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 planets (19c), the sun gear (19a) comprising a first pinion having a first set of teeth and each planet (19c) comprising a second pinion having a second set of teeth (19cd) adapted to mesh with the first set of teeth of the first pinion, the reduction mechanism (19) comprising a lubrication circuit (36a) adapted to convey lubricant between the teeth, in which the first pinion has, with respect to at least a 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 the abbreviation: 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 blower section, a compressor section which may include a low pressure compressor and a high pressure compressor, a combustion chamber and a turbine section which may include a high pressure turbine and a low pressure turbine.

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

[0004] Climate change is a major concern for many legislative and regulatory bodies worldwide. 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 and to those already in service, requiring the implementation of technological solutions to bring them into compliance with current regulations. Civil aviation has been actively working for several years now to contribute to the fight against climate change.

[0005] Technological research efforts have already led to significant improvements in the environmental performance of aircraft. The Applicant takes into account the factors impacting all phases of design and development in order to obtain less energy-intensive and 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 operation of virtuous development and manufacturing processes and limiting greenhouse gas emissions to the minimum possible in order to reduce the environmental footprint of its activity.

[0007] This sustained research and development work focuses on 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 provide propulsion, and, as essential complements to technological progress, aviation biofuels.

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

[0009] For example, in order to improve the propulsive efficiency of an aircraft propulsion system and reduce its specific fuel 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 mass of the aircraft, and thus reduce its fuel consumption, it has been found that it is advantageous to make 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 lifespan.

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

[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] The new generations of double-flow turbomachinery, in particular those having High dilution ratios are achieved by incorporating such a mechanical gearbox to drive the blower shaft (also called a "fan"). Typically, the gearbox's purpose is to transform the high rotational speed of a power turbine shaft into a slower rotational speed for the blower driving shaft, thus allowing independent control of the blower and power turbine rotational speeds.

[0014] Such a reduction gear comprises a central pinion, called the sun gear, a ring gear, and pinions called planet gears, which mesh between the sun gear and the ring gear. The planet gears are held by a frame called a planet carrier. The sun gear, ring gear, and planet carrier are planetary gears because their axes of revolution coincide with the longitudinal axis of the turbomachine. Each planet gear has an axis of revolution, these axes being different and equally spaced on the same operating diameter around the axis of the planetary gears. These axes are parallel to the longitudinal axis.

[0015] There are several gearbox architectures. In the state of the art of double-flow turbomachinery, gearboxes are of the planetary or epicyclic type.

[0016] In other similar applications, there are architectures called differential or "compound" in English.

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

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

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

[0020] Gear reducers can be composed of one or more meshing stages. This meshing is achieved in various ways, such as by contact, friction, or magnetic fields. There are several types of contact meshing, such as with spur, helical, or herringbone teeth.

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

[0022] A satellite may comprise one or two gear stages. A single-stage satellite comprises teeth that may be straight, helical, or chevron-shaped, and whose teeth are located on the same diameter. These teeth cooperate with both the sun gear and the crown gear.

[0023] A two-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 satellite carrier may be a single unit or may comprise a cage defining an internal housing designed to accommodate solar panels and satellites.

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

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

[0027] To ensure high operating performance of the reducer, it is necessary to ensure a sufficient supply of lubricant to the gear mesh. This supply of lubricant, particularly oil, improves the efficiency of 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 gear(s).

[0028] Parameters have been defined in the prior art to define conditions under which the gear is supplied with lubricant so as to meet the needs stated above. One can cite in particular 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 height, of the lubricant film, especially the oil film, is the parameter that best represents the lubrication system of the contact surfaces of the teeth.

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

[0031] In particular, it is necessary to ensure the thickest, or highest, lubricant film possible to prevent metal-to-metal contact between the two active tooth profiles. Indeed, eliminating metal-to-metal contact limits the risk of contact fatigue due to mixed lubrication, such as micro-pitting, and the risk of seizure, namely the wear of two gears that mesh together.

[0032] Thus, it is necessary to guarantee a minimum lubricant film height during operation to ensure lubrication of the gearbox and prevent metal-to-metal contact between the gears. However, the minimum lubricant film height depends on numerous parameters related to the gear teeth of the reducer 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 gears of a reduction mechanism so as to be able to dimension 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 aircraft performance and, in this sense, contributes to reducing the environmental impact of aircraft.

[0035] For this purpose, the invention relates to a reduction mechanism of an aeronautical propulsion system, comprising a solar element, a ring gear, a satellite carrier and a series of satellites mounted rotatably on the satellite carrier, the solar element comprising a first pinion having a first set of teeth and each satellite comprising a second pinion having a second set of teeth suitable for meshing with the first set of teeth of the first pinion,

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

[0037] wherein the first pinion has, with respect to at least a 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 pinion, in radians per second (rad / s), intended to be reached by the first pinion in operation, ^2 is a rotational speed of the second pinion, in radians per second (rad / s), intended to be achieved by 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 T1 and B, in meters (m), B being a characteristic point of the meshing that corresponds to the transition from N1 to N teeth in mesh (N being the maximum number of teeth in mesh according to the drive ratio), and T1 being the point of tangency between the line of action and the circle of the base 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 pinion, in meters (m),

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

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

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

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

[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 / s

[0077] and in which the relative sliding velocity 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 such 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 slip velocity 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 oil, between the active profiles of the first tooth of the first pinion and the second tooth of at least one second pinion 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 Newtons per meter (N / m),

[0130] P° is the Hertzian pressure, in megapascals (MPa),

[0131] L is a dimensionless thermal parameter,

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

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

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

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

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

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

[0138] Pn is the radius of curvature at the point of contact 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 Pas £ rq < 0.32 Pas,

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

[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 in such a way that: 0.07 x 10-6 m < Hm < 0.2 x 10-6 m

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

[0153] In one embodiment:

[0154] - each satellite comprises one or two interlocking stages, and / or

[0155] - the satellite carrier is a single unit or comprises a cage defining a housing internal to receive solar and satellite signals, and / or

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

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

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

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

[0160] - a reduction mechanism as defined above, comprising an input connected to the turbine drive shaft and an output connected to the blower shaft, suitable for driving the blower rotor in rotation around the longitudinal axis via the turbine drive shaft and the blower shaft at a rotational speed lower than that of the power turbine.

[0161] In addition, the invention also relates, according to another aspect, 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 rotationally coupled 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 blower shaft, and being suitable for driving the blower rotor in rotation around the longitudinal axis by means of the turbine drive shaft and the blower shaft at a rotational speed lower than that of the power turbine,

[0163] the reduction mechanism comprising a solar element, a crown, a satellite carrier and a series of satellites rotatably mounted on the satellite carrier,

[0164] the solar element comprising a first pinion having a first set of teeth and each satellite comprising a second pinion having a second set of teeth suitable for meshing with the first set of teeth of the first pinion,

[0165] the reduction mechanism further comprising a lubrication circuit designed to convey lubricant between the teeth of the first and second gears,

[0166] wherein the first pinion has, with respect to at least a 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 pinion, in radians per second (rad / s), intended to be achieved by the first pinion in operation, û2 is a rotational speed of the second pinion, in radians per second (rad / s), intended to be reached by 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 on the second pinion,

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

[0193] J is a center distance variation, 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 pinion, in meters (m),

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

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

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

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

[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 dimensioning step of the reduction mechanism during which the relative rolling speed Vr is chosen such that:

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

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

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

[0208] and:

[0209] fl] is chosen such that 20 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 includes 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 slip velocity Vg is chosen such that:

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

[0220] In one embodiment, the process includes a sizing step of the reduction mechanism in 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 includes 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] et2 <GÆ<4.

[0232] In one embodiment, the method includes 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 includes 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 includes 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 includes 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 oil, between the active profiles of the first tooth of the first pinion and the second tooth 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 - [0.5x (-^ + 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 Newtons per meter (N / m), P° is the Hertzian pressure, in megapascals (MPa). L is a dimensionless thermal parameter, E is the Young's modulus of the first or second gear, designated Ei for the first tooth and E2 for the second tooth, in pascals (Pa), E' is the reduced modulus of elasticity, in pascals (Pa), v₀ is the initial Poisson's ratio, 'i is the Poisson's ratio of the first gear, v2 is the Poisson's ratio of the second gear, 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 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 / 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 Pas < rq < 0.32 Pas,

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

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

[0279] In one embodiment, the process includes a sizing step of the reduction mechanism in 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] In addition, the invention also relates, according to another of its aspects, to a reduction mechanism manufactured from a dimensioning process as defined above. PRESENTATION OF THE DRAWINGS

[0281] Other features and advantages will become apparent from the following description, which is purely illustrative and not exhaustive, and should be read in conjunction with the accompanying figures, among which:

[0282] - [Fig. 1] schematically represents an aircraft comprising systems propulsives,

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

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

[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 epicycloidal 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 epicycloidal reduction mechanism,

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

[0290] - [Fig.9] represents, schematically and partially, the highlighting of the relative slippage 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 defining a reduction mechanism according to the invention. DETAILED DESCRIPTION OF IMPLEMENTATION METHODS

[0292] In the example illustrated in [Fig. 1], 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 by means of a pylon. In another embodiment, the aircraft could include one or more propulsion system(s) attached to fuselage 101.

[0293] Figure 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 twin-body gas turbine engine with a shrouded fan.

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

[0296] The blower section 2 comprises a blower 22 and a blower housing 12. The blower 22 comprises a blower rotor 9. The blower housing 12 surrounds the blower rotor 9. The blower rotor 9 is rotatably mounted relative to the blower 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 variable pitch. In the latter case, each of the fan blades 14 is pivotally mounted relative to the fan hub 13 about a pitch axis and is connected to a pitch-changing mechanism (not shown) mounted in the propulsion system 1. The pitch-changing mechanism allows the pitch angle of the fan blades 14 to be adjusted according to the flight phases.

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

[0299] Furthermore, in this example, the blower section 2 also includes a blower stator 16 fixedly mounted on the blower housing 12. The blower stator 16 includes fixed blades 17 generally referred to as "outlet guide vanes" (or "OGV"). This set of fixed blades serves to straighten and regulate the airflow downstream of the blower rotor 9 to contribute to engine thrust. This set of fixed blades also plays a role in noise reduction.

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

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

[0303] Compressor section 29 includes a low pressure compressor 4 and a high pressure compressor 5.

[0304] The low-pressure compressor 4 includes a rotor 41 suitable for being driven in rotation relative to the housing 31 of the propulsion system 1 and a stator 42 fixedly mounted on the housing 31.

[0305] The rotor 41 of the low-pressure compressor 4 comprises movable wheels 4a and the stator 42 of the low-pressure compressor 4 comprises fixed wheels 4b. The movable 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 includes a rotor 51 suitable for being driven in rotation relative to the housing 31 of the propulsion system 1 and a stator 52 fixedly mounted on the housing 31.

[0307] The rotor 51 of the high-pressure compressor 5 includes movable wheels 5a and the stator 52 of the high-pressure compressor 5 includes fixed wheels 5b. The movable 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 adapted to be driven in rotation relative to the housing 31 of the propulsion system 1 and a stator 72 fixedly mounted on the housing 31.

[0310] The rotor 71 of the high-pressure turbine 7 comprises rotating wheels 7a and the stator 72 of the high-pressure turbine 7 comprises fixed wheels 7b. The rotating 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 adapted to be driven in rotation relative to the housing 31 of the propulsion system 1 and a stator 82 fixedly mounted on the housing 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 includes 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 mounted rotatably relative to the housing 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 blower shaft 20 and a reduction mechanism 19. The blower rotor 9 is rotationally coupled to the blower 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 blower shaft 20. Thus, when the propulsion system 1 is in operation, the rotor 81 of the low-pressure turbine 8 drives not only the rotor 41 of the low-pressure compressor 4, but also the blower rotor 9, via the low-pressure shaft 11, the reduction mechanism 19, and the blower shaft 20.

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

[0317] The reduction mechanism 19 thus allows independent control of the rotation speed of the blower 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 blower shaft 20, the reduction mechanism 19 and the blower 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 housing 31 about 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 through 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 can 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 can be contra-rotating, i.e., driven in opposite directions of rotation around the longitudinal axis X.

[0323] The double-body propulsion system 1 may in particular include 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 in [Fig.2]).

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

[0325] The low-pressure turbine 8 comprises at least three stages (as illustrated in the example in [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 airflow F entering the propulsion system 1 passes through the blower 22 and is then divided between a primary airflow Fl and a secondary airflow F2, which flow upstream to downstream in the propulsion system 1.

[0328] The secondary airflow F2, also called the "bypass airflow", flows in the secondary vein, around the primary body 3. The secondary airflow F2 cools the periphery of the primary body 3 and is used to generate most of the thrust provided by the propulsion system 1.

[0329] The primary airflow Fl flows in a primary channel 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 airflow Fl through the turbine section 30, receiving energy from the combustion chamber 6, causes rotation of the impellers 7a, 8a of the turbine section 30, which in turn rotate the impellers 4a, 5a of the compressor section 29 as well as the blower rotor 9.

[0330] In order to improve the propulsive efficiency of the propulsion system 1 and to reduce its specific fuel consumption as well as the noise emitted by the fan section 2, the propulsion system 1 has a high bypass ratio. A "high" bypass ratio is defined as 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 the ratio of the mass flow rate of the secondary airflow F2 to the mass flow rate of the primary airflow Fl, 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 being then simpler to perform.

[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 blower 22 and The rotational speed of the low-pressure turbine 8 allows for a reduction in the rotational speed and pressure ratio of the blower rotor 9 while increasing the power extracted by the low-pressure turbine 8. Indeed, the overall efficiency of the propulsion system 1 is primarily determined by the propulsion efficiency, which is favorably influenced by minimizing the variation in kinetic energy of the air as it passes through the propulsion system 1. In a propulsion system with a high bypass ratio, the majority of the flow generating the propulsive force consists of the secondary airflow F2 of the propulsion system 1, the kinetic energy of the secondary airflow F2 being mainly affected by the compression that the secondary airflow F2 undergoes as it passes through the blower section 2.The propulsive efficiency and the pressure ratio of the blower section 2 are therefore linked: the lower the pressure ratio of the blower section 2, the better the propulsive efficiency. In order to improve the propulsive efficiency of the propulsion system 1, the blower pressure ratio, which corresponds to the ratio between the average pressure at the outlet of the blower stator 16 (or, in the absence of a stator 16, of the blower rotor 9) and the average pressure at the inlet of the blower 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, that is to say from the surface which radially delimits inside the airflow duct at the inlet of the fan rotor 9 to the top 21 of the fan blade 14. .

[0332] The peripheral velocity at the tip 21 of the fan blades 14 can also be between 260 meters per second (m / s) and 400 meters per second (m / s) 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 can 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 on the order of 90 inches (228.6 cm), which allows the propulsion system 1 to be integrated 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 a 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-shaft gas turbine engine with an unducted fan. It may be an "Open Rotor" or "Unducted Single Fan" type gas turbine engine.

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

[0340] Since the fan section 2 is unfaired, the fan blades 14 have variable pitch. Thus, each fan blade 14 is pivotally mounted about a pitch axis relative to the fan hub 13 and is connected to a pitch-changing mechanism 15 mounted in the propulsion system 1. The pitch-changing mechanism allows the pitch angle of the fan blades 14 to be adjusted according to the flight phases. Similarly, the outlet blades 17 have variable pitch, the base of the outlet blades 17 being pivotally mounted about a pitch axis and connected to a pitch-changing mechanism 15, the pitch being adjusted according to the flight phases by the pitch-changing mechanism.

[0341] Alternatively, the propulsion system 1 could comprise two unducted, counter-rotating fan rotors 9. Such a propulsion system 1 is known, in Anglo-Saxon terminology, by the acronym "CROR" for "Contra-Rotating Open Rotor" or "UDF" for "Unducted Double Fan". The fan rotors 9 can be positioned 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 puller type.

[0342] The absence of a fairing around the fan rotor 9 allows for a significant increase in the bypass ratio without the propulsion system 1 being negatively impacted by the mass of the housings 12 or nacelles intended to surround the fan section 2. The bypass ratio of the propulsion system 1, including an unfaired fan section 2, is thus greater than or equal to 40, for example, between 40 and 80 inclusive. The peripheral velocity at the tip 21 of the fan blades 14 of the fan rotor(s) 9 can also be between 210 meters per second (m / s) and 260 meters per second (m / s) inclusive. The fan pressure ratio can then preferably be between 0.90 and 1.20 inclusive.

[0343] The diameter D of the blower rotor 9 can 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 blower rotor 9 is measured here in a plane normal to the longitudinal axis X, which is the axis of rotation of the blower rotor 9, at the intersection between a vertex 21 and a leading edge 22 of the blower blades 14.

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

[0345] The reduction mechanism 19 may include an epi-cycloidal, planetary or differential reduction mechanism, single-stage, also called monostage, or multi-stage, in particular two-stage, also called bistage.

[0346] For example, [Fig. 4] illustrates a planetary (or "star") type reduction mechanism 19. The reduction mechanism 19 comprises a sun pinion 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 pinion 19a and configured to drive the blower shaft 20 in rotation about its axis X of rotation, and a series of satellites 19c distributed circumferentially around the axis X of rotation of the rotor 9 of the blower section 2, between the sun pinion 19a and the ring gear 19b, each satellite gear 19c being internally meshed with the sun pinion 19a and externally with the ring gear 19b.The series of satellites 19c is mounted on a satellite carrier 19d which is fixed relative to a stator part 19e of the propulsion system 1, for example relative to a housing of the compressor section 4, 5.

[0347] In another example, [Fig.5] illustrates an epi-cycloidal (or "planetary" in English) type reduction mechanism 19, in which case the ring 19b is fixedly mounted on the stator part 19e of the propulsion system 1 and the blower shaft 20 is driven in rotation by the planet carrier 19d.

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

[0349] Regardless of the configuration of the reduction mechanism 19, the diameter of the ring gear 19b and the planet carrier 19d are greater than the diameter of the solar pinion 19a, so that the rotational speed of the rotor 9 of the blower section 2 is less than the rotational 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 ducted fan propulsion system 1, the 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 unfaired blower, 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 epicycloidal type, whose planet carrier 19d and sun 19a are mobile in rotation, the ring 19b of the reducer 19 being fixed in the frame 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 planet gears 19c, which are equally spaced around the same diameter about the axis of rotation X. This diameter is equal to twice the operating center distance between the sun gear 19a and the planet gears 19c. The number of planet gears 19c is generally defined as between three and seven for this type of application.

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

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

[0355] In another planetary configuration, the set of satellites 19c is held by a planet carrier 19d which is fixed to the motor or stator housing. Each satellite 19c drives the ring gear 19b which is connected to the blower shaft 20 via a ring carrier 23.

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

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

[0358] For the same reasons as those mentioned above, the teeth 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, each satellite 19c comprising two sets of chevron teeth cooperating with a ring 19b separated into two half-rings, is detailed below.

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

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

[0361] If the helix widths vary between the solar 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 tooth set 19cd of each satellite 19c cooperates with both the solar 19a and the ring gear 19b. Even though the tooth set 19cd comprises two sets of teeth, these teeth have the same average diameter and form a single set of teeth called a chevron.

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

[0364] The arrows FH in [Fig. 7] describe the oil supply to the gearbox 19. The oil enters the gearbox 19 from the stator section via a distributor 36 by various means, which will not be specified in this view as they are specific to one or more types of architecture. The distributor 36 comprises injectors 36a and arms 36b. The injectors 36a lubricate the gear teeth, and the arms 36b lubricate the bearings. The oil is supplied to the injector 36a and exits through the end 36c to lubricate the gear teeth. The oil is also supplied to the arm 36b and circulates through the bearing's supply port 36d. The oil then flows through the shaft into one or more buffer zones 25c and then out through the orifices 25d to lubricate the bearings 24 of the satellites 19c.

[0365] A reduction mechanism 19 thus comprises several meshes formed between the solar 19a and the satellites 19c. In each mesh, a first pinion Pi1 transmits a rotational mechanical energy to a second pinion Pi2 by means of the drive made on the active profile of the teeth.

[0366] Figure 8 schematically represents the lubricant film, in particular oil, formed between the active profiles of a first toothing of a first pinion Pii of the solar element 19a of a reduction mechanism 19 and 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 through a lubrication circuit 36a of the reduction mechanism 19 allowing the lubricant to be routed between the first tooth of the first pinion Pii and the second tooth 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 with respect to the first gear Pii and the second gear Pi2, between the active profiles of the first tooth of the first gear Pii and the second tooth 19cd of the second gear Pi2, or the normal minimum distance between the active profiles of the first tooth of the first gear Pii and the second tooth 19cd of the second gear 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 gear mesh. For this purpose, the value of the minimum height Hm of the lubricant film must be controlled as closely as possible.

[0370] In particular, a thick lubricant film, therefore with a significant minimum height Hm, which remains controlled during operation, can prevent metal / metal contact between the two active tooth profiles, and thus limits the risk of contact fatigue, of the micro-pitting type, and the risk of seizing, namely wear in the meshing of the gears.

[0371] The minimum height Hm, expressed in meters (m), of the lubricant film between the active profiles of the first tooth of the first pinion Pii and the second tooth 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 point of contact B, in meters (m),

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

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

[0404] L is a dimensionless thermal parameter,

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

[0406] E' is the reduced modulus of elasticity, in pascals (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 gear,

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

[0411] 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, , û2 is a rotational speed of the second pinion Pi2, in radians per second (rad / s), intended to be achieved 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 drive 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 pinion Pii, in meters (m),

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

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

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

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

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

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

[0425] Figure 9 schematically represents the geometric parameters associated with the relative slippage between the first Pi1 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 Pi1 and second Pi2 pinions whose line of action LAC is tangent at T1 and T2 to the base circles C1b, of diameter dM, and C2, of diameter db2, of the first pinion Pi1 and the second pinion Pi2. By the very definition of 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 C1, of diameter d1, and C2, of diameter d1.

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

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

[0429] On [Fig. 10], which shows a single tooth D, the references Ft and Fp These respectively designate the tooth flank and the root. The references ha and hf respectively designate the projection height, corresponding to the head diameter, and the concave height. The reference h is the height of the tooth D.

[0430] In addition, on [Fig.1 1], the reference d corresponds to the diameter of the primitive circle, d / 2 being the radius of the primitive 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 gear 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 αt onto a plane normal to the teeth. It is defined by the fact that tan α = tan θ x cos θ. In the case of straight teeth, the angles αt and αt 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 on [Fig. 13], the reference d on this [Fig. 13] corresponding to the pitch 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 point of contact. 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 this application are well known to the person skilled in the art and are mentioned in particular in the literature cited above, especially ISO 6336-22 and 21771-2014 standards.

[0438] Advantageously, the parameters listed above and used in calculating 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 GPa,

[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 Pas xq < 0.32 Pas,

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

[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 Pi1 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 according to 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 velocity Vs is chosen such that if Vr > 4 m / s then Vg < 5 m / s.

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

[0461] Furthermore, the relative slip velocity Vg can be chosen such that 0 < Vg < 30 m / 5, and the relative rolling speed Vr and the total reduction ratio GRs 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 mjS, 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 10⁶ m < Hm < 0.4 x 10⁶ m, or even in such a way 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 obtaining an adequate lubricant film, making it possible in particular to limit any metal / metal contact between the tooth profiles of the first Pi1 and second Pi2 pinions.

Claims

Demands

1. A 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) having a first set of teeth and each planet gear (19c) comprising a second pinion (Pii) having a second set of teeth (19cd) adapted to mesh with the first set of teeth of the first pinion (Pii), the reduction mechanism (19) further comprising a lubrication circuit (36a) adapted to convey lubricant between the first set of teeth of the first pinion (Pii) and the second set of teeth (19cd) of at least one second pinion (Pii), wherein the first pinion (Pii) has, relative to at least one second pinion (Pii), a relative sliding velocity Vg, in meters per second (m / s), and a relative rolling speed Vr, in meters per second (m / s),between the two surfaces of involutes or active profiles, defined according to 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 pinion (Pii), in radians per second (rad / s), intended to be reached by the first pinion (Pii) in operation. O2 is a rotational speed of the second pinion (Pi2), in radians per second (rad / s), intended to be reached by 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 that corresponds to the transition from N-1 to N meshed teeth (N being the maximum number of meshed teeth according to the drive 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 pitch angle, in degrees (°), / 7* is the height of the active head diameter for the first gear, a' is the transverse or apparent pressure angle, in degrees (°), an is the normal pressure angle, in degrees (°), in which the rolling speed relative Vr is chosen such that: 4 m / s < Vr < 50 m / s and in which the relative sliding velocity 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 0.7 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, wherein the relative rolling speed V,- is chosen such that: Vr >30 mis.

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

4. Reduction mechanism (19) according to any one of the preceding claims, wherein the parameter U2 is chosen such that: 0 < U2 < 45 mls

5. Reduction mechanism (19) according to claim 3 or 4, wherein 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, wherein for the first pinion (Pi1) and at least one second pinion (Pi2) a minimum height parameter Hm, in meters (m), or minimum thickness, of the lubricant film, in particular oil, between the active profiles of the first toothing of the first pinion (Pi1) and the second toothing (Pi2) is defined, of at least one second pinion (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: Va I 0 \ E*p„ / |C7\-U21 | C71H I72| Or : W is the linear load of the teeth, in Newtons per meter (N / m), P° is the pressure in Hertz, in megapascals (MPa), i is a dimensionless thermal parameter, E is the Young's modulus of the first or second tooth, designated Ei for the first tooth and E2 for the second tooth, in pascals (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 gear teeth, v2 is the Poisson's ratio of the second gear teeth, 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} 0.3 x 10⁻³ s < L < 2 x 10⁻⁶, E is chosen such that 200 GPa <E< 230 GPa. aP is chosen such that 1 x 10⁸ 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. Reduction mechanism (19) according to any one of the preceding claims, wherein the first teeth of the first pinion (Pii) and the second teeth (19cd) of each second pinion (Pi2) have straight, helical or chevron-type teeth.

10. Reduction mechanism (19) according to any one of the preceding claims, wherein: - each satellite (19c) has one or two meshing stages, and / or - the satellite carrier (19d) is monobloc or has 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 satellite carrier (19d), each bearing being of the rolling element type or of the hydrodynamic type.

11. 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 input connected to the turbine drive shaft (11) and an output connected to the fan shaft (20), 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).

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 blower rotor (9) and a blower shaft (20), the blower rotor (9) being rotationally coupled to the blower shaft (20), the reduction mechanism (19) having an inlet for connection to the turbine drive shaft (11), and an outlet for connection to the blower shaft (20), and being adapted to drive the blower rotor (9) in rotation about the longitudinal axis (X) by means of the turbine drive shaft (11) and the blower shaft (20) at a rotational speed lower than that of the power turbine (8), the reduction mechanism (19) comprising a solar element (19a), a ring (19b), a satellite carrier (19d) and a series of satellites (19c) mounted rotatably on the satellite carrier (19d), the solar element (19a) comprising a first pinion (Pii) having a first set of teeth and each satellite element (19c) comprising a second pinion (Pi2) having a second set of teeth (19cd) suitable for meshing with the first set of teeth of the first pinion (Pii), the reduction mechanism (19) further comprising a lubrication circuit (36a) suitable for conveying lubricant between the teeth of the first (Pi1) and second (Pi2) pinions, in which the first pinion (Pi2) has, relative 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 U1 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 pinion (Pii), in radians per second (rad / s), intended to be reached by the first pinion (Pii) in operation, fT is a rotational speed of the second pinion (Pi2), in radians per second (rad / s), intended to be reached by 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 on 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 mesh 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 drive 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 pitch angle, in degrees (°), is the height of the active head diameter for the first tooth, a' is the transverse or apparent pressure angle, in degrees (°), an is the normal pressure angle, in degrees (°), the process comprising a dimensioning step of 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 velocity 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. A dimensioning method according to claim 12, comprising a dimensioning step of 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 sizing step of 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 sizing step of 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 sizing step of the reduction mechanism (19) in which the parameter U1 is chosen such that: 0 < U1 < 0.5 m / 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 sizing step of the reduction mechanism (19) in 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. A sizing method according to any one of claims 12 to 17, wherein for the first pinion (Pi1) and at least one second pinion (Pi2) 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 (Pi1) and the second toothing (Pi2) of at least one second pinion (Pi2) is 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 Newtons per meter (N / m), P° is the pressure in Hertz, in megapascals (MPa), i is a dimensionless thermal parameter, E is the Young's modulus of the first or second tooth denture, designated Ei for the first denture and E2 for the second denture, in pascals (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 gear teeth, v2 is the Poisson's ratio of the second gear teeth, aP is the piezoelectric coefficient of the lubricant (Pa'), Pn is the radius of curvature at the contact point B, in meters (m), the process comprising a dimensioning step of 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 10⁸ <L<2x 10A E est choisi de telle sorte que 200 GPa <E< 230 GPa. ai> is chosen such that 1 x 10⁸ Pa₁ ≤ ap < 1.8 x 10⁻⁸ Pa, Pₙ is chosen such that 0.5 mm < pₙ < 60 mm, vi is chosen such that 0.25 Pt < Vₙ ≤ 0.32 Pt, v₂ is chosen such that 0.25 Pt < v₂ - 0.32 Pt, Vₙ is chosen such that 8 x 10⁻² Pt < v₀ < 2 x 10⁻³ Pt

19. A sizing method according to claim 18, comprising a sizing step of 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. Reduction mechanism (19) manufactured from a sizing process according to any one of claims 12 to 19.

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