CN104019091B - The design method of low-pressure turbine rear axle - Google Patents

Abstract

The invention discloses a kind of low-pressure turbine rear axle and design method thereof, for solving existing low-pressure turbine rear axle front extension fitting surface and the technical problem of the radial interference fit place seal action difference between runway fitting surface of obturaging.Technological scheme is front extension fitting surface is the conical surface, corresponding in the two-dimensional axisymmetric plane structure of equivalent-simplification, the cross section of front extension fitting surface is the line segment of the in axial direction right low left high that is connected to form by front extension fitting surface cross section left end point and fitting surface cross section, front extension right endpoint, and front extension fitting surface and the magnitude of interference at radial interference fit place obturaged between runway fitting surface in axial direction increase from left to right successively.Because front extension fitting surface adopts the conical surface, the balanced distribution situation of the radial displacement of front extension fitting surface and the radial displacement of runway fitting surface of obturaging, front extension fitting surface and the radial interference fit place of obturaging between runway fitting surface operationally do not produce gap, improve the seal action of runway of obturaging.

Description

The design method of low-pressure turbine rear axle

Technical field

The present invention relates to a kind of low-pressure turbine rear axle, also relate to the design method of this low-pressure turbine rear axle.

Background technique

With reference to Fig. 1 ~ 3, document " Chen Guang, Hong Jie, horse bright red. aero gas turbine engine structure [M]. Beijing: publishing house of BJ University of Aeronautics & Astronautics, 2010. " a kind of low-pressure turbine rear axle is disclosed, this low-pressure turbine rear axle is by low-pressure turbine rear shaft neck 2, angled transition section 3, rear extension is obturaged runway 5, vertical changeover portion 7, the axis of comb tooth 9 and front extension 10 formation of obturaging is the hollow disc type part of gyration center 1, the top of angled transition section 3 has circumferentially uniform oil through 4, the root of vertical changeover portion 7 has circumferentially uniform vent 6, the top of vertical changeover portion 7 has circumferentially uniform bolt hole 8, the vertical section of front extension 10 has circumferentially uniform rivet pin nail 14.The radial interference fit 13 that low-pressure turbine rear axle and the radial Placement of obturaging between runway 12 are front extension fitting surface 15 and obturage between runway fitting surface 18, axial Placement is the riveted joint of circumferentially uniform riveted joint pin 11.Front extension fitting surface 15 is cylndrical surface, corresponding in the two-dimensional axisymmetric plane structure of equivalent-simplification, the cross section of front extension fitting surface 15 is a line segment being parallel to axial direction be connected to form by fitting surface cross section, front extension left end point 19 and fitting surface cross section, front extension right endpoint 20.The magnitude of interference of radial interference fit 13 is in axial direction equal everywhere, is Δ=0.1mm.Low-pressure turbine rear axle is set up and the equivalent simplified model of runway assembly of obturaging in commercial FEM-software ANSYS, suppose the join strength engineering demands of riveting pin 11, riveted joint pin joint is connected, ignore oil through 4, vent 6, the dentation structure of bolt hole 8 and comb tooth 9 of obturaging, assembly is reduced to axisymmetric two-dimensional model, use axisymmetric Plane Entity unit PLANE82 to assembly grid division, osculating element TARGE169 and CONTA172 is used to simulate radial interference fit 13, apply displacement boundary conditions, rotating speed and temperature loading, carry out the finite element analysis considering contact.Finite element analysis results shows, and the quality of assembly is M ₀=6.1kg, operationally there is gap in radial interference fit 13 place, and the stress concentration degree at runway knuckle 16 place of obturaging is very large, vonMises equivalent stress is herein 1169MPa, also be the maximum vonMises equivalent stress of the overall situation of assembly, exceeded the yield limit 700MPa of runway material therefor of obturaging.

The major technique shortcoming of the rear axle of low-pressure turbine disclosed in document is, front extension fitting surface 15 and radial interference fit 13 place of obturaging between runway fitting surface 18 operationally there will be gap, have impact on the seal action of runway to Low Pressure Turbine Rotor countershaft brought forward lubricating cavity lubricating oil of obturaging, can oil leakage be caused and catch fire and cause turbine to lose efficacy, cause the containment of motor to lose efficacy and wrap up thus.

Summary of the invention

In order to overcome existing low-pressure turbine rear axle front extension fitting surface and the deficiency of the radial interference fit place seal action difference between runway fitting surface of obturaging, the invention provides a kind of low-pressure turbine rear axle.The front extension fitting surface of this low-pressure turbine rear axle is the conical surface, corresponding in the two-dimensional axisymmetric plane structure of equivalent-simplification, the cross section of front extension fitting surface is the line segment of the in axial direction right low left high that is connected to form by front extension fitting surface cross section left end point and fitting surface cross section, front extension right endpoint, and front extension fitting surface and the magnitude of interference at radial interference fit place obturaged between runway fitting surface in axial direction increase from left to right successively.

The present invention also provides the design method of this low-pressure turbine rear axle.The assembly equivalent-simplification of low-pressure turbine rear axle and runway of obturaging is axisymmetric two-dimension plane structure by the method, in commercial FEM-software ANSYS, use the radial interference fit that osculating element is simulated front extension and obturaged between runway, carry out the finite element analysis considering contact.The coordinate choosing front extension fitting surface cross section left end point and right endpoint is design variable, using the maximum radial displacement of the node on the fitting surface of front extension as objective function, introduce the constraint conditio that the contact of osculating element is not less than a less positive pressure, by the quality of structure, the maximum vonMises equivalent stress of the maximum contact pressure of osculating element and low-pressure turbine rear axle and runway each several part of obturaging is also as constraint conditio, set up shape optimum model, the parameter of setting genetic algorithm, genetic algorithm is used to carry out iterative, finally be optimized design result.The present invention can ensure front extension fitting surface and the radial interference fit place of obturaging between runway fitting surface does not operationally produce gap, and seal action is good.The stress simultaneously reducing the knuckle place of runway of obturaging when structure is not overweight and stress does not transfinite is concentrated.

The technical solution adopted for the present invention to solve the technical problems is: a kind of low-pressure turbine rear axle, by low-pressure turbine rear shaft neck 2, angled transition section 3, rear extension is obturaged runway 5, vertical changeover portion 7, obturage comb tooth 9 and front extension 10 forms the hollow disc type part that axis is gyration center 1, the top of angled transition section 3 has circumferentially uniform oil through 4, the root of vertical changeover portion 7 has circumferentially uniform vent 6, the top of vertical changeover portion 7 has circumferentially uniform bolt hole 8, the vertical section of front extension 10 has circumferentially uniform rivet pin nail 14, be characterized in that front extension fitting surface 15 is for the conical surface, corresponding in the two-dimensional axisymmetric plane structure of equivalent-simplification, the cross section of front extension fitting surface 15 is the line segment of the in axial direction right low left high that is connected to form by fitting surface cross section, front extension left end point 19 and fitting surface cross section, front extension right endpoint 20, front extension fitting surface 15 and the magnitude of interference at radial interference fit 13 place between runway fitting surface 18 of obturaging axially increase from left to right successively.

The tapering of described front extension fitting surface 15 is in formula, x ₁for the radial coordinate of fitting surface cross section, front extension left end point, y ₁for the axial coordinate of fitting surface cross section, front extension left end point, x ₂for the radial coordinate of fitting surface cross section, front extension right endpoint, y ₂for the axial coordinate of fitting surface cross section, front extension right endpoint.

A design method for above-mentioned low-pressure turbine rear axle, is characterized in adopting following steps:

Step one, low-pressure turbine rear axle is set up and the equivalent simplified model of runway assembly of obturaging in commercial FEM-software ANSYS, suppose the join strength engineering demands of riveting pin place, riveted joint pin joint is connected, ignore oil through, vent, bolt hole, the dentation structure of rivet pin nail and comb tooth of obturaging, assembly is reduced to axisymmetric two-dimensional model, extension fitting surface radial coordinate everywhere Δ=0.1mm less of the radial coordinate of runway fitting surface of obturaging before making when modeling, simulate front extension fitting surface and the magnitude of interference of the radial interference fit between runway fitting surface of obturaging, it can be used as the initial designs of shape optimization problem.Setting x ₁, y ₁and x ₂for variable element.Wherein, x ₁for the radial coordinate of fitting surface cross section, front extension left end point, y ₁for the axial coordinate of fitting surface cross section, front extension left end point, x ₂for the radial coordinate of fitting surface cross section, front extension right endpoint.

Step 2, low-pressure turbine rear axle and runway of obturaging to be composed respectively with respective material properties.

Step 3, the setting grid length of side, use Plane Entity dividing elements structured grid to assembly.The solid element of front extension fitting surface generates one deck object element as target face, the solid element of runway fitting surface of obturaging generates one deck osculating element as surface of contact, to object element and osculating element compose with identical real constant numbering target face and surface of contact be identified as contact right, in order to the radial interference fit simulating front extension fitting surface and obturage between runway fitting surface.

Step 4, displacement boundary conditions and rotating speed, temperature loading condition are applied to the FEM (finite element) model of structure.

Step 5, all or part of as design variable in three variable elements in selecting step one, the maximum radial displacement of the node in the past on the fitting surface of extension is objective function, the contact of osculating element is not less than a less positive pressure as first constraint conditio, the contact of osculating element is no more than contact allowable as second constraint conditio, the maximum vonMises equivalent stress of the maximum vonMises equivalent stress of axle unit after low-pressure turbine and runway unit of obturaging is no more than the allowable stress of respective material as third and fourth constraint conditio, the quality of assembly is no more than the upper limit as the 5th constraint conditio, finally increase other constraint conditios as required, set up the mathematical model of shape optimum:

$\left\{\begin{array}{cc}find& X,\\ \min & f\left(X\right)=u_{\max }^t=\max \{u_1^t,u_2^t,\mathrm{...},u_i^t,\mathrm{...},u_{Nnum}^t\}\\ s.t.& {\mathrm{\σ}}_j^{CN}\≥\underset{\‾}{{\mathrm{\σ}}^{CN}},j=1,2,\mathrm{...},Cnum\\ & {\mathrm{\σ}}_j^{CN}\≤\stackrel{\‾}{{\mathrm{\σ}}^{CN}},j=1,2,\mathrm{...},Cnum\\ & \mathrm{\σ}_{\max }^{VN}{}_1=\max \{\mathrm{\σ}_1^{VN}{}_1,\mathrm{\σ}_2^{VN}{}_1,\mathrm{...},\mathrm{\σ}_k^{VN}{}_1,\mathrm{...},\mathrm{\σ}_{Enum1}^{VN}{}_1\}\≤\stackrel{\‾}{\mathrm{\σ}_{\max }^{VN}{}_1},\\ & \mathrm{\σ}_{\max }^{VN}{}_2=\max \{\mathrm{\σ}_1^{VN}{}_2,\mathrm{\σ}_2^{VN}{}_2,\mathrm{...},\mathrm{\σ}_l^{VN}{}_2,\mathrm{...},\mathrm{\σ}_{Enum2}^{VN}{}_2\}\≤\stackrel{\‾}{\mathrm{\σ}_{\max }^{VN}{}_2},\\ & M\≤\stackrel{\‾}{M},\\ & G_m\left(X\right)\≤0,m=1,2,\mathrm{...},Gnum\\ & H_n\left(X\right)=0,n=1,2,\mathrm{...},Hnum\end{array}\right.$

Wherein, X is design variable sequence; F (X) is the objective function of optimization problem, the maximum radial displacement of the node on the fitting surface of front extension, be the radial displacement of i-th node on the fitting surface of front extension, Nnum is the number of node on the fitting surface of front extension; the contact of a jth osculating element, σ ^cN be the lower limit of contact, be generally a smaller positive pressure, be contact allowable, Cnum is the number of osculating element; the maximum vonMises equivalent stress of axle unit after low-pressure turbine, be the vonMises equivalent stress of axle unit after a kth low-pressure turbine, Enum1 is the number of unit of low-pressure turbine rear axle, it is the allowable stress of shaft material after low-pressure turbine; the maximum vonMises equivalent stress of runway unit of obturaging, be that l to obturage the vonMises equivalent stress of runway unit, Enum2 is the number of unit of runway of obturaging, obturage the allowable stress of track material; M is the quality of assembly, it is the quality upper limit of assembly; G _m(X) represent other inequality constraints condition of m, Gnum is the number of inequality constraints condition; H _n(X) represent the n-th other equality constraint, Hnum is the number of equality constraint.

In step 6, the basis of Optimized model set up in step 5, setting design variable upper and lower, Population Size, random seed produce probability, mutation probability, crossover probability and genetic algebra parameter, adopt genetic algorithm to be optimized design.

The invention has the beneficial effects as follows: because front extension fitting surface adopts the design of the conical surface, the magnitude of interference at the radial interference fit place making front extension fitting surface and obturage between runway fitting surface in axial direction increases from left to right successively, the balanced operationally distribution situation of the radial displacement of front extension fitting surface and the radial displacement of runway fitting surface of obturaging, the radial interference fit place meeting front extension fitting surface and obturage between runway fitting surface does not operationally produce the requirement in gap, improves the seal action of runway to lubricating cavity lubricating oil before bearing of obturaging.The radial interference fit place that the invention solves front extension fitting surface and obturage between runway fitting surface operationally can produce the problem in gap, simultaneously under stress does not transfinite the prerequisite not overweight with structure, the stress reducing runway knuckle place of obturaging is concentrated, and improves the fatigue life of structure.

After low-pressure turbine in embodiment 1,2,3,4, operationally, front extension fitting surface and the radial interference fit place of obturaging between runway fitting surface operationally all do not produce gap to the assembly of axle construction and runway of obturaging.

In embodiment 1, the quality of assembly is 6.005kg, does not exceed quality upper limit 6.1kg; The maximum vonMises equivalent stress of the overall situation of assembly is 730.407MPa, does not exceed the allowable stress 890MPa of its material; The vonMises stress at runway knuckle place obturaged is 476.808MPa, does not exceed the allowable stress 700MPa of its material, reduces 59.21% than the 1169MPa in document.

In embodiment 2, the quality of assembly is 5.988kg, does not exceed quality upper limit 6.1kg; The maximum vonMises equivalent stress of the overall situation of assembly is 744.567MPa, does not exceed the allowable stress 890MPa of its material; The vonMises stress at runway knuckle place obturaged is 380.353MPa, does not exceed the allowable stress 700MPa of its material, reduces 67.46% than the 1169MPa in document.

In embodiment 3, the quality of assembly is 6.004kg, does not exceed quality upper limit 6.1kg; The maximum vonMises equivalent stress of the overall situation of assembly is 715.073MPa, does not exceed the allowable stress 890MPa of its material; The vonMises stress at runway knuckle place obturaged is 449.779MPa, does not exceed the allowable stress 700MPa of its material, reduces 61.52% than the 1169MPa in document.

In embodiment 4, the quality of assembly is 5.988kg, does not exceed quality upper limit 6.1kg; The maximum vonMises equivalent stress of the overall situation of assembly is 738.503MPa, does not exceed the allowable stress 890MPa of its material; The vonMises stress at runway knuckle place obturaged is 386.718MPa, does not exceed the allowable stress 700MPa of its material, reduces 66.92% than the 1169MPa in document.

Below in conjunction with the drawings and specific embodiments, the present invention is elaborated.

Accompanying drawing explanation

Fig. 1 is the assembly relation schematic diagram of background technique low-pressure turbine rear axle and runway of obturaging.

Fig. 2 is the structural representation of background technique low-pressure turbine rear axle.

Fig. 3 is the enlarged view at background technique low-pressure turbine rear axle front extension fitting surface and the radial interference fit place between runway fitting surface of obturaging.

Fig. 4 is the structural representation of low-pressure turbine rear axle of the present invention.

Fig. 5 is equivalent-simplification two-dimensional axisymmetric areal model and boundary conditions, the load schematic of low-pressure turbine rear axle of the present invention and runway assembly of obturaging.

Fig. 6 is the enlarged view at the embodiment of the present invention 1 mesolow turbine rear axle front extension fitting surface and the radial interference fit place between runway fitting surface of obturaging.

Fig. 7 is the enlarged view at the embodiment of the present invention 2 mesolow turbine rear axle front extension fitting surface and the radial interference fit place between runway fitting surface of obturaging.

Fig. 8 is the embodiment of the present invention 3 design variable definition schematic diagram.

Fig. 9 is the enlarged view at the embodiment of the present invention 3 low-pressure turbine rear axle front extension fitting surface and the radial interference fit place between runway fitting surface of obturaging.

Figure 10 is the embodiment of the present invention 4 design variable definition schematic diagram.

Figure 11 is the enlarged view at the embodiment of the present invention 4 low-pressure turbine rear axle front extension fitting surface and the radial interference fit place between runway fitting surface of obturaging.

In figure, 1-gyration center, 2-low-pressure turbine rear shaft neck, 3-angled transition section, 4-oil through, extends runway of obturaging after 5-, 6-vent, the vertical changeover portion of 7-, 8-bolt hole, 9-obturages comb tooth, the front extension of 10-, 11-rivets pin, 12-obturages runway, 13-radial interference fit, 14-rivet pin nail, 15-front extension fitting surface, 16-obturages runway knuckle, 17-front extension chamfering, and 18-obturages runway fitting surface, fitting surface cross section, 19-front extension left end point, fitting surface cross section, 20-front extension right endpoint.

Embodiment

Following examples are with reference to Fig. 4-11.

Embodiment 1: low-pressure turbine rear axle, be the hollow disc type part of gyration center 1 by obturage runway 5, axis that vertically changeover portion 7, comb tooth 9 of obturaging, front extension 10 are formed of low-pressure turbine rear shaft neck 2, angled transition section 3, rear extension, the top of angled transition section 3 has circumferentially uniform oil through 4, the root of vertical changeover portion 7 has circumferentially uniform vent 6, the top of vertical changeover portion 7 has circumferentially uniform bolt hole 8, and the vertical section of front extension 10 has circumferentially uniform rivet pin nail 14.Front extension fitting surface 15 is the conical surface, its tapering is 1:19.9643, corresponding in the two-dimensional axisymmetric plane structure of equivalent-simplification, the cross section of front extension fitting surface 15 is the line segment of the in axial direction y right low left high that is connected to form by fitting surface cross section, front extension left end point 19 and fitting surface cross section, front extension right endpoint 20.The magnitude of interference of front extension fitting surface 15 and the radial interference fit 13 between runway fitting surface 18 of obturaging axially y increases from left to right successively, the magnitude of interference at left end point 19 place, fitting surface cross section, front extension is 0.0022mm, the magnitude of interference at right endpoint 20 place, fitting surface cross section, front extension is 0.201mm, and front extension chamfering 17 is 45 degree with the angle of axial direction y.

The equivalent-simplification two-dimensional axisymmetric areal model of the assembly of the low-pressure turbine rear axle in commercial FEM-software ANSYS in modeling analysis the present embodiment and runway of obturaging, Finite element analysis results shows, and front extension fitting surface 15 and radial interference fit 13 place of obturaging between runway fitting surface 18 operationally do not produce gap; The quality of assembly is 6.005kg, does not exceed quality upper limit 6.1kg; The maximum vonMises equivalent stress of assembly is 730.407MPa, does not exceed the allowable stress 890MPa of its material; The vonMises equivalent stress at runway knuckle place of obturaging is 476.808MPa, does not exceed the allowable stress 700MPa of its material, reduces 59.21% than the 1169MPa in document.

Embodiment 2: low-pressure turbine rear axle, be the hollow disc type part of gyration center 1 by obturage runway 5, axis that vertically changeover portion 7, comb tooth 9 of obturaging, front extension 10 are formed of low-pressure turbine rear shaft neck 2, angled transition section 3, rear extension, the top of angled transition section 3 has circumferentially uniform oil through 4, the root of vertical changeover portion 7 has circumferentially uniform vent 6, the top of vertical changeover portion 7 has circumferentially uniform bolt hole 8, and the vertical section of front extension 10 has circumferentially uniform rivet pin nail 14.Front extension fitting surface 15 is the conical surface, its tapering is 1:24.8403, corresponding in the two-dimensional axisymmetric plane structure of equivalent-simplification, the cross section of front extension fitting surface 15 is the line segment of the in axial direction y right low left high that is connected to form by fitting surface cross section, front extension left end point 19 and fitting surface cross section, front extension right endpoint 20.The magnitude of interference of front extension fitting surface 15 and the radial interference fit 13 between runway fitting surface 18 of obturaging axially y increases from left to right successively, the magnitude of interference at left end point 19 place, fitting surface cross section, front extension is 0.0692mm, the magnitude of interference at right endpoint 20 place, fitting surface cross section, front extension is 0.1553mm, and front extension chamfering 17 is 19 degree with the angle of axial direction y.

The equivalent-simplification two-dimensional axisymmetric areal model of the assembly of the low-pressure turbine rear axle in commercial FEM-software ANSYS in modeling analysis the present embodiment and runway of obturaging, Finite element analysis results shows, and front extension fitting surface 15 and radial interference fit 13 place of obturaging between runway fitting surface 18 operationally do not produce gap; The quality of assembly is 5.988kg, does not exceed quality upper limit 6.1kg; The maximum vonMises equivalent stress of assembly is 744.567MPa, does not exceed the allowable stress 890MPa of its material; The vonMises equivalent stress at runway knuckle place of obturaging is 380.353MPa, does not exceed the allowable stress 700MPa of its material, reduces 67.46% than the 1169MPa in document.

Embodiment 3: the application maintenance front extension chamfering of the inventive method and the angle of axial direction y are the low-pressure turbine rear axle optimal design of the geometric properties of 45 degree.

Step one, low-pressure turbine rear axle is set up and the equivalent simplified model of runway assembly of obturaging in commercial FEM-software ANSYS, suppose the join strength engineering demands of riveting pin place, riveted joint pin joint is connected, ignore oil through, vent, bolt hole, the dentation structure of rivet pin nail and comb tooth of obturaging, assembly is reduced to axisymmetric two-dimensional model, extension fitting surface radial coordinate everywhere Δ=0.1mm less of the radial coordinate of runway fitting surface of obturaging before making when modeling, simulate front extension fitting surface and the magnitude of interference of the radial interference fit between runway fitting surface of obturaging, it can be used as the initial designs of shape optimization problem.Setting x ₁, y ₁and x ₂for variable element.In order to keep the angle of front extension chamfering and axial direction y to be the geometric properties of 45 degree, make x ₁, y ₁and x ₂following relation is met in optimizing process: $y_1=y_1^{\left(0\right)}+(x_1^{\left(0\right)}-x_1)$

Wherein, x ₁the radial coordinate of fitting surface cross section, front extension left end point, y ₁the axial coordinate of fitting surface cross section, front extension left end point, x ₂the radial coordinate of fitting surface cross section, front extension right endpoint, the radial coordinate of fitting surface cross section, the front extension left end point in document, it is the axial coordinate of fitting surface cross section, the front extension left end point in document.

Step 2, to low-pressure turbine rear axle compose with the attribute of material in table 1, to obturage runway compose with the attribute of material in table 2.

Table 1

Table 2

Step 3, the setting grid length of side are 0.5mm, Plane Entity unit PLANE82 partition structure grid is used to assembly, the solid element of front extension fitting surface generates one deck object element TARGE169, as target face, the solid element of runway fitting surface of obturaging generates one deck osculating element CONTA172, as surface of contact, to object element and osculating element compose with identical real constant numbering target face and surface of contact be identified as contact right, in order to the radial interference fit simulating front extension fitting surface and obturage between runway fitting surface.

Step 4, displacement boundary conditions and rotating speed, temperature loading are applied to the FEM (finite element) model of structure.Displacement boundary conditions: radial displacement boundary conditions ux1=0.2mm and ux2=0.5mm, axial displacement boundary conditions uy=0; Rotating speed load: the angular velocity rotated around gyration center 1 is ω=1200rad/s; Temperature loading: AB place temperature is 160 DEG C, CD place temperature is 180 DEG C, EF place temperature is 280 DEG C, GH place temperature is 220 DEG C, IJ place temperature is 350 DEG C, KL place temperature is 325 DEG C, MN place temperature is 260 DEG C, temperature between AB and CD is x linear distribution radially, temperature between EF and GH is x linear distribution radially, temperature between IJ and KL is y linear distribution in axial direction, and the temperature between KL and MN is y linear distribution in axial direction, the temperature radially x linear distribution in all the other regions between CD and EF.

Variable element x in step 5, selecting step one ₁, y ₁and x ₂in x ₁and x ₂as design variable, the maximum radial displacement of the node in the past on the fitting surface of extension is objective function, the contact of osculating element is not less than a less positive pressure as first constraint conditio, the contact of osculating element is no more than contact allowable as second constraint conditio, the maximum vonMises equivalent stress of the maximum vonMises equivalent stress of axle unit after low-pressure turbine and runway unit of obturaging is no more than the allowable stress of respective material as third and fourth constraint conditio, using the quality of assembly as the 5th constraint conditio, the angle that the present embodiment also contemplates front extension chamfering and axial direction y is that the geometric properties of 45 degree retrains, it is an equality constraint, it can be used as the 6th constraint conditio, set up the mathematical model of shape optimum:

$\left\{\begin{array}{cc}find& X=\[x_1,x_2\],\\ \min & f\left(X\right)=u_{\max }^t=\max \{u_1^t,u_2^t,\mathrm{...},u_i^t,\mathrm{...},u_{Nnum}^t\}\\ s.t.& {\mathrm{\σ}}_j^{CN}\≥\underset{\‾}{{\mathrm{\σ}}^{CN}}=0.01MPa,j=1,2,\mathrm{...},Cnum\\ & {\mathrm{\σ}}_j^{CN}\≤\stackrel{\‾}{{\mathrm{\σ}}^{CN}}=700MPa,j=1,2,\mathrm{...},Cnum\\ & \mathrm{\σ}_{\max }^{VN}{}_1=\max \{\mathrm{\σ}_1^{VN}{}_1,\mathrm{\σ}_2^{VN}{}_1,\mathrm{...},\mathrm{\σ}_k^{VN}{}_1,\mathrm{...},\mathrm{\σ}_{Enum1}^{VN}{}_1\}\≤\stackrel{\‾}{\mathrm{\σ}_{\max }^{VN}{}_1}=890MPa,\\ & \mathrm{\σ}_{\max }^{VN}{}_2=\max \{\mathrm{\σ}_1^{VN}{}_2,\mathrm{\σ}_2^{VN}{}_2,\mathrm{...},\mathrm{\σ}_l^{VN}{}_2,\mathrm{...},\mathrm{\σ}_{Enum2}^{VN}{}_2\}\≤\stackrel{\‾}{\mathrm{\σ}_{\max }^{VN}{}_2}=700MPa,\\ & M\≤\stackrel{\‾}{M}=M_0=6.1kg,\\ & y_1^{\left(0\right)}+(x_1^{\left(0\right)}-x_1)-y_1=0.\end{array}\right.$

Wherein, X is design variable sequence; F (X) is the objective function of optimization problem, the maximum radial displacement of the node on the fitting surface of front extension, be the radial displacement of i-th node on the fitting surface of front extension, Nnum is the number of the node on the fitting surface of front extension; the contact of a jth osculating element, σ ^cN be the lower limit of contact, be generally a smaller positive pressure, in the present embodiment, be taken as 0.01MPa, be contact allowable, be taken as 700MPa in the present embodiment, Cnum is the number of osculating element; the maximum vonMises equivalent stress of axle unit after low-pressure turbine, be the vonMises equivalent stress of axle unit after a kth low-pressure turbine, Enum1 is the number of unit of low-pressure turbine rear axle, be the allowable stress of shaft material after low-pressure turbine, being taken as the yield limit of shaft material after 0.8 times of low-pressure turbine in the present embodiment, is 890MPa; the maximum vonMises equivalent stress of runway unit of obturaging, be that l to obturage the vonMises equivalent stress of runway unit, Enum2 is the number of unit of runway of obturaging, be obturage the allowable stress of track material, being taken as the yield limit of 0.8 times of track material of obturaging in the present embodiment, is 700MPa; M is the quality of structure, be the upper limit of the quality of structure, in the present embodiment, be taken as M ₀=6.1kg.

In step 6, the basis of Optimized model set up in step 5, setting design variable x ₁and x ₂the upper limit be 92.2mm, lower limit is 91.5mm; The parameter of setting genetic algorithm: Population Size is 20, it is 0.1221 that random seed produces probability, and mutation probability is 0.5, and crossover probability is 0.9, and genetic algebra is 100, adopts genetic algorithm to be optimized design.

Design variable x in the Optimum Design Results of embodiment 3 ₁value be 91.9991mm, x ₂value be 91.8119mm.Front extension fitting surface 15 is the conical surface, its tapering is 1:21.2049, corresponding in the two-dimensional axisymmetric plane structure of equivalent-simplification, the cross section of front extension fitting surface 15 is the line segment of the in axial direction right low left high that is connected to form by fitting surface cross section, front extension left end point 19 and fitting surface cross section, front extension right endpoint 20.Front extension fitting surface 15 and the magnitude of interference of radial interference fit 13 obturaged between runway fitting surface 18 axially increase from left to right successively, the magnitude of interference at left end point 19 place, fitting surface cross section, front extension is 0.0009mm, the magnitude of interference at right endpoint 20 place, fitting surface cross section, front extension is 0.1881mm, and front extension chamfering 17 is 45 degree with the angle of axial direction.Finite element analysis results shows, and front extension fitting surface 15 and radial interference fit 13 place of obturaging between runway fitting surface 18 operationally do not produce gap; The quality of assembly is 6.004kg, does not exceed quality upper limit 6.1kg; The maximum vonMises equivalent stress of assembly is 715.073MPa, does not exceed the allowable stress 890MPa of its material; The vonMises equivalent stress at runway knuckle place of obturaging is 449.779MPa, does not exceed the allowable stress 700MPa of its material, reduces 61.52% than the 1169MPa in document.

Embodiment 4: the angle of front extension chamfering and axial direction y that do not keep of application the inventive method is the low-pressure turbine rear axle optimal design of the geometric properties of 45 degree.

Step one, low-pressure turbine rear axle is set up and the equivalent simplified model of runway assembly of obturaging in commercial FEM-software ANSYS, suppose the join strength engineering demands of riveting pin place, riveted joint pin joint is connected, ignore oil through, vent, bolt hole, the dentation structure of rivet pin nail and comb tooth of obturaging, assembly is reduced to axisymmetric two-dimensional model, extension fitting surface radial coordinate everywhere Δ=0.1mm less of the radial coordinate of runway fitting surface of obturaging before making when modeling, simulate front extension fitting surface and the magnitude of interference of the radial interference fit between runway fitting surface of obturaging, it can be used as the initial designs of shape optimization problem.Setting x ₁, y ₁and x ₂for variable element.

Wherein, x ₁the radial coordinate of fitting surface cross section, front extension left end point, y ₁the axial coordinate of fitting surface cross section, front extension left end point, x ₂it is the radial coordinate of fitting surface cross section, front extension right endpoint.

Step 2, to low-pressure turbine rear axle compose with the attribute of material in table 1, to obturage runway compose with the attribute of material in table 2.

Table 1

Table 2

Step 3, the setting grid length of side are 0.5mm, Plane Entity unit PLANE82 partition structure grid is used to assembly, the solid element of extension fitting surface generates one deck object element TARGE169, as target face, the solid element of runway fitting surface of obturaging generates one deck osculating element CONTA172, as surface of contact, to object element and osculating element compose with identical real constant numbering target face and surface of contact be identified as contact right, in order to simulate the interference fit of the radial interference fit between the fitting surface of front extension and the fitting surface of runway of obturaging.

Step 4, displacement boundary conditions and rotating speed, temperature loading are applied to the FEM (finite element) model of structure.Displacement boundary conditions: radial displacement boundary conditions ux1=0.2mm and ux2=0.5mm, axial displacement boundary conditions uy=0; Rotating speed load: the angular velocity rotated around gyration center 1 is ω=1200rad/s; Temperature loading: AB place temperature is 160 DEG C, CD place temperature is 180 DEG C, EF place temperature is 280 DEG C, GH place temperature is 220 DEG C, IJ place temperature is 350 DEG C, KL place temperature is 325 DEG C, MN place temperature is 260 DEG C, temperature between AB and CD is x linear distribution radially, temperature between EF and GH is x linear distribution radially, temperature between IJ and KL is y linear distribution in axial direction, and the temperature between KL and MN is y linear distribution in axial direction, the temperature radially x linear distribution in all the other regions between CD and EF.

Three variable element x in step 5, selecting step one ₁, y ₁and x ₂in whole in design variable, the maximum radial displacement of the node in the past on the fitting surface of extension is objective function, the contact of osculating element is not less than a less positive pressure as first constraint conditio, the contact of osculating element is no more than contact allowable as second constraint conditio, the maximum vonMises equivalent stress of the maximum vonMises equivalent stress of axle unit after low-pressure turbine and runway unit of obturaging is no more than the allowable stress of respective material as third and fourth constraint conditio, using the quality of assembly as the 5th constraint conditio, set up the mathematical model of shape optimum:

$\left\{\begin{array}{cc}find& X=\[x_1,y_1,x_2\],\\ \min & f\left(X\right)=u_{\max }^t=\max \{u_1^t,u_2^t,\mathrm{...},u_i^t,\mathrm{...},u_{Nnum}^t\},\\ s.t.& {\mathrm{\σ}}_j^{CN}\≥\underset{\‾}{{\mathrm{\σ}}^{CN}}=0.01MPa,j=1,2,\mathrm{...},Cnum\\ & {\mathrm{\σ}}_j^{CN}\≤\stackrel{\‾}{{\mathrm{\σ}}^{CN}}=700MPa,j=1,2,\mathrm{...},Cnum\\ & \mathrm{\σ}_{\max }^{VN}{}_1=\max \{\mathrm{\σ}_1^{VN}{}_1,\mathrm{\σ}_2^{VN}{}_1,\mathrm{...},\mathrm{\σ}_k^{VN}{}_1,\mathrm{...},\mathrm{\σ}_{Enum1}^{VN}{}_1\}\≤\stackrel{\‾}{\mathrm{\σ}_{\max }^{VN}{}_1}=890MPa,\\ & \mathrm{\σ}_{\max }^{VN}{}_2=\max \{\mathrm{\σ}_1^{VN}{}_2,\mathrm{\σ}_2^{VN}{}_2,\mathrm{...},\mathrm{\σ}_l^{VN}{}_2,\mathrm{...},\mathrm{\σ}_{Enum2}^{VN}{}_2\}\≤\stackrel{\‾}{\mathrm{\σ}_{\max }^{VN}{}_2}=700MPa,\\ & M\≤\stackrel{\‾}{M}=M_0=6.1kg.\end{array}\right.$

Wherein, X is design variable sequence; F (X) is the objective function of optimization problem, the maximum radial displacement of the node on the fitting surface of front extension, be the radial displacement of i-th node on the fitting surface of front extension, Nnum is the number of the node on the fitting surface of front extension; the contact of a jth osculating element, σ ^cN be the lower limit of contact, be generally a smaller positive pressure, in the present embodiment, be taken as 0.01MPa, be contact allowable, be taken as 700MPa in the present embodiment, Cnum is the number of osculating element; the maximum vonMises equivalent stress of axle unit after low-pressure turbine, be the vonMises equivalent stress of axle unit after a kth low-pressure turbine, Enum1 is the number of unit of low-pressure turbine rear axle, be the allowable stress of shaft material after low-pressure turbine, being taken as the yield limit of shaft material after 0.8 times of low-pressure turbine in the present embodiment, is 890MPa; the maximum vonMises equivalent stress of runway unit of obturaging, be that l to obturage the vonMises equivalent stress of runway unit, Enum2 is the number of unit of runway of obturaging, be obturage the allowable stress of track material, being taken as the yield limit of 0.8 times of track material of obturaging in the present embodiment, is 700MPa; M is the quality of structure, be the upper limit of the quality of structure, in the present embodiment, be taken as M ₀=6.1kg.

In step 6, the basis of Optimized model set up in step 5, setting design variable x ₁and x ₂the upper limit be 92.2mm, lower limit is 91.5mm; Setting design variable y ₁the upper limit be 62mm, lower limit is 58.2mm; The parameter of setting genetic algorithm: Population Size is 30, it is 0.1221 that random seed produces probability, and mutation probability is 0.3, and crossover probability is 0.9, and genetic algebra is 100, adopts genetic algorithm to be optimized design.

Design variable x in the Optimum Design Results of embodiment 4 ₁value be 91.9293mm, y ₁value be 61.9974mm, x ₂value be 91.8419mm.Front extension fitting surface 15 is the conical surface, its tapering is 1:24.4428, corresponding in the two-dimensional axisymmetric plane structure of equivalent-simplification, the cross section of the fitting surface 15 of front extension is the line segment of the in axial direction right low left high that is connected to form by fitting surface cross section, front extension left end point 19 and fitting surface cross section, front extension right endpoint 20.Front extension fitting surface 15 and the magnitude of interference of radial interference fit 13 obturaged between runway fitting surface 18 axially increase from left to right successively, the magnitude of interference at left end point 19 place, fitting surface cross section, front extension is 0.0707mm, the magnitude of interference at right endpoint 20 place, fitting surface cross section, front extension is 0.1581mm, and front extension chamfering 17 is 19 degree with the angle of axial direction.Finite element analysis results shows, and front extension fitting surface 15 and radial interference fit 13 place of obturaging between runway fitting surface 18 operationally do not produce gap; The quality of assembly is 5.988kg, not overweight; The maximum vonMises equivalent stress of assembly is 738.503MPa, does not exceed the allowable stress 890MPa of its material; The vonMises equivalent stress at runway knuckle place of obturaging is 386.718MPa, does not exceed the allowable stress 700MPa of its material, reduces 66.92% than the 1169MPa in document.

Claims (2)

1. the design method of a low-pressure turbine rear axle, described low-pressure turbine rear axle is by low-pressure turbine rear shaft neck (2), angled transition section (3), rear extension is obturaged runway (5), vertical changeover portion (7), obturage comb tooth (9) and front extension (10) form the hollow disc type part that axis is gyration center (1), the top of angled transition section (3) has circumferentially uniform oil through (4), the root of vertical changeover portion (7) has circumferentially uniform vent (6), the top of vertical changeover portion (7) has circumferentially uniform bolt hole (8), the vertical section of front extension (10) has circumferentially uniform rivet pin nail (14), it is characterized in that: front extension fitting surface (15) is the conical surface, corresponding in the two-dimensional axisymmetric plane structure of equivalent-simplification, the cross section of front extension fitting surface (15) is the line segment of the in axial direction right low left high that is connected to form by fitting surface cross section left end point, front extension (19) and fitting surface cross section right endpoint, front extension (20), front extension fitting surface (15) and the magnitude of interference at radial interference fit (13) place between runway fitting surface (18) of obturaging axially increase from left to right successively, it is characterized in that described low-pressure turbine rear axle adopts following steps design:

Step one, low-pressure turbine rear axle is set up and the equivalent simplified model of runway assembly of obturaging in commercial FEM-software ANSYS, suppose the join strength engineering demands of riveting pin place, riveted joint pin joint is connected, ignore oil through, vent, bolt hole, the dentation structure of rivet pin nail and comb tooth of obturaging, assembly is reduced to axisymmetric two-dimensional model, extension fitting surface radial coordinate everywhere Δ=0.1mm less of the radial coordinate of runway fitting surface of obturaging before making when modeling, simulate front extension fitting surface and the magnitude of interference of the radial interference fit between runway fitting surface of obturaging, it can be used as the initial designs of shape optimization problem, setting x ₁, y ₁and x ₂for variable element, wherein, x ₁for the radial coordinate of fitting surface cross section, front extension left end point, y ₁for the axial coordinate of fitting surface cross section, front extension left end point, x ₂for the radial coordinate of fitting surface cross section, front extension right endpoint,

Step 2, compose with respective material properties respectively to low-pressure turbine rear axle and runway of obturaging;

Step 3, the setting grid length of side, use Plane Entity dividing elements structured grid to assembly; The solid element of front extension fitting surface generates one deck object element as target face, the solid element of runway fitting surface of obturaging generates one deck osculating element as surface of contact, to object element and osculating element compose with identical real constant numbering target face and surface of contact be identified as contact right, in order to the radial interference fit simulating front extension fitting surface and obturage between runway fitting surface;

Step 4, displacement boundary conditions and rotating speed, temperature loading condition are applied to the FEM (finite element) model of structure;

Step 5, all or part of as design variable in three variable elements in selecting step one, the maximum radial displacement of the node in the past on the fitting surface of extension is objective function, the contact of osculating element is not less than a less positive pressure as first constraint conditio, the contact of osculating element is no more than contact allowable as second constraint conditio, the maximum vonMises equivalent stress of the maximum vonMises equivalent stress of axle unit after low-pressure turbine and runway unit of obturaging is no more than the allowable stress of respective material as third and fourth constraint conditio, the quality of assembly is no more than the upper limit as the 5th constraint conditio, finally increase other constraint conditios as required, set up the mathematical model of shape optimum:

$\left\{\begin{array}{cc}find& X,\\ \min & f\left(X\right)=u_{\max }^t=\max \left\{u_1^t,u_2^t,...,u_i^t,...,u_{Nnum}^t\right\}\\ s.t.& {\mathrm{\σ}}_j^{CN}\≥\underset{\‾}{{\mathrm{\σ}}^{CN}},j=1,2,...,Cnum\\ & {\mathrm{\σ}}_j^{CN}\≥\stackrel{\‾}{{\mathrm{\σ}}^{CN}},j=1,2,...,Cnum\\ & \mathrm{\σ}_{\max }^{VN}{}_1=\max \left\{\mathrm{\σ}_1^{VN}{}_1,\mathrm{\σ}_2^{VN}{}_1,...,\mathrm{\σ}_k^{VN}{}_1,...,\mathrm{\σ}_{Enum1}^{VN}{}_1\right\}\≤\stackrel{\‾}{\mathrm{\σ}_{\max }^{VN}{}_1},\\ & \mathrm{\σ}_{\max }^{VN}{}_2=\max \left\{\mathrm{\σ}_1^{VN}{}_2,\mathrm{\σ}_2^{VN}{}_2,...,\mathrm{\σ}_l^{VN}{}_2,...,\mathrm{\σ}_{Enum2}^{VN}{}_2\right\}\≤\stackrel{\‾}{\mathrm{\σ}_{\max }^{VN}{}_2},\\ & M\≤\stackrel{\‾}{M},\\ & G_m\left(X\right)\≤0,m=1,2,...,Gnum\\ & H_n\left(X\right)\≤0.n=1,2,...,Hnum\end{array}\right.$

Wherein, X is design variable sequence; F (X) is the objective function of optimization problem, the maximum radial displacement of the node on the fitting surface of front extension, be the radial displacement of i-th node on the fitting surface of front extension, Nnum is the number of node on the fitting surface of front extension; the contact of a jth osculating element, σ ^cN be the lower limit of contact, be generally a smaller positive pressure, be contact allowable, Cnum is the number of osculating element; the maximum vonMises equivalent stress of axle unit after low-pressure turbine, be the vonMises equivalent stress of axle unit after a kth low-pressure turbine, Enum1 is the number of unit of low-pressure turbine rear axle, it is the allowable stress of shaft material after low-pressure turbine; the maximum vonMises equivalent stress of runway unit of obturaging, be that l to obturage the vonMises equivalent stress of runway unit, Enum2 is the number of unit of runway of obturaging, obturage the allowable stress of track material; M is the quality of assembly, it is the quality upper limit of assembly; G _m(X) represent other inequality constraints condition of m, Gnum is the number of inequality constraints condition; H _n(X) represent the n-th other equality constraint, Hnum is the number of equality constraint;

In step 6, the basis of Optimized model set up in step 5, setting design variable upper and lower, Population Size, random seed produce probability, mutation probability, crossover probability and genetic algebra parameter, adopt genetic algorithm to be optimized design.

2. the design method of low-pressure turbine rear axle according to claim 1, is characterized in that: the tapering of described front extension fitting surface (15) is in formula, x ₁for the radial coordinate of fitting surface cross section, front extension left end point, y ₁for the axial coordinate of fitting surface cross section, front extension left end point, x ₂for the radial coordinate of fitting surface cross section, front extension right endpoint, y ₂for the axial coordinate of fitting surface cross section, front extension right endpoint.