CN113420473B - Method for predicting turbine wheel life - Google Patents
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Abstract
The invention discloses a method for predicting the service life of a turbine impeller, which comprises the following steps: setting a simulation criterion for simulating crack propagation of the turbine; setting initial conditions and termination conditions for simulating crack propagation of the turbine according to stress analysis of the turbine; based on the initial conditions, performing crack growth simulation on the turbine impeller by using a preset crack growth algorithm until the termination conditions are met, obtaining simulation results, and determining the predicted life of the crack growth of the turbine impeller. According to the method for predicting the service life of the turbine impeller, based on a method for simulating the crack propagation of the turbine by using the extended finite element method, the collapse unit is adopted to simulate the crack tip stress singularity, so that the effect of predicting the crack propagation service life by means of segmentation simulation is realized. By using the method provided by the invention, the crack extension life of the turbine can be effectively predicted, the stress intensity factors of cracks with different lengths of the turbine can be calculated, the crack extension path can be determined, and a powerful basis is provided for fatigue analysis of the turbine.
Description
Technical Field
The invention relates to a method for predicting the service life of a turbine impeller, and belongs to the technical field of turbines of micro-combustion engines.
Background
The micro-combustion engine takes continuously flowing gas as working medium to drive the impeller to rotate at high speed, and converts the energy of fuel into useful work, thus being a rotary impeller type heat engine. The device mainly comprises three parts, namely a gas compressor, a combustion chamber and a turbine; the air compressor sucks air from the external atmospheric environment, compresses the air step by step to boost the pressure, and simultaneously the air temperature is correspondingly increased; compressed air is sent to a combustion chamber under pressure to be mixed with injected fuel for combustion to generate high-temperature and high-pressure gas; then the gas enters the turbine to expand and do work, the turbine is pushed to drive the gas compressor and the external load rotor to rotate together at high speed, the chemical energy of the gas or liquid fuel is partially converted into mechanical work, and the electric energy can be output through the connection of the generator.
The turbine is used as one of hot end components of a micro-combustion engine key, has a severe working environment and a complex structure, and is a mechanical failure multiple component. The turbine affects the efficiency and economy of the micro-gas engine on the one hand and determines the safety and service life of the gas engine on the other hand. In order to ensure the service life of the micro-gas turbine, the turbine has higher safety and reliability and service life reserve under the actions of centrifugal force, aerodynamic force, thermal stress and the like. Particularly, centrifugal force is generated when the turbine rotor rotates, and each time the turbine rotor is started, stopped or the rotating speed changes correspondingly to the change of the load, so that the rotor is subjected to tension and compression fatigue load and is easy to crack; according to the damage tolerance theory, the crack in the structure does not need to be scrapped immediately, so long as the crack does not extend to the critical length yet can be safely used. Therefore, when the turbine is designed, static strength and fatigue strength analysis are required to be carried out, and the structure is ensured to meet the requirements of strength and fatigue life. Most of the previous studies have been limited to static strength, and have been insufficient in terms of fatigue and damage tolerance.
Disclosure of Invention
In view of the above prior art, the present invention provides a method for predicting turbine wheel life for a turbine design stage that compensates for the deficiencies of the prior art.
The invention is realized by the following technical scheme:
a method of predicting turbine wheel life, comprising:
setting a simulation criterion for simulating crack propagation of the turbine;
setting initial conditions and termination conditions for simulating crack propagation of the turbine according to stress analysis of the turbine;
based on initial conditions, performing crack growth simulation on the turbine impeller by using a preset crack growth algorithm until termination conditions are met, so as to obtain a simulation result;
and analyzing the simulation result to determine the predicted life of the crack growth of the turbine wheel.
Further, the setting of the simulation criteria for simulating the crack growth of the turbine includes: the damage criterion selects the maximum principal stress criterion, the evolution criterion selects the damage evolution criterion based on energy, and the fracture criterion selects the energy release rate criterion based on the virtual crack closure technology.
Further, setting initial conditions and termination conditions for simulating crack propagation of the turbine according to stress analysis of the turbine, wherein the initial conditions and the termination conditions comprise:
setting an initial crack with a preset size as an initial condition at the maximum point of Mises stress of the turbine, wherein the initial crack is used for representing the initial crack initiation of the turbine;
the critical dimensions of the cracks (the size of the critical crack dimensions, both related to the material's solidity and to the load size, and not related to other factors) are set as termination conditions to characterize the crack dimensions at the time of fracture of the turbine wheel.
Further, the initial crack is semicircular in shape, and the radius of the initial crack is 0.75mm; the critical dimension of the crack was 2mm.
Further, the performing crack growth simulation on the turbine wheel by using a preset crack growth algorithm based on the initial condition until the termination condition is met includes: and performing simulated expansion based on the initial crack until the simulated expansion crack meets the termination condition.
Further, the preset crack propagation algorithm comprises a finite element expansion method and a collapse unit method;
the method comprises the following steps of:
s1, taking a plurality of points at the front edge of an initial crack according to an extended finite element method, and calculating stress intensity factors of the points, wherein the stress intensity factors of the crack tip are calculated by adopting a collapse unit method;
s2, determining crack extension lengths of corresponding points according to stress intensity factors of the points;
s3, drawing a new crack front through a spline curve, and then calculating a new stress intensity factor and an expansion increment;
repeating the steps S1 to S3 until the simulated propagation crack size reaches the termination condition.
Further, the point taking rules for taking a plurality of points at the initial crack front include:
according to the stress analysis of the numerical analysis model of the turbine, the number of the points in the area with the large change rate of the stress intensity factor is larger than that in the area with the small change rate of the stress intensity factor;
the locating point comprises crack front 0 DEG, 90 DEG and 180 deg.
Further, the crack tip calculates a stress intensity factor thereof by adopting a collapse unit method, which comprises the following steps: performing collapse treatment by using a second-order quadrilateral eight-node unit, wherein three nodes a, b and c on one side are all collapsed to the crack tip, namely the two sides have the same geometric position, and meanwhile, the middle nodes of the two sides connected with the crack tip can move to a quarter position close to the crack tip; and obtaining the stress intensity factor of the crack tip.
Further, the determining the crack propagation length of each point according to the stress intensity factor of each point includes:
approximately considering that the stress intensity factors of each point are unchanged in the delta N=5000 cycles, and calculating the crack extension length of each point according to a Paris formula;
Δa=c(ΔK) m ΔN
wherein delta N represents a sectional simulation stage, the stress cycle period of each stage, the delta a direction is perpendicular to the tangential direction of the crack front edge, delta K is the stress intensity factor variation, and c and m are material parameters.
Further, the analyzing the simulation results to determine a predicted life of the turbine wheel includes: when the simulated crack growth reaches the termination condition, the number of stress cycles of the turbine is determined as the predicted life of the turbine wheel.
According to the method for predicting the service life of the turbine impeller, based on a method for simulating the crack propagation of the turbine by using the extended finite element method, the collapse unit is adopted to simulate the crack tip stress singularity, so that the effect of predicting the crack propagation service life by means of segmentation simulation is realized.
The method for predicting the service life of the turbine impeller can effectively predict the crack extension service life of the turbine, can calculate stress intensity factors of cracks with different lengths of the turbine, can determine crack extension paths, and provides a powerful basis for fatigue analysis of the turbine.
In the turbine design phase, the method of the present invention is utilized to predict the designed turbine wheel life. When the turbine generates initial crack initiation (such as initial crack initiation caused by material defect) in the actual working process, a worker acquires information (including the position, the size and the like) of the initial crack initiation through detection, and then inputs the information into the model constructed by the invention, and the crack propagation cycle life of the turbine impeller can be obtained through calculation. The method can accurately predict the residual life of the turbine impeller, so that a worker can accurately know the service condition of the turbine, plays a guiding role in maintenance, and avoids the situation that the turbine impeller is replaced when the service life period is longer.
The various terms and phrases used herein have the ordinary meaning known to those skilled in the art. The terms and phrases used herein are not to be construed and interpreted to have a meaning consistent with the meaning of the terms and phrases in accordance with the present invention.
Drawings
Fig. 1a, b: schematic of a turbine geometry model.
Fig. 2: three cell model schematics in the extended finite element method (XFEM).
Fig. 3: a flow chart of a method of predicting turbine blade life.
Fig. 4: turbine Mises stress distribution schematic.
Fig. 5: collapse units were created to simulate crack tip singularities.
Fig. 6: a crack propagation path schematic obtained by using an extended finite element method (XFEM) simulation, wherein a: a path diagram; b: a.
Fig. 7: schematic diagram of crack face stress distribution and angle specification, wherein a: stress distribution; b: the angle is specified.
Fig. 8: schematic of crack front propagation.
Fig. 9: stress intensity factors for different crack lengths are schematically shown.
Detailed Description
The invention is further illustrated below with reference to examples. However, the scope of the present invention is not limited to the following examples. Those skilled in the art will appreciate that various changes and modifications can be made to the invention without departing from the spirit and scope thereof.
The present invention generally and/or specifically describes the materials used in the test as well as the test methods. Although many materials and methods of operation are known in the art for accomplishing the objectives of the present invention, the present invention will be described in as much detail herein.
The instruments, reagents, materials, etc. used in the examples described below are conventional instruments, reagents, materials, etc. known in the art, and are commercially available. The experimental methods, detection methods, and the like in the examples described below are conventional experimental methods, detection methods, and the like that are known in the prior art unless otherwise specified.
Example 1 method of predicting turbine wheel life
The material of the turbine treated in this embodiment is illustratively selected as a K424 superalloy. The K424 alloy is a novel cast nickel-based superalloy which is independently developed in China, has high-temperature strength, good plasticity and manufacturability, and high comprehensive performance, and is suitable for manufacturing parts such as turbine rotor blades, guide blades and the like working below 950 ℃.
As shown in FIGS. 1a and b, the geometric model of the turbine has 12 blades, the radius of the wheel disc is 37mm, the radius of a central hole matched with a shaft is 4.5mm, and grooves and holes are formed in the turbine.
The specific material parameters of the K424 casting superalloy are shown in Table 1.
Table 1 Material parameters (600 ℃ C.) of K424 alloy
The solution for predicting the life of turbine blades is mainly based on the extended finite element method (XFEM) to simulate the crack propagation of turbines. The extended finite element method (XFEM) is based on the idea of unit decomposition, and a jump function capable of reflecting discontinuity and a crack tip progressive displacement field function are added into a conventional finite element mode, so that the obtained finite element grid is independent of cracks, and the finite element grid is not required to be reconstructed in the crack extension process, thereby being capable of conveniently analyzing the discontinuity problems such as fracture and the like.
In XFEM, the expression of the displacement is as follows:
wherein N is I (x) Is a conventional node shape function; u (u) I Is a node continuous displacement vector corresponding to a conventional finite element; a, a I Is an enriched degree of freedom vector of a crack penetrating through a unit node; h (x) is a hopping function (Heaviside function) reflecting crack face displacement discontinuities;is an enrichment degree of freedom vector of the crack tip node; f (F) α (x) Is a corresponding crack tip elastic asymptotic displacement field function for reflecting the singularity of the stress, and has the expression form as follows:
wherein r is the distance from a certain point to the tip of the crack under the polar coordinate system, and θ is the angle.
There are three types of cells in XFEM, conventional, crack tip and crack face penetrating, respectively, as shown in fig. 2.
The service life of the wheel blade mainly comprises two parts of crack initiation service life and crack propagation service life, wherein the crack initiation service life refers to the service life of a component with macroscopic visible cracks; crack propagation life is the life from the appearance of a macrocrack to the failure of a component, fracture. The solution of the present invention focuses on crack propagation life.
The method for predicting the life of a turbine blade according to the present invention comprises the following steps, as shown in FIG. 3:
(1) Simulation criteria are set to simulate crack propagation of the turbine. The simulation criteria for simulating crack propagation of the turbine may be based on damage criteria, evolution criteria, and fracture criteria, among others. Specifically, the damage criterion selects a maximum principal stress criterion, for example, a direction of maximum principal stress is taken as an initial expansion direction of damage; the evolution criterion selects an energy-based lesion evolution criterion, such as an expansion delta for evolving the lesion based on the energy consumed required for the lesion to expand a unit length; the fracture criteria selects the energy release rate criteria based on virtual crack closure techniques, such as starting fracture, i.e., crack propagation, when the energy release rate reaches a critical value.
(2) Based on the stress analysis of the turbine, initial conditions and termination conditions are set that simulate crack propagation of the turbine:
setting a semicircular initial crack with the radius of 0.75mm at the maximum point of Mises stress of the turbine, and taking the semicircular initial crack as an initial condition as shown in figure 4, wherein the semicircular initial crack is used for representing the initial crack initiation of the turbine;
the critical dimension of the crack was set to 2mm as a termination condition to characterize the crack size at the time of fracture of the turbine wheel.
(3) Based on initial conditions, performing crack propagation simulation on the turbine impeller by using a preset crack propagation algorithm (comprising a finite element expansion method and a collapse unit method) until termination conditions are met, so as to obtain a simulation result; the method comprises the following specific steps:
s1, taking a plurality of points including 0 DEG, 90 DEG and 180 DEG at the front edge of an initial crack according to an extended finite element method, and taking more points in a region with a large change rate of stress intensity factors than in a region with a small change rate of the stress intensity factors according to stress analysis of a numerical analysis model of a turbine; calculating stress intensity factors of each point;
for the crack tip, calculating the stress intensity factor by adopting a collapse unit method;
taking a two-dimensional unit as an example (as shown in fig. 5), when a second-order quadrilateral eight-node unit is used for collapse treatment, three nodes a, b and c on one side collapse to the crack tip, namely have the same geometric position, and meanwhile, the middle nodes on two side unit edges connected with the crack tip move to a quarter position close to the crack tip; the stress intensity factor of the crack tip can be obtained through the two steps of operation. Similarly, a similar operation can be performed for the three-dimensional unit to simulate crack tip singularities.
S2, determining crack extension lengths of corresponding points according to stress intensity factors of the points:
approximately considering that the stress intensity factors of each point are unchanged in the delta N=5000 cycles, and calculating the crack extension length of each point according to a Paris formula;
Δa=c(ΔK) m ΔN
wherein delta N represents a sectional simulation stage, the stress cycle period of each stage, the delta a direction is perpendicular to the tangential direction of the crack front edge, delta K is the stress intensity factor variation, and c and m are material parameters.
S3, drawing a new crack front through a spline curve, and then calculating a new stress intensity factor and an expansion increment;
the above steps S1 to S3 are repeated until the simulated propagating crack size reaches the termination condition (critical crack size 2 mm).
The simulated crack propagation path and its enlarged view are shown in fig. 6, and it can be seen that the crack propagation path is substantially perpendicular to the circumferential stress direction, although bending and waviness occur.
(4) And analyzing the simulation result to determine the stress cycle times of the turbine as the predicted life of the crack growth of the turbine impeller.
The stress distribution in the crack region was calculated and the result is shown in fig. 7. As can be seen, there is a significant stress concentration around the crack, and the crack is in an open state, typically an I-type crack state. In addition, the change of the stress intensity factor along the circumferential direction theta is analyzed, wherein the theta is defined in the figure, 0 DEG and 180 DEG are at the surface, and 0 DEG to 90 DEG are at the side close to the right side end face.
The crack front geometry changes and the corresponding number of cycles are shown in fig. 8. It can be seen that the crack shape approximates an ellipse, and thus the long axis radius thereof represents the crack length. When the number of cycles reached 25000, the crack length reached 2.06mm, exceeded the set critical crack size of 2mm, so the simulation stopped with a total cycle number of 25000. Turbine life is approximately 25000 cycles.
The stress intensity factors with different crack lengths obtained through calculation are shown in fig. 9, and it can be seen that the stress intensity factors with different theta angles have larger difference values, and obvious three-dimensional crack characteristics are shown. Taking the crack length a=0.75 mm as an example, the stress intensity factor at 90 ° is the smallest, onlyWhereas the stress intensity factor at 3℃is maximum, which reaches +.>Is 1.20 times the minimum value. It can also be seen that there is a small range of increasing and decreasing trend in the angular range of 0 deg. to 5 deg. and 175 deg. to 180 deg. because the crack is closer to a planar stress state near the surface and the interior is closer to a stress planar state.
As can be seen by comparing the stress intensity factors of different crack lengths, the distribution is symmetrical when the crack length is shorter, and the result of one side of 0-90 degrees is gradually larger than the result of 90-180 degrees along with the increase of the crack length, because the 0-90 degrees is the side close to the end face of the wheel disc, the mass is more concentrated, and the circumferential stress is larger. When the crack size is small, it can be approximately considered that the crack is subjected to a uniform tensile load, and as the crack propagates, the load on the 0 ° to 90 ° side is greater than that on the 90 ° to 180 ° side.
While the foregoing has been described in conjunction with the embodiments of the present invention, it will be apparent to those skilled in the art that many modifications and variations are possible without the need for inventive faculty.
Claims (4)
1. A method of predicting turbine wheel life, comprising:
setting a simulation criterion for simulating crack propagation of the turbine;
setting initial conditions and termination conditions for simulating crack propagation of the turbine according to stress analysis of the turbine;
based on the initial conditions, performing crack growth simulation on the turbine impeller by using a preset crack growth algorithm until the termination conditions are met, so as to obtain a simulation result;
analyzing the simulation results to determine a predicted life of crack propagation of the turbine wheel, comprising: when the simulated turbine crack growth reaches the termination condition, determining the stress cycle number of the turbine as the predicted life of the turbine wheel;
the setting of simulation criteria for simulating crack propagation of a turbine comprises: the damage criterion selects the maximum principal stress criterion, the evolution criterion selects the damage evolution criterion based on energy, and the fracture criterion selects the energy release rate criterion based on the virtual crack closure technology;
setting initial conditions and termination conditions for simulating crack propagation of the turbine according to stress analysis of the turbine, wherein the initial conditions and the termination conditions comprise:
setting an initial crack with a preset size as an initial condition at the maximum point of Mises stress of the turbine, wherein the initial crack is used for representing the initial crack initiation of the turbine;
setting critical dimensions of cracks as termination conditions to characterize crack dimensions when the turbine wheel breaks;
the performing crack growth simulation on the turbine wheel by using a preset crack growth algorithm based on initial conditions until the termination conditions are met comprises: performing a simulated propagation based on the initial crack until the simulated propagation crack meets the termination condition;
the preset crack propagation algorithm comprises a finite element expansion method and a collapse unit method;
the performing of the simulated propagation based on the initial crack until the simulated propagation crack meets the termination condition comprises the steps of:
s1, taking a plurality of points at the front edge of the initial crack according to an expansion finite element method, and calculating stress intensity factors of the points, wherein the stress intensity factors of the crack tip are calculated by adopting a collapse unit method;
s2, determining crack extension lengths of corresponding points according to stress intensity factors of the points;
s3, drawing a new crack front through a spline curve, and then calculating a new stress intensity factor and an expansion increment;
repeating the steps S1 to S3 until the size of the simulated expansion crack reaches the termination condition;
the crack tip calculates stress intensity factors by adopting a collapse unit method, and the method comprises the following steps: performing collapse treatment by using a second-order quadrilateral eight-node unit, wherein three nodes a, b and c on one side are all collapsed to the crack tip, namely the two sides have the same geometric position, and meanwhile, the middle nodes of the two sides connected with the crack tip can move to a quarter position close to the crack tip; and obtaining the stress intensity factor of the crack tip.
2. The method of predicting turbine wheel life of claim 1, wherein the initial crack is semi-circular in shape and the initial crack has a radius of 0.75mm;
the critical dimension of the crack was 2mm.
3. The method of predicting turbine wheel life of claim 1, wherein taking a point specification of a plurality of points at the initial crack front comprises:
according to the stress analysis of the numerical analysis model of the turbine, the number of the points in the area with the large change rate of the stress intensity factor is larger than that in the area with the small change rate of the stress intensity factor;
the locating point comprises crack front 0 DEG, 90 DEG and 180 deg.
4. The method of predicting turbine wheel life as recited in claim 1, wherein determining crack propagation lengths for each point based on stress intensity factors for each point comprises:
the crack extension length of each point is calculated according to the Paris formula,
wherein delta N represents a sectional simulation stage, the stress cycle period of each stage, the delta a direction is perpendicular to the tangential direction of the crack front edge, delta K is the stress intensity factor variation, and c and m are material parameters.
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