REDUCTION MECHANISM FOR AERONAUTICAL PROPULSION SYSTEM

Abstract

The invention relates to a reduction mechanism (19) of an aeronautical propulsion system, comprising a sun gear (19a), a ring gear (19b), a planet carrier (19d) and a series of planet gears (19c), the sun gear (19a) comprising a first pinion comprising a first toothing and each planet gear (19c) comprising a second pinion comprising a second toothing (19cd) capable of meshing with the first toothing of the first pinion, the reduction mechanism (19) comprising a lubrication circuit (36a) capable of conveying lubricant between the toothings, in which the first pinion has, with respect to at least one second pinion, a relative sliding speed and a relative rolling speed between the two involute surfaces or active profiles, defined as a function of the parameters and as and , in which the relative rolling speed is chosen such that , and the relative sliding speed is chosen such that if then .Figure for abstract: Figure 7.

Description

Title of the invention: REDUCTION MECHANISM FOR AERONAUTICAL PROPULSION system FIELD OF THE INVENTION

[0001] The invention relates to the field of reduction mechanisms, or reducers, for aeronautical propulsion systems. It thus relates to a reduction mechanism of an aeronautical propulsion system, an aeronautical propulsion system comprising such a reduction mechanism and a method for dimensioning such a reduction mechanism. STATE OF THE ART

[0002] An aeronautical propulsion system generally comprises, from upstream to downstream in the direction of gas flow, a fan section, a compressor section which may comprise a low pressure compressor and a high pressure compressor, a combustion chamber and a turbine section which may comprise a high pressure turbine and a low pressure turbine.

[0003] When the propulsion system is in operation, the high-pressure compressor is rotated by the high-pressure turbine via a high-pressure shaft. The fan and, where applicable, the low-pressure compressor are rotated by the low-pressure turbine via a low-pressure shaft.

[0004] Climate change is a major concern for many legislative and regulatory bodies around the world. Indeed, various restrictions on carbon emissions have been, are being or will be adopted by various states. In particular, an ambitious standard applies both to new types of aircraft but also to those in circulation requiring the implementation of technological solutions in order to make them compliant with current regulations. Civil aviation has been mobilizing for several years now to make a contribution to the fight against climate change.

[0005] Technological research efforts have already made it possible to significantly improve the environmental performance of aircraft. The Applicant takes into consideration the impact factors in all phases of design and development to obtain less energy-intensive, more environmentally friendly aeronautical components and products whose integration and use in civil aviation have moderate environmental consequences with the aim of improving the energy efficiency of aircraft.

[0006] Consequently, the Applicant is constantly working to reduce its climate impact through the use of methods and the exploitation of virtuous development and manufacturing processes and limiting greenhouse gas emissions to the minimum possible to reduce the environmental footprint of its activity.

[0007] This sustained research and development work covers new generations of aircraft engines, the lightening of aircraft, in particular through the materials used and lighter on-board equipment, the development of the use of electrical technologies to ensure propulsion, and, as essential complements to technological progress, aeronautical biofuels.

[0008] One of the objectives of technological research is thus to improve the environmental performance of aircraft, in all phases of design and development, the relevant factors are taken into account to obtain less energy-consuming, more environmentally friendly aeronautical components and products whose integration and use in civil aviation have moderate environmental consequences, and this with the aim of improving the energy efficiency of aircraft.

[0009] For example, in order to improve the propulsive efficiency of an aeronautical propulsion system and reduce its specific consumption, it has been found that it is advantageous to increase the rotational speed of the low-pressure turbine and the low-pressure compressor, and to decrease the rotational speed of the fan. Similarly, in order to limit the drag and the mass of the aircraft, and thus reduce its fuel consumption, it has been found that it is advantageous to make the propulsion systems more compact, that is to say to reduce the size of all or part of their components.

[0010] However, in doing so, it appears that the rotating components of aeronautical propulsion systems, in particular those present within the compressor section and the turbine section, are subjected to increased centrifugal forces, while having smaller dimensions, which is likely to alter their mechanical strength and / or limit their service life.

[0011] The rotational drive of the fan at a speed lower than the rotational speed of the low pressure turbine and the low pressure compressor is typically obtained by means of a mechanical reduction mechanism, also called a mechanical reducer. Examples of mechanical reducers are described in international application WO 2010 / 092263 A1 and French patent applications FR 2 987 416 A1, FR 3 008 462 A1, FR 3 008 463 A1, FR 3 041 054 A1, FR 3 095 251 A1 and FR 3 116 096 A1.

[0012] The role of a mechanical reducer is to modify the speed and torque ratio between the input shaft and the output shaft of a mechanical system.

[0013] New generations of dual-flow turbomachines, in particular those having a high bypass ratio, include such a mechanical reducer to drive the fan shaft. Usually, the reducer aims to transform the so-called fast rotation speed of a power turbine shaft into a slower rotation speed for the shaft driving the fan, and thus makes it possible to independently control the rotation speed of the fan and the rotation speed of the power turbine.

[0014] Such a reducer comprises a central pinion, called a sun gear, a crown gear and pinions called satellites, which are engaged between the sun gear and the crown gear. The satellites are held by a frame called a planet carrier. The sun gear, the crown gear and the planet carrier are planetary gears because their axes of revolution coincide with the longitudinal axis of the turbomachine. The satellites each have an axis of revolution, these axes being different and equally distributed over the same operating diameter around the axis of the planetary gears. These axes are parallel to the longitudinal axis.

[0015] There are several reducer architectures. In the state of the art of double-flow turbomachines, the reducers are of the planetary or epicyclic type.

[0016] In other similar applications, there are so-called differential or “compound” architectures.

[0017] On a planetary reducer, the planet carrier is fixed and the crown constitutes the output shaft of the device which rotates in the opposite direction to the solar.

[0018] On an epicyclic reducer, the crown is fixed and the planet carrier constitutes the output shaft of the device which rotates in the same direction as the sun.

[0019] On a differential reducer, no element is fixed in rotation. The crown rotates in the opposite direction to the sun and the planet carrier.

[0020] Reducers can be composed of one or more meshing stages. This meshing is ensured in different ways such as by contact, by friction or even by magnetic fields. There are several types of contact meshing such as with straight, helical or herringbone teeth.

[0021] In the present application, the term "stage" or "teeth" means a series of teeth meshing with a series of complementary teeth. A toothing can be internal or external.

[0022] A satellite may comprise one or two meshing stages. A single-stage satellite comprises a toothing which may be straight, helical or herringbone and whose teeth are located on the same diameter. This toothing cooperates with both the sun gear and the crown.

[0023] A double-stage satellite comprises two sets of teeth or two series of teeth which are located on different diameters. A first set of teeth cooperates with the sun gear and a second set of teeth cooperates with the crown gear.

[0024] The planet carrier can be single-piece or even include a cage defining an internal housing intended to accommodate solar and satellites.

[0025] Furthermore, each satellite is centered and guided in rotation around an axis by a bearing which is carried by the planet carrier. There are several bearing technologies for this application such as rolling element bearings, or even plain or hydrodynamic bearings which have higher load capacities and are therefore preferable in terms of size.

[0026] A reducer thus comprises several meshes made between the satellites and the solar. In each mesh, a first pinion transmits mechanical rotational energy to a second pinion by means of the drive made on the active profile of the teeth.

[0027] In order to guarantee high operating performance of the reducer, it is necessary to ensure a necessary supply of lubricant to the meshing. This supply of lubricant, in particular oil, makes it possible to improve the efficiency of the power transmission, the cooling of the parts as well as the mechanical strength and wear resistance of the active profiles of the teeth, the active profile of a tooth being the contact surface meshing with the adjacent pinion(s).

[0028] Parameters have been defined in the prior art in order to define conditions under which the gear is supplied with lubricant so as to meet the needs stated above. In particular, the article “Elastohydrodynamic Lubrication”, D. Dowson, GR Higginson, Pergamon Press, Oxford, 1966, the article “Minimum Film Thickness in Eleptical Contacts for Different Regimes of Fluid Film Lubrication”, BJ Hamrock, D. Dowson, Proceedings of the Leeds-Lyon Symposium on Tribology, 1979, pages 22-27, and standards ISO 6336-22 and 21771-2014.

[0029] In particular, the thickness, or even the height, of the lubricant film, in particular the oil film, is the parameter best representing the lubrication system of the contact surfaces of the teeth.

[0030] In order to improve the performances described above, it is therefore necessary to control the lubricant film as well as possible.

[0031] It is particularly necessary to ensure the thickest, or highest, lubricant film possible to avoid metal / metal contact between the two active tooth profiles. Indeed, the elimination of metal / metal contact makes it possible to limit the risk of contact fatigue due to mixed lubrication, of the micro-scaling type (or "micropitting" in English), and the risk of seizure, namely the wear of two pinions which mesh together.

[0032] Thus, it is necessary to guarantee during operation a minimum height of the lubricant film in order to ensure lubrication of the reducer making it possible to avoid metal / metal contact between the pinions. However, the minimum height of the lubricant film depends on numerous parameters related to the gear teeth including: the normal module; the normal pressure angle; the helix angle; the number of teeth; the total reduction ratio, among others. Summary of the invention

[0033] One of the aims of the present invention is to determine the values ​​of the parameters conditioning a minimum height of lubricant film between the pinions of a reduction mechanism so as to be able to size the lubricant film to meet the needs stated above.

[0034] To this end, the invention is the result of technological research aimed at significantly improving the performance of aircraft and, in this sense, contributes to reducing the environmental impact of aircraft.

[0035] For this, the invention relates to a reduction mechanism of an aeronautical propulsion system, comprising a sun gear, a crown, a planet carrier and a series of satellites rotatably mounted on the planet carrier, the sun gear comprising a first pinion comprising a first toothing and each satellite comprising a second pinion comprising a second toothing suitable for meshing with the first toothing of the first pinion,

[0036] the reduction mechanism further comprising a lubrication circuit capable of conveying lubricant between the first toothing of the first pinion and the second toothing of at least one second pinion,

[0037] in which the first pinion has, with respect to at least one second pinion, a relative sliding speed Vg, in meters per second (m / s), and a relative rolling speed Vr, in meters per second (m / s), between the two involute surfaces or active profiles, defined as a function of the parameters U1 and U2 as:

[0038] Vg = \ U2-UÏ\

[0039] and:

[0040] Vr= | t / l+ t / 2|

[0041] with:

[0042] U1 = T1B x

[0043] and:

[0044] U2 = T2B x

[0045] and:

[0046] T2B — aw x sinaz - TlBet

[0047] (Z1+Z2) aW= 2XCOS / ! +J

[0048] and:

[0049] Zl~ 22 and: 1 GR [°°5°1 TW = | X - pf :

[0051] p^ = mrX7TXcosar

[0052] and:

[0053] =

[0054] and:

[0055] dNa} = mn x + 2 xh*

[0056] and:

[0057] db^ mn xZl^

[0058] and:

[0059] _ tan-i j

[0060] where:

[0061] is a rotational speed of the first gear, in radians per second (rad / s), intended to be achieved by the first gear in operation, ^2 is a rotational speed of the second pinion, in radians per second (rad / s), intended to be reached by the at least one second pinion in operation, T2B is the distance between points T2 and B, in meters (m), T2 being the point of tangency between the line of action and the base circle of the second pinion,

[0062] Z2 is the number of teeth of the second pinion,

[0063] aw is the operating center distance, in meters (m),

[0064] J is a center distance variation, in meters (m), between 0 mm and 0.8 mm,

[0065] GR is the total reduction ratio,

[0066] TW is the distance between points Tl and B, in meters (m), B being a characteristic point of the meshing which corresponds to the passage from Nl to N teeth in mesh (N being the maximum number of teeth in mesh according to the driving ratio), and Tl being the point of tangency between the line of action and the base circle of the first pinion,

[0067] dNai is the active head diameter of the first pinion at point B, in meters (m),

[0068] dh} is the diameter of the base circle of the first gable, in meters (m),

[0069] mn is the normal modulus, in millimeters (mm),

[0070] Z1 is the number of teeth of the first pinion,

[0071] is the helix angle or primitive inclination angle, in degrees (°),

[0072] fa* is the projection height corresponding to the active head diameter for the first toothing,

[0073] ai is the transverse or apparent pressure angle, in degrees (°),

[0074] an is the normal pressure angle, in degrees (°),

[0075] in which the relative rolling speed Vr is chosen such that:

[0076] 4 m / s< V,.<50 m / 5

[0077] and in which the relative sliding speed Vg is chosen such that:

[0078] - if Vr > 4 m / s then Vg <5 m / s,

[0079] and:

[0080] is chosen such that 20 radIs 1000 rad / 5

[0081] is chosen such that 200 rad ! s < &2 5 1000 rad I s, mn is chosen so that 2.5 mm m 5 mm,

[0082] Z1 is chosen such that 20 < Zi < 60,

[0083] is chosen such that Qj x mn < < 1.3 X mn'

[0084] / 3 is chosen such that 12° < / 3 < 35°,

[0085] an is chosen such that 15° < an < 28°,

[0086] GR is chosen such that 2.5 < GR < 3.5.

[0087] The reduction mechanism may have one or more of the following characteristics:

[0088] In one embodiment, the relative rolling speed Vr is chosen such that:

[0089] Vr>30m / s

[0090] and the relative sliding speed Vg is chosen such that: [0091 ] - if V,. > 4 m / 5 then Vg <5 mj s.

[0092] In one embodiment, the relative sliding speed Vg is chosen such that:

[0093] 0 <Vg<30mls

[0094] and the relative rolling speed Vr and the total reduction ratio GR are chosen such that:

[0095] - if Vg < 5 m ! s then Vr > 4 mj s,

[0096] - if Vg > 5 m / s then y- > [ 15,

[0097] and 2 < GR < 4.

[0098] In one embodiment, the relative sliding speed VL is chosen such that:

[0099] 0 <Vg<10m / s

[0100] and the relative rolling speed Vr and the total reduction ratio GR are chosen such that:

[0101] - if Vs < 5 m! s then Vr > 4 m! s,

[0102] - if Vg > 5 m / s then > 1.15,

[0103] and 2 < GR < 4.

[0104] In one embodiment, parameter 171 is chosen such that:

[0105] 0.5 m / s <Ul< 40 m / s,

[0106] or even 0.5 m / s < U1 < 40 m / s,

[0107] or even 2 m / s < U1 < 40 m / s.

[0108] In one embodiment, the parameter U2 is chosen such that:

[0109] 0 <U2<45m / s

[0110] In one embodiment, the parameter £71 is chosen such that: [YES] 0< £71 <0.5 m / s

[0112] and the parameter U2 is chosen such that:

[0113] 672 <5-671

[0114] In one embodiment, the parameter Ul is chosen such that:

[0115] Ui>0.5m / s

[0116] and the parameter U2 is chosen such that:

[0117] U2< 14x671

[0118] In one embodiment, for the first pinion and at least one second pinion, a minimum height parameter Hm, in meters (m), or minimum thickness, of the lubricant film, in particular of the oil, is defined between the active profiles of the first toothing of the first pinion and of the second toothing of at least one second gable defined as: [0i 19] Hm = Pn x [qxo.985 x G0'6 xx VT0'13]

[0120] with:

[0121] = Z “ 1+0.21 3x(l+2.23xSÆS3)xL0'64

[0122] and:

[0123] G — a^xEet:

[0124] , r unr1 E - 0.5 x I -g- + 1

[0125] and:

[0126] / ij[+u2 \et : U — Vn X —: \ Ex^ /

[0127] j£l£2[_ ~ |t71|+|ï72|

[0128] where:

[0129] VT is the linear load of the teeth, in Newton per meter (N / m),

[0130] P° is the Hertz pressure, in megapascal (MPa),

[0131] L is a dimensionless thermal parameter,

[0132] E is the Young's modulus of the first toothing or the second toothing, designated Ei for the first toothing and E2 for the second toothing, in pascal (Pa),

[0133] E' is the reduced modulus of elasticity, in pascal (Pa),

[0134] vo is the initial Poisson's ratio,

[0135] vi is the Poisson's ratio of the first toothing,

[0136] v2 is the Poisson's ratio of the second toothing,

[0137] aP is the piezoelectricity coefficient of the lubricant (Pa '),

[0138] Pn is the radius of curvature at the contact point B, in meters (m),

[0139] in which the minimum height Hm of the lubricant film is chosen such that:

[0140] o,O2 x 1CT6 m < Hm < 0.4 x ICÏ6 m

[0141] and:

[0142] W is chosen such that 200 N / mm < W < 1600 N ! mm,

[0143] P° is chosen such that 500 MPa < po < 1800 MPa,

[0144] L is chosen such that ],3 x 108 < L 2 x 10 6'

[0145] E is chosen such that 200 GPa < E < 230 GPa,

[0146] aP is chosen such that 1 x 1(fs Pa 1 £ ap £ 1.8 x 1()'8 Pa~

[0147] Pn is chosen such that 0.5 mm < pn < 60 mm,

[0148] vi is chosen such that 0.25 Steps £ rq < 0.32 Steps,

[0149] v2 is chosen such that 0.25 Steps < v2 - 0.32 Steps,

[0150] vo is chosen such that gxj q-2 not < < 2 X 1O-3 Not-

[0151] In one embodiment, the minimum height Hm of the lubricant film is chosen so that: 0.07 x 10-6 m < Hm < 0.2 x 10-6 m

[0152] In one embodiment, the first toothing of the first pinion and the second toothing of each second pinion comprise straight, helical or herringbone type teeth.

[0153] In one embodiment:

[0154] - each satellite has one or two gear stages, and / or

[0155] - the planet carrier is in one piece or comprises a cage defining a housing internal to receive solar and satellites, and / or

[0156] - each satellite is centered and guided in rotation around an axis by a bearing carried by the planet carrier, each bearing being of the rolling element type or of the hydrodynamic type.

[0157] Furthermore, the invention also relates, according to another of its aspects, to an aeronautical propulsion system comprising:

[0158] - a power turbine, in particular a low pressure turbine, and a shaft turbine drive, in particular a low pressure shaft, driven in rotation by the power turbine around a longitudinal axis,

[0159] - a fan rotor and a fan shaft, the fan rotor being coupled rotating on the fan shaft,

[0160] - a reduction mechanism as defined previously, comprising an input connected to the turbine drive shaft and an output connected to the fan shaft, adapted to drive the fan rotor to rotate about the longitudinal axis via the turbine drive shaft and the fan shaft at a rotational speed lower than that of the power turbine.

[0161] Furthermore, the invention also relates, according to another of its aspects, to a method for dimensioning a reduction mechanism of an aeronautical propulsion system comprising a power turbine, in particular a low pressure turbine, and a turbine drive shaft, in particular a low pressure shaft, driven in rotation by the power turbine around a longitudinal axis, and a fan rotor and a fan shaft, the fan rotor being coupled in rotation to the fan shaft,

[0162] the reduction mechanism comprising an input intended to be connected to the turbine drive shaft, and an output intended to be connected to the fan shaft, and being adapted to drive the fan rotor in rotation about the longitudinal axis by means of the turbine drive shaft and the fan shaft at a rotational speed lower than that of the power turbine,

[0163] the reduction mechanism comprising a sun gear, a crown, a planet carrier and a series of satellites rotatably mounted on the planet carrier,

[0164] the solar comprising a first pinion comprising a first toothing and each satellite comprising a second pinion comprising a second toothing suitable for meshing with the first toothing of the first pinion,

[0165] the reduction mechanism further comprising a lubrication circuit capable of conveying lubricant between the teeth of the first and second pinions,

[0166] in which the first pinion has, with respect to at least one second pinion, a relative sliding speed Vg, in meters per second (m / s), and a relative rolling speed Vr, in meters per second (m / s), between the two involute surfaces or active profiles, defined as a function of the parameters Ul and U2 as:

[0167]

[0168] and:

[0169] V,~ |U\+U21

[0170] with:

[0171] L / l^rWxDi

[0172] and:

[0173] U2=T2BxQ2

[0174] and:

[0175] T2B = aw x sinaf - TlBel ;

[0176] (Z1+Z2) , aw= m„x 2œœ / ) +J

[0177] and :

[0178] j — and i GR

[0179] T1B= ±x ^dNal2-dlA2 -pf-

[0180] n = X TT X COSfif ' and ' '

[0181] and :

[0182] mr. mt -

[0183] and :

[0184] = mnx^+2xlp,

[0185] and :

[0186] , cosa, dh! = mnxZlx^

[0187] and :

[0188] ,, _ / tana« ]

[0189] where:

[0190] is a rotational speed of the first gear, in radians per second (rad / s), intended to be achieved by the first gear in operation, û2 is a rotational speed of the second pinion, in radians per second (rad / s), intended to be reached by the at least one second pinion in operation, T2B is the distance between points T2 and B, in meters (m), T2 being the point of tangency between the line of action and the base circle of the second pinion,

[0191] Z2 is the number of teeth of the second pinion,

[0192] aw is the operating center distance, in meters (m),

[0193] J is a variation in center distance, in meters (m), between 0 mm and 0.8 mm,

[0194] GR is the total reduction ratio,

[0195] T IB is the distance between points Tl and B, in meters (m), B being a characteristic point of the meshing which corresponds to the passage from Nl to N teeth in mesh (N being the maximum number of teeth in mesh according to the driving ratio), and Tl being the point of tangency between the line of action and the base circle of the first pinion,

[0196] is the active head diameter of the first pinion at point B, in meters (m),

[0197] dhl is the diameter of the base circle of the first gable, in meters (m),

[0198] mn is the normal modulus, in millimeters (mm),

[0199] Zl is the number of teeth of the first pinion,

[0200] fi is the helix angle or primitive inclination angle, in degrees (°),

[0201] ]ia is the projection height corresponding to the active head diameter for the first toothing,

[0202] at is the transverse or apparent pressure angle, in degrees (°),

[0203] an is the normal pressure angle, in degrees (°),

[0204] the method comprising a step of dimensioning the reduction mechanism during which the relative rolling speed Vr is chosen such that:

[0205] 4 m / s < Vr < 50 m / 5

[0206] and in which the relative sliding speed V8 is chosen such that:

[0207] - if Vr > 4 m / s then V g < 5 m / s,

[0208] and:

[0209] fl] is chosen such that 20 radI if 1000 rad / s

[0210] O2 is chosen such that 200 rad / s < H, - 1000 rad / 5, mn is chosen such that 2.5 mm < m < 5 mm,

[0211] ZI is chosen such that 20 < Zi < 60,

[0212] is chosen such that Qj x mn < < 13 x

[0213] fi is chosen such that 12 0 < p < 35 0 ,

[0214] an is chosen such that 15 0 < an < 28 0 ,

[0215] GR is chosen such that 2.5 < GR < 3.5.

[0216] In one embodiment, the method comprises a step of dimensioning the reduction mechanism during which the relative rolling speed Vr is chosen such that:

[0217] Vr>30m / s

[0218] and the relative sliding speed Vg is chosen such that:

[0219] - if Vr > 4 m / y then Vg < 5 m / .y.

[0220] In one embodiment, the method comprises a step of dimensioning the reduction mechanism during which the relative sliding speed Vg is chosen such that:

[0221] 0 <Vg<30m / s

[0222] and the relative rolling speed Vr and the total reduction ratio GR are chosen such that:

[0223] - if Vg <5 m / s then Vr > 4 m / s,

[0224] - if Vs > 5 m / s then 22 > | [5, K? '

[0225] and 2 < GR < 4.

[0226] In one embodiment, the method comprises a step of dimensioning the reduction mechanism during which the relative sliding speed Vg is chosen such that:

[0227] O <Vg<lOm / s

[0228] and the relative rolling speed Vr and the total reduction ratio GR are chosen such that:

[0229] - if V<5 ml s then Vr > 4 m / s,

[0230] - if Vg > 5 m / ,v then G s 1 15, V„ M-1

[0231] and2 <GÆ<4.

[0232] In one embodiment, the method comprises a step of dimensioning the reduction mechanism during which the parameter U1 is chosen such that:

[0233] 0 < 171 <40 / rt / s,

[0234] or even 0.5 ni / s < C71 < 40 m / s,

[0235] or even 2 mjs < U\ < 40 m / S.

[0236] In one embodiment, the method comprises a step of dimensioning the reduction mechanism during which the parameter U2 is chosen such that:

[0237] 0 < U2 < 45 m / 5

[0238] In one embodiment, the method comprises a step of dimensioning the reduction mechanism during which the parameter C71 is chosen such that:

[0239] 0 <Ul<0,5m / s

[0240] and the parameter U2 is chosen such that:

[0241] G2<5-G1

[0242] In one embodiment, the method comprises a step of dimensioning the reduction mechanism during which the parameter U\ is chosen such that:

[0243] Ul>0.5m / s

[0244] and the parameter U2 is chosen such that:

[0245] G2< 14x6 / 1

[0246] In one embodiment, for the first pinion and at least one second pinion, a minimum height parameter Hm, in meters (m), or minimum thickness, of the lubricant film, in particular of the oil, between the active profiles of the first toothing of the first pinion and of the second toothing of at least one second pinion is defined as:

[0247] Hm = x [qx (.985 x G0.6 x ^.7 x 13]

[0248] with:

[0249] _ “ 1+0.213x( 1+2.2 3x,SA^

[0250]

[0251]

[0252]

[0253]

[0254]

[0255]

[0256]

[0257]

[0258]

[0259]

[0260]

[0261]

[0262]

[0263]

[0264]

[0265]

[0266] And : G = ap x Eci: E - [o,5x (-^ + And : v / t / l+U2 \et : I , I 0 \ ; 2x |t / l-ï / 2j | Ul|+j ï / 2] Or : W is the linear load of the teeth, in Newton per meter (N / m), P° is the Hertz pressure, in megapascals (MPa), L is a dimensionless thermal parameter, E is the Young's modulus of the first or second toothing, designated Ei for the first toothing and E2 for the second toothing, in pascal (Pa), E' is the reduced modulus of elasticity, in pascals (Pa), vo is the initial Poisson's ratio, ' i is the Poisson's ratio of the first tooth, v2 is the Poisson's ratio of the second toothing, aP is the piezoelectric coefficient of the lubricant (Pa'), Pn is the radius of curvature at the point of contact B, in meters (m),

[0267] the method comprising a step of dimensioning the reduction mechanism during which the minimum height Hm of the lubricant film is chosen such that so that:

[0268] 0.02 x 10'6 m < Hm < 0.4 x 10'6 m

[0269] and:

[0270] IV is chosen such that 200 N / mm < IV < 1600 N j mm,

[0271] P° is chosen such that 500 MPa < po < 1800 MPa,

[0272] L is chosen such that 1.3 x 10'8 < L < 2 x 10'6'

[0273] E is chosen such that 200 GPa < E < 230 GPa,

[0274] aP is chosen such that 1 x 10'8 Pa1 10'8 Pd

[0275] Pn is chosen such that 0.5 mm < pn < 60 mm,

[0276] vi is chosen such that 0.25 Steps < rq < 0.32 Steps,

[0277] v2 is chosen such that 0.25 Steps < v2 - 0.32 Steps.

[0278] ''o is chosen such that 8 x ] Pas < Vq <2x1 (f3 Pas-

[0279] In one embodiment, the method comprises a step of dimensioning the reduction mechanism during which the minimum height Hm of the lubricant film is chosen such that: 0.07 x 1 (T6 m < Hm < 0.2 x 10'6 m

[0280] Furthermore, the invention also relates, according to another of its aspects, to a reduction mechanism manufactured from a dimensioning method as defined previously. PRESENTATION OF THE DRAWINGS

[0281] Other characteristics and advantages will emerge from the following description, which is purely illustrative and non-limiting, and must be read in conjunction with the appended figures, among which:

[0282] - [Fig.l] schematically represents an aircraft comprising systems propulsive,

[0283] - [Fig.2] schematically represents, in partial view and in section, a example of a propulsion system in which the fan section is ducted,

[0284] - [Fig.3] schematically represents, in partial view and in section, a example of a propulsion system in which the fan section is unducted,

[0285] - [Fig.4] schematically represents a first example of a mechanism of planetary reduction,

[0286] - [Fig.5] schematically represents a first example of a mechanism of epicyclic reduction,

[0287] - [Fig.6] schematically represents a first example of a mechanism of differential reduction,

[0288] - [Fig.7] represents, schematically and partially, an axial section of a example of an epicyclic reduction mechanism,

[0289] - [Fig.8] represents, schematically and partially, the film of lubricant formed between the active profiles of a first toothing of a first pinion of the sun gear of a reduction mechanism according to the invention and of a second toothing of a second pinion of a satellite of a series of satellites of the reduction mechanism according to the invention,

[0290] - [Fig.9] represents, in a schematic and partial manner, the highlighting of the relative sliding between the first and second pinions of the reduction mechanism according to the invention, and

[0291] - Figures 10 to 15 illustrate, schematically and partially, parameters used in the definition of a reduction mechanism according to the invention. DETAILED DESCRIPTION OF EMBODIMENTS

[0292] In the example illustrated in [Fig.l], the aircraft is an airplane 100 comprising a fuselage 101 and two wings 102. In this example, the aircraft comprises two propulsion systems 1, each propulsion system 1 being attached to a respective wing 102 of the airplane 100 via a pylon. In another embodiment, the aircraft could include one or more propulsion system(s) attached to the fuselage 101.

[0293] [Fig.2] schematically represents, in partial view and in section, a first example of a propulsion system 1.

[0294] In this example, the propulsion system 1 is a double-spool, ducted-fan gas turbine engine.

[0295] In [Fig.2], the propulsion system 1 has a main direction extending along a longitudinal axis X. The propulsion system 1 comprises a fan section 2 and a primary body 3, often called a “gas generator”.

[0296] The fan section 2 comprises a fan 22 and a fan housing 12. The fan 22 comprises a fan rotor 9. The fan housing 12 surrounds the fan rotor 9. The fan rotor 9 is rotatably mounted relative to the fan housing 12.

[0297] The fan rotor 9 comprises a fan hub 13 and fan blades 14 extending radially from the hub 13. The fan blades 14 may be fixed relative to the fan hub 13 or have a variable pitch. In the latter case, each of the fan blades 14 is pivotally mounted relative to the fan hub 13 along a pitch axis and is connected to a pitch change mechanism (not shown) mounted in the propulsion system 1. The pitch change mechanism makes it possible to adjust the pitch angle of the fan blades 14 according to the flight phases.

[0298] The fan rotor 9 comprises at least fourteen fan blades 14 and at most twenty-four fan blades 14, preferably at least sixteen fan blades 14 and at most twenty-two fan blades 14.

[0299] In addition, in this example, the fan section 2 also comprises a fan stator 16 fixedly mounted on the fan casing 12. The fan stator 16 comprises fixed vanes 17 generally referred to as “outlet guide vanes” (or “OGV”). This set of fixed vanes has the function of straightening and regulating the airflow which flows downstream of the fan rotor 9 to contribute to the thrust of the engine. This set of fixed vanes also plays a noise reduction role.

[0300] Alternatively, the outlet blades 17 could have a variable pitch. If necessary, and similarly to the fan blades 14 of the fan rotor 9, the root of the outlet blades 17 is pivotally mounted along a pitch axis and is connected to a pitch change mechanism (not shown), the pitch being adjusted according to the flight phases by the pitch change mechanism.

[0301] The number of outlet blades 17 depends on the acoustic criteria defined for the propulsion system 1 and is at least equal to the number of fan blades 14.

[0302] The primary body 3 comprises a compressor section 29, a chamber of combustion 6 and a turbine section 30.

[0303] The compressor section 29 comprises a low pressure compressor 4 and a high pressure compressor 5.

[0304] The low pressure compressor 4 comprises a rotor 41 capable of being driven in rotation relative to the casing 31 of the propulsion system 1 and a stator 42 mounted fixedly on the casing 31.

[0305] The rotor 41 of the low pressure compressor 4 comprises moving wheels 4a and the stator 42 of the low pressure compressor 4 comprises fixed wheels 4b. The moving wheels 4a are arranged alternately with the fixed wheels 4b, thus forming a succession of low pressure compressor stages.

[0306] Similarly, the high-pressure compressor 5 comprises a rotor 51 capable of being driven in rotation relative to the casing 31 of the propulsion system 1 and a stator 52 mounted fixedly on the casing 31.

[0307] The rotor 51 of the high-pressure compressor 5 comprises moving wheels 5a and the stator 52 of the high-pressure compressor 5 comprises fixed wheels 5b. The moving wheels 5a are arranged alternately with the fixed wheels 5b, thus forming a succession of high-pressure compressor stages.

[0308] The turbine section 30 comprises a high pressure turbine 7 and a low pressure turbine 8.

[0309] The high-pressure turbine 7 comprises a rotor 71 capable of being driven in rotation relative to the casing 31 of the propulsion system 1 and a stator 72 mounted fixedly on the casing 31.

[0310] The rotor 71 of the high-pressure turbine 7 comprises moving wheels 7a and the stator 72 of the high-pressure turbine 7 comprises fixed wheels 7b. The moving wheels 7a are arranged alternately with the fixed wheels 7b, thus forming a succession of high-pressure turbine stages.

[0311] Similarly, the low pressure turbine 8 comprises a rotor 81 capable of being driven in rotation relative to the casing 31 of the propulsion system 1 and a stator 82 mounted fixedly on the casing 31.

[0312] The rotor 81 of the low pressure turbine 8 comprises moving wheels 8a and the stator 82 of the low pressure turbine 8 comprises fixed wheels 8b. The moving wheels 8a are arranged alternately with the fixed wheels 8b, thus forming a succession of low pressure turbine stages.

[0313] The propulsion system 1 comprises a low pressure shaft 11 connecting the rotor 41 of the low pressure turbine 4 to the rotor 81 of the low pressure compressor 8, the low pressure shaft 11 being rotatably mounted relative to the casing 31 around the longitudinal axis X.

[0314] When the propulsion system 1 is in operation, the rotor 81 of the low pressure turbine 8 drives the rotor 41 of the low pressure compressor 4 in rotation by means of of the low pressure shaft 11.

[0315] The propulsion system 1 further comprises a fan shaft 20 and a reduction mechanism 19. The fan rotor 9 is rotatably coupled to the fan shaft 20. The reduction mechanism 19 has an inlet and an outlet. The inlet of the reduction mechanism 19 is connected to the low-pressure shaft 11 and the outlet of the reduction mechanism 19 is connected to the fan shaft 20. Thus, when the propulsion system 1 is in operation, the rotor 81 of the low-pressure turbine 8 rotates not only the rotor 41 of the low-pressure compressor 4, but also the fan rotor 9, via the low-pressure shaft 11, the reduction mechanism 19 and the fan shaft 20.

[0316] Thanks to the reduction mechanism 19, the fan rotor 9 is driven into rotation at a speed lower than the rotation speed of the rotor 41 of the low pressure turbine 4.

[0317] The reduction mechanism 19 thus makes it possible to independently control the rotation speed of the fan 22 and the rotation speed of the low-pressure turbine 8 and the low-pressure compressor 4.

[0318] The low pressure turbine 8, the low pressure shaft 11, the low pressure compressor 4, the fan shaft 20, the reduction mechanism 19 and the fan 22 together form the “low pressure body” of the propulsion system 1.

[0319] The propulsion system 1 further comprises a high pressure shaft 10 connecting the rotor 51 of the high pressure turbine 5 to the rotor 71 of the high pressure compressor 7, the high pressure shaft 10 being rotatably mounted relative to the casing 31 around the longitudinal axis X. The high pressure shaft 10 is coaxial with the low pressure shaft 11 and extends around the low pressure shaft 11.

[0320] When the propulsion system 1 is in operation, the rotor 81 of the low pressure turbine 8 drives the rotor 51 of the low pressure compressor 5 in rotation via the low pressure shaft 11.

[0321] The high pressure turbine 7, the high pressure shaft 10 and the high pressure compressor 4 together form the “high pressure body” of the propulsion system 1.

[0322] The low pressure shaft 11 and the high pressure shaft 10 may be co-rotating, i.e. driven in the same direction of rotation around the longitudinal axis X. Alternatively, the low pressure shaft 11 and the high pressure shaft 10 may be counter-rotating, i.e. driven in opposite directions of rotation around the longitudinal axis X.

[0323] The dual-body propulsion system 1 may in particular comprise a single-stage high-pressure turbine 7, i.e. comprising exactly one stage, or a two-stage high-pressure turbine 7, i.e. comprising exactly two stages (as illustrated in the example of [Fig.2]).

[0324] The high pressure compressor 5 comprises at least eight stages (as illustrated in the example of [Fig.2]) and at most eleven stages.

[0325] The low pressure turbine 8 comprises at least three stages (as illustrated in the example of [Fig.2]) and at most seven stages.

[0326] The low pressure compressor 4 comprises at least two stages and at most four stages.

[0327] When the propulsion system is in operation, an air flow F entering the propulsion system 1 passes through the fan 22 and is then divided between a primary air flow F1 and a secondary air flow F2, which circulate from upstream to downstream in the propulsion system 1.

[0328] The secondary air flow F2, also called “bypass air flow”, flows in the secondary vein, around the primary body 3. The secondary air flow F2 makes it possible to cool the periphery of the primary body 3 and is used to generate the majority of the thrust provided by the propulsion system 1.

[0329] The primary air flow Fl flows in a primary vein inside the primary body 3, passing successively through the compressor section 29 (low pressure compressor 4 and high pressure compressor 5), the combustion chamber 6 where it is mixed with fuel to serve as an oxidizer, and the turbine section 30 (high pressure turbine 7 and low pressure turbine 8). The passage of the primary air flow Fl through the turbine section 30 receiving energy from the combustion chamber 6 causes rotation of the movable wheels 7a, 8a of the turbine section 30, which in turn drive rotation of the movable wheels 4a, 5a of the compressor section 29 as well as the fan rotor 9.

[0330] In order to improve the propulsive efficiency of the propulsion system 1 and to reduce its specific consumption as well as the noise emitted by the fan section 2, the propulsion system 1 has a high bypass ratio. By "high" bypass ratio, is meant a bypass ratio greater than or equal to 10, for example between 10 and 80 inclusive, preferably between 10 and 35 inclusive, preferably between 10 and 18 inclusive. The bypass ratio is defined as a ratio between the mass flow rate of the secondary air flow F2 and the mass flow rate of the primary air flow F1, these mass flow rates being measured when the propulsion system 1 is stationary, uninstalled, in takeoff mode in a standard atmosphere (as defined by the International Civil Aviation Organization (ICAO) manual, Doc 7488 / 3, 3rd edition) and at sea level.By "not installed" it is meant that the measurements are carried out when the propulsion system 1 is on a test bench (and not installed on an aircraft), the measurements then being simpler to carry out.

[0331] In a propulsion system including a reduction mechanism 19 such as that illustrated in [Fig.2], the decoupling between the rotational speed of the fan 22 and the rotational speed of the low pressure turbine 8 makes it possible to reduce the rotational speed and the pressure ratio of the fan rotor 9 while increasing the power extracted by the low pressure turbine 8. Indeed, the overall efficiency of the propulsion system 1 is conditioned to the first order by the propulsive efficiency, which is favorably influenced by a minimization of the variation in kinetic energy of the air when passing through the propulsion system 1. In a propulsion system with a high bypass ratio, the majority of the flow generating the propulsive force is constituted by the secondary air flow F2 of the propulsion system 1, the kinetic energy of the secondary air flow F2 being mainly affected by the compression that the secondary air flow F2 undergoes when passing through the fan section 2.The propulsive efficiency and the pressure ratio of the fan section 2 are therefore linked: the lower the pressure ratio of the fan section 2, the better the propulsive efficiency. In order to improve the propulsive efficiency of the propulsion system 1, the pressure ratio of the fan, which corresponds to the ratio between the average pressure at the outlet of the fan stator 16 (or, in the absence of stator 16, of the fan rotor 9) and the average pressure at the inlet of the fan rotor 9, is less than or equal to 1.70, preferably less than or equal to 1.50, for example between 0.90 and 1.45. The average pressures are measured here over the height of at least one of the fan blades 14, i.e. of the surface which radially delimits on the inside the air flow path at the inlet of the fan rotor 9 at the tip 21 of the fan blade 14.

[0332] The peripheral speed at the tip 21 of the fan blades 14 can also be between 260 meters per second (ms') and 400 meters per second (ms') inclusive. The fan pressure ratio can then be between 1.20 and 1.45.

[0333] In a direct-drive propulsion system, the fan rotor 9 can, alternatively, be directly coupled to the low-pressure shaft 11, i.e. without a reduction mechanism. The low-pressure shaft 11 is then combined with the fan shaft 20 so that the fan rotor 9 is driven by the low-pressure shaft 11 at the same rotational speed as the rotor 81 of the low-pressure turbine 8.

[0334] The propulsion system 1 is configured to provide a thrust of between 18,000 Ibf (80,068 N) and 51,000 Ibf (226,859 N), preferably between 20,000 Ibf (88,964 N) and 35,000 Ibf (155,688 N).

[0335] The diameter D of the fan rotor 9 may be between 80 inches (203.2 cm) and 185 inches (469.9 cm) inclusive. When the fan rotor 9 is shrouded, the diameter D is preferably between 85 inches (215.9 cm) and 120 inches (304.8 cm) inclusive, for example of the order of 90 inches (228.6 cm), which allows the integration of the propulsion system 1 in a conventional manner, in particular under a wing of the aircraft 1.

[0336] [Fig. 3] schematically represents, in partial view and in section, a second example of propulsion system 1.

[0337] In [Fig.3], components identical or similar to those of the propulsion system of [Fig.2] are designated by identical references.

[0338] In the example illustrated in [Fig.3], the propulsion system 1 is a twin-spool, unducted fan gas turbine engine. It may be an “Open Rotor” or “Unducted Single Fan” type gas turbine engine in English terminology.

[0339] Unlike the first example of [Fig.2], the fan rotor 9, which can also be referred to as a "propeller", is not surrounded by a fan casing.

[0340] The fan section 2 being unducted, the fan blades 14 have a variable pitch. Thus, each of the fan blades 14 is pivotally mounted relative to the fan hub 13 along a pitch axis and is connected to a pitch change mechanism 15 mounted in the propulsion system 1. The pitch change mechanism makes it possible to adjust the pitch angle of the fan blades 14 as a function of the flight phases. Similarly, the outlet blades 17 have a variable pitch, the root of the outlet blades 17 being pivotally mounted along a pitch axis and connected to a pitch change mechanism 15, the pitch being adjusted as a function of the flight phases by the pitch change mechanism.

[0341] Alternatively, the propulsion system 1 could comprise two unducted and counter-rotating fan rotors 9. Such a propulsion system 1 is known, in English terminology, by the acronym “CROR” for “Contra-Rotating Open Rotor” or “UDF” for “Unducted Double Fan”. The fan rotors 9 can be placed at the rear of the primary body 3 so as to be of the pusher type or at the front of the primary body 3 so as to be of the tractor type (“puller” in English).

[0342] The absence of fairing around the fan rotor 9 makes it possible to increase the bypass ratio significantly without the propulsion system 1 being penalized by the mass of the casings 12 or nacelles intended to surround the fan section 2. The bypass ratio of the propulsion system 1 comprising an unfairly fairinged fan section 2 is thus greater than or equal to 40, for example between 40 and 80 inclusive. The peripheral speed at the tip 21 of the fan blades 14 of the fan rotor(s) 9 may also be between 210 meters per second (ms ') and 260 meters per second (ms ') inclusive. The fan pressure ratio may then preferably be between 0.90 and 1.20 inclusive.

[0343] The diameter D of the fan rotor 9 may be between 80 inches (203.2 cm) and 185 inches (469.9 cm) inclusive. When the rotor 9 is unshrouded, the diameter D is preferably greater than or equal to 100 inches (254 cm), for example between 120 inches (304.8 cm) and 156 inches (396.2 cm). The diameter of the fan rotor 9 is measured here in a plane normal to the longitudinal axis X, which is the axis of rotation of the fan rotor 9, at an intersection between a tip 21 and a leading edge 22 of the fan blades 14.

[0344] It should be noted that, [Fig.2] and [Fig.3] being partial views, the diameter D is only partially visible.

[0345] The reduction mechanism 19 may comprise an epicycloidal, planetary or differential reduction mechanism, with a single stage, also called a single stage, or with several stages, in particular with two stages, also called a two-stage.

[0346] For example, [Fig.4] illustrates a reduction mechanism 19 of the planetary type (or "star" in English). The reduction mechanism 19 comprises a sun gear 19a (input of the reduction mechanism 19), centered on an axis of rotation of the reduction mechanism 19 generally coincident with the longitudinal axis X and configured to be driven in rotation by the low pressure shaft 11, a ring gear 19b (output of the reduction mechanism 19) coaxial with the sun gear 19a and configured to drive in rotation the fan shaft 20 about its axis X of rotation, and a series of satellites 19c distributed circumferentially about the axis X of rotation of the rotor 9 of the fan section 2, between the sun gear 19a and the ring gear 19b, each satellite 19c being meshed internally with the sun gear 19a and externally with the ring gear 19b.The series of satellites 19c is mounted on a planet carrier 19d which is fixed relative to a stator part 19e of the propulsion system 1, for example relative to a casing of the compressor section 4, 5.

[0347] In another example, [Fig.5] illustrates a reduction mechanism 19 of the epicycloidal (or “planetary” in English) type, in which case the crown 19b is fixedly mounted on the stator part 19e of the propulsion system 1 and the fan shaft 20 is driven in rotation by the planet carrier 19d.

[0348] In yet another example, [Fig. 6] illustrates a differential type reduction mechanism 19, in which case no element is fixed in rotation. The set of satellites 19c is held by a planet carrier 19d which is connected to a first fan shaft 20a, each satellite 19c driving the ring gear 19b attached to a second counter-rotating fan shaft 20b

[0349] Whatever the configuration of the reduction mechanism 19, the diameter of the crown 19b and of the planet carrier 19d are greater than the diameter of the sun gear 19a, so that the rotation speed of the rotor 9 of the fan section 2 is lower than the rotation speed of the low pressure shaft 11.

[0350] The reduction ratio of the reduction mechanism 19 is greater than or equal to 2.5 and less than or equal to 11. In the case of a propulsion system 1 with a ducted fan, the reduction ratio can be greater than or equal to 2.7 and less than or equal to 3.5, typically around 3.0. In the case of a propulsion system 1 with an unducted fan, the reduction ratio can be between 9.0 and 11.0.

[0351] [Fig.7] schematically and partially represents, in axial section, an example of a mechanical reducer 19 of the epicyclic type, of which the planet carrier 19d and the sun gear 19a are mobile in rotation, the crown 19b of the reducer 19 being fixed in the frame of reference of the motor.

[0352] At the input, the reducer 19 is connected to the low pressure shaft 11, for example via internal splines 77a. Thus, the low pressure shaft 11 drives the sun gear 19a. The sun gear 19a, whose axis of rotation coincides with the longitudinal axis X, drives a series of satellite gears 19c, which are equally distributed over the same diameter around the axis of rotation X. This diameter is equal to twice the operating center distance between the sun gear 19a and the satellites 19c. The number of satellites 19c is generally defined between three and seven for this type of application.

[0353] The set of satellites 19c is held by a frame formed by the planet carrier 19d. Each satellite 19c rotates around its own rotation axis Y, and meshes with the crown 19b.

[0354] At the output, in this configuration shown in [Fig.7], the set of satellites 19c drives the planet carrier s 19d in rotation around the longitudinal axis X. The crown 19b is fixed to the engine casing or stator via a crown carrier 23 and the planet carrier 19d is fixed to the fan shaft 20.

[0355] In another planetary configuration, the set of planet gears 19c is held by a planet gear carrier 19d which is fixed to the engine casing or stator. Each planet gear 19c drives the ring gear 19b which is attached to the fan shaft 20 via a ring gear carrier 23.

[0356] In another differential configuration, the set of satellites 19c is held by a planet carrier 19d which is connected to a first fan shaft 20a. Each satellite drives the ring gear 19b which is connected to a second counter-rotating fan shaft 20b via a ring gear carrier 23.

[0357] Each satellite 19c is mounted to rotate freely using a bearing 24, for example of the rolling bearing type or of the hydrodynamic type. Each bearing 24 is mounted on one of the axes 25a of the planet carrier 19d and all the axes are positioned relative to each other using one or more structural frames 25b of the planet carrier 19d. There are a number of axes 25a and bearings 24 equal to the number of satellites 19c. For reasons of operation, assembly, manufacturing, control, repair or replacement, the axes 25a and the frame 25b can be separated into several parts.

[0358] For the same reasons as those cited previously, the toothing of a satellite 19c can be separated into several helices or teeth each having a median plane P, P'. In this example, the operation of a reducer 19 of which each satellite 19c comprises two series of chevron teeth cooperating with a crown 19b separated into two half-crowns is detailed below.

[0359] An upstream half-crown 26 consisting of a rim 26a and a fixing half-flange 26b. On the rim 26a is the front propeller meshed with a propeller of the toothing 19cd of each satellite 19c. The propeller of the toothing 19cd also meshes with that of the sun 19a.

[0360] A downstream half-crown 27 consisting of a rim 27a and a fixing half-flange 27b. On the rim 27a is the rear propeller meshed with a propeller of the toothing 19cd of each satellite 19c. The propeller of the toothing 19cd also meshes with that of the sun 19a.

[0361] If the helix widths vary between the sun gear 19a, the satellites 19c and the crown 19b because of the tooth overlaps, they are all centered on a median plane P for the upstream teeth and on another median plane P' for the downstream teeth.

[0362] [Fig.7] thus illustrates the case of a single-stage gear reducer, i.e. the same toothing 19cd of each satellite 19c cooperates with both the sun gear 19a and the crown wheel 19b. Even if the toothing 19cd comprises two series of teeth, these teeth have the same average diameter and form a single toothing called a chevron.

[0363] The fixing half-flange 26b of the upstream crown 26a and the fixing half-flange 27b of the downstream crown 27a form the fixing flange 28 of the crown 19b. The crown 19b is fixed to a crown holder 23 by assembling the fixing flange 28 of the crown 19b and the fixing flange 35 of the crown holder 23 using a bolted assembly for example.

[0364] The arrows FH of [Fig.7] describe the routing of the oil in the reducer 19. The oil arrives in the reducer 19 from the stator part in a distributor 36 by different means which will not be specified in this view because they are specific to one or more types of architecture. The distributor 36 comprises injectors 36a and arms 36b. The injectors 36a have the function of lubricating the teeth and the arms 36b have the function of lubricating the bearings. The oil is brought to the injector 36a to exit through the end 36c in order to lubricate the teeth. The oil is also brought to the arm 36b and circulates via the supply mouth 36d of the bearing. The oil then circulates through the shaft in one or more buffer zones 25c and then exits through the orifices 25d in order to lubricate the bearings 24 of the satellites 19c.

[0365] A reduction mechanism 19 thus comprises several meshes formed between the sun gear 19a and the satellites 19c. In each mesh, a first pinion Pii transmits mechanical rotational energy to a second pinion Pi2 by means of the drive carried out on the active profile of the teeth.

[0366] [Fig.8] schematically represents the film of lubricant, in particular oil, formed between the active profiles of a first toothing of a first pinion Pii of the solar 19a of a reduction mechanism 19 and of a second toothing 19cd of a second pinion Pi2 of a satellite 19c of a series of satellites 19c of the reduction mechanism 19.

[0367] The lubricant film is obtained by means of a lubrication circuit 36a of the reduction mechanism 19 allowing the lubricant to be conveyed between the first toothing of the first pinion Pii and the second toothing 19cd of the second pinion Pi2.

[0368] The minimum height Hm, or minimum thickness, of the lubricant film is shown in [Fig.8]. This is the minimum distance, projected in a radial plane relative to the first pinion Pii and the second pinion Pi2, between the active profiles of the first toothing of the first pinion Pii and the second toothing 19cd of the second pinion Pi2, or the normal minimum distance between the active profiles of the first toothing of the first pinion Pii and the second toothing 19cd of the second pinion Pi2.

[0369] In order to guarantee high operating performance of the reduction mechanism 19, it is essential to ensure a controlled supply of lubricant to the meshing. For this, the value of the minimum height Hm of the lubricant film must be controlled as well as possible.

[0370] In particular, a thick lubricant film, therefore with a significant minimum height Hm, which remains controlled during operation, can make it possible to avoid metal / metal contact between the two active tooth profiles, and therefore makes it possible to limit the risk of contact fatigue, of the micro-chip type (or "micropitting" in English), and the risk of seizure, namely wear in the meshing of the pinions.

[0371] The minimum height Hm, expressed in meters (m), of the lubricant film between the active profiles of the first toothing of the first pinion Pii and the second toothing 19cd of the second pinion Pi2 is defined as:

[0372] Hm = x |qx 0 985 x G0.6 x ^0.7 x 13]

[0373] with:

[0374] _ ? ~ 14^213^1+2,23^83)^0^

[0375] and:

[0376] apXÆet:

[0377] - r MH'1 E = 0.5 x -+2 + | yt ^2 /

[0378] and:

[0379] _ j ui+u2 )et: U Va KI ; I 0 \ '

[0380] 9 |f71| + p2l

[0381] and:

[0382] Ul = TlBx^

[0383] and:

[0384] U2 = T2B x

[0385] and:

[0386] T2B = aw x sin«r - T IBet:

[0387] (Z1+Z2) T = m„x 2xcœ / s +J

[0388] and:

[0389] ZA- Zlet: GR

[0390] ™ = 4 x JdNal2-dM2 -p J*:

[0391] p = mtx.nK cosa,

[0392] and:

[0393] mn

[0394] and:

[0395] “ mn X + 2 X ha

[0396] and:

[0397] db^

[0398] and:

[0399] ,, _ t,,,-,-! ( talion \ «f-tan

[0400] where:

[0401] Pn is the radius of curvature at the contact point B, in meters (m),

[0402] W is the linear load of the teeth, in Newton per meter (N / m),

[0403] P° is the Hertz pressure, in megapascal (MPa),

[0404] L is a thermal parameter, dimensionless,

[0405] E is the Young's modulus of the first tooth or the second tooth, designated Ei for the first tooth and E2 for the second tooth, in pascal (Pa),

[0406] E' is the reduced modulus of elasticity, in pascal (Pa),

[0407] vo is the initial Poisson's ratio,

[0408] vi is the Poisson's ratio of the first tooth,

[0409] v2 is the Poisson's ratio of the second toothing,

[0410] aP is the piezoelectricity coefficient of the lubricant (Pa *),

[0411] is a rotation speed of the first pinion Pii, in radians per second (rad / s), intended to be reached by the first pinion Pii in operation, , û2 is a rotational speed of the second pinion Pi2, in radians per second (rad / s), intended to be reached by the second pinion Pi2 in operation, T2B is the distance between points T2 and B, in meters (m), T2 being the point of tangency between the line of action and the base circle of the second pinion Pi2,

[0412] Z2 is the number of teeth of the second pinion Pi2,

[0413] aw is the operating center distance, in meters (m),

[0414] J is a center distance variation, in meters (m), between 0 mm and 0.8 mm,

[0415] GR is the total reduction ratio,

[0416] T1B is the distance between points Tl and B, in meters (m), B being a characteristic point of the meshing which corresponds to the passage from Nl to N teeth in mesh (N being the maximum number of teeth in mesh according to the driving ratio), and Tl being the point of tangency between the line of action and the base circle of the first pinion Pii,

[0417] dNal is the active head diameter of the first pinion Pii at point B, in meters (m),

[0418] dJA is the diameter of the base circle of the first gable Pii, in meters (m),

[0419] mn is the normal module, in millimeters (mm),

[0420] ZI is the number of teeth of the first pinion Pii,

[0421] fi is the helix angle or primitive inclination angle, in degrees (°),

[0422] h* is the projection height corresponding to the active head diameter for the first toothing,

[0423] at is the transverse or apparent pressure angle, in degrees (°),

[0424] an is the normal pressure angle, in degrees (°).

[0425] [Fig.9] schematically represents the geometric parameters associated with the relative sliding between the first Pii and second Pi2 pinions of the reduction mechanism 19 according to the invention.

[0426] In particular, [Fig.9] represents the meshing of the pair of conjugate profiles of the teeth of the first Pii and second Pi2 pinions whose line of action LAC is tangent at Tl and T2 to the base circles Cbl, of diameter dM, and Cb2, of diameter db2, of the first pinion Pii and the second pinion Pi2. By the very definition of the conjugate profiles, these roll on each other and are constantly tangent. In this [Fig.9] also, the first and second pitch circles are respectively denoted Cyl, of diameter dyi, and Cy2, of diameter dy2.

[0427] Point B is a characteristic point of the meshing which corresponds to the passage from Nl to N teeth in mesh (N being the maximum number of teeth in mesh according to the driving ratio).

[0428] Furthermore, Figures 10 to 15 also make it possible to define other parameters used for the definition of a reduction mechanism according to the invention.

[0429] In [Fig. 10], which represents a tooth D in isolation, the references Ft and Fp respectively designate the tooth flank and the root. The references ha and hf designate respectively the projection height, corresponding to the head diameter, and the hollow height. The reference h is the height of the tooth D.

[0430] Furthermore, in [Fig.l 1], the reference d corresponds to the diameter of the pitch circle, d / 2 being the radius of the pitch circle, and the reference db corresponds to the diameter of the base circle, db / 2 being the radius of the base circle.

[0431] In a cross-section, the transverse or apparent pressure angle at is thus the acute angle formed between the tangent to the involute dv of the toothing at its point of intersection with the pitch circle and the radius passing through this point.

[0432] The normal pressure angle is the projection of the transverse pressure angle at in a plane normal to the teeth. It is defined by the fact that tana„ = tancq x cos / >. In the case of straight teeth, the angles an and at are identical.

[0433] Furthermore, in Figure 12, the active head diameter dNaX of the first pinion Pii and the active head diameter dNa2 of the second pinion Pi2 are shown. Similarly, the base circle diameter dhi of the first pinion Pii and the base circle diameter dh2 of the second pinion Pi2 are shown.

[0434] The projection height corresponding to the active head diameter fa* is also shown in [Fig. 13], the reference d in this [Fig. 13] corresponding to the primitive diameter and the reference da corresponding to the head diameter.

[0435] Figure 14 illustrates the operating center distance aw between the two axes passing through Oi and O2 of the two pinions.

[0436] Furthermore, Figure 15 illustrates the helix angle which is the angle between a tangent ta to a reference helix Hr and the envelope line of the reference cylinder Le passing through the tangent contact point. In this [Fig. 15], PN denotes a normal plane and AX denotes the central axis of the pinion.

[0437] It should be noted that the parameters described in the present application are well known to those skilled in the art and are notably mentioned in the literature cited above, in particular the ISO 6336-22 and 21771-2014 standards.

[0438] Advantageously, the parameters listed above and entering into the calculation of the minimum height Hm of the lubricant film are such that:

[0439] W is chosen such that 200 N / mm < W < 1600 N / mm,

[0440] P° is chosen such that 500 MPa < po < 1800 MPa,

[0441] £ is chosen such that 1.3x 10s <L<2x 10-6>

[0442] E is chosen such that 200 GPa < E < 230 GP a,

[0443] aP is chosen such that I x 10'8 Pd1 < ap < l.8x Hf8 Pa\

[0444] O । is chosen such that 20 rad / s < < 1000 rad / 5

[0445] O2 is chosen such that 200 rad / s < 1000 rad / s, mn is chosen such that 2.5 mm < m < 5 mm,

[0446] ZI is chosen such that 20 < Zj < 60,

[0447] is chosen such that 0.7 xm„ < h* < 1.3 xm^

[0448] P is chosen such that 12° < P < 35°,

[0449] an is chosen such that 15° < an < 28°,

[0450] Pn is chosen such that 0.5 mm < pn < 60 mm,

[0451] vi is chosen such that 0.25 Steps xq < 0.32 Steps,

[0452] v2 is chosen such that 0.25 Steps < v2 - 0.32 Steps,

[0453] vo is chosen such that gxj 0“2 peLS < v0 < 2 X 10"3 PcLS'

[0454] GR is chosen such that 2.5 < GR < 3.5.

[0455] Furthermore, in accordance with the invention, the first Pii and second Pi2 have a relative sliding speed Vg, in meters per second (m / s), and a relative rolling speed Vr, in meters per second (m / s), between the two involute surfaces or active profiles, defined as a function of the parameters O4 and U2 as:

[0456] VS=\U2-U1\

[0457] and:

[0458] Vr=|l / l+t72|

[0459] The relative rolling speed Vr is chosen such that 4 m / s < V). < 50 m / s, and the relative sliding speed Vs is chosen such that if Vr > 4 m / s then Vg < 5 m / s.

[0460] According to a particular embodiment, the relative rolling speed Vr is chosen such that Vr > 30 m / s, and the relative sliding speed L? is chosen such that if Vr > 4 m / s then Vg <5 ml s.

[0461] Furthermore, the relative sliding speed Vg can be chosen such that 0 < Vg < 30 m / 5, and the relative rolling speed Vr and the total reduction ratio GR can be chosen such that:

[0462] - if Vg < 5 m! s then > 4 m! s,

[0463] - if Vg > 5 mf s then 22 > 1.15,

[0464] and 2 < GR < 4.

[0465] Furthermore, according to a particular embodiment, the relative sliding speed Vg is chosen such that 0 < VL < 10 m / s, and the relative rolling speed V,- and the total reduction ratio GR are chosen such that:

[0466] - if Vg <5 ml s then Vr > 4 m! s,

[0467] - if Vg > 5 m / s then 22 > ] [5,

[0468] and 2 < GR < 4.

[0469] Furthermore, the parameter U1 can be chosen such that 0 < Ul < 40 m / 5, or even still 0.5 mj s < / 71 < 40 m / 5, or even: 2 m / S < Ul< 40 mj s.

[0470] Similarly, the parameter U2 can be chosen such that 0 < U2 < 45 m / s.

[0471] According to a particular embodiment, the parameter U1 is chosen such that 0 < / 71 < 0.5 m / s, and the parameter / 72 is chosen such that / 72 < 5 - / 71.

[0472] According to yet another particular embodiment, the parameter U1 is chosen such that / 71 > 0.5 m / s, and the parameter U2 is chosen such that Z72 < 14x ¢ / 1.

[0473] Furthermore, the minimum height Hm of the lubricant film can be chosen such that 0.02 x 10'6 m < Hm < 0.4 x 1() 6 im or in particular such that 0.07 x 10'6 m < Hm < 0.2 x 10"6 m-

[0474] The choice of parameters as proposed in the present invention advantageously allows the obtaining of an adequate lubricant film, making it possible in particular to limit any metal / metal contact between the tooth profiles of the first Pii and second Pi2 pinions.

Claims

Claims

1. Reduction mechanism (19) of an aeronautical propulsion system (1), comprising a sun gear (19a), a ring gear (19b), a planet carrier (19d) and a series of planet gears (19c) rotatably mounted on the planet carrier (19d), the sun gear (19a) comprising a first pinion (Pii) comprising a first toothing and each planet gear (19c) comprising a second pinion (Pi2) comprising a second toothing (19cd) capable of meshing with the first toothing of the first pinion (Pii), the reduction mechanism (19) further comprising a lubrication circuit (36a) capable of conveying lubricant between the first toothing of the first pinion (Pii) and the second toothing (19cd) of at least one second pinion (Pi2), in which the first pinion (Pii) has, with respect to at least one second pinion (Pi2), a relative sliding speed Vg, in meters per second (m / s), and a relative rolling speed Vr, in meters per second (m / s),between the two involute surfaces or active profiles, defined as a function of the parameters U1 and U2 as:, | U2 - t / l| and: Vr = | (71+ (72| with : t / l^TLBxQ, And : U2 = T2B x Q2 And : T2B — aw x sinaj. - TIBet ; And : Zl = Zlet: 1 GR T1B = | x jdN2dh? ~ PJ* : P = m; X TT X cos«r And : min ,n<-^ And : ~ mn X + 2 X ha And : , r~ri COS«r m„xZlx^ And : ar = tan-'(^ ) where: O. is a rotational speed of the first gear (Pii), in radians per second (rad / s), intended to be reached by the first gear (Pii) in operation, O2 is a rotational speed of the second pinion (Pi2), in radians per second (rad / s), intended to be reached by the at least one second pinion (Pi2) in operation, T2B is the distance between points T2 and B, in meters (m), T2 being the point of tangency between the line of action and the base circle of the second pinion (Pi2), Z2 is the number of teeth of the second pinion (Pi2), aw is the operating center distance, in meters (m), J is a center distance variation, in meters (m), between 0 mm and 0.8 mm, GR is the total reduction ratio, T\B is the distance between points Tl and B, in meters (m), B being a characteristic point of the meshing which corresponds to the passage from N-1 to N meshed teeth (N being the maximum number of meshed teeth according to the driving ratio), and Tl being the point of tangency between the line of action and the base circle of the first pinion (Pii), ^Nai is the active head diameter of the first pinion (Pii) at point B, in meters (m), dhl is the diameter of the base circle of the first pinion (Pii), in meters (m), mn is the normal module, in millimeters (mm), Z1 is the number of teeth of the first pinion (Pii), P is the helix angle or primitive inclination angle, in degrees (°), / 7* is the height of the active head diameter for the first toothing, a' is the transverse or apparent pressure angle, in degrees (°), an is the normal pressure angle, in degrees (°), in which the relative rolling speed Vr is chosen such that: 4 m / 5 < Vr <50 m / s and wherein the relative sliding speed Vg is chosen such that: V7 <5 ml s, and: is chosen such that 20 rad / s < < 1000 rad / 5 is chosen such that 200 rad / s < < 1000 rad / s, mn is chosen such that 2.5 mm mn < 5 mm, ZI is chosen such that 20 < < 60, A* is chosen such that o.7 X mn < 1.3 XP is chosen such that 12 ° < fi < 35 ° , an is chosen such that 15 ° < an < 28 ° , GR is chosen such that 2.5 S GR < 3.

5.

2. Reduction mechanism (19) according to claim 1, in which the relative rolling speed V,- is chosen such that: Vr >30 mis.

3. A reduction mechanism (19) according to claim 1 or 2, wherein the parameter U1 is chosen such that: 0 < (71 < 40 m / s

4. A reduction mechanism (19) according to any preceding claim, wherein the parameter U2 is chosen such that: 0 < U2<45mls

5. Reduction mechanism (19) according to claim 3 or 4, in which the parameter Ul is chosen such that: 0 <Ul<Q,5m / s et dans lequel le paramètre U2 est choisi de telle sorte que : U2 <5- (71 [Revendication 6] Mécanisme de réduction (19) selon la revendication 3 ou 4, dans lequel le paramètre U1 est choisi de telle sorte que : (71 > 0.5 mj s and in which the parameter U2 is chosen such that: U2< 14 x [71

7. Reduction mechanism (19) according to any one of the preceding claims, in which for the first pinion (Pii) and at least one second pinion (Pi2) is defined a minimum height parameter Hm, in meters (m), or minimum thickness, of the lubricant film, in particular of the oil, between the active profiles of the first toothing of the first pinion (Pii) and of the second toothing (19cd) of at least one second gable (Pi2) defined as: Hm^ px\Ct xQ,9$5x G?' 6 x U®' 1 rn LJ with : l-13.2x(f )xL'42 1+0.213x(i+2.23xS°-83)xL0^4 And : G - apx Eet ; And : V y | £l±met: Go I 0 \ E*p„ / |C7\-U21 | C71H I72| Or : W is the linear load of the teeth, in Newton per meter (N / m), P° is the Hertz pressure, in megapascal (MPa), i is a thermal parameter, dimensionless, E is the Young's modulus of the first or second toothing, designated Ei for the first toothing and E2 for the second toothing, in pascal (Pa), E' is the reduced modulus of elasticity, in pascals (Pa), vo is the initial Poisson's ratio, vi is the Poisson's ratio of the first toothing, v2 is the Poisson's ratio of the second toothing, aP is the piezoelectric coefficient of the lubricant (Pa '), Pn is the radius of curvature at the contact point B, in meters (m), in which the minimum height Hm of the lubricant film is chosen such that: 0.02 x 10*6 m < Hm < 0.4 x 10*6 m And : W is chosen such that 200 N / mm < IV < 1600 N / mm, P° is chosen such that 500 MPa < po < 1800 MPa, I is chosen such that} ,3 x 10“s < L < 2 x 10"6 , E is chosen such that 200 GPa <E< 230 GPa. aP is chosen such that 1 x 10'8 Pa 1 < ap < 1.8 x Kï8 Pdl, Pn is chosen such that 0.5 mm < p < 60 mm, vi is chosen such that 0.25 Steps < < 0.32 Steps, v2 is chosen such that 0.25 Steps < v2 - 0.32 Steps, vo is chosen such that gx 10'2 steps < < 2 x 1Q-3

8. Reduction mechanism (19) according to claim 7, wherein the minimum height Hm of the lubricant film is chosen such that: 0.07 x 10-6 m < Hm < 0.2 x 10-6 m

9. A reduction mechanism (19) according to any preceding claim, wherein the first toothing of the first pinion (Pii) and the second toothing (19cd) of each second pinion (Pi2) comprise straight, helical or herringbone type teeth.

10. Reduction mechanism (19) according to any one of the preceding claims, in which: - each satellite (19c) comprises one or two meshing stages, and / or - the planet carrier (19d) is in one piece or comprises a cage defining an internal housing for receiving the solar (19a) and the satellites (19c), and / or - each satellite (19c) is centered and guided in rotation about an axis by a bearing carried by the planet carrier (19d), each bearing being of the rolling element type or of the hydrodynamic type.

11. An aeronautical propulsion system (1) comprising: - a power turbine (8), in particular a low-pressure turbine, and a turbine drive shaft (11), in particular a low-pressure shaft, driven in rotation by the power turbine (8) about a longitudinal axis (X), - a fan rotor (9) and a fan shaft (20), the fan rotor (9) being rotationally coupled to the fan shaft (20), - a reduction mechanism (19) according to any one of the preceding claims, comprising an inlet connected to the turbine drive shaft (11) and an outlet connected to the fan shaft (20), capable of driving the fan rotor (9) in rotation about the longitudinal axis (X) via the turbine drive shaft (11) and the fan shaft (20) at a rotational speed lower than that of the power turbine (8).

12. Method for dimensioning a reduction mechanism (19) of an aeronautical propulsion system (1) comprising a power turbine (8), in particular a low-pressure turbine, and a turbine drive shaft (11), in particular a low-pressure shaft, driven in rotation by the power turbine (8) about a longitudinal axis (X), and a fan rotor (9) and a fan shaft (20), the fan rotor (9) being rotatably coupled to the fan shaft (20), the reduction mechanism (19) having an input for connection to the turbine drive shaft (11), and an output for connection to the fan shaft (20), and being adapted to drive the fan rotor (9) in rotation about the longitudinal axis (X) by means of the turbine drive shaft (11) and the fan shaft (20) at a rotational speed lower than that of the power turbine (8), the reduction mechanism (19) comprising a sun gear (19a), a crown gear (19b), a planet carrier (19d) and a series of satellites (19c) rotatably mounted on the planet carrier (19d), the solar (19a) comprising a first pinion (Pii) comprising a first toothing and each satellite (19c) comprising a second pinion (Pi2) comprising a second toothing (19cd) capable of meshing with the first toothing of the first pinion (Pii), the reduction mechanism (19) further comprising a lubrication circuit (36a) capable of conveying lubricant between the teeth of the first (Pii) and second (Pi2) pinions, in which the first pinion (Pii) has, with respect to a second pinion (Pi2), a relative sliding speed Vg, in meters per second (m / s), and a relative rolling speed Vr, in meters per second (m / s), between the two involute surfaces or active profiles, defined as a function of the parameters U\ and U2 as: | U2 - t / l| and: Vr = | t / l + f / 2| with : And : U2 = T2B x Q2 And : T2B — aw x sinaf - TIBet: (Z1+Z2) j aw= +J And : 71 — . / ¾. and i Zl ~ GR TIB= pet — mt xnx cosat et: min And : d N a\ ~ mn X + 2 X ha And : -fr~z | COSt^i ^1 = m«xZlx7^ and: «r = tan“!(~™J Or : is a rotational speed of the first gear (Pii), in radians per second (rad / s), intended to be reached by the first gear (Pii) in operation, fT is a rotation speed of the second pinion (Pi2), in radians per second (rad / s), intended to be reached by the at least one second pinion (Pi2) in operation, T2B is the distance between points T2 and B, in meters (m), T2 being the point of tangency between the line of action and the base circle of the second gable (Pi2), Z2 is the number of teeth of the second pinion (Pi2), aw is the operating center distance, in meters (m), J is a center distance variation, in meters (m), between 0 mm and 0.8 mm, GR is the total reduction ratio, T1B is the distance between points Tl and B, in meters (m), B being the characteristic point of the meshing which corresponds to the passage from N-1 to N teeth in mesh (N being the maximum number of teeth in mesh according to the driving ratio), and Tl being the point of tangency between the line of action and the base circle of the first pinion (Pii), dNa} is the active diameter of the head of the first pinion (Pii) at point B, in meters (m), dhi is the diameter of the base circle of the first pinion (Pii), in meters (m), mn is the normal module, in millimeters (mm), Z1 is the number of teeth of the first pinion (Pii), fi is the helix angle or primitive inclination angle, in degrees (°), is the height of the active head diameter for the first toothing, a' is the transverse or apparent pressure angle, in degrees (°), an is the normal pressure angle, in degrees (°), the method comprising a step of dimensioning the reduction mechanism (19) during which the relative rolling speed V r is chosen such that: 4 m / s < V,.< 50 m / s and in which the relative sliding speed V? is chosen such that: Vg<5m / s, and: H, is chosen such that 20 rad / 5 < < 1000 rad / 5 is chosen such that 200 rad} s < < 1000 rad / s, mn is chosen such that 2.5 mm < m < 5 mm, Z1 is chosen such that 20 < Zt < 60, h* is chosen such that 0.7 x mn < fa* < 1.3 X m^, fi is chosen such that 12° < P < 35 ° , an is chosen such that 15° < an < 28 ° , GR is chosen such that 2.5 < GR < 3.

5.

13. Dimensioning method according to claim 12, comprising a step of dimensioning the reduction mechanism (19) during which the relative rolling speed is chosen such that: Vr>30m / s and in which the relative sliding speed Vg is chosen such that: - if Vr > 4 m / s then Vg < 5 m / s.

14. A sizing method according to claim 12 or 13, comprising a step of sizing the reduction mechanism (19) during which the parameter U1 is chosen such that: 0 < <40 m / .y

15. A sizing method according to any one of claims 12 to 14, comprising a step of sizing the reduction mechanism (19) during which the parameter U2 is chosen such that: 0 <U2<45m / s

16. A sizing method according to claim 14 or 15, comprising a step of sizing the reduction mechanism (19) during which the parameter U1 is chosen such that: 0< Ul<0.5m / s and in which the parameter U2 is chosen such that: U2<5- U1

17. A sizing method according to claim 14 or 15, comprising a step of sizing the reduction mechanism (19) during which the parameter U1 is chosen such that: U1 > 0.5 mjs and in which the parameter U2 is chosen such that: U2 < 14 x U1

18. Sizing method according to any one of claims 12 to 17, wherein for the first pinion (Pii) and at least one second pinion (Pi2) is defined a minimum height parameter Hm, in meters (m), or minimum thickness, of the lubricant film, in particular of the oil, between the active profiles of the first toothing of the first pinion (Pii) and the second toothing (19cd) of at least one second pinion (Pi2) defined as: Hm pn x [ü / x 0.985 x G0'6 x G0'7 x IT0'13] with: cw^f)*^42 1+0.213x( i+2.23x1S0'83)xL064 and: G - ap^ Eet ; E= [0^x(^+ ^)]4 and: tt / UMn iet: U = ynx ° \ Expn 1 If7l472| R71Hl72| where: W is the linear load of the teeth, in Newton per meter (N / m), P° is the Hertz pressure, in megapascal (MPa), i is a thermal parameter, dimensionless, E is the Young's modulus of the first or second teeth toothing, designated Ei for the first toothing and E2 for the second toothing, in pascal (Pa), E' is the reduced modulus of elasticity, in pascal (Pa), vo is the initial Poisson's ratio, vi is the Poisson's ratio of the first toothing, v2 is the Poisson's ratio of the second toothing, aP is the piezoelectric coefficient of the lubricant (Pa '), Pn is the radius of curvature at the point of contact B, in meters (m), the method comprising a step of dimensioning the reduction mechanism (19) during which the minimum height Hm of the lubricant film is chosen such that: 0.02 x 10-6 m < Hm < 0.4 x 10'6 m And : W is chosen such that 200 N / mm < W < 1600 N / mm, P° is chosen such that 500 MPa < po < 1800 MPa, L is chosen such that 1 3 x 10'8 <L<2x 10A E est choisi de telle sorte que 200 GPa <E< 230 GPa. ai> is chosen so that 1 x 10'8 Pa1 £ ap <1.8x10“s Pa Pn is chosen so that 0.5 mm < pn < 60 mm, vi is chosen so that 0.25 Pas < V j £ 0.32 Pas, v2 is chosen so that 0.25 Pas < v2 - 0.32 Pas, V° is chosen so that 8 x 10'2 Pas < v0 < 2 x 10'3 Pas-

19. A sizing method according to claim 18, comprising a step of sizing the reduction mechanism (19) during which the minimum height Hm of the lubricant film is chosen such that: 0.07 x 10-6 m < Hm < 0.2 x 10-6 m

20. A reduction mechanism (19) manufactured from a dimensioning method according to any one of claims 12 to 19.

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