RULES FOR CLASSIFICATION Ships Edition October 2015
Part 3 Hull Chapter 14 Rudders and steering
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DNV GL AS FOREWORD
DNV GL rules for classification contain procedural and technical requirements related to obtaining and retaining a class certificate. The rules represent all requirements adopted by the Society as basis for classification.
© DNV GL AS October 2015
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This is a new document. r u
The rules enter into force 1 January 2016. c
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s e g n a h C
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r e t p a h C
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t r a P
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DNV GL AS s t
CONTENTS n e t n
Changes – current...... 3 o C
Section 1 Rudders, sole pieces and rudder horns...... 6 4
1 General...... 6 1
1.1 Basic assumptions...... 6 r e
1.2 Definitions...... 6 t p
1.3 Documentation requirements...... 7 a
1.4 Certification requirements...... 9 h C
1.5 Design considerations...... 9 3
1.6 Materials...... 10 t 1.7 Equivalence...... 11 r a
2 Rudder force and rudder torque...... 11 P 2.1 Rudder blades without cut-outs...... 11 2.2 Rudder blades with cut-outs (semi-spade rudders)...... 14 3 Rudder strength...... 15 3.1 Strength calculations...... 15 4 Rudder stock and rudder shaft scantlings...... 16 4.1 Rudder stock scantlings...... 16 4.2 Rudder shaft scantlings...... 17 5 Rudder blade...... 18 5.1 Permissible stresses...... 18 5.2 Rudder plating...... 19 5.3 Connections of rudder blade structure with solid parts...... 20 5.4 Single plate rudders...... 22 6 Rudder stock and shaft couplings...... 23 6.1 Connection to steering gear...... 23 6.2 Horizontal flange couplings...... 23 6.3 Vertical flange couplings...... 25 6.4 Cone couplings with key...... 26 6.5 Cone couplings with special arrangements for mounting and dismounting the couplings...... 28 6.6 Rudder shaft couplings...... 31 7 Pintles...... 31 7.1 Scantlings...... 31 7.2 Couplings...... 31 7.3 Dimensions of threads and nuts...... 31
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DNV GL AS 7.4 Pintle housing...... 32 s 8 Rudder stock bearing, rudder shaft bearing and pintle bearing...... 32 t n
8.1 Liners and bushes...... 32 e t
8.2 Minimum bearing surface...... 32 n o 8.3 Bearing dimensions...... 33 C
8.4 Bearing clearances...... 34 9 Strength of sole pieces and of rudder horns...... 34 4 1
9.1 Sole piece...... 34 r e
9.2 Rudder horn...... 35 t 9.3 Rudder trunk...... 37 p a h
Appendix A Guidelines for calculation of bending moment and shear force C distribution...... 39 3
1 General...... 39 t r
2 Spade rudder...... 39 a 2.1 Data for the analysis...... 39 P 2.2 Moments and forces...... 39 3 Spade rudder with trunk...... 40 3.1 Data for the analysis...... 40 3.2 Moments and forces...... 40 4 Rudder supported by sole piece...... 40 4.1 Data for the analysis...... 40 4.2 Moments and forces...... 41 5 Semi spade rudder with one elastic support...... 41 5.1 Data for the analysis...... 41 5.2 Moments and forces...... 42 5.3 Rudder horn...... 42 6 Semi spade rudder with 2-conjugate elastic support...... 43 6.1 Data for the analysis...... 43 6.2 Moments and forces...... 44 6.3 Rudder horn bending moment...... 44 6.4 Rudder horn shear force...... 45 6.5 Rudder horn shear stress calculation...... 45 6.6 Rudder horn bending stress calculation...... 46
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DNV GL AS SECTION 1 RUDDERS, SOLE PIECES AND RUDDER HORNS 1
n o
1 General i t c 1.1 Basic assumptions e S
1.1.1 Vessels shall be provided with means for steering (directional control) of adequate strength and 4 1
suitable design. The means for steering shall be capable of steering the ship at maximum ahead service speed, which shall be demonstrated. r e t
1.1.2 Steering may be achieved by means of rudders, foils, flaps, steerable propellers or jets, yaw control p
ports or side thrusters, differential propulsive thrust, variable geometry of the vessel or its lift system a
components, or by any combination of these devices. h C 1.1.3 Requirements in this section are related to rudder and rudder design. For requirement to steering gear 3 operating the rudder, reference is made to Pt.4 Ch.10 Sec.1. t
If steering is achieved by means of waterjet or thrusters reference is made to Pt.4 Ch.5 Sec.2 and Pt.4 Ch.5 r
Sec.3 respectively. Other means of steering is subject to special consideration. a P 1.1.4 All scantlings requirements given in this chapter are based on gross scantlings, hence the gross scantlings are to be equal or greater than these required gross scantlings.
1.1.5 This chapter applies to ordinary profile rudders, and to some enhanced profile rudders with special arrangements for increasing the rudder force. Rudders not conforming to the profile types included in this chapter will be subject to special consideration.
1.1.6 This chapter applies to rudders made of steel. Rudders made of material different from steel will be subject to special consideration.
1.2 Definitions
1.2.1 Maximum ahead service speed and maximum astern speed shall be specified.
1.2.2 Maximum ahead service speed is the maximum service speed V. See Ch.1 Sec.4 [3.1.8].
1.2.3 Maximum astern speed is the speed which it is estimated the ship can attain at the designed maximum astern power at the deepest seagoing draught.
1.2.4 Some terms used for rudder, rudder stock and supporting structure are shown in Figure 1.
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DNV GL AS 1
n o i t c e S
4 1
r e t p a h C
3
t r a P
Figure 1 Rudders
1.3 Documentation requirements
1.3.1 Documentation shall be submitted as required by Table 1.
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DNV GL AS Table 1 Documentation requirements 1
Object Documentation type Additional description Info n o i
Covering rudders, propeller outlines, actuators, t
stocks, horns, stoppers and bearing lubrication c
Z030 – Arrangement e system. FI
plan S
Including specification of maximum speed ahead and
aft, and Ice Class notation when applicable. 4 1
Mounting and dismounting or rudder (including flaps
Z250 – Procedure FI r as a detached component), rudder stock and pintles. e t Z250 – Procedure Measurement of bearing clearances. FI Rudder arrangement p a Z163 – Maintenance Flap rudders: Hinges, link systems and criteria for FI h manual allowable bearing clearances. C
Non-conventional rudder designs: Torque 3
Z110 – Data sheet characteristics (torque versus rudder angle in FI t
homogeneous water stream). r a
Z265 – Calculation Expected life time of bearings subjected to P AP report1) extraordinary wear rate due to dynamic positioning.
Sole pieces and rudder H050 – Structural AP horns drawing
H050 – Structural Rudder blades Including details of bearings, shafts and pintles. AP drawing
H030 – Detailed Rudder stocks Including details of connections, bolts and keys. AP drawing
Rudder and steering gear H050 – Structural Including fastening arrangements (bolts, chocking AP supporting structures drawing and side stoppers).
1) Only for rudders included under DP-Control documentation, see Pt.6 Ch.3.
AP = For approval; FI = For information; ACO = As carried out; L = Local handling; R = On request; TA = Covered by type approval; VS = Vessel specific
1.3.2 For general requirements to documentation, see Pt.1 Ch.3 Sec.2.
1.3.3 For a full definition of the documentation types, see Pt.1 Ch.3 Sec.3.
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DNV GL AS 1 1.4 Certification requirements n o
1.4.1 Components shall be certified as required by Table 2. i t c
Table 2 Certification requirements e S
Certification Object Certificate type Issued by Additional description 4 standard* 1
Structural parts r e
Shaft t p
Pintles a
MC Society h
Stock C
Rudder
Carrier 3
t
Bolts for flanged couplings r a
Stoppers P MC Manufacturer Bolts, except for flanged couplings
* Unless otherwise specified the certification standard is the Society's rules.
1.4.2 For a definition of the certificate types, see Pt.1 Ch.3 Sec.5.
1.5 Design considerations
1.5.1 Effective means are to be provided for supporting the weight of the rudder without excessive bearing pressure, e.g. by a rudder carrier attached to the upper part of the rudder stock. The hull structure in way of the rudder carrier is to be suitably strengthened.
1.5.2 All rudder bearings shall be accessible for measuring of wear without lifting or dismantling the rudder. Guidance note: In case cover plates are permanently welded to the side plating, it is recommended to arrange peep holes for inspection of securing of nuts and pintles.
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1.5.3 Suitable arrangements are to be provided to prevent the rudder from lifting. The arrangement shall effectively limit vertical movement of rudder in case of extreme (accidental) vertical load on rudder.
1.5.4 Means for draining the rudder completely after pressure testing or possible leakages shall be provided. Drain plugs shall be fitted with efficient packing.
1.5.5 In rudder trunks which are open to the sea, a seal or stuffing box is to be fitted above the deepest load waterline, to prevent water from entering the steering gear compartment and the lubricant from being washed away from the rudder carrier. If the top of the rudder trunk is below the deepest waterline, two separate stuffing boxes are to be provided. Guidance note: One stuffing box with two separate lip seal rings in an acceptable alternative solution.
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DNV GL AS 1.5.6 Vibrations in the rudder structural elements are not considered in relation to the requirements for 1 scantlings given in these rules.
Guidance note: n o
Vibration analysis should be considered for semi-spade rudders. i t
The lowest natural frequencies will normally fall in a frequency span which includes the blade passing frequency of a propeller. c
Particularly a coupled mode where torsion of rudder stock and bending of rudder horn are dominating may result in increased dynamic e
stresses in way of the lower pintle bearing. S
The natural frequencies will mainly depend on the torsion stiffness of the rudder stock, the bending stiffness of the rudder horn and 4 the distance between the centre of gravity of rudder and its rotational axis. The size of the rudder will also govern the frequency 1
range in which these natural modes will fall. It is recommended to keep the lowest fundamental modes of a rudder away from the r blade passing frequency in the full speed range. Normally it may not be possible to keep all the modes above the blade passing e
frequency. Thus it is recommended to apply a method to determine the natural frequencies of a rudder either by means of Finite t
Element Analyses or other reliable methods based on analytical approach/experience p a ---e-n-d---of---g-u-i-d-a-n-c-e---n-o-t-e--- h C 1.5.7 Over-balanced rudders are subject to special consideration with respect to type of steering gear and 3
risk of an unexpected and uncontrolled sudden large movement of rudder causing severe change of ship's pre-set course. See Pt.4 Ch.10 Sec.1 [2.9]. t r
Guidance note: a
A rudder shall be considered over-balanced, when balanced portion exceed 30% in any actual load condition. Special rudder types, P such as flap rudders, are subject to special consideration.
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1.6 Materials
1.6.1 Welded parts of rudders are to be made of approved rolled hull materials.
1.6.2 Material factor k for normal and high tensile steel plating may be taken into account when specified in each individual rule requirement. The material factor k is to be taken as defined in Ch.3 Sec.1 [2.2], unless otherwise specified.
1.6.3 Material grades for plates and sections for rudders, rudder trunks and rudder horns are in general to be selected based on Class II in Ch.3 Sec.1 Table 9. The steel used for the rudder trunk is to be of weldable quality, with a carbon content not exceeding 0.23% on ladle analysis and a carbon equivalent Ceq not exceeding 0.41. Rudder trunks made of materials other than steel are to be specially considered by the Society. For rudder and rudder body plates subjected to stress concentrations, e.g. in way of lower support of semi- spade rudders or at upper part of spade rudders, Class III as given in Ch.3 Sec.1 Table 9 shall be applied.
1.6.4 Rudder stocks, pintles, coupling bolts, keys, rudder horns and rudder members shall be made of rolled, forged or cast carbon manganese or alloy steel in accordance with Pt.2 Ch.2. Guidance note: It is recommended that rudder stocks and pintles are of weldable quality in order to obtain satisfactory weldability for any future repairs by welding in service.
---e-n-d---of---g-u-i-d-a-n-c-e---n-o-t-e--- For rudder stocks, pintles, keys and bolts the minimum yield stress shall not be less than 200 N/mm2.
1.6.5 Nodular cast iron may be accepted in certain parts after special considerations. Materials with minimum specified tensile strength lower than 400 N/mm2 or higher than 900 N/mm2 will normally not be accepted in rudder stocks, shafts or pintles, keys and bolts.
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DNV GL AS Nodular cast iron and cast steel parts for transmission of rudder torque by means of conical connections shall 1 be stress relieved. n 2 1.6.6 For rudder stocks, pintles, keys and bolts the minimum yield stress is not to be less than 200 N/mm . o 2 i The requirements of this chapter are based on a material's yield stress of 235 N/mm . If material is used t having a yield stress differing from 235 N/mm2 the material factor k is to be determined as follows: c e S
4 1
r
e t where: p
2 a
e = 0.75 for ReH > 235 N/mm h = 1.00 for R ≤ 235 N/mm2 e eH C 2 ReH = specified minimum yield stress, in N/mm , of material used, and is not to be taken greater than
2 3
0.7Rm or 450 N/mm , whichever is the smaller value 2 R = specified minimum tensile strength, N/mm , of material used t
m r a P 1.7 Equivalence
1.7.1 The Society may accept alternative calculation methods to those shown in this chapter provided it is demonstrated that the scantling and arrangements are of equivalent or better than those derived using the rule calculation methods.
1.7.2 Direct analyses adopted to justify an alternative design are to take into consideration all relevant modes of failure, on a case by case basis. These failure modes may include, amongst others: yielding, fatigue, buckling and fracture. Possible damages caused by cavitation are also to be considered.
1.7.3 If deemed necessary by the Society, lab tests, or full scale tests may be requested to validate the alternative design approach.
2 Rudder force and rudder torque
2.1 Rudder blades without cut-outs
2.1.1 The rudder force upon which the rudder scantlings are to be based, in N, is to be determined from the following formula:
where:
CR = rudder force A = area of rudder blade, in m2, including area of flap and rudder bulb, if any = vertical projected area of nozzle rudder V = maximum service speed, in knots, as defined in Ch.1 Sec.4 [3.1.8]. When the speed is less than 10 knots, V is to be replaced by the expression:
Vmin = (V + 20) / 3
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DNV GL AS For the astern condition the maximum astern speed is to be used, however, in no case less than: 1
Vastern = 0.5 V n o
K1 = factor depending on the aspect ratio λ of the rudder area i K = (λ + 2) / 3, with λ not to be taken greater than 2 t
1 c = b2 / A ,
λ t e
b = mean height of the rudder area in m. Mean breadth and mean height of rudder are calculated S according to the coordinate system in Figure 2
2 4 At = sum of rudder blade area A and area of rudder post or rudder horn, if any, within the height b in m 1
K2 = coefficient depending on the type of the rudder and the rudder profile according to Table 3 K3 = 0.8 for rudders outside the propeller jet r e
= 1.15 for rudders behind a fixed propeller nozzle t
= 1.0 otherwise p
a h C
3
t r a P
Figure 2 Rudder dimensions
Table 3 Rudder profile type - coefficient
K2 Profile Type Ahead condition Astern condition
NACA-00 series Göttingen
1.10 0.80
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DNV GL AS K 2 1
Profile Type
Ahead condition Astern condition n o Flat side i t
c e 1.10 0.90 S
4
1
r Hollow e
t p
1.35 0.90 a h C
3
High lift rudders t r a
to be specially considered; if not P 1.70 known: 1.30
Fish tail
1.40 0.80
Single plate
1.00 1.00
Mixed profiles (e.g. HSVA) 1.21 0.90
2.1.2 The rudder torque, in Nm, is to be calculated for both the ahead and astern condition according to the formula:
where: r = c (α – k), in m c = mean breadth of rudder area, in m, see Figure 2 α = 0.33 for ahead condition
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DNV GL AS α = 0.66 for astern condition 1 k = Af / A,
Af = portion of the rudder blade area situated ahead of the centre line of the rudder stock, see Figure 3 n o rmin = 0.1c, in m, for ahead condition i t c e
2.2 Rudder blades with cut-outs (semi-spade rudders) S
4 2.2.1 The total rudder force CR is to be calculated according to [2.1.1]. The pressure distribution over the 1 rudder area, upon which the determination of rudder torque and rudder blade strength is to be based, is to be derived as follows: r e t
The rudder area may be divided into two rectangular or trapezoidal parts with areas A1 and A2, so that A = p
A1 + A2 (see Figure 3). a h C
3
t r a P
Figure 3 Rudder area distribution
The levers r1 and r2 are to be determined as follows: r1 = c1 (α – k1) in m r2 = c2 (α – k2) in m where: c1, c2 = mean breadth of partial areas A1, A2 determined, where applicable, in accordance with Figure 2 k1 = A1f / A1, k2 = A2f / A2, A1f = portion of A1 situated ahead of the centre line of the rudder stock A2f = portion of A2 situated ahead of the centre line of the rudder stock α = 0.33 for ahead condition α = 0.66 for astern condition
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DNV GL AS For parts of a rudder behind a fixed structure such as the rudder horn 1
α = 0.25 for ahead condition
α = 0.55 for astern condition n o
The resulting force of each part may be taken as: i t C = CR · A1/A in N R1 c = C · A /A in N CR2 R 2 e
The resulting torque of each part may be taken as: S
QR1 = CR1 r1 in Nm 4 Q = CR2 r2 in Nm
R2 1
The total rudder torque is to be calculated for both the ahead and astern condition according to r
the formula: e t = Q + Q in Nm QR R1 R2 p
For ahead condition QR is not to be taken less than a h C
3
t
r a P 3 Rudder strength
3.1 Strength calculations
3.1.1 The rudder force and resulting rudder torque as given in [2] cause bending moments and shear forces in the rudder body, bending moments and torques in the rudder stock, supporting forces in pintle bearings and rudder stock bearings and bending moments, shear forces and torques in rudder horns and heel pieces. The rudder body is to be stiffened by horizontal and vertical webs enabling it to act as a bending girder.
3.1.2 The bending moments, shear forces and torques as well as the reaction forces are to be determined by a direct calculation or by an approximate simplified method considered appropriate by the Society. For rudders supported by sole pieces or rudder horns these structures are to be included in the calculation model in order to account for the elastic support of the rudder body. Guidelines for calculation of bending moment and shear force distribution are given in App.A.
3.1.3 At and above the upper carrier bearing above neck bearing the bending moment is to be taken as zero, except as follows: — for rotary vane type actuators with two rotor bearings, calculation of bending moment influence may be required if bending deflection in way of upper bearing, based on the design rudder force FR, exceeds two times the diametrical bearing clearances. In lieu of a direct calculation, the deflection of the rudder stock,
in mm, between the rotor bearings, δub may be taken equal to:
4 Ia = moment of inertia of rudder stock in cm . ℓ = ℓb - hf for arrangements with upper pintle bearing. ℓa = ℓb for arrangements with neck bearing. ℓb = distance in m from mid-height of neck bearing or upper pintle bearing, as applicable, to mid-height of upper stock bearing.
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DNV GL AS hf = distance in m from upper end of rudder to mid-height neck bearing. 1
hub = centre distance of the rotor bearings in mm. — the actuator force induced bending moment, in kNm, is to be taken as the greater of the following: n o
i t c e
S
and 4 1
r e t p a = vertical distance between force and bearing centre in m. ha h = net radial force, in kN, on rudder stock in way of actuator corresponding to rudder torque FMTR C MTR, ref. Pt.4 Ch.10. 3
M BU = bending moment, in kNm, at bearing above neck bearing. F = radial force, in kN, induced by actuator at design pressure. t des r a P 4 Rudder stock and rudder shaft scantlings
4.1 Rudder stock scantlings
4.1.1 Rudder stock diameter required for the transmission of the rudder torque The rudder stock diameter required for the transmission of the rudder torque is to be dimensioned such that the torsional stress is not exceeding the following value:
The rudder stock diameter for the transmission of the rudder torque, in mm, is therefore not to be less than:
where:
QR = total rudder torque, in Nm, as calculated in [2.1.2] and/or [2.2]. k = material factor for the rudder stock as given in [1.6.6]
4.1.2 Rudder stock scantlings due to combined loads If the rudder stock is subjected to combined torque and bending, the von Mises stress in the rudder stock is not to exceed 118 / k. k = material factor for the rudder stock as given in [1.6.6]
The von Mises stress, in N/mm2, is to be determined by the formula:
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DNV GL AS 1
n o i
2 3 t Bending stress, in N/mm : σb = 10.2 · M/dc c e 2 3
Torsional stress, in N/mm : τt = 5.10 · QR/dC S
The rudder stock diameter, in mm, is therefore not to be less than: 4 1
r e t p
a M = bending moment, in Nm, at the station of the rudder stock considered, as described in [3]. h C dt = rudder stock diameter for the transmission of the rudder torque, in mm, as defined [4.1.1]. 3
4.1.3 High strength steel t r Before significant reductions in rudder stock diameter due to the application of steels with yield stresses 2 a
exceeding 235 N/mm are granted, the Society may require the evaluation of the rudder stock deformations. P Large deformations of the rudder stock are to be avoided in order to avoid excessive edge pressures in way of bearings. The slope of the stock is to be related to the bearing clearance, see [8.4].
4.1.4 In steering systems with more than one rudder where the torque from one actuator can be transferred to another, for instance by means of a connecting rod, the rudders stock shall not be permanently damaged when exposed to the sum of actuating loads.
4.2 Rudder shaft scantlings
4.2.1 At the lower bearing, the rudder shaft diameter, in mm, shall not be less than:
c =
ℓ, a and b are given in Figure 4, in mm.
The diameter, df in mm, below the coupling flange shall be 10% greater than dℓ. If, however, the rudder shaft is protected by a corrosion-resistant composition above the upper bearing, df may be equal to dℓ.
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DNV GL AS 1
n o i t c e S
4 1
r e t p a h C
3
t r a P
Figure 4 Rudder shaft
5 Rudder blade
5.1 Permissible stresses
5.1.1 The section modulus and the web area of a horizontal section of the rudder blade are to be such that the following stresses, in N/mm2, will not be exceeded: a) In general
(i) bending stress, σb 110 / k
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DNV GL AS (ii) shear stress, 50 / k 1
n o (iii) von Mises stress 120 / k i t c
e S k = material factor for the rudder plating as given in [1.6.2] 4
b) In way of the recess for the rudder horn pintle on semi-spade rudders 1
r (i) bending stress, σb 75 e t (ii) shear stress, 50 p
a h
(iii) von Mises stress 100 C
3
t
Guidance note: r a The stresses in b) apply equally to high tensile and ordinary steels. P
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Guidance note: The permissible stresses are to be understood as nominal stresses, i.e. stress concentrations are not considered.
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5.2 Rudder plating
5.2.1 The thickness of the rudder side, top and bottom plating, in mm, is not to be less than:
where: d = summer loadline draught, in m CR = rudder force, in N, according to [2.1.1] A = rudder area, in m2 = β ; max. 1.0 if b/s ≥ 2.5 s = smallest unsupported width of plating, in m b = greatest unsupported width of plating, in m k = material factor for the rudder plating as given in [1.6.2].
The thickness of the nose plates may be increased to the discretion of the Society. The thickness of web plates is not to be less than the greater of 70% of the rudder side plating thickness and 8 mm.
The rudder plating in way of the solid part, e.g. forged or cast steel, is to be of increased thickness per [5.3.4].
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DNV GL AS 1 5.3 Connections of rudder blade structure with solid parts n o
5.3.1 Solid parts in forged or cast steel, which house the rudder stock or the pintle, are normally to be i t
provided with protrusions. c
These protrusions are not required when the web plate thickness is less than: e S
— 10 mm for web plates welded to the solid part on which the lower pintle of a semi-spade rudder is housed
and for vertical web plates welded to the solid part of the rudder stock coupling of spade rudders 4 1
— 20 mm for other web plates. r e
5.3.2 The solid parts are in general to be connected to the rudder structure by means of two horizontal web t
plates and two vertical web plates. p a
5.3.3 Minimum section modulus of the connection with the rudder stock housing h 3 The section modulus of the cross-section of the structure of the rudder blade, in cm , formed by vertical web C plates and rudder plating, which is connected with the solid part where the rudder stock is housed is to be 3 not less than: t r
a P
where: cS = coefficient, to be taken equal to: 1.0 if there is no opening in the rudder plating or if such openings are closed by a full penetration welded plate 1.5 if there is an opening in the considered cross-section of the rudder dc = rudder stock diameter, in mm HE = vertical distance between the lower edge of the rudder blade and the upper edge of the solid part, in m HX = vertical distance between the considered cross-section and the upper edge of the solid part, in m k = material factor for the rudder blade plating as given in [1.6.2]. ks = material factor for the rudder stock as given in [1.6.6].
The actual section modulus of the cross-section of the structure of the rudder blade is to be calculated with respect to the symmetrical axis of the rudder.
The breadth of the rudder plating, in m, to be considered for the calculation of section modulus is to be not greater than:
where: sV = spacing between the two vertical webs, in m, see Figure 5.
Where openings for access to the rudder stock nut are not closed by a full penetration welded plate, they are to be deducted.
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DNV GL AS 1
n o i t c e S
4 1
r e t p a h C
3
t r a P
Figure 5 Cross-section of the connection between rudder blade structure and rudder stock housing
5.3.4 The thickness of the horizontal web plates connected to the solid parts, in mm, as well as that of the rudder blade plating between these webs, is to be not less than the greater of the following values: tH = 1.2 t tH = 0.045 dS² / sH where: t = defined in [5.2] dS = diameter, in mm, to be taken equal to: dc, as per [4.2], for the solid part housing the rudder stock
dp, as per [7.1], for the solid part housing the pintle sH = spacing between the two horizontal web plates, in mm
The increased thickness of the horizontal webs is to extend fore and aft of the solid part at least to the next vertical web.
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DNV GL AS 5.3.5 The thickness of the vertical web plates welded to the solid part where the rudder stock is housed 1 as well as the thickness of the rudder side plating under this solid part is to be not less than the values obtained, in mm, from Table 4. n o i
Table 4 Thickness of side plating and vertical web plates t c e Thickness of vertical Thickness of rudder plating, in mm S web plates, in mm
Type of rudder 4
Rudder blade Rudder blade Rudder blade 1
Area with opening without opening with opening without opening r e
Rudder supported by sole piece 1.2 t 1.6 t 1.2 t 1.4 t t p Semi-spade and spade rudders 1.4 t 2.0 t 1.3 t 1.6 t a
t = thickness of the rudder plating, in mm, as defined in [5.2] h C
The increased thickness is to extend below the solid piece at least to the next horizontal web. 3
t r
5.4 Single plate rudders a P
5.4.1 Mainpiece diameter The mainpiece diameter is calculated according to [4.1] and [4.2] respectively. For spade rudders the lower third may taper down to 0.75 times stock diameter.
5.4.2 Blade thickness The blade thickness, in mm, is not to be less than:
where: s = spacing of stiffening arms, in m, not to exceed 1 m; V = speed in knots, see [2.1.1]; k = material factor for the rudder plating as given in [1.6.2].
5.4.3 Arms The thickness of the arms, in mm, is not to be less than the blade thickness:
The section modulus, in cm3, is not to be less than:
where:
C1 = horizontal distance from the aft edge of the rudder to the centreline of the rudder stock, in m k = material factor as given in [1.6.2] or [1.6.6], respectively.
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DNV GL AS 1 6 Rudder stock and shaft couplings n o i 6.1 Connection to steering gear t c e
6.1.1 The connection between rudder stock and steering gear is to be according to Pt.4 Ch.10. S
4 1
r e t p a h ds C
3
t r a P
lt
dt
hn
dg
dn
Figure 6 Cone coupling
6.2 Horizontal flange couplings
6.2.1 The diameter of the coupling bolts, in mm, is not to be less than:
Where: d = stock diameter, taken equal to the greater of the diameters dt or dc according to [4.1] and [4.2], in mm n = total number of bolts, which is not to be less than 6
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DNV GL AS em = mean distance [mm] of the bolt axes from the centre of the bolt system 1 ks = material factor for the stock as given in [1.6.6] kb = material factor for the bolts as given in [1.6.6]. n o i 6.2.2 The thickness of the coupling flanges, in mm, is not to be less than the greater of the following t c
formulae: e S
4 1
r
e t p
a h Where: C
k = material factor for flange as given in [1.6.6] 3
f kb = material factor for the bolts as given in [1.6.6] t db = bolt diameter, in mm, calculated for a number of bolts not exceeding 8. r a P 6.2.3 The thickness of coupling flanges at the root section, in mm, shall not be less than:
kf = material factor for flange. M = bending moment in kNm at coupling. a = mean distance from centre of bolts to the longitudinal centre line of the coupling, in mm. d = diameter of rudder stock for stock flange, breadth of rudder for rudder flange, both in mm. β = factor to be taken from Table 5
Table 5 Table of β
d/a 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
β 1.8 1.5 1.25 1.0 0.8 0.6 0.45 0.35 0.25
β shall not be taken less than 0.25 when d/a is greater than 1.6. kr is determined according to Table 6.
Table 6 Table of kr
kf 0.5 0.4 0.3
kr 70 75 84
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DNV GL AS where: 1
rf = radius of fillet, in mm, not to be taken less than 0.3∙(a – 0.5d). n o Guidance note: i t
The mean distance, in mm, from centre of bolts to the longitudinal centreline of the coupling, a, may in general be taken as: c e S
4 1
r
The mean distance, e, in mm, from the centre of bolts to the centre of the bolt system may in general be taken as: e t p a h C
3
t r a P
n = Number of bolts. yi = Distance, in mm, from the longitudinal centreline of the rudder to the centre of bolt i. xi = Longitudinal distance, in mm, from, e.g. the rudder axis to the centre of bolt i.
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6.2.4 The width of material between the perimeter of the bolt holes and the perimeter of the flange is not to be less than 0.67 db.
6.2.5 Coupling bolts are to be fitted bolts and their nuts are to be locked effectively.
6.2.6 Requirements for welding and design details when the rudder stock is connected to the rudder by horizontal flange coupling are described in Ch.13 Sec.1 [6.1.9].
6.3 Vertical flange couplings
6.3.1 The diameter of the coupling bolts, in mm, is not to be less than
where: d = stock diameter in way of coupling flange, in mm n = total number of bolts, which is not to be less than 8 kb = material factor for bolts as given in [1.6.6] ks = material factor for stock as given in [1.6.6].
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DNV GL AS 6.3.2 The first moment of area of the bolt assembly about the centre of the coupling, in cm3, is to be not 1 less than:
n o i t
c e S
6.3.3 The thickness of the coupling flanges is to be not less than the bolt diameter, and the width of the flange material between the perimeter of the bolt holes and the perimeter of the flange is to be not less than 4
0.67 db. 1
r
6.3.4 Coupling bolts are to be fitted bolts and their nuts are to be locked effectively. e t p a
6.4 Cone couplings with key h C 6.4.1 A rudder stock cone coupling connection without hydraulic arrangement for mounting and dismounting 3
shall not be applied for spade rudders. t r 6.4.2 An effective sealing shall be provided at each end of the cone coupling. a P 6.4.3 Tapered key-fitted (keyed) connections shall be designed to transmit rudder torque in all normal operating conditions by means of friction in order to avoid mutual movements between rudder stock and hub. The key shall be regarded as a securing device.
6.4.4 Tapering and coupling length Cone couplings without hydraulic arrangements for mounting and dismounting the coupling shall have a taper c on diameter of 1:8 - 1:12 where (see Figure 7):
The cone coupling is to be secured by a slugging nut. The nut is to be secured, e.g. by a securing plate.
The cone shapes are to fit exactly. The coupling length ℓ is to be, in general, not less than 1.5d0.
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DNV GL AS 1
n o i t c e S
4 1
r e t p a h C
3
t r a P
Figure 7 Cone coupling with key
6.4.5 Dimensions of key The shear area of the key, in cm2, is not to be less than:
where:
QF = design yield moment of rudder stock, in Nm:
dt = stock diameter, in mm, according to [4.1] k = material factor for stock as given in [1.6.6] d = mean diameter of the conical part of the rudder stock, in mm, at the key k 2 ReH1 = specified minimum yield stress of the key material, in N/mm
Where the actual diameter dta is greater than the calculated diameter dt, the diameter dta is to be used. However, dta applied to the above formula need not be taken greater than 1.145 dt.
The effective surface area, in cm2, of the key (without rounded edges) between key and rudder stock or cone coupling is not to be less than:
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DNV GL AS 1
n o
i t where: c e
2 S ReH2 = specified minimum yield stress of the key, stock or coupling material, in N/mm , whichever is less. 4 1
6.4.6 The dimensions of the slugging nut, in mm, are to be as follows (see Figure 7): r
external thread diameter: dg ≥ 0.65 d0 e t
height: hn ≥ 0.6dg p a
outer diameter: dn ≥ 1.2 du or 1.5 dg, whichever is the greater. h C
6.4.7 Push up 3
It is to be proved that 50% of the design yield moment is solely transmitted by friction in the cone couplings. t
This can be done by calculating the required push-up pressure and push-up length according to [6.5.3] and r a [6.5.4] for a torsional moment Q'F = 0.5QF. P
6.5 Cone couplings with special arrangements for mounting and dismounting the couplings
6.5.1 An effective sealing shall be provided at each end of the cone coupling.
6.5.2 Where the stock diameter exceeds 200 mm, the press fit is recommended to be effected by a hydraulic pressure connection. In such cases the cone is to be more slender, c ≈1:12 to ≈1:20. In case of hydraulic pressure connections the nut is to be effectively secured against the rudder stock or the pintle, see Figure 8. For the safe transmission of the torsional moment by the coupling between rudder stock and rudder body the push-up pressure and the push-up length are to be determined according to [6.5.3] and [6.5.4], respectively.
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DNV GL AS 1
n o i t c e S
4 1
r e t p a h C
3
t r a P
Figure 8 Cone coupling without key
6.5.3 Push up pressure The push-up pressure, in N/mm2, is not to be less than the greater of the two following values:
where:
QF = design yield moment of rudder stock, as defined in [6.4.5], in Nm dm = mean cone diameter in mm ℓ = cone length in mm µ0 = frictional coefficient, equal to 0.15 Mb = bending moment in the cone coupling (e.g. in case of spade rudders), in Nm
It has to be proved by the designer that the push-up pressure does not exceed the permissible surface pressure in the cone. The permissible surface pressure, in N/mm², is to be determined by the following formula:
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DNV GL AS 1
n o i
t c where: e S
2
ReH = specified minimum yield stress of the material of the gudgeon in N/mm 4
α = dm / da 1
dm = diameter, in mm r da = outer diameter of the gudgeon to be not less than 1.5 dm, in mm e t p
6.5.4 Push-up length a
The push-up length, in mm, is to comply with the following formula: h C
3
t r a
where: P
Rtm = mean roughness, in mm, taken equal to 0.01 c = taper on diameter according to [6.5.2].
Notwithstanding the above, the push up length is not to be less than 2 mm. Guidance note: Note: In case of hydraulic pressure connections the required push-up force, in N, for the cone may be determined by the following formula:
The value 0.02 is a reference for the friction coefficient using oil pressure. It varies and depends on the mechanical treatment and roughness of the details to be fixed. Where due to the fitting procedure a partial push-up effect caused by the rudder weight is given, this may be taken into account when fixing the required push-up length, subject to approval by the Society.
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DNV GL AS 1 6.6 Rudder shaft couplings n o
6.6.1 The cone coupling at the lower end of the rudder shaft shall be as required in [6.4] or [6.5], using i t
relevant parameters for the shaft instead of the stock in the formulas. c e
6.6.2 The vertical coupling at the upper end of the rudder shaft shall be as required in [6.3], using relevant S parameters for the shaft instead of the stock in the formulas. 4 1
7 Pintles r e t p
7.1 Scantlings a h
7.1.1 The pintle diameter, in mm, is not to be less than: C
3
t r a
P where:
B = relevant bearing force, in N kp = material factor for pintle as given in [1.6.6].
7.2 Couplings
7.2.1 Tapering Pintles are to have a conical attachment to the gudgeons with a taper on diameter not greater than: 1:8 - 1:12 for keyed and other manually assembled pintles applying locking by slugging nut, 1:12 - 1:20 on diameter for pintles mounted with oil injection and hydraulic nut.
7.2.2 Push-up pressure for pintle bearings The required push-up pressure for pintle bearings, in N/mm², is to be determined by the following formula:
where:
B1 = supporting force in the pintle bearing, in N d0 = pintle diameter, in mm.
The push up length is to be calculated similarly as in [6.5.4], using required push-up pressure and properties for the pintle bearing.
7.3 Dimensions of threads and nuts
7.3.1 The minimum dimensions of threads and nuts are to be determined according to [6.4.6].
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DNV GL AS 1 7.4 Pintle housing n o
7.4.1 Length i t
The length of the pintle housing in the gudgeon is not to be less than the pintle diameter Dp. Dp is to be c measured on the outside of liners. e S
The thickness of the pintle housing is not to be less than 0.25 Dp. 4
7.4.2 Thickness 1
The thickness of the pintle housing is not to be less than 0.25 Dp. r e t
8 Rudder stock bearing, rudder shaft bearing and pintle bearing p a h C
8.1 Liners and bushes 3
8.1.1 Rudder stock bearing t Liners and bushes are to be fitted in way of bearings. The minimum thickness of liners and bushes is to be r equal to: a P
— tmin = 8 mm for metallic materials and synthetic material
— tmin = 22 mm for lignum material. The difference in hardness of bushing and liners shall not be less than 65 Brinell. 13% Chromium steel shall be avoided. The bushing shall be effectively secured to the bearing. Guidance note: Bushing fitted by means of shrink fitting alone is not considered effectively secured. Additional physical stoppers need to be arranged to prevent the bushing from accidentally rotating or shifting in vertical direction.
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8.1.2 Pintle bearing The thickness of any liner or bush, in mm, is neither to be less than:
where:
B = relevant bearing force, in N nor than the minimum thickness defined in [8.1.1].
8.2 Minimum bearing surface
8.2.1 An adequate lubrication is to be provided.
2 The bearing surface Ab (defined as the projected area: length · outer diameter of liner), in mm , is not to be less than:
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DNV GL AS 1
n o
where: i t
F = reaction force, in N, in bearing as determined in [3.1]. For ram type actuator, F for the upper c bearing shall be calculated considering reaction force induced by one ram e
2 S pa = allowable surface pressure, in N/mm , according to Table 4. 4 1
The maximum surface pressure pa for the various combinations is to be taken as listed in Table 4. Higher values than given in the table may be taken in accordance with makers’ specifications if they are verified by r e
tests: t p
Table 7 Maximum surface pressure pa a h
2 C
Bearing material pa [N/mm ] 3
Lignum vitae 2.5 t r White metal, oil lubricated 4.5 a
Synthetic material with hardness between 60 and 70 Shore D1) 5.52) P
Steel3) and bronze and hot-pressed bronze-graphite materials 7.0
Notes: 1) Indentation hardness test at 23°C and with 50 % moisture, are to be carried out according to a recognized standard. Synthetic bearing materials are to be of an approved type. 2) Surface pressures exceeding 5.5 N/mm2 may be accepted in accordance with bearing manufacturer's specification and tests, but in no case more than 10 N/mm2. 3) Stainless and wear-resistant steel in an approved combination with stock liner.
8.3 Bearing dimensions
8.3.1 The length/diameter ratio of the bearing surface is not to be greater than 1.2.
The bearing length ℓp of the pintle, in mm, is to be such that
where:
Dp = actual pintle diameter measured on the outside of liners, in mm.
Bearing arrangements with a height of the bearing greater than above, may be accepted based on direct calculations provided by the designer showing acceptable clearances at the upper and lower edges of the bearing.
8.3.2 The thickness, in mm, of bearing material outside of the bushing shall not be less than: For balanced rudder or semi-spade rudders:
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DNV GL AS 1
n
o i
For spade rudders: t c
e S
4
1
Smaller thickness may be accepted based on direct analysis. r e t
8.4 Bearing clearances p a h 8.4.1 With metal bearings, clearances in mm shall not be less than db / 1000 + 1.0 on the diameter. If non- C metallic bearing material is applied, the bearing clearance is to be specially determined considering the material’s swelling and thermal expansion properties. This clearance is not to be taken less than 1.5 mm on 3
bearing diameter unless a smaller clearance is supported by the manufacturer’s recommendation and there is t documented evidence of satisfactory service history with a reduced clearance. r a P 9 Strength of sole pieces and of rudder horns
9.1 Sole piece
9.1.1 Section modulus and sectional area
Figure 9 Sole piece
Referring to Figure 9, the section modulus around the vertical (z)-axis, in cm3, is not to be less than:
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DNV GL AS The section modulus around the transverse (y)-axis, in cm3, is not to be less than: 1
n o i t c
e
2 S
The sectional area, in mm , is not to be less than: 4
1
r e t
p a
where: h C k = material factor as given in [1.6.2] or [1.6.6] respectively. 3
9.1.2 von Mises stress t 2 r
At no section within the length ℓ50 is the von Mises stress to exceed 115 / k. The von Mises stress, in N/mm , a is to be determined by the following formula: P
where:
2 σb = Mb / Zz(x) in N/mm 2 τ = B1 / As in N/mm Mb = bending moment at the section considered in Nm Mb = B1 x in Nm Mbmax = B1 ℓ50 in Nm B1 = supporting force in the pintle bearing in N, normally B1 = CR / 2 k = material factor as given in [1.6.2] or [1.6.6], respectively.
9.1.3 The sole piece shall be sloped in order to avoid pressure from keel blocks when docking. The sole piece shall extend forward of the after edge of the propeller boss, for sufficient number of frame spaces to provide adequate fixation at the connection with deep floors of the aft ship structure. The cross section of this extended part may be gradually reduced to the cross section necessary for an efficient connection to the plate keel.
9.2 Rudder horn
9.2.1 Rudder horn The bending moments and shear forces are to be determined by a direct calculation or in line with the guidelines given in App.A [5] and App.A [6] for semi spade rudder with one elastic support and semi spade rudder with 2-conjugate elastic support respectively.
The section modulus around the horizontal x-axis, in cm3, is not to be less than:
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DNV GL AS 1
n
o i where: t c
Mb = bending moment at the section considered in Nm. e S
2
The shear stress, in N/mm , is not to be larger than: 4 1
r e t
p a where: h C
k = material factor as given in [1.6.2] or [1.6.6], respectively. 3
t
9.2.2 von Mises stress r At no section within the height of the rudder horn is the von Mises stress to exceed 120 / k N/mm2. The von a P Mises stress, in N/mm2, is to be calculated by the following formula:
where:
2 σb = Mb / Zx in N/mm 2 τ = B1 / Ah in N/mm
B = supporting force in the pintle bearing in [N] 1 2 Ah = effective shear area of rudder horn in y-direction in [mm ]; 3 2 τT = MT 10 / (2 AT th) in N/mm
M = torsional moment in [Nm]; T 2 AT = area in the horizontal section enclosed by the rudder horn in [mm ]; th = plate thickness of rudder horn in [mm];
9.2.3 Rudder horn plating The thickness of the rudder horn side plating, in mm, is not to be less than:
where:
L = rule length as defined in Ch.1 Sec.4 Table 2 k = material factor as given in [1.6.2] or [1.6.6], respectively.
9.2.4 Connection to hull structure
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DNV GL AS The rudder horn plating is to be effectively connected to the aft ship structure, e.g. by connecting the plating 1 to side shell and transverse/longitudinal girders, in order to achieve a proper transmission of forces, see
Figure 10. n o
When the connection between the rudder horn and the hull structure is designed as a curved transition into i the hull plating, special consideration is to be given to the effectiveness of the rudder horn plate in bending t c and to the stresses in the transverse web plates. e
Brackets or stringer are to be fitted internally in horn, in line with outside shell plate, as shown in Figure 10. S
4 1
r e t p a h C
3
t r a P
Figure 10 Connection of rudder horn to aft ship structure
Transverse webs of the rudder horn are to be led into the hull up to the next deck in a sufficient number and must be of adequate thickness. Strengthened plate floors are to be fitted in line with the transverse webs in order to achieve a sufficient connection with the hull. The centre line bulkhead (wash-bulkhead) in the after peak is to be connected to the rudder horn. Scallops are to be avoided in way of the connection between transverse webs and shell plating.
9.2.5 Requirements for welding of rudder horns are described in Ch.13 Sec.1 [6.1.3].
9.3 Rudder trunk
9.3.1 Scantlings The requirement applies to both trunk configurations, extending below stern frame or not.
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DNV GL AS Where the rudder stock is arranged in a trunk in such a way that the trunk is stressed by forces due to 1 rudder action, the scantlings of the trunk are to be such that: n
— the von Mises stress due to bending and shear does not exceed 0.35 ReH, o i
— the bending stress, in N/mm2, in welded rudder trunk is to be in compliance with the following formula: t c
σ ≤ 80 / k e S
with: 4
σ = bending stress in the rudder trunk, as defined in [9.3.1] 1
k = material factor for the rudder trunk as given in [1.6.2] or [1.6.6] respectively, not to be taken less r
than 0.7 e
2 t ReH = specified minimum yield stress, in N/mm , of the material used. p a
For calculation of bending stress, the span to be considered is the distance between the mid-height of the h
lower rudder stock bearing and the point where the trunk is clamped into the shell or the bottom of the skeg. C
3
9.3.2 Requirements for welding of rudder trunks are described in Ch.13 Sec.1 [6.1.8]. t r a P
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DNV GL AS APPENDIX A GUIDELINES FOR CALCULATION OF BENDING MOMENT A AND SHEAR FORCE DISTRIBUTION x i d
1 General n e
The evaluation of bending moments, shear forces and support forces for the system rudder – rudder stock p
may be carried out for some basic rudder types as outlined in [2] – [6]. p A
2 Spade rudder 4 1
r e
2.1 Data for the analysis t
ℓ10 - ℓ30 = lengths of the individual girders of the system in m p 4 a I10 – I30 = moments of inertia of these girders in cm h C
Load of rudder body, in kN/m: 3
3 PR = CR / (ℓ10 10 ) t r a P 2.2 Moments and forces The moments, in Nm, and forces, in N, may be determined by the following formulae:
Mb = CR (ℓ20 + (ℓ10 (2 c1 + c2) / 3 (c1 + c2))) B3 = Mb / ℓ30 B2 = CR + B3
Figure 1 Spade rudder
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DNV GL AS A 3 Spade rudder with trunk x i d
3.1 Data for the analysis n e = lengths of the individual girders of the system in m ℓ - ℓ p 10 30 4
I10 – I30 = moments of inertia of these girders in cm p A Load of rudder body, in kN/m: 4
3 1 PR = CR / ((ℓ10+ ℓ20)10 ) r e t
3.2 Moments and forces p a
For spade rudders with rudders trunks the moments, in Nm, and forces, in N, may be determined by the h
following formulae: C
3
MRis the greatest of the following values: t r
MR = CR2 (ℓ10 – CG2Z) a
MR = CR1 (CG1Z– ℓ10) P where:
CR1 = Rudder force over the rudder blade area A1 CR2 = Rudder force over the rudder blade area A2 CR1Z = Vertical position of the centre of gravity of the rudder blade area A1 CG2Z = Vertical position of the centre of gravity of the rudder blade area A2 MB = CR2 (ℓ10 – CG2Z) B3 = (MB+ MCR1) / (ℓ20 + ℓ30) B2 = CR+ B3
Figure 2 Spade rudder with trunk.
4 Rudder supported by sole piece
4.1 Data for the analysis
ℓ10 - ℓ50 = lengths of the individual girders of the system in m
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DNV GL AS 4 I10 – I50 = moments of inertia of these girders in cm A
x
For rudders supported by a sole piece the length ℓ20 is the distance between lower edge of rudder body and i
centre of sole piece and I20 the moment of inertia of the pintle in the sole piece. d
4 n I50 = moment of inertia of sole piece around the z-axis in cm e ℓ50 = effective length of sole piece in m p p A
Load of rudder body, in kN/m:
3 4
PR = CR / (ℓ10 10 ) 1
Z = spring constant of support in the sole piece, in kN/m: r 3 = 6.18 · I50 / ℓ50 e Z t p a
4.2 Moments and forces h C
Moments and shear forces are indicated in Figure 3. 3
t r a P
Figure 3 Rudder with neck bearing and sole piece.
5 Semi spade rudder with one elastic support
5.1 Data for the analysis ℓ - ℓ = lengths of the individual girders of the system in m 10 50 4 I10 – I50 = moments of inertia of these girders in cm Z = spring constant of support in the rudder horn, in kN/m: Z = 1 / (fb + ft) for the support in the rudder horn, see Figure 4 = unit displacement of rudder horn, in m, due to a unit force of 1 kN acting in the centre of support 3 fb = 1.3 d / (6.18 In) in m/kN (guidance value) 4 In = moment of inertia of rudder horn around the x-axis, in cm , (see also Figure 4) ft = unit displacement due to torsion ft = in m/kN
Rules for classification: Ships — DNVGL-RU-SHIP-Pt3Ch14. Edition October 2015 Page 41 Rudders and steering
DNV GL AS 2 FT = mean sectional area of rudder horn in m ] A ui = breadth, in mm, of the individual plates forming the mean horn sectional area t = thickness within the individual breadth ui in mm x i i
d = Height of the rudder horn, in m, defined in Figure 4. This value is measured downwards from d
the upper rudder horn end, at the point of curvature transition, to the mid-line of the lower n
rudder horn pintle e e = distance, in m, as defined in Figure 5 p p A
Load of rudder body, in kN/m:
3 4
PR10 = CR2 / (ℓ10 · 10 ) 1 = C / (ℓ · 103) PR20 R1 10 r e t for CR, CR1, CR2, see [3]. p a 5.2 Moments and forces h C
Moments and shear forces are indicated in Figure 4. 3
t r
5.3 Rudder horn a P Referring to Figure 5, the loads on the rudder horn are as follows:
Mb = bending moment in Nm = min(B1z; B1d) Q = shear force in N = B1 MT(z) = torsional moment in Nm = B1 e(z)
An approximation for B1, in N, is
B1 = CRb / (ℓ20 + ℓ30).
Figure 4 Semi-spade rudder.
Rules for classification: Ships — DNVGL-RU-SHIP-Pt3Ch14. Edition October 2015 Page 42 Rudders and steering
DNV GL AS
A
x i d n e p p A
4 1
r e
Figure 5 Rudder horn. t p a
6 Semi spade rudder with 2-conjugate elastic support h C
3
6.1 Data for the analysis t = rudder horn compliance constants calculated for rudder horn with 2-conjugate elastic r K11, K22, K12 a
supports (Figure 6). The 2-conjugate elastic supports are defined in terms of horizontal P displacements, yi, by the following equations: — at the lower rudder horn bearing: y1 = - K12B2- K22B1 — at the upper rudder horn bearing: y2 = - K11B2- K12B1 where: y1, y2 = horizontal displacements, in m, at the lower and upper rudder horn bearings, respectively B1, B2 = horizontal support forces, in kN, at the lower and upper rudder horn bearings, respectively K11, K22, K12 = obtained, in m/kN, from the following formulae:
d = height of the rudder horn, in m, defined in Figure 6. This value is measured downwards from the upper rudder horn end, at the point of curvature transition, to the mid-line of the lower rudder horn pintle λ = length, in m, as defined in Figure 6. This length is measured downwards from the upper rudder horn end, at the point of curvature transition, to the mid-line of the upper rudder
Rules for classification: Ships — DNVGL-RU-SHIP-Pt3Ch14. Edition October 2015 Page 43 Rudders and steering
DNV GL AS horn bearing. For λ = 0, the above formulae converge to those of spring constant Z for a A
rudder horn with 1-elastic support, and assuming a hollow cross section for this part e = rudder-horn torsion lever, in m, as defined in Figure 6 (value taken at z = d/2) x i = moment of inertia of rudder horn about the x axis, in m4, for the region above the upper I1h d rudder horn bearing. Note that I is an average value over the length ℓ (see Figure 6) 1h n 4
I2h = moment of inertia of rudder horn about the x axis, in m , for the region between the upper e
and lower rudder horn bearings. Note that I2his an average value over the length d - λ p
(see Figure 6) p
= torsional stiffness factor of the rudder horn, in m4 A Ith 4 1
For any thin wall closed section: r e t p
FT = mean of areas enclosed by outer and inner boundaries of the thin walled section of rudder a horn, in m2 h C ui = length, in mm, of the individual plates forming the mean horn sectional area ti = thickness, in mm, of the individual plates mentioned above. 3
t r Note that the Ithvalue is taken as an average value, valid over the rudder horn height. a P Load of rudder body, in kN/m:
3 PR10 = CR2 / (ℓ10 · 10 ) 3 PR20 = CR1 / (ℓ-10 · 10 ) for CR, CR1, CR2, see [3.2].
6.2 Moments and forces Moments and shear forces are indicated in Figure 6.
6.3 Rudder horn bending moment The bending moment acting on the generic section of the rudder horn is to be obtained, in Nm, from the following formulae:
— between the lower and upper supports provided by the rudder horn:
MH= FA1z — above the rudder horn upper-support:
MH= FA1z + FA2 (z - dlu) where:
FA1 = support force at the rudder horn lower-support, in N, to be obtained according to Figure 6, and taken equal to B1 FA2 = support force at the rudder horn upper-support, in N, to be obtained according to Figure 6, and taken equal to B2 z = distance, in m, defined in Figure 7, to be taken less than the distance d, in m, defined in the same figure
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DNV GL AS dlu = distance, in m, between the rudder-horn lower and upper bearings (according to Figure 6, dlu= d - A
λ). x i d
6.4 Rudder horn shear force n e The shear force Q acting on the generic section of the rudder horn is to be obtained, in N, from the following H p
formulae: p A — between the lower and upper rudder horn bearings: 4 1
QH= FA1 r
— above the rudder horn upper-bearing: e t p QH= FA1 + FA2 a where: h C
FA1, FA2 = support forces, in N. 3
t
The torque acting on the generic section of the rudder horn is to be obtained, in Nm, from the following r formulae: a P — between the lower and upper rudder horn bearings:
MT= FA1e(z) — above the rudder horn upper-bearing:
MT= FA1e(z) + FA2e(z) where:
FA1, FA2 = support forces, in N. e(z) = torsion lever, in m, defined in Figure 7.
6.5 Rudder horn shear stress calculation For a generic section of the rudder horn, located between its lower and upper bearings, the following stresses are to be calculated:
2 — τS = shear stress, in N/mm , to be obtained from the following formula:
2 — τT = torsional stress, in N/mm , to be obtained for hollow rudder horn from the following formula:
Rules for classification: Ships — DNVGL-RU-SHIP-Pt3Ch14. Edition October 2015 Page 45 Rudders and steering
DNV GL AS For solid rudder horn, τT is to be considered by the Society on a case by case basis. A
For a generic section of the rudder horn, located in the region above its upper bearing, the following stresses x i are to be calculated: d n 2 — τS = shear stress, in N/mm , to be obtained from the following formula: e
p p A
4
1 2 — τT = torsional stress, in N/mm , to be obtained for hollow rudder horn from the following formula: r e
t p a h C
3
For solid rudder horn, τT is to be considered by the Society on a case by case basis where: t r
F , F = support forces, in N a A1 A2 2 AH = effective shear sectional area of the rudder horn, in mm , in y-direction P MT = torque, in Nm FT = mean of areas enclosed by outer and inner boundaries of the thin walled section of rudder horn, in m2 tH = plate thickness of rudder horn, in mm. For a given cross section of the rudder horn, the maximum value of τT is obtained at the minimum value of tH.
6.6 Rudder horn bending stress calculation For the generic section of the rudder horn within the length d, the following stresses are to be calculated:
2 — σB = bending stress, in N/mm , to be obtained from the following formula:
where:
M = bending moment at the section considered, in Nm H 3 WX = section modulus, in cm , around the x-axis (see Figure 7).
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DNV GL AS A
x i d n e p p A
4 1
r e t p a h C
3
t r a P
Figure 6 Semi-spade rudder with 2-conjugate elastic support.
Figure 7 Rudder horn.
Rules for classification: Ships — DNVGL-RU-SHIP-Pt3Ch14. Edition October 2015 Page 47 Rudders and steering
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