AN EXHAUST CASING FOR A TURBOMACHINE
The invention relates to an exhaust casing for a turbomachine. It is applicable to any type of turbomachine, whether terrestrial or for aviation purposes, and more particularly to airplane turbojets.
More precisely, the invention relates to an exhaust casing for a turbomachine, comprising:
• a hub centered on an axis and carrying, on each of its upstream and downstream faces, an annular endplate that is coaxial with the hub;
• an outer shroud coaxial with the hub; and
• a plurality of arms interconnecting said hub and said shroud, each arm presenting opposite first and second side faces in which the hub and the outer shroud are spaced apart radially by a length written L;
in which, in a radial section plane, the first side face of each arm forms an acute angle with the tangent to the outer periphery of each endplate, said angle lying in the range 60° to 85°; and in which the first side face of each arm is connected to each endplate via a connection portion.
In the present application, "upstream" and "downstream" are defined relative to the normal flow direction of fluid flowing through the turbomachine (from upstream to downstream). Furthermore, the axial direction corresponds to the direction of the axis of rotation A of the turbomachine rotor, and a radial direction is a direction perpendicular to the axis A. Similarly, an axial plane is a plane that includes the axis of rotation A, and a radial plane is a plane perpendicular to the axis A. Finally, unless specified to the contrary, adjectives such as "inner" and "outer" are used with reference to a radial direction such that an inner portion (i.e. radially inner) of an element is closer to the axis A than is the outer portion (i.e. radially outer) of the same element.

Accompanying Figures 1 to 3 show an example of an exhaust casing 12 of the above-specified type.
Figure 1 is an axial half-section on the axis of rotation A of the rotor of the turbojet showing a two-spool bypass turbojet 1. From upstream to downstream, the turbojet 1 comprises: a fan 2; a low-pressure compressor 4; a high-pressure compressor 6; a high-pressure turbine 8; a low-pressure turbine 10; and said exhaust casing 12.
The casing 12 is thus situated downstream from the low-pressure turbine 10. The casing 12 contributes to defining the primary flow section of the fluid passing through the turbojet. Furthermore, the casing 12 supports the rotor of the turbojet and ensures that the rotor and the stator are coaxial. Finally, the oil that lubricates the bearings of the turbojet is fed and removed via the casing 12.
With reference to Figures 2 and 3, the casing 12 comprises:
• a hub 14 centered on the axis A and carrying respectively on its upstream and downstream faces upstream and downstream annular endplates 16 and 18, coaxial with the hub 14;
• an outer shroud 20 coaxial with the hub 14; and
• a plurality of arms 22 connecting the hub 14 to the shroud 20 (there being sixteen arms in the example shown).
The upstream and downstream annular endplates 16 and 20 are contained substantially in a radial plane and they project outwards towards the shroud 20.
Each arm 22 presents first and second opposite side faces 22a and 22b. In a radial plane, such as the plane of Figure 3, the first side face 22a of each arm 22 forms an acute angle "a" with the tangent to the outer periphery of each endplate 16, 18, the angle "a" lying in the range 60° to 85°. Furthermore, the first side face

22a of each arm 22 is connected to each endplate 16, 18 via a connection portion 24.
The lifetime of presently known exhaust casings is found to be insufficient, and an object of the invention is to increase said lifetime.
In their research that led to the invention, the inventors have found that when the turbojet is in operation, the exhaust casing is subjected to the temperature gradient between the outer shroud and the hub, which temperature gradient gives rise to stresses in the connection portion; and since the level of stress reached in this connection portion is high, the lifetime of the casing suffers therefrom.
Until now, in known exhaust casings, the profile of the connection portion in a radial section plane has been defined by a circular arc having a radius of 3 millimeters (mm).
The invention proposes an exhaust casing of the above-specified type having a connection portion with a profile that is optimized in such a manner as to reduce the level of stress in the connection portion, and thus increase the lifetime of the exhaust casing.
Thus, the present invention provides an exhaust casing for a turbomachine comprising:
• a hub centered on an axis and carrying, on each of its upstream and downstream faces, an annular endplate that is coaxial with the hub;
• an outer shroud coaxial with the hub; and
• a plurality of arms interconnecting said hub and said shroud, each arm presenting opposite first and second side faces in which the hub and the outer shroud are spaced apart radially by a length written L; and
in which, in a radial section plane, the first side face of each arm forms an acute angle with the tangent to the outer periphery of each endplate, said angle lying in the range 60° to 85°;
wherein the first side face of each arm is connected to
each endplate by a connection root of profile, in a
radial section plane, that is defined by a spline passing
via N control points, N being an integer greater than or
equal to 10, these N control points being defined as
follows:
let O be the point of intersection in said radial section
plane between the straight-line extending the first side
face and the outer periphery of an endplate;
let there be a first straight-line segment H starting
from the point 0 and following the straight line
extending said first side face in said radial plane, this
segment being of length written il lying in the range 3%
to .15% of the length L, and this segment being subdivided
into N equal segments by N+l points written H(l), H(2),
..., H(N+1), the point H(N+1) coinciding with the point
0;
let there be a second straight-line segment B starting
from the point 0 and following the tangent at the point 0
to the outer periphery of said endplate in said radial
plane, said segment having a length written (2 lying in
the range 25% to 50% of 11, and said segment being
subdivided into N equal segments by N+l points written
B(l), B(2), ..., B(N+1), the point B(N+1) being the
furthest from the point O, and
let D(l), D(2), ..., D(N+1) be the N+l straight lines
respectively interconnecting the points B(l) to H(l),
B(2) to H(2), ..., and B(N+1) to H(N+1);
said N control points are the points of intersection
between D(l) and D(2), between D(2) and D(3), ..., and
between D(N) and D(N+1).
It is recalled that the length written L is the radial distance between the hub and the outer shroud of the casing.
According to the invention, the profile of the connection root is thus a spline (a spline curve) that is

determined in particular by the choices made for the two parameters (1 and 12.
The length (1 is selected to be greater than 3% of the length L so that the profile of the connection root is sufficiently extended to provide a good distribution of stresses in the root. This good distribution determines a lower level of stress, and thus improves the lifetime of the casing. In addition, when the length {1 is less than 3% of the length L, the feasibility problems can be encountered in the connection root, in particular when the casing is made by casting.
The length II is selected to be less than 15% of the length L so as to avoid excessively stiffening the connection between the hub and the arm, and so as to limit the weight of the casing.
In analogous manner, the length 12 is selected to be greater than 25% of the length (1 so as to ensure a good distribution of the stresses in the connection portion, and so as to guarantee that the connection root can be made, in particular by casting. The length (2 is selected to be less than 50% of the length tl so as to avoid excessively stiffening the connection between the hub and the arm in question, and so as to limit the weight of the casing.
The shape selected for the profile of the connection root, namely a spline, also contributes to optimizing the distribution of stresses in the root, and thus to minimizing the level of stress in said root so as to improve the lifetime of the casing.
The invention and its advantages can be better understood on reading the following detailed description of an embodiment of an exhaust casing of the invention. This detailed description makes reference to the accompanying figures, in which:
• Figure 1 is an axial half-section on the axis A of rotation of a turbojet rotor and showing an example of an airplane turbojet;

• Figure 2 is a front view in perspective of an example of an exhaust casing of the same type as the invention;
• Figure 3 is a rear view of the exhaust casing of Figure 2, the plane of Figure 3 being a radial plane, perpendicular to the axis A; and
• Figure 4 is a detailed view of the connection root between the downstream annular endplate of the hub and the first side face of one of the structural arms of the casing, in a radial section plane containing said connection root.
Figures 1 to 3 are described above and show an example of an exhaust casing of the same type as the invention. The invention relates more particularly to the connection portion (see Figures 3 and 4) between the first side face 22a of each arm 22 and each annular endplate 16, 18 of the hub 14.
Such a connection portion 24 is shown in detail in Figure 4, in section in a radial section plane containing said portion 24. In Figure 4, it can be seen that the connection portion 24 between the first side face 22a of an arm 22 and the outer periphery of the downstream annular endplate 18 is a connection root of profile that is defined by a spline S.
The spline S passes through N control points, where N is equal to 10 in this example. These N control points are defined as follows: let 0 be the point of intersection in the radial section plane of Figure 4 between the straight line extending the first side face 22a and the outer periphery of the downstream annular endplate 18. A first straight line segment H is selected starting from the point 0 and following the straight line that extends the first side face 22a in the section plane of Figure 4. This segment H has a length (1. This length (1 is selected to be 3% to 15% of the length L (shown in Figure 3). This segment H is subdivided into 10 equal segments by 11 points marked HI, H2, ..., Hll,

wnere the point Hll coincides with the point 0, as shown in Figure 4. Thereafter, a second straight line segment B is selected starting from the point 0 and following the tangent at the point 0 to the outer periphery of the downstream annular endplate 18, in the section plane of Figure 4. The segment B is generally much shorter than the circular outer periphery of the annular endplate, so this segment remains very close to the outer periphery, and in Figure 4 it appears to coincide with said outer periphery. The segment B has a length written (2 selected to lie in the range 25% to 50% of the length 11. This segment is subdivided into 10 equal segments by 11 points marked Bl, B2, ..., Bll, where the point Bll is the furthest from the point 0, as can be seen in Figure 4. Thereafter, the 11 straight lines written Dl, D2,..., Dll are drawn that interconnect respectively the points Bl and HI, B2 and H2, ..., and Bll and Hll (it should be observed that the straight line Dl comprises LUG segment H and LUCIL une s^raignu j_ine JJ_i_l comprises the segment B). Thereafter, the points of intersection between the straight lines Dl and D2, D2 and D3, ..., and D10 and Dll are identified. This produces the 10 points of intersection identified by crosses in Figure 4. Finally, a spline S is caused to pass through these 10 control points.
By way of illustration, an exhaust casing of the type shown in the figures can present the following dimensions:
inside diameter of the shroud 20: 1000 mm; outside diameter of the annular endplates 16 and 18: 4 65 mm;
spacing between the arms 22 at the shroud 20: 200 mm; length L: 535 mm (1000 - 465);
length tl: 40 mm (i.e. about 7.5% of L); and length 12: 16 mm (i.e. about 40% of 11).

CLAIMS
1. An exhaust casing (12) for a turbomachine, the casing
comprising:
• a hub (14) centered on an axis (A) and carrying, on each of its upstream and downstream faces, an annular endplate (16, 18) that is coaxial with the hub;
• an outer shroud (20) coaxial with the hub; and
• a plurality of arms (22) interconnecting said hub and said shroud, each arm presenting opposite first and second side faces (22a, 22b) in which the hub and the outer shroud are spaced apart radially by a length written L; and
in which, in a radial section plane, the first side face (22a) of each arm forms an acute angle (a) with the tangent to the outer periphery of each endplate (16, 18), said angle (a) lying in the range 60° to 85°; the casing being characterized in that the first side face (22a) of each arm is connected to each endplate (16, 18) by a connection root of profile, in a radial section plane, that is defined by a spline passing via N control points, N being an integer greater than or equal to 10, these N control points being defined as follows: let 0 be the point of intersection in said radial section plane between the straight-line extending the first side face and the outer periphery of an endplate; let there be a first straight-line segment (H) starting from the point 0 and following the straight-line extending said first side face in said radial plane, this segment being of length written 11 lying in the range 3% to 15% of the length L, and this segment being subdivided into N equal segments by N+l points written H(l), H(2), ..., H(N+1), the point H(N+1) coinciding with the point 0;
let there be a second straight-line segment (B) starting from the point 0 and following the tangent at the point O to the outer periphery of said endplate in said radial plane, said segment having a length written (2 lying in

the range 25% to 50% of 11, and said segment being
subdivided into N equal segments by N+l points written
B(l), B(2), ..., B(N+1), the point B(N+1) being the
furthest from the point 0, and
let D(l), D(2), ..., D(N+1) be the N+l straight lines
respectively interconnecting the points B(l) to H(l),
B(2) to H(2), ..., and B(N+1) to H(N+1);
said N control points are the points of intersection
between D(l) and D(2), between D(2) and D(3), ..., and
between D(N) and D(N+1).
2. A turbomachine including an exhaust casing according to claim 1.
3. An exhaust casing (12) for a turbomachine substantially as hereinbefore described with reference to the accompanying drawings.