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International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
p-ISSN: 2395-0072
Volume: 10 Issue: 09 | Sep 2023 www.irjet.net
Design optimization and new product development of hub idler gear
CHIDANANDA .V. R1 , Dr. RAJESH .M2
1CHIDANANDA V R M.tech student (Final year) Dept of Mech engg Dr AIT ,BANGLORE
2 Dr. RAJESH. M Assistant Professor, Department of Mechanical Engineering,Dr. AIT, Bangalore
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - In business and engineering, new product
development (NPD) covers the complete process of bringing a
new product to market, renewing an existing product or
introducing a product in a new market. A central aspect of
NPD is product design, along with various business
considerations. New product development is describedbroadly
as the transformation of a market opportunity into a product
available for sale. The products developed by an organization
provide the means for it to generate income. For many
technology-intensive firms their approach is based on
exploiting technological innovation in a rapidly changing
market.
Market share by a regular development of new products.
There are many uncertainties and challenges which
companies must face throughout the process. The use of best
practices and the elimination of barriers to communication
are the main concerns for the management of the NPD.
Importance of introducing new products can be summarized
in these “Seven reasons why new product development is
necessary
Key Words: NPD, HUB IDLER GEAR, FEA
1. INTRODUCTION
The most effective way to transmit power between two
shafts is through gears. They are utilised more frequently in
power transmission than belts and chains. The teeth on the
gears might be straight, spiral/helical, or bevelled. Bevel
gears are used to transfer power between perpendicular
shafts, while straight toothed gears are used to transfer
power between horizontal shafts. Since helical gears can
rotate at higher speeds without wearing out, they are now
preferred over straight tooth gears in many applications.
Machines for spinning and weaving frequently use gears.
They are utilized for take up and let off motions in weaving
machines. Both sizing machines and the movements of the
speed frame constructor use bevel gears. Gears are thought
of as positive drives.
The idle gear rattle phenomenon is associated with the
characteristic noise that unselected impacting gears
radiate to the environment. The phenomenon occurs atlow
impact forces, qualitatively similar to the noise produced,
when a marble hits a tin can. The problem is induced by
engine order vibrations in the presence of backlash in
meshing pairs, and is particularly troublesome in vehicles
with diesel engines, because ofhigher output torques [1]).
Rattle has a distinct sound quality that differentiates it
from noises produced by other sources in the vehicle [2],
while the attenuation of engine noise during the past
decades has brought it to the forefront of noise and
vibration issues, as a major concern for the automotive
industry [3]. Vehicle owners are usually annoyed by this
noise and often attribute it to some form of malfunction. In
addition topossible warranty claims, a low-quality image
accompanies the manufacturers’ products.
2. LITERATURE REVIEW
Most previous studies of such phenomena proposeanalytical
models for the vibroacoustic behavior of the entire
mechanical system (gears, transmission chain). In [1], Singh
et al. retain a Lumped Model, non-linear, and find analytical
solutions, derived piecewise, section after section, from a
linear analysis. In this particular case, the stiffness is
described with functions which have non-continuous
derivatives.
In [2], the authors improved the latter model by the
introduction of friction. Moreover the authors derive
analytical solutions based on the Harmonic Balance Method.
Many investigations have been performed to define contact
characteristics of simple or multi-mesh gear trains, taking
into account friction phenomena and the influence of
backlash.
The first experiments focused on the detection and the
analysis of non-linear phenomena [3]. The instantaneous
characteristics in the signals can be obtained from the ridges
and skeletons of the Wavelet Transform [4]. Such non-linear
systems can also be described with a Volterra Functional
Series, which generalizes the Superposition Principle and
allows impulse Responses and Transfer Functions of various
orders to be obtained [5].
© 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 256
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
p-ISSN: 2395-0072
Volume: 10 Issue: 09 | Sep 2023 www.irjet.net
Other detection methods are based on the speed variations
[6]; in this paper, the authors show that a low-cost
conventional tachometer is sufficient for measuring the
induced speed variations due to backlash. They can also be
predicted via simulation. For example, Tjahjowidodo et al.
[4], uses a detailed multi-body simulation to develop and test
the effectiveness of the proposed detection approach. The
idle gear noise is chaotic [7].
The chaotic behavior gets stronger with increasing backlash,
see [8]. In [9], Tjahjowidodo et al., quantify the chaotic
responses and correlate them to the parameters of the non-
linear system, in particular the magnitude of the backlash.
Al shyyabetal.
[11] And Ajmietal. [10] Proposed models to introduce non-
linearity in the contact elasticity. They also take into account
the structural elasticity of gears. Ajmietal. [10] Considers a
continuous non-linear model concentrated on contact lines
in gears with a finite element global description.
3. MANUFACTURING OF HUB IDLE GEAR
3.1) Turning
Turning is a type of machining where the work piece rotates
while a cutting tool, usually a non-rotary tool bit, moves
more or less linearly to describe a helical tool path. Turning
can be done manually, on a traditional type of lathe, which
frequently necessitates constant operator supervision, or on
an automated lathe, which necessitates none. Computer
numerical control, or CNC, is the current most used method
of automation.
3.2) Milling
By moving a cutter into a work piece, milling is the method
of machining that uses rotating cutters to remove material
[1]. This can be accomplished by adjusting cutter headspeed,
pressure, and direction [2] on one or more axes.[3] Small
individual pieces to massive, heavy-duty gang milling
processes are all included in the broad category of milling
activities. One of the most popular methods for producing
custom parts with exact tolerances is this one.
3.3) Grinding
The grinding machine consists of a bed with a fixture to
guide and hold the workpiece, and a power-driven grinding
wheel spinning at the required speed. The speed is
determined by the wheel’s diameter and manufacturer’s
rating. The grinding head can travel across a fixed work
piece, or the work piece can be moved while the grind head
stays in a fixed position.
Fine control of the grinding head or table positionis possible
using a vernier calibrated hand wheel, or using the features
of numerical controls.
3.4) Marking
The process of utilising lasers to carve an object is known as
laser engraving. Contrarily, laser marking is a broader group
of techniques that can include charring, foaming, melting,
ablation, and other processes in addition to changing the
colour of an object owing to chemical or molecular
changes.[1] The method has an advantage over other
engraving or marking technologies since it doesn't require
the use of inks or tool bits with worn-out bit heads that come
into contact with the engraving surface.
For specially created "laserable" materials and some paints,
the effects of laser marking have been more noticeable.
These include new metal alloys and polymers that are
sensitive to lasers. [2
Fig -1: Turning
© 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 257
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
p-ISSN: 2395-0072
Volume: 10 Issue: 09 | Sep 2023 www.irjet.net
Fig -2: Milling
Fig -3: CNC grinding machine
4.) RESULTS AND DISCUSSSIONS
f
The earlier design of the Hub Idle Gear is shown in the is
CAD model and includes all design specifications. Hereit can
be clearly seen that the old design contains a six through
hole at various locations along the area of the component. In
this design the wall thickness was found to be 10 mm.
It is necessary to calculate all such important
responses like outer diameter, cross hole, depth and total
length because they all represent competing requirements in
the design process. The key element in formulating an
optimization problem is the selection of the independent
design variables that are necessary to characterize the
design of the system. Normally, it is good to choose those
variables that have a significant impact on the objective
function. As listed above, typical constraints here include
limits on bending strength, surface durability, scoring,
weight, size, contact ratio, interference and width-to-
diameter ratio. One of the design capabilities developed as
part of this study is for hub idle gear.
,
Table -1: Critical Parameters involved in the optimization
Sl
no.
Critical
Parameter
Range
Minimum in
mm
Maximum in
mm
1. Big outer
diameter
89.975 89.958
2. Small outer
diameter
15.9942. 15.983
3. Cross hole 11.4 11.8
4. Depth 28.1 28.2
5. Total Length 37.8 38.2
© 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 258
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
p-ISSN: 2395-0072
Volume: 10 Issue: 09 | Sep 2023 www.irjet.net
b) CAD Model of the old design Hub Idle Gear
© 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 259
Figure -5: a) CAD Model of the old design Hub Idle Gear
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
p-ISSN: 2395-0072
Volume: 10 Issue: 09 | Sep 2023 www.irjet.net
Figure -6: a) Applied Boundary Condition and Torque on
old design Hub Idle Gear b) Applied Boundary condition
and Torque on old design Hub Idle Gear
Figure -7: Contour plot showing the von Misses stress of
old design Hub Idle Gear &Contour plot showing the von
Misses stress of new design Hub Idle Gear
Figure -8: Contour plot showing the displacement of old
design Hub Idle Gear & Contour plot showing the
displacement of old design Hub Idle Gear
© 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 260
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
p-ISSN: 2395-0072
Volume: 10 Issue: 09 | Sep 2023 www.irjet.net
Figure-9: The histogram of the outer diameter vs
frequency
Figure -10: The histogram of the small diameter vs
frequency
5.) CONCLUSIONS
The design optimization of hub idler gear the part which is
used in specialized Volvo buses & trucks IC engines was
carried out. It consists of old design which had circular cut-
outs at specified locations. The design considerations like
intermediate wall thickness 2.5 mm, big outer diameter
89.965mm, Small outer diameter 15.989 mm, cross hole
11.6mm, depth 28.15mm & total length 38mm were chosen.
By incorporating these constraints, the part design was build
which had flower design cut-outs.The CAD model of both old
& new design of hub idler gear drafted using computer
software as per the requirements. The parts were meshed
using solid mesh the elements used were the combination of
linear & parabolic tetrahedron further finite element
analysis was carried out.
The boundary conditions were to fix the holes at the bottom
surface of the parts all DOFs. The torque 4.9 Nm was applied
on the circumference in clockwise direction.
The results showed that the von mises stress of the new part
was found to be 0.079 GN/m2 which is 8.76% of reduced
stress compared to old part design. The results showed that
the displacement of the new part was found to be
0.01669mm which is 14% reduced displacement compared
to old part design. The results showed that the strain of the
new part was found to be 9.213X10-04 which is 4%
reducedstrain values compared to old part design.
These above comparisons of values indicate that the new
part design of hub idler gear can potentially be the strong
replacement for the old design.
6.) REFERENCES
[1] R.J. Comparin, R. Singh, H. Xie, Analysis of automotive
neutral gear rattle, Journal of Sound and Vibration 131
(1989) 177–196.
[2] P. Velex, P. Sainsot, An analytical study of tooth friction
excitations in errorless spur and helical gears, Mechanism
and Machine Theory 37 (1996) 641–658.
[3] M.-C. Pan, H. Van Brussel, P. Sas, Intelligent joint fault
diagnosis of industrial robots, Mechanical Systems and
Signal Processing 12 (4) (1998) 571–588.
[4] T. Tjahjowidodo, F. Al-Bender, H. Van Brussel,
Experimental dynamic identification of backlash using
skeleton methods, Mechanical Systems and Signal Processing
21 (2007) 959–972.
[5] I. Tawfiq, T. Vinh, Contribution to the extension of modal
analysis to non-linear structure using volterra functional
series, Mechanical Systems and Signal Processing 17 (2)
(2003) 379–407.
[6] Jeffrey L. Stein, Churn-Hway Wang, Automatic detection
of clearance in mechanical systems: experimental validation,
Mechanical Systems and Signal Processing 10 (4) (1996)
395–412.
[7] R.M. Lin, D.J. Ewins, Chaotic vibration of mechanical
systems with backlash, Mechanical Systems and Signal
Processing 7 (3) (1993) 257–272.
[8] I. Trendafilova, H. Van Brussel, Non-linear dynamics
tools for the motion analysis and condition monitoring of
robot joints, Mechanical Systems and Signal Processing 15
(6) (2001) 1141–1164.
© 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 261
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
p-ISSN: 2395-0072
Volume: 10 Issue: 09 | Sep 2023 www.irjet.net
[10] M. Ajmi, P. Velex, Model for simulating the quasi-static
and dynamic behaviour of solid wide-faced spur and helical
gears, Mechanism and Machine Theory 40 (2005) 173–190.
© 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 262
[9] T. Tjahjowidodo, F. Al-Bender, H. Van Brussel,
Quantifying chaotic responses of mechanical systems with
backlash component, Mechanical Systems and Signal
Processing 21 (2007) 973–993.

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Design optimization and new product development of hub idler gear

  • 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 p-ISSN: 2395-0072 Volume: 10 Issue: 09 | Sep 2023 www.irjet.net Design optimization and new product development of hub idler gear CHIDANANDA .V. R1 , Dr. RAJESH .M2 1CHIDANANDA V R M.tech student (Final year) Dept of Mech engg Dr AIT ,BANGLORE 2 Dr. RAJESH. M Assistant Professor, Department of Mechanical Engineering,Dr. AIT, Bangalore ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - In business and engineering, new product development (NPD) covers the complete process of bringing a new product to market, renewing an existing product or introducing a product in a new market. A central aspect of NPD is product design, along with various business considerations. New product development is describedbroadly as the transformation of a market opportunity into a product available for sale. The products developed by an organization provide the means for it to generate income. For many technology-intensive firms their approach is based on exploiting technological innovation in a rapidly changing market. Market share by a regular development of new products. There are many uncertainties and challenges which companies must face throughout the process. The use of best practices and the elimination of barriers to communication are the main concerns for the management of the NPD. Importance of introducing new products can be summarized in these “Seven reasons why new product development is necessary Key Words: NPD, HUB IDLER GEAR, FEA 1. INTRODUCTION The most effective way to transmit power between two shafts is through gears. They are utilised more frequently in power transmission than belts and chains. The teeth on the gears might be straight, spiral/helical, or bevelled. Bevel gears are used to transfer power between perpendicular shafts, while straight toothed gears are used to transfer power between horizontal shafts. Since helical gears can rotate at higher speeds without wearing out, they are now preferred over straight tooth gears in many applications. Machines for spinning and weaving frequently use gears. They are utilized for take up and let off motions in weaving machines. Both sizing machines and the movements of the speed frame constructor use bevel gears. Gears are thought of as positive drives. The idle gear rattle phenomenon is associated with the characteristic noise that unselected impacting gears radiate to the environment. The phenomenon occurs atlow impact forces, qualitatively similar to the noise produced, when a marble hits a tin can. The problem is induced by engine order vibrations in the presence of backlash in meshing pairs, and is particularly troublesome in vehicles with diesel engines, because ofhigher output torques [1]). Rattle has a distinct sound quality that differentiates it from noises produced by other sources in the vehicle [2], while the attenuation of engine noise during the past decades has brought it to the forefront of noise and vibration issues, as a major concern for the automotive industry [3]. Vehicle owners are usually annoyed by this noise and often attribute it to some form of malfunction. In addition topossible warranty claims, a low-quality image accompanies the manufacturers’ products. 2. LITERATURE REVIEW Most previous studies of such phenomena proposeanalytical models for the vibroacoustic behavior of the entire mechanical system (gears, transmission chain). In [1], Singh et al. retain a Lumped Model, non-linear, and find analytical solutions, derived piecewise, section after section, from a linear analysis. In this particular case, the stiffness is described with functions which have non-continuous derivatives. In [2], the authors improved the latter model by the introduction of friction. Moreover the authors derive analytical solutions based on the Harmonic Balance Method. Many investigations have been performed to define contact characteristics of simple or multi-mesh gear trains, taking into account friction phenomena and the influence of backlash. The first experiments focused on the detection and the analysis of non-linear phenomena [3]. The instantaneous characteristics in the signals can be obtained from the ridges and skeletons of the Wavelet Transform [4]. Such non-linear systems can also be described with a Volterra Functional Series, which generalizes the Superposition Principle and allows impulse Responses and Transfer Functions of various orders to be obtained [5]. © 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 256
  • 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 p-ISSN: 2395-0072 Volume: 10 Issue: 09 | Sep 2023 www.irjet.net Other detection methods are based on the speed variations [6]; in this paper, the authors show that a low-cost conventional tachometer is sufficient for measuring the induced speed variations due to backlash. They can also be predicted via simulation. For example, Tjahjowidodo et al. [4], uses a detailed multi-body simulation to develop and test the effectiveness of the proposed detection approach. The idle gear noise is chaotic [7]. The chaotic behavior gets stronger with increasing backlash, see [8]. In [9], Tjahjowidodo et al., quantify the chaotic responses and correlate them to the parameters of the non- linear system, in particular the magnitude of the backlash. Al shyyabetal. [11] And Ajmietal. [10] Proposed models to introduce non- linearity in the contact elasticity. They also take into account the structural elasticity of gears. Ajmietal. [10] Considers a continuous non-linear model concentrated on contact lines in gears with a finite element global description. 3. MANUFACTURING OF HUB IDLE GEAR 3.1) Turning Turning is a type of machining where the work piece rotates while a cutting tool, usually a non-rotary tool bit, moves more or less linearly to describe a helical tool path. Turning can be done manually, on a traditional type of lathe, which frequently necessitates constant operator supervision, or on an automated lathe, which necessitates none. Computer numerical control, or CNC, is the current most used method of automation. 3.2) Milling By moving a cutter into a work piece, milling is the method of machining that uses rotating cutters to remove material [1]. This can be accomplished by adjusting cutter headspeed, pressure, and direction [2] on one or more axes.[3] Small individual pieces to massive, heavy-duty gang milling processes are all included in the broad category of milling activities. One of the most popular methods for producing custom parts with exact tolerances is this one. 3.3) Grinding The grinding machine consists of a bed with a fixture to guide and hold the workpiece, and a power-driven grinding wheel spinning at the required speed. The speed is determined by the wheel’s diameter and manufacturer’s rating. The grinding head can travel across a fixed work piece, or the work piece can be moved while the grind head stays in a fixed position. Fine control of the grinding head or table positionis possible using a vernier calibrated hand wheel, or using the features of numerical controls. 3.4) Marking The process of utilising lasers to carve an object is known as laser engraving. Contrarily, laser marking is a broader group of techniques that can include charring, foaming, melting, ablation, and other processes in addition to changing the colour of an object owing to chemical or molecular changes.[1] The method has an advantage over other engraving or marking technologies since it doesn't require the use of inks or tool bits with worn-out bit heads that come into contact with the engraving surface. For specially created "laserable" materials and some paints, the effects of laser marking have been more noticeable. These include new metal alloys and polymers that are sensitive to lasers. [2 Fig -1: Turning © 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 257
  • 3. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 p-ISSN: 2395-0072 Volume: 10 Issue: 09 | Sep 2023 www.irjet.net Fig -2: Milling Fig -3: CNC grinding machine 4.) RESULTS AND DISCUSSSIONS f The earlier design of the Hub Idle Gear is shown in the is CAD model and includes all design specifications. Hereit can be clearly seen that the old design contains a six through hole at various locations along the area of the component. In this design the wall thickness was found to be 10 mm. It is necessary to calculate all such important responses like outer diameter, cross hole, depth and total length because they all represent competing requirements in the design process. The key element in formulating an optimization problem is the selection of the independent design variables that are necessary to characterize the design of the system. Normally, it is good to choose those variables that have a significant impact on the objective function. As listed above, typical constraints here include limits on bending strength, surface durability, scoring, weight, size, contact ratio, interference and width-to- diameter ratio. One of the design capabilities developed as part of this study is for hub idle gear. , Table -1: Critical Parameters involved in the optimization Sl no. Critical Parameter Range Minimum in mm Maximum in mm 1. Big outer diameter 89.975 89.958 2. Small outer diameter 15.9942. 15.983 3. Cross hole 11.4 11.8 4. Depth 28.1 28.2 5. Total Length 37.8 38.2 © 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 258
  • 4. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 p-ISSN: 2395-0072 Volume: 10 Issue: 09 | Sep 2023 www.irjet.net b) CAD Model of the old design Hub Idle Gear © 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 259 Figure -5: a) CAD Model of the old design Hub Idle Gear
  • 5. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 p-ISSN: 2395-0072 Volume: 10 Issue: 09 | Sep 2023 www.irjet.net Figure -6: a) Applied Boundary Condition and Torque on old design Hub Idle Gear b) Applied Boundary condition and Torque on old design Hub Idle Gear Figure -7: Contour plot showing the von Misses stress of old design Hub Idle Gear &Contour plot showing the von Misses stress of new design Hub Idle Gear Figure -8: Contour plot showing the displacement of old design Hub Idle Gear & Contour plot showing the displacement of old design Hub Idle Gear © 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 260
  • 6. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 p-ISSN: 2395-0072 Volume: 10 Issue: 09 | Sep 2023 www.irjet.net Figure-9: The histogram of the outer diameter vs frequency Figure -10: The histogram of the small diameter vs frequency 5.) CONCLUSIONS The design optimization of hub idler gear the part which is used in specialized Volvo buses & trucks IC engines was carried out. It consists of old design which had circular cut- outs at specified locations. The design considerations like intermediate wall thickness 2.5 mm, big outer diameter 89.965mm, Small outer diameter 15.989 mm, cross hole 11.6mm, depth 28.15mm & total length 38mm were chosen. By incorporating these constraints, the part design was build which had flower design cut-outs.The CAD model of both old & new design of hub idler gear drafted using computer software as per the requirements. The parts were meshed using solid mesh the elements used were the combination of linear & parabolic tetrahedron further finite element analysis was carried out. The boundary conditions were to fix the holes at the bottom surface of the parts all DOFs. The torque 4.9 Nm was applied on the circumference in clockwise direction. The results showed that the von mises stress of the new part was found to be 0.079 GN/m2 which is 8.76% of reduced stress compared to old part design. The results showed that the displacement of the new part was found to be 0.01669mm which is 14% reduced displacement compared to old part design. The results showed that the strain of the new part was found to be 9.213X10-04 which is 4% reducedstrain values compared to old part design. These above comparisons of values indicate that the new part design of hub idler gear can potentially be the strong replacement for the old design. 6.) REFERENCES [1] R.J. Comparin, R. Singh, H. Xie, Analysis of automotive neutral gear rattle, Journal of Sound and Vibration 131 (1989) 177–196. [2] P. Velex, P. Sainsot, An analytical study of tooth friction excitations in errorless spur and helical gears, Mechanism and Machine Theory 37 (1996) 641–658. [3] M.-C. Pan, H. Van Brussel, P. Sas, Intelligent joint fault diagnosis of industrial robots, Mechanical Systems and Signal Processing 12 (4) (1998) 571–588. [4] T. Tjahjowidodo, F. Al-Bender, H. Van Brussel, Experimental dynamic identification of backlash using skeleton methods, Mechanical Systems and Signal Processing 21 (2007) 959–972. [5] I. Tawfiq, T. Vinh, Contribution to the extension of modal analysis to non-linear structure using volterra functional series, Mechanical Systems and Signal Processing 17 (2) (2003) 379–407. [6] Jeffrey L. Stein, Churn-Hway Wang, Automatic detection of clearance in mechanical systems: experimental validation, Mechanical Systems and Signal Processing 10 (4) (1996) 395–412. [7] R.M. Lin, D.J. Ewins, Chaotic vibration of mechanical systems with backlash, Mechanical Systems and Signal Processing 7 (3) (1993) 257–272. [8] I. Trendafilova, H. Van Brussel, Non-linear dynamics tools for the motion analysis and condition monitoring of robot joints, Mechanical Systems and Signal Processing 15 (6) (2001) 1141–1164. © 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 261
  • 7. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 p-ISSN: 2395-0072 Volume: 10 Issue: 09 | Sep 2023 www.irjet.net [10] M. Ajmi, P. Velex, Model for simulating the quasi-static and dynamic behaviour of solid wide-faced spur and helical gears, Mechanism and Machine Theory 40 (2005) 173–190. © 2023, IRJET | Impact Factor value: 8.226 | ISO 9001:2008 Certified Journal | Page 262 [9] T. Tjahjowidodo, F. Al-Bender, H. Van Brussel, Quantifying chaotic responses of mechanical systems with backlash component, Mechanical Systems and Signal Processing 21 (2007) 973–993.