Calculation of Crankshafts for Internal Combustion Engines I PDF

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Rules for Classification and Construction VI Additional Rules and Guidelines 4 Diesel Engines 2 Calculation of Crankshafts for Internal Combustion Engines Edition 2012 The following Rules come into force on 1 May 2012. Alterations to the preceding Edition are marked by beams at the text margin. Germ...

Description

VI

Rules for Classification and Construction Additional Rules and Guidelines

4

Diesel Engines

2

Calculation of Crankshafts for Internal Combustion Engines

Edition 2012

The following Rules come into force on 1 May 2012. Alterations to the preceding Edition are marked by beams at the text margin. Germanischer Lloyd SE Head Office Brooktorkai 18, 20457 Hamburg, Germany Phone: +49 40 36149-0 Fax: +49 40 36149-200 [email protected] www.gl-group.com "General Terms and Conditions" of the respective latest edition will be applicable (see Rules for Classification and Construction, I - Ship Technology, Part 0 - Classification and Surveys). Reproduction by printing or photostatic means is only permissible with the consent of Germanischer Lloyd SE. Published by: Germanischer Lloyd SE, Hamburg

VI - Part 4 GL 2012

Table of Contents

Chapter 2 Page 3

Table of Contents

Section 1 A. B. C. D. E. F. G. H.

Calculation of Crankshafts for Internal Combustion Engines General ....................................................................................................................................... Calculation of Stresses ............................................................................................................... Calculation of Stress Concentration Factors .............................................................................. Additional Bending Stresses ...................................................................................................... Calculation of Equivalent Alternating Stress .............................................................................. Calculation of Fatigue Strength .................................................................................................. Acceptability Criteria ................................................................................................................. Calculation of Shrink-fits of Semi-built Crankshafts ..................................................................

Annex A

Definition of Stress Concentration Factors in Crankshaft Fillets

Annex B

Stress Concentration Factors and Stress Distribution at the Edge of Oil Drillings

Annex C

Alternative Method for Calculation of Stress Concentration Factors in the Web Fillet Radii of Crankshafts by utilizing Finite Element Method

A. B. C.

General ....................................................................................................................................... Model Requirements .................................................................................................................. Load Cases .................................................................................................................................

1- 1 1- 3 1- 7 1- 10 1- 10 1- 10 1- 11 1- 11

C- 1 C- 1 C- 2

VI - Part 4 GL 2012

Section 1

A

Calculation of Crankshafts for Internal Combustion Engines

Chapter 2 Page 1–1

Section 1 Calculation of Crankshafts for Internal Combustion Engines

A.

General

1.

Scope

These Rules for the scantlings of crankshafts are to be applied to diesel engines for main propulsion and auxiliary purposes, where the engines are so designed as to be capable of continuous operation at their rated power when running at rated speed. Crankshafts which cannot satisfy these Rules will be subject to special consideration as far as detailed calculations or measurements can be submitted. In case of: –

surface treated fillets

–

tested parameters influencing the fatigue behaviour

–

measured working stresses

stress is then compared with the fatigue strength of the selected crankshaft material. This comparison will then show whether or not the crankshaft concerned is dimensioned adequately. 4.

For the calculation of crankshafts, the documents and particulars listed in the following are to be submitted: –

crankshaft drawing which must contain all data in respect of the geometrical configuration of the crankshaft

–

type designation and kind of engine (in-line engine or V-type engine with adjacent connecting rods, forked connecting rod or articulatedtype connecting rod)

–

operating and combustion method (2-stroke or 4-stroke cycle, direct injection, precombustion chamber, etc.)

–

number of cylinders

–

rated power [kW]

–

rated engine speed [min-1]

–

sense of rotation (see Fig. 1.1)

–

ignition sequence with the respective ignition intervals and, where necessary, V-angle αv (see Fig. 1.1)

–

cylinder diameter [mm]

–

stroke [mm]

–

maximum cylinder pressure pmax [bar]

–

charge air pressure [bar] (before inlet valves or scavenge ports, whichever applies)

–

nominal compression ratio [–]

–

connecting rod length LH [mm]

–

oscillating weight of one crank gear [kg] (in case of V-type engines, where necessary, also for the cylinder unit with master and articulatedtype connecting rod or forked and inner connecting rod)

–

digitalized gas pressure curve presented at equidistant intervals (bar versus crank angle, but not more than 5° CA)

these data can be considered on special request. 2.

Field of application

These Rules apply only to solid-forged and semi-built crankshafts of forged or cast steel, with one crank throw between main bearings. 3.

Principles of calculation

The design of crankshafts are based on an evaluation of safety against fatigue in the highly stressed areas. The calculation is also based on the assumption that the areas exposed to highest stresses are: –

fillet transitions between the crankpin and web as well as between the journal and web,

–

outlets of crankpin oil bores.

When journal diameter is equal or larger than the crankpin one, the outlets of main journal oil bores are to be formed in a similar way to the crankpin oil bores. Otherwise, the engine manufacturer if requested by GL shall submit separate documentation of fatigue safety. Calculation of crankshaft strength consists initially in determining the nominal alternating bending and nominal alternating torsional stresses which, multiplied by the appropriate stress concentration factors using the theory of constant energy of distortion (v. Mises' Criterion), result in an equivalent alternating stress (uni-axial stress). This equivalent alternating

Drawings and particulars to be submitted

Chapter 2 Page 1–2

Section 1

Calculation of Crankshafts for Internal Combustion Engines

A

6 4

3

5

2

A1

1

A2

A3

A4

A5

B1

VI - Part 4 GL 2012

A6

B2

B3

B4

B5

B6

a

V

counter clockwise

driving shaft flange

Fig. 1.1

–

driving shaft flange

counter clockwise

clockwise

Designation of the cylinders

for engines with articulated-type connecting rod (see Fig. 1.2)

–

- distance to link point LA [mm] -

link angle αN [°]

-

connecting rod length LN [mm]

clockwise

details of crankshaft material -

material designation (according to ISO, DIN, AISI, etc.)

-

mechanical properties of material (minimum values obtained from longitudinal test specimens) The minimum requirements of the GL Rules II – Materials and Welding must comply with:

LN

aN

LA

LH

Fig. 1.2 –

Articulated-type connecting rod

maximum cylinder pressure pmax [bar]

-

charge air pressure [bar] (before inlet valves or scavenge ports, whichever applies)

-

nominal compression ratio [–]

-

digitalized gas pressure curve presented at equidistant intervals [bar/°CA]

tensile strength [N/mm2]

-

yield strength [N/mm2]

-

reduction in area at fracture [%]

-

elongation A5 [%]

-

impact energy – KV [J]

-

method of material melting process (openhearth furnace, electric furnace, etc.)

-

type of forging (free form forged, continuous grain flow forged, drop-forged, etc., with description of the forging process)

–

heat treatment

–

surface treatment of fillets, journals and pins (induction hardened, flame hardened, nitrided, rolled, shot peened, etc. with full details concerning hardening)

for the cylinder with articulated-type connecting rod -

-

–

-

hardness at surface [HV]

-

hardness as a function of depth of hardening

-

extension of surface hardening

particulars for alternating torsional stresses, see B.2.

Section 1

VI - Part 4 GL 2012

B

Calculation of Crankshafts for Internal Combustion Engines

Chapter 2 Page 1–3

B.

Calculation of Stresses

length between the two main bearings (distance L3) see Figs. 1.3 and 1.4.

1.

Calculation of alternating stresses due to bending moments and radial forces

1.1

Assumptions

The bending moments MBR, MBT are calculated in the relevant section based on triangular bending moment diagrams due to the radial component FR and tangential component FT of the connecting-rod force, respectively (see Fig.1.3). For crank throws with two connecting-rods acting upon one crankpin the relevant bending moments are obtained by superposition of the two triangular bending moment diagrams according to phase (see Fig.1.4).

Centre Line of Connecting rod

The calculation is based on a statically determinate system, so that only one single crank throw is considered of which the journals are supported in the centre of adjacent bearings and which is subject to gas and inertia forces. The bending length is taken as the

Centre Lines of Connecting rod

L1

L1

L1

L2

L2

L2

L3

L3

Connecting-rod acting component forces (FR or Ft)

Radial shear force diagrams (QR)

Bending moment diagrams (MBRor MBt)

Fig. 1.3

Crankthrow for in-line engine

Fig. 1.4

Crank throw for Vee engine with 2 adjacent connecting rods

1.1.1

Section 1

Calculation of Crankshafts for Internal Combustion Engines

B

Bending moments and radial forces acting in web

The bending moment MBRF and the radial force QRF are taken as acting in the centre of the solid web (distance L1) and are derived from the radial component of the connecting-rod force.

Mean stresses are neglected.

B

E

W DG

Overlapped crankshaft

Th RH

Wred L1

B

W Crankshaft without overlap

Fig. 1.5

VI - Part 4 GL 2012

The alternating bending and compressive stresses due to bending moments and radial forces are to be related to the cross-section of the crank web. This reference section results from the web thickness W and the web width B (see fig. 1.5).

DG - S 2

Chapter 2 Page 1–4

Reference area of crankweb cross section

VI - Part 4 GL 2012

1.1.2

Section 1

B

Calculation of Crankshafts for Internal Combustion Engines

Chapter 2 Page 1–5

The decisive alternating values will then be calculated according to:

Bending acting in outlet of crankpin oil bore

The two relevant bending moments are taken in the crankpin cross-section through the oil bore. FR

XN = ± XN

1 ⎡X max − X min ⎤⎦ 2⎣

= considered as alternating force, moment or stress

Xmax = maximum value within one working cycle

MBTO

Xmin = minimum value within one working cycle 1.2.1

MBRO

FT

Nominal alternating bending and compressive stresses in web cross section

The calculation of the nominal alternating bending and compressive stresses is as follows:

Y

σ BFN =

M BRFN ⋅ 103 ⋅ Ke Weqw

σQFN =

Q RFN ⋅ Ke F

σBFN = nominal alternating bending stress related to the web [N/mm2] MBRO = bending moment of the radial component of the connecting-rod force

MBRFN = alternating bending moment related to the centre of the web [Nm] (see Fig. 1.3 and 1.4)

MBTO = bending moment of the tangential component of the connecting-rod force

Fig. 1.6

Crankpin section through the oil bore

The alternating stresses due to these bending moments are to be related to the cross-sectional area of the axially bored crankpin. Mean bending stresses are neglected. 1.2

M BRFN = ±

Weqw = section modulus related to cross-section of web [mm3] Weqw Ke

Calculation of nominal alternating bending and compressive stresses in web

The radial and tangential forces due to gas and inertia loads acting upon the crankpin at each connectingrod position will be calculated over one working cycle. A simplified calculation of the radial and tangential forces may be used at the discretion of GL. Using the forces calculated over one working cycle and taking into account of the distance from the main bearing midpoint, the time curve of the bending moments MBRF, MBRO, MBTO and radial forces QRF (defined in 1.1) will then be calculated. In case of V-type engines, the bending moments – progressively calculated from the gas and inertia forces – of the two cylinders acting on one crank throw are superposed according to phase, the different designs (forked connecting rod, articulated-type connecting rod or adjacent connecting rods) shall be taken into account. Where there are cranks of different geometrical configuration (e.g. asymmetric cranks) in one crankshaft, the calculation is to cover all crank variants.

1 ⎡M BRFmax − M BRFmin ⎤⎦ 2⎣

=

B ⋅ W2 6

= empirical factor considering to some extent the influence of adjacent crank and bearing restraint with: Ke = 0.8 for 2-stroke engines Ke = 1.0 for 4-stroke engines

σQFN = nominal alternating compressive stress due to radial force related to the web [N/mm2] QRFN = alternating radial force related to the web [N] (see Fig. 1.3 and 1.4) Q RFN = ± F

1 ⎡Q RFmax − Q RFmin ⎦⎤ 2⎣

= area related to cross-section of web [mm2] F = B⋅W

1.2.2

Nominal alternating bending stress in outlet of crankpin oil bore

The calculation of the nominal alternating bending stress is as follows: σ BON =

M BON ⋅ 103 We

Chapter 2 Page 1–6

Section 1

B

Calculation of Crankshafts for Internal Combustion Engines

VI - Part 4 GL 2012

σBON = nominal alternating bending stress related to crank pin diameter [N/mm2]

2.

Calculation of alternating torsional stresses

MBON = alternating bending moment calculated at the outlet of crankpin oil bore [N/mm2]

2.1

General

M BON = ±

1 ⎡M BO max − M BO min ⎤⎦ 2⎣

MBO = MBTO ⋅ cos ψ + MBRO ⋅ sin ψ ψ

= angular position [°] (see Fig. 1.6)

We

= section modulus related to cross-section of axially bored crankpin [mm3]

We = 1.3

π 32

⎡ D 4 − D 4BH ⎤ ⎢ ⎥ D ⎣⎢ ⎦⎥

Calculation of alternating bending stresses in fillets

The calculation for nominal alternating torsional stresses is to be undertaken by the engine manufacturer according to the information contained in 2.2. The maximum value obtained from such calculations will be used by GL when determining the equivalent alternating stress, according to E. In the absence of such a maximum value it will be necessary for GL to incorporate a fixed value in the calculation for the crankshaft dimensions on the basis of an estimation. In case GL is entrusted with carrying out a forced vibration calculation on behalf of the engine manufacturer to determine the torsional vibration stresses to be expected in the engine and possibly in its shafting, the following data are to be submitted to GL additionally to A.4.: –

The calculation of stresses is to be carried out for the crankpin fillet as well as for the journal fillet. –

For the crankpin fillet: σ BH = ± (α B ⋅ σ BFN ) σBH = alternating bending stress in crankpin fillet [N/mm2] αB

= stress concentration factor for bending in crankpin fillet [–] (determination, see C.)

For the journal fillet:

(

σ BG = ± βB ⋅ σBFN + βQ ⋅ σQFN

–

βB βQ

1.4

-

inertialess torsional stiffnesses [Nm/rad]

Vibration dampers -

type designation

-

mass moments of inertia [kgm2]

-

inertialess torsional stiffnesses [Nm/rad]

-

damping coefficients [Nms]

Flywheels

[N/mm2] –

= stress concentration factor for shearing [–] (determination, see C.)

–

= stress concentration factor for bending in crankpin oil bore (determination, see C.)

shaft diameter of gear shafts, thrust shafts, intermediate shafts and propeller shafts

Shafting -

Calculation of alternating bending stresses in outlet of crankpin oil bore

dynamic characteristics and damping data

Gearing data -

= stress concentration factor for bending in journal fillet [–] (determination, see C.)

σBO = alternating bending stress in outlet of crankpin oil bore [N/mm2]

mass moment of inertia [kgm2]

Coupling -

σ BO = ± ( γ B ⋅ σ BON )

γB

mass moment of inertia of every mass point [kgm2]

If the whole installation is to be considered, the above information is to be extended by the following:

–

σBG = alternating stresses in journal fillet

-

-

–

)

Equivalent dynamic system of the engine comprising

diameter of thrust shafts, intermediate shafts and propeller shafts

Propellers -

propeller diameter

-

number of blades

-

pitch and area ratio

–

Natu...