R. PANNEERDHASS AND A. GNANAVEL BABU - ..:: …serialsjournals.com/serialjournalmanager/pdf/139108327… · · 2017-06-24static stress analysis of composite gears using a three-

R. PANNEERDHASS1 AND A. GNANAVEL BABU2

1Assistant Professor, Department of Mechanical Engineering, A.R.Engineering College, Villupuram, Tamilnadu – 605 601, India2Professor and Head, Department of Automobile Engineering, Karpaga vinayaga College of Engineering and Technology

Chennai, TamilNadu - 603 308, India

Corresponding author: [email protected], [email protected]

ABSTRACT

Engineering components made of composite materialsfind increasing applications ranging from spacecraft tosmall instruments. Modernadvanced polymer compositematerials have opened a new level ofnoiseless, lubricantfree, high resilience and precision gearing in powerandmotion transmission.In this paper results obtained bystatic stress analysis of composite gears using a three-dimensional finite element approach are presented.Performance of two orthotropic material gears arepresented and compared with mild steel gear. The properunderstanding and evaluation of gearstrength andperformance is an important prerequisite for anyreliableapplication. The tooth root region of a gearwhichusually experiences high stress and potential to failurehasbeen carefully investigated. This computer simulationmethod can be usedas a useful tool for evaluating strengthand predicting failureof the polymer composite spurgears. From the results it is concluded that compositematerial such as carbon/epoxy and E-glass/epoxy canbe through as a material for power transmission spurgears in the gear box.

The paper explore the characteristics of compositematerial gear box at conceptual design stage for specificweight reduction to get improved energy efficiency, noisereduction, higher natural frequency, corrosion resistanceand to resist higher torque.The study proposed for highcycle fatigue (LCF), low cycle fatigue (LCF), creep rupture,and static material properties as part of the life predictionprocess. The modeling is done by pro-e wild fire 5 andthe static model of spur gear in gear box has beenperformed using ANSYS 10.0.

Keywords: (Composite Materials, Spur Gear, Carbon/Epoxy, E-Glass/Epoxy)

I. INTRODUCTION

A gearbox is a mechanical device utilized to increasethe output torque or change the speed (RPM) of amotor. The motor’s shaft is attached to one end ofthe gearbox and through the internal configurationof gears of a gearbox, provides a given outputtorque and speed determined by the gear ratio. Themost common type of gear is the spur gear. Spurgears are made with straight teeth mounted on aparallel shaft. The noise level of spur gears isrelatively high due to colliding teeth of the gears

which make spur gear teeth prone to wear. Spurgears come in a range of sizes and gear ratios tomeet applications requiring a certain speed ortorque output.

The gear material used for the manufacture ofgear depends upon the strength and serviceconditions like wear and noise etc. Weightreduction can be achieved primarily by theintroduction of better material, design optimizationand better manufacturing processes. Theintroduction of composite material was made itpossible to reduce the weight of spur gear withoutany reduction on load carrying capacity andstiffness. More over the use of composite materialhas increased because of their properties such ashigh specific stiffness, corrosion free, ability toproduce complex shapes, high strength and highimpact energy absorption etc.

II. LITERATURE REVIEW

The review mainly focuses on replacement of mildsteel spur gear with the composite material carbon/ epoxy and shaft with polycarbonate in the gearbox.

• World Journal of Mechanics, 2012, 2, 239-245... used to compare conventional spur gearswith symmetric teeth and spur gears withasymmetric teeth. By using this pro- gram,gear.... researches, in literature.

• Journal of Mechanics, Vol. 28, No. 2, June2012. 373. TOOTH ... compared with resultsfrom literature and the model is verified.Keywords: Spur gear pair, Profilemodification, Localized defect, Dynamicmodeling.

• International Journal of Mechanical Science andCivil Engineering, vol-1 December 2012.Helps to study the performance ofcomposite material polyamide used in thegear box and the static analysis.

172 R. Panneerdhass and A. Gnanavel Babu

III. GEAR

A gear is a rotatingmachine part having cut teeth,or cogs, which mesh with another toothed part inorder to transmit torque. Two or more gearsworking in tandem are called a transmission and canproduce a mechanical advantage through a gearratio and thus may be considered a simple machine.Geared devices can change the speed, torque, anddirection of a power source. The most commonsituation is for a gear to mesh with another gear;however, a gear can also mesh with a non-rotatingtoothed part, called a rack, thereby producingtranslation instead of rotation.

(A) Spur

Spur gears or straight-cut gears are the simplest typeof gear. They consist of a cylinder or disk with theteeth projecting radically, and although they are notstraight-sided in form, the edge of each tooth isstraight and aligned parallel to the axis of rotation.These gears can be meshed together correctly onlyif they are fitted to parallel shafts.

gearboxes to be developed and manufactured atlower costs. Toothed gear systems have evolvedfrom fixed axis gear systems to new and improvedgears including helical, cycloid, spur, worm andplanetary gear systems. Gearboxes are widely usedin applications that require desired output speed(RPM), control the direction of rotation, and totranslate torque or power from one input shaft toanother.

(1) Gearboxes are used in a Variety of Industries

• Aerospace – In the aerospace industry,gearboxes are used in space and air travel, i.e.airplanes, missiles, space vehicles, spaceshuttles and engines.

• Agriculture – In the agriculture industry,gearboxes are used for plowing, irrigation, pestand insect control, tractors and pumps.

• Automotive – In the automotive industry,gearboxes are used in cars, helicopters, busesand motorcycles.

• Construction – In the construction industry,gearboxes are used in heavy machinery such ascranes, forklifts, bulldozers and tractors.

IV. COMPOSITE MATERIAL

Composite materials are materials made from twoor more constituent materials with significantlydifferent physical or chemical properties, that whencombined, produce a material with characteristicsdifferent from the individual components. Theindividual components remain separate anddistinct within the finished structure.Typicalengineered composite materials include:

• Composite building materials such ascements, concrete

Figure 1: Spur Gear

(B) Spur Gear Box

Spur gears are made with straight teeth mountedon a parallel shaft. The noise level of spur gears isrelatively high due to colliding teeth of the gearswhich make spur gear teeth prone to wear. Spurgears come in a range of sizes and gear ratios tomeet applications requiring a certain speed ortorque output.

(C) Uses of Gear Box

Advancements in technology and the evolution ofgears have made more efficient and powerful

Figure 2: Spur Gearboxes

Fatigue and Creep Life Prediction for Composite Material Using Fea 173

• Reinforced plastics such as fiber-reinforcedpolymer

• Metal Composites

• Ceramic Composites (composite ceramicand metal matrices)

Composite materials are generally used forbuildings, bridges and structures such as boat hulls,race car bodies, shower stalls, bathtubs, and storagetanks, imitation granite and cultured marble sinksand countertops. The most advanced examplesperform routinely on spacecraft in demandingenvironments.

(A) Resins

Typically, most common polymer-based compositematerials, including fiberglass, carbon fiber, and[[Kevlar]], include at least two parts, the substrateand the resin.

Polyester resin tends to have yellowish tint, andis suitable for most backyard projects. Itsweaknesses are that it is UV sensitive and can tendto degrade over time, and thus generally is alsocoated to help preserve it. It is often used in themaking of surfboards and for marine applications.Its hardener is a peroxide, often MEKP (methylethyl ketone peroxide). When the peroxide is mixedwith the resin, it decomposes to generate freeradicals, which initiate the curing reaction.Hardeners in these systems are commonly calledcatalysts, but since they do not re-appearunchanged at the end of the reaction, they do notfit the strictest chemical definition of a catalyst.

Vinylester resin tends to have a purplish tobluish to greenish tint. This resin has lower viscositythan polyester resin, and is more transparent. Thisresin is often billed as being fuel resistant, but willmelt in contact with gasoline. This resin tends to bemore resistant over time to degradation thanpolyester resin, and is more flexible. It uses the samehardeners as polyester resin (at a similar mix ratio)and the cost is approximately the same.

Epoxy resin is almost totally transparent whencured. In the aerospace industry, epoxy is used as astructural matrix material or as a structural glue.

(B) Reinforcement

Reinforcement usually adds rigidity and greatlyimpedes crack propagation. Thin fibers canhave very high strength, and provided theyare mechanically well attached to the matrix they

can greatly improve the composite’s overallproperties.

(1) Fiber

Fiber-reinforced composite materials can be dividedinto two main categories normally referred to asshort fiber-reinforced materials and continuousfiber-reinforced materials. Continuous reinforcedmaterials will often constitute a layered orlaminated structure. The woven and continuousfiber styles are typically available in a variety offorms, being pre-impregnated with the given matrix(resin), dry, uni-directional tapes of various widths,plain weave, harness satins, braided, and stitched.

The short and long fibers are typically employedin compression moulding and sheet mouldingoperations. These come in the form of flakes, chips,and random mate (which can also be made from acontinuous fibre laid in random fashion until thedesired thickness of the ply / laminate is achieved).

(C) Carbon-Fiber-Reinforced Polymer

Carbon-fiber-reinforced polymer, carbon-fiber-reinforced plastic or carbon-fiber reinforcedthermoplastic (CFRP, CRP, CFRTP or often simplycarbon fiber), is an extremely strong and light fiber-reinforced polymer which contains carbon fibers.The polymer is most often epoxy, but otherpolymers, such as polyester, vinyl ester or nylon,are sometimes used. The composite may containother fibers, such as aramid e.g. Kevlar, Twaron,aluminium, or glass fibers, as well as carbon fiber.The strongest and most expensive of theseadditives, carbon nanotubes, are contained in someprimarily polymer baseball bats, car parts and evengolf club where economically viable. Carbon fiberis commonly used in the transportation industry;normally in cars, boats and trains

Although carbon fiber can be relativelyexpensive, it has many applications in aerospaceand automotive fields, such as Formula One. Thecompound is also used in sailboats, rowing shells,modern bicycles, and motorcycles, where its highstrength-to-weight ratio and very good rigidity isof importance. Improved manufacturing techniquesare reducing the costs and time to manufacture,making it increasingly common in small consumergoods as well, such as certain Think Pads since the600 series, tripods, fishing rods, hockey sticks,paintball equipment, archery equipment, tent poles,racquet frames, stringed instrument bodies, drum


shells, golf clubs, helmets used as a paraglidingaccessory and pool/billiards/snooker cues.

The material is also referred to as graphite-reinforced polymer or graphite fiber-reinforcedpolymer (GFRP is less common, as it clashes withglass-(fiber)-reinforced polymer). In productadvertisements, it is sometimes referred to simplyas graphite fiber for short.

Table IMechanical Properties of Carbon /Epoxy

Sl. No. Properties Value

1 Compressive strength 800-1300(longitudinal) Mpa

2 Compressive strength 50-250(transverse) Mpa

3 Density g.cm-3 1.64 Flexural modulus (longitudinal) Gpa 1255 Flexural modulus (transverse) Gpa 12006 Tensile strength (longitudinal) Mpa 1100-19007 Tensile strength (transverse) Mpa 508 Thermal expansion coefficient -0.3 to -0.7 x

(longitudinal) 10-4 k-1

9 Thermal expansion coefficient 28 x10-4 k-1

(transverse)10 Ultimate compressive strain 0.8%

(longitudinal)11 Ultimate compressive strain 2.5%

(transverse)12 Ultimate tensile strain (longitudinal) 1.1%13 Ultimate tensile strain (transverse) 0.5%14 Volume fraction of fibers 55-60 %15 Youngs modulus(longitudinal) Gpa 120-14016 Youngs modulus (transverse) Gpa 10

Table IIMechanical Properties of E-glass/Epoxy

Sl. No. Properties Value

1 Tensile modulus along 34000X-direction (Ex), MPa

2 Tensile modulus along 6530Y-direction (Ey), MPa

3 Tensile modulus along 6530Z-direction (Ez), MPa

4 Tensile strength of the material, Mpa 9005 Compressive strength of the material, Mpa 4506 Shear modulus along XY-direction 2433

(Gxy), Mpa7 Shear modulus along YZ-direction 1698

(Gyz), Mpa8 Shear modulus along ZX-direction 2433

(Gzx), Mpa9 Poisson ratio along XY-direction (Nuxy) 0.21710 Poisson ratio along YZ-direction (NUyz) 0.36611 Poisson ratio along ZX-direction (NUzx) 0.21712 Mass density of the material (?), 2.6x 10-6

kg/mm313 Flexural modulus of the material, MPa 4000014 Flexural strength of the material, MPa 1200

(D)Modeling of Spur Gear in Gear Box

V. ANSYS ANALYSIS

ANSYS is a finite-element analysis package usedwidely in industry to simulate the response of aphysical system to structural loading, and thermaland electromagnetic effects. ANSYS uses the finite-element method to solve the underlying governingequations and the associated problem-specificboundary conditions.

(A) 3-D Finite Element Analysis

To design composite spur gear, a stress analysis wasperformed using the finite element method doneusing ANSYS software. Modeling was done forevery sur gear with eight-node 3D brick element(solid 45) and five-node 3Dcontact element (contact49) used to represent contact and sliding betweenadjacent surfaces of gear. Also, analysis carried outfor composite spur gear with bonded end joints forCarbon/Epoxy. The maximum and shear stressesalong gears were measured; represent FEA resultsfor composite spur gear (carbon/Epoxy).

(B) Meshed Model of Gear

Figure 5.1: Meshed Model


VI. ANALYSIS OF METTALIC GEAR BOX (A) Analysis of Composite Gear ( Carbon/Epoxy)

Figure 6.1: Displacement (Metallic Gear)

Figure 6.2: Equivalent (von-mises) Stress (Metallic Gear)

Figure 6.3: Equivalent (von-mises) Strain (Metallic Gear)

Figure 6.4: Displacement (Carbon / Epoxy)

Figure 6.5: Equivalent (von-mises) Stress (Carbon / Epoxy)

Figure 6.6: Equivalent (von-mises) Strain (Carbon / Epoxy)


(B) Analysis of Composite Gear (E-glass / Epoxy ) VII. RESULT ANALYSIS OF GEAR BOX

At constant pressure of 500 N along the teeth.

Composite MaterialGear Box Gear BoxMaterial Carbon/ E-glass/ MetallicComparative Epoxy Epoxy Gear BoxValue

Equivalent 1805.6 1630.33 1557.88(von-misesElastic Stress))

Equivalent 0.0144 0.408e-3 0.52e-3(von-misesElastic Strain))

Displacement 0.1371 0.004266 0.00567

(A) Weight Reduction Calculations

(1) Main Shaft

Volume of Trapezoidal Section * *2

a bh t

��

= 1.5 3.5

* 3 * 162��

� ��

= 120mm3

Gear 1

VT = 120mm3

No of Teeth =11VT =120*11

= 1320mm3

Volume of Hollow Section

= 2 2( )4 o iD D l�

�

= 2 2(18 12 )164�

�

= 2261.947mm3

Total Volume = 3581.95mm3

Gear 2VT = 120mm3

No of Teeth = 17VT = 120*17

= 2040mm3


= 2 2( )4 o iD D l�

�

= 2 2(30 12 )114�

�

= 6531.37mm3

Figure 6.7: Displacement (E-glass/epoxy)

Figure 6.8: Equivalent (von-mises) Stress (E-Glass/Epoxy)

Figure 6.9: Equivalent (von-mises) Strain (E-Glass/Epoxy)


Total Volume= 8571.37mm3

Gear 3VT = 120mm3

No of Teeth =21VT = 120*21

= 2520mm3


= � �2 2

4 o iD D l�

�

= � �2 238 12 104�

�

= 10210.17mm3


Gear 4VT = 120mm3


= 2880mm3


= � �2 2

4 o iD D l�

�

= � �2 242 12 104�

�

= 12723.45mm3


(2) Counter Shaft

Volume of counter shaft= �/4 * (20)2*113= 35499.9mm3

Gear-1VT = 120mm3


= 4200mm3


= � �2 2

4 o iD D l�

�

= � �2 265 20 134�

�

= 39053.92mm3


Gear-2VT = 120mm3

No of Teeth = 29

VT = 120*29= 3480mm3

Volume of Hollow Section = � �2 2

4 o iD D l�

�

= � �2 253 20 134�

�

= 24596.3mm3


Gear 3VT = 120mm3


= 3120mm3


= � �2 2

4 o iD D l�

�

= � �2 245 20 114�

�

= 14038.99mm3


Gear 4VT = 120mm3


= 2880mm3


= � �2 2

4 o iD D l�

�

= � �2 241 20 114�

�

= 11067.04mm3


Total Volume of 8 Spur Gear= v1+v2+v3+………………+v8

= 3581.95 + 8571.37 + 12730.176 + 15603.45 +43253.924 + 28076.314 + 17158.9 + 13947.04

vt = 142923.124mm3Total Volume of 2 Shaft

= Vms+Vcs= 12779.9+35499.9= 48279.89mm3

MILD STEELWEIGHT OF SPUR

GEAR=VOLUME*DENSITY


= (142923.124)*(7.85*10-3)

= 1121.946g

Weight of the shaft =v*�= (48279.89)*(7.85*10-3)

= 378.997g

CARBON/EPOXY

WEIGHT OF SPURGEAR = VOLUME*DENSITY

= (142923.124)*(1.6*10-3)

= 228.976g

Weight of the shaft = v*�= (48279.89)*(1.6*10-3)

= 77.247g

E-GLASS/EPOXY

WEIGHT OF SPUR GEAR= VOLUME*DENSITY

= (142923.124)*(2.6e-3)

= 371.60g

Weight of the shaft = v*�= (48279.89)*(2.6e-3)

W = 125.527g

OPTIMIZATION

1. FOR CARBON/EPOXY

% of wt Reduction = 1121.946 228.976

* 1001121.946

�

= 79.6%

2. FOR E-GLASS/EPOXY

% of wt Reduction = 1121.946 371.60

* 1001121.946

�

= 66.87%

(B) Weight Reduction

Sl. No. Gear Box Material Weight

1. Metallic 1500.9 g

2. Carbon/Epoxy 306.22 g

3. E-Glass/Epoxy 497.13 g

Sl. No. Gear Box Material % of WeightReduction

1. Carbon/Epoxy 79.6%

2. E-Glass/Epoxy 66.87%

VIII. FATIGUE

(A) Stress-life Data Options/Features

• Fatigue material data stored as tabularalternating stress vs. life points.

• The ability to define mean stress dependent ormultiple r-ratio curves if the data is available.

• Options to have log-log, semi-log, or linearinterpolation.

• Ability to graphically view the fatigue materialdata The fatigue data is saved in XML formatalong with the other static material data.

Figure 7.1 is a screen shot showing a user editingfatigue data in ANSYS.

Figure 7.1: SN Curves in ANSYS

(B) Analysis

Fatigue results can be added before or after a stresssolution has been performed. To create fatigueresults, a fatigue tool must first be inserted into thetree. This can be done through the solution toolbar

Figure 7.2: Fatigue Tool Information Page in ANSYS


or through context menus. The details view of thefatigue tool is used to define the various aspects ofa fatigue analysis such as loading type, handling ofmean stress effects and more. A graphicalrepresentation of the loading and mean stress effectsis displayed when a fatigue tool is selected by theuser. This can be very useful to help a noviceunderstand the fatigue loading and possible effectsof a mean stress.

(C) Loading

Fatigue, by definition, is caused by changing theload on a component over time. Thus, unlike thestatic stress safety tools, which perform calculationsfor a single stress, fatigue damage occurs when thestress at a point changes over time. ANSYS canperform fatigue calculations for either constantamplitude loading or proportional non-constantamplitude loading. A scale factor can be applied tothe base loading if desired. This option, locatedunder the “Loading” section in the details view, isuseful to see the effects of different finite elementload magnitudes without having to re-run the stressanalysis. (i). Constant amplitude, proportionalloading, (ii). Non-constant amplitude, proportionalloading.

(D)Result Output

number of cycles allowed at that stress intensity is3595. The partial usage value, 1.39063, is the ratioof cycles used/cycles allowed. The combination ofevent 1, load 1 and event 1, load 2 produces analternating stress intensity of 37412 N/cm2. Thespring was subjected to 500,000 cycles while fromthe S-N Table, the maximum number of cyclesallowed at that stress intensity is 421,300. The partialusage value, 1.18669, is the ratio of cycles used/cycles allowed.

The Cumulative Fatigue Usage value is sum ofthe partial usage factors (Miner’s rule).

Location: 1 Node 65 at the fixed end.

The combination of event 2, load 1 and event 2,load 2 produces an alternating stress intensity of55744 N/cm2. The spring was subjected to 5000cycles while from the S-N Table, the maximum

IX. CONCLUSION

This paper clearly shows that the compositematerial gearboxes will replace the existing metallicgearbox for weight reduction and other compositebenefits. A comparative study has been madebetween composite and steel spur gearbox with


respect to weight, cost, and strength. From theresults, it is observed that the composite spurgearbox is lighter and more economical than theconventional steel spur gear box with similar designspecifications. Composite spur gearbox reduces theweight by 80% for Carbon/Epoxy, and 66.87% forE-Glass/Epoxy over conventional spur gearbox.

The proposed life prediction methodology wasimplemented in ANSYS and has been found to bein good agreement with the direct cycle-by-cyclesimulations. This work represents the first attemptin developing a simulation-based approach in thefield where the design is dominated byexperiments.

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R. PANNEERDHASS AND A. GNANAVEL BABU - ..:: …serialsjournals.com/serialjournalmanager/pdf/139108327… · · 2017-06-24static stress analysis of composite gears using a three-