Section 3 Crankshaft Design

3.1.1 Pt 5, Ch 2, 3 Crankshaft Design is not applicable to auxiliary engines having powers of less than 110 kW.

3.2.1 The formulae given in this Section are applicable to solid or semi-built crankshafts of forged or cast steel, having a main support bearing adjacent to each crankpin.

3.2.2 This section uses the statically determinate method; alternative methods, including a fully documented stress analysis, will be considered.

3.2.3 Calculations are to be carried out for the maximum continuous power rating for all designed operating conditions.

3.2.4 Designs of crankshafts not included in this scope will be subject to special consideration.

3.2.5 Where a crankshaft design involves the use of surface treated fillets, or when fatigue parameter influences are tested, or when working stresses are measured, the relevant documents with calculations/analysis are to be submitted to LR.

3.2.6 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; and
• outlets of crankpin oil bores.

3.2.7 When the journal diameter is equal to or larger than the crankpin diameter, the outlets of main journal oil bores are to be formed in a similar way to the crankpin oil bores, otherwise separate documentation of fatigue safety will be specially considered.

3.2.8 Calculation of crankshaft strength consists initially in determining the nominal alternating bending (see Pt 5, Ch 2, 3.6 Calculation of bending stresses) and nominal alternating torsional stresses (see Pt 5, Ch 2, 3.7 Calculation of torsional stresses) which when multiplied by the appropriate stress concentration factors (SCF) (see Pt 5, Ch 2, 3.8 Stress concentration factors), result in an equivalent alternating stress (uniaxial stress) (see Pt 5, Ch 2, 3.10 Equivalent alternating stress). This equivalent alternating stress is then compared with the fatigue strength of the selected crankshaft material (see Pt 5, Ch 2, 3.11 Fatigue strength). This comparison will show whether or not the crankshaft concerned is dimensioned adequately (see Pt 5, Ch 2, 3.12 Acceptability criteria).

3.2.9 Further information and guidance on crankshaft design is provided in the LR Guidance Notes for the Calculation of Stress Concentration Factors, Fatigue Enhancement Methods and Evaluation of Fatigue Tests for Crankshafts.

3.3.1 For the calculation of crankshafts, the documents and particulars listed below are required. This information is provided by completing LR Form 2073 and submitting the applicable plans required in Table 2.1.1 Plans and particulars to be submitted:

• crankshaft drawing (which must 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, precombustion chamber, etc.);
• number of cylinders;
• output power at maximum continuous rating (MCR), in kW;
• output speed at maximum continuous power, in rpm;
• maximum firing pressure, P_max, in MPa;
• mean indicated pressure, in MPa;
• charge air pressure (before inlet valves or scavenge ports, whichever applies), in MPa;
• digitised gas pressure/crank angle cycle for MCR (presented at equidistant intervals at least every 5° CA);
• mean piston speed;
• compression ratio;
• vee angle α_v, in degrees;
• firing order numbered from driving end, see Figure 2.3.1 Designation of cylinders;
• direction of rotation;
• cylinder diameter, in mm;
• piston stroke, in mm;
• centre of gravity of connecting rod from large end centre, in mm;
• radius of gyration of connecting rod, in mm;
• length of connecting rod between bearing centres, L_H, in mm;
• mass of single crankweb (indicate if webs either side of pin are of different mass values), in kg;
• centre of gravity of crankweb mass from shaft axis, in mm;
• mass of counterweights fitted (for complete crankshaft) indicate positions fitted, in kg;
• centre of gravity of counterweights (for complete crankshaft) measured from shaft axis, in mm;
• all individual reciprocating masses acting on one crank, in kg;
• crankshaft material specification(s) (according to ISO, EN, DIN, AISI, etc.);
• mechanical properties of material (minimum values obtained from longitudinal test specimens):
  • tensile strength, in N/mm²
  • yield strength, in N/mm²
  • reduction in area at break, percentage
  • elongation, percentage
• method of manufacture (free form forged, continuous grain flow forged, drop-forged, etc.; with description of the forging process);
• for semi-built crankshafts – minimum and maximum diametral interference, in mm; and
• particulars of alternating torsional stress calculations, see Pt 5, Ch 2, 3.7 Calculation of torsional stresses.

3.3.2 The following information is also required for appraisal of the crankshaft (not contained in Form 2073):

• for engines with articulated-type connecting rod (see Figure 2.3.2 Articulated-type connecting rod);
  • distance to link point L_A, in mm
  • link angle α_N, in degrees
  • connecting rod length L_N, in mm
• firing interval (if applicable) i.e. if not evenly distributed
• mass of connecting rod (including bearings), in kg;
• mass of piston (including piston rod and crosshead where applicable), in kg;
• every surface treatment affecting fillets or oil holes shall be specified so as to enable calculation according to Chapter 3 of the LR Guidance Notes for the Calculation of Stress Concentration Factors, Fatigue Enhancement Methods and Evaluation of Fatigue Tests for Crankshafts;
  • this is to include crankshaft fatigue enhancement factors K₁ and K₂ where applicable.
• maximum alternating torsional stress τ_a (N/mm²)
• mechanical properties of material (minimum values obtained from longitudinal test specimens), in addition to the information listed above:

• Impact energy K_V, in Joules.

3.5.1 The calculation is based on a statically determined system, composed of a single crankthrow supported in the centre of adjacent main journals and subject to gas and inertia forces. The bending length is taken as the length between the two main bearing midpoints (distance L₃, see Figure 2.3.9 Bending moment and shear force for in-line engine crankthrows and Figure 2.3.10 Bending moment and shear force for V engine crankthrows.

3.5.2 The bending moments, M_BR and M_BT, are calculated in the relevant section based on triangular bending moment diagrams due to the radial component F_R and tangential component F_T of the connecting-rod force, respectively (see Figure 2.3.9 Bending moment and shear force for in-line engine crankthrows). For crankthrows with two connecting-rods acting upon one crankpin the relevant bending moments are obtained by superposition of the two triangular bending moment diagrams according to phase (see Figure 2.3.10 Bending moment and shear force for V engine crankthrows).

3.5.3 The bending moment M_BRF and the radial force Q_RF 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 are to be related to the cross-section of the crankweb. This reference section results from the web thickness W and the web width B (see Figure 2.3.3 Crank dimensions for overlapped crankshaft and Figure 2.3.4 Crank dimensions for crankshaft without overlap). Mean stresses are neglected.

M_BRO is the bending moment of the radial component of the connecting-rod force and M_BTO is the bending moment of the tangential component of the connecting-rod force. The alternating stresses due to these bending moments are to be related to the cross-sectional area of the axially bored crankpin. Mean bending stresses are neglected.

3.6.1 The radial and tangential forces due to gas and inertia loads acting upon the crankpin at each connecting-rod position are to 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, M_BRF, M_BRO and M_BTO, and radial forces, Q_RF, as defined in Pt 5, Ch 2, 3.5 Calculation of alternating stresses due to bending moments and radial forces – assumptions 3.5.3 and Pt 5, Ch 2, 3.5 Calculation of alternating stresses due to bending moments and radial forces – assumptions 3.5.4 are then calculated.

3.6.2 Nominal bending stresses are referred to the web bending modulus.

3.6.3 In case of V-type engines, the bending moments – progressively calculated from the gas and inertia forces – of the two cylinders acting on one crankthrow are superposed according to phase. Different designs (forked connecting-rod, articulated-type connecting-rod or adjacent connecting-rods) shall be taken into account.

3.6.4 Where there are cranks of different geometrical configurations in one crankshaft, the calculation is to cover all crank variants.

where

X_N is considered as the alternating force, moment or stress

X_max is the maximum value within one working cycle

X_min is the minimum value within one working cycle

where

M_BON is taken as the ½ range value M_BON = ± ½ (M_BOmax – M_BOmin) Nm

3.6.8 Alternating bending stresses for the crankpin fillet and journal fillet are calculated as follows:

1. For the crankpin fillet:

   σBH

   =

   where

   α_B is calculated according to Pt 5, Ch 2, 3.8 Stress concentration factors 3.8.6.(a)

2. For the journal fillet:

   σBG

   =

   where

   β_B is calculated according to Pt 5, Ch 2, 3.8 Stress concentration factors 3.8.7.(a)

   β_Q is calculated according to Pt 5, Ch 2, 3.8 Stress concentration factors 3.8.7.(b)

where

γ_B is calculated according to Pt 5, Ch 2, 3.8 Stress concentration factors 3.8.8.(a)

3.7.1 The nominal alternating torsional stress, τ_N, is to be taken into consideration. The value is to be derived from forced-damped vibration calculations of the complete dynamic system. Alternative methods will be given consideration. The engine designer is to advise the maximum level of alternating vibratory stress that is permitted (τ_a).

3.7.2 τ_a or τ_N(as applicable) is to be applied as a limiting value for the torsional vibration assessment required by Pt 5, Ch 8, 2 Torsional vibration.

where

τ_N is to be ascertained from assessment of the torsional vibration calculations where the maximum and minimum torques are determined 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 first 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 must be made for the damping that exists in the system and for unfavourable conditions (misfiring in one of the cylinders when no combustion occurs but only on the compression cycle). 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.

3.7.4 For the purpose of the crankshaft assessment, the nominal alternating torsional stress considered in calculations is to be the highest calculated value, according to the method described in Pt 5, Ch 2, 3.7 Calculation of torsional stresses 3.7.3, occurring at the most torsionally loaded mass point of the crankshaft system.

3.7.5 The approval of the crankshaft will be based on the installation having the largest nominal alternating torsional stress (but not exceeding the maximum figure specified by the engine manufacturer). For each installation it is to be ensured by calculation that the maximum approved nominal alternating torsional stress is not exceeded. See Pt 5, Ch 8, 2 Torsional vibration.

3.8.1 Stress concentration factors (SCF) are to be calculated using the analytical formulae outlined in this Section.

3.8.2 Crankshaft variables to be used in calculating the geometric stress concentrations factors are shown in Table 2.3.1 Crankshaft variables for SCF calculation, their limits of applicability are shown in Table 2.3.2 Crankshaft variable boundaries for analytical SCF calculation.

3.8.3 Where the geometry of the crankshaft is outside the boundaries (see Table 2.3.2 Crankshaft variable boundaries for analytical SCF calculation) of the analytical SCF the calculation method detailed in Chapter 1 and Chapter 4 of the LR Guidance Notes for Calculation of Stress Concentration Factors, Fatigue Enhancement Methods and Evaluation of Fatigue Tests for Crankshafts may be undertaken.

3.8.4 Where reliable experimental measurements and/or calculations are available, which can allow direct assessment of SCF, these can be used. The relevant documents and their analysis are to be submitted for consideration in order to demonstrate their equivalence. This is always to be performed when dimensions are outside the boundaries shown in Table 2.3.2 Crankshaft variable boundaries for analytical SCF calculation.

3.8.5 Chapters 1 and 4 of the LR Guidance Notes for Calculation of Stress Concentration Factors, Fatigue Enhancement Methods and Evaluation of Fatigue Tests for Crankshafts describe how finite element (FE) analyses can be used for the calculation of the SCF. Care needs to be taken to avoid mixing equivalent (von Mises) stresses and principal stresses.

3.9.1 In addition to the alternating bending stresses in fillets (see Pt 5, Ch 2, 3.6 Calculation of bending stresses 3.6.8) further bending stresses due to misalignment and bedplate deformation as well as due to axial and bending vibrations are to be considered by applying σ_add as given by Table 2.3.3 Additional bending stresses

3.9.2 It is recommended that a value of ±20 N/mm² be used for the axial vibration component for assessment purposes where axial vibration calculation results of the complete dynamic system (engine/shafting/gearing/propeller) are not available. Where axial vibration calculation results of the complete dynamic system are available, the calculated figures can be used instead.

3.10.1 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 assumptions that bending and torsion stresses are time phased and the corresponding peak values occur at the same location (see Figure 2.3.7 Stress concentration factors in crankshaft fillets). As a result the equivalent alternating stress is to be calculated for the crankpin fillet as well as for the journal fillet by using the von Mises criterion.

3.10.2 At the oil hole outlet, bending and torsion lead to two different stress fields which can be represented by an equivalent principal stress equal to the maximum of principal stress resulting from combination of these two stress fields with the assumption that bending and torsion are time phased (see Figure 2.3.8 Stress concentration factors and stress distribution at the edges of oil drillings).

3.10.3 The above two different ways of equivalent stress evaluation both lead to stresses which can be compared to the same fatigue strength value of crankshaft assessed according to the von Mises criterion.

Where a value of K₁ or K₂ greater than unity is to be applied, details of the manufacturing process are to be submitted. An enhanced K₁ factor will be considered, subject to special approval of the manufacturing specification. See Materials and Qualification Procedures for Ships, Book E, Procedure MQPS 5-2.

3.11.2 The formulae in Pt 5, Ch 2, 3.11 Fatigue strength 3.11.1 are subject to geometry limits. The junction of the oil hole with the crankpin or main journal surface is to be formed with an adequate radius and smooth surface finish down to a minimum depth equal to 1,5 times the oil bore diameter and for calculation purposes R_H, R_G or R_X are to be taken as not less than 2 mm.

3.11.3 Fatigue strength calculations or, alternatively, fatigue test results determined by experiment based either on full size crankthrow (or crankshaft), or on specimens taken from a full size crankthrow, may be required to demonstrate acceptability. The experimental procedure for fatigue evaluation of specimens and fatigue strength of crankshaft assessment are to be submitted for approval by LR. The procedure is to include as a minimum: method, type of specimens, number of specimens (or crankthrows), number of tests, survival probability, and confidence number. See also Chapter 2 of the LR Guidance Notes for the Calculation of Stress Concentration Factors, Fatigue Enhancement Methods and Evaluation of Fatigue Tests for Crankshafts.

3.11.4 When journal diameter is equal or larger than the crankpin diameter, the outlets of main journal oil bores are to be formed in a similar way to the crankpin oil bores, otherwise separate fatigue strength calculations or, alternatively, fatigue test results may be required.

3.11.5 Only surface treatment processes approved by LR are permitted. Guidance for calculation of surface treated fillets and oil bore outlets is presented in Chapter 3 of the LR Guidance Notes for the Calculation of Stress Concentration Factors, Fatigue Enhancement Methods and Evaluation of Fatigue Tests for Crankshafts.

3.13.1 The following formulae are applicable to crankshafts assembled by shrinking main journals into the crankwebs, see also Figure 2.3.6 Crankthrow of semi-built crankshaft.

3.13.2 In general, the radius of transition, R_G, between the main journal diameter, D_G, and the shrink diameter, D_S, is to be not less than 0,015D_G or 0,5(D_S – D_G) where the greater value is to be considered.

3.13.3 Deviations from these parameters will be specially considered.

3.13.5 The actual oversize Z of the shrink fit must be within the limits Z_min and Z_max calculated in accordance Pt 5, Ch 2, 3.13 Shrink fit of semi-built crankshafts 3.13.6 and Pt 5, Ch 2, 3.13 Shrink fit of semi-built crankshafts 3.13.7. When Pt 5, Ch 2, 3.13 Shrink fit of semi-built crankshafts 3.13.4 cannot be complied with, then the calculated values of Z_min and Z_max are not applicable due to multizone-plasticity problems. In such cases Z_min and Z_max are to be established from FEM calculations.

This condition serves to restrict the shrinkage induced mean stress in the fillet.

3.13.8 Reference marks are to be provided on the outer junction of the crankwebs with the journals.