Volume 4, Issue 6, June – 2019 International Journal of Innovative Science and Research Technology

ISSN No:-2456-2165

Optimization Finite Element Analysis of 3D Spur

Gears of Steel and Cast-Iron Reinforced Angles
1
Ifeoluwa E. Elemure, 2Edwin A. Oshin, 3Temitope V. Adebanwo, 4Aderinsola M. Olawumi, 5James O. Akinyoola
1
Department of Mechanical and Design Engineering, University of Portsmouth, UK
2
Department of biomedical engineering, Old Dominion University, USA
3
physics department, Federal University of Agriculture, Makurdi
4
Department of Physics Electronics, Federal University of Technology, Akure, Nigeria
5
Department of Mechanical & Mechatronics, Engineering, Afe Babalola University, Ado-Ekiti, Nigeria

Abstract:- In this research, spur gears made from this multi-flank poker chip formation tools often get to the
graphite epoxy normal and shear stresses are examined. tool life due to unwarranted wear from the tool corner
The stresses of spur gear are calculated from outer to radius [6]. This community wear limits the usable tool Life
interior divided into three zones for different angles in run production. Furthermore, the tool wears correlated.
reinforcement fibres. 3D finite element model (FEM) Problems cannot be considered all through the design
was used in this study. Also, a novel design, model, and period of spur gears. Some authors are inflicted with been
analyse the differential gears by using composite investigated the hob Geometry, cold forces measurements,
materials. The manual transmission consists of cast iron the poker chip formation Process all through machining and
or mild steel. Composite materials may be an the tool wear prediction [7]. Moreover, several authors
alternative to conventional materials due to the urban various simulations Codes of the gear hobbing
advantages of low weight, rust and less maintenance. process, such as SPARTpro and 3D software, [8]. Gear
Modelling spur gears performed by stable applications analysis is one of the generally outstanding issues in the
and finite element analysis will be performed in Ansys. apparatus elements theory, particularly in the meadow of
Eight-node three-dimensional isoperimetric elements gear Design and gear manufacturing. Many of the
are chosen as the finite element method. In the study researchers are inflicted with projected several concepts of
calculation of normal and shear stresses in different pro gear design Optimization to enhance the performance
fibre reinforcement orientations has been carried out of gear systems. [9,10]. Recently metal matrix composite
and are plotted in the graphs. From the analysis, results (MMC) equipment is used to manufacture a digit of
suggest the use of short reinforcing fibre (SCF) instead engineering components, due to their unique advantages,
of cast iron or mild steel for applications that are such as light consequence, unique strength, privileged
Limited weight below 1,500 watts. The results of dimensional Stability and deterioration resistance, as
plotting graphs are examined. The force applied to the compared with polymer-based composite equipment,
surface of the first gear orthotropic consisting of the though the cost of MMCs is very distinguished. [11,12]
normal stresses of the internal gear. It is higher by Power transmission gears are lone such can get on to aid of
about 30%, and the stress value is close to each other. MMC equipment. Al- SiC composite can be manufactured
by stir casting, and it provides increased resistance and
Keywords:- Spur Gear; Composite Material; Stress tensile strength with much reduced in consequences [13]. In
Analysis; FEM; Steel; Cast Iron. addition to being lightweight composite materials are both
very high strength properties, which of materials use the
I. INTRODUCTION area more and more. It is expanding. Composite materials,
air and land and sea transport in addition to the space
The principal function of gear mechanisms is to industry, chemical industry they are corrosion resistant
transmit rotation and torque linking bar axes. The gear veer electrical and electronics insulator) industry, robot
is an apparatus element with the intention of has intrigued construction (less inertia and they are rigid), medical
many engineers since of numerous technological problems supplies, sports equipment. Such as are used in various
arising in a Complete mesh cycle [1]. In order to realise fields. It is diversity in the composite material. Due to the
distinguished load transportation, room with the cut-rate option of creating unlimited will further increase is an
consequence of gear drives, but with Increased strength of indisputable fact. Power transmission properties of
gear transmission, gear design based on tooth stress composite materials It has also shown itself in gear, and the
analysis, tooth modifications and Optimum design of gear first carbon including a wide variety of fibre composite
drives are apt major investigate areas [2]. Gears with gears responding to the need of using fibre supplements
involute teeth are inflicted with widely been used in the composite gears are obtained. This desire of gear Even
industry sense of the low cost of manufacturing. The though many of the best features of this Scientific studies in
distinguished performance of the gear transmission logic is the field are not enough. Experimental and isotropic gear in
Obtained through the unique quality of involute gears. The the literature, theoretical studies are many.
different methods of production of gears, hobbing is the
Generally widely useful manufacturing process pro the
Construction of involute gear in the industry, [3-5]. Inside

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Volume 4, Issue 6, June – 2019 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
Again, a similar It is aimed, [14] glass- epoxy, and the Analysis point is used. The global stiffness matrix
isotropic steel and cast-iron material made spur of the use dimensions 360 x 360 and has been according to bandwidth
in power transmission. They examine and steel and cast- appeared as 141 [19,20].
iron best features They concluded owned. Stresses the
composite spur gear analysis with the 3D finite element A. Element Stiffness Matrix
method they did [15] multiple fibre BOND angle in the
composite polymer gears they have emphasised stress. In Strain energy in a single element,
this study; graphite fibre composites straight gear a variety
of three defined regions from outside to inside normal and
the shear angle formed in the fibre reinforcement, stress
applying the finite element method it was examined [16].

II. FINITE ELEMENT METHOD Here, {ε} is the vector strain displacement vector,

Three-dimensional investigations; x, y and z-axes, the

gear tooth thickness, tooth height and tooth obtained by
placing across the width geometry is based. A curvilinear
tooth geometry structure because it has eight-node
isoperimetric cubic element It was used [18]. The spur gear Here; u, v and w for displacement in x, y and z is
only Calculations are made based on a tooth. It is only the formed along the axis of displacement of It is. Elastic
dental geometrise finite element-boundary sensitive regions matrix for orthotropic material. It shaped. Here, the terms
separated smaller element precision worked to catch. x and used, E1, E2, E3 values selected according to the fibre
y are placing the resulting two-dimensional finite axis direction the axes respectively l, t, z directions modulus of
element z-axis perpendicular to the axis of the network elasticity are. The values lt, TZ, shifts in LZ plane modulus
team placing the resulting three-dimensional finite element and Poisson's ratio.
mesh otherwise. Fifty-six elements and 120 nodes in

Fig 1:- Shows a Layer Average Vector Rotational Direction Movement

Steel and cast iron material properties in Table Fibre direction is given these values [T] using the
1describe Composite Material Features Used transformation matrix, x, y, z It reached the value in the
direction. The maximum contact stress at Hertz stress of
Feature Steel and cast iron compressive stress and contact pressure,
First Principal Strain (E1 ) 180994.5 N/mm2
Third Principal Strain (E2 ) 10702.7 N/mm2
Young modulus (G12) 7171.1 N/mm2
Poisson Ratio (V12) 0.28
Table 1:- Composite Material Used Features

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Volume 4, Issue 6, June – 2019 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
Where Contact width Obtained from Eq. Where ε, η and ξ axis local
coordinates, x, y and z-axes of the global It refer to
coordinates. Local coordinates The written equations Jacobi
matrix ([J]) is a global It is converted to the coordinates.
Therefore, the following equality can write:

Where, F = Applied Force D1 & D2 = Diameters of

the gears, E1 & E2 = Modulii of Elasticity of gear
materials, V 1 = Poisson’s ratios of gear materials. [T]
matrix = c and h = it is sinα cosα. [T] transformation matrix
and composite materials, elastic matrix ([D]) Include Obtained in local coordinates for each element
Incorporating global stiffness matrix It was obtained. Using
global stiffness matrix substitutions

[K]{U} = {F} (10)

Using the matrix obtained by writing equations, the Calculated using the equation in [9]. The displacement
conversion is achieved. Strain matrix given in Equation 2 vector of the system {F} vector is a force acting on the
can be written as follows [12]. Here [B] displacement-strain system. Force vector by a uniform load of the node It was
transformation matrix and {the} nodes spot the obtained by dispersing. So load node points were collected.
displacement vectors. [B] Displacement-way changing the
transformation matrix. It shaped the Jacobian matrix B. Method of FEA
functions derivative it is the matrix. Gear having the The methodology to be followed was adopted to
geometry of curvilinear Due to the three-dimensional, 8- achieve the objective of developing a 3D gear model using
node isoparametric cubic elements were used. This element solid work. The model was developed and turned into a
shape functions model of excellent, straight gear elements and solved the
same using Ansys and to determine the bending and contact
stresses of different gears of straight teeth. Compare the
results of different materials and finish the observations

Fig 2:- The Finite Element Method of a Single Tooth Spur Gear of Steel and Cast Iron Reinforce Angle Application.

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Volume 4, Issue 6, June – 2019 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
Dental load distribution across the width (W) F/W = were found. These values are different for different angles
150 N/mm. Spread the load is static, and the tooth tip effect supplements. It is shown separately calculated and
was adopted. Clutch along the line The impact load(F) to graphics. The force applied to the outer surface of the
the outer end, the clutch angle dependent α'y as it is divided composite gear σx stresses II. The tension in the region It is
into radial and tangential components. The tangential more than 30% — however, II. and III. Area stress
component of the load Fx = F cosα Radial Components of difference between the stresses is minimal. Σ largest areas
them in the form Fy = F sinα. Equality found ten σx strain 30o and 45o have taken place in terms of
displacement vectors and stress matrix considering equality reinforcing them is 0o, 15o 60o 75o and 90o reinforcement is
6 It can be written as follows. followed angles (Figure 3). σy A little stress is higher than
the 90o, 75o, 60o, 45o, 30o, 15o and 0o follow fibre
reinforcement angles It. Stress values applied force max in
the first region (160N/mm2) as It is realized in the second
Stress matrix open of 100 N/mm2, In the third of 90N/mm2. Σx as with the
stress σy of the I and II in the stretching. Between regions
stress differences are high, it is next II. and III. Area stress
differences have emerged as very small. σz stresses σx and
σy small by stress. It has value. For example; In the first of
As written. Where σxx, σyy, σzz terms normal σx and σy maximum values of stress were 60N/mm2 and
stresses τxy, τxz, τyz, per cent In terms slipping It shows 160N/mm2 while σz maximum stress 33N/mm2 'dr. σ z
the stress. stress values higher than small to 45o, 30o, 60o, 15o, 0o, 75o
and 90o fibre reinforcement angles realised. σz and σw
III. STRESS ANALYSIS OF GEAR stresses that show the same value σw charts also shown.
The most significant σL strains 75 and 90 fibre
Steel and cast-iron spur gear belonging parameters It reinforcement It has emerged in the angles. , The remaining
is given in Table 2. terms of supplements ranking 45o, 30o, 15o, 0o, It shaped.
The maximum in the region stress values is around 140
Parameter Value N/mm2, 75 N/mm2 and 70 N/mm2.
Pressure angle 20o
Module 12.7 mm IV. RESULTS
Head height Tooth 1.0mm
Tooth bottom height 1.2mm Normal stresses in x, y, z-direction and shear stresses
Tooth root curvature 0.35mm in xy, yz, xz planes were found on a single tooth of the steel
Tooth width (W) 3mm and cast iron spur gear. These stresses; It was obtained for
The number of teeth 20 each part of the tooth obtained by dividing into two central
Table 2:- Parameters of Spur Gear. regions in the middle, on the right and left. In the front of
the first region, the elements 1, 5, 9, 13, 17, 21, 25 are
Made of steel and cast-iron spur are one on female x, arranged from bottom to top, and the elements 29, 33, 37,
y, z-direction standard stress per cent, the shear stresses in 41, 45, 49, 53 from the bottom to the rear. The elements of
the x-y, xz, yz planes respectively. This stress of teeth right the second region are numbered according to the order
and left the centre is divided into two main areas, including obtained by adding the element numbers 1 to the first
It was obtained for each region obtained. First In front of region and the elements of the third region by adding 2.
the region upward from below 1, 5, 9, 13, 17, 21, 25'node Since the stresses on the front and rear elements of the
element is on the back side again bottom-up towards 29, regions are the same, only the front elements are based on
33, 37, 41, 45, 49, 53'node the elements have been ranked. I., II., And III. Graphics related to the region were drawn.
The second of the elements by adding 1 to the first number Stresses were calculated at the same loading state and
of elements, obtained by adding the elements of the third different fibre reinforcement angles (00, 150, 300, ... 900).
region two they are numbered based on the order. On Then, normal stresses in the fibre reinforcement direction
element in the region of the front and rear Stresses in only and two other directions (t and z) perpendicular to this
the front side is the same element based on the I, II, and III. direction and shear stresses in the lt, TZ, lz planes were also
About the region graphs were drawn. Stresses the same found. These values are calculated separately for different
loading in case of and in terms of different fibre reinforcement angles and are shown graphically. The σx
reinforcement (0o, 15o, 30o ... 90o) It was calculated. Then stresses on the force-applied outer surface (I. zone) of the
the reinforcing fibre direction (First direction) and in the composite gear II. 30% higher than the stresses in the
other two directions perpendicular to this direction, (t and region. However, II. and III. Stress differences between the
z) the usual stresses and lt, TZ, lz shear stress in the plane region stresses are minimal.

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Volume 4, Issue 6, June – 2019 International Journal of Innovative Science and Research Technology
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Fig 3:- σ Reinforcement in Composite According to Different Gears in Different Regions z of (A) I, (B) II, (C) III, and (D) σL
Stresses

The largest σx stresses in the regions occurred at 30 0 occurred at 750 and 900 fibre reinforcement angles. 60o
and 450 reinforcement angles, followed by reinforcement followed immediately. The remaining reinforcement angle
angles of 150,600, 00, 750 and 900. σy stresses followed by sequence is 450,300, 150 and 00. The maximum stress values
fibre reinforcement angles of 600, 750, 450, 900, 300, 150 in the regions were approximately 140N/mm2, 75N/mm2
and 00 from large to small. Stress values were maximum and 70 N/mm2, respectively. σT stresses were 450, 300, 600,
60N/mm2 in the first region where the force was applied 150, 750, 00 and 900. This sequence is the same in all three
and decreased to 100N/mm2 in the second region and regions of the gear. Stress values in the regions are
90N/mm2 in the third region (Figure 5). As in σx stresses, 160N/mm2, 95 N / mm2 and 90N/mm2, respectively. The
in the σy stresses, The Ii region and II. Stress difference shear stresses τxy, τlt and τlw shown in Figure 9 are
between the regions is large, besides II. and III. Region obtained for the first region. II. Moreover, III. Since the
stress differences were minimal. The σz stresses are smaller shear stresses in the regions are much smaller, it is not
than the σx and σy stresses. For example; The maximum necessary to put the graphs. The results show that the
values of σx and σy stresses in the first region are 60N/mm2 maximum shear stress τxy is 125N/mm2, while the
and 160 N/mm2, while the maximum stress of σz is maximum shear stresses τyz and τxz is 3N/mm2 and
33N/mm2. Stress values σz were observed at 450, 300, 600, 3.5N/mm2, respectively. The shear stress τlt is greater than
150, 00, 750 and 900 fibre reinforcement angles from large to τtw and τlw. The shear stresses of τlt have positive values
small. Since σz and σw stresses show the same values, σw at 150, 300 and 00 fibre reinforcement angles and negative
graphs are not shown separately. The greatest σL stresses values at 450, 900, 750 and 600 fibre reinforcement angles.

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Volume 4, Issue 6, June – 2019 International Journal of Innovative Science and Research Technology
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Fig 4:- σL According to Different Supplements in the Different Regions of (A) II, (B) III, τ According to Different Supplements
in Different Regions of the Composite Gear (C) τlt (D) τlw

 Finite Element Analysis addition to minimising weight, materials and costs. The
The finite element analysis of the spur gear is MEF provides a detailed view of where structures bend or
performed in the ANSYS 14, a popular FEA tool. Within bend and show the distribution of stresses and
the structure of the mechanical engineering discipline (such displacements. FEM software offers a wide range of
as the aerospace, biomechanics and automotive industries), simulation options to control the complexity of modelling
several specialisations usually use integrated MEFs to and analysis of a system. In the same way, the desired level
design and develop their products. Some new FEM of precision and the associated calculation time
packages include particular components, such as thermal, requirements can be managed simultaneously for most
electromagnetic, fluid and vertical work environments. In a engineering applications. The FEM guarantees that all
structural simulation, the FEM is a tremendous help in the projects are built, improved and optimised before the
production of visualisations of hardness and durability, in project is done.

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Volume 4, Issue 6, June – 2019 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
`

Fig 5:- Finite Element Analysis of

V. CONCLUSION 30%. The inner gear region (II. And III. Area) The stress
values occur very close to each other and a rise in terms of
In this research calculation of normal and shear different fibre reinforcement regarding the following stress
stresses in different fibre reinforcement orientations has values results obtained. Also, the maximum values of σx
been carried out and are plotted in the graphs. Generally, stress and σy stress occur at 30degree and 45degree and
the maximum value of the τxy stress occurs at zero degree 60degree and 75degree fibre reinforcement angles,
and 90degree fibre reinforcement angles. The results of respectively. Based on static analysis, we observe that the
plotted graphs are evaluated and discovered that the force von Mises stress and the deviation of the gear increase
applied to the surface of the gear 1 Orthotropic consisting when the pressure on the surface of the blade increases. The
of the normal stresses of the inner gear it is higher by about voltage received for the helical gears added with the SCF is

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Volume 4, Issue 6, June – 2019 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
below the safety limit compared to cast iron and mild steel. [14]. N. Sabkhi, C. Pelaingre, C. Barlier, A. Moufki, M.
From studies suggesting the use of analytical results and Nouari, Characterization of the cutting forces
additional gear results, SCF will be the best choice for cast generated during the gear hobbing process: Spur gear,
iron gears and mild steel gears in applications with a Procedia CIRP 31 ( 2015 ) 411 – 416.
maximum usage limit of 1500 watts. [15]. B. I Oladapo, B. A Vincent, A. O Oke, E. A Agbor,
Design and finite element analysis on car seat height
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