EP2045183A1

EP2045183A1 - Surface-piercing propeller propulsion system and boat integrating such a propulsion system

Info

Publication number: EP2045183A1
Application number: EP07425620A
Authority: EP
Inventors: Luca Andreassi; Daniele Coloccini; Antonio Ricci; Giuseppe Vairo
Original assignee: Tms Srl
Current assignee: Tms Srl
Priority date: 2007-10-05
Filing date: 2007-10-05
Publication date: 2009-04-08

Abstract

A surface-piercing propeller propulsion system for propelling a boat (100), comprising a drive apparatus apt to engage to the transom (101) of the boat (100); the drive apparatus comprising a spherical group (50), apt to be anchored to the transom (101); and a propeller shaft (1), apt to be driven by a driving group of the boat (100); wherein the spherical group (50) is apt to carry out a twin function of: element for supporting and moving the propeller shaft (1); and element for protecting and waterproofing the drive apparatus and/or the driving group; the configuration of the spherical group (50) being such as to allow the rotation of the propeller shaft about at least one axis, orthogonal to the propeller shaft (1), passing through the ideal center of the spherical group (50).

Description

The present invention refers to a propeller propulsion system, and more specifically to a surface-piercing propeller propulsion system, with particular reference to the drive apparatus comprised by such a propulsion system.
The present invention is useful in the production of propulsion systems for crafts, with particular reference to the market of propulsion systems specifically studied for new-generation pleasure crafts, however optionally adaptable to any boat typology.
Surface-piercing propellers are commonly positioned so as to let pass through the hub of the propeller itself the so-called "waterline", or the line identifying the free surface of the water flow, relatively flat and even, exiting the bottom edge of the transom of the craft when the latter is sailing and assumes an operative configuration.
Therefore, in their revolving motion the blades are found partly inside and partly outside water, continuously entering therein and exiting therefrom, therefore piercing the water-air interface twice per each rotation.
This is one of those cases in which a discontinuous physical process can, under certain conditions, be definitely more efficient than its continuous counterpart.
Hereinafter, it will be expounded by virtue of which phenomena surface-piercing propellers are more efficient than fully submerged ones.
As it is universally known, in the field of experimental fluid dynamics dimensionless parameters are often resorted to for the characterization of physical processes intended to be investigated. Surface-piercing propellers do not elude this rule. The scientific literature currently available on the subject tells us that two are the fundamental parameters that may be utilized to describe their operation: the thrust coefficient K_T (or its equivalent referred to the torque K_Q) and the advance coefficient J. Hereinafter, we report one of the possible definitions for K_T, K_Q and J: $K_{T} = T_{M} / {ρn}^{2} D^{4}$
$K_{Q} = Q_{M} / {ρn}^{2} D^{5}$
$J = V_{A} / nD$

where T_M and Q_M are respectively the mean values of thrust and absorbed torque, V_A is the theoretical speed of advance of the propeller, ρ is the density of the medium in which the propeller is operating, n is the rotation speed in rpm and D is the diameter of the blades.
By reporting on a graph the value of K (or of K_Q) as a function of J, what is obtained are three main operation areas: a "Partially-Ventilated Regime", a "Transition Regime" and a "Fully-Ventilated Regime".
Moreover, inside of each area further subdivisions may be effected, briefly described as follows:
For J values such as to make K_T (or K_Q) vanish, the operation mode of the propeller is referred to as Base-Ventilated Regime.
In this operation stage the amount of air entrained underwater by the blades during their motion is rather modest, and it remains concentrated in the trailing edge zone. Therefore, in this type of regime, blades remain almost fully submerged during their transit in water, since air bubbles are unable to "follow" them, save from a short initial length. The phenomenon is quite similar to cavitation in conventional propellers, with the substantial difference that this time gaseous cavities are directly connected to the atmosphere.
As may be found in Fig. 3, as J decreases, there ensues the actual Partially-Ventilated Regime: both propulsion thrust and suction on the back side of the propellers grow, the suction tending to entrain an ever greater amount of air under the free water surface. The cavities are still basically thickening near to the trailing edge, but some streaks succeed to propagate in depth.
A further reduction of J leads to the so-called "Transition Regime", in which the air-filled cavities become markedly unstable. The back side of the blades continuously passes from a fully wetted to a completely dry condition, passing through the intermediate stage in which streaks appear.
This operation mode extends over a rather narrow belt of J values, inside which it is not possible to univocally determine K_T and K_Q, as they depend just on the conditions in which the back of the blades lies, conditions that as mentioned above vary in a random manner.
Upon overcoming the transition, the blades start to operate constantly under a complete ventilation condition and the entrained air volume becomes inversely proportional to the value of J. From now on, the pattern of K_T and K_Q totally differs from that of a traditional propeller as thrust does not depend anymore from suction (in fact, on the back of the blades there is only air connected with the atmosphere), but mainly from the pressure field on the blade surface.
Moreover, the increasing thickness of the air layer enhances the interaction between one blade and the other one, generating a "waterfall effect" that tends to decrease the values of K_T and K_Q.
This operation area may be divided into three parts, in order of decreasing J: a first zone, simply referred to as fully-ventilated, in which the K_T/Q decrease rate is not very high; a second zone, where the so-called inflow retardation phenomenon appears: air bubbles become so extended as to interrupt in some spots the interblade water flow, generating a brisk drop of K_T/Q; a third and last zone, at extremely low J values, in which air requirements of the cavities cannot be met anymore and therefore the pressure therein becomes lower than the atmospheric one: the result is a reversal in the trend of K_T and K_Q, which in some cases may even lead to a new increase thereof.
Depending on the type of use of the craft on which it is meant to be mounted, a surface-piercing propeller may achieve performances markedly superior with respect to the other more widespread propulsion systems, with particular reference to submerged propellers.
The main strongpoints of the surface-piercing propellers lie in: reducing the hydrodynamic drag; eliminating the cavitation phenomenon; offering the option of varying the degree of submersion of the blades; and in the optimum performances offered also in shallow water sailing.
Referring to the first of the above-mentioned advantages, it has to be pointed out that driving shafts, propeller hubs, optional bottoms, are all elements that, when submerged, contribute to generate drag to the advance and therefore to reduce the propulsive efficiency.
The use of a surface-piercing propeller allows to greatly reduce the amount of such a drag, as the submerged component merely consists of the rudder and a certain fraction of propeller diameter (that, as it will be apparent hereinafter, may vary casewise). The effects of such an advantage are felt above all at high speeds (over 40-50 knots), when the propulsive efficiency of the surface-piercing propellers greatly exceeds that of their conventional counterparts, as well as that of water jets.
It is said that a propeller begins cavitating when, on the low-pressure side of the blades, saturation drops below the value for those given water temperature conditions: as a result, vapour pockets form which hinder the interblade water flow, causing a loss of efficiency. However, the most negative effect of such pockets is had when they, by migrating to higher-pressure zones, implode near the blade surface, impinging thereon with a local stress that can be likened to a strong impact. The propeller, continuously impinged upon by these impacts, begins to erode, taking on the typical "pitted" shape and losing part of its functionality.
Cavitation is a rather common phenomenon in traditional submerged propellers, constituting one of the main factors restricting their field of use.
In the case of surface-piercing propellers, the situation assumes an advantageously different shape: in fact, therein the back of the blades is constantly ventilated, thus there is no formation of vapour pockets, which instead are replaced by the hereto-mentioned air-filled cavities.
The latter never implode, as air filling them can at most be compressed, yet, unlike vapour, it certainly cannot change its state. Accordingly, despite the flow on a blade in a ventilated regime may at first sight seem quite alike that on a supercavitating blade, use of a surface-piercing propeller eliminates the near-totality of effects of vibration, surface erosion and underwater acoustic emissions (a problem deeply felt in the military field) linked to the cavitation phenomenon.
Referring to the third one of the above-mentioned advantages of the surface-piercing propellers with respect to the submerged ones and generally to the most widespread propulsion systems, it has to be observed that, when a surface-piercing propeller is coupled with a revolving shaft drive, who controls the craft has the option of varying the degree of submersion of the blades (sometimes even while sailing): this type of intervention can be compared with the expediency of varying the diameter in the case of a submerged propeller, thereby satisfying a wide range of different operative conditions. Moreover, in case the drive allows rotations also on the horizontal plane, by using this ability in combination with the rudder there can be had a marked increase of steering (maneuvering) abilities at high speeds.
Finally, the very nature of surface-piercing propellers yields optimum performances in shallow waters: compared with other systems used under scanty draught conditions (in particular, water jets) the former provide a superior propulsive efficiency at any point of sailing. Moreover, the optional use of revolving drives allows, when necessary, to come onto shore with no risk whatsoever of damaging the propeller.
However, in front of said advantages with respect to more traditional propulsion systems, currently known surface-piercing propellers entail drawbacks limiting their use and spreading.
A crucial difficulty is the tightness of the driving members upstream of the surface-piercing propeller, said members being the components of greater interest to the ends of a good operation of the propulsion system at issue here.
Evidently, the ultimate aim of the propeller-drive pair is to achieve, above all in terms of thrust provided - both in an absolute sense and depending on the torque absorbed with respect to that available at the hub - the design specifications
Contrarily to what might be surmised, at high speeds the propulsion systems based on surface-piercing propellers generally vibrate much less than submerged propeller systems.
This peculiar feature is mainly due to two reasons: first of all, to the near-complete suppression of the cavitation phenomenon, which has already been discussed hereto; and then to the relatively unperturbed flow that is generated beneath the transom at working speed.
However, vibration-related problems can occur anyhow.
Despite the fact that the flow in which surface-piercing propellers operate may be considered remarkably "smoother" with respect to that surrounding, on average, the submerged propellers, their very operation mode, with the continuous entering and exiting of the blades into and from the water, generates a cyclic variation of the overall resultants of the actions between fluid and structure, variation which will be all the more marked the smaller the number of the same blades.
In fact, the unavoidable eccentricity of the center of thrust, due to the merely partial submersion of the blades, leads to the onset of a vertical force component F_V, a horizontal component F_H and bending moments M_H and M_V, respectively lying on the plane parallel to the waterline and on that perpendicular thereto.
From this perspective, it is particularly important to avoid, in the first instance, the drawback of a misalignment between driving shaft and propeller shaft.
In variable-geometry systems, to date the use of a double cardan joint in the connection between the driving shaft and the propeller shaft cannot be left out of consideration. However, as it is known from cardan joint theory, for a double cardan joint to be actually considered homokinetic, or apt to transmit a rotary motion in a regular manner, with neither accelerations nor decelerations, some geometrical conditions have to be met.
First of all, the angles formed by the intermediate element with the driving shaft and with the driven shaft should be approximately the same, so as to compensate for the angular acceleration generated by the first individual joint with an analogous acceleration in the opposite sense generated by the second individual joint. Moreover, said two angles should never exceed 15°, though as a general rule it is suggested anyhow not to go beyond 8-10° (in such a case the maximum overall tilt between driving shaft and driven shaft would be assessable in the order of 20°) and to contain deviation between one angle and the other one within the range of 0.5°.
It may happen, e.g. owing to assembling errors or insufficiently accurate machining, that any one of these conditions cease to be met: this leads to the occurrence of remarkably strong dynamic stresses, which, in the best of cases, negatively influence the operation of the entire driveline, while sometimes can even cause its breakage.
Moreover, existing surface-piercing propeller propulsion systems entail further drawbacks hindering a broader use thereof and discouraging a substantial preference to propeller propulsion systems.
The drawbacks of the structural arrangements currently used for the production of propulsion systems having surface-piercing technology relate not merely to the operation, but also the management of the relevant drivelines.
To date, not even the most widely known manufacturers, holding a distinctly predominant position inside the market of propulsion systems for pleasure crafts, really succeeded at overcoming said drawbacks; to date, their most widespread designs of drivelines for surface-piercing propeller propulsion systems still suffer from corresponding faults.
In particular, during steering (maneuvering) and at low-rotation regimes, therefore not at high speeds, known-art surface-piercing propeller propulsion systems nearly always exhibit the following drawbacks:

propellers operate under cross-flow conditions, undergoing a marked drop in performances;
flow misalignment is partly compensated by a fin (skeg) placed under the shaft casing, which however generates an increase in hydrodynamic drag;
a certain slowness occurs in the reaction times of the horizontal moving system, due to the remarkable weight of the structure; and
in the presence of strong wind, steering operations get complicated, to the point of requiring intervention by harbour assistance units.

In addition to the foregoing, from a maintenance standpoint it should be taken into account that:

the twin motion required to the shaft line makes the conventional systems particularly complex, therefore requiring a very detailed and costly maintenance;
the commonly adopted watertight sealing system, though generally avoiding infiltrations into the hull, is however much less safe with regard to the protection of the external spherical joint, operating in an oil bath.

Object of the present invention is to solve said drawbacks, by proposing a surface-piercing propeller propulsion system according to claim 1; such a propulsion system comprising a drive apparatus, and optionally providing a solution of assembly of the rudder relative to the propeller, such as to obtain the utmost simplification of the driveline; optimize alignment between the driving shaft and the propeller shaft; enhance maneuverability and versatility of use, concomitantly ensuring protection of vital parts from water.
Object of the present invention is also to propose a boat according to claim 15, incorporating a propulsion system as defined above, which comprises said drive apparatus and/or adopts said assembling of the rudder with regard to the propeller.
As already mentioned in the introduction, the ultimate object of the design proposed by TMS, in the making of which also the Department of Mechanical Engineering of Tor Vergata University was involved, is to obtain a commercially competitive product capable of providing a valid technical solution to said criticalities, conceived during its design according to two main guidelines providing the utmost simplification of the driveline and the positioning of the rudder into the wake of the propeller.
The guideline of utmost simplification of the driveline entails the advantageous reduction of external movable parts.
This demand is met by the manufacturing of a bearing-block on the transom, advantageously allowing the required moving, yet concomitantly ensuring also the protection of vital parts, such as the cardan joint, from water, with the entailed positive impact on maintenance costs.
The positioning of the rudder into the propeller wake makes necessary the sole vertical moving.
Moreover, it reproduces some of the merits of the traditional submerged-propeller propulsion systems, with reference to a newly found good steering (maneuvering) ability even at low speeds, thanks to the stream that, accelerated by the propeller, impinges upon the rudder allowing it to provide an adequate lateral thrust; and to quick response times, by virtue of the fact that moving only the rudder is much simpler than a horizontal adjustment involving the entire external structure.
In order to comply with the demands of simplification of the mechanical componentry of the drive, and of an anyhow broad versatility thereof, the design advantageously envisages a variable-geometry operation mode, yet with a moving limited to the sole trimming apt to vertically adjust the trim; and with a correctly contained maximum angular excursion.
In particular it is arranged a rotation of at most ±7°, with respect to the direction orthogonal to the transom.
Referring to the installed power, the drive according to the present invention may advantageously be manufactured in three different versions, each corresponding to a given motor vehicle class. Such classes may be defined as follows, in a lower-to-higher power order:

200-600 HP (150-440 KW).
600-900 HP (440-660 KW).
Over 900 HP (Over 660 KW).

The drive apparatus for a surface-piercing propeller propulsion system according to the present invention proposes a simplified structure acting as optimal interface between driving shaft and revolving shaft of the propeller; and a limited componentry enhancing the maintainability thereof.
Thanks to its versatility and simplified configuration, the drive apparatus according to the present invention may be advantageously and inexpensively installed on any commercially available model of boat propelled by surface-piercing propeller, since its installation entails no carrying out of costly and complex modifications onto the original boat structure.
The propulsion system according to the present invention enhances safety, in the sense of protecting its mechanisms from water infiltrations with greater effectiveness than the systems according to the known art.
Therefore, the propulsion system according to the present invention, and the drive apparatus integrated thereby, ensure an increase in safety for the driver and the occupants of the boat on which the apparatus is applied, concomitantly fostering an increase in the life of the overall propulsion system.
Advantageously, the surface-piercing propeller propulsion system obtained according to the present invention allows a simple steering (maneuvering) of said boat, an easy control and an immediate stabilization thereof.
Further advantages, features and operation modes of the present invention will be made apparent in the following detailed description of two embodiments thereof, given by way of example and not for limitative purposes, with reference to the figures of the annexed drawings, wherein:

Fig. 1 is a side view apt to sketch the positioning of a surface-piercing propeller with respect to the waterline;
Fig. 2 comprises two views, front and side, of a detail on the propeller of Fig. 1, in which parameter h_t denotes the submersion depth;
Fig. 3 is a diagram apt to depict the pattern of the thrust and torque coefficients with respect to the advance coefficient for the propeller of Fig. 1;
Fig. 4 is a photo of the submerged portion of the surface-piercing propeller of Fig. 1 under partial ventilation conditions, apt to highlight the annular shape of the ventilated cavities, due to vibrations triggered by the impact of the blades with the water surface;
Fig. 5 is a photo of the detail of a blade of a submerged propeller, in which the destructive effects of cavitation are clearly evident;
Fig. 6 reports a schematization of a variable-geometry surface-piercing propeller, highlighting how motion is adjusted by suitable hydraulic pistons, whereas the connection with the engine occurs by a double cardan joint;
Fig. 7 shows an experimental apparatus for assessing the performances of a surface-piercing propeller and the loads generated thereby, said apparatus comprising in this case, besides the classical dynamometer for measuring thrust and torque, flexure units allowing to measure the transversal (lateral and vertical) forces and the bending moments;
Fig. 8 reports a diagram of the horizontal and vertical forces, and of the bending moments produced by a surface-piercing propeller. In the selected coordinate system, X is the axis of rotation, Y is the horizontal axis, whereas Z is the vertical axis. The thrust and the torque referred to a single blade are denoted by T _B and Q_B, while θ_B is the angular coordinate;
Fig. 9 is a graph showing the pattern of the thrust, with the varying of the angular coordinate θ, in a three-blade propeller with the following parameters set: J=1.2 ; I/D=-0.167 ; (ϕ=0° . The latter is the lateral tilt angle, whereas I/D is the degree of submersion normalized with respect to the propeller diameter: -0.167 corresponds to 33% of the submerged area;
Fig. 10 is a schematization of a double cardan homokinetic joint, in the configuration called "with concurrent axes": there are denoted: the driving shaft by number "1", the driven shaft by "2" and the intermediate shaft by letter "i". Fig. 10 highlights how in order to ensure homokinetism, besides the above-mentioned conditions on the angles it is necessary that the forks of the intermediate element be coplanar;
Fig. 11 illustrates a detail of the end portion of a surface-piercing drive according to the known Arneson technique, in which there may be observed the "skeg", placed before the propeller with the function of assisting the steering action set by the lateral displacement of the propeller itself at high speeds;
Fig. 12 illustrates a detail of a surface-piercing drive according to the known Anderson technique, in which it is clearly evident the elastic cowl (blackcoloured) covering the metal shell in which the spherical joint lies: in spite of the fact that the presence of a set of O-ring type gaskets ensures a good protection of the engine compartment, any cowl rupture (even small ones) can cause a contact between the seawater and the joint, with an entailed irreparable damage on the latter;
Fig. 13 is a three-dimensional isometric perspective view of a preferred embodiment of the drive apparatus according to the present invention;
Fig. 14 is a detail of a sectional view of the drive apparatus of Fig. 13, apt to highlight the components thereof It is also indicated the clearance (in mm) to be left for the adjustment of taper roller bearings;
Fig. 15 is an isometric perspective view of a spherical group in the drive assembly of Fig. 13, in an exploded configuration thereof;
Fig. 16 depicts a flange and a propeller shaft of the drive apparatus of Fig. 13 in an assembled configuration: the fastening is obtained by means of a threaded locking ring, which exerts the tractive force required to keep pressed the one against the other the frustoconical surface of the shaft and the analogous surface present inside the flange;
Fig. 17 depicts the components of Fig. 16, in an exploded configuration thereof. It is highlighted how, when needed, the locking ring is unscrewed and the shaft unthreaded merely by drawing it back, whereas the flange can remain in place, anchored on rolling supports, typically bearings;
Figs. 18a and 18b depict isometric views of a first half-sphere component of the drive of Fig. 13, located on the hull side;
Figs. 19a and 19b depict isometric views of a second half-sphere component of the drive of Fig. 13, located on the propeller side, apt to couple with the half-sphere of Figs. 18a and 18b;
Fig. 20 is an isometric perspective view of a support for oil retainers of the drive of Fig. 13, located on the hull side;
Fig. 21 is an isometric perspective view of a first support for oil retainers of the drive of Fig. 13, located on the propeller side;
Fig. 22 is an isometric perspective view of a second support for oil retainers of the drive of Fig. 13, located on the propeller side;
Figs. 23a and 23b depict isometric views of a first spherical half-housing component of the drive of Fig. 13, apt to house the half-sphere of Fig. 18a and 18b located on the hull side;
Figs. 24a and 24b depict isometric views of a second spherical half-housing component of the drive of Fig. 13, apt to house the half-sphere of Fig. 19a and 19b located on the propeller side;
Fig. 25 is an isometric depiction of the assembly of a bearing block of the drive of Fig. 13;
Fig. 26 is a sectional view of the bearing block of Fig. 25;
Fig. 27 depicts a wooden model of the drive apparatus according to the present invention, supported by a movable structure rising above the propeller shaft of said drive apparatus;
Fig. 27' depicts a metallic strengthening plate, apt to anchor to the transom of a boat the drive apparatus according to the present invention, as well as the movable structure of Fig. 27 apt to support said drive apparatus;
Fig. 28 is a perspective view depicting a viable framework for the movable structure of Fig. 27, apt to highlight the modes by which said structure supports a drive apparatus according to the present invention;
Fig. 29 illustrates the configuration of the movable supporting structure of Fig. 27, coupled to the strengthening and anchoring metallic plate of Fig. 27', at the end of the campaign of numerical analysis of strength conducted to achieve the present invention. It highlights the extension of a top beak of the structure, apt to space the point of attachment of a rudder with respect to the propeller;
Fig. 30 depicts a configuration with two movable supporting structures, of the type of Fig. 27, coupled and connected by means of a steel rod. Such a schematization simulates a preferred configuration for the actual assembling. The advantage of such a choice lies in the option of assembling two contra-rotating propellers, so as to self-balance the lateral stresses produced thereby,
Fig. 31 depicts an assembly in which to the unit of Fig. 29 it is applied a respective drive apparatus according to the present invention;
Fig. 32 depicts an assembly in which to the unit of Fig. 30 it is respectively applied a pair of drive apparatuses according to the present invention;
Fig. 33 is a detail of a sectional view of the drive apparatus of a second embodiment of the propulsion system according to the present invention;
Fig. 34 reports a schematization of the loads produced by a rudder positioned according to the constructive modules adopted for the propulsion system according to the present invention;
Fig. 35 discloses an experimental graph indicative of the propeller tested by INSEAN and containing the patterns of the dimensionless coefficients of torque and thrust (K_Q and K_T) and of the propulsive efficiency (η), with the change of the advance coefficient J. The characteristic data of the propeller are: P/D =1.2 ; I/D = 0.5 (50% of submerged area); ϕ = 0°. Referring to the notation adopted hereto, I/D is the degree of submersion whereas ϕ represents the lateral tilt angle. P/D is instead the propeller pitch/diameter ratio;
Fig. 36 reports a dimensioned drawing, still without machining, of the hull-side end of a propeller shaft designed according to an embodiment of the present invention: the dimensions of the threaded tang intended for the fastening device were decided in favour of safety and so as to have the space required for a locking ring and any anti-unthreading systems. As to the sizes of the frustoconical surface, assuming a 45-mm diameter for the central body of the shaft, we relied on values typically present on suchlike mechanical elements;
Fig. 37 reports a dimensioned drawing, still without machining, of the propeller-side end of a propeller shaft designed according to an embodiment of the present invention. There may be observed a number of teeth of the spline markedly greater than those typical of standard profiles, almost in the same way as a splining system for aeronautical propellers; the cylindrical surface immediately close to the profile, acting as element for centering and redistributing propeller-transmitted loads, so as to preserve the spline from stresses other than the torsional one;
Fig. 38 is a schematization of a propeller shaft, apt to set the orientation of the coordinated axes and the propeller-generated loads;
Fig. 39 is a static diagram of the propeller shaft of Fig. 38 on XZ plane. Point A lies at the spherical hinge, point B on the center line of a support bushing, connected to a support arm. Compatibly with the typology of constraint indicated, there are reported the various reactions and the loads acting on said plane, as well as the rigidity constants of the yielding double pendulum (corresponding to the arm-bushing group), both with respect to horizontal translations (Ko) and to a rotation on XZ (Kϕo). Note the denomination of the reactive torque in B, which was merely denoted by Mo (where "o" stands for horizontal), so as to tell it apart from the applied torque Mx (not present on this plane), corresponding instead to the propeller-generated moment about axis X;
Fig. 40 reports a static diagram of the propeller shaft of Fig. 38 on the YZ plane. The same considerations made for the XZ plane with reference to Fig. 39 hold true, adapted for transposition from a horizontal plane to a vertical one: Mo becomes Mv and Ko, Kϕo become Kv, Kϕv. Of course, the loads and reactions already present in the diagram on XZ have been omitted;
Fig. 41 illustrates the sectioning assumed for the propeller shaft;
Fig. 42 reports the Equivalent Isostatic Structure (E.I.S.) corresponding to the diagram on YZ plane of Fig. 40. Since Mv was designated as unknown hyperstatic value, its denomination was changed to Xv and the sense was (arbitrarily) selected in accord with Mx;
Fig. 43 reports reference subdiagrams for calculating the unknown hyperstatic value according to the Equivalent Isostatic Structure (E.I.S.) of Fig. 42;
Fig. 44 reports graphs indicating the pattern of: the shear; the bending moment; and the torque for the propeller shaft of Fig. 38;
Fig. 45 is a first perspective view of a flange of the drive apparatus according to the present invention, apt to highlight the applying of the virtual rigid part with contact on the sides of the spline, to the ends of the modelization to finished elements;
Fig. 46 is a second perspective view of a flange of the drive apparatus according to the present invention, apt to highlight the application of loads to the ends of the modelization to finished elements;
Fig. 47 depicts a detail of the flange of Fig. 45, on the point in which maximum stress is reached following structural analysis, in terms of Von Mises strains;
Fig. 48 depicts a detail of the flange of Fig. 45, apt to highlight stresses at the shoulder beside the threaded zone following structural analysis, in terms of Von Mises strains. To assess its gradient, the value scale was recalibrated downward, setting a maximum of 20 MPa.;
Fig. 49 reports the dimensioned drawing of a flange as resulting from a structural analysis onto finished elements in the design activity;
Fig. 50 depicts a sectional detail of the bearing-group, highlighting stress concentrations in correspondence of the bottom of the shoulder and of the slots for the O-rings (indicated by red-coloured arrows), following structural analysis, in terms of Von Mises strains;
Fig. 51 reports the dimensioned drawing of a sectional view of the hull-side half-housing as resulting from a structural analysis onto finished elements in the design activity. The detail on the right shows the slots for the O-ring type gaskets;
Fig. 52 reports the dimensioned drawing of a (front and sectional) view of the propeller-side "capping" half-housing. In this case, three are the slots for the O-rings (in fact, on this side there is contact with water), whereas there can be clearly seen, in a sectional view, the curved housings for the insertion of a pair of slidable tabs; aim of said tabs is to fix the position of the sphere at assembling;
Fig. 53 reports the dimensioned drawing of respective sectional views of the hull-side and propeller-side half-housings, as resulting from a structural analysis onto finished elements in the design activity; apt to highlight in the propeller-side half (leftwise) the housings with threaded holes for tightening the tabs mentioned in the preceding figure; and, on both pieces, further threaded holes intended for mounting supports for the oil retainers;
Fig. 54 is a two-dimensional schematization of the spherical contact of the spherical group, or of the sphere-housing set, with discretization of calculation domain to the ends of the thermal modelization onto the finished elements;
Figs. 55 and 56 express the results of the modelization of Fig. 54, in terms of temperature distribution and heat flow; as well as of displacement vectors;
Fig. 57 is a detail of the hull-side half-housing of Fig. 51, in which there are shown, beside some additional dimensions, also the centering and matching tolerances between the two half-housings, and particularly between sphere and housing. Also roughnesses are provided, for surface machining (extremely refined machining is required on the internal spherical surface);
Fig. 58 reports two graphs expressing the pattern of the deformed configuration of the propeller shaft of Fig. 38, on the vertical plane and on the horizontal plane, respectively;
Fig. 59 reports a simplified model of the shaft-supports system of a drive apparatus of the propulsion system according to the present invention, to the ends of a flexural analysis onto the finished elements. Both the case of a perfectly rigid propeller-side support, and that of a yielding support were considered. Of course, the rigidity constants Kv, Kϕv, Ko, Kϕo are the same whose value had already been estimated along the fatigue calculation;
Fig. 60 illustrates viable vibrating modes, in accordance with the simplified model for flexural analysis of Fig. 59, in case of a perfectly rigid bushing;
Figs. 61 to 63 depict analogous diagrams, in which own flexural frequencies (with the related critical speeds of shaft rotation) appear with the change in the mass of the propeller, respectively with regard to the cases of a propeller-side support: perfectly rigid; yielding and referred to the horizontal plane; and yielding and referred to the vertical plane;
Fig. 64 depicts the pattern of the critical torsional frequency with the change in the rotative inertias of propeller and engine, in conformity with a simplified model for the torsional analysis of the shaft-supports-propeller system;
Figs. 65 to 68 show dimensioned drawings of respective views, front side and partially sectional side ones, of a propeller shaft as resulting from a structural analysis onto the finished elements upon completing the design activity. Fig. 65 specifically shows as dimensioned the central section and the frustoconical surfaces. Fig. 66 shows front views of the flange-side (right) and propeller-side (left) splined profiles: the dimensioning of the latter was deliberately left incomplete, so as to allow the manufacturer to effect small adjustments according to the type of hub of the propeller used. Fig. 67 is a side view of the flange-side end. Sizes remain substantially unvaried with respect to what has already been shown in Fig. 36, yet in this case also surface machining specifications and tolerances for coupling to the flange were added. Fig. 68 is a side view of the propeller-side end;
Fig. 69 shows dimensioned drawings of front and side sectional views of a support for hull-side oil retainer as resulting from a structural analysis onto the finished elements upon completing the design activity. It is highlighted the standard-size threaded hole, added to allow the fastening of an oiler assigned to lubrication of the taper roller bearings;
Fig. 70 reports the drawings, of which the first one three-dimensional and the second one dimensioned, respectively of an isometric view and a side view, of a rear locking ring 11, intended for fastening and adjusting the bearings 3, as resulting from a structural analysis onto the finished elements upon completing the design activity; and
Fig. 71 reports the drawings, of which the first one three-dimensional and the second one dimensioned, respectively of an isometric view and a side view, of a tab for the initial positioning of the spheroidal element of the spherical group of a drive apparatus of the propulsion system according to the present invention, as resulting from a structural analysis onto the finished elements upon completing the design activity.

To describe a preferred embodiment of the present invention, hereinafter reference will be made to the above-indicated figures.
A surface-piercing propeller propulsion system according to the present invention, preferably variable-geometry, is suitable for propelling a boat 100.
It comprises a drive apparatus apt to engage to the transom 101 of the boat 100.
As it may be noticed in Fig. 14, the drive apparatus comprises a spherical group 50, apt to be anchored to the transom 101; and a propeller shaft 1, apt to be driven by a driving group of the boat 100.
The spherical group 50 is apt to carry out a twin function of element for supporting and moving the propeller shaft 1; as well as of element for protecting and water-proofing said drive apparatus and/or said driving group.
The configuration of the spherical group 50 is such as to allow the rotation of the propeller shaft 1 about at least one axis, orthogonal to the propeller shaft 1, passing through the ideal center of the spherical group 50.
The drive apparatus comprises sealing systems, external to the spherical group 50, preferably of stationary type, substantially different from the elastic cowls for covering, in use in conventional shipbuilding according to the known art and depicted in Fig. 12.
Such sealing systems, external to the spherical group 50, may comprise rigid supports 6,7,8 for oil retainers.
In fact, one of the pivotal points of the present design is to overcome the drawback of a protection of the entire engine compartment entrusted solely to an external elastic cowl, in all analogous to those used on Arneson systems, as it may be inferred from Fig. 12. Such a drawback is usually due to a constructive misalignment of the means for connecting the drive apparatus with the cardan joint associated to the driving shaft.
Such a misalignment typically forces to keep the end of the axis entering the hull free to rotate on a vertical plane, preventing the adoption of stationary sealing systems of oil retainer type.
More specifically, the spherical group 50 of the surface-piercing propeller propulsion system according to the present invention comprises a spheroidal element splined onto the propeller shaft 1 by means of support bearings 3; and a spheroidal housing apt to house the spheroidal element, shaped so as to reproduce in negative form the shape of the spheroidal element.
The project design of the present invention is preferably such that the ideal center of the spherical group 50 substantially coincides with the center of the spheroidal element, as well as with the center of the spheroidal housing.
With regard to a preferred embodiment of the present invention, the coupling of the spheroidal element with the spheroidal housing is such as to allow rotations about any axis passing through the ideal center of the spherical group 50.
In this case, the spherical group 50 substantially configures as a three-dimensional spherical hinge, in which said spheroidal element preferably comprises two pieces 4,5, made substantially integral.
These two pieces 4,5 may substantially be a first half-sphere 5, splined on the propeller side of the propeller shaft 1; and a second half-sphere 4, splined on the hull side of the propeller shaft 1.
Thus, the assembly is such as to facilitate the introduction of the bearings 3 into the spherical group 50 at the assembling, as well as to facilitate the maintenance steps.
The spheroidal housing preferably comprises two pieces 9,10, made substantially integral.
These two pieces may substantially be respectively a first spheroidal half-housing 10, located on the propeller side and apt to be mounted substantially on the first half-sphere 5; and a second spheroidal half-housing 9, located on the hull side and apt to be anchored to the transom 101 of the boat 100, preferably by engaging the second half-sphere 4.
Thanks to such a structural conception of the drive system of the propulsion system according to the present invention, the spherical group 50 is susceptible of performing an effective tight sealing function, protecting and water-proofing the same mechanisms of the drive apparatus and preventing water from reaching the engine compartment.
To this end, the spherical group 50 preferably provides the interposition of gaskets in an intermediate interface region between the spheroidal element, and therefore the pieces 4,5; and the spheroidal housing, the pieces 9, 10, respectively.
Thus, by interposing gaskets respectively between the pieces 4,5 and the pieces 9,10, it is attained the blocking of any type of infiltration from the outside of the spherical group 50.
As it may be seen in Fig. 33, a second embodiment of the propulsion system according to the present invention provides said spheroidal element to comprise two pieces 4,5^*, made substantially integral.
Said two pieces 4,5^* are respectively a half-sphere 4, substantially splined on the hull side of the propeller shaft 1 and apt to be anchored to the transom 101 of the boat 100; and a substantially cylindrical piece 5^*, splined on the propeller side of the propeller shaft 1.
Preferably, the substantially cylindrical piece 5^* is pivotably connected to the transom 101 by pins 13, e.g. substantially cylindrical.
The configuration is such that the axes of rotation a-a of the substantially cylindrical pins 13 are substantially aligned with the ideal center of the half-sphere 4.
In Figs. 16, 17 and 14 it is highlighted how a drive apparatus of the propulsion system according to the present invention comprises an intermediate connecting flange 2, apt to connect the propeller shaft 1 with a driving shaft of the driving group.
Preferably, said intermediate flange 2 has a length such as to form an interposition element between the propeller shaft 1 itself and the support bearings 3.
Thus, there can be made easier the disassembling of the propeller shaft 1, as well as its drawing out.
The surface-piercing propeller propulsion system according to the present invention further comprises a supporting structure 200, which can be anchored to the transom 101 of the boat 100, apt to support a rudder 22 downstream of the surface-piercing propeller.
Thus, the rudder 22 is positioned into the propeller wake.
Preferably, the surface-piercing propeller propulsion system according to the present invention has a variable geometry.
For this purpose, the supporting structure 200 is apt to support the propeller shaft 1 by a support bushing 23, which can be modelized as a compliant constraint, connected to a support arm 24.
The engagement of such a support bushing 23 with the propeller shaft 1 concomitantly allowing a trimming of the propeller shaft 1, e.g. by means of a trim adjustment piston.
A trimming that can be performed in this manner preferably has an angular excursion comprised in a range of ± 7° with respect to the direction orthogonal to the transom 101, the motions of interest in this case being eminently those apt to obtain the rotation about an axis horizontal with respect to the waterline.
Engagement of drive apparatus to transom 101 of boat 100 is preferably consolidated by interposition of a strengthening plate 103, e.g. metallic, depicted in a viable prototype embodiment thereof in Fig. 27'.
In Figs. 28 and 31 it may be seen how the spherical group 50, as well as the supporting structure 200, are preferably anchored to the transom 101 via the intermediate strengthening plate 103.
Clearly, to construct the spherical group 50 it is preferable the use of materials having a low friction coefficient, e.g. alloys with a high Pb content.
The drawings of components of the propulsion system according to the present invention in the annexed figures are CAD drawings made with the assistance of software Catia V5R14 (Dassault Systemes). This software was also used for volume (and therefore weight) calculation.
In Fig. 15 it is depicted the assembly of the components of the sphere-housing set, in an exploded configuration.
In Fig. 13 it is depicted the assembly of the components of the sphere-housing set, in connection with the propeller shaft 1, in an assembled configuration.
From Fig. 14 it is inferred how, with regard to the preferred embodiment of the present invention disclosed hereto, preferably rolling X-mounted taper roller bearings are used. Moreover, there can be noticed the three supports for the oil retainers, components 7, 8 and 9, the first one from the hull-side and the other two from the propeller side, respectively, for a greater protection against water.
As it may be observed in Fig. 17, the end of the propeller shaft 1 has a configuration with splined profile for better torque transmission.
Specifically, for the dimensioning of said end the Italian standard currently in force was used, i.e. UNI 8953 for straight side profiles.
In accordance with a first attempt, purely indicative, non-limiting and functional to a mere exemplary design, at preliminarily defining the dimensioning of the propeller shaft 1 of the propulsion system according to the present invention, at first there were assumed input data as realistic as possible, based on the following considerations regarding the actual stressing conditions deriving from external loads and the materials to be used (weights are evaluated by assuming for each of the pieces at issue a general metallic material of density equal to that of common steel):

➢ Maximum engine power = P = 900 HP (660 KW)
➢ Rotation regime at which P is expressed = n = 3000 rpm
➢ Reduction ratio = 1/2
➢ Actual rotation regime = n* = n/2 =1500 rpm
➢ Torque = Q = 60P/2πn* = 4200 Nm
➢ Material = stainless steel AISI 630

For P and n values commercial catalogues were relied upon, indicating at 3000 rpm a rotation regime rather usual for naval propellers having a power ranging from 600 to 900 HP, whereas the maximum viable reduction ratio was selected, since, as also indicated by nautical workshops, for pleasure crafts said ratio usually ranges from 1/1.2 to 1/2. As to the material, it is a stainless steel widely used in the shipyard field. Results obtained for the dimensioning of said propeller shaft 1, according to standard, were:

➢ Internal diameter = 62 mm
➢ External diameter = 72 mm
➢ Number of teeth = 10
➢ Minimum useful bearing length = 80 mm

Finally, as a last step, a frustoconical surface (required, together with the tang threaded at the tip, for the axial fastening of the shaft) was added immediately after the splined portion, bringing the maximum diameter to 83 mm.
Then, the other components were defined about the shaft dimensions.
Fig. 17 shows a particularly relevant component, the connecting flange 2.
It is a piece whose configuration was studied together with the Ri.Va workshop to allow the former to carry out its additional task of forming an interposition element between the propeller shaft 1 and the support bearings 3. This allows to have remarkable advantages during maintenance, as making extremely easy the disassembling of the shaft or its pulling out for any repairing steps or a replacement thereof.
The fastening of the flange 2 to the propeller shaft 1 is obtained, e.g., by means of a threaded locking ring, exerting the tractive force required to keep pressed the one against the other the frustoconical surface of the shaft and the corresponding surface inside the flange. In case of need, the locking ring is unscrewed and the shaft unthreaded merely by drawing it back, whereas the flange remains in place, anchored on the rolling supports 13.
As to the type of bearing 3 to be used, we chose to preferably rely on a taper roller configuration, allowing to split on two separate elements the function of absorbing the thrust in the two running senses and also to have a better support with respect, e.g., to a single bearing with a double crown of rollers.
In this first stage it was decided to mount the two elements in an X-like shape, and this made necessary the use of respective different diameters.
For the hull-side bearing a SKF design, mod. 32020X with a 100-mm internal diameter was selected; whereas for the propeller-side bearing an SKF mod. 32019X, with a 95-mm internal diameter was adopted.
As illustrated above in the description of the constructive diagram, it was chosen to divide the spheroidal element into two pieces 4,5, to facilitate introduction of bearings 3 and overall assembling. Figs. 18a and 18b refer to the half 4 positioned on the transom side: there may be discerned the threaded blind holes intended for connection with the other half 5 and those for the fastening of the support for the hull-side oil retainer 7.
Moreover, there may be seen the centering surfaces (centering is carried out with a classical male-female coupling) and the shoulder for the bearing 3, whereas to lighten the whole (and to leave space useful for lubrication) the spherical surface that, limitedly to the specific case, has a 140-mm radius, is truncated along a cylinder plane coaxial with the bearings.
Referring to Figs. 19a and 19b, it is depicted the second half 5 of the spherical element, it also truncated at the same height of the preceding one. Of course, the radius of the remaining portion of spherical surface remains of 140 mm, whereas the centering surface and the shoulder for the bearing are again clearly visible. The main difference with respect to the corresponding hull side is to be traced in the connecting holes, which for the second half 5 are preferably through (in fact, at this preliminary design stage it was provided for the connection to be carried out by means of gripping screws). Instead, there remains a single crown of blind holes on the outside, intended for the concomitant fastening of a pair of supports for oil retainers, protecting from water.
The drawings of the supports for oil retainers 7,8 in Figs. 21 and 22 are a schematization of those that will then be the real supports: a refining thereof is to be provided in the light of the actual number and typology of gaskets to be used in a final design configuration.
Figs. 23a and 23b depict isometric views of a first spherical half-housing 9, apt to provide a housing for the sliding of the spherical element 4 onto the hull-side and intended to act as anchoring element with the transom 101.
Analogously to said half-spheres, there may be noticed the blind holes for connecting with the other spherical half-housing 10, whereas the centering surfaces for the male-female coupling can be discerned. With regard to the present design, there is also an external crown of considerable diameter, preferably in the specific case of at most 440 mm, in which holes were made for bolting to the hull.
Seats for the O-ring gaskets are provided, intended to act as insulation between the engine compartment of the boat 100 and the outside.
Figs. 24a and 24b depict isometric views of the second spherical half-housing 10, apt to house the half-sphere 5 of Fig. 19a and 19b located on the propeller side.
From Fig. 14 it may be noticed how said half-housing gets to assume shapes preferably lighter-weighted with respect to the hull-side portion, as it is free from the task of support element that burdens the latter.
In any case, since it has to be however capable of enduring a rather sizeable thrust when into reverse, concomitantly ensuring compactness to the assembly, the connection between the two halves is provided by means of a rather high number of large-diameter gripping screws.
With regard to the specific case depicted, 8 12-mm screws were used; yet, as it will be apparent hereinafter, such a number may be further increased.
A locking ring 11 for fastening and adjusting the taper roller bearings 3 serves to lock the propeller-side bearing and to adjust the two taper roller elements the one against the other.
Exactly alike the supports for the oil retainers, the locking rings have been depicted in a purely schematic manner, as subject to change in terms of dimensions, constructive shape and, optionally, also arrangement into the assembly, depending on the specific case.
Then, upon ending the preliminary definition of the spherical group 50, a discussion was made on the supporting structure 200 intended to support the propeller shaft 1 and allow the trimming thereof.
The supporting structure 200 proposes to provide a movable structure that rises above the propeller shaft 1; acts as intermediate element between the propeller shaft 1 and an adjustment piston for the trimming; and supports the rudder 22 downstream of the propeller.
A wooden model of the supporting structure 200, from which to take inspiration during the properly called designing, is depicted in Fig. 27.
On the model of the strengthening plate 103 of Fig. 27' there can be seen seats for optional pins, useful for moving the supporting structure 200.
Further object of the present invention is to propose a boat 100 comprising a surface-piercing propeller propulsion system according to one of the claims 1 to 14.
Hereinafter, purely by way of example, there will be detailed the steps carried out at the designing stage for the dimensioning and the structural testing of the components of a specific preferred embodiment of a propulsion system according to the present invention.

Premise

After the initial exploratory stage, widely discussed above, work channelled into a properly called design stage, aimed at prototyping a specific preferred embodiment of the present invention.
Development of such a prototype of the propulsion system according to the present invention was referred to the lowest motor vehicle class.
This operation was aimed at carrying out experimental tests on the propulsion system according to the present invention, in an operative configuration when mounted on a test craft. The following paragraphs include an account of the sequence of steps that led to the achievement of the aim set.

Analysis of external loads

The main sources of external stresses may essentially be traced back to two elements: the rudder 22 and the propeller, in accordance with what is depicted in Fig. 34.
In the first case, it is the hydrodynamic forces created each time a tacking maneuver is performed, and that tend to turn the craft in a sense opposite with respect to that in which the rudder is rotated.
Referring to Fig. 34, said loads could be subdivided into a lateral force FP, acting on a direction orthogonal with respect to the flow impinging on the rudder, a resisting force FR, acting parallelly to the flow, and a torque M, acting on the rudder but obviously affecting also the structure to which it is anchored. To assess FP, FR and M the following relations may be used: $FP = Cp \frac{1}{2} ρ U^{2} Lh$
$FR = Cr \frac{1}{2} ρ U^{2} Lh$
$M = Cm \frac{1}{2} ρ U^{2} - L^{2} - h$
U is the cruising speed of the craft; ρ the density of the medium in which the rudder is submerged (i.e., of water); L the longitudinal extension of the latter and h the submersion depth thereof.
Cp, Cr and Cm are dimensionless coefficients for which, by assuming a tacking angle at most equal to 16°, referring to maximum rotation values generally set for crafts of the typology taken into account, there may be considered dependable the values: $Cp = 1.2$
$Cr = 0.35$
$Cm = 0.4$
To complete the calculation, the characteristic dimensions of the rudder, L and h, were instead assumed equal to 0.15 m and 0.3 m, respectively, whereas a cruising speed of 40 Kts (20.58 m/s) was hypothesized. Finally, by replacing density ρ with a value of 1000 Kg/m³, the following estimate was attained: $FP = 11440 N$
$FR = 3340 N$
$M = 572 Nm$

As to the assessment of propeller-generated forces, given their complexity this task was entrusted to INSEAN, which at the end of the experimentation work performed on a 0.52 m ∅ propeller coupled to a 400 HP engine has sent to the Department the following Table:

400 HP- SOLUTION III
DESIGN DATA
Design engine power	P		400	HP
		294	KW
Ship speed	Vs	36	KN

Motor drive and reduction ratio selection
Engine selected for this power		IFO NEF		400
Power of selected engine	PM	294	KW
Operating rev of selected engine	NM	3000	RPM
Reduction ratio deemed suitable		1.2
Propeller revolutions	n	41.7	Hz
Torque available to hub	Qm=P/(2p1n)	1123	N*m
		115	Kg*m

Propeller selection
Number of blades	Z		5
Diameter	D	0.52	m
Pitch/Diameter ratio	p/D	1.2

Operation parameters of selected propeller
Propeller revolutions	n	41.7	Hz
Speed	v	18.52	m/s
Advance coefficient	J=V/(n*d)	0.855
Thrust coefficient
(from experimental data)	KT	0.063
Torque coefficient
(from experimental data)	10*KQ	0.155
Thrust provided	T-KT(rhon^2*D^4)	832	Kg
Torque absorbed	Q=KQ(rhon^2*D^5)	100	Kg*m

In support of the data reported in the above Table, in Fig. 35 it is attached a complete performance graph of the propeller at issue.

Outline of the design of the supporting structure

To design the supporting structure 200, use of a numerical approach to finished elements became necessary. The software set to this aim was again Catia V5R14 (Dassault Systemes) which besides from the above-mentioned CAD functionality is also equipped with a module dedicated to structural analysis (Catia Generative Structural Analysis). This decision is essentially justified with the need to avoid any conflict in the importing of CAD drawings inside of dedicated FEM programs. Once selected the tool to be used, the next step was clearly that of hypothesizing a geometry compatible with the required characteristics. During design development, the supporting structure underwent drastic evolutions; the first step carried out to define a structure capable of meeting the characteristics sought was that of following the wooden model, proposed by Ri.Va in Fig. 27, of a "laminate" structure: This type of structure soon encountered remarkable manufacturing difficulties, by reason of machining costs; owing to the fact that specific machineries are needed to make a sheet metal integrating the required curvature; and to the fact that, by not responding well to stresses generated by propeller and rudder 22, it however needs reinforcements applied in an attempt to distribute loads more uniformly.
Hence, eventually a supporting structure 200 having reticular beam constructive modes according to the annexed Figs. 28 and 29 was opted for.
The ultimate aim sought was to ensure strength to applied loads, always keeping under control the weight factor and therefore seeking to optimize use of construction material.
Weight saving is evident: compared to the preceding case, and referring to the sole supporting structure 200, we have a weight reduction in the neighbourhood of 90 kg. Hereinafter we report the main procedure that led to the current result.
As to the starting dimensions to be used in the simulation, a 700-750 mm distance between the axis of the hypothetical cylindrical pins and the center line of the bushing was assumed, so as to have an overall length (from the transom 101 to the end tip of the propeller shaft 1) of about 1 m, compatibly with the dimensions of the surface-piercing drives already existing for these power classes.
As regards the support bushing 23, the length, equal to 150 mm, was obtained from catalogue, as this type of component, which can be likened to an actual rolling bearing provided with a self-lubricating internal coating, is present on the market in an array of standard lengths and internal diameters.
The internal diameter was obviously left as an unknown quantity, depending on the definite diameter of the propeller shaft 1 (initially a 50-mm value was adopted). By using this data as a starting point, a battery of numerical simulations was carried out, which allowed the gradual optimizing of the number, diameter and arrangement of the tubular elements forming the reticular beam, as well as the defining of the overall geometry of the supporting structure 200, comprehensive of strengthening plate 103 for connecting to the hull. The results were obtained by using as input data the above-determined loads generated by the rudder 22, suitably increased by safety factors taking into account the remaining external stresses.
There may be noticed, with respect to the initial version, two side plates 104 for connecting to the strengthening plate 103, spaced of 424 mm therebetween, which have become necessary for the strengthening of the assembly with respect to lateral stresses; and the lengthening of the top "beak" of the supporting structure, so as to set farther the point of attachment of the rudder with respect to the propeller.
Estimated weight, when the material is AISI 630 steel, is of 45-50 Kg, plate 103 excluded.

Propeller shaft dimensioning

Upon obtaining dimensions and configuration of the supporting structure, we turned to the theoretical calculation of the propeller shaft , based on Italian standards UNI 8953 and UNI 7670, containing respectively indications for the dimensioning of cylindrical splined profiles with straight sides and fatigue-stressed axes or shafts. In the case of UNI 7670, given the high number of coefficients into play, an Excel worksheet was used.

Splined profiles

The first step to determining the diameter of the propeller shaft 1 was the torsion calculation of the flange-side end 2, which, as already observed hereto, should be provided with a splined profile and a frustoconical fastening surface. First of all, it was defined the minimum internal diameter of the splined profile, obtained via a simple strength relation based on V. Mises' hypothesis.
The starting data was of course the reference absorbed torque Q, present inside of the experimental table provided by INSEAN; while as material the above-mentioned one was selected (AISI 630 austenitic stainless steel, a high Cr (15-17%) alloy with relatively limited percentages of Ni (3-5%), widely used and appreciated in the shipyard field for its high corrosion strength, but also for its excellent features of structural strength.
Hereinafter we report the main mechanical features of the material and the short calculation procedure. Table 1 Strength properties of AISI 630 steel

AlSl 630 Data

Type Stainless steel

R (Mpa) 930

S (Mpa) 725

σ_d-1 (Mpa) 465

$τ_{o} = \frac{0.577 S}{x} = 278 MPa$
$d_{\min} = \sqrt[3]{\frac{16 Q}{π τ_{o}}} = 27 mm$
$d_{eff} = 32 mm$

where τo is the maximum admissible tangential stress, deriving from V. Mises' hypothesis and from the assumption of a safety coefficient x equal to 1.5 (standard value for static problems). Taking as starting data the minimum diameter d, we chose, in the wide support battery, an effective diameter deff, capable of guaranteeing a margin on torsional strength of about 40%. For an internal diameter equal to deff, the remaining geometrical parameters of the splined profile obtained from the wide support battery are: D = 40 mm (external diameter), Z = 10 (number of teeth). Then, we turned to the defining of the minimum useful length of the splined profile so as to have the latter transmit all of the torque with which the shaft is loaded (a condition this actually not occurring, as an anyhow non-negligible fraction of the torque is transmitted by means of the frustoconical surface for axial fastening). Performed calculations yielded the ratio: $l / d = 0.456$

from which it is obtained: $l_{\min} = 15 mm$
However, since the standard suggests to keep the l/d ratio in a range of from 1.5 to 2.5 (for a better distribution of the load acting on the teeth), by assuming an intermediate value equal to about 2 a final definition of the effective useful length of the splined profile was achieved, i.e.: $l = 62 mm$
By exploiting this data, the geometry of the entire tip of the hull-side propeller shaft 1 was obtained.
For its dimensions and configuration, reference can be made to Fig. 36.
Concerning the propeller-side end of the shaft 1, no actual dimensioning could be carried out, since the hubs of propellers on the market are not shaped according to the standard. However, by keeping unvaried the external and internal diameters of the splined profile, the following parameters were defined: l = 36 mm; Z = 25. For the geometry of the entire end, reference is made to Fig. 36.

Static diagram, reference system and load applying

The first step to applying the standard UNI 7670 was the defining of a likely static diagram, a coordinate system and, consequently, the sense and point of application of the propeller-generated loads. Clearly, to solve this issue we had to act with the dimensions and the geometry of the supporting structure 200; in particular, for the reference triad and the sense of the loads, the orientation reported in Fig. 38 was selected.
What is shown in Fig. 38 ensues from the following considerations: 1) origin of the reference system positioned in what ideally would be the center of the spherical group 50, singled out by the intersection between the axis of the holes on the connecting plates and the central axis of the shaft 1; 2) direction Z coincident with the axis of symmetry of the shaft 1 and oriented toward the propeller (X and Y directed accordingly); 3) load-applying senses obtained according to the operation mode of surface-piercing propellers. As to the static diagram, it was decided to adopt a beam-like configuration, bearing on the one side on a three-dimensional spherical hinge (the center of the spherical group or bearing block) and on the other side on a double pendulum, it also three-dimensional, placed in the center line of the support bushing 23 and considered as elastically yielding both in the vertical plane YZ and in the horizontal one XZ. This second assumption ensues from the impossibility to neglect the axial extension of said bushing 23, which may be recalled as preferably being of 150 mm, and allowing the support element to oppose both translations (vertical and horizontal) and rotations (in the vertical plane YZ and in the horizontal one XZ). In Figs. 39 and 40 it is reported the modelization diagram, resolved in planes XZ and YZ for simplicity's sake in the depiction.
Instead, as to the length of the propeller shaft 1, it was split into three pieces according to the criterion illustrated in Fig. 41.
The most significant lengths from the standpoint of strength calculation are the distance between the hinge and the yielding support L2 and the distance between said support and the point of application of the propeller-generated loads, i.e, L3. The first one of these two lengths is automatically set by the dimensions of the supporting structure, leading us to consider it as equal to 725 mm, whereas for determining L3 it was set that the constant-section central length (the diameter of which had temporarily been assumed as equal to 45 mm, following the dimensioning of the ends with splined profiles) would continue for other 17 mm (suggested minimum value is of 15 mm) beyond the bushing, before the frustoconical surface thereof would reduce its dimensions. Starting from this consideration, it was then hypothesized that the point of application of the loads would be located midway of the length comprising the frustum of cone, the cylindrical surface and the splined profile, i.e. roughly in the center line of the hub of the of the splined propeller: on the basis of this, a value of 140.5 mm was obtained for L3. At this stage, no attention was paid to the defining of the section L1, comprising all that precedes the center of the spherical group and that may be obtained only upon having ended the dimensioning of the remaining components forming part of it.

Calculation of stress reactions and characteristics

To complete this step, there had to be resolved the two diagrams in planes XZ and YZ of Figs. 39 and 40, both once hyperstatic. The approach adopted was that based on the Method of Forces, with respect to which the reactive pairs Mo and Mv were selected as hyperstatic unknown values. Hereinafter we report a brief account of the resolving procedure, concerning the sole vertical diagram (in fact, conceptually there is no difference whatsoever between the two diagrams):
Referring to Fig. 42, where it is reported the Equivalent Isostatic Structure (E.I.S.) corresponding to the diagram of Fig. 39, first of all an adequate congruence condition was set on rotation in point B: $φ_{BV} = {φ_{BV}}^{(0)} + X_{V} {φ_{BV}}^{(1)} = - \frac{X_{V}}{K_{φV}}$

where apexes "0" and "1" refer to the subdiagrams reported in Fig. 43, of reference for the calculation of the unknown hyperstatic value.
Then, to calculate the numerical value of Xv (and of its analog value Xo on the horizontal plane) an assessment of rigidity constants Kv, Kϕv, Ko and Kϕo was necessary. For this purpose, it was decided to exploit the potentialities of the G.S.A. module present in the Catia V5R14 software, by performing a few simple static tests on two coupled twin structures, as shown in Fig. 30, obtaining the values: $K_{v} = 2.0 \cdot 10^{7} N / m$
$K_{o} = 3.33 \cdot 10^{7} N / m$
$K_{φv} = 1.41 \cdot 10^{6} Nm / rad$
$K_{φvo} = 1.50 \cdot 10^{6} Nm / rad$
Finally, upon ending the calculation procedures in the two planes (horizontal and vertical), there were obtained the values (signs are to be construed as with respect to a positive left-to-right sense, as shown in Fig. 43: $Xv = - 776 Nm = - 776000 Mmm$
$Xo = 400 Nm = 400000 Mmm$
Once known Xv and Xo, it was possible to turn to the determining of reactions deriving from applied loads, obtaining the results reported in Tables 2 and 3. Table 2 Propeller-generated loads. For numerical values, the following criteria were followed: 1) T,Q directly provided by INSEAN for the 400-HP configuration and 1/1.2 reduction ratio; 2) Fx, Fy calculated as a function of T, using notable ratios suggested by INSEAN (Fx = 0.17T; Fy = 3Fx); 3) Mx value calculated by setting the center of thrust at a distance equal to 0.6R, where R is the radius of the reference propeller considered; 4) My value calculated as a function of Mx: for this purpose, it was used the article in which the Mx/My ratio is equal to about 8 (i.e., substantially the torque Mx is almost one order of magnitude greater than My).

Loads

Q (Nmm) 1060000

T (N) -8320

Fx (N) 1414.4

Fy (N) 4243.2

Mx (Nmm) 1297920

My (Nmm) 164835.8

Table 3 Constraining reactions.

Reactions

YZ XZ

Ha (N) 8320 Ha (N) 8320

Ray (N) 100.4741 Rax (N) -51.37116

Rby (N) -4343.67 Rbx (N) -1363.029
The immediately subsequent step was instead that of calculating the three main characteristics of stress (shear, bending moment and torque) onsetting in the various sections of the propeller shaft 1 as a consequence of the loads and reactions. As to torque, it has to be pointed out that it is deemed constant, of modulus equal to Q and acting along the entire length of the shaft: substantially, it was assumed that two torques applied in self-balance would act at the two ends. In Fig. 44 there are reported in graphic form the patterns of said characteristics with the change of coordinate Z, starting from point A (values are to be construed as overall and in module, as deriving from the sum of what is obtained in the horizontal and vertical planes):

Fatigue testing according to UNI 7670.

Once collected the required data, a fatigue calculation was performed according to the Italian standard in force on the matter; with respect thereto, however, some specially devised considerations were made (in particular on the corrective coefficients of the limit stress). The procedure followed may synthetically be expressed as follows: $σ_{d} = \frac{σ_{d - 1} \cdot K_{k}}{K_{d} K_{c} K_{I} K_{f}}$
$σ_{ok} = \frac{σ_{d} K_{R} K_{I}}{γ_{k} γ_{sic}}$
$τ_{ok} = \frac{0.577 S}{x}$
Strength condition: $(\frac{σ}{σ_{ok}})^{2} + (\frac{τ}{τ_{ok}})^{2} < 1.1$
For clarity's sake, it is reported the meaning of all symbols used in the above expressions, starting from those dedicated to stresses:

➢ σ _ok = maximum admissible normal stress. It is calculated by means of the fatigue limit stress σd-1 (which is an intrinsic mechanical property of the material, usually equal to 0.5 times the breaking load), suitably rescaled by means of a set of coefficients;
➢ τ _ok = maximum admissible tangential stress. Unlike σ_o _k, it is determined by purely static considerations, deriving from the relation already shown in the torsion calculation of the splined profiles. This is so since in a slender beam (in fact, in our case the diameter/free deflection length ratio is well above 1/10) shear-deriving stresses can be neglected, therefore the sole tangential stresses present will be those from torsion that, apart from fluctuations in the torque by which they are caused, can be considered static;
➢ σ= maximum normal stress actually acting. It is calculated in some sections deemed "critical", on the basis of the bending moment and the normal strain present therein;
➢ τ= maximum tangential stress actually acting. It is calculated in "critical" sections, on the basis of torque. In general, also shear contribution should be added - yet, in this case it is not considered due to the reasons disclosed hereto;
➢ S = yield point. It is the intrinsic characteristic that, along with the breaking load R and the fatigue limit σd-1 defines the strength properties of the material used.

Coefficients:

➢ Kd = pejorative coefficient. Used to assess the diminution in strength of the material with the increase in dimensions of the element considered. Usually its influence is not considered and therefore its value can be set as equal to 1 (as was done in our case as well);
➢ Kc = pejorative coefficient. Depends on the corrosion strength of the material used: the values in UNI 7670 are excessively severe to be applicable to a case like ours, since diagrams in the standard refer to steels without a specific corrosion strength ability, whereas the material we took as reference, i.e. stainless steel AISI 630, has been expressly contrived to work in highly corrosive saline environments, such as seawater. To solve the problem, we carried out a comparison (breaking loads under standard conditions being equal) between the characteristics of a stainless steel analogous to our one and those of a high-strength Ni steel, which we deemed indicative of materials diagrammed on the standard, obtaining as a result a corrosion strength in seawater about 4.5-fold in favour of AISI 630. Having divided Kc of the standard (equal to about 5 for the breaking load considered) by ameliorative factor 4.5 we reached the actual coefficient to be used in the calculations, which was set equal to 1.15;
➢ K_I = pejorative coefficient. Depends on the surface finishing condition at the critical section considered. We assumed, rather conservatively, a general planing, equivalent to a value of 1.1;
➢ Kf = pejorative coefficient. Constitutes the extension of the stress concentration factor to cases of fatigue strength. Theoretically, in the section considered by us there should be no sensible variations in shape, yet, given the nearness of the propeller-side splined profile, Kf was prudentially set equal to 1.3 (mean value found in the diameter-varying zone of the splined profile following some FEM tests with bending and tensile stresses, performed with the GSA module);
➢ Kk = ameliorative or ininfluent coefficient. Constitutes the factor for adjusting the load cycle with respect to the reference alternate-symmetrical cycle: since the latter is also the more demanding cycle, the coefficient will always be greater than or at most equal to 1, depending on the load cycle actually present in the critical sections considered;
➢ K_T = pejorative or ininfluent coefficient. Used to adjust the stress typology with respect to the reference one, which is bending. In our case the dominant stress is just the bending, therefore the coefficient was again set equal to 1;
➢ Kn = life coefficient. May be ameliorative, pejorative or ininfluent. Has the purpose of considering the number of cycles needed to reach the required life, using as reference the so-called "fatigue knee" (slope change of the fatigue curve of the material), conventionally set at 2.000.000 cycles. In our case it was selected a number of cycles corresponding to 250 hours of continuous operation at 2500 rpm (reduction ratio 1:1.2 with respect to the 3000 rpm of the engine): as this number proved to be greater than 2.000.000, the coefficient assumed a value lower than 1;
➢ γ _k = pejorative coefficient (safety coefficient). Its expression depends on the exponent of the fatigue curve of the material, in turn depending on the reference stress σ _d (the expression of which was introduced at the beginning of the paragraph) and on the intrinsic characteristics of the material (R and S);
➢ (γ _sic ) = fictitious safety coefficient. Initially introduced for additional safety, yet, given the anyhow conservative character of the other coefficients in the standard, in the end it was decided to assign it an unitary value.

This said, there remains to be indicated the sole critical section selected. It is:

➢ Section 1 = section corresponding to the point of application of the loads: it is a section belonging to the cylindrical surface close to the splined profile of Fig. 37, and it is that in which there are the greater stresses and where the resisting area is the smaller viable one.

The Tables below resume the values of the coefficients, stresses and results of the test:

Table 4 Coefficients and reference stresses for fatigue calculation

Data for fatigue calculation (Section 1)
d (mm)	42
x	1.5
Kd	1
Kf	1.3
Kc	1.15
Ki	1.1
Norm. strain	0
σmax (Mpa)	179.8765636
σmin (Mpa)	-179.8765636
k	-1
Kk	1
K_T	1
N (cycles)	3.80E+07
Kn	0.730631819
σ _d (Mpa)	282.7607175
c	4.637608875
c'	9.381807024
γk	1.131992552
γsic	1

Table 5 Admissible stresses, actual stresses and test outcome.

Test outcome
σok (Mpa)	182.5047144
τok (Mpa)	278.8833333
σ (Mpa)	179.8765636
τ (Mpa)	72.86653263
Comparison factor	1.1
Obtained value	1.039673506
Result	TESTED!!!

Dimensioning of the spherical group

Upon having set, by and large, the geometry of the propeller shaft 1, evidently we turned to the dimensioning of the main components of the spherical group, or bearing block, starting from the inner component (the flange 2) until getting to the seats. Unlike what was done for the shaft, most of the structural calculations were performed by means of Catia GSA module, owing to the foreseeable lack of adequate theoretical relations for complex-shape elements.

Flange definition

The design drawing of the flange 2 remained essentially the same already illustrated hereto, yet it was adapted for a shaft 1 of markedly smaller dimensions: this yielded a greater thickness in some points, with an entailed advantageous strengthening of the assembly. As already mentioned, to perform a piece strength analysis a modelling to finished elements was resorted to, carried out by Catia; its outcomes are disclosed hereinafter. First of all, it was chosen to use tetrahedral elements, with a parabolic-type shape function, whereas concerning the characterization of the material steel-type elastic properties were opted for (in fact, it is envisaged that the flange be made of AISI 316, a steel having high corrosion strength, yet with mechanical characteristics lower than those of 630). To simulate the presence of the propeller shaft, a virtual rigid part was introduced, depicted in Fig. 45, to which there was assigned the connection with contact property at the sides of the splined profile complementary to that of the shaft end. As it may be noticed in Fig. 46, applied loads were a torque equal to Q and distributed on the face for connecting to the counterflange; and a thrust in the normal direction equal to T and distributed on the internal frustoconical surface. As constraint, an axial blocking in the rear threading zone was opted for, so as to simulate the effect of the locking ring 11 for fastening and adjusting the bearings 3.
Then, a calculation grid was set, imposing an overall dimension of 5 mm for the individual elements, which was suitably thickened at the points deemed critical (contact interface with the virtual part and shoulder close to the threaded surface); then, calculation was launched in static analysis mode, yielding the results disclosed in Figs. 47 and 48.
Dominant stresses in the flange zone are those due to thrust T and torque Q that, being based on mean values, can be deemed constant over time.
As it may easily be noticed, stresses are rather low overall, and also in points potentially more at risk there are values entirely acceptable, when compared with the static limit stress of AISI 316. $σ_{L} = \min (S; 0.7 R)$
$σ_{o} = \frac{σ_{I}}{x}$
$σ_{i} < σ_{o}$

where σi is the maximum ideal stress acting. By setting as usual x = 1.5, it is had, for the material considered by us, the specifications of which are are reported in Table 7: $σ_{o} = 136 MPa$
$σ_{i} = 117 MPa$
Table 6 Analysis - general data.

Analysis Report

Element type Tetrahedral (parabolic)

n. of elements 141561

n. of nodes 202642

Material properties Steel

Estimated error < 3%

Max. nodal stress (MPa) 117

Table 7 Mechanical characteristics of AISI 316.

AISI 316

Type Stainless steel

R (MPa) 515

S (MPa) 205
Moreover, to further support what has been stated above, it may be added that in the zone where higher stresses are found, the latter are very likely overestimated with respect to those actually present, due to non-deformability of the virtual part into contact with the teeth of the splined profile. Finally, to sum up, some report information on the simulation and AISI 316 data are reported, together with the drawing, reported in Fig. 49, of the flange 2 with dimensions thereof.

Selection and testing of rolling taper roller bearings

Procedure used was the standard one suggested by SKF in its general catalogue: once known the dimensions, set by the external dimensions of the flange, and the axially and radially acting loads, there are set a minimum life and an operating temperature (which may be assumed in the neighbourhood of 50°C: we raised the limit to 80°C for higher safety) and it is obtained the minimum viscosity ISO VG that the lubricant intended for the bearings should have in order to ensure the required life. For the results, refer to the following tables:

Table 8 Characteristic parameters of the selected typology of bearing and test assumptions.

Bearing data
Type	SKF 32014 X
De (mm)	110
Di (mm)	70
C (N)	101000
C₀ (N)	153000
Pu (N)	17300
e	0.43
y	1.4
y₀	0.8
m	3.333333333
Fr (N)	112.8452323
Fa (N)	8320

Assumptions
Lh	8000
n (rpm)	2500
Tf (°C)	80

Table 9 Life and static strength tests

Static test
P ₀	6712.422616
Result	TESTED!!!

Determination of a ₁ a _skf
Fa/Fr	73.72930013
P (N)	11693.13809
a ₁ a _skf	0.907570273

Determination of a _skf
a₁	1
a _skf	0,907570273
Dm	90
ν₁ (mm² /s)	10
ηp	0.8
ηp(Pu*/P)	1.18360015
k₂	0.6
ν (mm² /s)	6
ISO grade	VG 32

Notice how, due to extremely low radial loads (see shear value shown in Fig. 44 at A), the life Lh of the bearings is of over 4000 hours, even with a lubricant not having a particularly high viscosity (ISO grade VG 32).

Spherical contact: stress analysis

A critical point in the dimensioning of the bearing block may certainly be singled out in the stress state onsetting during thrust at the interface between spherical surfaces. Theoretically, a very wide and complete treatise is available for the study of such a problem, due to the reknown work by Hertz on contact stresses between various kinds of curved surfaces. In particular, for contact between spherical surfaces it is recalled the formula: $p_{o} = 0.578 \sqrt[3]{\frac{F ({}^{1}{/_{R 1}} \pm {}^{1}{/_{R 2}})^{2}}{Δ^{2}}}$

wherein po is just the maximum pressure from Hertzian squashing, F is the pushing force and R1,R2 are the radii of curvature of the surfaces involved in the phenomena. Parameter Δ instead encompasses the elastic characteristics of the materials of which elements into contact are made, and is expressed by the following relation, in which Young moduli and Poisson coefficients of said materials appear: $Δ = \frac{1 - {v_{1}}^{2}}{E_{1}} + \frac{1 - {v_{2}}^{2}}{E_{2}}$
Finally, it has to be specified that the sign ± refers to the modes by which contact occurs: a positive sign is assumed if surface curvatures are discordant, a negative sign is assumed if they are concordant. Unfortunately, just this latter statement is cause of inapplicability of the Hertzian theory to the above-disclosed problem: in fact, the contact at the sphere-housing interface occurs between surfaces having curvatures practically identical, and concordant therebetween, therefore, a near-nil pressure value would be obtained by using the above-indicated formula. Therefore, the numerical way had to be again resorted to, and for this purpose it was decided to simulate the contact between the half-sphere and the half-housing on the hull side, which are involved during the forward thrust. The type of element used was was once again the tetrahedron, with a parabolic-type shape function, allowing an improved accuracy of calculation (element number being equal) with respect to the tetrahedron with a linear shape function. For the half-housing once again steel AISI 316 was devised, therefore the costituent material thereof was characterized as steel, whereas bronze-type properties were assigned to the half-sphere, as it is envisaged that the latter be made of an aluminium bronze alloy. Bronze-Aluminium alloys (Trade name Bronzal) are highly appreciated in the shipyard field and in that of precision mechanics in general, thanks to the virtues of mechanical strength (far superior than those of a common bronze) and corrosion strength, joining the well-known characteristics of material with a low friction coefficient.
To the interface elements between the spherical surface the hereto-mentioned connection with contact property was assigned, whereas obviously the applied load was the thrust T, distributed over the shoulder intended for blocking the hull-side bearing within the half-sphere 4.
Imposed constraints were a rigid joint on the back of the half-housing (to simulate anchoring to the metallic plate) and a restiction of the translations to the sole axial direction for the half-sphere, so as to prevent undesired relative rotations between the two pieces.
Upon carrying out this, and having suitably configured the calculation grid, calculation in static mode was started, obtaining the results specifically disclosed in Fig. 50.
In this case as well, it may readily be noticed how stresses are really low: in the zones more at risk, i.e., near the slots for the O-ring type gaskets and at the shoulder bottom, on average 20 MPa are not exceeded; whereas the absolute maximum is reached on an isolated node just nearby the slots, it being equal to 33 MPa. Comparison with AISI 316 limit stress may be done by taking the value calculated in the structural analysis of the flange, whereas concerning the half-housing there may be taken as reference the alloy G-Cu Al11 Fe4 Ni4 (denomination UNI 5275), for which it is had : Table 10 Mechanical characteristics of the Bronze-Aluminium alloy.

G-Cu Al11 Fe4 Ni4

Type Bronzal alloy

R (MPa) 650÷750

S (MPa) 300÷400

$σ_{z} = \min (S; 0.7 R)$
$σ_{o} = \frac{σ_{z}}{x}$
$σ_{i} < σ_{o}$
By setting again x = 1.5: $σ_{o} = 200 MPa$
$σ_{i} = 33 Mpa$

To sum up, besides from showing a report analogous to that disclosed for flange analysis and some construction drawings displaying the novel geometry of the sphere-housing set, we should like to emphasize the lack of need of a surface pitting test alike that prescribed for gears: in fact, in this case, unlike what happens in gears, surface loads are low and the relative motion between surfaces occurs at very low speeds, sporadically and almost never under maximum stress conditions.

Table 11 Analysis: general data.

Analysis report
Element type	Tetrahedral (parabolic)
n. of elements	105648
n. of nodes	158753
Material properties	Steel (housing); Bronze (sphere)
Estimated error	< 5%
Max. nodal stress (MPa)	33

Spherical contact: thermal analysis

A second particularly significant point, related to the contact between sphere and housing, concerns the problem of thermal dilation of materials owing to heat developed by friction in rolling bearings: in fact, under operative conditions the temperature of the lubricant (and therefore of the hollow inside of the sphere) can exceed 50°C, whereas it is reasonably foreseen that the external temperature, owing to the contact with water, may hardly exceed 20°C. Therefore, to assess bearing block behaviour under action of a thermal load it was decided to perform a further numerical simulation, this time based on the software Comsol multiphysics 3.2. Referring to Fig. 54, one can get an idea of the schematization of the problem in terms of 2D modelling of the sphere-housing set; and of discretization of calculation domain, with the entailed calculation grid.
In order not to overburden the calculation, geometry was simplified and carried out in 2D, imposing an axial-symmetry constraint. Sphere tips projecting with respect to the housing were supposed as one (the bottom one) into contact with water and the other one (the top one, facing onto the engine compartment) thermally insulated. The outside of the housing was considered as into contact with water, except for the hull-anchored portion, it also supposed thermally insulated.
Overall, imposed boundary conditions were:

➢ 80° C inside of the sphere: it was decided to impose the same lubricant temperature value used in bearings life calculation, as may be observed in Table 8.
➢ Temperature of water(and of all surfaces wetted thereby) :20°C.
➢ Thermal insulation for all other surfaces (top sphere tip included).
➢ Temperature at which all components are built and assembled (reference temperature): 25°C.

Concerning materials characterization, we have: Table 12 Thermophysical properties of sphere material.

G-Cu Al11 Fe4 Ni4

Type Bronzal alloy

Density (Kg/m³) 7600

Linear dilation coefficient (K^-1) 16*10^-6

Thermal conductivity (W/mK) 40

Specific heat (J/KgK) 400

Table 13 Thermophysical properties of housing material.

AISI 316

Type Stainless steel

Density (Kg/m³) 7860

Linear dilation coefficient (K^-1) 11.8*10^-6

Thermal conductivity (W/mK) 15

Specific heat (J/KgK) 500
Analysis results are reported in Figs. 55 and 56. The former depicts temperature distribution and heat flux lines (in violet), whereas in the latter translation vectors appear. From the latter data the software was made to perform an integral of the displacements on the surface of the sphere into contact with the seat, then dividing what was yielded by the value of the surface itself, and finally obtaining a mean deviation (with respect to the initial diameter) of about 22 µm. This value was used as reference to set an adequate matching tolerance, so as to totally avoid the possibility (anyhow rather remote) of a locking of the sliding between sphere and housing. A putative hole-base matching (for a dimensional class of from 80 to 120 mm), capable of ensuring a negative deviation of 12-34 µm, is that indicated in Fig. 57.

Tests on the structural stability of the propeller shaft

Once obtained a nearly definite geometry for the sphere-housing set, it was decided to perform some additional tests on the propeller shaft, with particular reference to the phenomenon of Eulerian instability, deformation calculations and dynamic behaviour analysis.

Instability test

Balance instability phenomena are among the most dangerous for correct operation and for the strength of any mechanical element or structure: in fact, a collapse associated thereto is extremely quick and may lead to deformations of catastrophic entity. Alas, in general, with regard to dimensioning against instability, there is a remarkable lack of relations that may be applied with a sufficient certainty. However, there are some significant problems that have been subjected to in-depth studies in the past, and for which accordingly there are different theoretical formulations, whose recognized degree of reliability allows their use even in design. From this point of view, Euler study for tip-loaded slender beams assumes a specific interest: in fact, in our case we have a shaft whose length is much greater than the diameter (and therefore it can be likened to a slender beam) and subjected to a compression load generated by the propeller thrust. The fundamental parameter on which Euler critical stress formula is based is slenderness λ, which may be defined as: $λ = \frac{l}{ρ_{\min}}$

wherein l is the free deflection length and ρmin the minimum radius of gyration of the cross section. Knowing the value of λ serves first of all to establish whether the danger of instability can occur in the elastic field or the critical stress is so high as to exceed the yield point of the material. In fact two cases are possible:

λ > λ _l → Instability in the elastic field (Euler formula)
λ < λ _l → Instability in the plastic field (Johnson formula)

_l

λl = \sqrt{(\frac{2 π^{2} nE}{S})}

σ_{ce} = \frac{π^{2} nE}{λ}

Then, having assigned a suitable safety coefficient xc (the suggested value is xc = 3) and calculated the stress from a normal and an actually acting strain σ, finally there can be performed the test, whose outcomes are resumed in the Table below.

Table 14 Resume list containing all parameters used in the Eulerian test and the outcome of a comparison between the normal limit strain σo, equal to the critical stress σce divided by the safety coefficient xc, and the acting strain σ.

Instability test
E (Mpa)	200600
r (mm)	21
ρmin (mm)	10.5
L (mm)	725
λlim	52.25722379
λ	69.04761905
σce (Mpa)	415.2725829
Xc	3
σo (Mpa)	138.4241943
σ (Mpa)	6.005302161
Result	TESTED!!!

Deformation calculation

To obtain the deformed configuration of the propeller shaft under load, a simple theoretical calculation was carried out, based on an integration of indefinite elasticline equations. The results, graphically reported in Fig. 58, were obtained in the horizontal and vertical planes from the reference static diagrams already used in the fatigue calculation of Fig. 39 and subsequent ones; hence, a certain degree of approximation thereof has to be reckoned: in fact, hypotheses on constraints are correct from the standpoint of reactions carried out, but do not consider the physical extension of the constraints themselves (in particular of the support bushing 23). In any case, as it may be noticed from the graphs, in the section comprised between the supports, the overall arrow keeps below 5/100 of mm (1/14000 ratio with respect to the length of said section), whereas displacement in the point of application of the loads keeps within the range of one-tenth of mm. As to rotations at the supports, they were subjected to no test, as the spherical group can be considered to the extent of a revolving bearing (in fact, any rotation thereof is compensated for by the sliding abilities of the sphere), whereas it is deemed that the system bushing 23-arm 24 be capable of enduring small angular displacements, thanks to its non-negligible elastic compliance, already mentioned hereto.

Analysis of flexural behaviour

For an as complete as possible assessment of the phenomenon, once again it was decided to rely on a numerical approach to finished elements, based on the "Block Lanczos" formulation present in the dedicated Ansys FEM software. There were estimated the first three own flexural frequencies (and the corresponding vibrating modes) besides from the corresponding critical speeds of the drive. Said quantities were obtained by considering different values of propeller weight (20-50 Kg) and analyzing the influence of the compliance of the propeller-side support. The schematization of the problem and the graphic representation of the first three modes, in the case in which the support bushing is considered perfectly rigid, are depicted in Figs. 59 and 60.
Hereinafter, we report the complete results of the analysis, in form of tables, making reference also to the diagrams of Figs. 61 to 63, reporting the flexural frequencies with the change of the propeller mass.
In the light of the above-indicated data, it can be stated that:

➢ Drive behaviour under flexural free vibration, associated to modes I and III (for the latter, only when the propeller-side support is considered deformable) is slightly sensitive to the variation in propeller weight, within the variation range analyzed. In particular, with the increase in the propeller weight, a decrease in the own frequencies of the system is observed;
➢ Drive behaviour under flexural free vibration is slightly influenced by the compliance of the support casing. In particular, a realistic taking into account of the compliance of the support system (casing) leads to a reduction of the natural frequencies (and therefore of the critical rotation regimes) of the system with respect to the case of a perfectly rigid support, considering the behaviour under free vibration of the system both in the horizontal plane and in the vertical one;
➢ The critical rotation regimes of the drive are amply above the transient or functional regime conditions (2500-3000 rpm), even when the compliance effect of the support casing is taken into account.

Analysis of torsional behaviour

In this case it was preferred to proceed as simply as possible, through a theoretical-analytical approach with two degrees of freedom, widely consolidated in the field of design. By assuming for the shaft a mean diameter of 44mm (obtained as weighted mean on the longitudinal dimensions of the various sections involved in the reference static diagram), it was possible to estimate a torsional rigidity equal to: $K_{t} = GIp / ℓ = 8 \cdot 10^{10} (N / m^{2}) 3.7 \cdot 10^{- 7} (m^{4}) / 0.10625 (m) = 2.79 \cdot 10^{5} N / m$

from which it is then obtained the following critical torsional frequency: $f_{t} = \frac{1}{2 π} \sqrt{\frac{K (Y_{e} + Y_{m})}{Y_{e} Y_{m}}}$

whose value actually can be calculated only once the polar moments of inertia of the propeller mass (Y_e ) and of the rotating masses associated to the propeller (Y_m ) are e m known. As these data were unavailable, it was chosen to assess parametrically the critical torsional frequency of the structure, to be compared with own action frequencies of the adopted propeller. To this end, the diagram of Fig. 64 is reported.

Final configuration of the propeller shaft

The good outcome of the additional tests performed on this component allowed to define the complete geometry thereof in a nearly definite manner. In Figs. 65 to 68 we report some among the more relevant constructive details.

Bearing block completion

Finally, thanks to the data obtained in the preceding paragraphs it was possible to refine the spherical block, or sphere-housing block, in any component thereof, achieving the end result disclosed, e.g., in Fig. 14.

Components 1, 2 and 3: propeller shaft, flange and bearings

As to the shaft and flange, constructive details have already been provided in the preceding paragraphs of the present section. The typology of bearing preferably used remains the same one as indicated: only dimensions change, which now decrease to an internal diameter of 70 mm and an external one of 110 mm (in this regard, see also Tables 8 and 9).

Components 4 and 5: half-spheres

Technical notes have already been provided also for these components. Finally, the propeller-side half-sphere 5 has housings for tabs 12 fixing the initial position.

Components 6, 7 and 8: supports for oil retainers

These elements do not change much with respect to what has been defined to a first approximation: the work done was essentially of optimization with regard to the new dimensions of sphere and housing and of adjustment about the gasket rings, whose dimensions are standardized. The hull-side support 6 is an exception: some dimensional modfications were effected thereto, as reported in Fig. 69.

Components 9 and 10: half-housings

Main constructive details thereof have already been reported in the preceding paragraphs (in particular, refer to Figs. 51, 52 and 53 ).

Component 11: locking ring for fastening and adjusting the bearings

Concerning the locking rings, it is provided that the one applicable to the shaft 1-flange 2 coupling, not numbered, be of standard type. The rear locking ring 11, intended for the bearings 3, was instead specially made for that purpose, and it is reported in the drawing of Fig. 70.

Component 12: tabs for fastening the initial position

As already mentioned hereto about the definition of housing and sphere, with respect to the first hypotheses on the geometry of the bearing block these two new elements have been added, whose main object is to keep the sphere stationary to facilitate assembling steps. Said tabs also serve to prevent the half- spheres 4,5 from rotating about the axis of rotation of the rolling bearings 3 under operative conditions.

Final notes on the design.

To sum up, we will add some notes on construction and assembling.
The final overall assembly corresponds to that depicted in Fig. 13.
The bolts and nuts and the threaded couplings are dimensioned on the basis of the minimum pull to be transmitted according to the UNI-ISO standards in force; in particular, for bolts and screws tightening the spherical group adoption of the hexagon socket cylindrical head typology described in UNI 5931 was preferred, owing to dimensional reasons.
Bearing lubrication can be performed by oiler; instead, for the sphere-housing interface there should be provided only an initial greasing at assembling, since operative conditions (intermittent and very low-speed relative motion), along with the already good sliding abilities of bronze on steel, make superfluous any further contrivance in that sense.
When not indicated, preferably the material to be used for water-contacting pieces is austenitic stainless steel AISI 316.
Said design of a definite propulsion system according to the present invention was reported merely by way of illustration and not for limitative purposes, and described with reference to a specific variant of a preferred embodiment.
The propulsion system according to the present invention optimizes the alignment between driving shaft and propeller shaft 1; and it minimizes the chance of a less than accurate assembling between said components, rather simplifying, by virtue of the design drawing adopted, their reliable and efficient interconnection.
Another object of the present invention is to disclose a boat, comprising a propulsion system according to the claims hereinafter and described hereto according the two embodiments and the respective variants thereof.
Advantageously, in a boat incorporating a steering system according to the present invention, high-performance demands optimally combine with stability; high maneuverability, also in reverse motion, and comfortable steering controllability, even in the presence of wind.
Thanks to the fact that advantageously the present invention makes the steering of a boat, even when maneuvering, much simpler with respect to state-of-the-art propulsion systems, it is possible to conquer a wide group of new putative users in the related field.
Advantageously, no substantial and costly variation of the structure is needed to house the propulsion system according to the present invention in an existing boat, as the interface require minimal modifications.
A person skilled in the art, in order to satisfy further and contingent needs, may effect several further modifications and variants to the above-described surface-piercing propeller propulsion system and to a boat incorporating such a system, all falling within the protective scope of the present invention as defined by the appended claims.

Claims

A surface-piercing propeller propulsion system for propelling a boat (100), comprising a drive apparatus apt to engage to the transom (101) of said boat (100); said drive apparatus comprising:
- a spherical group (50), apt to be anchored to said transom (101); and

- a propeller shaft (1), apt to be driven by a driving group of said boat (100);
wherein said spherical group (50) is apt to carry out a twin function of:
- element for supporting and moving said propeller shaft (1); and

- element for protecting and water-proofing said drive apparatus and/or said driving group;

the configuration of said spherical group (50) being such as to allow the rotation of said propeller shaft about at least one axis, orthogonal to said propeller shaft (1), passing through the ideal center of said spherical group (50).
The surface-piercing propeller propulsion system according to claim 1, wherein said drive apparatus comprises sealing systems, external to said spherical group (50), of stationary type.
The surface-piercing propeller propulsion system according to claim 2, wherein said sealing systems external to said spherical group of stationary type comprise rigid supports (6,7,8) for oil retainers.
The surface-piercing propeller propulsion system according to one of the claims 1 to 3, wherein said spherical group (50) comprises:
- a spheroidal element (4,5) splined onto the propeller shaft (1) by means of support bearings (3); and

- a spheroidal housing (9,10) apt to house said spheroidal element (4,5), shaped so as to reproduce in negative form the shape of said spheroidal element (4,5); the ideal center of said spherical group (50) substantially coinciding with the center of said spheroidal element (4,5) and with the center of said spheroidal housing (9,10).
The surface-piercing propeller propulsion system according to claim 4, wherein the coupling of said spheroidal element (4,5) with said spheroidal housing (9,10) is such as to allow rotations about any axis passing through said ideal center of said spherical group (50); said spherical group (50) being substantially a three-dimensional spherical hinge.
The surface-piercing propeller propulsion system according to claim 4 or 5, wherein said spheroidal element comprises two pieces (4,5), made substantially integral; said two pieces being substantially a first half-sphere (5), splined on the propeller side of said propeller shaft (1); and a second half-sphere (4), splined on the hull-side of said propeller shaft (1); the assembling being thus such as to facilitate the insertion of said bearings (3) into said spherical group (50), the assembling in general as well as the maintenance steps.
The surface-piercing propeller propulsion system according to one of the claims 4 to 6, wherein said spheroidal housing comprises two pieces (9,10), made substantially integral; said two pieces substantially being respectively a first spheroidal half-housing, located on the propeller side (10) and apt to be mounted substantially on said first half-sphere (5); and a second spheroidal half-housing (9), located on the hull-side and apt to be anchored to the transom (101) of said boat (100).
The surface-piercing propeller propulsion system according to one of the claims 4 to 7, wherein said spherical group (50) comprises gaskets in an intermediate interface region between said spheroidal element (4,5) and said spheroidal housing (9,10), so as to attain the blocking of any type of infiltration from the outside of said spherical group (50).
The surface-piercing propeller propulsion system according to one of the claims 4 to 8, wherein said drive apparatus comprises an intermediate connecting flange (2), apt to connect said propeller shaft (1) with a driving shaft of said driving group; said intermediate flange (2) having a length such as to form an interposition element between said propeller shaft (1) and said support bearings (3), so as to make easier the disassembling of said propeller shaft (1), as well as its drawing out.
The surface-piercing propeller propulsion system according to one of the claims 1 to 4; as well as to claims 8 and 9 when dependent from claim 4; wherein said spheroidal element comprises two pieces (4,5^*), made substantially integral; said two pieces being respectively a half-sphere (4), substantially splined on the hull side of said propeller shaft (1) and apt to be anchored to the transom (101) of said boat (100); and a substantially cylindrical piece (5^*) splined on the propeller-side of said propeller shaft (1); said substantially cylindrical piece (5^*) being pivotably connected to said transom (101) by substantially cylindrical pins (13); the configuration being such that the axes of rotation (a-a) of said substantially cylindrical pins (13) are substantially aligned with the ideal center (C) of said half-sphere (4).
The surface-piercing propeller propulsion system according to one of the claims 1 to 10, comprising a supporting structure (200), anchored to the transom (101) of said boat (100), apt to support a rudder (22) downstream of said surface-piercing propeller, so as to position said rudder (22) into the wake of said propeller.
The surface-piercing propeller propulsion system according to claim 11, having variable geometry; said supporting structure being apt to support also said propeller shaft (1) by a compliant support bushing (23); the engagement of said support bushing (23) with said propeller shaft (1) concomitantly allowing a trimming of said propeller shaft (1) by means of a trim adjustment piston.
The surface-piercing propeller propulsion system according to claim 12, wherein said trimming has an angular excursion comprised in a range of ± 7° with respect to the direction orthogonal to the transom (101).
The surface-piercing propeller propulsion system according to one of the claims 1 to 13, wherein the engagement of said drive apparatus to the transom (101) of said boat (100) is consolidated by interposition of a metallic strengthening plate (103), said spherical group (50) and/or said supporting structure (200) being anchored to said transom (101) via said intermediate strengthening plate (103).
A boat (100) comprising a surface-piercing propeller propulsion system according to one of the claims 1 to 14.