Design and Analysis of High Speed Helical Gear By … 3D modeling is done in Pro/Engineer ... DESIGN In order to design a helical gear ... Length of hub is < face width i.e = 360mm

Sai Bharath -International Journal of Computer Science information and Engg., Technologies ISSN 2277-4408 || 01112013-021

IJCSIET-ISSUE3-VOLUME3-SERIES3 Page 1

Design and Analysis of High Speed Helical Gear By Using Ansys

A. Sai Bharath*1, T .v .s .r .k. Prasad*2

M.Tech Student (Cad/ Cam) Mechanical Engineering, NCET, Jupudi, Ibrahimpatnam, Vijayawada, Krishna (dt),A.P, India.

Professor, Mechanical Engineering in NCET, Jupudi, Ibrahimpatnam, Vijayawada, Krishna (dt),A.P, India

Email: [email protected]

ABSTRACT

Marine engines are among heavy-duty machineries, which need to be taken care of in the best way during prototype

development stages. These engines are operated at very high speeds which induce large stresses and deflections in the gears as

well as in other rotating components. For the safe functioning of the engine, these stresses and deflections have to be minimized.

In this project, static-structural analysis on a high speed helical gear used in marine engines, have been performed. The

dimensions of the model have been arrived at by theoretical methods. The stresses generated and the deflections of the tooth have

been analyzed for different materials. Finally the results obtained by theoretical analysis and finite element Analysis are

compared to check the correctness. A conclusion has been arrived on the material which is best suited for the marine engines

based on the results. The present used material for helical gears is Mild Steel. In this project, gear is designed using two different

aluminum alloys 7475 and 6061. Theoretical calculations and analysis are done for Helical gear using Mild Steel, Aluminum

alloys 7475 and 6061. Parametric 3D modeling is done in Pro/Engineer and analysis is done in Ansys.

Key words: Gear design, Computer aided analysis, Gear Hobbing, Gear shaving, Structural Analysis.

1. INTRODUCTION

A gear is a rotating machine part having cut teeth, which

mesh with another toothed part in order to transmit torque.

Two or more gears working in tandem are called a

transmission and can produce a mechanical advantage

through a gear ratio and thus may be considered a simple

machine. Geared devices can change the speed, magnitude,

and direction of a power source. The most common

situation is for a gear to mesh with another gear however a

gear can also mesh with a non-rotating toothed part, called

a rack, thereby producing translation instead of rotation.

The gears in a transmission are analogous to the wheels in a

pulley. An advantage of gears is that the teeth of a gear

prevent slipping. When two gears of unequal number of

teeth are combined, a mechanical advantage is produced,

with both the rotational speeds and the torques of the two

gears differing in a simple relationship. In transmissions

which offer multiple gear ratios, such as bicycles and cars,

the term gear, as in first gear, refers to a gear ratio rather

than an actual physical gear. The term is used to describe

similar devices even when gear ratio is continuous rather

than discrete, or when the device does not actually contain

any gears, as in a continuously variable transmission.

2. METHODOLOGY OF SYSTEM

DESIGN

In order to design a helical gear system the following

procedure should be followed; The input conditions are

power, speed, helix angle, gear ratio.

Gear design starts with material selection. Proper

material selection is very important; Aluminum

has been selected as a material. If the material for

gear and pinion is same then the design should be

based since it is weak.

Find out the minimum central distance based on

the surface compression stress is

a≥ (i+1)3√ (0.7/σc) 2 E (Mt) iψ……. [Design

data]

Here Mt=torque transmitted by the

pinion=97420(KW/N)*Kd*K

Where Kd*K=1.3 , ψ=b/a………..[Design data].

Minimum normal modules may e determined as

mn≥1.15Cosβ {Mt/Yv σb ψm Z1} ^1/3..[design data]

Assume Z1=18, ψm=b/mn=10 from ..[design data]

Virtual number of teeth Zv=Z1/cos3β ,

Lewis form factor Yv=0.1540.192/Zv ….[ Design data]

Number of teeth on pinion Z1=2acosβ/mn*(i+1) , Number

of teeth on gear Z2=iZ1

Diameter of pinion D1=mn*Z1/cosβ , Diameter of gear

D2=mn*Z2/cosβ

Centre distance a=D1+D2/2 , Face width b= ψa

checking the calculations:

i): based on the compressive stress,

σc=0.7(i+1)/a*√{(i+1/ib)*E[mt]}

mailto:[email protected]



ii): based on the bending stress, σb=0.7(i+1)

(Mt)/{a.b.mn.Yv}

Here the bending and compressive stress values obtained

are less than the material property values, then the design is

safe.

2.1. Theoretical design calculation The theoretical design calculations are performed using the

input parameters such as power for marine high speed

engine, pinion speed, gear ratio, helix angle, pressure angle

etc. i.e Power P = 9000 KW, Speed of Pinion N = 3500

rpm, Gear Ratio i = 7, Helix Angle, β = 25oMinimum

centre distance based on surface compression strength is

given by

a ≥ (7+1) ]2.x

2.2 Material Selection Let the material for Pinion & Gear is Aluminum Alloy ;

Its design compressive stress & bending stresses are [σc =

25000 kgf/cm2 ], [σb = 3500 kgf/cm2]

2.2.1 Properties for Aluminum Alloy 6061

Speed of the pinion = 2000rpm

Power = p =240KW = 240 W

Gear ratio =6

Center distance = x =

Helix angle = 450 = α

Material used = mild steel

Properties = BHN =30

Minimum tensile strength = 500MPa

Young’s modulus = 68.9GPa=68.9 MPa

Compressive stress =

Bending stress = =392265.9 N/mm2

Module = m = 18

WKT gear ratio = GR =

We have GR =6 and

GR = No of teeth on gear =

Diameter of gear ,

mm

No of teeth on gear =

No of teeth on pinion = =15

Diameter of pinion =

center distance = mm

GR =

Normal pitch

m

m

mm

Normal pressure angle = фN

tan фN = tan ф (ф=20)

tan фN = tan 20

фN =

a) Face width

Usually recommended that the overlap should be 15 percent of the circular pitch

b =

The maximum face width may taken as 12.5 m to 20m

b = 20m = 360mm

Formative or equivalent no of teeth for helical gears =

Equivalent no of teeth on pinion =

Equivalent no of teeth on gear =



Tooth form factor for pinion for 200 full depth involute

Y1P = 0.154

Tooth form factor for gear for 200 full depth involute

Y1G = 0.154

Properties for helical gears:

Pressure angle ф = 20

Helix angle α = 450

Addendum = 0.8M(maximum) = 14. 4mm

Dedendum = 1M(minimum) = 18mm

Minimum total depth = 1.8m =32.4mm

Minimum clearance 0.2M =3.6mm

Thickness of tooth = 1.5708M =28.2744mm

Strength of helical gears:

b = face width

M = module

Y1 =tooth form factors

Both the pinion and gear are made of the same material the pinion is weaker thus the design will be based upon pinion

The allowable static stress ( ) for steel gears is

approximately one third of the ultimate tensile strength

= ,

Peripheral speed = V

= m/s

The value of velocity factor C depending upon peripheral

velocities greater than 20 m/s is given by

= ( ) Y1P

=

41.333

The dynamic tooth load on the helical gear is given by

Where v, b, c have usual meaning as discussed in spur gears

C = deformation factor =

K =0.111 for 200 full depth involute system

in N/mm2

C= =122.366N/mm

The static tooth load or endurance strength of the tooth for bevel gear is given by

(BHN=30) =flexural

endurance limit

N

DP, b, Q and K have usual meanings as discussed in spur gears in this case

K =load stress factor =



K=

Q =

b) Design for pinion shaft

Tangential load on pinion

Axial load of pinion

Bending moment of pinion shaft

X = over hang =1296

Bending moment of pinion shaft due to the axial load =

=

Torque transmitted by pinion T =

Equivalent twisting moment

We know that equivalent twisting moment

=

Let us now check for the principle shear stress WKT the shear stress induced

direct stress due to axial load = σ= 0.32

principle shear stress =

the principle shear stress is less than the permissible shear stress of 230 Mpa therefore the design is satisfactory

WKT the diameter of pinion hub =1.8 mm

Length of the hub = 1.25 mm

If the pitch circle diameter of the pinion is less than or equal to 14.7M+60mm = 14.7

c) Design for the gear shaft

Let

We have already calculated that the tangential load =

Axial load =

Bending moment due to the tangential load =

= (x = 1296)

Bending moment due to axial load =

N mm

= 20464606.45

Torque on the gear shaft = T

=torque on the pinion shaft N mm

We Know that equivalent twisting moment =

We also know that equivalent twisting moment

=

=



Let us know check for the principle shear stress;

We Know that shear stress = τ =

230

Direct stress due to axial load σ =

Principle shear stress =

The principle shear stress is same as the permissible stress of 230 Mpa the design is satisfactory

We Know that diameter of gear hub = 1.8 =138.276mm

Length of hub =1.25 =96.025mm

Length of hub is < face width i.e = 360mm

3. MODEL OF HELICAL GEAR

2D DRAWING

3.1 Analysis Significant Development in analysis of strength

properties of gear transmission follows the achievements in

computation design, simulation of meshing and tooth

contact analysis made by Lewiki,Handschuh.They carried

out 2D analyses using finite element method, boundary

element methods & Compared the results to experimental

ones validated crack simulation based on calculated stress

intensity factors and mixed mode crack angle prediction. In

practice, simplified formulas are usually used in gear

transmission design. They enables estimation of stresses at

tooth root with accuracy acceptable for engineering design.

In every case, strength properties of gear transmissions are

strongly influenced by gear geometry, applied

manufacturing processes, and dimensional accuracy of

manufactured gears.

3.2 Gear Manufacturing

Gears are manufactured by various processes. These are,

casting, stamping, rolling, extruding, and machining. Gears

can also be produced by powder metallurgy. Among the

above said process, machining process in most commonly

used. It is an accurate method. Basically gears are produced

by machining by a) Forming method. b) Generating

method.

3.2.1 Forming Method



In this method a form cutter is used. The formed cutter

may be single point cutting tool or a multipoint milling

cutter. The cutting edges formed cutter has been finished to

the shape between the gear teeth being cut. Forming

method is used for producing very small number of gears.

Gears produced by forming are less accurate. Forming

process is simple and cheaper. This method is takes more

time.

3.2.2 Gear Generating processes

This method of gear manufacturing is based on the

fact that any two involute gears of the same module will

mesh together. Here one of the meshing gears is made as

the cutter. The other gear rotates and also reciprocates

along the width of the gear blank. Because of the relative

rolling motion between cutter and the blank, gear teeth are

generated on the gear blank. The gear may be generated by

rack cutter, pinion cutter or a hob. Using the generated

method, profile of the gear teeth can be very accurately

produced. The following generating methods used for gear

production are Gear shaping, Gear planning, Gear hobbing.

3.2.3 Gear Hobbing It is a process of generating a gear by means of a

rotating cutter called hob. The hob has helical threads.

Grooves are cut in the threads parallel to the axis. This will

provide the edges. Proper rake and clearance angle are

ground on these cutting edges. The rotating hob acts like a

continuously moving rack as it cuts. The blank is mounted

on a vertical arbour. The hob is mounted in a rotating

arbour. The hob axis is tilted the hob lead angle so that its

teeth are parallel to the axis of the gear blank.

Then = (90º-1).

Where 1 = helix angle of the hob thread. NOTE: (hob lead

angle = 90º-hob helix angle)

The hob is rotated at suitable cutting speed. It is fed across

the blank face. The hob and blank are made to rotate in

correct relationship to each other; they rotate like a worm

and worm gear in mesh. For one relation of the hob, the

blank rotates by one tooth. (In case of single start hob).

For helical gears, the axis of the hob is inclined to

horizontally. Where a= θ + (90º-1).

(If the helix of the hob and the helix of the gear to be cut

are different. One is right and another is left handed.)

a= θ (90º-1)

(if the helix of the hob and the helix of the gear to be cut

are both right handed or both is left handed.)

Where, a = helix angle of the helical gear to be cut.,1 =

helix angle of the hob.

The gear hobbing technique is used for generating spur,

helical and worm gears. Gear hobbing is used in

automobiles, machine tools, various components,

instruments, clocks and other equipment.

In the present the helical gears were produced by gear

hobbing technique and finished by gear shaving operation.

The gear teeth generating process by milling machine is

shown in fig 2.3.1.

Fig.2.3.1. Image showing milling machine

3.2.4 Finishing Process Gears manufactured by different machining processes

will have rough surfaces. The machined gears may have

errors in tooth profiles, concentricity and helix angles. For

quiet and smooth running of gears, these errors and rough

surfaces should be removed. Gear finishing operations are

done for this purpose. The various gear finishing processes

like gear burnishing, gear shaving etc.

3.2.5 Gear Burnishing Is a method of finishing of gear teeth which are not

hardened. This is a cold working process. This method is

used to improve the surface finish of the gear teeth. This

also increases the hardness at the teeth surface. The teeth of

burnishing gears are very hard, smooth and accurate. They

are arranged at 120º position around the work gear. The

gears are rotated in one direction for some period. Then

they are rotated in the reverse direction for the some period.

The pressure is applied by the harder burnishing teeth on

the work gear.

3.2.6 Gear Shaving This is the most common method of gear

finishing. In this method a very hard gear shaving cutter is

used to remove fine chips from the gear teeth. The shaving

cutter may be in the form of a rack or a pinion. The rotary

method using pinion cutter is used on all types of gears.

The rotating cutter will have helical teeth of about 15º helix

angle. The cutter has a number of serrations on its

periphery. These act as cutting edges. In the rotary type of

gear shaving the work gear is held between centres and is

free to rotate. The shaving cutter meshes with the work

gear. The axis of the cutter is inclined to the gear at an

angle equal to the helix angle of the cutter (θ) when the

cutter rotate, the cutter reciprocates in a direction parallel to

the gear axis. The cutting edges of the shaving cutter

remove burrs, nicks and high points on the surface of the

work gear. It can remove from the teeth flank, chips up to

0.1mm thick.



4. ANALYSIS OF HELICAL GEAR

MATERIAL – ALUMINUM

ALLOY 6061 STRUCTURAL

AND RESULT ANALYSIS

Imported Model from Pro/Engineer

Element Type: Solid 20 node 95

Material Properties: Youngs Modulus (EX)

: 68900N/mm2

Poissons Ratio (PRXY) : 0.33

Density : 0.00000270 kg/mm3

Meshed Model

Loads

Pressure – 0.0084721 N/mm2

Solution

Solution – Solve – Current LS – ok

Displacement Vector Sum

Von Mises Stress

Strain

MODAL ANALYSIS



Main menu>Preprocessor>Loads>Analysis Type> New

Analysis> Select Modal> Click> OK

Main menu>Preprocessor>Loads>Analysis Type>

Analysis Options> No. Of Modes to Extract: 5 Click> OK

Main menu>Solution>Solve>Current Ls>Ok

RESULTS

Mode 1

Mode 2

Mode

3

Mode 4

Mode 5



RESULTS TABLE

STRUCTURAL RESULTS

ALUMINUM ALLOY 6061 ALUMINUM ALLOY 7475 MILD STEEL

DISPLACEMENT (mm) 0.898e-04 0.362e-03 0.117e-03

STRESS (N/mm2) 0.050801 0.159783 0.165659

STRAIN 0.745e-06 0.229e-05 0.794e-06

MODAL RESULTS

WEIGHT COMPARISON

MILD STEEL AL ALLOY 6061 AL ALLOY 7475

Kg 5632.034 1932.2 2010.92

5. CONCLUSION

In this project, static-structural analysis on a high speed

helical gear used in marine engines, have been performed.

The dimensions of the model have been arrived at by

theoretical methods. The stresses generated and the

deflections of the tooth have been analyzed for different

materials.The present used material for helical gears is

Mild Steel. In this project, gear is designed using two

different aluminum alloys 7475 and 6061. Theoretical

calculations and analysis are done for helical gear using

Mild Steel, Aluminum alloys 7475 and 6061. While using

Mild Steel for helical gears, the weight is more. By

replacing with aluminum alloys, the weight is reduced.

Parametric 3D modeling is done in Pro/Engineer and

analysis is done in Ansys.

By observing the analysis results, the stress values are less

by using all the 3 materials than their respective yield stress

values. So using aluminum alloys is better for helical gear

used in high speed marine engines. In aluminum alloys,

using aluminum alloy 6061 is better as its weight is less

than aluminum alloy 7475.

ALUMINUM ALLOY

6061

ALUMINUM ALLOY

7475 MILD STEEL

MODE 1 FREQUENCY (Hz) 15.861 15.704 16.551

DISPLACEMENT (mm) 0.3645 0.035725 0.021412


DISPLACEMENT (mm) 0.052211 0.051179 0.030543


DISPLACEMENT (mm) 0.066233 0.064924 0.038727


DISPLACEMENT (mm) 0.053395 0.05234 0.030758


DISPLACEMENT (mm) 0.056598 0.05234 0.032597



REFERENCES

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Erroreffect of wheel body deformation and interactions

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2. Zeping Wei., 2004”Stresses and Deformations in

Involute spur gears by Finite Element method,” M.S,

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University of Saskatchewan, Saskatchewan.

3. PSG,2008, “Design data,” Kalaikathir Achchagam

publishers, Coimbatore India

4. Joseph E.Shigley.charles R.Mischike, 2003, Mechanical

Engineering design, Tata McGraw Hill.

5. Andrzej kawalec, Jerzy Wiktor., 2006, “Comparative

analysis of tooth root strength Using ISO and AGMA

6. Standards in spur and helical gears with FEM based

verification,” ASME Journal of Mechanical Design,Vol

128/114

7. Lazar Chalik, DE, 1996, “Preloaded Gearing for high

speed application” Vol 88, ASME Power transmission

&Gearing conference

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Documents

Design and Analysis of High Speed Helical Gear By … 3D modeling is done in Pro/Engineer ... DESIGN In order to design a helical gear ... Length of hub is < face width i.e = 360mm