Calculation of Crankshafts for Internal Combustion Engines

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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.

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 Table of Contents Chapter 2 GL 2012 Page 3

Table of Contents

Section 1 Calculation of Crankshafts for Internal Combustion Engines A. General ...... 1- 1 B. Calculation of Stresses ...... 1- 3 C. Calculation of Stress Concentration Factors ...... 1- 7 D. Additional Bending Stresses ...... 1- 10 E. Calculation of Equivalent Alternating Stress ...... 1- 10 F. Calculation of Fatigue Strength ...... 1- 10 G. Acceptability Criteria ...... 1- 11 H. Calculation of Shrink-fits of Semi-built Crankshafts ...... 1- 11

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. General ...... C- 1 B. Model Requirements ...... C- 1 C. Load Cases ...... C- 2

VI - Part 4 Section 1 A Calculation of Crankshafts for Internal Combustion Engines Chapter 2 GL 2012 Page 1–1

Section 1

Calculation of Crankshafts for Internal Combustion Engines

A. General 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 1. Scope dimensioned adequately. These Rules for the scantlings of crankshafts are to be applied to diesel engines for main propulsion and 4. Drawings and particulars to be submitted auxiliary purposes, where the engines are so designed as to be capable of continuous operation at their rated For the calculation of crankshafts, the documents and power when running at rated speed. particulars listed in the following are to be submitted: Crankshafts which cannot satisfy these Rules will be – crankshaft drawing which must contain all data subject to special consideration as far as detailed cal- in respect of the geometrical configuration of culations or measurements can be submitted. the crankshaft In case of: – type designation and kind of engine (in-line – surface treated fillets engine or V-type engine with adjacent connecting rods, forked connecting rod or articulated- – tested parameters influencing the fatigue behav- type connecting rod) iour – operating and combustion method (2-stroke or – measured working stresses 4-stroke cycle, direct injection, precombustion these data can be considered on special request. chamber, etc.) – number of cylinders 2. Field of application – rated power [kW] These Rules apply only to solid-forged and semi-built crankshafts of forged or cast steel, with one crank – rated engine speed [min-1] throw between main bearings. – sense of rotation (see Fig. 1.1) 3. Principles of calculation – ignition sequence with the respective ignition intervals and, where necessary, V-angle α (see The design of crankshafts are based on an evaluation v of safety against fatigue in the highly stressed areas. Fig. 1.1) The calculation is also based on the assumption that – cylinder diameter [mm] the areas exposed to highest stresses are: – stroke [mm] – fillet transitions between the crankpin and web as well as between the journal and web, – maximum cylinder pressure pmax [bar] – outlets of crankpin oil bores. – charge air pressure [bar] (before inlet valves or scavenge ports, whichever applies) When journal diameter is equal or larger than the crankpin one, the outlets of main journal oil bores are – nominal compression ratio [–] to be formed in a similar way to the crankpin oil bores. Otherwise, the engine manufacturer if requested – connecting rod length LH [mm] by GL shall submit separate documentation of fatigue safety. – oscillating weight of one crank gear [kg] (in case of V-type engines, where necessary, also Calculation of crankshaft strength consists initially in for the cylinder unit with master and articulated- determining the nominal alternating bending and type connecting rod or forked and inner con- nominal alternating torsional stresses which, multi- necting rod) plied by the appropriate stress concentration factors using the theory of constant energy of distortion – digitalized gas pressure curve presented at equi- (v. Mises' Criterion), result in an equivalent alternating distant intervals (bar versus crank angle, but not stress (uni-axial stress). This equivalent alternating more than 5° CA) Chapter 2 Section 1 A Calculation of Crankshafts for Internal Combustion Engines VI - Part 4 Page 1–2 GL 2012

6 A6 5 A5 B6 4 A4 B5 3 A3 B4 2 A2 B3 1 A1 B2 B1 a V

counter clockwise driving shaft flange counter driving shaft flange clockwise clockwise clockwise

Fig. 1.1 Designation of the cylinders

– for engines with articulated-type connecting rod – details of crankshaft material (see Fig. 1.2) - material designation (according to ISO, DIN, - distance to link point LA [mm] AISI, etc.)

- link angle αN [°] - mechanical properties of material (minimum values obtained from longitudinal test speci- - connecting rod length LN [mm] mens) The minimum requirements of the GL Rules a N II – Materials and Welding must comply with: - tensile strength [N/mm2] - yield strength [N/mm2] - reduction in area at fracture [%]

- elongation A5 [%]

N - impact energy – KV [J] L L H - method of material melting process (open- hearth furnace, electric furnace, etc.)

A L - type of forging (free form forged, continuous grain flow forged, drop-forged, etc., with de- scription of the forging process) – heat treatment Fig. 1.2 Articulated-type connecting rod – surface treatment of fillets, journals and pins – for the cylinder with articulated-type connecting (induction hardened, flame hardened, nitrided, rod rolled, shot peened, etc. with full details con- cerning hardening) - maximum cylinder pressure pmax [bar] - hardness at surface [HV] - charge air pressure [bar] (before inlet valves or scavenge ports, whichever applies) - hardness as a function of depth of hardening - nominal compression ratio [–] - extension of surface hardening - digitalized gas pressure curve presented at – particulars for alternating torsional stresses, see equidistant intervals [bar/°CA] B.2. VI - Part 4 Section 1 B Calculation of Crankshafts for Internal Combustion Engines Chapter 2 GL 2012 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 The bending moments MBR, MBT are calculated in the bending moments and radial forces relevant section based on triangular bending moment diagrams due to the radial component FR and tangen- 1.1 Assumptions tial component FT of the connecting-rod force, respec- The calculation is based on a statically determinate tively (see Fig.1.3). system, so that only one single crank throw is consid- For crank throws with two connecting-rods acting upon ered of which the journals are supported in the centre one crankpin the relevant bending moments are ob- of adjacent bearings and which is subject to gas and tained by superposition of the two triangular bending inertia forces. The bending length is taken as the moment diagrams according to phase (see Fig.1.4).

Centre Lines of Connecting rod Centre Line of Connecting rod L L1 1 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 Chapter 2 Section 1 B Calculation of Crankshafts for Internal Combustion Engines VI - Part 4 Page 1–4 GL 2012

1.1.1 Bending moments and radial forces acting The alternating bending and compressive stresses due in web to bending moments and radial forces are to be related to the cross-section of the crank web. This reference The bending moment M and the radial force Q BRF RF section results from the web thickness W and the web are taken as acting in the centre of the solid web (dis- width B (see fig. 1.5). tance L1) and are derived from the radial component of the connecting-rod force. Mean stresses are neglected.

W S E

G 2 D

G D

Overlapped crankshaft

Wred

L1 B

Crankshaft without overlap

Fig. 1.5 Reference area of crankweb cross section VI - Part 4 Section 1 B Calculation of Crankshafts for Internal Combustion Engines Chapter 2 GL 2012 Page 1–5

1.1.2 Bending acting in outlet of crankpin oil The decisive alternating values will then be calcu- bore lated according to: The two relevant bending moments are taken in the 1 XXX=±⎡ − ⎤ crankpin cross-section through the oil bore. Nmaxmin2 ⎣ ⎦ FR XN = 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 Nominal alternating bending and com- MBRO FT pressive stresses in web cross section The calculation of the nominal alternating bending and compressive stresses is as follows:

Y MBRFN 3 σBFN =⋅⋅10 Ke Weqw Q σ =⋅RFN Ke QFN F

σBFN = nominal alternating bending stress related to the web [N/mm2]

M = alternating bending moment related to the M = bending moment of the radial component BRFN BRO centre of the web [Nm] (see Fig. 1.3 and 1.4) of the connecting-rod force 1 MBTO = bending moment of the tangential compo- MMMBRFN=±⎣⎡ BRFmax − BRFmin ⎦⎤ nent of the connecting-rod force 2

Fig. 1.6 Crankpin section through the oil bore Weqw = section modulus related to cross-section of web [mm3] The alternating stresses due to these bending moments are to be related to the cross-sectional area of BW⋅ 2 W = the axially bored crankpin. eqw 6 Mean bending stresses are neglected. Ke = empirical factor considering to some extent the influence of adjacent crank and bearing 1.2 Calculation of nominal alternating bend- restraint with: ing and compressive stresses in web Ke = 0.8 for 2-stroke engines The radial and tangential forces due to gas and inertia Ke = 1.0 for 4-stroke engines loads acting upon the crankpin at each connecting- rod position will be calculated over one working σQFN = nominal alternating compressive stress due cycle. A simplified calculation of the radial and tan- to radial force related to the web [N/mm2] gential forces may be used at the discretion of GL. QRFN = alternating radial force related to the web Using the forces calculated over one working cycle [N] (see Fig. 1.3 and 1.4) and taking into account of the distance from the main bearing midpoint, the time curve of the bending mo- 1 QQQRFN=±⎣⎡ RFmax − RFmin ⎦⎤ ments MBRF, MBRO, MBTO and radial forces QRF 2 (defined in 1.1) will then be calculated. F = area related to cross-section of web [mm2] In case of V-type engines, the bending moments – progressively calculated from the gas and inertia F = B ⋅ W forces – of the two cylinders acting on one crank throw are superposed according to phase, the differ- 1.2.2 Nominal alternating bending stress in ent designs (forked connecting rod, articulated-type outlet of crankpin oil bore connecting rod or adjacent connecting rods) shall be The calculation of the nominal alternating bending taken into account. stress is as follows: Where there are cranks of different geometrical con- MBON 3 figuration (e.g. asymmetric cranks) in one crankshaft, σBON =⋅10 the calculation is to cover all crank variants. We Chapter 2 Section 1 B Calculation of Crankshafts for Internal Combustion Engines VI - Part 4 Page 1–6 GL 2012

σBON = nominal alternating bending stress related to 2. Calculation of alternating torsional crank pin diameter [N/mm2] stresses 2.1 General MBON = alternating bending moment calculated at the outlet of crankpin oil bore [N/mm2] The calculation for nominal alternating torsional stresses is to be undertaken by the engine manufac- 1 turer according to the information contained in 2.2. MMMBON=±⎣⎦⎡⎤ BOmax − BOmin 2 The maximum value obtained from such calculations will be used by GL when determining the equivalent MBO = MBTO ⋅ cos ψ + MBRO ⋅ sin ψ alternating stress, according to E. In the absence of such a maximum value it will be necessary for GL to ψ = angular position [°] (see Fig. 1.6) incorporate a fixed value in the calculation for the crankshaft dimensions on the basis of an estimation. We = section modulus related to cross-section of axially bored crankpin [mm3] 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 π ⎡⎤DD44− BH in the engine and possibly in its shafting, the following We = ⎢⎥ 32⎣⎦⎢⎥ D data are to be submitted to GL additionally to A.4.: – Equivalent dynamic system of the engine com- 1.3 Calculation of alternating bending prising stresses in fillets - mass moment of inertia of every mass point 2 The calculation of stresses is to be carried out for the [kgm ] crankpin fillet as well as for the journal fillet. - inertialess torsional stiffnesses [Nm/rad]

For the crankpin fillet: – Vibration dampers - type designation

σ=±α⋅σBH() B BFN - mass moments of inertia [kgm2] - inertialess torsional stiffnesses [Nm/rad] σBH = alternating bending stress in crankpin fillet - damping coefficients [Nms] [N/mm2] – Flywheels αB = stress concentration factor for bending in - mass moment of inertia [kgm2] crankpin fillet [–] (determination, see C.) If the whole installation is to be considered, the above For the journal fillet: information is to be extended by the following: – Coupling

σBG = ±() β B ⋅σ BFN +β Q ⋅σ QFN - dynamic characteristics and damping data – Gearing data 2 σBG = alternating stresses in journal fillet [N/mm ] - shaft diameter of gear shafts, thrust shafts, intermediate shafts and propeller shafts βB = stress concentration factor for bending in – Shafting journal fillet [–] (determination, see C.) - diameter of thrust shafts, intermediate shafts and propeller shafts βQ = stress concentration factor for shearing [–] (determination, see C.) – Propellers - propeller diameter 1.4 Calculation of alternating bending - number of blades stresses in outlet of crankpin oil bore - pitch and area ratio – Natural frequencies with their relevant modes σ=±γ⋅σ BO() B BON of vibration and the vector sums for the har- monics of the engine excitation. σBO = alternating bending stress in outlet of crank- – Estimated torsional vibration stresses in all pin oil bore [N/mm2] important elements of the system with particu- lar reference to clearly defined resonance γB = stress concentration factor for bending in speeds of rotation and continuous operating crankpin oil bore (determination, see C.) ranges. VI - Part 4 Section 1 C Calculation of Crankshafts for Internal Combustion Engines Chapter 2 GL 2012 Page 1–7

2.2 Calculation of nominal alternating tor- 2.3 Calculation of alternating torsional sional stresses stresses in fillets and outlet of crankpin oil The maximum and minimum alternating torques are bore to be ascertained for every mass point of the system The calculation of stresses is to be carried out for the and for the entire speed range by means of a har- crankpin fillet, the journal fillet and the outlet of the monic synthesis of the forced vibrations from the 1st crankpin oil bore. order up to and including the 15th order for 2-stroke cycle engines and from the 0,5th order up to and For the crankpin fillet: including the 12th order for 4-stroke cycle engines. τH = ± (αT ⋅ τN) Whilst doing so, allowance must be made for the dampings that exist in the system and for unfavour- τH = alternating torsional stress in crankpin fillet able conditions (misfiring in one of the cylinders). [N/mm2] The speed ranges shall be selected in such a way that α = stress concentration factor for torsion in the transient response can be recorded with sufficient T accuracy. crankpin fillet [–] (determination, see C.) The values received from such calculation are to be τN = nominal alternating torsional stress related to submitted. crankpin diameter [N/mm2] The nominal alternating torsional stress in every mass For the journal fillet (not applicable to semi-built crank- point, which is essential to the assessment, results shafts): from the following equation: τG = ± (βT ⋅ τN) MT 3 τ=±N ⋅10 τG = alternating torsional stress in journal fillet Wp [N/mm2] 1 β = stress concentration factor for torsion in M(MM)=± − T TN2 Tmax Tmin journal fillet [–] (determination, see C.)

44 44 τ = nominal alternating torsional stress related to ππ⎛⎞DD− ⎛⎞DD− N WorW==BH GBG crankpin diameter [N/mm2] pp⎜⎟ ⎜⎟ 16⎝⎠ D 16⎝⎠ DG For the outlet of crankpin oil bore: τ = nominal alternating torsional stress referred N σ =± γ ⋅τ to crankpin or journal [N/mm2] TO( T N ) MTN = nominal alternating torque [Nm] σTO = alternating stress in outlet of crankpin oil bore due to torsion [N/mm2] Wp = polar section modulus related to cross- sectional area of bored crankpin or bored γΤ = stress concentration factor for torsion in journal [mm3] outlet of crankpin oil bore [–] (determination, see C.) MTmax, MTmin = extreme values of the torque with consideration of the mean torque τN = nominal alternating torsional stress related to [Nm] crankpin diameter [N/mm2] For the purpose of the crankshaft assessment, the nominal alternating torsional stress considered in further calculations is the highest calculated value, C. Calculation of Stress Concentration Fac- according to above method, occurring at the most tors torsionally loaded mass point of the crankshaft. Where barred speed ranges are necessary, the torsional stresses within these ranges are to be neglected 1. General in the calculation of the acceptability factor. The stress concentration factors are evaluated by means of the formulae according to 2., 3. and 4. ap- Barred speed ranges are to be so arranged that satis- plicable to the fillets and crankpin oil bore of solid factory operation is possible despite of their exis- forged web-type crankshafts and to the crankpin tence. There are to be no barred speed ranges above a fillets of semi-built crankshafts only. It must be no- speed ratio of λ ≥ 0,8 of the rated speed. ticed that stress concentration factor formulae con- The approval of crankshafts is to be based on the cerning the oil bore are only applicable to a radially installation having the largest nominal alternating drilled oil hole. All formulae are based on investiga- torsional stress (but not exceeding the maximum tions of FVV (Forschungsvereinigung Verbren- figure specified by engine manufacturer). nungskraftmaschinen) for fillets and on investigations of ESDU (Engineering Science Data Unit) for oil Thus, for each installation, it is to be ensured by holes. suitable calculation that the approved nominal alternating torsional stress is not exceeded. This calcula- Where the geometry of the crankshaft is outside the tion is to be submitted for assessment. boundaries of the analytical stress concentration fac- Chapter 2 Section 1 C Calculation of Crankshafts for Internal Combustion Engines VI - Part 4 Page 1–8 GL 2012

tors (SCF) the calculation method detailed in Annex DG = journal diameter [mm] C may be undertaken. DBG = diameter of axial bore in journal [mm] All crank dimensions necessary for the calculation of stress concentration factors are shown in Fig. 1.7. RG = fillet radius of journal [mm] T = recess of journal [mm] The stress concentration factors for bending (αB, βB) G are defined as the ratio of the maximum equivalent E = pin eccentricity [mm] stress (von Mises) - occurring in the fillets under S = pin overlap [mm] bending load - to the nominal stress related to the web cross-section, see Annex A. DD+ = G − E The stress concentration factor for compression (βQ) 2 in the journal fillet is defined as the ratio of the maximum equivalent stress (von Mises) - occurring in the W*) = web thickness [mm] fillet due to the radial force - to the nominal compressive stress related to the web cross-section. B*) = web width [mm]

*) The stress concentration factor for torsion (αT, βT) is in case of semi-built crankshafts: defined as the ratio of the maximum equivalent shear – when T > R stress - occurring in the fillets under torsional load - H H to the nominal torsional stress related to the axially the web thickness must be considered as equal to bored crankpin or journal cross-section (see Annex Wred = W – (TH – RH) A). see Fig. 1.7

The stress concentration factors for bending (γB) and – web width B must be taken in way of crankpin torsion (γT) are defined as the ratio of the maximum fillet radius centre acc. to Fig. 1.7 principal stress - occurring at the outlet of the crankpin oil-hole under bending and torsional loads - to the The following related dimensions will be applied for corresponding nominal stress related to the axially the calculation of stress concentration factors in: bored crankpin cross section (see Annex B). Crankpin fillets Journal fillets When reliable measurements and/or calculations are available, which can allow direct assessment of stress r = RH/D r = RG/D concentration factors, the relevant documents and their analysis method have to be submitted to Classi- s = S/D fication Societies in order to demonstrate their w = W/D crankshafts with overlap equivalence to present rules evaluation. Wred/D crankshafts without overlap Actual dimensions: b = B/D D = crankpin diameter [mm] dO = DO/D d = D /D DBH = diameter of axial bore in crankpin [mm] G EG dH = DBH/D DO = diameter of oil bore in crankpin [mm] tH = TH/D RH = fillet radius of crankpin [mm] t = T /D T = recess of crankpin [mm] G G H

B DO - S 2 RG G BH D D D W W S E - S RH 2 G G - S D BG 2 D G D D

TG TH

Fig. 1.7 Crank dimensions necessary for the calculation of stress concentration factors VI - Part 4 Section 1 C Calculation of Crankshafts for Internal Combustion Engines Chapter 2 GL 2012 Page 1–9

Stress concentration factors are valid for the ranges of 3. Journal fillet related dimensions for which the investigations have (not applicable to semi-built crankshaft) been carried out. Ranges are as follows: The stress concentration factor for bending βB is: s ≤ 0,5 βB = 2,7146 ⋅ fB (s, w) ⋅ fB (w) ⋅ fB (b) ⋅ fB (r) 0,2 ≤ w ≤ 0,8 ⋅ fB (dG) ⋅ fB (dH) ⋅ f (recess) 1,1 ≤ b ≤ 2,2 2 0,03 ≤ r ≤ 0,13 fB (s,w) = – 1,7625 + 2,9821 ⋅ w – 1,5276 ⋅ w

0 ≤ dG ≤ 0,8 + (1 – s) ⋅ (5,1169 – 5,8089 ⋅ w + 3,1391 ⋅ w2 ) + (1 – s)2 ⋅ (– 2,1567 + 2,3297 ⋅ w 0 ≤ d ≤ 0,8 H – 1,2952 ⋅ w2) 0 ≤ dO ≤ 0,2 0,7548 fB (w) = 2,2422 ⋅ w Low range of s can be extended down to large nega- 2 tive values provided that: fB (b) = 0,5616 + 0,1197 ⋅ b + 0,1176 ⋅ b

– if calculated f (recess) < 1 then the factor f (re- f (r) = 0,1908 ⋅ r – 0,5568 cess) is not to be considered (f (recess) = 1) B 2 – if s < –0,5 then f (s, w) and f (r, s) are to be fB (dG) = 1,0012 – 0,6441 ⋅ dG + 1,2265 ⋅ dG evaluated replacing actual value of s by –0,5 2 fB (dH) = 1,0022 – 0,1903 ⋅ dH + 0,0073 ⋅ dH 2. Crankpin fillet f (recess) = 1 + (tH + tG) ⋅ (1,8 + 3,2 ⋅ s) The stress concentration factor for bending αB is: The stress concentration factor for compression βQ αB = 2,6914 ⋅ f (s, w) ⋅ f(w) ⋅ f(b) ⋅ f(r) ⋅ f(dG) due to the radial force is: ⋅ f(dH) ⋅ f (recess) βQ = 3,0128 ⋅ fQ (s) ⋅ fQ (w) ⋅ fQ (b) ⋅ fQ (r) ⋅ fQ (dH) ⋅ f (recess) f (s, w) = – 4,1883 + 29,2004 ⋅ w – 77,5925 ⋅ w2 + 91,9454 ⋅ w3 – 40,0416 ⋅ w4 + (1 – s) fQ (s) = 0,4368 + 2,1630 ⋅ (1 – s) – 1,5212 ⋅ (1 – s)2 ⋅ (9,5440 – 58,3480 ⋅ w + 159,3415 ⋅ w2 – 192,5846 ⋅ w3 + 85,2916 ⋅ w4 ) + (1 – s)2 2 w ⋅ (– 3,8399 + 25,0444 ⋅ w – 70,5571 ⋅ w fQ (w) = + 87,0328 ⋅ w3 – 39,1832 ⋅ w4) 0,0637+ 0,9369⋅ w f (w) = 2,1790 ⋅ w 0,7171 fQ (b) = – 0,5 + b

– 0,2038 f (b) = 0,6840 – 0,0077 ⋅ b + 0,1473 ⋅ b2 fQ (r) = 0,5331 ⋅ r

–0,5231 2 f (r) = 0,2081 ⋅ r fQ (dH) = 0,9937 – 1,1949 ⋅ dH + 1,7373 ⋅ dH

2 f (dG) = 0,9993 + 0,27 ⋅ dG – 1,0211 ⋅ dG f (recess) = 1 + (tH + tG) ⋅ (1,8 + 3,2 ⋅ s) 3 + 0,5306 ⋅ dG The stress concentration factor for torsion βT is: 2 f (dH) = 0,9978 + 0,3145 ⋅ dH – 1,5241 ⋅ dH 3 βT = αT + 2,4147 ⋅ dH if the diameters and fillet radii of crankpin and journal f (recess) = 1 + (tH + tG) ⋅ (1,8 + 3,2 ⋅ s) are the same, and if crankpin and journal diameters and/or radii are of different sizes: The stress concentration factor for torsion (αT) is: βT = 0,8 ⋅ f (r,s) ⋅ f (b) ⋅ f (w) αT = 0,8 ⋅ f (r, s) ⋅ f (b) ⋅ f (w) f (r,s), f (b) and f (w) are to be determined in accor- (– 0,322 + 0,1015 ⋅ (1 – s)) f (r, s) = r dance with 2. (see calculation of αT), however, the radius of the journal fillet is to be related to the journal f (b) = 7,8955 – 10,654 ⋅ b + 5,3482 ⋅ b2 diameter: – 0,857 ⋅ b3 R r = G – 0,145 f (w) = w DG Chapter 2 Section 1 F Calculation of Crankshafts for Internal Combustion Engines VI - Part 4 Page 1–10 GL 2012

4. Outlet of crankpin oil bore two stress fields with the assumption that bending and torsion are time phased (see Annex B). The stress concentration factor for bending γ is: B The above two different ways of equivalent stress 2 γB = 3 – 5,88 ⋅ dO + 34,6 ⋅ dO evaluation both lead to stresses which may be compared to the same fatigue strength value of crankshaft assessed according to von Mises criterion. The stress concentration factor for torsion γT is

2 γT = 4 – 6 ⋅ dO + 30 ⋅ dO 2. Equivalent alternating stress The equivalent alternating stress is calculated in accordance with the formulae given. D. Additional Bending Stresses For the crankpin fillet:

In addition to the alternating bending stresses in fillets σ =±()3 σ +σ22 + ⋅τ (see B.1.3) further bending stresses due to mis- vBHaddH alignment and bedplate deformation as well as due to For the journal fillet: axial and bending vibrations are to be considered by applying σadd as given by the following table: 22 σvBGaddG=±()3 σ +σ + ⋅τ

2 Type of engine σadd [N/mm ] For the outlet of crankpin oil bore: Crosshead engines ± 30 *) ⎡ 2 ⎤ 19⎛⎞σ σ=±σ ⋅⎢121 + + TO ⎥ Trunk piston engines vBO⎢ ⎜⎟⎥ ± 10 34⎝⎠σBO ⎣⎢ ⎦⎥ *) The additional stress of ± 30 N/mm2 is composed of two 2 components: σv = equivalent alternating stress [N/mm ] – an additional stress of ± 20 N/mm2 resulting from For other parameters, see B.1.3, B.2.3 and D. axial vibration – an additional stress of ± 10 N/mm2 resulting from misalignment / bedplate deformation F. Calculation of Fatigue Strength It is recommended that a value of ± 20 N/mm2 be used for the axial vibration component for assessment purpose where axial vibration calculation results of the complete The fatigue strength is to be understood as that value dynamic system (engine / shafting / gearing / propeller) of equivalent alternating stress (von Mises) which a are not available. crankshaft can permanently withstand at the most highly stressed points; the fatigue strength may be Where axial vibration calculation results of the complete evaluated by means of the following formulae: dynamic system are available, the calculated figures may be used instead. Related to the crankpin diameter:

σ=±⋅DWK0,42( ⋅σ+ B 39,3)

E. Calculation of Equivalent Alternating ⎡ −0,2 785 −σB ⋅+⋅+⎢0, 264 1,073 D Stress ⎣ 4900 196 1 ⎤ 1. General +⋅ ⎥ σBXR ⎥ In the fillets, bending and torsion lead to two different ⎦ biaxial stress fields which can be represented by a von Mises equivalent stress with the additional assump- RX = RH in the fillet area tions that bending and torsion stresses are time phased R = D /2 in the oil bore area and the corresponding peak values occur at the same X O location (see Annex A). Related to the journal diameter: As a result the equivalent alternating stress is to be σ=±⋅K0,42( ⋅σ+ 39,3) calculated for the crankpin fillet as well as for the DW B journal fillet by using the von Mises criterion. ⎡ −0,2 785 −σB ⋅+⋅+⎢0, 264 1,073 DG At the oil hole outlet, bending and torsion lead to two ⎣ 4900 different stress fields which can be represented by an 196 1 ⎤ equivalent principal stress equal to the maximum of +⋅ ⎥ principal stress resulting from combination of these σBGR ⎦⎥ VI - Part 4 Section 1 H Calculation of Crankshafts for Internal Combustion Engines Chapter 2 GL 2012 Page 1–11

σDW = allowable fatigue strength of crankshaft In any case the experimental procedure for fatigue [N/mm2] evaluation of specimens and fatigue strength of crankshaft assessment have to be submitted for approval to K = factor for different types of crankshafts with- GL (method, type of specimens, number of specimens out surface treatment [–] (or crankthrows), number of tests, survival probability, Values greater than 1 are only applicable to confidence number …). fatigue strength in fillet area. = 1,05 for continuous grain flow forged or drop-forged crankshafts G. Acceptability Criteria = 1,0 for free form forged crankshafts The sufficient dimensioning of a crankshaft is con- firmed by a comparison of the equivalent alternating = factor for cast steel crankshafts with cold stress and the fatigue strength. This comparison has to rolling treatment in fillet area [–] be carried out both for the crankpin fillet, the journal = 0,93 for cast steel crankshafts manufac- fillet, the outlet of crankpin oil bore and is based on tured by companies using a GL ap- the formula: proved cold rolling process σ Q = DW σB = minimum tensile strength of crankshaft mate- σv rial [N/mm2] Q = acceptability factor [–] For other parameters see C.1. Adequate dimensioning of the crankshaft is ensured if When a surface treatment process is applied, it must the smaller of both acceptability factors satisfies the be approved by GL. criterion: These formulae are subject to the following condi- Q ≥ 1,15 tions: – surface of the fillet, the outlet of the oil bore and inside the oil bore (down to a minimum depth H. Calculation of Shrink-fits of Semi-built equal to 1,5 times the oil bore diameter) shall be Crankshafts smoothly finished.

– for calculation purposes RH, RG or RX are to be 1. General taken as not less than 2 mm. All crank dimensions necessary for the calculation of As an alternative the fatigue strength of the crankshaft the shrink-fit are shown in Fig. 1.8. can be determined by experiment based either on full DS = shrink diameter [mm] size crankthrow (or crankshaft) or on specimens taken from a full size crankthrow. LS = length of shrink-fit [mm] D RG y BG D G S D D x

LS DA

Fig. 1.8 Crank throw of semi-built crankshaft Chapter 2 Section 1 H Calculation of Crankshafts for Internal Combustion Engines VI - Part 4 Page 1–12 GL 2012

DA = outside diameter of web [mm] or μ = coefficient for static friction [–] twice the minimum distance x between cen- A value not greater than 0.2 is to be taken tre-line of journals and outer contour of web, unless documented by experiments. whichever is less. σSP = minimum yield strength of material for jour- y = distance between the adjacent generating nal pin [N/mm2] lines of journal and pin [mm] This condition serves to avoid plasticity in the hole of y ≥ 0,05 ⋅ DS the journal pin.

Where y is less than 0,1 ⋅ DS, special consid- 3. Necessary minimum oversize of shrink-fit eration is to be given to the effect of the stress due to the shrink on the fatigue strength at the The necessary minimum oversize is determined by the crankpin fillet. greater value calculated according to: For other parameter, see C.1. (Fig. 1.7). σSW⋅ D S Zmin ≥ Regarding the radius of the transition from the journal Em to the shrink diameter, the following must be ob- served: and

RG ≥ 0,015 ⋅ DG and RG ≥ 0,5 ⋅ (DS – DG) 4000 SM⋅−⋅ 1QQ22 Z ≥⋅Rmax ⋅ AS min μ⋅πEDL ⋅ ⋅ 22 where the greater value is to be considered. mSS()()1Q−⋅−AS 1Q The actual oversize Z of the shrink-fit must be within Zmin = minimum oversize [mm] the limits Zmin and Zmax calculated in accordance with items 2. and 3. Em = Young’s modulus [N/mm²] In the case where H.2. condition cannot be fulfilled σSW = minimum yield strength of material for crank then H.3. and H.4. calculation methods of Zmin and web [N/mm²] Zmax are not applicable due to multizone-plasticity problems. In such case Z and Z have to be estab- D min max Q = web ratio [-] Q = S lished based on FEM calculations. A A DA

2. Maximum permissible hole in the journal DBG QS = shaft ratio [-] QS = . pin DS The maximum permissible hole diameter in the journal pin is calculated in accordance with the following 4. Maximum permissible oversize of formula: shrink-fit

4000⋅⋅ S M The maximum permissible oversize is calculated in DD1=⋅− Rmax BG S 2 accordance with the following formula: μ⋅π⋅DLSSSP ⋅ ⋅σ σ ⋅⋅D0,8D Z ≤+SW S S S = safety factor against slipping [–] max R E1000m A value not less than 2 is to be taken unless documented by experiments. Zmax = maximum oversize [mm]

Mmax = absolute maximum value of the torque MTmax The condition serves to restrict the shrinkage induced in accordance with B.2.2 [Nm] mean stress in the fillet.

VI - Part 4 Annex A Definition of Stress Concentration Factors in Crankshaft Fillets Chapter 2 GL 2012 Page A–1

Annex A

Definition of Stress Concentration Factors in Crankshaft Fillets

VI - Part 4 Annex B Stress Concentration Factors and Stress Distribution at the Edge of Chapter 2 GL 2012 Oil Drillings Page B–1

Annex B

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

VI - Part 4 Annex C B Alternative Method for Calculation of Stress Concentration Factors in Chapter 2 GL 2012 the Web Fillet Radii of Crankshafts by utilizing Finite Element Method Page C–1

Annex C

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

A. General 2. Element mesh recommendations In order to fulfil the mesh quality criteria it is advised 1. The objective of the analysis is to develop to construct the FE model for the evaluation of Stress Finite Element Method (FEM) calculated figures as an Concentration Factors according to the following alternative to the analytically calculated Stress Con- recommendations: centration Factors (SCF) at the crankshaft fillets. The analytical method is based on empirical formulae – The model consists of one complete crank, from developed from strain gauge measurements of various the main bearing centreline to the opposite side crank geometries and accordingly the application of main bearing centreline these formulae is limited to those geometries. – Element types used in the vicinity of the fillets: – 10 node tetrahedral elements 2. The SCF’s calculated according to the rules – 8 node hexahedral elements of this Annex are defined as the ratio of stresses calculated by FEM to nominal stresses in both journal and – 20 node hexahedral elements pin fillets. When used in connection with the present – Mesh properties in fillet radii. The following method or the alternative methods, von Mises stresses applies to ±90 degrees in circumferential direc- shall be calculated for bending and principal stresses tion from the crank plane: for torsion. – Maximum element size a = r/4 through the entire fillet as well as in the circumferential direction. 3. The procedure as well as evaluation guide- When using 20 node hexahedral elements, the lines are valid for both solid cranks and semibuilt element size in the circumferential direction may cranks (except journal fillets). be extended up to 5a. In the case of multi-radii fillet r is the local fillet radius. (If 8 node hexa- 4. The analysis is to be conducted as linear hedral elements are used even smaller element elastic FE analysis, and unit loads of appropriate mag- size is required to meet the quality criteria.) nitude are to be applied for all load cases. – Recommended manner for element size in fillet depth direction 5. The calculation of SCF at the oil bores is not – First layer thickness equal to element size of a covered by this Annex. – Second layer thickness equal to element to size of 2a 6. It is advised to check the element accuracy of the FE solver in use, e.g. by modeling a simple ge- – Third layer thickness equal to element to size ometry and comparing the stresses obtained by FEM of 3a with the analytical solution for pure bending and tor- – Minimum 6 elements across web thickness. sion. – Generally the rest of the crank should be suitable for numeric stability of the solver. 7. Boundary Element Method (BEM) may be used instead of FEM. – Counterweights only have to be modeled only when influencing the global stiffness of the crank significantly. – Modeling of oil drillings is not necessary as long B. Model Requirements as the influence on global stiffness is negligible and the proximity to the fillet is more than 2r, 1. General see Fig. C.1. – Drillings and holes for weight reduction have to The basic recommendations and perceptions for build- be modeled. ing the FE-model are presented in 2. It is obligatory for the final FE-model to fulfill the requirement in – Sub-modeling may be used as far as the soft- 4. ware requirements are fulfilled. Chapter 2 Annex C C Alternative Method for Calculation of Stress Concentration Factors in VI - Part 4 Page C–2 the Web Fillet Radii of Crankshafts by utilizing Finite Element Method GL 2012

radius. Ideally, this stress should be zero. With princi-

pal stresses σ1, σ2 and σ2 the following criterion is required: Oil bore min( σ123 ,σσ< ,) 0.03 ⋅ max() σσσ 123 , ,

Crankpin > 2 r 4.2 Averaged/unaveraged stresses criterion The criterion is based on observing the discontinuity r Web of stress results over elements at the fillet for the calculation of SCF:

– Unaveraged nodal stress results calculated from Fig. C.1 Oil bore proximity to fillet each element connected to a nodei should differ less than by 5 % from the 100 % averaged nodal 3. Material stress results at this nodei at the examined location. These Rules do not consider material properties such as Young’s Modulus (E) and Poisson’s ratio (ν). In FE analysis those material parameters are required, as C. Load Cases strain is primarily calculated and stress is derived from strain using the Young’s Modulus and Poisson’s ratio. Reliable values for material parameters have to be 1. General used, either as quoted in literature or as measured on To substitute the analytically determined SCF in these representative material samples. Rules the following load cases have to be calculated.

For steel the following is advised: E = 2.05 ⋅ 105 MPa 1.1 Torsion and ν = 0.3. In analogy to the testing apparatus used for the inves- 4. Element mesh quality criteria tigations made by FVV the structure is loaded pure torsion. In the model surface warp at the end faces is If the actual element mesh does not fulfil any of the suppressed. following criteria at the examined area for SCF evaluation, then a second calculation with a refined Torque is applied to the central node located at the mesh is to be performed. crankshaft axis. This node acts as the master node with 6 degrees of freedom and is connected rigidly to 4.1 Principal stresses criterion all nodes of the end face. The quality of the mesh should be assured by checking Boundary and load conditions are valid for both in- the stress component normal to the surface of the fillet line and V-type engines.

y Multi-point constraint: All nodes of cross section x are rigidly connected to central node (= master) z

Load: Torque T applied to central node Centre Line of Connecting rod

Boundary L conditions: 1 DOFs for all nodes are fully L2 restrained u = 0 L x, y, z 3

Fig. C.2 Boundary and load conditions for the torsion load case VI - Part 4 Annex C C Alternative Method for Calculation of Stress Concentration Factors in Chapter 2 GL 2012 the Web Fillet Radii of Crankshafts by utilizing Finite Element Method Page C–3

For all nodes in both the journal and crank pin fillet Boundary and load conditions are valid for both in- principal stresses are extracted and the equivalent line- and V- type engines. torsional stress is calculated: For all nodes in both the journal and pin fillet von ⎛⎞σ−σ σ−σ σ−σ Mises equivalent stresses σequiv are extracted. The τ=max12 ,23 , 13 equiv ⎜⎟maximum value is used to calculate the SCF accord- ⎝⎠222 ing to:

The maximum value taken for the subsequent calcula- σequiv,α tion of the SCF: α=B σN τ α= equiv,α τ σ τN equiv,β β=B σN τequiv,β β=τ τN Nominal stress σN is calculated as per Section 1, B.1.2.1 with the bending moment M: where τN is nominal torsional stress referred to the crankpin and respectively journal as per Section 1, B. 2.2 M with the torsional torque T: σ=N Weqw T τ=N WP 1.3 Bending with shear force (3-point bending) This load case is calculated to determine the SCF for 1.2 Pure bending (4 point bending) pure transverse force (radial force, βQ) for the journal In analogy to the testing apparatus used for the inves- fillet. tigations made by FVV the structure is loaded in pure bending. In the model surface warp at the end faces is In analogy to the testing apparatus used for the inves- suppressed. tigations made by FVV, the structure is loaded in 3- point bending. In the model, surface warp at the both The bending moment is applied to the central node end faces is suppressed. All nodes are connected rig- located at the crankshaft axis. This node acts as the idly to the centre node; boundary conditions are ap- master node with 6 degrees of freedom and is con- plied to the centre nodes. These nodes act as master nected rigidly to all nodes of the end face. nodes with 6 degrees of freedom.

y Multi-point constraint: All nodes of cross section x are rigidly connected to central node (= master) z

Load: In-plane bending by moment M applied at central node Centre Line of Connecting rod

Boundary L conditions: 1 DOFs for all nodes are fully L2 restrained u = 0 x, y, z L3

Fig. C.3 Boundary and load conditions for the pure bending load case Chapter 2 Annex C C Alternative Method for Calculation of Stress Concentration Factors in VI - Part 4 Page C–4 the Web Fillet Radii of Crankshafts by utilizing Finite Element Method GL 2012

Load: Boundary conditions: Force F3p applied Displacement in z direction for at central node at master node is restrained, uz = 0; connecting rod uy, ux and j =/ 0 (axial, vertical dis- y centre line. placements and rotations are free)

x z Multi-point constraint: All nodes of cross section are connected to a central node (= master)

Boundary conditions: Boundary conditions: Displacements for Displacements in y and z master node are Centre Line of Connecting rod directions for master node are restrained u = 0. fully restrained y, z u = 0; L1 u , j =/ 0 (axial displacement x, y, z x and rotations are free) j =/ 0 (rotations are free) L2

Fig. C.4 Boundary and load conditions for the 3-point bending load case of an inline engine Centre Line of Connecting rod Centre Line of Connecting rod

L 1 L1 L 2 L2 L 3 L3

Fig. C.5 Load applications for in-line and V-type engines VI - Part 4 Annex C C Alternative Method for Calculation of Stress Concentration Factors in Chapter 2 GL 2012 the Web Fillet Radii of Crankshafts by utilizing Finite Element Method Page C–5

The force is applied to the central node located at the σQ3P = Q3P/(B ⋅ W) where Q3P is the radial (shear) pin centre-line of the connecting rod. This node is force in the web due to the force F3P [N] applied to the connected to all nodes of the pin cross sectional area. centre-line of the actual connecting rod, see also Warping of the sectional area is not suppressed. Section 1, Fig. 1.3 and 1.4. Boundary and load conditions are valid for in-line and V-type engines. V-type engines can be modeled with 1.3.2 Method 2 one connecting rod force only. Using two connecting This method is not analogous to the FVV investiga- rod forces will make no significant change in the SCF. tion. In a statically determined system with one crank throw supported by two bearings, the bending moment The maximum equivalent von Mises stress σ3P in the and radial (shear) force are proportional. Therefore the journal fillet is evaluated. The SCF in the journal fillet journal fillet SCF can be found directly by the 3-point can be determined in two ways as shown below. bending FE calculation. The SCF is then calculated according to 1.3.1 Method 1

This method is analogue to the FVV investigation. σ3P β=BQ The results from 3-point and 4-point bending are σN3P combined as follows: For symbols see 1.3.1.

σ=σ⋅β+σ⋅β3P N3P B Q3P Q When using this method the radial force and stress determination becomes superfluous. The alternating where: bending stress in the journal fillet as per Section 1, B.1.3 is then evaluated: σ3P as found by the FE calculation. σ=±β⋅σBG BQ BFN σN3P Nominal bending stress in the web centre due to the force F3P [N] applied to the centre-line of the ac- Note that the use of this method does not apply to the tual connecting rod, see Fig. C.5 crankpin fillet and that this SCF must not be used in connection with calculation methods other than those βB as determined in 1.2. assuming a statically determined system.