Calcolo Ingranaggi Iso 9336 ABS Part 4 Ottimo

8/16/2019 Calcolo Ingranaggi Iso 9336 ABS Part 4 Ottimo

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ABS

RULES FOR BUILDING AND CLASSING

STEEL VESSELS

2002

PART 4 VESSEL SYSTEMS AND MACHINERY

American Bureau o f Shipping Incorporated by Act o f Legislature of the State of New York 1862

Copyright © 2001 American Bureau o f Shipping ABS Plaza16855 Northchase Drive Houston, TX 77060 USA


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P A R T

4

c h a p t e r 3 Propulsion & Maneuvering

Machinery

CONTENTS __________________________________

SECTION 1 Gears ..............................................................................107

1 G enera l.............................................................................. 109

3 Materials ............................................................................ 112

5 Design ................................................................................. 113

7 Piping Systems for G ea rs ............................................ 116

9 Testing, Inspection and Certification of Ge ars 116

SECTION 2 Propulsio n Sh afti ng ................................................... 193

I Genera l.............................................................................. 195

3 Materials ............................................................................ 197

5 Design and Co nstruction ............................................... 198

7 Propulsion Shaft Alignm ent and Vib ratio ns 207

9 Inspection, Testing and C ertificatio n ......................... 210

I I Installation and T rials.....................................................

211

SECTION 3 Pro pell ers ...................................................................... 213

1 G enera l.............................................................................. 215

3 Materials ............................................................................ 217

5 Design................................................................................ 217

7 Certification ...................................................................... 228

9 Installation, Tests and T ria l.......................................... 228

SECTION 4 Steering Gear s ............................................................. 231

I Genera l.............................................................................. 233

3 Materials ............................................................................ 235

5 System Arrangem ents................................................... 236

7 Mechanical Component D esig n ................................. 237

9 Hydraulic Sys tem ............................................................ 240

I I Electr ical System s........................................................... 242

13 Control Sys tems .............................................................. 243

15 Instrumentat ion ............................................................... 244

17 Communicat ions............................................................. 244

19 Certification ...................................................................... 244

A B S RULES FOR BUILDING AND CLASSING STEEL VESSELS 2002 1 0 5


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21 Installation, Tests and T ria ls ........................................ 245

23 Additional Requ irements for Passeng er

Vesse ls............................................................................. 247

25 Additional Requ irements for Oil or Fuel Oil

Carriers, Chemical Carriers and GasCarr iers 247

SECTION 5 Thr us ters........................................................................

251I General............................................................................... 253

3 Materials ............................................................................ 255

5 Des ign ................................................................................ 255

7 Controls and Instrum entation ....................................... 260

9 Communicat ions.............................................................. 261

I I Miscellaneous Requirements for

Thruster Room s ............................................................. 261

13 Certification and T rial ..................................................... 261

15 Dynam ic Positioning Sy stem s..................................... 262

SECTION 1 Ap pen dix 1 - Rating of Cylind rical andBevel Gears .................................................................. 119

SECTION 1 A ppen dix 2 - Guidance for Spare Parts ..................181

SECTION 1 Appen dix 3 - Gear Param eters ................................ 183

106 ABS RULES FOR BUILDING AND CLASSING STEEL VESSELS 2002


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P A R T

4


Machinery

s e c t i o n 1 Gears

CONTENTS __________________________________

1 General............................................................................................. 109

1.1 Application ............................................................................................ 109

1.3 Definitions ............................................................................................. 109

1.5 Plans and Particulars to be Su bm itted ......................................... 110

3 Materials ........................................................................................... 112

3.1 Ma terial Sp ec ifica tion s and Te st Req uir em en ts.........................112

3.3 Alternative Material Test Re quire m ents ....................................... 112

5 Design .............................................................................................. 113

5.1 Gea r Tooth Fin ish ............................................................................... 113

5.3 Bear ings ................................................................................................ 113

5.5 Gear Cases ........................................................................................... 113

5.7 Access for Inspe ction ........................................................................ 114

5.9 Calculation of Shafts for G ea rs ...................................................... 114

5.11 Rating of Cylindrical and Bevel Ge ars .......................................... 115

5.13 Alternative Gear Rating Sta nd ard s ............................................... 115

7 Piping Systems for Gear s .......................................................... 116

9 Testing, Inspection and Certif ication of G ear s .................... 116

9.1 Material T e sts ...................................................................................... 116

9.3 Dynamic Balan cing ............................................................................ 116

9.5 Shop Inspection .................................................................................. 116

9.7 Certification of G ea rs........................................................................

117

9.9 Shipboard Trials .................................................................................. 117

Appen dix 1 Rat in g of Cy li ndric al and Bevel Gears ........................119

Appen dix 2 Gu id ance for Spare Par ts ............................................... 181

Appen dix 3 Gear Par am eters .............................................................. 183

ABS RULES FOR BUILDING AND CLASSING STEEL VESSELS 2002 107


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P A R T

4


Machinery

s e c t i o n 1 Gears

1 G e n e r a l

1 . 1 A p p l i c a t i o n

Gears having a rated power of 100 kW (135 hp) and over intended for propulsion and for auxiliary services essential for propulsion, maneuvering and safety (see 4-1-1/1.3) of the vessel are to be designed, constructed, certified and installed in accordance with the provisions of this section.

Gears having a rated power of less than 100 kW (135 hp) are not required to comply with the provisions of this section but are to be designed, constructed and equipped in accordance with good commercial and marine practice. Acceptance of such gears will be based on manufacturer’s affidavit, verification of gear nameplate data and subject to a satisfactory performance test after installation conducted in the presence o f the Surveyor.

Gears having a rated power of 100 kW (135 hp) and over intended for services considered not essential for propulsion, maneuvering and safety are not required to be designed, constructed and certified by the Bureau in accordance with the requirements of this section, but are to be installed and tested to the satisfaction o f the Surveyor.

Piping systems of gears, in particular, lubricating oil and hydraulic oil, are addressed in Section 4-6-5 and Section 4-6-7 respectively.

1 . 3 D e f i n i t i o n s

For the purpose of this section the following definitions apply:

1.3.1 Gears

The term Gears as used in this section covers external and internal involute spur and helical cylindrical gears having parallel axis as well as bevel gears used for either main propulsion or auxiliary services.

1.3.2 Rated Power

The R a te d P ow er of a gear is the maximum transmitted power at which the gear is designed to operate continuously at its rated speed.



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Part 4 Vessel System s and MachineryChapter 3 Propulsion & Maneuvering MachinerySection 1 Gears 4-3-1

1.3.3 Rated Torque

The R a te d To rque is defined by the rated power and speed and is the torque used in the gear rating calculations.

1.3.4 Gea r Rating

The Gear R at ing is the rating for which the gear is designed in order to carry its rated torque.

1 .5 P l a n s a n d P a r t ic u l a r s t o b e S u b m i tt e d

1.5.1 Ge ar Construction

General arrangement

Sectional assembly

Details o f gear casings

Bearing load diagram

Quill shafts, gear shafts and hubs

Shrink fit calculations and fitting instructions

Pinions

Wheels and rims

Details o f welded construction o f gears

1.5.2 Gear Sy stem s and Appurtenances

Couplings

Coupling bolts

Lubricating oil system and oil spray arrangements

1.5.3 DataTransmitted rated power for each gear

Revolutions per minute for each gear at rated transmitted power

Bearing lengths and diameters

Length of gap between helices, if any

Distance between inner ends o f bearings

Tooth form layout (see 4-3-1A1/Figure 1) or calculated data

Facewidths, net and total

Width of tooth at highest stressed section

He lix angle at reference and at pitch diameter

Helix deviation

Normal pressure angle

Transverse pressure angle at reference cylinder

Transverse pressure angle at working pitch cylinder

Reference cone angle for gears



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Tip angle for gears

Cone distance for gears

Middle cone distance for gears

Normal module

Transverse module

Bending moment arm for tooth root bending stress for application of load at the point of single tooth pair contact

Working pitch diameter of gears

Tip diameter o f gears

Root diameter of gears

Reference diameters

Addendum

Addendum modification coe fficient o f gears

Dedendum

Transverse diametral pitch

Normal base pitch

Number o f gear teeth

Virtual number of spur teeth for gears

Center distance between mating gears

Length o f contact in plane of rotation

Root fillet radius of gears in the critical section

Axial lead modification or lead mismatch, if any, for reference

Method o f cutting and finishing gear teeth

Tooth thickness modification coe fficient (midface)

Sketch o f basic rack tooth form

Root radius, addendum, dedendum o f basic rack

Degree o f finish o f tooth flank

Grade o f accuracy

Tooth hardness range, including core hardness and total depth of hardness, surface to core

Mean peak-to-valley roughness o f tooth root fillets

Mass o f rotating partsBalancing data

Spline data

Shrink allowance for rims and hubs

Type of coupling between prime mover and reduction gears

Type and viscosity of lubricating oil recommended by manufacturer

For a comprehensive listing o f data, see Appendix 4-3-1A3.



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1.5.4 Materials

The follo win g typica l properties o f gear materials are to be submitted:

range o f chemical composition,

physical properties at room temperature,

endurance limits for pitting resistance, contact stress and tooth root bending stress,

heat treatment of gears, coupling elements, shafts, quill shafts, and gear cases.

1.5.5 Hardening Procedure

The hardening procedure for surface hardened gears is to be submitted for review. The submittal is to include materials, details for the procedure itself, quality assurance procedures and testing procedures. The testing procedures are to include surface hardness, surface hardness depth (e.g. case depth) and core hardness. Surface hardness depth and core hardness (and their shape) are to be determined from sectioned test samples. These test samples are to be of sufficient size to provide for determination of core hardness and are to be of the same material and heat treated as the gears that they represent. Forgings are to be tested in accordance with Part 2, Chapter 3.

1.5.6 Calculations and An alyses

Bearing life calculations

Tooth coupling and spline connection calculations

3 M a t e r i a l s

3 .1 M a t er ia l S p e c i f i c a t i o n s a n d T e s t R e q u i r e m e n t s

3.1.1 Material Cer tificates

Material for gears and gear units is to conform to specifications approved in connection with the design in each case. Copies of material specifications and purchase orders are to be submitted to the Surveyor for information.

3.1.2 Material T ests

Except as noted in 4-3-1/3.3, the following materials are to be tested in the presence of and inspected by the Surveyor. The materials are to meet the specifications in Part 2, Chapter 3 or that approved in connection with the design.

Forgings for gears, shafting, couplings, coupling bolts.

Castings approved for use in place of any of the above forgings.

3 . 3 A l te r n a t i v e M a t e ri al T e s t R e q u i r e m e n t s

3.3.1 Alternative Spec ifications

The Surveyor will inspect and test material manufactured to other specifications than those given in Part 2, Chapter 3, provided that such specifications are approved in connection with the designs and that they are clearly indicated on purchase orders which are provided for the Surveyor's information.



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3.3.2 Gea rs Certified Under Quality Assura nce A ssessm en t

For gears units certified under quality assurance assessment provided for in 4-3-1/9.7 hereunder, material tests and inspections required in 4-3-1/3.1 need not be witnessed by the Surveyor; such tests and inspections are to be conducted by the gear manufacturer whose certified material test reports will be accepted instead.

3.3.3 Steel-bar Stock

Hot-rolled steel bars up to 305 mm (12 in) in diameter may be used when approved for use in place of any of the forgings as per 4-3-1/3.1(a) above, under the conditions outlined in Section 2-3-8.

3.3.4 Gea r Units of 375 kW (500 hp) or Le ss

Material for gear units of 375 kW (500 hp) or less, including shafting, gears, couplings, and coupling bolts will be accepted on the basis of the manufacturer's certified material test reports and a satisfactory surface inspection and hardness check witnessed by the Surveyor. Coupling bolts manufactured to a recognized bolt standard do not require material testing.

3.3.5 Power Takeoff Gears and Couplings

Materials for power tak eoff gears and couplings that are

for transmission of power to drive auxiliaries that are for use in port only (e.g. cargo oil pump), and

declutchable from propulsion shafting

may be treated in the same manner as 4-3-1/3.3.4 above, regardless of power rating.

5 D e s i g n

5 .1 G e a r T o o t h F i n i s h

In general the gear teeth surface finish is not to be rougher than 1.05 pm (41 pin.) arithmetic or centerline average. However, gears having a rated power below 3728 kW (5000 hp) and with a surface finish rougher than 1.05 pm (41 pin.) arithmetic or centerline average will be specially considered taking into account the lubricant recommended by the manufacturer.

5 . 3 B e a r i n g s

Bearings of gear units are to be so designed and arranged that their design lubrication rate is assured in service under working conditions.

The minimum L10 bearing life is not to be less than 20,000 hours for ahead drives and 5,000 hours for astern. Shorter life may be considered in conjunction with an approved bearing inspection and replacement program reflecting the actual calculated bearing life. See 4-3-1/5.9 for application to

thrusters.

5 .5 G e a r C a s e s

Gear cases are to be o f substantial construction in order to minim ize elastic deflectio ns and maintainaccurate mounting of the gears. They are to be designed to withstand without deleterious deflection: static loads, the forces generated by the power transmitted and the inertial effects of the gears within the case due to the dynamic forces of the ship's motion in a seaway. The dynamic forces generated by the ship are to be considered as 1g horizontally and 2 g vertically.



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5 .7 A c c e s s f o r I n s p e c ti o n

The construction of gear cases is to be such that sufficient number of access is provided for adequate inspection of gears, checking of gear teeth contacts and measurement of thrust bearing clearance. Alternative methods such as use o f special viewing devices m ay be considered.

5 .9 C a l c u la t io n o f S h a f t s f o r G e a r s

5.9.1 General

The diameter o f shafts for gears is to be determined by the fo llow ing equations:

d = k 6 ( b T )2 + ( m M ) 2

b = 0.073 +-

m = — ¿—C2 + Y

where (in SI (MKS and US units), respectively):

d = shaft diameter at section under consideration; mm (mm, in.)

Y = yie ld strength (see 2-1-1/13 .3 ); N/m m2 (kgf/mm2, psi)

T = torsional moment at rated speed; N-m (kgf-cm, lbf-in.)

M = bending moment at section under consideration; N-m (kgf-cm, lbf-in.)

k, n, c 1 and c2 are constants given in the follo win g table:

SI units M K S units US units

k 5.25 2.42 0.10

n 191.7 19.5 27800

c 1 1186 121 172000

C2 413.7 42.2 60000

5.9.2 Shaft Diameter in way of Gear W heel

Where gear wheels are fitted by keying, the diameter of the shaft in way of the fitted member is to be increased not less than 10%.

5.9.3 Astern Power

In determining the required size of gear, coupling and shafting transmitting astern power, the astern torque is to be considered when it exceeds the transmitted ahead torque. See also 4-1-1/7.5.

5.9 .4 Quill Sha fts

In the specific case of quill shafts, subjected to small stress raisers and no bending moments, the least diameter may be determined by the following equation:


d = 5.25 3b T d = 2.42 3b T d = 0.1 ^fbT

187.8 b = 0.053 +

Y

19.1 b = 0.053 + '

Y

27200 b = 0.053 +

Y

n

c



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5.9.5 Shaft Couplings

For shaft couplings, coupling bolts, flexible coupling and clutches, see 4-3-2/5.19. For keys, see 4-3-2/5.7.

5.9 .6 Torsional Vibration

Gears forming a part of propulsion shafting system are to be evaluated for harmful torsional vibratory stresses in accordance with the criteria provided in 4-3-2/7 .5.

5.9.7 Shrink Fitted Pinions and W hee ls

For pinions and wheels shrink-fitted on shafts, preloading and stress calculations and fitting instructions are to be submitted for review. In general, the torsional holding capacity is to be at least 2.8 times the transmitted mean torque plus vibratory torque due to torsional vibration. For calculation purpose, to take account of torsional vibratory torque, the following factors may be applied to the transmitted torque, unless the actual measured vibratory torque is higher, in which case the actual vibratory torque is to be used.

for direct diesel engine drives: 1.2 ;

for all other drives, including diesel engine drives with elastic couplings: 1 .0.

The preload stress based on the maximum available interference fit or maximum pull-up length is not to exceed 90% of the minimum specified yield strength.

The following friction coefficients are to be used:

oil injection method o f fit: 0.13;

dry method o f fit: 0.18.

5.9 .8 Shrink Fitted W hee l Rim

For shrink-fitted wheel rims, preloading and stress calculations and fitting instructions are to be submitted for consideration. In general, the preloading stress based on the maximum interference fit or maximum pull-up length is not to exceed 90% of the minimum specified yield strength.

5 .1 1 R a t i n g o f C y l i n d r ic a l a n d B e v e l G e a r s

The calculation procedures for the rating of external and internal involute spur and helical cylindrical gears, having parallel axes, and of bevel gears, with regard to surface durability (pitting) and tooth root bending strength, may be as given in Appendix 4-3-1A1. These procedures are in substantial agreement with ISO 6336 and ISO-DIS 10300 for cylinder and bevel gears respectively.

5 .1 3 A l t e r n a ti v e G e a r R a t in g S t a n d a r d s

Consideration wil l be given to gears that are rated based on any o f the fol low ing alternative standards. In which case, gear rating calculations and justification of the applied gear design coefficients in accordance with the applicable design standard are to be submitted to the Bureau for review.

C ylindrical gears B evel gears

AGMA 6032-A94 AGMA 2003-A86

ISO 6336 ISO-DIS 10300

DIN 3990, Part 31 DIN 3991



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7 P i p i n g S y s t e m s f o r G e a r s

The requirements of piping systems essential for operation of gears for propulsion, maneuvering, electric power generation and vessel’s safety are in Section 4-6-5 for diesel engine and gas turbine

installations and in Section 4-6-6 for steam turbine installations. Additionally, requirements for hydraulic and pneumatic systems are provided in Section 4-6-7. Specifically, the following references are applicable:

lubricating oil system:

cooling system:

hydraulic system:

pneumatic system:

piping system general requirements:

4-6-5/5 and 4-6-6/9 ;

4-6-5/7 and 4-6-6/11 ;

4-6-7/3 ;

4-6-7/5 ;

Section 4-6-1 and Section 4-6-2.

9

9.1

9 .3

T e s t i n g , I n s p e c t i o n a n d C e r t i f i c a t i o n o f G e a r s

M a t e ri al T e s t s

For testing of materials intended for gear construction see 4-3-1/3.1 and 4-3-1/3.3.

D y n a m ic B a l a n c in g

Finished pinions and wheels are to be dynamically balanced in two planes where their pitch line velocity exceeds 25 m/s (4920 ft/min).

Where their pitch line velocity does not exceed 25 m/s (4920 ft/min) or where dynamic balance is impracticable due to size, weight, speed or construction of units, the parts may be statically balanced in a single plane.

The residual unbalance in each plane is not to exceed the value determined by the following equations:


B = 24-W/N B = 2400-W/N B = 15.1-W/N where

B

W

N

maximum allowable residual unbalance; Nmm (gf-mm, oz-in)

weight o f rotating part; N (kgf, lbf)

rpm at rated speed

9 .5 S h o p I n s p e c t i o n

Each gear unit that requires to be certified by 4-3-1/1.1 is to be inspected during manufacture by a Surveyor for conformance with the design approved. This is to include but not limited to checks on gear teeth hardness, and surface finish and dimension checks of main load bearing components The accuracy of meshing is to be verified for all meshes and the initial tooth contact pattern is to be checked by the Surveyor.

Reports on pinions and wheels balancing as per 4-3-1/9.3 are to be made available to the Surveyor for verification.



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9 . 7 C e r t if ic a t io n o f G e a r s

9.7.1 General

Each gear required to be certified by 4-3 -1/1.1 is:

i) to have its design approved by the Bureau; for which purpose, plans and data as required by 4-3-1/1.5 are to be submitted to the Bureau for approval;

ii) to be surveyed during its construction, whic h is to include, but not limited to, material tests as indicated in 4-3-1/9.1, meshing accuracy and tooth contact pattern checks as indicated in 4-3-1/9.5, and verification of dynamic balancing as indicated in 4-3-1/9.3.

9.7.2 Approval Under the Type Approval Program

9.7.2( a) P ro duct de sign as se ssm en t. Upon application by the manufacturer, each rating of a type of gear may be design assessed as described in 1-1-A3/5.1. For this purpose, each rating of a gear type is to be approved in accordance with 4-3-1/9.7.1i). The type test, however, is to be conducted in accordance with an approved test schedule and is to be witnessed by a Surveyor. Gear so approved may be applied to the Bureau for listing in the Bureau’s

publication L is t o f Ty pe A ppro ved Eq uipm en t. Once listed, gear particulars will not be required to be submitted to the Bureau each time the engine is proposed for use on board a vessel.

9.7. 2( b) P ro duct qu al ity as su ra nce as se ssm en t. Manufacturer o f mass-produced gears, who operates a quality assurance system in the manufacturing facilities, may apply to the Bureau for quality assurance assessment described in 1-1-A3/5.3. Upon satisfactory assessment, gears produced in those facilities will not require a Surveyor to witness the tests and inspections indicated in 4-3-1/9.7.1ii). Such tests and inspections are to be carried out by the manufacturer whose quality control documents will be accepted. Certification of each gear will be based on verification of approval of the design and on an audit of the quality control documents. Manufacturing facilities so approved are eligible for listing in L is t o f Ty pe

A pproved E qu ipm en t.

9. 7.2( c) Type A ppro val Pro gr am . Gear types which have their ratings approved in accordance with 4-3-1/9.7.2(a) and the quality assurance system of their manufacturing facilities approved in accordance with 4-3-1 /9.7.2(b) w ill be deem ed Type Approved and will be eligible for so listing in L is t o f Type A pproved E qu ipm en t.

9 . 9 S h i p b o a r d T r i a ls

After installation on board a vessel, the gear unit is to be operated in the presence of the Surveyor to demonstrate its ability to function satisfactorily under operating conditions and its freedom from harmful vibration at speeds within the operating range. When the propeller is driven through reduction gears, the Surveyor is to ascertain that no gear-tooth chatter occurs throughout the operating range; otherwise a barred speed range as specified in 4-3-2/7.5.5 is to be provided.

For conventional propulsion gear units above 1120 kW (1500 hp) a record of gear-tooth contact is to be made at the trials. To facilitate the survey of extent and uniformity of gear-tooth contact, selected bands of pinion or gear teeth on each meshing are to be coated beforehand with copper or layout dye. See also 7-2-4/1.3 for the first annual survey after the vessel enters service.

Post trial examination of spur and helical type gears is to indicate essentially uniform contact across 90% o f the effective face width o f the gear teeth excluding end relief.

The gear-tooth examination for spur and helical type gear units of 1120 kW (1500 hp) and below, all epicyclical gear units and bevel type gears will be subject to special consideration. The gear manufacturers’ recommendations will be considered.



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P A R T

4


Machinery

s e c t i o n 1 App end ix 1 - Rating of Cyl in dri cal

and B evel Gears

CONTENTS __________________________________

I Appl icat ion ....................................................................................... 123

3 Symbo ls and Units ........................................................................ 123

5 Geometrical Definiti on s ............................................................... 125

7 Bevel Gear Conversio n and Specific For m ula s .................... 126

9 Nomin al Tangenti al Load, F t , F mt...................................................... 129

I I Appl icat ion Factor, K A................................................................... 130

13 Load Sharing Factor, K y................................................................ 130

15 Dynam ic Factor, K .........................................................................

13115.1 Dete rmina tion of K v - S impli fied M etho d .................................... 131

15.3 Determination of K v - Single Resonance Method .................... 132

17 Face Load Distri but ion Factors , K H ß and K F ß .............................139

17.1 Factors Used for the Dete rmina tion of K H ß ................................. 139

17.3 Face Load Distribution Factor for Contact Stress K H ß ..............142

17.5 Face Load Distribution Factor for Tooth Root Bending

Stress K F ß ......................................................................................... 142

19 Transverse Load Distribution Factors, K H a and K Fa ............. 143

19.1 Determ ination of K H a for Contact Stress K Fa for ToothRoot Bending S tress ........................................................................ 143

19.3 Lim itations of K H a an d K Fa ............................................................... 144

21 Surface Du rab ilit y .......................................................................... 145

21.1 Con tact S tres s ..................................................................................... 145

21.3 Permissible Contact Stre ss .............................................................. 146

21.5 Single Pair Mesh Factors, Z B, Z D and Mid-zone

Factor Z M-B .......................................................................................147



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21.7 Zon e Factor, ZH .................................................................................. 148

21.9 Elasticity Factor, ZE............................................................................ 148

21.11 Co ntact Ratio Fac tor (Pitting), Ze ...................................................149

21.13 Bevel Gea r Load Sharing Factor, ZLS ........................................ 149

21.15 Bevel Gea r Factor (Flank), ZK ......................................................

149

21.17 Helix Ang le Factor, Z ß .....................................................................149

21.19 Allow able Stress Nu mb er (Contact), ö-M im ..................................150

21.21 Life Factor, ZN ...................................................................................... 150

21.23 Influence Fac tors on Lubrication Film, ZL, ZV and ZR 150

21.25 Hardness Ratio Factor; ZW ............................................................. 153

21.27 Size Factor, ZX.................................................................................. 154

21.29 Safety Factor for Contact Stress, SH ............................................. 154

23 Tooth Root Bending Streng th ................................................... 155

23.1 Tooth Root Bending Stress for Pinionand Wheel....................

155

23.3 Permissible Tooth Root Bending S tre ss ................................... 155

23.5 Tooth Form Factor, YF, YFa..........................................................156

23.7 Stress Corre ction Factor, YS, YSa.................................................... 160

23.9 Helix Ang le Factor, Y ß ..................................................................... 161

23.11 Co ntact Ratio Factor, Y e .................................................................. 161

23.13 Bevel Gear Factor, YK ....................................................................... 162

23.15 Load Sharing Factor, YLS................................................................. 162

23.17 Allowable Stress Num ber (Bending),


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TABLE 6 Constant K ' fo r the Calculation of the PinionOffset Factor y ................................................................. 174

FIGURE 1 Tooth in Normal Sect io n ................................................175

FIGURE 2 Dimens ion s and Basic Rack Profile of the Tooth(Finished Profile)............................................................. 176

FIGURE 3 Wheel Blank Factor CR , Mean Values fo r Mating

Gears of Similar or Stiffer Wheel Blank Design ....177

FIGURE 4 Bevel Gear Conversion to Equivalent Cylindric alGear .................................................................................... 178

FIGURE 5 Definitions of the Various Diam eter s ........................ 179



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P A R T

4

C H A P T E R 3 Propulsion & Maneuvering

Machinery

S E C T I O N 1 App end ix 1 - Rating of Cyl in dr ical

and Bevel Gears

1 A p p l i c a t i o n

The following calculation procedures cover the rating of external and internal involute spur and helical cylindrical gears, having parallel axis, and of bevel gears with regard to surface durability (pitting) and tooth root bending strength.

For normal working pressure angles in excess of 25° or helix angles in excess of 30°, the results obtained from these calculation procedures are to be confirmed by experience data which are to be submitted by the manufacturer.

The influence factors are defined regarding their physical interpretation. Some o f the influence factors are determined by the gear geometry or have been established by conventions. These factors are to be calculated in accordance w ith the equations provided.

Other influence factors, which are approximations, and are indicated as such may also be calculated according to appropriate alternative methods for which engineering justification is to be provided for verification.

3 S y m b o l s a n d U n i t s

The main symbols used are listed below. Symbols specifically introduced in connection with the definition o f influence factors are described in the appropriate sections.

Units of calculations are given in the sequence of SI units (MKS units, and US units.)

a center distance mm (mm, in.) b common facewidth mm (mm, in.)

b1’ b2 facewidth of pinion, wheel mm (mm, in.) beH effective facewidth mm (mm, in.)

bs web thickness mm (mm, in.)

bB facewidth of one helix on a double helical gear mm (mm, in.)

d 1 , d2 reference diameter of pinion, wheel mm (mm, in.)

da1' da2 tip diameter of pinion, wheel (refer to 4-3-1A1/Figure 5) mm (mm, in.)

db1• db2 base diameter of pinion, wheel (refer to 4-3-1A1/Figure 5) mm (mm, in.)

df1 ' df2 root diameter of pinion, wheel (refer to 4-3-1A1/Figure 5) mm (mm, in.)



21/109

PartChapter Section

4 Vessel Systems and Machinery3 Propulsion & Maneuvering Machinery1 Ap pen dix 1 - Rating of Cylind rical and Bevel Gears 4-3-1A1

d;1 di2 dsh

dshi

dw 1> dw2 ffa1'ffa2

fpb1'fpb2 h1, h2

ha1 • ha2

ha01 ha02

hf1 ’ hf2

hfp1 hfp2 hF1 hF2

l

l b m„

n1• n2 pr01’pr02Í1> Í2

sFn1 sFn2 s u v

x1• x2

xsm

z 1•z2

zn1 • zn2 B

bt F

Ft pQ

R

Rf ’Rzfi Rzr1 Rzr2

T1 T2U

aen1 aen2

aFen1 aFen2

ß ßb

F .&!

Sa1 ’Sa2

in.) in.) in.) in.) in.) in.) in.) in.) in.) in.) in.) in.)

in.) in.)

in.) in.) in.)

in.) in.) in.) in.)

m/s (m/s, ft/min)

rim inside diameter of pinion, wheel (refer to4-3-1A1/Figure 5) mm (mm,external diameter of shaft mm (mm,internal diameter of hollow shaft mm (mm,working pitch diameter of pinion, wheel mm (mm,profile form deviation of pinion, wheel mm (mm,transverse base pitch deviation of pinion, wheel mm (mm,tooth depth of pinion, wheel mm (mm,addendum of pinion, wheel mm (mm,addendum of tool of pinion, wheel mm (mm,dedendum of pinion, wheel mm (mm,dedendum of basic rack of pinion, wheel mm (mm,bending moment arm for tooth root bendingstress for application of load mm (mm,at the outer point of single tooth pair contact for pinion , wheelbearing span mm (mm,length of contact mm (mm,

normal module mm (mm,outer normal module mm (mm,transverse module mm (mm,

rotational speed of pinion, wheel rpmprotuberance of tool for pinion, wheel mm (mm,machining allowance of pinion, wheel mm (mm,tooth root chord in the critical section of pinion, wheel mm (mm,distance between mid-plane of pinion and themiddle of the bearing span mm (mm,gear ratio -tangential speed at reference diameter addendum modification coefficient of pinion, wheel tooth thickness modification coefficient (midface) number of teeth of pinion, wheel virtual number of teeth of pinion, wheel total facewidth, of double helical gear including gap width nominal tangential load on base cylinder in the transverse section nominal transverse tangential load at reference cylinder transmitted rated power ISO grade of accuracy cone distance middle cone distance flank roughness of pinion, wheel fillet roughness of pinion. Wheel nominal torque of pinion, wheelminimum ultimate tensile strength of core (applicable to through hardened, nomalized and cast gears only) form-factor pressure angle: pressure angle at the outer point of single degreespair tooth contact for pinion, wheelload direction angle: relevant to direction of application of load at the degrees outer point of single pair tooth contact of pinion, wheelnormal pressure angle at reference cylinder degrees

transverse pressure angle at reference cylinder degreestransverse pressure angle at working pitch cylinder degrees

helix angle at reference cylinder degreeshelix angle at base cylinder degrees

reference cone angle of pinion, wheel degrees

tip angle of pinion, wheel degrees

transverse contact ratio -

overlap ratio -

mm (mm, in.)N (kgf, lbf)N (kgf, lbf) kW (mhp, hp)

mm (mm, in.) mm (mm, in.)

pm (pm, pin.) pm (pm, pin.)N-m (kgf-m, lbf-ft)

N/mm2 (kgf/mm2, lbf/in2)

m na m

R m

a tw



22/109

Part 4 Vessel System s and MachineryChapter 3 Propulsion & Maneuvering MachinerySection 1 Appendix 1 - Rating o f Cylindrical and Bevel Gears 4-3-1A1

pa01 p a02

Pc

PF1 PF2

Subscripts

total contact ratio

tip radius of tool of pinion, wheel

radius of curvature at pitch surface

root radius of basic rack

root fillet radius at the critical section of pinion, wheel

1 = pinion; 2 = wheel; 0 = tool

mm (mm, in.)

mm (mm, in.)

mm (mm, in.)

mm (mm, in.)

5 G e o m e t r i c a l D e f i n i t i o n s

For internal gearing z2 , a , d2 , da2, db2, dw2 and u are negative.

The pinion is defined as the gear with the smaller number of teeth, therefore the absolute value of the gear ratio, defined as fo llow s is always greater or equal to the unity:

u = z2 /z 1 = dw2 /dw1 = d 2 /d 1

In the equation o f surface durability b is the common facewidth on the pitch diameter.

In the equation of tooth root bending stress b1or b2 are the facewidths at the respective tooth roots. In

any case, b1 and b2 are not to be taken as greater than b by more than one normal module mn on either side.

The common facewidth b may be used also in the equation of teeth root bending stress if significant crowning or end relief have been applied.

Additional geometrical definitions are given in the following expressions.

tan a t = ta n an/c o sß

ta nßb = tanß cos at

d12 = z12 ' m jc o s ß

db1,2 = d1,2 cosat = dw1,2 cosa w

a = °-5(dw1 + dw2)

z n 1,2 = z1,2/(co s2ßb cosß )

mt = mn /cos ß

inv a = tana - n a/180, a in degrees

inv a tw = inv a t + 2 tanan

x1 + x2 (z1+ z2 ) -( in v a tw - inv a t)

2 •tan a n

x ha0 d 1 - d f 1 x ha0 d2 - d f 2x1 1 , x2 --------

m n 2 • m n m n 2 • m n



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Part 4 Vessel Systems and MachineryChapter 3 Propulsion & Maneuvering MachinerySection 1 A ppendix 1 - Rating o f Cylindrical and Bevel Gears 4-3-1A1

0 5 V d a1 - d bi ± 0 5 Vda2 - d b. ... .. . a2 ~ d b2 - a s m a hcosa,

n m ncos ß

(The positive sign is to be used for external gears; the negative sign for internal gears.)

b sin ß s ß = -

(For double helix, b is to be taken as the width of one helix.)

ey = Sa+ Sß

a sin a tw u p c =

n mn

v = d i 2 ni 2/19099 [SI and MKS units]

v = di 2 ni 2 /3 .82 [US units]

7 B e v e l G e a r C o n v e r s i o n a n d S p e c i f i c F o r m u l a s

Conversion of bevel gears to virtual (equivalent) cylindrical gears is based on the bevel gear midsection.

Index v refers to the virtual (equivalent) cylindrical gear.

Index m refers to the midsection of bevel gear.

I I < <r reference cone angle pinion, wheel

I I C N tip angle pinion, wheel

X = shaft angle

ßm = helix angle at reference cylinder

R = cone distance pinion, wheel

R m = middle cone distance

Number o f teeth of virtual cylindrical gear:

z z vi e

c o s ö 1

z . z v2 =v2 ' 0

cos^2

Gear ratio of virtual cylindrical gear:

zJ

zvi

Geometrical definitions:

¿ + ¿2 = K = 90°)

uv = ^ z v

mn



24/109


tan a vt =tan a n

COS ß m

tanßbm= tanßm COS a vt

dl,2 R = 2 •sin S l2

Rm = R - - , b < R m 2 3

Reference diameter of pinion, wheel refers to the midsection of the bevel gear:

dm1 = d1 - b sin^1

dm2 = d2 - b sind2

Modules:

Outer normal module:

m na = mt Cosßm

Normal module at mid-facewidth:

R

mmn = mt • R ^Cosßm

mmn = — Cosßm

d m2

zCosßm

2

Base pitch:

p mmn •cos a vt Pbtm n

cos ßm

Reference diameter of pinion, wheel refers to the virtual (equivalent) cylindrical gear:

dvi = c o s b 1

d = d m2 a v2 ~ c

cosö 2

Base diameter of pinion, wheel:

dvb1 = dv1 cosavt

dvb2 = dv2 cosavt

Center distance:

av = °-5 (dv1 + dv2)

z1

mmn =



25/109


Transverse working pressure angle:

dvb1 + d vb 2

V 2 • av J a w in degrees

Add en du m:

For gears with constant addendum Zyk lo -P al lo id (K lin ge lnbe rg):

ham1 = mmn ' (1 + Xm1)

ham2 = mmn ' (1 + xml)

For gears with variable addendum (Gleason):

ham1 = hal - | ' tan(â1 - ^1)

ham2 = ha2 - | ' tan( â2 - S2>

Addendum modification coefficients:

x _ ham1 —ham2 x m1 _ '

2 • m mn

ham2 ham1 x m2 *2 • m ^ ,,tmn

Deden du m:

For gears with constant dedendum Zyk lo -P al lo id (K lin ge lnbe rg ):

h p = (1.25...1.30) • mmn

Pfp = (°.2 . . .°.3) • mmn

For gears with variable dedendum (Gleason):

hfm1 = hf1 - 2 •tan(â1 - ^1)

hfm2 = hf2 - -2 ^tan(â2 - S2)

hf1 = hfm1 + xm1 • mmn

hf2 = hfm2 + xm2 ' mmn

Tip diameter of pinion, wheel:

dva1 = dv1 + 2 • ham1

dva2 = dv2 + 2 • ham2

Transverse contact ratio:

£ _ 0 5 •V d va1 - d vb12 + 0 5 •V d va2 - d vb2 a cos a.t

n - mm n-----------cos ß m

- av • sin avt



26/109


Overlap ratio:

S r — b sin ß m

n -

Total contact ratio:

Sy — + S2 2 a + Sß

Tangential speed at midsection:

d m1,2 -n1,2v mt —--------------- m 19099

dm1,2 - n1,2

m/s [SI and MKS units]

3.82ft/min [US units]

Radius of curvature (normal section):

Pvc

cos ß bm (1 + uv )2Length o f contact:

b Sa Sy2 - [(2 - Sa) - (1 - Sß)]2

cos ßbm

b - s a

SY - cos ß bm

for Sß < 1

for Sß > 1

9 N o m i n a l T a n g e n t i a l L o a d , F t , F m t

The nominal tangential load, Ft or Fmt, tangential to the reference cylinder and perpendicular to the

relevant axial plane, is calculated directly from the rated power transmitted by the gear by means of the following equations:

av s in a vt uv

2


T12 = 9549P/nu

N-m

T ,2= 716 .2-P/n1>2 kgf-m

Tl2 = 525 2-P/nj 2

lbf-ft

Cylindricalgears

^ 2000T12 19.1P x 106 F — ’2 —

d1,2 n1,2d1,2N

2000T12 1.4325P x 106 Ft —--------— —-----------------

d1,2 n1,2d1,2

kgf

^ 24T12 126.05P x 103 Ft —-----— —-----------------

d1,2 n1,2d1,2

lb f

Bevel

gears

2000T] 2 19.1P x 106 F — ’ — t 1 1

dm1,2 n1,2dm1,2N

f 2OOOT12 1.4325P x 106 Fmt 7 _ j

dm1,2 n1,2dm1,2kgf

24T12 126.05P x 103 Fmt 7 _ j

dm1,2 n1,2dm1,2lb f

Where the vessel, on which the gear unit is being used, is receiving an Ice Class notation, the ice corrected torque va lues Tt as determined from 6-1-1/57 or 6-1-2/33 for the relevant Ice Class are to be

used in the above equation in place of T 1,2.



27/109


1 1 A p p l i c a t i o n F a c t o r , K A

The application factor, KA, accounts for dynamic overloads from sources external to the gearing.

The application factor, K A, for gears designed for infinite life is defined as the ratio between the

maximum repetitive cy clic torque applied to the gear set and the nominal rated torque.

The factor mainly depends on:

characteristics o f driving and driven machines;

ratio of masses;

type of couplings;

operating conditions as e.g. overspeeds, changes in propeller load conditions.

When operating near a critical speed of the drive system, a careful analysis of these conditions must be made.

The application factor, KA, should be determined by measurements or by appropriate system analysis.

Where a value determined in such a way cannot be provided, the following values are to be used:

a) M ain pro pu ls io n ge ar s:

turbine and electric drive: 1.00

diese l engine with hydraulic or electromagnetic slip coupling: 1.00

diese l engine with high elasticity coupling: 1.30

diese l engine with other couplings: 1.50

b) A uxi lia ry ge ar s:

electric motor, diese l engine with hydraulic or electromagnetic slip coupling: 1.00

diese l engine with high elasticity coupling: 1.20

diese l engine with other couplings: 1.40

1 3 L o a d S h a r i n g F a c t o r , K Y

The load sharing factor K y accounts for the maldistribution of load in multiple path transmissions as

e.g. dual tandem, epicyclical, double helix.

The load sharing factor K y is defined as the ratio between the maximum load trough an actual path and

the evenly shared load. The factor mainly depends on accuracy and flexibility of the branches.

The load sharing factor K y should be determined by measurements or by appropriate system analysis.

Where a value determined in such a way cannot be provided, the following values are to be used:

a) E pi cy cl ic al g ea rs :

up to 3 planetary gears: 1.00



6 planetary gears and over: 1.40

b) O th er g ear arrange m en ts: 1.00



28/109


c) B eve l g ea rs :

for s y < 2 : 1.00

for 2 < ̂ < 3.5 : 1 + 0 . 2 ^ - 2) •(5 - e y )

for er > 3.5 : 1.30

1 5 D y n a m i c F a c t o r , K v

The dynamic factor K v accounts for internally generated dynamic loads due to vibrations of pinion

and whee l against each other.

The dynamic factor K v is defined as the ratio between the maximum load which dynamically acts on

the tooth flanks and the maximum externally applied load (Ft KA K Y).

The factor mainly depends on:

transmission errors (depending on pitch and profile errors);

masses o f pinion and wheel;

gear mesh stiffness variation as the gear teeth pass through the meshing cycle;

transmitted load including application factor;

pitch line velocity;

dynamic unbalance o f gears and shaft;

shaft and bearing stiffnesses;

damping characteristics of the gear system.

The dynamic factor, K v, is to be advised by the manufacturer as supported by his measurements,

analysis or experience data or is to be determined as per 4-3-1/15.1 except that where vz1/100 is 3 m/s

(590 ft/min.) or above, K v may be obtained from Appendix 4-3-1A1 /15.3.

1 5 .1 D e t e r m i n a t io n o f K v - S i m p l if ie d M e th o d

Where all of the following four conditions are satisfied, K v may be determined in accordance with

Appendix 4-3-1A1/15.1.

a) Steel gears o f heavy rims sections.

b) Values of F t /b are in accordance with the following table:


> 150 N/mm > 15 kgf/mm > 856 lbf/in

c) z 1< 50



29/109


1 5 . 3

d) Running speeds in the subcritical range are in accordance with the follo wing table:

(v z 1) / 10 0

SI & M KS units US units

Helical gears < 14 m/s < 2756 ft/min

Spur gears < 10 m/s < 1968 ft/min

All types o f gears < 3 m/s < 590 ft/min

For gears other than specified above, the single resonance method as per 4-3-1A1/15.3 below may be applied.

The methods of calculation are as follows:

SI and M K S units US units

For helical gears of overlap ratio Sp > unity

Kv = Kvh = 1 + K v Z1/100 K v = K vh = 1 + K1 v z 1/19685

For helical gears of overlap ratio Sp < unity K v is obtained by means o f linear interpolation: K v = K vs - eß K vs - K vh)

For spur gears Kv = Kvs = 1 + K 1 v Z1/100 K v = K vs = 1 + K1 v z 1/19685

For bevel gears In the above conditions (b, c and d) and in the above formulas:• the real z 1is to be used instead o f the virtual (equivalent) zv1;• v is to be substituted by vmt; (tangential speed at midsection); and

• F t is to be substituted by Fmt.

For all gears K 1 values are specified in table below.

K1for different values of Q (ISO Grades of accuracy)

3 4 5 6 7 8

Spur gears 0.0220 0.0300 0.0430 0.0620 0.0920 0.1250

Helical gears 0.0125 0.0165 0.0230 0.0330 0.0480 0.0700

Q is to be according to ISO 1328. In case o f mating gears with different grades o f accuracy the grade corresponding to the lower accuracy should be used.

D e t e r m i n a ti o n o f K v - S i n g l e R e s o n a n c e M e th od

For single stage gears, the dynamic factor K v may be determined from 4-3-1A1/15.3.3 through 4-3-1 A1/1 5.3.6 for the ratio N in 4-3-1A1 /15.3.1 and using the factors given in 4-3-1A 1/15.3.2.

15.3.1 R eson an ce Ratio N

N = -n L nE1

nE1 = '30 x 10,3

n • z.

CY

m red

93.947 x103 C Y nE1 = '

n •z1 m

rpm

rpm red

[SI units]

[MKS units]



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PartChapter Section


589.47 4 x 103 \ ~ C ~ nE1 = -------------------- — — rpm [US units]

n z i V mred

where:

m red = relative reduced mass of the gear pair, per unit facewidth referred to the

n m red =~Z

8

line o f action:

( d ̂ d m1

{ db1 /

d 2

( (i - qi4) P i ) + (1 / ( i - q ( P 2 u 2)kg/mm (kg/mm, lb/in.)

mred = ------------------i^ - 2-------------- kg/mm (kg/mm, lb/in.) J i J 2

' • * { % r+ j 2 { ^ 2for planetary gears, p = number o f planets

j d ai,a2 d f i, f 2 , . .

dmi, m2 = 2 mm ’ (mm’ in )

qi = ; q2 = for reference, see 4-3 -iA i/Fi gu re 5 d mi d m2

J i = moment o f inertia per unit facewidth for pinion:

n d 4Ji = n ~ kg-mm2 /mm, (kg-mm2 /mm , lb- in2 /in .)

J 2 = moment o f inertia per unit facewidth for wheel:

4

32

p i 2 = density o f pinion, whe el materials

p = density o f steel material:

p = 7.83 x i0 -6 kg/mm3, [SI and MKS units]

p = 2.83 x i0 -i lb/in3 [US units]

B evel ge ar s:

For bevel gears the real z i (not the equivalent) and the equivalent base diameter for pinion and

wheel dvbi , dvb2 should be inserted in the above formulas.

Mesh stiffness per unit facewidth, C Y:

n d 4J 2 = n Pp,n—~ kg-mm2 /mm , (kg-mm 2 /mm, lb-in2 /in .)

20C = Bb N/m m-um [SI units]

Y 0.85 b

2.039CY = 0 85 Bb kgf/mm -pm [MKS units]

2 90iCY = ------------ Bb lbf/in.-pin. [US units]

Y 0.85 b

Tooth stiffness of one pair of teeth per unit facewidth (single stiffness), c ':



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PartChapter Section


14 c — Bb N/m m-um [SI units]

0.85

1.428 c' = 0 85 ' Bb kgf/mm -pm [MKS units]

2 031 c ' —------------ Bb lbf/in.-uin. [US units]0.85 b

For combination of different materials for pinion and wheel, c' is to be multiplied by 4,

where

E 4 = E st

B = eH Bb

2 E E E where values of £ 1 and £ 2 are to be obtained from 4-3-1A1/Table 1

E1+ E2

Est = You ng’s modulus of steel; see 4-3-1A1/Ta ble 1

Overall facewidth, B b:

be b

where: beH = effective facewidth, mm (mm, in.)

N ote: Higher values than B b = 0.85 are not to be used.

Cylindrical gears:

Mesh stiffness per unit facewidth, C Y:

C Y = c' (0.75 ea + 0.25) N/mm -pm (kgf/mm-pm, lbf/in.-pin.)

Tooth stiffness of one pair of teeth per unit facewidth (single stiffness), c ' :

cos fì c' —0 .8 ------------CBS CR N/m m-pm [SI units]

q

c' —8.158 •10-2 • cos ß •C BS •CR kgf/mm -pm [MKS units]

c ' —11.603 •10-2 •c os ß •C BS CR lbf/in. -pin. [US units]

For combination of different materials for pinion and wheel, c ' is to be multiplied by 4,where

4 - -£ E st

2 •£1 •£2 E — 1— - where values o f £1 and £2 are to be obtained from 4-3-1A1/Table 1

£ 1 + £ 2 1 2

Est = You ng’s modulus of steel; see 4-3-1A1/Ta ble 1



32/109

Part 4 Vessel System s and MachineryChapter 3 Propulsion & Maneuvering MachinerySection 1 Append ix 1 - Rating of Cylindrical and Bevel Gears 4-3-1A1

0.15551 0.25791 ° .n 6 54- x a 2418» 2 2 1 -0.00193-x 2 ' - - — ¿q' _ 0.04723+ --------+ 0.00635- x1 -

n1 zn2

Zn1 _

n1 2

n2- + 0.00529- x f + 0.00182- X2

n1 2 n ncos ßb •cos ß

zn2cos ß b •cos ß

N ote: For internal gears, use z n2 ( = * ) equal infinite and x2 = 0.

CBS _

( 1 + 0.5 •

hP Ì 1.2 — ]fp-

mn• [1 - 0.02 •(20 - a n )]

When the pinion basic rack dedendum is different from that of the wheel, the arithmetic mean o f CBS1 for a gear pair conjugate to the pinion basic rack and CBS2 for a gear pair conjugate to

the basic rack of the wheel:

CBS = 0 -5 • (CBS1 + CBS2>Gear blank factor, C R:

Cr _ 1 + -ln(bs I b)

5 •e(sR | 5-m„)

when: 1) b jb < 0.2 , use 0.2 for b jb

2) b jb > 1.2 , use 1.2 for b jb

3) SRImn < 1 ,

For bs and sR see 4-3-1A1IFigure 3

use 1.0 for sRImn

15.3.2 Factors B p, B, , and B kF J K a) Values for f pt and ya according to ISO grades of accuracy Q :

z1

z 2

Q (1) 3 4 (3) 5 6 7 8 9 10 11 (4) 12

fpt qm 3 6 12 25 45 70 100 150 201 282

qin 118 236 472 984 1772 2756 3937 5906 7913 11102

y (2) a qm 0 0.5 1.5 4 7 15 25 40 55 75

qin 0 19.7 59.1 157 276 591 984 1575 2165 2953

Notes

1 ISO grades of accuracy according to ISO 1328. In case of mating gears with differentgrades of accuracy the grade corresponding to the lower accuracy should be used.

2 For specific determination of ya , see b) through d) below.3 Hardened nitrided.4 Tempered normalized.



33/109


b) Determination of y a for structural steels, through hardened steels and nodular cast iron

(perlite, bainite):


160 y a — f pb

°Hlim

16.315 y a — J pb

°Hlim

2.331x104 y a — Jpb

°Hlim

For v < 5 m/s :

no restriction

For v < 5 m/s :

no restriction

For v < 984 ft/min :

no restriction

For 5 m/s < v < 10 m/s :

12800yamax — and

CTHlim

fpbmax = 80 M-m

For 5 m/s < v < 10 m/s :

1.305 x103yamax — and

a Hlim

fpbmax = 80 M-m

For 984 ft/min < v < 1968 ft/min :

7.341x 107yamax — and

CTHlim

fpbmax = 3150 în

For v > 10 m/s :

6400y amax — and a Hlim

fpbmax = 40 M-m

For v > 10 m/s :

652.618yamax — and

CTHlim

fpbmax = 40 M-m

For v > 1968 ft/min :

3.67 x 107y amax — and

°Hlim

fpbmax = 1575 în

c) Determination of y a for gray cast iron and nodular cast iron (ferritic):

SI and M K S units US units

ya = °.275 fpb m ya = 0.275 fpb în

For v < 5 m/s :no restriction For v < 984 ft/min :no restriction

For 5 m/s < v


34/109


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15.3.3 Dynamic Factor, K v in the Subcritical Range (N < 0.85)

Cv1 = 0.32

C v2 = 0.34 for eY<

Cv2 0.57eY _ 0 .3

for eY>

C v3 = 0.23 for eY<

Cv30.096

e Y _ 1.56for eY >

K = (Cv1 Bp) + (Cv2 Bf) + (Cv3

K v = (N K ) + 1

15.3.4 Dynamic Factor, Kv in the Main Resonance Range (0.85 < N < 1.15)

Cv4 0.90 for eY 2

(Cvi Bp) + (Cv2 Bf) + (Cv4 Bk) + 1

For Cv1 and Cv2, see 4-3-1A1/15.3.3 above.

15.3.5 Dynamic Factor, K v, in the Supercritical Range (N > 1.5)

C v5

C

0.47

v6 - 0.47C 0.12

Cv6 = er - 1.74

for eY< 2

for eY> 2

Cv7 = 0.75

Cv7 = 0.12 5-sin [^(e Y_ 2)] + 0.875

for 1.0 < eY


36/109


1 7 F a c e L o a d D i s t r i b u t i o n F a c t o r s , K H ß a n d K F ß

The face load distribution factor, K Hß for contact stress, KFß for tooth root bending stress, accounts for

the effects of non-uniform distribution of load across the facewidth.

K Hß is defined as follows:

K = maximum load per unit facewidth

Hß mean load per unit facewidth

K Fß is defined as follows:

K Fß =maximum bending stress at tooth root per unit facewidth

mean bending stress at tooth root per unit facewidth

Note: The mean bending stress at tooth root relates to the considered facewidth b 1 or b2

K Fß can be expressed as a function o f the factor KHß.

The factors K Hß and K Fß mainly depend on:

gear tooth manufacturing accuracy;

errors in mounting due to bore errors;

bearing clearances;

wheel and pinion shaft alignment errors;

elastic deflections of gear elements, shafts, bearings, housing and foundations which support the gear elements;

thermal expansion and distortion due to operating temperature;

compensating design elements (tooth crowning, end relief, etc.).

These factors can be obtained from 4-3-1A1/17.3 and 4-3-1A1/17.5 using the factors in 4-3-1A1/17.1.

1 7.1 F a c t o r s U s e d f o r t h e D e t e r m i n a t io n o f K , Hß

17.1.1 Helix Deviation Fß

The helix deviation Fß is to be determined by the designer or by the followin g equations:

SI and MKS units, |im US units, |iin.Q-1 (

Fß = 10 10 •Vb

+ 2 for Q < 7

Q-4 ( Fß = 10 5

4 b+ 2 for Q > 7

Q-1 ( Fß = 10 10 •

V

Q-4 ( Fß = 10 5

4 bA

0.02016

4 b

0.02016

- + 78.74 for Q < 7

A+ 7 8.7 4 for Q > 7

4

4



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17.1.2 Mesh Alignment f ma [pm (am, pin.)]

Generally: m = l.O-iß

For gear pairs with well designed end relief: f ma = 0 .7Fß .

For gear pairs with provision for adjustment (lapping or running-in under light load, adjustment bearings or appropriate helix modification) and gear pairs suitably crowned:

f ma = 0-5F ß

For helix deviation due to manufacturing inaccuracies: f ma = 0.5F ß

17.1.3 Initial Equivalent Misalignment Fßx [pm (pm, pin.)]

Fßx is the absolute value of the sum of manufacturing deviations and pinion and shaft

deflections, measured in the plane of action.

Fßx = 1.33 f h + fma

= Ft - K a - K y - K v

Jsh JshO * , b

f sh0min = 0.005 pm-mm/N [SI units]

f sh0min = 0.049 pm-mm /kgf [MKS units]

fsh0min = 0 03445 pin.-in ./lb f [US units]

Part 4 Vessel System s and MachineryChapter 3 Propulsion & Maneuvering MachinerySection 1 Ap pen dix 1 - Rating of Cylind rical and Bevel Gears 4-3-1A1

SI units

[pm-mm/N]

MKS units

[pm-mm/kgf]

US units

[pin-in./lbf]

For spur and helical gears without crowning or end relief f sh0 = °.023' Y

fsh0 = 0.22555 -y fsh0 = 0.15858- y

For spur and helical gears without crowning but with end relief f sh0 = 0.016' Y fsh0 = 0.15691- Y fsh0 = 0.11032 -y

For spur and helical gears with crowning fsh0 = 0.012- Y fsh0 = 0.11768-Y fsh0 = 0.08274 -y

For spur and helical gears with crowning and end relief fsh0 = 0.010- Y

fsh0 = 0.09807- y fsh0 = 0.06895- y

Y = , Ns_

d12

f ± V

\ d sh y- 0.3 + 0.3

v d i yfor spur and single he lical gears

Y = 2 • 1.5 + K , t- s_

d12

( A V

V d sh y

- 0.3 + 0.3f b ^ bB

v d i y

for double helical gears

where bB = b /2 is the width o f one helix.

The constant K makes allowances for the position of the pinion in relation to the torqued end. It can be taken from 4-3-1A1/Table 6.

2



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17.1 .4 Determination of y p and Xß for Structural Stee ls, Through Hardened St ee ls and

Nodular Cast Iron (Perlite, Bainite)


320 F y ß = „ • FßX um

H lim

32.63 F y ß = „ • FßX Um

H lim

4.662-104 ^ y ß = „ • FßX uin-

a H lim320

X ß = 1 a H lim

w ith yß < FßX; Xß —0

, 32.63 X ß = 1

a H lim

w i thy ß < FßX; Xß—0

, 4 .662 4 0 4 X ß = 1

°H lim

w i thy ß < FßX; Xß—0

For v < 5 m/s no restriction

For v < 5 m/s no restriction

For v < 984 ft/min no restriction

For 5 m/s < v < i0 m/s :25600

y ß max = a H lim

corresponding to FßX = 80 um

For 5 m/s < v < 10 m/s :

2 6 1 - 1 0 3 y ß max =

a H limcorresponding to FßX = 80 um

For 984 ft/min < v < 1968 ft/min :

14.682-107 y ß max =

a H limcorresponding to FßX = 3150 uin.

For v > 10 m/s :

12800 y ß max =

a H lim

corresponding to FßX = 40 um

For v > 10 m/s :

1.305-103 y ß max =

a H limcorresponding to FßX = 40 um

For v > 1968 ft/min :

7 . 3 4 M 0 7 y ß max =

a H limcorresponding to FßX = 1575 uin.

For 1968 ft/min

y ßmax = 866corresponding to FßX = 1575 uin.

17.1.6 Determination of y ß and Xß for Case Hardened, Nitrided or Nitrocarburized Steels;

SI & MKS units US units y ß = ° .15 FßX um y ß = 0.15 F ßX uin.

X ß= 0.85 Xß = 0.85For all velocities but with the restriction:

yßmax = 6 corresponding to FßX = 40 um

For all velocities but with the restriction: yßmax = 236 corresponding to FßX = 1575 uin.

When the material of the pinion differs from that of the wheel, yßi and Xßi for pinion, and y ß

and Xßi for wheel are to be determined separately. The mean o f either value:



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1 7 . 3

1 7 . 5

>ß= 0.5 (jß + yp2)

Xß = 0 5 (Xßi + X ß )

is to be used for the calculation.

F a c e L o a d D i st r ib u t io n F a c t o r f o r C o n t a c t S t r e s s K¡

17.3.1 K h ß for Helical and Spur Gears

K Hß = 1 + b Fßy C Y

2 • Ft • K a •K r - K v< 2, for

Hß

b • Fßy •C Y

2 • Ft • K a • K r - K v< 1

K Hß =2 • b • Fßy •C Y

Ft • K a •K y •K v> 2 for

b • Fßy • C Y

2 • Ft • K a •K y •K v> 1

where:

Fßy = Fßx - y ß or Fßy = Fßx Xß

Calculated values of K Hß > 2 are to be reduced by improvement accuracy and helix deviation.

17.3.2 K Hß for Bevel Gea rs

K = 15 0 85 K K Hß 1.5

B b Hßbe

The bearing factor, K Hß e, represents the influence of the bearing arrangement on the faceload

distribution, is given in the follow ing table:

M ou nting co ndi tio ns o f pinion an d w hee l

Both m embers straddle

mounted

One member straddle

mounted

Neither member straddle

mounted1.10 1.25 1.50

Based on optimum tooth contact pattern under maximum operating load as evidence by results of a deflection test on the gears in their mountings.

F a c e L o a d D i st r ib u t io n F a c t o r f o r T o o t h R o o t B e n d i n g S t r e s s K Fß

17.5.1 In C as e the Hardest Contact is at the End of the Face-w idth K Fß is Given by the

Following Equations

K Fß = (KHß)N

N =

(b / h) 2

1 + (b / h) + (b / h)2 1 + (h / b) + (h / b)2

(b/h) = (facewidth/tooth depth), the lesser of b 1 /h 1 or b2 /h2. For double helical gears, the

facewidth o f only one helix is to be used, i.e. bB = b/2 is to be substituted for b in the equation

for N .

17.5.2 In C as e of Gears W here the Ends of the Facewidth are Lightly Loaded or Unloaded (End R elief or Crowning)

K Fß = KHß

1



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1 9

19.1

17.5.3 Bevel Gears:

K Pß - K Hß

PO

K po - 0.211'

q -

+ 0.789 for spiral bevel gears.

0.279

log(sin ßm )

where

K po = 1

R m

for straight or zero bevel gears.

cutter radius, mm (mm, in.)

mean cone distance, mm (mm, in.)

Limitations of K, PO

If KPO < unity, use K PO = unity

If KPO > 1.15, use K PO = 1.15

T r a n s v e r s e L o a d D i s t r i b u t i o n F a c t o r s , K H a a n d K P a

The transverse load distribution factors, KHa for contact stress and K Pa for tooth root bending stress,

account for the effects of pitch and profile errors on the transversal load distribution between two or more pairs o f teeth in mesh.

The factors K Ha and K Pa mainly depend on:

total mesh stiffness; total tangential load P t, KA, K y, K v, K Hß

base pitch error;

tip relief;

running-in allowances.

The load distribution factors, K Ha and K Pa are to be advised by the manufacturer as supported by his

measurements, analysis or experience data or are to be determined as follows.

D e t e r m i n a ti o n o f K H a fo r C o n t a c t S t r e s s K P a f o r T o o th R o o t B e n d i n g S t r e s s

KHa = K P a= 0.9 + 0.4' 2 •(sr - 1) CY •( fpb e - y a ) b

Ptfor Sy> 2

tH

K Ha K P a ~ Y ' 0.9 + 0.4CY •( f pbe - y a) •b

Pt tH for Sy< 2

P tH = P t K - K K K hß N (kgf, lbf)

eo

reo

ABS RULES FOR BUILDING AND CLASSING STEEL VESSELS 1 2002 143


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fpbe fpb 'co s a t

For bevel gears, Fmt and a vt (equivalent) are to be substituted for F t and a t in the above formulas.

1 9 . 3 L i m i ta t io n s o f K H a a n d K ,

19.3.1 K, Ha

When K Ha< 1 use 10 for K Ha

When K Ha> Ha> 2 , use 2 for K Ha Ha p • 7 2 p • 7 2 Ha a s a

for K H

J 4 - s Pß — - p a • (1 - Pß) + — , contact ratio factor (pitting) for helical gears for Pß< 13 a

Zp =

7p = 4 - pa

contact ratio factor (pitting) for helical gears for Pß> 1

contact ratio factor (pitting) for spur gears

19.3.2 K, Fa

When K Fa < 1, use 1.0 for K F a .

When KF a> — :— , use — :— P •Y P •Y ‘'a ±e ''a ±e

for K Fa

Ys = 0.25 +0.75

contact ratio factor for pß = 0

YP = 0.25 +0.75 0.75

- 0.375 •Pß, contact ratio factor for 0 < pß < 1

or:

Ys = 0.625,

YP = 0.25 +

contact ratio factor for pß > 1

0.75 •cos2 ß b

3



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2 1

2 1 . 1

S u r f a c e D u r a b i l i t y

The criterion for surface durability is based on the Hertzian pressure on the operating pitch point or at the inner point of single pair contact. The contact stress aH is not to exceed the permissible contact

stress a HP-

C o n t a c t S t r e s s

aH1 = aHO1' yJK A ' K y ' K v ' K Ha ' K Hß - aHP1

aH2 = aHO2 ^ K A ' K y ' K v ' K Ha ' K Hß - aH

Cylindrical gears:

aHO12 = basic va lue o f contact stress for pinion and wheel

HP2

aHO1 ZB'ZH ZE Zs'Zß

where

a = Z n Z HZ EZ - Z n

' Ft u +1

d 1 b u

1 Ft u +1

d 1 b u

for pinion

for wheel

Z H

Z E

Z„

single pair mesh factor for pinion, see 4-3-1A 1/21.5 below

ZD = single pair mesh factor for wheel, see 4-3-1A 1/21.5 below

zone factor, see 4-3-1A1/21.7 below

elasticity factor, see 4-3-1A 1/21.9 b elow

contact ratio factor (pitting), see 4-3-1A1/21.11 below

helix angle factor see 4-3-1A1/21.17 below

F t = nominal transverse tangential load, see 4-3 -1A 1/9 o f this Appendix.

Gear ratio u for external gears is positiv e, for internal gears u is negative

Regarding factors KA, K v, K Ha and K Hß , see 4-3-1A1/11, 4-3-1A1/13, 4-3-1A1/15, 4-3-1A1/19

and 4-3-1A1 /17 o f this appendix.

B eve l gea rs :

Z ß

a HO1 basic value of contact stress for pinion

a HO1 ZM-BZH ZE ZLS Zß ZK Fm uv + 1

dv1 1 b

For the shaft angle Z = 81 + S2 = 90° the following applies:

Í a HO1 ZM-BZH ZE ZLSZß ZK

F J mt \ju 2 + 1

d v1 1 b u

uv



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2 1 . 3

where

ZM_B = mid-zone factor, see 4-3-1A 1/21.5 below)

ZH = zone factor, see 4-3-1 A1/2 1.7 below)

ZE = elasticity factor, see 4-3-1A 1/21.9 below)

ZLS = load sharing factor, see 4-3-1A 1/21.13 below)

Zß = helix angle factor, see 4-3-1A 1/21.1 7 below)

ZK = bevel gear factor (flank), see 4-3-1A 1/21.15 below)

Fmt = nominal transverse tangential load, see 4-3- 1A1/9o f this appendix.

dv1 = reference diameter o f pinion o f virtual (equivalent) cylindrical gear

l b = length of contact

uv = gear ratio o f virtual (equivalent) cylindrical gear

u = gear ratio o f bevel gear

P e r m i ss ib l e C o n t a c t S t r e s s

The permissible contact stress aHP is to be evaluated separately for pinion and wheel.

^ _ °H limS

- Z N - Z L ' Z V ' Z R - Z W - Z X N/mm2 (kgf/mm2, psi) H

where:

H lim

Z N

ZL

Z V

ZR

Z W

Z X

S H

endurance limit for contact stress, see 4-3-1A1/21.19 below

life factor for contact stress, see 4-3-1 A1/21 .21 below

lubrication factor, see 4-3-1A 1/21.23 below

speed factor, see 4-3-1A1 /21.23 b elow

roughness factor, see 4- 3-1A1 /21.23 below

hardness ratio factor, see 4-3-1A1/21.25 below

size factor for contact stress, see 4-3 -1A1 /21.27 below

safety factor for contact stress, see 4-3-1A 1/21.29 below

For shrink-fitted wheel rims cth p is to be at least K S times the mean contact stress cth , where

K S = safety factor available for induced contact stresses, and is to be calculated as

follows:

K = 1 , ¿max -2.2 X105

d ri 0.25mn

d w2 PF 2

K = 1 , ¿max - 2.243 X104 d ri 0.25mn

d w2 p F 2

[SI units]

[MKS units]

2

2



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K = 1 + ¿max •3. 194x 10 d ri 0.25mn

d 2

w2 p F 2[US units]

where

d r,

dw2

m n

Y

maximum available interference fit or maximum pull-up length; mm (mm, in.)

inner diameter of wh eel rim; mm (mm, in.)

working pitch diameter of wheel; mm (mm, in.)

normal module; mm (mm, in.)

yield strength of wheel rim material is to be as follows:

minimum specified yield strength for through hardened (quenched and tempered) steels

500 N/mm2 (51 kgf/mm2, 72520 psi) for case hardened, nitrided steels

2 1 . 5 S i n g l e P a ir M e s h F a c t o r s , ZB, ZD a n d M i d -z o n e F a c t o r ZM_B

The single pair mesh factors, ZB for pinion and ZD for wheel, account for the influence on contact

stresses of the tooth flank curvature at the inner point of single pair contact in relation to ZH.

The factors transform the contact stresses determined at the pitch point to contactstresses consideringthe flank curvature at the inner point o f single pair contact.

21.5.1 For Cylindrical and Bevel Gea rs whe n Sß = 0

ZB = ZM_B = M 1 or 1 whichever is the larger value

ZD = ZM_B = M2 or 1 whichever is the larger value

tan «w,M 1 =

M 2 =

4 (d a1¡d b1 )2 - 1 - (2n/ z1) • V (d «2 / d b2 )2 - 1 - ( s a - 1) i 2 n z 2 )

tanah

J ( d a21d b2 )2 - 1 - (2n/ z 2 ) • - ( s a - z j

for cylindrical gears

for cylindrical gears

For bevel gears a tw, da, d b and z are to be substituted by a vt, dva, dvb and zv respectively in the

above formulas.

21 .5.2 For Cylindrical and Bevel Gears whe n sß > 1

ZB

ZM-B

M =

ZD = 1 for cylindrical gears

M or 1 whichever is the larger value, for bevel gears

tan a vt

4 (d va1¡ d vb1)2 - 1 - S a - ( n zv1) • V(d va 21 d vb2 )2 - 1 - S a \ n l zv2)

&



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M =

21 .5.3 For Cylindrical and Bevel Gea rs whe n 0 < Sß < 1

Cylindrical gears:

The values of ZB , ZA are determined by linear interpolation betwe en ZB , ZA for spur gears and

ZB , ZA for helical gears having Sß < 1

Thus:

ZB = M 1 - S ß ( M 1 - 1) and ZB > 1

ZD = M 2 - Sß(M 2 - 1) and ZD > 1

B eve l gea rs :

ZM-B = M

Calcolo Ingranaggi Iso 9336 ABS Part 4 Ottimo

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