Project Report

A Project Report on

Gear Design(Tool Geometry Calculations

&

Case Study of its Basic Manufacturing Process)

1Project Report | Gear Design

DECLARATION

I hereby declare that the project work entitled is an authentic record of my own work

carried out at RDSO(LUCKNOW), under the guidance of Mr. A.K.Brahmane during

MAY- JULY 2011.

(Signature of student)

Shubham Tandon

Date: ___________________

Certified that the above statement made by the student is correct to the best of our knowledge and belief.

A.K.Brahmane

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ACKNOWLEDGEMENT

I would like to express my profound gratitude to all those who have been instrumental in the

preparation of this project report. I wish to place on records, my deep gratitude to my project guide Mr

A.K.Brahmane, a highly esteemed and distinguished guide, for his expert advice and help.

I would like to thank Dr. S.C.Sharma, HOD, as well as other professors from our department for their

support

I am deeply grateful to my friends who helped me to conduct this study, advising me on this project

report and furnishing the required information.

Lastly, I would like to thank God, my Parents for their constant help and support.

With RegardsShubham Tandon

3Project Report | Gear Design

COMPANY PROFILE:

Railways were introduced in India in 1853 and as their development progressed through to the twentieth century, several company managed systems grew up.To enforce standardisation and co-ordination amongst various railway systems, the Indian Railway Conference Association(IRCA) was set up in 1903, followed by the Central Standards Office (CSO) in 1930, for preparation of designs, standards and specifications. However, till independence, most of the designs and manufacture of railway equipments was entrusted to foreign consultants. With Independence and the resultant phenomenal increase in country’s industrial and economic activity, which increased the demand of rail transportation - a new organisation called Railway Testing and Research Centre (RTRC) was setup in 1952 at Lucknow

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MOTIVE POWER DIRECTORATE:-

Motive Power directorate has been engaged in designs and standards works related with diesel-electric, diesel-hydraulic and electric locomotives since 1960s. Important accomplishments from this time, through to late 1990s, ranged form indigenisation of a large number of diesel locomotive components, establishment of special maintenance code in areas with reliability problems, evolving and adapting standards. The main activities of the directorate are as under:-

a. Complete design development of diesel-electric and diesel-hydraulic locomotives, diesel rail cars, 700 hp diesel multiple units, 700 hp & 1400 hp diesel electric multiple units, BG,MG & NG rail buses, 140 ton diesel hydraulic break down cranes, re-railing equipments and rescue devices. For electric locomotives, only the mechanical assemblies, bogies, under- gear, brake-gear, underframe and superstructure.

b. Development and standardisation of locomotive systems and sub-assemblies.c. Technical investigation into operational and maintenance problems of Railways.d. Providing technical consultancy to Railway Management and other Public Sector

Undertakings in matters connected with Diesel Traction.e. Acquisition and assimilation of state-of-the-art technology in the field of diesel

locomotives and accident management equipments, e.g. 4000 HP locomotive, 140 T Break Down Crane.

f. Indigenisation of locomotive equipment.g. Nodal directorate for issue of speed certificates for all types of rolling stock. h. Nodal directorate for IRS/BIS specifications.

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CONTENTS PAGE

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Transmission:-

A transmission or gearbox provides speed and torque conversions from a rotating power source to another device using gear ratios.

The two most common mechanisms used for mechanical transmission are:-

Belt and Pulley:-

A belt is a loop of flexible material used to link two or more rotating shafts mechanically. Belts may be used as a source of motion, to transmit power efficiently, or to track relative movement. Belts are looped over pulleys. In a two pulley system, the belt can either drive the pulleys in the same direction, or the belt may be crossed, so that the direction of the shafts is opposite. As a source of motion, a conveyor belt is one application where the belt is adapted to continually carry a load between two points.

Gear:-

Gears are machine elements used to transmit rotary motion between two shafts, normally with a constant ratio. The pinion is the smallest gear and the larger gear is called the gear wheel.. A rack is a rectangular prism with gear teeth machined along one side- it is in effect a gear wheel with an infinite pitch circle diameter. In practice the action of gears in transmitting motion is a cam action each pair of mating teeth acting as cams. When the teeth action is such that the driving tooth moving at constant angular velocity produces a proportional constant velocity of the driven tooth the action is termed a conjugate action. The teeth shape universally selected for the gear teeth is the involute profile

7Project Report | Gear Design

THE GEOMETRY OF INVOLUTE SPUR GEARS

FIG 2.1

THE INVOLUTE

The gear teeth have an involute profile which satisfies the law of gearing and ensures a rolling contact which transmits a constant velocity ratio. An involute can be generated by:

FIG 2.2

A straight line rolling on a circle Cord unwinding from a circle

without slippage.

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When transmitting motion using an involute:

Force always acts along the line of common tangent to the base circles, also called the line of contact.

The force vector always passes through the pitch point irrespective of centre distance and is always normal to tooth surface.

Centre distance does not affect the velocity ratio transmitted. Only the line of force changes in direction.

FIG 2.3

Pressure Angle

Pressure angle is in general the angle at a pitch point between the line of pressure which is normal to the tooth surface, and the plane tangent to the pitch surface. The pressure angle gives the direction of the normal to the tooth profile and hence the direction of force. For a given material, smaller pressure angles correlate with weaker teeth.

FIG 2.3 (a) (b)

α is the pressure angle and varies with the tooth height. It is zero at base circle.

From the FIG. 2.3(b) фy= tan (α) - (α) = inv (α)

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The minimum number of teeth required to avoid interference varies inversely as sin (α). This suggests the use of higher pressure angles. But too high pressure angles lead to decrease in the length of contact and lower contact ratios. An optimum range is 14.5 to 22.5 degrees.

FILLET

Tooth fillet is produced by rounded rack tip. If the rack has a rounded tip then the fillet produced is the path of a series of circles .The circle centres lay on the trochoidal path produced by the centre of tip rounding.

FIG 1.4

Fillets produced by different trochoids:

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FIG 2.5

FORM DIAMETER

The involute and fillet curve together determine what is termed the Form Diameter. This is the transition point between the involute curve and the fillet curve. It determines the limit of the usable portion of the gear flank where contact may take place. It cannot exist below the base circle.

FIG 2.6

ADDENDUM MODIFICATION

In gear design a parameter known as addendum modification is used to adjust the gear teeth It is often called rack shift or profile shift It is usually expressed as a coefficient i.e. the value in mm divided by module If, when the gear is generated from the basic rack, the reference line of the rack co-insides with the

reference diameter of the gear, the addendum modification coefficient is zero. If, when the gear is generated from the basic rack:

The reference line of the rack is below the reference diameter, the addendum modification coefficient < 0.

The reference line of the rack is above the reference diameter, the addendum modification coefficient >0.

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FIG 2.7

EFFECT OF NUMBER OF TEETH ON ADDENDUM MODIFICATION:

FIG 2.8

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PATH OF CONTACT

The contact on a spur gear is a line that progresses from the root to the tip on the driving gear and the tip to

the root on the driven gear. The contact takes place on a line tangent to the base circles.

FIG 2.9

Contact is usually between 1 or 2 teeth pairs SAP: The position shown below is where contact first starts on tooth number 1, and is called the start

of active profile (SAP).

FIG 2.10

LPSTC: Tooth 0 is about to leave contact and tooth number 1 will be the only tooth pair in contact. This position is called the lowest point of single tooth contact (LPSTC).

FIG 2.11

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Pitch point: Tooth 1 is the only tooth in contact and the contact occurs where the tangent to the 2 base circles intersects the line joining the 2 centres.

FIG 2.12 HPSTC: Contact first starts on tooth number 2 and tooth number 1 will no longer be the only tooth in

contact. This is the highest point of single tooth contact (HPSTC)

FIG 2.13 EAP: The position where tooth 1 leaves contact and is called the end of active profile (EAP)

FIG 2.14

The length of the path of contact is from the start to the end of active profile.

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FIG 1.15

A position along the path of contact can be expressed as : roll distance roll angle radius up the tooth flank

FIG 2.16

Contact ratio: Contact ratio for spur gears is defined as length of path of contact divided by the base

pitch. It is an average measure of how many teeth are in contact through the mesh cycle. It will have effects on both noise and durability.

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A CASE STUDY of the GEAR & PINION (of TRACTION MOTOR TYPE

165) in WDM2 LOCOMOTIVE

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Brief Description of the Transmission in WDM2 LOCO

The class WDM-2 is Indian Railways’ workhorse diesel locomotive. The first units were imported fully built from the American Locomotive Company (Alco) in 1962. Since 1964, it has been manufactured in India by the Diesel Locomotive Works (DLW), Varanasi. The model name stands for broad gauge (W), diesel (D), mixed traffic (M) engine. The WDM-2 is the most common diesel locomotive of Indian Railways.

Technical specifications[2]

Manufacturers Alco, DLW

Engine

Alco 251-B, 16 cylinder, 2,600 hp (2,430 hp site rating) turbo supercharged engine. 1,000 rpm max, 400 rpm idle; 228 mm x 266 mm bore/stroke; compression ratio 12.5:1. Direct fuel injection, centrifugal pump cooling system (2,457 l/min at 1,000 rpm), fan driven by eddy current clutch (86 hp at 1,000 rpm)

Governor GE 17MG8 / Woodwards 8574-650 / Medha MEG 601

Transmission Electric, with BHEL TG 10931 AZ generator (1,000 rpm, 770 V, 4,520 amperes)

Traction motorsGE752 (original Alco models) (405 hp), BHEL 4906 BZ (435 hp) and (newer) 4907 AZ (with roller bearings)

Axle load 18.8 tonnes, total weight 112.8 t

Bogies Alco design cast frame trimount (Co-Co) bogies

Starting TE 30.4 t, at adhesion 27%

Length over buffer beams

15,862 mm

Distance between bogies

10,516 mm

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Transmission

The WMD2 locomotive uses electrical transmission. The 16 cylinder Alco 251-B runs the BHEL TG 10931 AZ generator. The generator has a Bull Gear (102 teeth) along with the exciter and the auxiliary generator. The exciter starts the engine by getting the engine running at its cranking velocity of around 100 rpm. When the rpm reaches 100 rpm then the exciter stops and the engine starts to produce power.

The auxiliary generator is responsible for producing the power required by the carriages (fans, tube lights, air conditioner etc.). But the maximum power produced by the generator is passed through a rectifier and converted to AC. These A.C. powers the six traction motors mounted on the axles of the bogies of the locomotive. These motors then transmit power via the gears.

18Project Report | Gear Design

Gear and Pinion Design

Known parameters:-

Centre Distance (as provided by BHEL) (a):- 468.48mmSpeed of loco (speed of gear):- 120 KmphRpm of Traction Motor (as provided by BHEL) (N):-2200 rpmWheel Diameter (D):-1092(mm) (New wheel)

1054(mm) (Half worn wheel)

Rpm of Wheel (rpm of gear) :- (120*1000/3600)*(60*1000/π*1054)= 604 rpm

Teeth Ratio (Gear: Pinion) (Z1/Z2):- (rpm of traction motor)/(rpm of wheel)= 2200/604=3.67

We know that: - a = (Z1+Z2)m/2-----(1)

The module (m) used in Indian Railways is 11.2889mm (the standard module available with the gear manufacturers Shanti Gears Ltd.)

So, from equation (1) , we calculate Z1 + Z2 :- Z1 + Z2 = 82.998 ~83

Using results from above, we calculate the values of Z1 & Z2 :-Z1 = 65.22~65 Z2 = 18

Therefore the GEAR RATIO obtained from the calculations = 65:18

The standardised pressure angle (αn) (as provided by the gear manufacturer) :- 200.

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Pitch Circle Diameter: - module*no. of teeth -----(2)

PCD of Gear (D1):- 11.2889*65

= 733.778 mm

PCD of Pinion (D2):- 11.2889*18

=203.200 mm

Actual centre distance (a) = 468.48 mm

Calculated centre distance (a0) = (Z1 + Z2 )m/2

= (65 +17.77)11.2889/2

=467.195mm

Operating Pressure angle (αn0 ) :- cos-1(a0/a*cos α)--------(3) = cos-1(467.195/468.48 * cos 200) = 20.420

Addendum Correction Factor (x):- (Z1 + Z2)*(Inv(αn0)-Inv(αn))/(2tan αn) -------(4) =(Z1 + Z2)*(Inv(20.42)-Inv(20))/(2tan20) =.1133

[ Inv(φ)= tanφ – φ*π/180 ]

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Tolerances(in accordance with BS 235)

Table 1.

Gear tooth Accuracy Grades(in accordance with BS 235)

Wheel and Pinion accuracy grade Approximate vehicle speed(Kmph)

5 >160

6 140-160

7 50-140

8 <50

Clearly from table 1. the accuracy grades to be followed in WDM4 Loco is grade 7.

Table 2.

Limits of Tolerances on Tooth Profile

Accuracy Grades Profile Tolerances(μm)5 0.40φ+5.0

6 0.63φ+6.5

7 1.00φ+8.0

8 1.60φ+10.0

[ φ :- m + .1(PCD)^(.5) Gear :- Φ = 13.99Pinion :- Φ= 12.714

Thus, from table 2. The Profile Tolerences are:-

Gear: -0 .022 mmPinion:- 0.021 mm

Table 3.

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Limits of Tolerances on total composite error

Accuracy Grade Total Composite Error(μm)

5 2.0φ+25.0

6 3.15φ+40.0

7 4.50φ+56.0

8 5.60φ+71.0

Following grade 7 accuracy the total composite error is:-Gear :- 0.118 mmPinion :- 0.112 mm

TABLE 4.

Limits of Tolerances on Tooth Alignment

Accuracy Grade Tolerances on Alignment(μm)

5 0.80(b) ^(.5) +4

6 (b) ^(.5) = 5

7 1.25(b) ^(.5) +6.3

8 2(b) ^(.5) + 10

[b:- face width = 127mm ]

Following Grade 7 accuracy the tolerances obtained are :-

Gear :- 0.020 mmPinion :- 0.020 mm

Table 5.

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Backlash(μm)Minimum Maximum20m+40 50m + 100

Therefore the maximum and the minimum backlash are :-0.266 mm(min) and 0.664 mm (max)

Tip Relief of 0.1 mm to be provided (as per BS 235)

Base tangent length23

Project Report | Gear Design

The base tangent length gives us the length which the disc micrometer measures over the calculated number of teeth. This measurement helps us to verify whether the final gear obtained after machining conforms the desired design standards. The formula for calculating the base tangent length as well as the span over which it is to be calculated can be obtained from the BS 235 standards for Traction gears.

No. of teeth over which base tangent span is measured (k)=K= 1\ π{z*tan[cos-1(db/d(1+2x/z))]sec2 βb- z*Inv αt- 2x*tan αt+ π} + x/8---------(5)

Where:-db:- base diameter in mmd:- pitch circle diameter in mmz :- no. of teethx:- addendum correction coefficient in mmβb:-base helix angle( 900 for spur gears)αt:-transverse pressure angle at the reference circle(PCD).

Base Tangent Span:-W= m*cos αt [π(k-0.5) +2x tan αn + z*inv αt]-------(6)

Where :-M:- module in mmK:- as calculated from eqn.(5)αn :- normal pressure angle at the reference circle in mm(PCD).z :- no. of teethx:- addendum correction coefficient in mm

(i) For GEARS :-

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Using the formula (5):-

K= [1\ π]*{65*tan[cos-1(689.525/733.778(1+2(0.345/65))]sec2 90- 65*Inv 70- 2*0.345*tan 70+ π} + 0.345/8

K= 6.778 ≈ 7 teeth

Base tangent Length:- [using the eqn(6)]W= 11.2889*cos 20 [π(7-0.5) +2*0.345 tan 20 + 65*inv 70]-------(6)W = 223.890 mm [ 223.989 mm (max) 223.798 mm (min) ] {As per BS 235 : Part 1}

(ii) For PINIONS :-

Using the formula (5):-

K= [1\ π]*{18*tan[cos-1(190.945/203.2(1+2(0.345/18))]sec2 90- 18*Inv 70- 2*0.345*tan 70+ π} + 0.345/8

K= 2.84 ≈ 3 teeth

Base tangent Length:- [using the eqn(6)]W= 11.2889*cos 20 [π(3-0.5) +2*0.345 tan 20 + 18*inv 70]-------(6)W = 88.650 mm [ 88.707 mm (max) 88.585 mm (min) ] {As per BS 235 : Part 1 }

Hoops Stress in Pinion

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(Torque carrying capacity & Hoop’s stress calculation for 18:65 Gear Ratio WDM4 Loco)

Centre Distance (a) = 468.48 mmm = 11.2889 mml= 127mm (face width)pinion bore taper = 1:9.6

Pinion root diameter (dr) = 179.4 mmPinion base diameter (da) = 113.78 mm

Pinion advance = ( 1.1 – 1.3 )mm

Interference (i) = 1.1/9.6 – 1.3/9.6 = 0.115 – 0.135

Interference per unit area (e) = ( 0.00101 – 0.0012)

P = E*e2

* { 1 - (da/dr)2 }------ (7)

P :- Pressure at the inner rim. Therefore, using eqn (7)---- P= 2.11 * 10^6 * 0.00101 * (1- 0.4022 )/2

= 636.986 Kg/cm2 (with min interference)

Similarly, calculating the pressure for maximum interference: - P= 747.77 Kg/cm2

Force acting on inner rim:- P*A = P * π * da * l--------(8)Torque Capacity:-T= μ* P * π * da * l * da/2----------(9) (μ:- Poisson’s ratio of steel)

Therefore, Tmin = 2567.61 kg-m And, Tmax = 2896.76 kg-m

Actual torque acting on the motor = T.E. * D/2 * G.R. -------------------- (10)Where:-T.E. :- Tractive Effort reqd. for the Locomotive.D: - Diameter of the wheel.G.R. :- Gear Ratio.

Therefore from eqn. (10) :- Torque on motor = (30450/6) * (1054/2) * (18/65)/1000 = 740.637 kg-m

Factor of Safety = Torque Capacity ------------- (11)

26Project Report | Gear Design

Torque on each motor

Therefore, Factor of Safety of our designed pinion = 2567.61/740.637 = 3.47 (min) = 2896.76/ 740.637 = 3.911 (max)

Calculated Factor of Safety = 3.47(min) – 3.911(max)Required factor of Safety = 2.5

So, we find out that the Factor of Safety is well above the desired safety level of 2.5.

27Project Report | Gear Design

Pressing Pressure of the Gears

Axle seat diameter = 254.0254(max)/ 254.000(min)

Bore diameter = 253.771(max)/ 253.746(min)

Length of journal = (177.3- 177.8) mm

Surface Roughness of axle = 0.4R μm

Surface Roughness of Gear = 0.6R μm

Interference (δ) (max) = (max shaft dia)- (min bore dia)

= 254.0254- 253.746

= 0.2734 mm

Interference (δ) (min) = (min shaft dia) – (max bore dia)

= 254.0 – 253.771

=0.223 mm

Diameter ratio of the shaft (Cc) = 0

Diameter ratio of the gear (Cc) = { ( 254 * 147.5 )/ 342 + ( 254 * 30.5 )/ 694 } / 178

= 0.678

Maximum Hc factor of gear = 1/22000 { [ (1+ 0.459 )/ (1- 0.459 )] + 0.3 }

= 1.3622 * 10-4

Maximum Hi factor for shaft = 1/22000 { [ (1+ 0 )/ (1 – 0)] – 0.3 }

= 3.1818 * 10-5

Joint Pressure for min interference (Pmin) = δ / {d * ( Hi + Hc) }

= 0.223 / { 254 ( 3.1818* 10-5 + 1.3622 * 10-4 ) }

= 5.224 Kg/mm2.

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Joint Pressure for max interference (Pmax ) = 6.405 Kg/ mm2 .

F = P * π * dl * μ

Fmax = 82 tonne.

Fmin = 99.960 tonne ≈ 100 tonne.

Therefore, the pressing pressure required for the given gear shaft combination is (82 – 100 ) tone.

29Project Report | Gear Design

KISSsoft - Release 08-2009DRDSO, Ministry of Railways

File Name : UnnamedChanged by : A.K.Bramhane on: 22.06.2011 at: 12:36:21

Important hint: At least one warning has occurred during the calculation:1-> Gear pair 1 - 2 :The dynamic coefficient KV is very high.The formulae in the standard probably do not suit this case.

2-> The circumferential speed is very high ( 24.4709 m/s)!You have to take adequate action toguarantee proper lubrication.

CALCULATION OF A CYLINDRICAL SPUR GEAR PAIR

Drawing or article number:Gear 1: 0.000.0Gear 2: 0.000.0

Calculation method DIN 3990 Method B

------- GEAR 1 -------- GEAR 2 --

Power (kW) [P] 184.224Speed (1/min) [n] 2300.0 636.9Torque (Nm) [T] 764.9 2762.0Application factor [KA] 1.25Required service life [H] 20000.00Gear driving (+) / driven (-) + -

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1. TOOTH GEOMETRY AND MATERIAL

(Geometry calculation according ISO 21771) ------- GEAR 1 -------- GEAR 2 --Center distance (mm) [a] 468.480Centre distance tolerance ISO 286 Measure js7Normal module (mm) [mn] 11.2889Pressure angle at normal section (°) [alfn] 20.0000Helix angle at reference circle (°) [beta] 0.0000Number of teeth [z] 18 65Facewidth (mm) [b] 127.00 127.00Hand of gear Spur gearAccuracy grade [Q-DIN3961] 6 6Inner diameter (mm) [di] 0.00 0.00Inside diameter of rim (mm) [dbi] 0.00 0.00

MaterialGear 1: 18CrNiMo7-6, Case-carburized steel, case-hardened ISO 6336-5 Figure 9/10 (MQ), core strength >=25HRC Jominy J=12mm<HRC28Gear 2: 18CrNiMo7-6, Case-carburized steel, case-hardened ISO 6336-5 Figure 9/10 (MQ), core strength >=25HRC Jominy J=12mm<HRC28

------- GEAR 1 -------- GEAR 2 --Surface hardness HRC 61 HRC 61Fatigue strength. tooth root stress (N/mm²) [sigFlim] 430.00 430.00Fatigue strength for Hertzian pressure (N/mm²) [sigHlim] 1500.00 1500.00Tensile strength (N/mm²) [Rm] 1200.00 1200.00Yield point (N/mm²) [Rp] 850.00 850.00Young's modulus (N/mm²) [E] 206000 206000Poisson's ratio [ny] 0.300 0.300Average roughness, Ra, tooth flank (µm) [RAH] 0.60 0.60Mean roughness height, Rz, flank (µm) [RZH] 4.80 4.80Mean roughness height, Rz, root (µm) [RZF] 20.00 20.00

Tool or reference profile of gear 1 :Reference profile 1.25 / 0.38 / 1.0 ISO 53.2 Profil AAddendum coefficient [haP*] 1.000Dedendum coefficient [hfP*] 1.250

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Tip radius factor [rhoaP*] 0.000Root radius factor [rhofP*] 0.380Tip form height coefficient [hFaP*] 0.000Protuberance height factor [hprP*] 0.000Protuberance angle [alfprP] 0.000Ramp angle [alfKP] 0.000 not topping

Tool or reference profile of gear 2 :Reference profile 1.25 / 0.38 / 1.0 ISO 53.2 Profil AAddendum coefficient [haP*] 1.000Dedendum coefficient [hfP*] 1.250Tip radius factor [rhoaP*] 0.000Root radius factor [rhofP*] 0.380Tip form height coefficient [hFaP*] 0.000Protuberance height factor [hprP*] 0.000Protuberance angle [alfprP] 0.000Ramp angle [alfKP] 0.000 not topping

Sum of reference profile gears:Dedendum reference profile (module) [hfP*] 1.250 1.250Tooth root radius Refer. profile (module) [rofP*] 0.380 0.380Addendum Reference profile (module) [haP*] 1.000 1.000Protuberance height (module) [hprP*] 0.000 0.000Protuberance angle (°) [alfprP] 0.000 0.000Buckling root flank height (module) [hFaP*] 0.000 0.000Buckling root flank angle (°) [alfKP] 0.000 0.000

Type of profile modification: NoTip relief (µm) [Ca] 2.00 2.00

Lubrication type oil bath lubricationType of oil Oil: ISO-VG 220Lubricant base Mineral-oil baseKinem. viscosity oil at 40 °C (mm²/s) [nu40] 220.00Kinem. viscosity oil at 100 °C (mm²/s) [nu100] 17.50FZG-Test A/8.3/90 (ISO 14635-1) [FZGtestA] 12

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Specific density at 15 °C (kg/dm³) [roOil] 0.895Oil temperature (°C) [TS] 70.000

------- GEAR 1 -------- GEAR 2 --Overall transmission ratio [itot] -3.611Gear ratio [u] 3.611Transverse module (mm) [mt] 11.289Pressure angle at Pitch circle (°) [alft] 20.000Working transverse pressure angle (°) [alfwt] 19.997 [alfwt.e/i] 20.007 / 19.986Working pressure angle at normal section (°) [alfwn] 19.997Helix angle at operating pitch diameter (°) [betaw] 0.000Base helix angle (°) [betab] 0.000Reference centre distance (mm) [ad] 468.489Sum of profile shift coefficients [Summexi] -0.0008Profile shift coefficient [x] 0.3452 -0.3460Tooth thickness (Arc) (module) [sn*] 1.8221 1.3189

Tip alteration (mm) [k] 0.000 0.000Reference diameter (mm) [d] 203.200 733.779Base diameter (mm) [dB] 190.946 689.526Tip diameter (mm) [da] 233.572 748.544 (mm) [da.e/i] 233.572 / 233.562 748.544 / 748.534Tip diameter allowances (mm) [Ada.e/i] 0.000 / -0.010 0.000 / -0.010Tip chamfer / tip rounding (mm) [hK] 0.000 0.000Tip form diameter (mm) [dFa] 233.572 748.544 (mm) [dFa.e/i] 233.572 / 233.562 748.544 / 748.534Operating pitch diameter (mm) [dw] 203.196 733.764 (mm) [dw.e/i] 203.210 / 203.182 733.813 / 733.715Root diameter (mm) [df] 182.772 697.744Generating Profile shift coefficient [xE.e/i] 0.3336 / 0.3276 -0.3673 / -0.3771Manufactured root diameter with xE (mm) [df.e/i] 182.511 / 182.373 697.263 / 697.043Theoretical tip clearance (mm) [c] 2.822 2.822Effective tip clearance (mm) [c.e/i] 3.209 / 3.031 3.058 / 2.921Active root diameter (mm) [dNf] 193.148 714.144 (mm) [dNf.e/i] 193.180 / 193.120 714.197 / 714.096Root form diameter (mm) [dFf] 192.745 708.327 [dFf.e/i] 192.643 / 192.590 708.007 / 707.861Reserve (dNf-dFf)/2 (mm) [cF.e/i] 0.295 / 0.239 3.168 / 3.045Addendum (mm) [ha] 15.186 7.383

33Project Report | Gear Design

(mm) [ha.e/i] 15.186 / 15.181 7.383 / 7.378Dedendum (mm) [hf] 10.214 18.017 (mm) [hf.e/i] 10.345 / 10.413 18.258 / 18.368Roll angle at dFa (°) [xsi_dFa.e/i] 40.364 / 40.359 24.208 / 24.205Roll angle to dNa (°) [xsi_dNa.e/i] 40.364 / 40.359 24.208 / 24.205Roll angle to dNf (°) [xsi_dNf.e/i] 8.790 / 8.672 15.463 / 15.431Roll angle at dFf (°) [xsi_dFf.e/i] 7.655 / 7.535 13.354 / 13.301Tooth height (mm) [H] 25.400 25.400Virtual gear no. of teeth [zn] 18.000 65.000Normal Tooth thickness at Tip cyl. (mm) [san] 5.927 9.316 (mm) [san.e/i] 5.824 / 5.760 9.142 / 9.056Normal Tooth space as Tip cylinder (mm) [efn] 0.000 10.017 (mm) [efn.e/i] 0.000 / 0.000 10.104 / 10.144Max. sliding velocity at tip (m/s) [vga] 10.001 6.213Specific sliding at the tip [zetaa] 0.617 0.639Specific sliding at the root [zetaf] -1.774 -1.613Sliding factor on tip [Kga] 0.409 0.254Sliding factor on root [Kgf] -0.254 -0.409Pitch (mm) [pt] 35.465Base pitch (mm) [pbt] 33.326Transverse pitch on contact-path (mm) [pet] 33.326Length of path of contact (mm) [ga, e/i] 52.718 (52.810 / 52.604)Length T1-A, T2-A (mm) [T1A, T2A] 14.542(14.450/14.647) 145.663(145.663/145.651)Length T1-B (mm) [T1B, T2B] 33.934(33.934/33.925) 126.272(126.180/126.373)Length T1-C (mm) [T1C, T2C] 34.743(34.723/34.763) 125.462(125.390/125.534)Length T1-D (mm) [T1D, T2D] 47.868(47.776/47.973) 112.337(112.337/112.324)Length T1-E (mm) [T1E, T2E] 67.260(67.260/67.251) 92.946(92.853/93.046)Length T1-T2 (mm) [T1T2] 160.205 (160.113 / 160.298)Diameter of single contact point B (mm) [d-B] 202.648(202.648/202.642) 734.319(734.256/734.389)Diameter of single contact point D (mm) [d-D] 213.602(213.519/213.696) 725.207(725.207/725.199)Addendum contact ratio [eps] 0.976( 0.976/ 0.975) 0.606( 0.608/ 0.604)Minimal length of contact line (mm) [Lmin] 127.000

Transverse contact ratio [eps_a] 1.582Transverse contact ratio with allowances [eps_a.e/m/i] 1.585 / 1.582 / 1.578Overlap ratio [eps_b] 0.000Total contact ratio [eps_g] 1.582Total contact ratio with allowances [eps_g.e/m/i] 1.585 / 1.582 / 1.578

34Project Report | Gear Design

2. FACTORS OF GENERAL INFLUENCE

------- GEAR 1 -------- GEAR 2 --Nominal circum. force at pitch circle (N) [Ft] 7528.3Axial force (N) [Fa] 0.0Radial force (N) [Fr] 2740.1Normal force (N) [Fnorm] 8011.4Tangent.load at p.c.d.per mm (N/mm) (N/mm) [w] 59.28Only for information: Forces at the pitch-circle :Nominal circumferential force (N) [Ftw] 7528.4Axial force (N) [Faw] 0.0Radial force (N) [Frw] 2739.7Circumferential speed pitch d.. (m/sec) [v] 24.47

Running-in value (µm) [yp] 1.1Running-in value (µm) [yf] 1.3Correction coefficient [CM] 0.800Gear body coefficient [CR] 1.000Reference profile coefficient [CBS] 0.975Material coefficient [E/Est] 1.000Singular tooth stiffness (N/mm/µm) [c'] 9.928Meshing stiffness (N/mm/µm) [cg] 14.261Reduced mass (kg/mm) [mRed] 0.14536Resonance speed (min-1) [nE1] 5255Nominal speed (-) [N] 0.438 Subcritical rangeRunning-in value (µm) [ya] 1.3Bearing distance l of pinion shaft (mm) [l] 254.000Distance s of pinion shaft (mm) [s] 25.400Outside diameter of the pinion shaft (mm) [dsh] 127.000Load according DIN 3990/1 Figure 6.8 [-] 4(0:6.8a, 1:6.8b, 2:6.8c, 3:6.8d, 4:6.8e)coefficient K' according to DIN 3990/1 diagram 6.8 [K'] -1.00Without support effectTooth trace deviation (active) (µm) [Fby] 6.18 from deformation of shaft (µm) [fsh*B1] 0.70 Tooth without tooth trace correction

35Project Report | Gear Design

Position of contact pattern: Favorable from production tolerances (µm) [fma*B2] 11.00 Tooth trace deviation, theoretical (µm) [Fbx] 7.27 Running-in value (µm) [yb] 1.1

Dynamic factor [KV] 1.676

Face coefficient - flank [KHb] 1.355 - Tooth root [KFb] 1.277 - Scuffing [KBb] 1.355

Transverse coefficient - flank [KHa] 1.158 - Tooth root [KFa] 1.158 - Scuffing [KBa] 1.158

Helix angle coefficient scuffing [Kbg] 1.000

Number of load changes (in mio.) [NL] 2760.000 764.308

3. TOOTH ROOT STRENGTH

------- GEAR 1 -------- GEAR 2 --Calculation of Tooth form coefficients according method: B(Calculate tooth shape coefficient YF with addendum mod. x)Tooth form factor [YF] 1.25 1.59Stress correction factor [YS] 2.15 1.82Working angle (°) [alfen] 22.07 18.97Bending lever arm (mm) [hF] 10.57 13.37Tooth thickness at root (mm) [sFn] 23.81 23.95Tooth root radius (mm) [roF] 5.25 6.63(hF* = 0.936/1.185 sFn* = 2.109/2.122 roF* = 0.465/0.587 dsFn = 186.44/702.78 alfsFn = 30.00/30.00)

Contact ratio factor [Yeps] 1.000Helix angle factor [Ybet] 1.000Effective facewidth (mm) [beff] 127.00 127.00Nominal shear stress at tooth root (N/mm²) [sigF0] 14.09 15.16Tooth root stress (N/mm²) [sigF] 43.64 46.95

Permissible bending stress at root of Test-gear

36Project Report | Gear Design

Support factor [YdrelT] 0.998 0.993Surface-factor [YRrelT] 0.957 0.957Size coefficient (Tooth root) [YX] 0.937 0.937Finite life factor [YNT] 1.000 1.000 [YdrelT*YRrelT*YX*YNT] 0.895 0.890Alternating bending coefficient [YM] 1.000 1.000Stress correction factor [Yst] 2.00Limit strength tooth root (N/mm²) [sigFG] 769.33 765.68Permissible tooth root stress (N/mm²) [sigFP=sigFG/SFmin] 549.52 546.91Required safety [SFmin] 1.40 1.40Safety for Tooth root stress [SF=sigFG/sigF] 17.63 16.31Transmittable power (kW) [kWRating] 2319.59 2145.87

4. SAFETY AGAINST PITTING (TOOTH FLANK)

------- GEAR 1 -------- GEAR 2 --Zone factor [ZH] 2.495Elasticity coefficient (N^.5/mm) [ZE] 189.812Contact ratio factor [Zeps] 0.898Helix angle factor [Zbet] 1.000Effective facewidth (mm) [beff] 127.00Nominal flank pressure (N/mm²) [sigH0] 259.48Surface pressure at Operating pitch diameter (N/mm²) [sigHw] 470.47Single tooth contact factor [ZB,ZD] 1.01 1.00Flank pressure (N/mm²) [sigH] 474.52 470.47

Lubrication factor [ZL] 1.020 1.020Speed factor [ZV] 1.026 1.026Roughness factor [ZR] 1.004 1.004Material mating factor [ZW] 1.000 1.000Finite life factor [ZNT] 1.000 1.000 [ZL*ZV*ZR*ZNT] 1.051 1.051Small amount of pitting permissible (0=no, 1=yes) 0 0Size coefficient (flank) [ZX] 0.994 0.994Limit strength pitting (N/mm²) [sigHG] 1565.92 1565.92Permissible surface pressure (N/mm²) [sigHP=sigHG/SHmin] 1565.92 1565.92

Safety for surface pressure at pitch diameter

37Project Report | Gear Design

[SHw] 3.33 3.33Required safety [SHmin] 1.00 1.00Transmittable power (kW) [kWRating] 2006.19 2040.90Safety for stress at single tooth contact [SHBD=sigHG/sigH] 3.30 3.33(Safety regarding nominal torque) [(SHBD)^2] 10.89 11.08)

5. STRENGTH AGAINST SCUFFING

Lubrication coefficient (Scoring) [XS] 1.000Relative structure coefficient (Scoring) [XWrelT] 1.000Thermal. contact factor (N/mm/s^.5/K) [BM] 13.795 13.795Effective facewidth (mm) [beff] 127.000Applicable circumferential force/tooth width (N/mm) [wBt] 194.874Angle factor [Xalfbet] 0.977(eps1: 0.976, eps2: 0.606)

Flash temperature-criteria (DIN3990)Tooth mass temperature (°C) [theM-B] 78.03 theM-B = theoil + XS*0.47*theflamax [theflamax] 17.08Scuffing temperature (°C) [theS] 408.58Coordinate gamma (point of highest temp.) [Gamma] -0.581 [Gamma.A]= -0.581 [Gamma.E]= 0.936Highest contact temp. (°C) [theB] 95.10Flash factor [XM] 50.002Geometry factor [XB] 0.410Distribution factor [XGam] 0.333Dynamic viscosity (mPa*s) [etaM] 30.62Coefficient of friction [mymy] 0.046Required safety [SBmin] 2.000Safety factor for scuffing (flash-temp) [SB] 13.482

Integral temperature-criteria (DIN3990)Tooth mass temperature (°C) [theM-C] 75.73 theM-C = theoil + XS*0.70*theflaint [theflaint] 8.19Integral scuffing temperature (°C) [theSint] 408.58Flash factor [XM] 50.002Contact ratio factor [Xeps] 0.240Dynamic viscosity (mPa*s) [etaOil] 41.77Mean coefficient of friction [mym] 0.034

38Project Report | Gear Design

Geometry factor [XBE] 0.385Meshing factor [XQ] 1.000Tip relief factor [XCa] 1.028Integral tooth flank temperature (°C) [theint] 88.02Required safety [SSmin] 1.800Safety factor for scuffing (intg.-temp.) [SSint] 4.642Safety referring to transferred torque [SSL] 18.793

6. MEASUREMENTS FOR TOOTH THICKNESS

------- GEAR 1 -------- GEAR 2 --Tooth thickness deviation DIN3967 cd25 DIN3967 cd25Tooth thickness allowance (normal section) (mm) [As.e/i] -0.095 / -0.145 -0.175 / -0.255

Number of teeth spanned [k] 3.000 7.000Base tangent length (no backlash) (mm) [Wk] 88.827 224.226Actual base tangent length ('span') (mm) [Wk.e/i] 88.738 / 88.691 224.062 / 223.986Diameter of contact point (mm) [dMWk.m] 210.548 725.006

Theoretical diameter of ball/pin (mm) [DM] 21.732 18.749Eff. Diameter of ball/pin (mm) [DMeff] 22.000 20.000Theor. dim. centre to ball (mm) [MrK] 121.823 377.852Actual dimension centre to ball (mm) [MrK.e/i] 121.735 / 121.688 377.615 / 377.507Diameter of contact point (mm) [dMMr.m] 211.139 728.430Diametral measurement over two balls without clearance (mm) [MdK] 243.646 755.489Actual dimension over balls (mm) [MdK.e/i] 243.470 / 243.377 755.016 / 754.799Theor. dimension over two pins (mm) [MdR] 243.646 755.489Actual dimension over rolls (mm) [MdR.e/i] 243.470 / 243.377 755.016 / 754.799Dimensions over 3 pins without clearance (mm) [Md3R] 0.000 755.274Actual dimensions over 3 rolls (mm) [Md3R.e/i] 0.000 / 0.000 754.801 / 754.585

Chordal tooth thickness (no backlash) (mm) ['sn] 20.534 14.888Actual chordal tooth thickness (mm) ['sn.e/i] 20.439 / 20.389 14.713 / 14.633Reference chordal height from da.m (mm) [ha] 15.704 7.456Tooth thickness (Arc) (mm) [sn] 20.569 14.889 (mm) [sn.e/i] 20.474 / 20.424 14.714 / 14.634

39Project Report | Gear Design

Backlash free center distance (mm) [aControl.e/i] 468.109 /467.930Backlash free center distance, allowances (mm) [jta] -0.371 / -0.550Centre distance allowances (mm) [Aa.e/i] 0.032 / -0.032Circumferential backlash from Aa (mm) [jt_Aa.e/i] 0.023 / -0.023Radial clearance (mm) [jr] 0.581 / 0.339Circumferential backlash (transverse section) (mm) [jt] 0.423 / 0.247Torsional angle using fixed values gear 1 (°) 0.0660 /0.0386Normal backlash (mm) [jn] 0.397 / 0.232

7. TOLERANCES

------- GEAR 1 -------- GEAR 2 --According DIN 3961:Accuracy grade [Q-DIN3961] 6 6Profile deviation (µm) [ff] 18.00 18.00Profile angular deviation (µm) [fHa] 12.00 12.00Profile total deviation (µm) [Ff] 21.00 21.00Helix form deviation (µm) [ffb] 12.00 12.00Helix slope deviation (µm) [fHb] 11.00 11.00Tooth helix deviation (µm) [Fb] 16.00 16.00Single pitch deviation (µm) [fpe] 13.00 14.00Single normal pitch deviation (µm) [fp] 13.00 14.00Difference between adjacent pitches (µm) [fu] 16.00 18.00Total cumulative pitch deviation (µm) [Fp] 40.00 51.00Cumulative circular pitch deviation over z/8 pitches (µm) [Fpz/8] 25.00 32.00Runout tolerance (µm) [Fr] 32.00 40.00Tooth Thickness Variation (µm) [Rs] 19.00 23.00Total radial composite tolerance (µm) [Fi"] 34.00 42.00Tooth-to-tooth radial composite tolerance (µm) [fi"] 16.00 19.00Total tangential composite deviation (µm) [Fi'] 49.00 58.00Tooth-to-tooth tangential composite deviation (µm) [fi'] 24.00 25.00

Tolerance for alignment of axes (recommendation acc. ISO/TR 10064, Quality 6)Maximum value for deviation error of axis (µm)

40Project Report | Gear Design

[fSigbet] 19.81Maximum value for inclination error of axes (µm) [fSigdel] 39.62

8. ADDITIONAL DATA

Torsional stiffness (MNm/rad) [cr] 16.5 215.3Mean coef. of friction (acc. Niemann) [mum] 0.028Wear sliding coef. by Niemann [zetw] 0.990Power loss from gear load (kW) [PVZ] 0.839(Meshing efficiency (%) [etaz] 99.545)Weight - calculated with da (g) [Mass] 42608.51 437612.52Moment of inertia (System referenced to wheel 1): calculation without consideration of the exact tooth shapesingle gears ((da+df)/2...di) (kgm²) [TraeghMom] 0.18275 26.65313System ((da+df)/2...di) (kgm²) [TraeghMom] 2.22668

9. DETERMINATION OF TOOTHFORM

Calculation of Gear 1Gear 1 (Step 1): Automatically (Tool: Hobbing cutter) haP*= 1.014, hfP*= 1.250, rofP*= 0.380

Calculation of Gear 2Gear 2 (Step 1): Automatically (Tool: Hobbing cutter) haP*= 1.026, hfP*= 1.250, rofP*= 0.380

REMARKS:- Specifications with [.e/i] imply: Maximum [e] and Minimal value [i] with consideration of all tolerances Specifications with [.m] imply: Mean value within tolerance- For the backlash tolerance, the center distance tolerances and the tooth thickness deviation are taken into account. Shown is the maximal and the minimal backlash corresponding the largest resp. the smallest allowances The calculation is done for the Operating pitch circle..- Details of calculation method: cg according to method B KV according to method B

41Project Report | Gear Design

KHb, KFb according methode C KHa, KFa according to method B End report lines: 476

42Project Report | Gear Design