Calculation of crankshafts for reciprocating internal combustion engines

Transcription

1 CLASS GUIDELINE DNVGL-CG-0037 Edition November 2015 Calculation of crankshafts for reciprocating internal combustion engines The electronic pdf version of this document, available free of charge from is the officially binding version.

2 FOREWORD DNV GL class guidelines contain methods, technical requirements, principles and acceptance criteria related to classed objects as referred to from the rules. November 2015 Any comments may be sent by to If any person suffers loss or damage which is proved to have been caused by any negligent act or omission of DNV GL, then DNV GL shall pay compensation to such person for his proved direct loss or damage. However, the compensation shall not exceed an amount equal to ten times the fee charged for the service in question, provided that the maximum compensation shall never exceed USD 2 million. In this provision "DNV GL" shall mean, its direct and indirect owners as well as all its affiliates, subsidiaries, directors, officers, employees, agents and any other acting on behalf of DNV GL.

3 CHANGES CURRENT This is a new document. Editorial corrections In addition to the above stated main changes, editorial corrections may have been made. Changes - current Page 3

4 Changes current... 3 Section 1 General Scope Field of application Principles of calculation Drawings and particulars to be submitted... 7 Section 2 Calculation of stresses Explanations and Basic principles Calculation of stresses due to bending moments and radial forces Calculation of alternating torsional stresses Section 3 Evaluation of stress concentration factors General Crankpin fillet Journal fillet (not applicable to semi-built crankshaft) Outlet of crankpin oil bore Outlet of journal oil bore Inclined oil bores...26 Section 4 Additional bending stresses General Section 5 Calculation of fatigue strength General Empirical formulae for non-surface treated fillets Surface treated fillets and/or oil holes Section 6 Acceptability criteria General The crankpin fillet criterion The journal fillet criterion The oil hole criterion Section 7 Calculation of shrink-fits of semi-built crankshaft General Maximum permissible hole in the journal pin Page 4 Contents CONTENTS

5 4 Maximum permissible oversize of shrink-fit Appendix A Definition of stress concentration factors in crankshaft fillets Appendix B Stress concentration factors and stress distribution at the edge of oil drillings...39 Appendix C Alternative method for calculation of stress concentration factors in the web fillet radii of crankshafts by utilising finite element method General Model requirements Load cases Appendix D Guidance for evaluation of fatigue tests Introduction Evaluation of test results Small specimen testing Full size testing Use of existing results for similar crankshafts Appendix E Surface tested fillets and oil bore outlets Introduction Definition of surface treatment Calculation principles Induction hardening Nitriding Cold forming Appendix F Stress concentration factors in the oilbore outlets of crankshafts by utilizing finite element method General Model requirements Load cases Page 5 Contents 3 Necessary minimum oversize of shrink-fit... 36

6 1 Scope This class guideline contains methods for calculation of safety against fatigue failure in pin and journal fillets and in oil bores, as well as safety against slippage for semi-built crankshafts. Note that also axial bores in crankpins can be critical. In principle, any relevant calculation method may be applied for this purpose. E.g. the fatigue criteria assume that maximum resp. minimum bending stresses occur simultaneously with the maximum resp. minimum torsional stresses. (This assumption yields results which are more or less to the safe side.) If properly documented an evaluation of the fatigue capacity by using multi-axial fatigue methods may replace the criteria applied in this class guideline. A crankshaft will be approved when the calculation method as presented in this class guideline and/or the IACS UR M53 method is fulfilled. Crankshafts that cannot satisfy these rules may be subject to special consideration when detailed calculations and/or measurements are made to demonstrate equivalence to these rules. 2 Field of application These methods apply to engines for both main propulsion and auxiliary purpose, being designed for continuous operation at the specified (nominal) rating. If frequent use of overload (in excess of nominal) rating is foreseen, i.e. accumulating several millions of stress cycles, this overload should form the basis for the calculation. Further, the methods apply to solid forged or semi-built crankshafts of forged or cast steel, and with one crank throw between main bearings. Designs with more than one crank throw between main bearings, fillets between offset crankpins, fully built crankshafts, or welded crankshafts will be specially considered on basis of equivalence with the normal requirements. This method is also valid: for surface treated fillets, when fatigue parameter influences are tested, when working stresses are measured. Note that surface treated fillets also include crankpin hardening that can influence the fillet fatigue strength. Principles of calculation 3 Principles of calculation The design of crankshafts is 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. outlets of journal oil bores. The methods of crankshaft fatigue are based on: A combination of bending and torsional stresses where bending fatigue strength and torsional fatigue strength are separately assessed, i.e. also valid for anisotropic material behaviour. Bending stress measurements, or continuous beam analysis, or 3-point bending, depending on manufacturer s documentation. Measured stress concentration factors, or analysed with FEM as described in App.C and App.F, or by using empirical formulae with one standard deviation above 50% reliability. Fatigue strength assessment based on full scale testing or small scale (see App.D), combined with a calculation procedure considering the influence of material strength, forging method, mean stress, and Page 6 Section 1 SECTION 1 GENERAL

7 For semi-built crankshafts, additional criteria cover the safety against slippage of shrink fits. In case of relatively small distance between the pin and the journal shrinkage diameter, the influence of the shrinkage stresses on the fatigue strength is considered. 4 Drawings and particulars to be submitted For the calculation of crankshafts, the documents and particulars listed below shall be submitted: crankshaft drawing (which shall contain all data in respect of the geometrical configurations of the crankshaft) type designation and kind of engine (in-line engine or V-type engine with adjacent connecting-rods, forked connecting-rod or articulated-type connecting-rod) operating and combustion method (2-stroke or 4-stroke cycle/direct injection, pre-combustion chamber, etc.) number of cylinders rated power [kw] rated engine speed [r/min] direction of rotation (see Figure 1) firing order with the respective ignition intervals and, where necessary, V-angle α v [ ] (see Figure 1) Figure 1 Designation of the cylinders cylinder diameter [mm] stroke [mm] maximum net cylinder pressure pmax [bar] charge air pressure [bar](before inlet valves or scavenge ports, whichever applies) mean indicated pressure [bar] reciprocating mass per cylinder [kg] rotating mass (ref. to crank radius) per connecting rod rotating mass (ref. to crank radius) of cranks incl. counter weights [kg] and positions (lengthwise and angular) digitized gas pressure curve presented at equidistant intervals [bar versus Crank Angle] (at least every 5 CA) connecting-rod length LH [mm] Page 7 Section 1 when applicable also fillet surface hardening, shot peening or cold rolling including the influence of the depth of this surface treatment (see App.E).

8 Section 1 for engines with articulated-type connecting-rod (see Figure 2) distance to link point LA [mm] link angle αn [ ] connecting-rod length LN [mm] Figure 2 Articulated-type connecting-rod details of crankshaft material material designation (according to ISO, EN, DIN, AISI, etc..) mechanical properties of material (minimum values obtained from longitudinal test specimens): tensile strength [N/mm²] yield strength [N/mm²] reduction in area at break [%] elongation A5 [%] impact energy KV [J] type of forging (free form forged, continuous grain flow forged, drop-forged, etc; with description of the forging process) finishing method of fillets and oil holes surface hardening of fillets, if applicable (induction hardened, nitrided etc.): extension of surface hardening (max and min) hardness at surface (HV) (max and min) hardness (HV) as a function of depth [mm] cold deformation of fillets, if applicable (shot peening, stroke peening, cold rolling): extension of treatment intensity (shot peening) depth of treatment (residual stresses) for stroke peening and cold rolling, as determined for the applied force and roller or ball geometry. Page 8

9 Section 1 particulars of alternating torsional stress calculations, see Sec.2[3]. Figure 3 Left: Crankthrow for in line engine. Figure 3 Right: Crankthrow for V- engine with 2 adjacent connecting-rods L1 = Distance between main journal centre line and crankweb centre (see also Sec.2 Figure 1 for crankshaft without overlap) Page 9

10 = Distance between main journal centre line and connecting-rod centre Section 1 L2 L3 = Distance between two adjacent main journal centre lines Page 10

11 1 Explanations and Basic principles Sec.2 deals with nominal stresses that later are multiplied with stress concentration factors from Sec.3. In the case that FE calculations are made of a global model that also includes local stresses, the directly determined stresses shall be used in the acceptance criteria in Sec.6. In addition to the alternating stresses, the mean stresses shall be determined in order to assess the mean stress influence on the fatigue strength. The maximum and minimum bending moments and radial forces during a complete working cycle, may be determined by thorough analysis, e.g. FEA. Continuous beam model analysis may be applied if its relevance can be documented. If no such analyses are available, the 3-point bending may be used as described in the following. 2 Calculation of stresses due to bending moments and radial forces 2.1 Assumptions The calculation is based on a statically determined system, composed of a single crankthrow supported in the centre of adjacent main journals and subjected to gas and inertia forces. The bending length is taken as the length between the two main bearing midpoints (distance L3, see Sec.1 Figure 3 diagrams "left" and "right". The bending moment 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 Sec.1 3). For crankthrows with two connecting-rods acting upon one crankpin the relevant bending moments are obtained by super position of the two triangular bending moment diagrams according to phase (see Sec.1 Figure 3) 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. The alternating bending- and compressive stresses due to bending moments and radial forces shall be related to the cross-section of the crank web. The corresponding mean stresses shall also be determined. This reference section results from the web thickness W and the web width B (see Figure 1). Page 11 Section 2 SECTION 2 CALCULATION OF STRESSES

12 Section 2 Overlapped crankshaft Crankshaft without overlap Figure 1 Reference area of crankweb cross section Bending acting in outlet of crankpin oil bore. The two relevant bending moments are taken in the crankpin cross-section through the oil bore. Figure 2 Crankpin section through the oil bore (clockwise rotation) MBRO = is the bending moment of the radial component of the connecting-rod force Page 12

13 is the bending moment of the tangential component of the connecting-rod force The alternating and mean stresses due to these bending moments shall be related to the cross-sectional area of the axially bored crankpin. Mean stresses also to be determined. 2.2 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 connecting-rod position will be calculated over one working cycle. 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 the radial force QRF as defined in Sec.2[2.1.1] and Sec.2[2.1.2] will then be calculated. In the case of V-type engines, the bending moments progressively calculated from the gas and inertia forces of two cylinders acting on one crankthrow are superimposed according to phase. 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 configurations in one crankshaft, the calculation shall cover all crank variants. The decisive alternating values will then be calculated according to: where : XN Xmax Xmin = is considered as alternating force, moment or stress = is maximum value within one working cycle = is minimum value within one working cycle A) Mean stresses The mean values XNM shall be calculated according to: Nominal alternating bending and compressive stresses in web cross section A) Alternating stresses The calculation of the nominal alternating bending and compressive stresses is as follows: Page 13 Section 2 MBTO =

14 Section 2 where: σbfn [N/mm²] MBRFN [Nm] = nominal alternating bending stress related to the web = alternating bending moment related to the centre of the web (see Sec.1 Figure 3) 3 Weqw [mm ] = first moment of area (sectional modulus) related to cross-section of web Ke = empirical factor considering to some extent the influence of adjacent crank and bearing restraint with: Ke = 0.8 for crosshead engines Ke = 1.0 for trunk engines σqfn [N/mm²] = nominal alternating compressive stress due to radial force related to the web F [mm²] = area related to cross-section of web F=B W B) Mean stresses The mean values shall be calculated according to: Page 14

15 Section Nominal Bending stress in outlet of crankpin oil bore A) Alternating stresses The calculation of nominal alternating bending stress is as follows: where: σbon [N/mm²] = = MBON [Nm] nominal alternating bending stress related to the crankpin diameter alternating bending moment calculated at the outlet of crankpin oil bore with and ψ [ ] angular position (see Figure 2) We(red) [mm3] first moment of area (sectional modulus) related to cross-section of axially bored crankpin B) Mean stresses The mean values shall be calculated according to: Page 15

16 Section Nominal bending stresses in outlet of journal oil bore A) Alternating stress If the 3-point bending method is applied (resulting in zero bending moment), the alternating bending moment in the journal MBONG shall be taken at least as 0.5 MBON. The nominal alternating bending stress is then: B) Mean stress If the 3-point bending method is applied, the mean bending moment in the journal MBONGM may be disregarded. 2.3 Calculation of bending stresses in fillets A) Alternating stresses The calculation of stresses shall be carried out for the crankpin fillet as well as for the journal fillet. For the crankpin fillet: σbh = ± (αb σbfn) where: σ BH [N/mm2] α B [-] = alternating bending stress in crankpin fillet = stress concentration factor for bending in crankpin fillet (determination see Sec.3). For the journal fillet (not applicable to semi-built crankshaft): where: σ BG [N/mm2] β B [-] = alternating bending stress in journal fillet = stress concentration factor for bending in journal fillet (determination - see Sec.3) Page 16

17 = stress concentration factor for compression due to radial force in journal fillet determination see Sec.3) Section 2 β Q [-] B) Mean stresses The mean stresses shall be calculated according to: For the crankpin fillet: σbhm = αb σbfnm For the journal fillet: Note that the signs above are only correct when the bending moment due to max gas pressure is more than twice the bending moment due to mass forces in TDC. 2.4 Calculation of bending stresses in outlet of crankpin oil bore A) Alternating stress σbo = ± ( γb σbon) where: σ BO [N/mm2] γ B [-] = alternating bending stress in outlet of crankpin oil bore = stress concentration factor for bending in crankpin oil bore (determination - see Sec.3) B) Mean stress The mean stress shall be calculated according to: σbom = γb σbonm 2.5 Calculation of bending stresses in outlet of journal oil bore A) Alternating stress σbog = ± ( γbg σbong) where: σbong [N/mm2] γbg [-] = alternating bending stress in outlet of journal oil bore = stress concentration factor for bending in journal oil bore (determination see Sec.3) B) Mean stress σbogm = γbg σbongm Page 17

18 3.1 General The calculation for nominal alternating torsional stresses shall be undertaken by the engine manufacturer according to the information contained in Sec.2 [3.2]. The manufacturer shall specify the maximum nominal alternating torsional stress. 3.2 Calculation of nominal alternating torsional stresses The max. and min. torques shall be ascertained for every mass point of the complete dynamic system and for the entire speed range by means of a harmonic synthesis of the forced vibrations from the 1st order up to and including the 15th order for 2-stroke cycle engines and from the 0.5th order up to and including the 12th order for 4-stroke cycle engines. Whilst doing so, allowance shall be made for the damping that exists in *) the system and for unfavourable conditions (misfiring in one of the cylinders). The speed step calculation shall be selected in such a way that any resonance found in the operational speed range of the engine shall be detected. *) Misfiring is defined as a cylinder condition when no combustion occurs but only compression cycle. Where barred speed ranges are necessary, they shall be arranged so that satisfactory operation is possible despite their existence. There shall be no barred speed ranges above a speed ratio of ℓ 0.8 for normal firing conditions. The values received from such calculation shall be submitted. Alternatively the crankshaft assessment can be based on the specified maximum alternating torsional stress. For type approvals it is advised to include a variation of the various standard dampers respectively flywheels etc. Directly coupled engines should take typical installations into account. Flexibly coupled engines may be considered as cut in the elastic coupling. Where calculations are not available as e.g. for some type approvals, the manufacturer shall state a limiting vibratory torque to be used in the calculation. The nominal alternating torsional stress in every mass point, which is essential to the assessment, results from the following equation: where: τn [N/mm²] = nominal alternating torsional stress referred to crankpin or journal Page 18 Section 2 3 Calculation of alternating torsional stresses

19 = maximum alternating torque MTmax MTmin = maximum value of the torque. = polar first u of area (sectional modulus) related to cross-section of axially bored crankpin or bored journal = minimum value of the torque For the purpose of the crankshaft assessment, the nominal alternating torsional stress considered in further calculations is the highest calculated value, according to above method, occurring at the most torsionally loaded mass point of the crankshaft system. Where barred speed ranges exist, the torsional stresses within these ranges shall not be considered for assessment calculations. The approval of crankshaft will be based on the installation having the largest nominal alternating torsional stress (but not exceeding the maximum figure specified by engine manufacturer). Thus, for each installation, it shall be ensured by suitable calculation that this approved nominal alternating torsional stress is not exceeded. This calculation shall be submitted for assessment. The nominal mean torsional stress is: This may be determined in every mass point which is essential to the crankshaft assessment, but a more practical approach shall use the mean stress at the crank that has the highest alternating torque. This can be determined from a quasistatic torque evaluation through the crankshaft (vectorial torque summation assuming clamped end and no dynamics). 3.3 Calculation of torsional stresses in fillets and outlet of oil bores The calculation of stresses shall be carried out for the crankpin fillet, the journal fillet and the outlet of the oil bores. For the crankpin fillet: A) Alternating stress where : τh [N/mm2] σt [-] = alternating torsional stress in crankpin fillet = stress concentration factor for torsion in crankpin fillet (determination - see Sec.3) Page 19 Section 2 MTN [Nm] WP [mm3]

20 = nominal alternating torsional stress related to crankpin diameter Section 2 τn [N/mm2] B) Mean stress where: τnm[n/mm2] = nominal mean torsional stress related to crankpin diameter For the journal fillet (not applicable to semi-built crankshafts): A) Alternating stress where: τg [N/mm2] βt [-] τn [N/mm2] = alternating torsional stress in journal fillet = stress concentration factor for torsion in journal fillet (determination - see Sec.3) = nominal alternating torsional stress related to journal diameter B) Mean stress where: τnm [N/mm2] = nominal mean torsional stress related to journal diameter. For the outlet of crankpin oil bore: A) Alternating stress where : σto [N/mm2] γt [-] τ 2 N [N/mm ] = alternating stress in outlet of crankpin oil bore due to torsion = stress concentration factor for torsion in outlet of crankpin oil bore (determination - see Sec.3) = nominal alternating torsional stress related to crankpin diameter B) Mean stress Page 20

21 Section 2 where τnm [N/mm2] = nominal mean torsional stress related to crankpin diameter. For the outlet of journal oil bore A) Alternating stress where σtgo [N/mm2] γtg [-] τn [N/mm2] = alternating stress in outlet of journal oil bore due to torsion = stress concentration factor for torsion in outlet of journal oil bore (see Sec.3) = nominal alternating torsional stress related to journal diameter B) Mean stress where τnm [N/mm2] = nominal mean torsional stress related to journal diameter. Page 21

22 1 General The stress concentration factors are evaluated by means of the formulae according to [2], [3] and [4] applicable to the fillets and crankpin oil bore of solid forged web-type crankshafts and to the crankpin fillets of semi-built crankshafts only. It shall be noticed that stress concentration factor formulae concerning the oil bore are only applicable to a radially drilled oil hole. All formulae are based on investigations of FVV (Forschungsvereinigung Verbrennungskraftmaschinen) for fillets and on investigations of ESDU (Engineering Science Design Unit) for oil holes. All crank dimensions necessary for the calculation of stress concentration factors are shown in Figure 1. The stress concentration factors in bending (αb, βb) are defined as the ratio between the maximum absolute value of the PRINCIPAL stresses in the fillets and the absolute value of the nominal bending stress referred to the web cross section. The stress concentration factor for compressive stresses in the journal fillet (βq) is defined as the ratio between the maximum fillet stress (absolute value) and the nominal compressive stress (absolute value) related to the web cross section. The stress concentration factor for torsion (αt, βt) is defined as the ratio of the maximum equivalent shear stress occurring in the fillets under torsional load to the nominal torsional stress related to the axially bored crankpin or journal cross-section (see App.A). The stress concentration factors for bending (γb) and torsion (γt) are defined as the ratio of the maximum principal stress occurring at the outlet of the crankpin oil-hole under bending and torsional loads to the corresponding nominal stress related to the axially bored crankpin cross section (see App.B). For outlet bores in journals the same definitions apply. When reliable measurements and/or calculations are available, which can allow direct assessment of stress concentration factors, the relevant documents and their analysis method shall be submitted in order to demonstrate their equivalence to present rules evaluation. This is always to be performed when dimensions are outside of any of the validity ranges for the empirical formulae presented in [2]. App.C describes how FE analyses can be used for this purpose. Care should be taken to avoid mixing equivalent (von Mises) stresses and principal stresses. Page 22 Section 3 SECTION 3 EVALUATION OF STRESS CONCENTRATION FACTORS

23 Section 3 Figure 1 Crank dimensions Actual dimensions: D [mm] DBH [mm] DO [mm] DOG [mm] RH [mm] TH [mm] DG[mm] DBG[mm] RG [mm] TG [mm] E [mm] S [mm] W (*) = [mm] B (*) = [mm] (*) = crankpin diameter = diameter of axial bore in crankpin = diameter of oil bore in crankpin = diameter of oil bore in journal = fillet radius of crankpin = recess of crankpin fillet = journal diameter = diameter of axial bore in journal = fillet radius of journal = recess of journal fillet = pin eccentricity = pin overlap web thickness web width In the case of 2 stroke semi-built crankshafts: when TH > RH, the web thickness shall be considered as equal to: Wred = W (TH RH) (refer to Sec.2 Figure 1) web width B shall be taken «in way of» crankpin fillet radius centre according to Sec.2 Figure 1 The following related dimensions will be applied for the calculation of stress concentration factors in : Page 23

24 Journal fillet r = RH / D rg = RG / DG s = S/D sg = S/DG w = W/D (with overlap) wg = W/DG (with overlap) w = Wred/D (without overlap) wg = Wred/DG (without overlap) b = B/D bg = B/DG do = DO/D dog = DOG/DG dh = DBH/D dg =DBG/DG th = TH/D th = TH/D tg = TG/D tg = TG/D Section 3 Crankpin fillet Stress concentration factors are valid for the ranges of related dimensions for which the investigations have been carried out. (It should be noted that the FVV investigations were made with models having D=DG. Using the empirical formulae on crankshafts with DG>D may lead to journal fillet stress concentration factors that are more uncertain than when D=DG.) Ranges are as follows: s w b r dg dh do 0.2 Low range of s can be extended down to large negative values provided that: if calculated f (recess) < 1 then the factor f (recess) shall not be considered (f (recess) = 1) if s < then f (s,w) and f (r,s) shall be evaluated replacing actual value of s by The same ranges of validity apply when the related dimensions are referred to the journal diameter. As the original (FVV) empirical formulae for the crankpin and the journal fillets were established on the basis of 50 percent reliability, and have standard deviations of approximately 10 percent (approximately 7 percent of torsion), the coefficients have been increased by a factor for bending (presently 1,10) and a factor for torsion (presently 1,07) for the purpose of higher reliability. 2 Crankpin fillet The stress concentration factor for bending (αb) is: αb = KαB f (s, w) f (w) f (b) f (r) f (dg) f (dh) f (recess) where: Page 24

25 = 3.30 (applicable to principal stresses and one standard deviation above 50% reliability) f(w) f(b) f(r) f(dg) f (dh) f(recess) = w 3 4 = w w² w w + (1-s) ( w w² w w ) + (1-s)² ( w w² w w ) = b b = r 2 ( ) 3 = dg dg² dg 3 = dh dh² dh = 1 + (th + tg) ( s) The stress concentration factor for torsion (αt) is: αt = KαT f (r,s) f (b) f (w) where: KαT f (r,s) f (b) f (w) = (applicable to one standard deviation above 50% reliability). = r ( (1-s)) 3 = b b² b = w (-0.145) 3 Journal fillet (not applicable to semi-built crankshaft) The stress concentration factor for bending (βb) is: βb = 3.33 fb (sg,wg) fb (w) fb (b) fb (r) fb (dg) fb (dh) f (recess) (applicable to principal stresses and one standard deviation above 50% reliability). where: fb (sg,wg) fb (wg) fb (b) fb (rg) fb (dg) fb (dh) f (recess) = wg wg² + (1 sg) ( wg wg²) + (1 sg)² ( wg wg²) = wg = bg bg = rg ( ) 2 = dg dg = dh dh = 1 + (th + tg) ( s) The stress concentration factor for compression (βq) due to the radial force is: βq = 3.69 fq (s) fq (w) fq (b) fq (r) fq (dh) f (recess) (applicable to principal stresses and one standard deviation above 50% reliability.) where: fq (sg) ² = (1-sG) (1-sG) Page 25 Section 3 KαB f (s,w)

26 = fq (bg) fq (rg) fq (dh) f (recess) = bg Section 3 fq (wg) ( ) = rg ² = dh dh = 1 + (th + tg) ( s) The stress concentration factor for torsion (βt) is: βt = f (rg,sg) f (bg) f (wg) (applicable to one standard deviation above 50% reliability.) where: f (rg,sg) f (bg) f (wg) = rg ( (1-s)) 3 = bg bg² bg = wg (-0.145) 4 Outlet of crankpin oil bore The stress concentration factor for bending (γb) is: The stress concentration factor for torsion (γt) is: 5 Outlet of journal oil bore The stress concentration factor for bending (γbg) is: The stress concentration factor for torsion (γtg) is: 6 Inclined oil bores Inclined oil bores have higher stress concentrations than oil bores perpendicular to the surface. Page 26

27 For bending: For torsion: Range of validity: φ < 25 degrees ψ < 40 degrees where φ ψ = is the angular deviation (degrees) from perpendicular oil bore direction as projected in the transverse (crosswise) plane. = is the angular deviation (degrees) from perpendicular oil bore direction as projected longitudinally in the crankpin plane. Page 27 Section 3 For small deviations from perpendicular oil bore exit the stress concentration factors in [4] and [5] shall be multiplied with:

28 1 General In addition to the alternating bending stresses in fillets (see Sec.2 [2.3]) further bending stresses due to misalignment and bedplate deformation as well as due to axial and bending vibrations shall be considered by applying σadd as given by table: Type of engine Crosshead engines Trunk piston engines (*) 2 σadd [N/mm ] ± 30 (*) ± 10 2 The additional stress of ± 30 N/mm is composed of two components: 1) 2) 2 an additional stress of ± 20 N/mm resulting from axial vibrations 2 an additional stress of ± 10 N/mm resulting from misalignment/bedplate deformation. 2 It is recommended that a value of ± 20 N/mm is used for the axial vibration component for assessment purposes where axial vibration results of the complete dynamic system (engine/shafting/gearing/propeller) are not available. Where axial vibration calculation results of the complete system are available, the calculated figures may be used instead. Page 28 Section 4 SECTION 4 ADDITIONAL BENDING STRESSES

29 1 General 7 The fatigue strength is defined as the permanently endurable (i.e. >>10 cycles) alternating principal stress considering influences as mean stress, mechanical strength, size effect, stress gradient, production method, surface roughness, and surface treatment as hardening and/or cold deformation if applicable. The fatigue strength may be determined by tests or by empirical formulae as given below. Test results may also be combined with pertinent elements of the empirical formulae; e.g. push-pull test results can be combined with mean stress influence, and so on. When the fatigue strength is determined by means of testing (full size or small specimen), the number of test and the statistical evaluation method shall be selected so as to enable determination of the fatigue strength as the average value minus one standard deviation. For more details, see App.D. It is also essential that the tested material is as representative as possible for the future production; i.e. material cleanliness, production method, surface roughness, and mechanical strength shall not be superior to the minimum requirements for the production. When full size tests are used to determine fatigue strength of crankshafts with surface treated fillets (and/ or oil holes), the acceptance shall be combined with an approved procedure for quality control of the surface treatment. 2 Empirical formulae for non-surface treated fillets The fatigue strengths in bending and torsion for web fillets are determined as: For oil holes: for Kb, Kt and Kh, see [2.1] for, see [2.2] for f(ra), see [2.3] for f(χ), see [2.4] for f(σm), see [2.5] for f(τm), see [2.5]. When crankpins and/or journals are surface hardened, special attention shall be given to the transition zones between surface hardened areas and the soft core material, see [3.1]. See also App.E. 2.1 Influence of production methods. Kb and Kt represent the influence of various production methods on fatigue in web fillet, and Kh in oil holes Groups Group 1: continuous grain flow forged Group 2: free form forged 2) 1) Kb Kt Kh Page 29 Section 5 SECTION 5 CALCULATION OF FATIGUE STRENGTH

30 Group 3: slab forged 3), form cut and twisted Group 4: cast steel Group 5: super clean 4) Kb Kt Kh forged steel see below Section 5 Groups 0,7 4) 1) Continuous grain flow (cgf) forged means documented forging that results in a flow of segregations tangential to the main principal stress direction in the web fillets. It does not apply to oil holes (where Kh = 1). The documentation shall be made on a crankthrow that is cut in the crank plane and etched in order to illustrate the grain flow. It is essential that this is made with fillets in finished condition. I.e. for recessed fillets, cgf may be difficult to obtain as the recess normally cuts the grain flow. 2) Free form forging means all kinds of forging processes that are neither cgf nor slab forging (see footnote 3). 3) Slab forging means processes where a forged slab is oxycut or machined to form crankthrows, and then twisted into positions. All similar processes where material from the centre of the slab ends up in the web fillets fall into this category. This does not apply to oil holes provided that they are not in a part that origins from the slab centre i.e. normally Kh = 1 for oil holes. 4) For steels with a especially high cleanliness (see; DNV GL rules for classification: Ships DNVGL-RU-SHIP Pt.2 Ch.2 Sec.5) the factors Kb = Kt = Kh = 1.1 for web fillets and oil holes and apply for both cgf and free form forging. When super-clean steels are combined with slab forging, 5) Kb = Kt = 1.0 for web fillets and Kh = 1.1 for oil holes. 2.2 Mechanical strength influence. f(σb;σ0.2) represents the influence of the mechanical strength on the push-pull fatigue strength. f(σb;σ0.2) is the smaller value of 0.30 σb + 40 and 0.40 σ (When using these two formulae realistic values shall be used. Generalised material minimum values from classification rules tend to give wrong relations between σ0.2 and σb.) It should be noted that use of σb>800 MPa or σ0.2 > 600 MPa may require stricter requirements for cleanliness than those given in some material specifications. 2.3 Surface roughness influence. f(ra) represents the influences of surfaces roughness. The surface roughness condition of all web fillets and oil holes (to a depth of at least 1,5 times the oil bore diameter) is assumed to be smooth grinding or better, preferably polishing. Web fillets should be polished along the fillet contour. Hence the f(ra) is unity. However, for oil bores that are not smoothly finished to the above mentioned depth, a factor of f(ra) = 0.9 applies. 2.4 Stress gradient influence. f(χ) represents the size influence due to the stress gradient. The other size influences such as statistical and metallurgical are not included because: Page 30

31 f(χ) is different for bending and torsion and may be taken as: for bending for torsion where RX is RH for crankpin fillets and RG for journal fillets and for oil bores. However, Rx shall not be taken <2mm for calculation purposes. 2.5 Mean stress influence The mean stress influence is considered by means of a parabolic relation as: respectively where For crankpin fillets: σmean = σbhm, see Sec.2 [1.3] B τmean = τhm, see Sec.2 [2.3] B For journal fillets: σmean = σbgm, see Sec.2 [1.3] B τmean= τgm, see Sec.2 [2.3] B It should be noted that crankpin fillet mean bending stresses normally are positive (tension) and hence reduce the fatigue strength. Journal fillet mean bending stresses are normally negative (compression) and hence increase the fatigue strength. For torsion, any mean stress regardless direction reduces the fatigue strength. For oil holes in crankpin: For σbom, see Sec.2 [2.4] B For σtom, see Sec.2 [3.3] B. For oil holes in journals: Page 31 Section 5 the statistical is covered by the use of one standard deviation below average for test results, respectively covered by the empirical formulae for push-pull the metallurgical is covered by use of representative test specimens taken from one (or both) extended end(s) of the forged crankshafts or equivalent for single throws.

32 Section 5 for σbogm, see Sec.2 [2.5] B for σtogm, see Sec.2 [3.3] B 3 Surface treated fillets and/or oil holes 3.1 General Surface treatment of fillets and oil holes means any method aiming at increased fatigue strength in local areas. It is divided into surface hardening and cold deformation. Surface hardening means all kinds of thermal treatment such as induction hardening and nitriding. These processes result in increased surface hardness, and if properly made, also compressive residual stresses to a certain depth. However, especially for induction hardening, the transition zones depth-wise and at the end of the layer have tensile residual stresses. It is therefore essential to check also transition zones for fatigue. Cold deformation means all kinds of cold treatments such as shot peening, stroke peening, cold rolling and ball coining (oil holes). These processes result in negligible hardness increase but in considerable compressive residual stresses to a certain depth. Also with these processes the transition zones shall be checked for fatigue. See App.D for fatigue testing and App.E for evaluation of safety against fatigue in surface treated fillets and/ or oil bore outlets. Page 32

33 Section 6 SECTION 6 ACCEPTABILITY CRITERIA 1 General For the fatigue criteria mentioned in [2], [3] and [4] a common minimum safety factor applies, as: 2 S = 1.15 All stresses are in N/mm. 2 The crankpin fillet criterion The stresses in the crankpin fillet shall fulfil the following criterion: where σh τh σfh τfh = σbh + σadd, see Sec.2 [2.3] respectively Sec.4. = see Sec.2 [3.3]. = σf as determined in Sec.5 for the crankpin fillet = τf as determined in Sec.5 for the crankpin fillet For semi-built crankshafts with a relatively low distance between the pin and the shrunk in journal (s = S / D > 0.1), it is necessary to consider the influence of the shrinkage stresses on the crankpin fillet fatigue strength. This applies in particular to the approximately 45 crankpin plane. The above mentioned criterion may be used, however, with some modifications as: nominal bending stresses as well as stress concentration factors to be calculated in the 45 plane. Shrinkage stresses in the fillet of the 45 plane to be added to the mean bending stresses when determining the fatigue strength. 3 The journal fillet criterion (Not applicable to semi-built crankshafts.) The stresses in the journal fillet shall fulfil the following criterion: where σg τg = σbg + σadd, see Sec.2 [2.3] respectively Sec.4. = see Sec.2 [3.3]. Page 33

34 = σf as determined in Sec.5 for the journal fillet = Section 6 σfg τfg τf as determined in Sec.5 for the journal fillet 4 The oil hole criterion The stresses in the oil holes shall fulfil the following criteria: Outlet of crankpin bores where σbo σto σfo = see Sec.2 [2.4] A. = see Sec.2 [2.2]. = σfh as determined in Sec.5 for the crankpin oil hole, with attention to Sec.6 [3] if the crankpin is surface hardened. Outlet of journal bores where σbog σtog σfog = see Sec.2 [2.5] A. = see Sec.2 [3.3]. = σfh as determined in Sec.5 for the journal oil hole, with attention to Sec.5 [3.1] if the journal is surface hardened. Page 34

35 1 General The criteria given in [2] to [4] serve the purpose of both safe torque transmission and to prevent detrimental fretting under the edge of the shrinkage. All crank dimensions necessary for the calculation of the shrink-fit are shown in Figure 1. Figure 1 Crankthrow of semi-built crankshaft Where: DA [mm] DS [mm] DG [mm] DBG [mm] LS [mm] RG [mm] y [mm] = outside diameter of web or twice the minimum distance x between centre-line of journals and outer contour of web, whichever is less = shrink diameter = journal diameter = diameter of axial bore in journal = length of shrink-fit = fillet radius of journal = distance between the adjacent generating lines of journal and pin y 0.05 DS Where y is less than 0.1 DS special consideration shall be given to the effect of the stress due to the shrink-fit on the fatigue strength at the crankpin fillet. Respecting the radius of the transition from the journal to the shrink diameter, the following should be complied with: RG DG and Page 35 Section 7 SECTION 7 CALCULATION OF SHRINK-FITS OF SEMI-BUILT CRANKSHAFT

36 where the greater value shall be considered. The actual oversize Z of the shrink-fit shall be within the limits Zmin and Zmax calculated in accordance with [3] and [4]. In the case where condition in [2] cannot be fulfilled then methods in [3] and [4] calculation of Zmin and Zmax are not applicable due to multizone-plasticity problems. In such case Zmin and Zmax shall be established based on FEM calculations. 2 Maximum permissible hole in the journal pin The maximum permissible hole diameter in the journal pin is calculated in accordance with the following formula: where : SR [-] Mmax [Nm] μ [-] σsp [N/mm2] = safety factor against slipping, however a value not less than 2 shall be taken unless documented by experiments. = absolute maximum value of the torque MTmax in accordance with Sec.2 [3.2] = coefficient for static friction, however a value not greater than 0.2 shall be taken unless documented by experiments. = minimum yield strength of material for journal pin This condition serves to avoid plasticity in the hole of the journal pin. 3 Necessary minimum oversize of shrink-fit The necessary minimum oversize is determined by the greater value calculated according to: and where: Zmin [mm] = minimum oversize Page 36 Section 7 RG 0.5 (DS DG)

37 = Young s modulus QS [-] = shaft ratio, Section 7 Em [N/mm²] σsw [N/mm²] QA [-] = minimum yield strength of material for crank web = web ratio, 4 Maximum permissible oversize of shrink-fit The maximum permissible oversize is calculated according to: Higher values may be accepted for forged steel, but limited to the shrinkage amount that result in a plasticized zone of 30% of the minimum web thickness in radial direction. Page 37

38 Page 38 Appendix A APPENDIX A DEFINITION OF STRESS CONCENTRATION FACTORS IN CRANKSHAFT FILLETS

39 Appendix B APPENDIX B STRESS CONCENTRATION FACTORS AND STRESS DISTRIBUTION AT THE EDGE OF OIL DRILLINGS Page 39

40 1 General The objective of the analysis is to substitute the analytically calculated stress concentration factors (SCF) at the crankshaft fillets by suitable FEM calculated figures. The analytical method is based on empirical formulae developed from strain gauge measurements of various crank geometries. Use of these formulae beyond any of the various validity ranges can lead to erroneous results in either direction, i.e. results that more inaccurate than indicated by the mentioned standard deviations. Therefore the FEM-based method is highly recommended. The SCF s calculated according to the rules of this appendix are defined as the ratio of stresses calculated by FEM to nominal stresses in both journal and pin fillets. When used in connection with the present method in M53 von Mises stresses shall be calculated for bending and principal stresses for torsion or when alternative methods are considered. The procedure as well as evaluation guidelines are valid for both solid cranks and semi-built cranks (except journal fillets). The analysis shall be conducted as linear elastic FE analysis, and unit loads of appropriate magnitude applied for all load cases. The calculation of SCF at the oil bores is at present not covered by this document. It is advised to check the element accuracy of the FE solver in use, e.g. by modelling of a simple geometry and compare the stresses obtained by FEM with the analytical solution for pure bending and torsion. Boundary element method (BEM) may be used instead of FEM. 2 Model requirements The basic recommendations and perceptions for building the FE-model are presented in App.C [2.1]. It is obligatory for the final FE-model to fulfil the requirement in App.C [2.3]. 2.1 Element mesh recommendations In order to fulfil the mesh quality criteria it is advised to construct the FE-model for the evaluation of stress concentration factors according to the following recommendations: the model consists of one complete crank, from main bearing centre-line to opposite side main bearing centre-line element types used in the vicinity of the fillets: 10 node tetrahedral elements 8 node hexahedral elements 20 node hexahedral elements mesh properties in fillet radii. The following applies to ±90 degrees in circumferential direction from the crank plane: maximum element size a = r/4 through the entire fillet as well as the in circumferential direction. When using 20 node hexahedral elements, the element size in the circumferential direction may be extended up to 5 a. In the case of multi-radii fillet, r is the local fillet radius. (If 8 node hexahedral elements are used even smaller element size is required to meet the quality criteria.) recommended manner for element size in fillet depth direction first layer thickness equal to element size of a second layer thickness equal element to size of 2 a Page 40 Appendix C APPENDIX C ALTERNATIVE METHOD FOR CALCULATION OF STRESS CONCENTRATION FACTORS IN THE WEB FILLET RADII OF CRANKSHAFTS BY UTILISING FINITE ELEMENT METHOD

41 minimum 6 elements across web thickness. generally the rest of the crank should be suitable for numeric stability of the solver counterweights only shall be modelled when influencing the global stiffness of the crank significantly modelling of oil drillings not necessary as long as the influence on global stiffness is negligible or the proximity to the fillet is more than 2r, Figure 1 below drillings and holes for weight reduction shall be modelled Figure 1 Proximity to fillet 2.2 Material UR M53 does not consider material properties such as Young s Modulus (E) and Poisson s ratio (n). In FE analysis those material parameters are required, as strain is primarily calculated and stress is derived from strain using the Young s Modulus and Poisson s ratio. Reliable values for material parameters shall be used, either as quoted in literature or measured on representative material samples. 5 For steel the following is advised: E= MPa and ν= Element mesh quality criteria If the actual element mesh does not fulfil any of the following criteria at the examined area for SCF evaluation, then a second calculation with a refined mesh shall be performed Principal stresses criterion The quality of the mesh should be assured by checking the stress component normal to the surface of the fillet radius. Ideally, this stress should be zero. With principal stresses σ1, σ2 and σ3 the following criterion is required: min( σ1, σ2, σ3 ) < 0.03 max( σ1, σ2, σ3 ) Averaged/un-averaged stresses criterion The criterion is based on observing the discontinuity of stress results over elements at the fillet for the calculated SCF: Un-averaged nodal stress results calculated from each element connected to a nodei should differ less than 5% from the 100% averaged nodal stress results at this nodei at the examined location. Page 41 Appendix C third layer thickness equal element to size of 3 a

42 To substitute the analytically determined SCF in UR M53 the following load cases shall be calculated. 3.1 Torsion In analogy to the testing apparatus used for the investigations made by FVV the structure is loaded in pure torsion. In the model surface warp at the end faces is suppressed. Torque is applied to the central node located at the crankshaft axis. This node acts as master node with 6 degrees of freedom and is connected rigidly to all nodes of the end face. Boundary and load conditions are valid for both in-line and V- type engines. Figure 2 Boundary and load conditions for the torsion case For all nodes in both journal and crank pin fillet principal stresses are extracted and the equivalent torsional stress is calculated: The maximum value taken for the subsequent calculation of the SCF: Page 42 Appendix C 3 Load cases

43 3.2 Pure bending (4 point bending) In analogy to the testing apparatus used for the investigations made by FVV the structure is loaded in pure bending. In the model surface warp at the end faces is suppressed. The bending moment is applied to the central node located at the crankshaft axis. This node acts as master node with 6 degrees of freedom and is connected rigidly to all nodes of the end face. Boundary and load conditions are valid for both in-line and V- type engines. For all nodes in both journal and pin fillet von Mises equivalent stresses σequiv are extracted. The maximum value is used to calculate the SCF according to: Nominal stress sn is calculated as per UR M with the bending moment M: 3.3 Bending with shear force (3 point bending) This load case is calculated to determine the SCF for pure transverse force (radial force, βq) for the journal fillet. In analogy to the testing apparatus used for the investigations made by FVV the structure is loaded in 3-point bending. In the model, surface warp at the both end faces is suppressed. All nodes are connected rigidly to the centre node; boundary conditions are applied to the centre nodes. These nodes act as master nodes with 6 degrees of freedom. The force is applied to the central node located at pin centre-line of the connecting rod. This node is connected to all nodes of the pin cross sectional area. Warping of the sectional area is not suppressed. Boundary and load conditions are valid for in-line and V- type engines. V-type engines can be modelled with one connecting rod force only. Using two connecting rod forces will make no significant change to the SCF. The maximum equivalent von Mises stress s3p in the journal fillet is evaluated. The SCF in the journal fillet can be determined in two ways as shown in App.C [3.3.1] and App.C [3.3.2]. Page 43 Appendix C Where tn is nominal torsion stress referred to the crankpin respectively journal as per UR M with the torsional torque τ:

44 Appendix C Figure 3 Boundary and load conditions for the pure bending load case Figure 4 Boundary and load conditions for the 3-point bending load case for an in-line engine Page 44

45 Appendix C Figure 5 Load applications for in-line and V-type engines Method 1 This method is analogue to the FVV investigation. The results from 3-point and 4-point bending are combined as follows: σ3p = σn3p βb + σq3p βq where: σ3p σn3p = as found by the FE calculation βb σq3p = as determined in [3.3] = nominal bending stress in the web centre due to the force F3P [N] applied at the centre-line of the actual connecting rod, Figure 4 and Figure 5 = Q3P/(B W) where Q3P is the radial (shear) force in the web due to the force F3P applied at the centre-line of the actual connecting rod, see Sec.1 Figure Method 2 This method is not analogous to the FVV investigation. In a statically determined system as one crank throw supported on two bearings, the bending moment and radial (shear) force are proportional. Therefore the journal fillet SCF can be found directly by the 3 point bending FE calculation. The SCF is then calculated according to: For symbols see method 1. When using this method the radial force and stress determination in M53 becomes superfluous. The alternating bending stress in the journal fillet as per UR M is then evaluated σbg = ± βbq σbfn where σbfn is calculated in M53. Page 45

46 Page 46 Appendix C Note that the use of this method does not apply to the crankpin fillet and that this SCF shall not be used in connection with calculation methods other than those assuming a statically determined system as in M53.

47 1 Introduction Fatigue testing can be divided into two main groups; testing of small specimens and full size crank throws. For crankshafts without any fillet surface treatment, the fatigue strength can be determined by testing small specimens taken from a full size crank throw. One advantage is the rather high number of specimens which can be then manufactured. Another advantage is that the tests can be made with different stress ratios (Rratios) and/or different modes e.g. axial, bending and torsion, with or without a notch. This is required for evaluation of the material data to be used with critical plane criteria. For crankshafts with surface treatment the fatigue strength can only be determined through testing of full size crank throws. For cost reasons this usually means a low number of crank throws. The load can be applied by hydraulic actuators in a 3- or 4-point bending arrangement, or by an exciter in a resonance test rig. The latter is frequently used, although it usually limits the stress ratio to R = -1. Testing can be made using the staircase method or a modified version thereof which is presented in this document. Other statistical evaluation methods may also be applied. 2 Evaluation of test results 2.1 Principles Prior to fatigue testing, the crankshaft shall be tested as required by quality control procedures, e.g. for chemical composition, mechanical properties, surface hardness, hardness depth and extension, fillet surface finish, etc. The test samples should be prepared so as to represent the "lower end" of the acceptance range e.g. for induction hardened crankshafts this means the lower range of acceptable hardness depth, the shortest extension through a fillet, etc. Otherwise the mean value test results should be corrected with a confidence interval: a 90% confidence interval may be used both for the sample mean and the standard deviation. The test results, when applied in M53, shall be evaluated to represent the mean fatigue strength, with or without taking into consideration the 90% confidence interval as mentioned above. The standard deviation should be considered by taking the 90% confidence into account. Subsequently the result to be used as the fatigue strength is then the mean fatigue strength minus one standard deviation. If the evaluation aims to find a relationship between (static) mechanical properties and the fatigue strength, the relation shall be based on the real (measured) mechanical properties, not on the specified minimum properties. The calculation technique presented in [2.4] was developed for the original staircase method. However, since there is no similar method dedicated to the modified staircase method the same is applied for both. 2.2 Staircase method In the original staircase method, the first specimen is subjected to a stress corresponding to the expected 7 average fatigue strength. If the specimen survives 10 cycles, it is discarded and the next specimen is subjected to a stress that is one increment above the previous, i.e. a survivor is always followed by the next using a stress one increment above the previous. The increment should be selected to correspond to the expected level of the standard deviation. 7 When a specimen fails prior to reaching 10 cycles, the obtained number of cycles is noted and the next specimen is subjected to a stress that is one increment below the previous. With this approach the sum of failures and run-outs is equal to the number of specimens. This original staircase method is only suitable when a high number of specimens are available. Through simulations it has been found that the use of about 25 specimens in a staircase test leads to a sufficient accuracy in the result. Page 47 Appendix D APPENDIX D GUIDANCE FOR EVALUATION OF FATIGUE TESTS

48 When a limited number of specimens are available, it is advisable to apply the modified staircase method. Here the first specimen is subjected to a stress level that is most likely well below the average fatigue 7 strength. When this specimen has survived 10 cycles, this same specimen is subjected to a stress level one increment above the previous. The increment should be selected to correspond to the expected level of the standard deviation. This is continued with the same specimen until failure. Then the number of cycles is recorded and the next specimen is subjected to a stress that is at least 2 increments below the level where the previous specimen failed. With this approach the number of failures usually equals the number of specimens. The number of run-outs, 7 counted as the highest level where 10 cycles were reached, also equals the number of specimens. The acquired result of a modified staircase method should be used with care, since some results available indicate that testing a runout on a higher test level, especially at high mean stresses, tends to increase the fatigue limit. However, this "training effect" is less pronounced for high strength steels (e.g. UTS > 800 MPa). If the confidence calculation is desired or necessary, the minimum number of test specimens is Calculation of sample mean and standard deviation A hypothetical example of tests for 5 crank throws is presented further in the subsequent text. When using the modified staircase method and the evaluation method of Dixon and Mood, the number of samples will be 10, meaning 5 run-outs and 5 failures, i.e.: Number of samples: n = 10 Furthermore the method distinguishes between Less frequent event is failure: C=1 Less frequent event is run-outs: C=2 The method uses only the less frequent occurrence in the test results, i.e. if there are more failures than runouts, then the number of run-outs is used, and vice versa. In the modified staircase method, the number of run-outs and failures are usually equal. However, the testing can be unsuccessful, e.g. the number of run-outs can be less than the number of failures if a specimen with 2 increments below the previous failure level goes directly to failure. On the other hand, if this unexpected premature failure occurs after a rather high number of cycles, it is possible to define the level below this as a run-out. Dixon and Mood's approach, derived from the maximum likelihood theory, which also may be applied here, especially on tests with few samples, presented some simple approximate equations for calculating the sample mean and the standard deviation from the outcome of the staircase test. The sample mean can be calculated as follows: when C = 1 when C = 2 The standard deviation can be found by Page 48 Appendix D 2.3 Modified staircase method

49 Appendix D Where Sa0 d F A B i fi = the lowest stress level for the less frequent occurrence = the stress increment = fi = i f i 2 = i fi = the stress level numbering = is the number of samples at stress level i The formula for the standard deviation is an approximation and can be used when and 0.5 s < d < 1.5 s If any of these two conditions are not fulfilled, a new staircase test should be considered or the standard deviation should be taken quite large in order to be on the safe side. If increment d is greatly higher than the standard deviation s, the procedure leads to a lower standard deviation and a slightly higher sample mean, both compared to values calculated when the difference between the increment and the standard deviation is relatively small. Respectively, if increment d is much less than the standard deviation s, the procedure leads to a higher standard deviation and a slightly lower sample mean. Guidance note: Example 1 Hypothetical test results may look as shown in Figure 1. The processing of the results and the evaluation of the sample mean and the standard deviation are shown in Figure 2. Figure 1 Log sheet of a modified staircase test Page 49

50 Appendix D Figure 2 Processing of the staircase test results ---e-n-d---of---g-u-i-d-a-n-c-e---n-o-t-e--- Page 50

51 If the staircase fatigue test is repeated, the sample mean and the standard deviation will most likely be different from the previous test. Therefore, it is necessary to assure with a given confidence that the repeated test values will be above the chosen fatigue limit by using a confidence interval for the sample mean. The confidence interval for the sample mean value with unknown variance is known to be distributed according to the t-distribution (also called student's t-distribution) which is a distribution symmetric around the average. Figure 3 Student's t-distribution If Sa is the empirical mean and s is the empirical standard deviation over a series of n samples, in which the variable values are normally distributed with an unknown sample mean and unknown variance, the (1 - a) 100% confidence interval for the mean is: The resulting confidence interval is symmetric around the empirical mean of the sample values, and the lower endpoint can be found as; which is the mean fatigue limit (population value) to be used to obtain the reduced fatigue limit where the limits for the probability of failure are taken into consideration. Guidance note: Example 2 Applying a 90% confidence interval (α = 0.1) and n = 10 (5 failures and 5 run-outs) leads to tα, n-1 = 1.383, taken from a table for statistical evaluations (E. Doughtery: Probability and Statistics for the Engineering, Computing and Physical Sciences, Note that v = 1 in the tables). Hence: To be conservative, some authors would consider n to be 5, as the physical number of used specimen, then tα, n-1= e-n-d---of---g-u-i-d-a-n-c-e---n-o-t-e--- Page 51 Appendix D 2.5 Confidence interval for mean fatigue limit

52 Appendix D 2.6 Confidence interval for standard deviation The confidence interval for the variance of a normal random variable is known to possess a chi-square distribution with n 1 degrees of freedom. Figure 4 Chi-square distribution 2 An assumed fatigue test value from n samples has a normal random variable with a variance of σ and has 2 an empirical variance s. Then a (1 - a) 100% confidence interval for the variance is: A (1 - s) 100% confidence interval for the standard deviation is obtained by the square root of the upper limit of the confidence interval for the variance and can be found by The standard deviation (population value) shall be used to obtain the fatigue limit, where the limits for the probability of failure are taken into consideration. Guidance note: Example 3 Applying a 90% confidence interval (α = 0.1) and n = 10 (5 failures and 5 run-outs) leads to = 4.168, taken from a table for statistical evaluations (E. Doughtery: Probability and Statistics for the Engineering, Computing and Physical Sciences, 1990). Hence, To be conservative, some authors would consider n to be 5, as the physical number of the used specimen, then = e-n-d---of---g-u-i-d-a-n-c-e---n-o-t-e--- Page 52

53 In this connection a small specimen is considered to be one of the specimens taken from a crank throw. Since the specimens shall be representative for the fillet fatigue strength, they should be taken out close to the fillets, as shown in Figure 5. Figure 5 Specimen locations in a crank throw The (static) mechanical properties shall be determined as stipulated by the quality control procedures. 3.1 Determination of bending fatigue strength It is advisable to use un-notched specimens in order to avoid uncertainties related to the stress gradient influence. Push-pull testing (stress ratio R = -1) is preferred, but for the purpose of critical plane criteria another stress ratio may be added. A. If the objective of the testing is to document the influence of high cleanliness, test samples taken from positions approximately 120 degrees in a circumferential direction may be used. See Sec.3 Figure 1. B. If the objective of the testing is to document the influence of continuous grain flow (cgf) forging, the specimens should be restricted to the vicinity of the crank plane. 3.2 Determination of torsional fatigue strength A. If the specimens are subjected to torsional testing, the selection of samples should follow the same guidelines as for bending above. The stress gradient influence shall be considered in the evaluation. B. If the specimens are tested in push-pull, the samples should be taken out at an angle of 45 degrees to the crank plane. When taking the specimen at a distance from the (crank) middle plane of the crankshaft along the fillet, this plane rotates around the pin center point making it possible to resample the fracture direction due to torsion (the results shall be converted into the pertinent torsional values.) Page 53 Appendix D 3 Small specimen testing

54 If the test purpose is to find fatigue properties and the crankshaft is forged in a manner likely to lead to cgf, the specimens may also be taken longitudinally from a prolonged shaft piece where specimens for mechanical testing are usually taken. The condition is that this prolonged shaft piece is heat treated as a part of the crankshaft and that the size is so as to result in a similar quenching rate as the crank throw. When using test results from a prolonged shaft piece, it shall be considered how well the grain flow in that shaft piece is representative for the crank fillets. 3.4 Correlation of test results When using the bending fatigue properties from tests mentioned in this section, it should be kept in mind that successful continuous grain flow (cgf) forging leading to elevated values compared to other (non cgf) forging (or empirical approaches), will normally not lead to a torsional fatigue strength improvement of the same magnitude. In such cases it is advised to either carry out also torsional testing or to make a conservative assessment of the torsional fatigue strength, e.g. by using no credit for cgf. This approach is applicable when using the Gough Pollard criterion. However, this approach is not recognised when using the von Mises or a multi-axial criterion such as Findley. If the found ratio between bending and torsion fatigue differs from V3, one should consider replacing the use of the von Mises criterion with the Gough Pollard criterion. Also, if critical plane criteria are used, it shall be kept in mind that cgf makes the material inhomogeneous in terms of fatigue strength, meaning that the material parameters differ with the directions of the planes. Any addition of influence factors shall be made with caution. If for example a certain addition for super clean steel is documented, it may not necessarily be fully combined with a K-factor for cgf. Direct testing of samples from a super clean and cgf forged crank is preferred. 4 Full size testing 4.1 Hydraulic pulsation A hydraulic test rig can be arranged for testing a crankshaft in 3-point or 4-point bending as well as in torsion. This allows for testing with any R-ratio. Although the applied load should be verified by strain gauge measurements on plain shaft sections for the initiation of the test, it is not necessarily used during the test for controlling load. It is also pertinent to check fillet stresses with strain gauge chains. Furthermore, it is important that the test rig provides boundary conditions as defined in App.C. The (static) mechanical properties shall be determined as stipulated by the quality control procedures. 4.2 Resonance tester A rig for bending fatigue normally works with an R-ratio of -1. Due to operation close to resonance, the 7 energy consumption is moderate. Moreover, the frequency is usually relatively high, meaning that 10 cycles can be reached within some days. Figure 6 shows a layout of the testing arrangement. The applied load should be verified by strain gauge measurements on plain shaft sections. It is also pertinent to check fillet stresses with strain gauge chains. Clamping around the journals shall be arranged in a way that prevents severe fretting which could lead to a failure under the edges of the clamps. If some distance between the clamps and the journal fillets is provided, the loading is consistent with 4-point bending and thus representative for the journal fillets also. In an engine the crankpin fillets normally operate with an R-ratio slightly above -1 and the journal fillets slightly below -1. If found necessary, it is possible to introduce a mean load (deviate from R = -1) by means of a spring pre-load. Page 54 Appendix D 3.3 Other test positions

55 Appendix D Figure 6 A testing arrangement of the resonance tester for bending loading Page 55

56 Appendix D Figure 7 A testing arrangement of the resonance tester for torsion loading A rig for torsion fatigue can also be arranged as shown in Figure 7. When a crank throw is subjected to torsion, the twist of the crankpin makes the journals move sideways. If one single crank throw is tested in a torsion resonance test rig, the journals with their clamped-on weights will vibrate heavily sideways. This sideways movement of the clamped-on weights can be reduced by having two crank throws, especially if the cranks are almost in the same direction. However, the journal in the middle will move more. Since sideway movements can cause some bending stresses, the plain portions of the crankpins should also be provided with strain gauges arranged to measure any possible bending that could have an influence on the test results. Similarly to the bending case the applied load shall be verified by strain gauge measurements on plain shaft sections. It is also pertinent to check fillet stresses with strain gauge chains as well. 5 Use of existing results for similar crankshafts For fillets or oil bores without surface treatment, the fatigue properties found by testing may be used for similar crankshaft designs providing: The same material type Cleanliness on the same or better level The same mechanical properties can be granted (size versus hardenability) Similar manufacturing process Induction hardened or gas nitrited crankshafts will suffer fatigue either at the surface or at the transition to the core. The surface fatigue strength as determined by fatigue tests of full size cranks, may be used on an Page 56

57 Fatigue initiation in the transition zone can be either subsurface, i.e. below the hard layer, or at the surface where the hardening ends. The fatigue strength at the transition to the core can be determined by fatigue tests as described above, provided that the fatigue initiation occurred at the transition to the core. Tests made with the core material only will not be representative since the tension residual stresses at the transition are lacking. For cold rolled or stroke peened crankshafts, the results obtained by one full-size crank test can be applied to another crank size, provided that the base material is of the same type and that the treatment is made in order to obtain the same level of compressive residual stresses at the surface as well as in the depth. This means that both the extension and the depth of rolling or peening shall be proportional to the fillet radius. It shall be noted also what some recent research has shown: The fatigue limit can decrease in the very high cycle domain with subsurface crack initiation due to trapped hydrogen that accumulates through diffusion around some internal defect functioning as an initiation point. In these cases it would be appropriate to 7 reduce the fatigue limit by some percent per decade of cycles beyond 10. Based on a publication by Yukitaka Murakami "Metal Fatigue: Effects of Small Defects and Nonmetallic Inclusions" the reduction is suggested to be 5% per decade. Page 57 Appendix D equal or similar design as the tested crankshaft when the fatigue initiation occurred at the surface. With the similar design it is meant that the same material type and surface hardness are used and the fillet radius and hardening depth are within approximately ± 30% of the tested crankshaft.

58 1 Introduction This appendix deals with surface treated fillets and oil bore outlets. The various treatments are explained and some empirical formulae are given for calculation purposes. Conservative empiricism has been applied intentionally, in order to be on the safe side from a calculation standpoint. Please note that measurements or more specific knowledge should be used if available. However, in the case of a wide scatter (e.g. for residual stresses) the values should be chosen from the end of the range that would be on the safe side for calculation purposes. 2 Definition of surface treatment Surface treatment is a term covering treatments such as thermal, chemical or mechanical operations, leading to inhomogeneous material properties such as hardness, chemistry or residual stresses from the surface to the core. 2.1 Surface treatment methods The following list covers possible treatment methods and how they influence the properties that are decisive for the fatigue strength. Table 1 Surface treatment methods and the characteristics they affect Treatment method Affecting Induction hardening Hardness and residual stresses Nitriding Chemistry, hardness and residual stresses Case hardening Chemistry, hardness and residual stresses Die quenching (no temper) Hardness and residual stresses Cold rolling Residual stresses Stroke peening Residual stresses Shot peening Residual stresses Laser peening Residual stresses Ball coning Residual stresses It is important to note that since only induction hardening, nitriding, cold rolling and stroke peening are considered relevant for marine engines; other methods are not dealt with in this document. In addition die quenching can be considered in the same way as induction hardening. 3 Calculation principles The basic principle is that the alternating working stresses shall be below the local fatigue strength (including the effect of surface treatment) wherein non-propagating cracks may occur, see also App.E [6.1] for details. This is then divided by a certain safety factor. This applies through the entire fillet or oil bore contour as well as below the surface to a depth below the treatment-affected zone i.e. to cover the depth all the way to the core. Page 58 Appendix E APPENDIX E SURFACE TESTED FILLETS AND OIL BORE OUTLETS

59 It is of vital importance that the extension of hardening/peening in an area with concentrated stresses be duly considered. Any transition where the hardening/peening is ended is likely to have considerable tensile residual stresses. This forms a weak spot and is important if it coincides with an area of high stresses. Alternating and mean working stresses shall be known for the entire area of the stress concentration as well as to a depth of about 1.2 times the depth of the treatment. The following figure indicates this principle in the case of induction hardening. The base axis is either the depth (perpendicular to the surface) or along the fillet contour. Figure 1 General principles of stresses as functions of depth The acceptability criterion shall be applied stepwise from the surface to the core as well as from the point of maximum stress concentration along the fillet surface contour to the web. 3.1 Evaluation of local fillet stresses It is necessary to have knowledge of the stresses along the fillet contour as well as in the subsurface to a depth somewhat beyond the hardened layer. Normally this will be found via FEA as described in App.C. However, the element size in the subsurface range will have to be the same size as at the surface. For crankpin hardening only the small element size will have to be continued along the surface to the hard layer. If no FEA is available, a simplified approach may be used. This can be based on the empirically determined stress concentration factors (SCFs), as in M53.3 if within its validity range, and a relative stress gradient inversely proportional to the fillet radius. Bending and torsional stresses shall be addressed separately. The combination of these is addressed by the acceptability criterion. The subsurface transition-zone stresses, with the minimum hardening depth, can be determined by means of local stress concentration factors along an axis perpendicular to the fillet surface. These functions ĮB-local and ĮT-local have different shapes due to the different stress gradients. The SCFs αβ and αt are valid at the surface, the local αβ-local and αt-local drop with increasing depth. The relative stress gradients at the surface depend on the kind of stress raiser, but for crankpin fillets they can be simplified to 2/RH in bending and 1/RH in torsion. The journal fillets are handled analogously by using RG. The Page 59 Appendix E Consideration of the local fatigue strength shall include the influence of the local hardness, residual stress and mean working stress. The influence of the giga-cycle effect, especially for initiation of subsurface cracks, should be covered by the choice of safety margin.

60 The local SCFs are then functions of depth t according to Equation E-1 as shown in Figure 2 for bending and respectively for torsion in Equation E-2 and Figure 3. Equation E-1 Equation E-2 Figure 2 Bending SCF in the crankpin fillet as a function of depth Page 60 Appendix E nominal stresses are assumed to be linear from the surface to a midpoint in the web between the crankpin fillet and the journal fillet for bending and to the crankpin or journal center for torsion.

61 Appendix E Figure 3 Torsional SCF in the crankpin fillet as a function of depth In Figure 2 the corresponding SCF for the journal fillet can be found by replacing RH with RG. In Figure 3 the corresponding SCF for the journal fillet can be found by replacing RH with RG and D with DG. If the pin is hardened only and the end of the hardened zone is closer to the fillet than three times the maximum hardness depth, FEA should be used to determine the actual stresses in the transition zone. 3.2 Evaluation of oil bore stresses Stresses in the oil bores can be determined also by FEA. The element size should be less than 1/8 of the oil bore diameter DO and the element mesh quality criteria should be followed as prescribed in App.C. The fine element mesh should continue well beyond a radial depth corresponding to the hardening depth. The loads to be applied in the FEA are the torque, App.C [3.1] and the bending moment, with four-point bending as in App.C [3.2]. If no FEA is available, a simplified approach may be used. This can be based on the empirically determined SCF from M53.3 if within its applicability range. Bending and torsional stresses at the point of peak stresses are combined as in M53.5. Page 61

62 Appendix E Figure 4 Stresses and hardness in induction hardened oil holes Figure 4 indicates a local drop of the hardness in the transition zone between a hard and soft material. Whether this drop occurs depends also on the tempering temperature after quenching in the QT process. The peak stress in the bore occurs at the end of the edge rounding. Within this zone the stress drops almost linearly to the center of the pin. As can be seen from Figure 4, for shallow (A) and intermediate (B) hardening, the transition point practically coincides with the point of maximal stresses. For deep hardening the transition point comes outside of the point of peak stress and the local stress can be assessed as a portion (1-2 th/d) of the peak stresses where th is the hardening depth. The subsurface transition-zone stresses (using the minimum hardening depth) can be determined by means of local stress concentration factors along an axis perpendicular to the oil bore surface. These functions γb- γt-local have different shapes, because of the different stress gradients. The stress concentration factors γb and γt are valid at the surface, the local SCFs γb-local and γt-local drop local and with increasing depth. The relative stress gradients at the surface depend on the kind of stress raiser, but for crankpin oil bores they can be simplified to 4/DO in bending and 2/DO in torsion. The local SCFs are then functions of the depth t: Equation E-3 Page 62