A method for the orientation design of nickel-based single crystal turbine blades

Abstract

The present invention relates to the field of single-crystal turbine blade strength, lifespan design, and optimization, and specifically to a method for nickel-based single-crystal turbine blade orientation design. The method primarily comprises the following steps: performing a mathematical description to obtain the angles α, β, and γ and their ranges; establishing a relationship between the Euler angles and the primary orientation β and the secondary orientation θ; conducting static strength and vibration simulations under three-dimensional spatial angles; converting the simulation results into a law governing the influence of the orientations β and θ on single-crystal performance; and determining the optimal design range for the orientations β and θ based on the results of the coupling of multiple laws. The present invention comprehensively considers the influence of the single-crystal turbine blade orientation on vibration, high-cycle fatigue, and static strength performance, thereby mitigating the adverse effects of crystal orientation and fully utilizing the performance of the single-crystal turbine blade.

Description

Technical Field

[0001] The present invention relates to the field of single crystal turbine blade strength, life design and optimization, and in particular to a method for orientation design of nickel-based single crystal turbine blades. Background Art

[0002] Nickel-based single-crystal alloys, with their excellent high-temperature mechanical properties, are widely used in the manufacture of aircraft engine turbine blades. However, single-crystal alloys also exhibit significant anisotropy. Under the same stress or strain level, the creep and fatigue life of the material can vary several or even dozens of times depending on the orientation. Therefore, optimal orientation design is one of the keys to improving the strength and life of aircraft engine turbine blades, and it is a crucial factor in the design of turbine blades for strength and longevity.

[0003] Currently, there is no clear design scheme for blade orientation in the engineering field. The National Aeronautics and Space Administration (NASA) stipulates that blades with an angle between the

[001] orientation and the blade stacking line direction of less than 15° are qualified products. This regulation provides a design range for the primary orientation, but does not provide a design range for the secondary orientation. In order to solve the above problem, there is an urgent need in engineering to design a secondary orientation and provide a scheme for specific secondary orientation design angles to guide the orientation design during the casting of single-crystal turbine blades. Based on the above reasons, the present invention will design the secondary orientation range and provide a specific design method and process. Summary of the Invention

[0004] In response to the problems raised in the background art, the present invention proposes a method for orientation design of nickel-based single crystal turbine blades. The technical solution of the present invention is implemented as follows:

[0005] The present invention provides a method for designing the orientation of nickel-based single crystal turbine blades, which specifically includes the following steps:

[0006] S1: Mathematically describe the three-dimensional spatial orientation of the single crystal blade based on the Euler angle, and obtain the α, β, and γ angles and ranges that reflect the three-dimensional spatial orientation of the material;

[0007] S2: Based on the original definition of orientation, the relationship between Euler angles and primary orientation α and secondary orientation θ is established;

[0008] S3: Conduct static strength and vibration simulation calculations in three-dimensional space based on the Euler angle range;

[0009] S4: According to the relationship between Euler angle and orientation β, θ, the simulation results are converted into the influence of orientation β, θ on the static strength, vibration and resonance point high cycle fatigue life reserve of single crystal turbine blades;

[0010] S5: Determine the optimal design range of orientation β and θ based on the results of coupling influence of multiple rules.

[0011] Furthermore, in step S1, α is the angle obtained by the first rotation about the Z axis, and α is less than 90°; β is the angle obtained by the second rotation about the Y′ axis, and β is less than 15°; γ is the angle obtained by the third rotation about the Z″ axis, and γ is less than 90°. This is because the engineering design in this field stipulates that the angle between the

[001] orientation and the blade stacking line direction is less than 15°, that is, the angle β is less than 15°. Although there are no strict requirements for α and γ, it can be seen from the Euler angle ZYZ rotation matrix that each rotation of 90° for the two angles α and γ is a cycle, so their range can be determined to be within 90°. The Euler angle rotation includes all existing three-dimensional spatial orientations.

[0012] Furthermore, in step S1, the specific method of mathematical description is: in the Cartesian coordinate system, the basic rotation matrix RZ,RY about the Z axis and the Y axis can be expressed as:

[0013]

[0014] The combined rotation matrix RZYZ corresponding to the Euler angle of ZYZ rotation can be expressed as:

[0015]

[0016] Where l, m, and n are the cosines of the directional angles between the coordinate axes of different coordinate systems, thus achieving a mathematical description of the blade orientation problem.

[0017] Furthermore, in step S2, the secondary orientation θ, α, and γ satisfy the following relationship:

[0018]

[0019] The first part of the formula indicates that θ is composed of two parts: the projection of α and γ. The specific calculation formula is expressed in the second half.

[0020] Considering that the three-dimensional spatial orientation of single crystal blades can be described by the mathematical tool Euler angle, but the Euler angle is not consistent with the primary and secondary orientation characteristics of the material, it is necessary to fully consider the relationship between the two and establish a corresponding relationship.

[0021] During the casting process of single-crystal turbine blades, the primary dendrite (equivalent to the

[001] direction) determines the actual growth direction, while the secondary dendrites (equivalent to the

[010] and

[100] directions) grow perpendicular to the primary dendrite. Therefore, the physical meaning of the primary orientation is the angle between the

[001] (primary dendrite) direction and the blade stacking line. The physical meaning of the secondary orientation can be interpreted as the angle between the projection of the secondary dendrite on the original plane and the engine main axis. Based on the casting process, the primary orientation is designed to be the β angle during the Euler angle rotation process, and the secondary orientation is designed to be the angle between the projection of the rotated coordinate axis on the XOY plane and the original coordinate axis. A single Euler angle cannot represent the secondary orientation.

[0022] Furthermore, in step S3, static strength and vibration simulation calculations are still performed according to the Euler angles α, β, and γ, and then converted to the secondary orientation deviation angle θ through a relationship to obtain the relevant influence of β and θ. Within the respective ranges of α, β, and γ, values are taken at equal intervals, and a limited calculation angle is used to represent the entire spatial angle range. Static strength and vibration calculations of the blade are performed according to the selected angles. At the same time, the vibration calculation should include multiple operating conditions to meet the requirements of the resonance margin assessment.

[0023] Furthermore, in step S4, the method for converting the simulation results into the influence of orientations β and θ on the static strength, vibration and high-cycle fatigue life reserve of single-crystal turbine blades is: performing orientation influence analysis based on the stress value of the static strength result to obtain the orientation design range based on the static strength; performing resonance margin influence analysis based on the vibration frequency to obtain the orientation design range based on the resonance margin; performing high-cycle fatigue influence analysis based on the vibration point stress amplitude to obtain the orientation design range based on the high cycle.

[0024] Furthermore, in step S5, vibration avoidance is the primary task in turbine design requirements, so the optimal range of vibration-affected orientation is prioritized, and then the influence of static strength and high-cycle fatigue life reserve of the resonance point is combined to determine the optimal orientation design range.

[0025] The method for designing the orientation of nickel-based single crystal turbine blades proposed in the present invention has the following beneficial effects:

[0026] The crystal orientation design method proposed in this paper is of great significance for improving the strength and lifespan of turbine blades. Existing standards still suffer from issues such as ambiguous definitions and difficulty controlling secondary orientation. This paper develops an orientation design process and solution that addresses the lack of a suitable orientation control method for single-crystal turbine blades, a key hot-end component of aircraft engines, to ensure they meet the long-life design requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 This is a flow chart of the orientation design method for nickel-based single-crystal turbine blades, a key hot-end component of an aero-engine disclosed in this disclosure.

[0028] Figure 2 Schematic diagram of ZYZ Euler angle rotation.

[0029] Figure 3 Schematic diagram of orientation control in single crystal turbine blade casting. DETAILED DESCRIPTION

[0030] The following will clearly and completely describe the technical solutions of the present invention in conjunction with the embodiments of the present invention. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0031] Example 1

[0032] The disclosed embodiment provides a solution for designing the orientation of nickel-based single-crystal turbine blades, which are key hot-end components of aircraft engines, and can be used to design the orientation of nickel-based single-crystal turbine blades, which are key hot-end components of aircraft engines, during casting. Figure 1 This is a schematic diagram of a process flow for designing the orientation of nickel-based single crystal turbine blades, a key hot end component of an aero-engine, in an exemplary embodiment of the present disclosure. Figure 1 As shown, the program includes:

[0033] S1: Mathematically describe the three-dimensional spatial orientation of the single crystal blade based on the Euler angle, and obtain the α, β, and γ angles and ranges that reflect the three-dimensional spatial orientation of the material;

[0034] S2: Based on the original definition of orientation, the relationship between Euler angle and primary orientation β and secondary orientation θ is established;

[0035] S3: Conduct static strength and vibration simulation calculations in three-dimensional space based on the Euler angle range;

[0036] S4: According to the relationship between Euler angle and orientation β, θ, the simulation results are converted into the influence of orientation β, θ on the static strength, vibration and resonance point high cycle fatigue life reserve of single crystal turbine blades;

[0037] S5: Determine the optimal design range of orientation β and θ based on the results of coupling influence of multiple rules.

[0038] The following is a detailed description of the orientation design scheme for nickel-based single crystal turbine blades, a key hot end component of an aero-engine, provided by an embodiment of the present disclosure:

[0039] In step S1, the three-dimensional spatial orientation of the single crystal blade is mathematically described according to the Euler angle to obtain the angles α, β, and γ and their ranges reflecting the three-dimensional spatial orientation of the material;

[0040] Nickel-based single crystals have a face-centered cubic unit cell, with three principal axes perpendicular to each other and identical properties, and can be described using a Cartesian coordinate system. Any deviation in orientation during casting can be considered a rotation of the coordinate system. When performing a ZYZ Euler angle rotation in a Cartesian coordinate system, the three Euler angles α, β, and γ reflect the material's three-dimensional orientation, facilitating orientation design.

[0041] According to the National Aeronautics and Space Administration (NASA) blade orientation manufacturing standard, the

[001] direction should be less than 15° from the blade stacking line direction. In coordinate rotation, this is reflected as the angle between the original Z axis and the final Z axis, that is, the β angle, which can determine the β range.

[0042] From the combined rotation matrix RZYZ corresponding to the Euler angle of the ZYZ rotation, it can be seen that α and γ form a cycle every 90°, and their range can be determined to be within 90°.

[0043] In step S2, based on the original definition of orientation, the relationship between Euler angles and primary orientation β and secondary orientation θ is established;

[0044] In step S1, the Euler angles reflecting the three-dimensional orientation of the material are obtained. However, in engineering, primary and secondary orientations are usually used to describe the material. The characteristics of the two are not consistent, so it is necessary to consider establishing a relationship between the two. The primary orientation is the angle between the

[001] direction and the blade stacking line, which is equal to the β angle. The secondary orientation angle is controlled according to the horizontal plane and is the angle between the projection of the crystal axis after rotation on the XOY plane and the original crystal axis, represented by θ. The established relationship is:

[0045]

[0046] In step S3, static strength and vibration simulation is carried out in three-dimensional space based on the Euler angle range. Step S3 includes the following three steps:

[0047] Step S31: Given the ranges of α, β, and γ from S1, β is 0-15°, and α and γ are 0-90°. α and γ are spaced at 15° intervals, and β is spaced at 5° intervals. A calculation matrix covering all orientation deviation angles is designed, as shown in Table 1:

[0048] Table 1

[0049]

[0050] After permutations and combinations, there are 7×7×4=196 sets of examples.

[0051] Step S32: modifying the Euler angle according to the calculation matrix to perform static strength simulation of the blade.

[0052] Step S33, changing the Euler angle according to the calculation matrix to perform vibration simulation of the blade. Each orientation in the vibration calculation should include five working conditions: normal temperature installation, ground slow speed, economic cruise, high temperature takeoff, and three red lines.

[0053] In step S4, the simulation results are converted into the influence of orientation β and θ on the static strength, vibration and high-cycle fatigue life reserve of the single crystal turbine blade according to the relationship between Euler angle and orientation β and θ. In step S3, static strength and vibration simulation under three-dimensional spatial angles is carried out based on the Euler angle range. In step S2, based on the original definition of orientation, the relationship between Euler angle and primary orientation β and secondary orientation θ is established. Therefore, in this step, the influence of β and θ on static strength, resonance margin and high-cycle reserve of vibration point can be analyzed. Step S4 includes the following steps:

[0054] Step S41: determining the primary and secondary orientation values corresponding to each spatial angle according to a formula.

[0055] Step S42 , extracting stress values of the same key points under different orientations from the static strength results to perform orientation influence analysis, including primary orientation influence analysis, secondary orientation influence analysis, and a mixed influence analysis of the two.

[0056] Step S43: determining the optimal orientation design range of static strength according to the analysis results.

[0057] Step S44 , making a Campbell diagram based on the vibration frequency values of different orientations and different working conditions of the same orientation to analyze the influence of the resonance margin orientation.

[0058] Step S45 : determining the optimal orientation design range of the resonance margin according to the analysis results.

[0059] Step S46, determine the vibration point position according to the vibration stress cloud map, extract the stress value σm at the vibration point in the static stress calculation, substitute σm into the Goodman curve to obtain the allowable vibration stress [σa], divide the measured vibration stress value σa by the allowable vibration stress [σa] to obtain the high-cycle reserve coefficient, and analyze the high-cycle reserve influence law according to the high-cycle reserve coefficient under different orientations.

[0060] Step S47: Determine the optimal orientation design range of the high-frequency reserve based on the analysis results.

[0061] In step S5, the orientation design range is determined based on the results of multiple coupling effects: three optimal orientation design ranges are obtained according to step S4. In turbine design, vibration avoidance is the primary task, so the optimal design range of resonance margin is given priority; then, the optimal orientation design range is given in combination with the static strength and the severity of high-frequency effects.

[0062] Although the embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the claims and their equivalents.

Claims

1. A method for designing the orientation of nickel-based single crystal turbine blades, characterized in that: The specific steps include: S1: Mathematically describe the three-dimensional spatial orientation of the single crystal blade based on the Euler angle, and obtain the α, β, and γ angles and ranges that reflect the three-dimensional spatial orientation of the material; S2: Based on the original definition of orientation, the relationship between Euler angle and primary orientation β and secondary orientation θ is established; S3: Conduct static strength and vibration simulation calculations in three-dimensional space based on the Euler angle range; S4: According to the relationship between Euler angle and orientation β, θ, the simulation results are converted into the influence of orientation β, θ on the static strength, vibration and resonance point high cycle fatigue life reserve of single crystal turbine blades; S5: Determine the optimal design range of orientation β and θ based on the results of coupling effects of multiple laws; In step S1, the specific method of mathematical description is: in the Cartesian coordinate system, the basic rotation matrix R about the Z axis and the Y axis is listed as follows: Z , R Y : The combined rotation matrix R corresponding to the Euler angle of ZYZ rotation ZYZ Expressed as: Where l, m, n are the cosines of the direction angles between the axes of different coordinate systems; In step S2, the secondary orientation θ, α, and γ satisfy the following relationship:

2. The method for designing the orientation of nickel-based single crystal turbine blades according to claim 1, characterized in that: In step S1, α is the angle obtained by the first rotation around the Z axis, and α is less than 90°; β is the angle obtained by the second rotation around the Y′ axis, and β is less than 15°; γ is the angle obtained by the third rotation around the Z″ axis, and γ is less than 90°. The Euler angle rotation includes all existing three-dimensional spatial orientations.

3. The method for designing the orientation of nickel-based single crystal turbine blades according to claim 1, characterized in that: In step S3, when performing static strength and vibration simulation calculations, the calculations are still performed according to the Euler angles α, β, and γ, and then converted into the secondary orientation angle θ through a relationship to obtain the relevant influence rules of β and θ.

4. The method for designing the orientation of nickel-based single crystal turbine blades according to claim 1, characterized in that: In step S4, the method for converting the simulation results into the influence of orientations β and θ on the static strength, vibration and high cycle fatigue life reserve of the single crystal turbine blade is as follows: performing orientation influence analysis based on the stress value of the static strength result to obtain the orientation design range based on the static strength; performing resonance margin influence analysis based on the vibration frequency to obtain the orientation design range based on the resonance margin; The high cycle fatigue influence analysis is carried out according to the stress amplitude of the vibration point, and the orientation design range based on high cycle is obtained.

5. The method for designing the orientation of nickel-based single crystal turbine blades according to claim 1, characterized in that: In step S5, the optimal range of vibration-affected orientation is given priority, and then the optimal orientation design range is determined in combination with the influence of static strength and high-cycle fatigue life reserve of the resonance point.

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