabh More, Kaustubh Ghadge and Shrenik Chillal


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)



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.



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



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.



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



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



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.



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



5.5. EXPERIMENTAL RESULTS USING INDUCTIVE PROXIMITY

SENSOR:

Transmission error at different speed and NO (constant) load:


SPEED (RPM) TE (µm)

100 0.01625

200 0.01704

300 0.01648

400 0.01605

Transmission error at same speed and different load:


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.



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.



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.

REFERENCES

[1] Dr. Malviya D. and Dr. Pushpendra Kumar Sharma,“Transmission Error in Gear”,

International Journal of Modern Engineering Research (IJMER), January 2014, pp. 1&2.

[2] Chung C. H. and Glen Steyer, “Gear Noise Reduction through Transmission Error Control

& Gear Blank Dynamic Tuning”, SAE International Journal, 1999, pp. 1&2, 6-8.

[3] W, Helinger, H. Ch. Raffel & et.al, “Numerical Methods to Calculate Gear Transmission

Noise”, SAE International Journal, 1997, pp. 751&752.

[4] Choi M. and J. W. David – “Mesh Stiffness & Transmission Error of Spur & Helical

Gears” SAE International Journal, pp. 1599.

[5] Dudley D. W., “Gear Handbook”, 1962, pp. 31-37.

[6] Dudley D. W., “Handbook of practical gear design”, 2002 edition, pp. 91-98, 221-227.

[7] Merritt H. E., “Precision gearing and theory”, 1997, pp. 113-116.

[8] Benoît, N. and Claude Bernard, L. N. New Technique for Power Transmission (A Beam

of Conductors) Mathematical Model-Numerical Simulation. International Journal of

Advanced Research in Engineering and Technology, 6(9), 2015, pp. 09-13.

[9] J. S. Ashwin, S. Sinthuja and Dr .N. Manoharan. A Review on Wireless Power

Transmission, International Journal of Electronics and Communication Engineering &

Technology, 6(10), 2015, pp. 01-05.

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