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CHAPTER 5

PREVENTION OF TOOTH DAMAGE IN HELICAL

GEAR BY PROFILE MODIFICATION

5.1 INTRODUCTION

In any gear drive the absolute and the relative transmission error

variations normally increases with an increase in pressure angle. Thus a gear

with higher pressure angle tends to be more sensitive to pitting damage. The

contact stress and the bending stresses are the sources of failure in the helical

gear. Tooth surface wear mainly occurs near the dedendum and the amount of

wear increases as the number of teeth in meshing increases. Increase in

module results in reduction of tooth deflection and root stresses. Tip relief is

provided for minimizing the contact stress and to enable smooth running of

the gear pair. Composite profile design reduces the bending stresses, tooth

deflection and contact stresses in the helical gear teeth. This chapter is

dedicated to analyze the performance of composite profile i.e the combination

of both involute profile and cycloid profile for preventing pinion failure in the

gearboxes used in the wind turbine generator. A comparative study was

carried out with the following four options to choose the best profile for the

helical gear pair drive engaged in WTG.

i) A conventional pinion made of involute profile with tiny tip

relief.

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ii) A pinion made of composite profile with tip relief.

iii) A least module helical pinion with next higher module helical

pinion comprising of tip relief.

iv) A higher module helical pinion made of composite profile

with tip relief.

5.2 PROBLEM PHASE

Wind Turbine Generator of 225 kW capacity built with gearbox

comprised of one planetary stage and two helical stages are selected for

investigation. The rst-helical stage called slow-speed line has 119/23 teeth

gear combination and the second-helical stage called high-speed line has

94/19 teeth gear combination to achieve a nal speed ratio of 1:25.60. This

increase in gearbox speed induces abnormal noise and vibration during the

operation of the gearbox at full load, in addition, both drive and non-drive

ank of high-speed pinion experience more standstill or pressure marks and

have scuf ng wear and pitting wear which ultimately leads to frequent pinion

failure. Besides failure of pinion in the high-speed stage when the WTG is in

operational mode, it requires huge man-hours and machine stoppage for

servicing the gearbox. Frequent turbine stoppages lead to enormous power

generation losses, customer dissatisfaction and so on. Sometimes, the

damaged high-speed pinion certainly affects smooth functioning of its mating

gear, bearings, and other stage gear trains.

Further, gear failure in the intermediate stage warrant either the

replacement of that gear in the gearbox or overhauling of the gearbox. This

complicates and leads to heavy repairing cost of the wind turbine generator

because of the tower height and weight of the gearbox. De-erection of nacelle

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necessitates a huge-capacity crane of the order of 200–400 tonne at the wind

turbine site to swap the gearbox in the turbine unit. The survey undertaken

during this research work confirms that the frequent pinion failure occurs in

the existing 94/19 teeth gear pair used in the high-speed stage.

The particular gear pair is made of ve module having 20° pressure

angle with tiny tip relief. So, an attempt has been made to modify the helical

gear profile for higher module with increased tip relief and introduction of a

composite pro le to avoid the pinion failure. Recent days gear manufacturers

and research consultants have explored the possibilities of the development of

advanced materials, new heat treatment methods, design of stronger tooth

pro le, and new gear manufacturing process. The objective of this research

study is to find out the solution for preventing pinion failure in the gearboxes

used in the WTG through pro le modi cation.

5.3 CONSTRUCTION OF COMPOSITE PROFILE

5.3.1 Tip Relief

Tooth modi cation is a method by which the tooth pro le is

changed from theoretical involute curve by reducing a tiny amount at the

tooth tip. In general, tooth modi cation methods are used to reduce the

meshing vibration and noise of the gear train. Pro le modi cations are done

towards involute curve, lead crowning towards face width and end relief.

Figure 5.1 shows 2-Dimensional (2D) geometry of half size tooth having

tooth tip relief So , length ho , S is the tooth tip thickness and in the radial

direction from the tip hf which are symmetrical on both sides of the tooth.

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Figure 5.1 Two-dimensional geometry of half-size tooth

5.3.2 Cycloid Pro le

The spur gear comprises of involute–cycloid conjugate pro le

(Figure 5.2). It consists of an involute pro le near the pitch point which is just

above and below the pitch point and a cycloid tooth pro le on the remaining

portion of addendum and dedendum.

Figure 5.2 Spur gear involute–cycloid conjugate pro le

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Figure 5.3 shows the basic rack form of involute–cycloid composite

pro le gear. The rack for the composite tooth pro le gear is of the form

PQR consisting of a straight line PQ and a cycloid curve QR which is

drawn by rolling a circle on the X-axis (the base pitch line). The tooth

strength is improved by proper selection of parameters such as pressure angle

and rolling circle (Gitin Maitra 1998). The addendum and dedendum of the

rack are symmetrical to each other with respect to the pitch point P because

of the interchangeability of the gear.

Using the coordinate system shown in Figure 5.3 the cycloid curve

PQR is expressed by the Equations (5.1) to (5.3)

x = a ( sin ) + X0 (5.1)

y = a (1 Cos ) (5.2)

and

X0 = 2a inv 0 (5.3)

Figure 5.3 Cycloid curve co-ordinate systems

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Where a is the radius of the rolling circle, is the rotational

angle of the rolling circle and 0 is the inclination of the straight line PQ to

the Y-axis, which is equal to the cutter (hob) pressure angle of the involute.

X0 is the distance between the pitch point P and the point where the

cycloid curve begins.

5.3.3 Helical Gear Pro le

The addendum and dedendum are symmetrical and conjugate in

cycloid pro le, whereas a special concept called helical composite pro le

comprising epi-cycloid with involute pro le in addendum and involute pro le

alone in dedendum was introduced as shown in Figure 5.4 (i.e. an addendum

is having a small portion of involute pro le just above the pitch point and the

remaining pro le with an epi-cycloid pro le). Pinion of 19 teeth ×5 modules

and 18 teeth × 5.5 modules encompassing this composite pro le have been

considered for analysis in this research study.

Figure 5.4 Composite pro le in helical gear comprising epi-cycloid with involute pro le

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5.4 DESIGNING THE MODIFIED HELICAL GEAR PROFILE

Conventional helical pinion is made up of 5 mm module whereas

the modi ed helical pinion is formed with 5 mm module with composite

profile and 5.5 mm module pinion with both the involute and composite

profile with tip relief for the same centre distance. Hence, higher module

pinion with lesser addendum modi cation co-efficient is analyzed in this

research study. Tip relief is introduced on pro le for noise reduction, which

will minimize the contact stress as well. Tables 5.1 and 5.2 give the

speci cations of the conventional and the proposed gears used in this

investigation.

Table 5.1 Specifications of 94/19 teeth gear pair

Description

Conventional helical gear pair

with involute profile

Modified helical gear pair with

composite profile

Number of teeth (Z1 /Z2 ) 94/19 94/19 Normal module (mn) 5 5Face width (b) in mm 100 100Normal pressure angle ( ) 20° 20°

Helix angle ( ) 14° 14°

Centre distance (a1) in mm 299 299Pitch circle diameter (d) in mm 97.908 97.908Addendum modification co-efficient (X1 /X2 )

1.06/0.65 1.06/0.65

Pinion tip circle diameter (da) in mm 114.408 114.408Total contact ratio (eps g) 2.865 2.865Gear ratio (u) 4.947 4.947Rotational speed (n) in rpm 1040 1040 Torque (T) in Nm 2066 2066Rolling circle radius (a) in mm - 6.5Rotational angle of the circle ( ) - 20°

Addendum (ha) in mm 8.25 8.25Dedendum (hf) in mm 3 3.15

Material and heat treatment18CrNiMo7

Case hardened and tempered

18CrNiMo7 Case hardened and tempered

Method of finishing teeth Profile grinding Profile grinding

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Table 5.2 Specifications of 85/18 teeth gear pair

DescriptionModified helical gear pair with

involute profile

Modified helical gear pair with

composite profileNumber of teeth (Z1 /Z2 ) 85/18 85/18Normal module (mn) 5.5 5.5Face width (b) in mm 100 100Normal pressure angle ( ) 20° 13°

Helix angle ( ) 14° 14°

Centre distance (a1) in mm 299 299Pinion Pitch Circle Diameter (d) in mm 102.031 102.031 Addendum modification coefficient (X1 /X2 )

0.6/0.79 0.6/0.79

Pinion tip circle diameter (da) in mm 119.631 119.631 Total contact ratio (eps g) 2.719 2.719Gear ratio (u) 4.722 4.722Rotational speed (n) in rpm 1040 1040 Torque (T )in Nm 2066 2066 Rolling circle radius (a) in mm - 7.25 Rotational angle of the circle ( ) - 15Addendum (ha) in mm 8.8 8.8Dedendum (hf) in mm 3.575 3.7

Material and heat treatment18CrNiMo7

Case hardened and tempered

18CrNiMo7 Case hardened and

temperedMethod of finishing teeth Profile grinding Profile grinding

5.5 FORCE ANALYSIS

The load-transmitting capability of gear tooth is analyzed and

checked for designing a gear system. The effective circumferential force on

the tooth at the pitch circle of the gear while in meshing is estimated. Two

kinds of stresses are induced in gear pair during the power transmission from

one shaft to another. They are:

i) Bending stress-induced on gear teeth due to the tangential

force developed by the power.

ii) Surface contact stress or compressive stress.

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The load is assumed as uniformly distributed along the face width

of the tooth.

5.6 FORCE COMPONENTS

The force exerted by the helical gear on its mating gear acts normal

to the contacting surface if the friction is neglected. However, a normal force

in case of helical gear has three components that is apart from the tangential

and radial components that are present in the spur gear, a third component

parallel to the axis of the shaft called axial or thrust force exists. These force

components are shown in Figure 5.5. For the given data various forces were

derived from standard Equations (5.4) to (5.8).

Figure 5.5 Forces in helical gear

Torque T = P× 60/2 n (5.4)

Tangential force Ft = 2 × T/d (5.5)

Normal force Fn = Ft / (cos × cos ) (5.6)

Radial force Fr = Ft × (tan /cos ) (5.7)

Axial force Fa = Ft × tan (5.8)

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These force components are computed for a power value of 225 kW

at speed 1040 rpm and are presented in Table 5.3. Figure 5.6 presents the

tangential forces that act along the line of contact in the meshed model of

helical pinion as recommended by ANSI/AGMA 1012–G05 standard.

Table 5.3 Force components in helical gear

Profile

Tangentialforce in Newton

(N)

Normal force in Newton

(N)

Radial force in Newton

(N)

Axial force in Newton

(N) In use 19 teeth involute 41340 37692 15507 10307 Proposed 19 teeth involutecycloid composite 41340 37692 15507 10307

Proposed 18 teeth involute 40508 36934 15195 10099Proposed 18 teeth involute cycloid composite 40508 38297 9638 10099

Figure 5.6 Tangential forces in helical pinion

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5.7 FINITE-ELEMENT ANALYSIS

Since the solid 186 elements have quadratic displacement behavior

and is well suited to model irregular meshes, this solid 186 element type with

20 nodes is selected to describe the helical gear and its tooth de ection in

ANSYS software version 11.0. As the gears are made out of heat-treated alloy

steel, carburized and case-hardened alloy steel (18CrNiMo7) is taken for

analysing the root stress concentrations. The material properties are given in

Table 5.4. The maximum stresses on the tensile and compressive sides of the

tooth are considered for analysis.

Table 5.4 Material properties

Gear material 18CrNiMo7 Density 7870 kg/m3

Young’s modulus (E) 206000 N/mm2

Poisson’s ratio (ny) 0.30 Yield strength (Rp) 850 N/m2

20 Nodes 3D solid element with three degrees of freedom per node

(UX, UY, and UZ) is stacked to model through the thickness discontinuities.

To obtain the individual tooth bending stresses, tooth de ection, and stiffness,

single tooth of both the pinion and the wheel with solid rim have been meshed

in Finite-Element Analysis (FEA) as per ANSI/AGMA 1012 – G05 standards

as given in Figure 5.6.

Virtual model analysis in ANSYS software is carried out for all the

four models. The meshed model of all the four gear teeth is shown in

Figures 5.7 to 5.10. The elements in the 19 teeth x 5mm module gear model

having involute profile are 68,181 (Figure 5.7) and in 19 teeth x 5mm module

gear model having composite profile are 42,382 (Figure 5.8). Similarly, for

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18 teeth x 5.5 mm module gear model having involute profile are 66,801

(Figure 5.9) and 18 teeth x 5.5 mm module gear model having composite

profile are 36,395 (Figure 5.10).

Figure 5.7 Meshed model of 19 teeth × 5 module involute pinion

Figure 5.8 Meshed model of 19 teeth × 5 module composite pinion

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Figure 5.9 Meshed model of 18 teeth × 5.5 module involute pinion with tip relief

Figure 5.10 Meshed model of 18 teeth × 5.5 module composite pinion with tip relief

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5.8 RESULTS AND DISCUSSION

The visual presentation of the induced tooth de ection and bending

stresses in pinion having different number of teeth and modules are depicted

in Figures 5.11 and 5.12 respectively. The induced tooth de ection and

bending stresses (von Mises) given in Table 5.5 were obtained using Finite

Element Analysis. It is observed from the ANSYS study and also from

Table 5.5 that the 18 teeth × 5.5 mm module pinion generated with helical

composite pro le has a smaller amount of tooth de ection (0.006 mm), lesser

root stress (150 N/mm2–von Mises) with higher tooth stiffness (6.75 × 10

6N/mm)

as compared with that of the existing 19 teeth × 5 mm module conventional

involute pinion.

Figure 5.11 Tooth deflections of pinions

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Figure 5.12 Bending stress of pinions

Table 5.5 FEA results at maximum speed (1040 rpm) of pinion

Gear strength 19 teeth × 5

module18 teeth × 5.5

moduleInvolute Composite Involute Composite

Tooth deflection in mm 0.007 0.009 0.007 0.006

Stiffness (N/mm) 5.36 × 106 4.59 × 106 5.78 ×

106 6.75 × 106

Bending stress (N/mm2) 1057 796 459 150Permissible tooth root stress (N/mm2) 825.50 825.50 820.72 820.72

Figure 5.13 predicts the trend how the tooth de ection varies at

maximum speed for pinion with different teeth and modules. The de ection

decreases in the modi ed pinion having 18 teeth×5.5 mm module with

composite pro le. Figure 5.14 shows bending stresses in pinions at maximum

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speed. Bending stress (von Mises) decreases drastically in pinion having

helical composite pro le with 18 teeth×5.5 mm module. Figure 5.15 indicates

how the tooth stiffness is varying for the change in profile and module.

Figure 5.13 Tooth deflection trend

Figure 5.14 Bending stress trend

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Figure 5.15 Tooth stiffness trend

5.9 CONCLUSION

The following conclusion is arrived from the foregoing analysis

and investigation pertaining to the tooth de ection, stiffness, and bending

stresses of the pinion having different modules:

i. The bending stresses (von Mises) of the modi ed composite

pro le gear pair having 5.5 mm module is comparatively less

than that of the conventional helical gear pair.

ii. The modi ed 18-teeth pinion having 5.5 mm module with

composite pro le exhibits less tooth de ection under load

condition and more tooth stiffness.

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iii. The bending stress of conventional 19-teeth helical pinion

having 5 mm module exceeds the permissible tooth root stress

(Table 5.5), which is the root cause for the failure of the

pinion very often.

iv. However any fault in the cutter design for generating

composite pro le leads to misalignment in the gearbox

assembly. Therefore, care must be taken in the gear-making

process; otherwise it would not at all serve the purpose.