An optimization method for the design of elastic support for turbine rotors of air turbine starters

Abstract

To overcome the shortcomings of traditional elastic support design methods that cannot consider assembly requirements and require multiple iterative calculations using the finite element method, this invention proposes an optimization method for the design of elastic supports for air turbine starter rotors. This method is a finite element design optimization method for elastic support structures with internal or external bosses, or both. This method can simultaneously consider the effects of assembly relationships and different material properties, and automatically perform modal and critical speed calculations of the rotor-support structure, which can significantly reduce the iteration time of the "design-analysis-correction-processing-assembly" process.

Description

Technical Field

[0001] This invention belongs to the field of aircraft starting system design, specifically relating to an optimization method for the design of elastic support for the turbine rotor of an air turbine starter. Background Technology

[0002] An air turbine starter is a rotating machine that uses compressed air to drive a turbine, and utilizes its own reduction gear system to amplify torque, achieving high torque and high speed output to start aircraft engines. An air turbine starter generally consists of three main parts: a turbine, a reducer, and a clutch. Its turbine is characterized by high power, high speed, and high load. Due to its application in aviation, air turbine starters are required to have a compact structure, smaller weight, and higher power. Unlike general high-speed rotors, the turbine rotor of air turbine starters in the industry can output a maximum power of 300kW. Currently, the highest turbine speed of domestic air turbine starters can reach 150,000 RPM. To achieve the practical requirements of weight reduction and compact structure, the turbine support adopts a cantilevered two-bearing support. The motion stability of a cantilevered rotor is generally worse than that of a symmetrically supported rotor. Furthermore, the vibration characteristics of a high-speed rotating cantilevered rotor are more difficult to control.

[0003] Rotor vibration characteristic control measures mainly involve increasing motion damping or changing support stiffness. Regarding increasing vibration damping, aero-engine rotors typically incorporate squeeze film dampers to increase motion damping and reduce vibration response during critical or normal operation. However, the compact structure of air turbine starters makes it impossible to install an oil pump structure for supplying high-pressure lubricating oil to the squeeze film damper. Furthermore, the normal operating state of an air turbine starter is a continuous, non-steady-state, high-speed operation, which does not effectively utilize the squeeze film damper's capabilities.

[0004] Therefore, adjusting the rotor system support stiffness is currently the only feasible solution. Adjusting support stiffness generally involves replacing rigid supports with elastic supports; the series stiffness of the elastic supports and bearings can adjust the rotor's dynamic characteristics. Summary of the Invention

[0005] The objective of this invention is to develop an optimized design method for the elastic support of the turbine rotor in an air turbine starter. This optimization method yields a rotor elastic support structure that is simple in structure and exhibits significant frequency modulation effects. Reducing the support stiffness can adjust the rotor vibration characteristics, thereby improving the reliability and safety of the air turbine starter.

[0006] Technical solution: A method for optimizing the design of an elastic support for an air turbine starter rotor, the optimization method comprising the following steps:

[0007] Step S1: Obtain the radial and axial dimensions of the turbine bearing and the bearing support stiffness to obtain the bearing design parameters;

[0008] Step S2: Based on the structural characteristics and support position of the turbine rotor, refer to the bearing dimensions and bearing stiffness parameters mentioned in step S1, calculate the rotor's modal and critical speed under this condition, and determine the adjustment direction and range of the rotor bearing stiffness.

[0009] Step S3: Establish a parametric model of the elastic support assembly, using an elastic shaft to simulate the bearing and an elastic ring to simulate the bearing mounting base;

[0010] Step S4: Use finite element software to automatically read material properties, assembly relationships, solve calculations, obtain calculation results, find optimization paths, and iterate to obtain an elastic support structure under a certain stiffness.

[0011] Step S5: Load the turbine model, start the rotor dynamics analysis module, and use the series stiffness of the elastic support stiffness obtained in step S4 and the bearing stiffness in step S1 as the overall stiffness to carry out rotor critical speed analysis.

[0012] Step S6: Analyze the current rotor critical speed. If it does not meet the design requirements, repeat steps S3-S5 until the design requirements are met.

[0013] Furthermore, in step S1, the bearing is selected based on the actual load and life requirements of the bearing, and the bearing design parameters include at least: structural parameters and bearing stiffness parameters; the structural parameters include inner diameter, outer diameter, and width.

[0014] Furthermore, step S2 includes the following steps: 1) obtaining the turbine rotor support position parameters; 2) obtaining the material parameters; 3) establishing a preliminary finite element analysis model; 4) performing calculations based on the finite element model to obtain the rotor's vibration modes and critical speed Campbell's diagram, evaluating the first-order critical speed of the rotor's bending mode, and obtaining preliminary calculation results; 5) determining the speed points at which the air turbine starter rotor needs to operate for a long time and the disengagement speed points based on actual usage requirements, and determining the adjustment direction and range of the support stiffness based on the evaluation criteria and the actual critical speed value.

[0015] Furthermore, in step S2, establishing the finite element analysis model involves importing the air turbine starter turbine rotor model into the finite element software, constraining the axial rotation and axial displacement degrees of freedom of the bearing mounting position in the rotor model, replacing the bearing with a spring element, and assigning the spring element the bearing stiffness value obtained in step S1.

[0016] Furthermore, when determining the operating speed and disengagement speed of the air turbine starter rotor, the first and second critical speeds should be at least ±20% away from the operating speed and disengagement speed. The adjustment direction and range of the support stiffness should be determined based on the evaluation criteria and the actual critical speed value.

[0017] Furthermore, step S3 includes: 1) selecting the basic type of elastic support; 2) establishing a parametric model of the elastic support; and 3) establishing a finite element model for stiffness analysis of the elastic support.

[0018] Furthermore, when establishing the parametric model of the elastic support, a parametric model containing all structural information of the elastic support is designed based on the finite element software ANSYS APDL language.

[0019] Furthermore, when establishing the finite element model for the stiffness analysis of the elastic support, an elastic ring simulating the bearing with the inner diameter of the elastic support being the outer diameter is established, and an elastic ring simulating the bearing housing with the outer diameter of the elastic support being the inner diameter is established.

[0020] Further, step S4 is executed as follows: 1) Read material mechanical property data; automatically read the material properties of the elastic support, elastic shaft, and elastic bearing ring. These material properties need to include elastic modulus, density, Poisson's ratio, yield strength, and plasticity. 2) Based on the actual usage environment, the elastic support is in contact with both the bearing and bearing support. To reduce wear between the elastic support and the bearing and bearing support under turbine vortex action, a small interference fit is given as an input condition in the initial calculation, and this interference fit is used as an optimization parameter in the later optimization design iteration. 3) Constrain all degrees of freedom of the outer wall surface of the elastic bearing housing; constrain the axial rotation, axial displacement, and radial rotation degrees of freedom of the elastic shaft; constrain the axial displacement degree of freedom of the elastic support, and set the interference contact relationship between the elastic support and the elastic shaft and elastic bearing housing.

[0021] To simulate the whirl displacement generated during rotor design, it is assumed that the rotor undergoes circular whirl, thereby applying two mutually perpendicular radial (x, y) displacement loads to the elastic circular shaft; the load values ​​vary between 0-1 mm, and these two displacement loads need to satisfy the requirement that the trajectory is circular; 4) Automatically solve the support reaction force of the elastic support on the elastic circular shaft under the current parameters, and obtain the stiffness value of the elastic support from the displacement load and support reaction force. Write the stress, strain, mass, and stiffness values ​​of the elastic support into the file scratch; 5) Direct optimization is performed using a finite element zero-order optimization, first-order optimization, or second-order optimization algorithm. In the optimization analysis step, the scratch file in step 4) is called and the design variables, objective function, and constraint variables are read, with the stiffness value and the internal stress value of the elastic support as the judgment criteria; the optimization path is searched and iterated until the result converges.

[0022] Beneficial technical effects:

[0023] This invention employs the finite element contact calculation and analysis method to establish a parametric design and optimization method for elastic support structures, which has the following significant advantages over existing elastic support design methods:

[0024] (1) The design optimization process of the support structure takes into account the accurate model structure.

[0025] The structure of the elastic support is fully parametrically modeled, integrating the dimensions of the inner boss, outer boss, and chamfer. This makes the geometric design more suitable for actual engineering processing and use.

[0026] (2) The design optimization process of the support structure takes into account structural strength, service life and assembly and installation requirements.

[0027] The support structure is installed between the bearing outer ring and the bearing housing, with both locations using an interference fit. Due to the strong nonlinear effect of the contact, the magnitude of the interference directly affects the stiffness of the elastic support. Furthermore, due to the whirling motion of the turbine rotor, the elastic support structure deforms synchronously, leading to a certain stress distribution within the structure. If this stress distribution is not adequately designed, it may cause rapid fatigue of the elastic support structure, resulting in failure and affecting rotor operating safety. Considering strength, lifespan, and assembly requirements during the design optimization process can make the design of the elastic support structure more closely aligned with actual engineering needs.

[0028] (3) The structural design optimization process directly calculates the mode and critical speed of the rotor-support structure.

[0029] Even after optimization, the elastic support structure still requires modal and critical speed analysis and verification on the rotor-support structure. Traditional methods verify the elastic support stiffness design, optimization, and rotor vibration characteristics separately, resulting in numerous iterations and high time costs. This invention allows the rotor's critical speed to be used as an optimization objective during the elastic support design optimization process, ensuring that the final optimized structure directly meets the rotor vibration characteristic requirements. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the actual installation of the rotor-support structure;

[0031] Among them, A-turbine, B-elastic support element, C-bearing;

[0032] Figure 2 This is a diagram of an elastic support structure that simultaneously has an inner boss and an outer boss.

[0033] Figure 3 This is a diagram of an elastic support structure with only an inner boss that is annular and circumferential.

[0034] Figure 4 This is a diagram of an elastic support structure with only an inner boss, and the boss is strip-shaped and axial.

[0035] Figure 5A schematic diagram of a parametric model of an elastic support structure that simultaneously has an inner boss and an outer boss;

[0036] Figure 6 This is a schematic diagram of the critical speed of a rotor without an elastic support structure.

[0037] Figure 7 This is a schematic diagram of the critical speed of a rotor with an elastic support structure.

[0038] Figure 8 A flowchart of the overall process for optimizing the design of elastic supports. Detailed Implementation

[0039] The following section, using the cantilevered support rotor of a certain type of air turbine starter as an example, describes the design optimization process and accompanying drawings of an elastic support structure that matches the support bearing to meet the power characteristic requirements of the rotor. However, the present invention is not limited to the design and optimization of elastic supports for air turbine starter rotors.

[0040] This invention discloses a design method for elastic supports based on finite element software. This method considers strength, lifespan, assembly requirements, and rotor vibration characteristic adjustment requirements, enabling automatic iterative calculations, reducing time costs, and more closely reflecting engineering realities. Designers only need to follow the disclosed process of this invention, considering the structural form and safety margin requirements of the elastic support; the rest of the work can be completely completed by the computer, encompassing calculation, analysis, optimization, and verification. The elastic support designed and optimized by this invention can meet practical application requirements.

[0041] Taking the design of a certain type of air turbine starter with an elastic support for the turbine rotor as an example, the air turbine starter consists of a turbine A, an elastic support element B, and a bearing C; the design of this invention mainly focuses on optimizing the elastic element; the optimization process includes the following steps:

[0042] Step 1: Obtain bearing design parameters: The support structure of the air turbine starter rotor consists of three parts: bearings, elastic supports, and bearing housings. Generally, bearing housings use a high-rigidity structure, so the turbine rotor stiffness is derived from the superposition of bearing stiffness and elastic support stiffness. Select the bearing based on the actual load and life requirements, obtaining the bearing structural parameters (inner diameter, outer diameter, width) and bearing stiffness parameters. Example: The rotor bearing has an inner diameter of 17mm, an outer diameter of 40mm, a width of 12mm, and a bearing stiffness parameter of 1E8N / m.

[0043] Step 2, 1) Obtain turbine rotor support position parameters: Determine the rotor support position parameters based on the actual structural requirements and installation requirements of the rotor;

[0044] 2) Obtain material parameters: In this example, the rotor material is TC4 alloy, and the elastic support material is 40CrNiMoA;

[0045] 3) Establish a preliminary finite element analysis model: Import the turbine rotor model of the air turbine starter into the finite element software, constrain the axial rotation and axial displacement degrees of freedom of the bearing installation position in the rotor model, replace the bearing with a spring element, and assign the bearing stiffness value of 1E8N / m obtained in step 1 to the spring element.

[0046] 4) Obtain preliminary calculation results: Based on the above finite element model, calculations are carried out to obtain the vibration modes and critical speeds of the rotor, and the Campbell diagram is used to evaluate the first-order critical speed of the rotor's bending mode.

[0047] 5) Based on actual usage requirements, determine the operating speed and disengagement speed of the air turbine starter rotor for long-term operation. Generally, the first and second critical speeds should be at least ±20% away from the operating speed and disengagement speed. Determine the adjustment direction and range of the support stiffness based on the evaluation criteria and the actual critical speed value. In this example, the rotor's first critical speed is 60838 RPM, and the required constant operating speed is 55000 RPM. Therefore, its vibration margin is only 9%, which does not meet the usage requirements. Furthermore, the critical speed is too high, resulting in a high over-critical response of the rotor. The critical speed needs to be adjusted to below 44000 RPM.

[0048] Step 3, 1) Select the basic type of elastic support. For example... Figure 2 , 3 The elastic support structures shown in Figures 1 and 4 can all achieve the purpose of stiffness adjustment. However, different types of elastic supports can be selected depending on the different stiffness adjustment ranges and actual application. In this example, because the critical speed adjustment range is relatively large, i.e., the elastic support needs to have relatively low stiffness, a type of elastic support is selected. Figure 2 The design incorporates an elastic support with both inner and outer bosses.

[0049] 2) Establish a parametric model of the elastic support. Based on the finite element software ANSYS APDL language, a parametric model containing all structural information of the elastic support is established for design. The parametric model of the elastic support can be referenced as follows: Figure 5 The parameters are parameterized, and it should be clearly stated that the number, size, relative angle, inner diameter, and outer diameter of the inner or outer bosses can all be used as optimization variables in the design. The example uses a parameterized model with four inner and four outer bosses, and the angular relationship between the bosses is symmetrical, for design optimization calculations.

[0050] 3) Establish a finite element model for the stiffness analysis of the elastic support. To simulate the stiffness feedback of the elastic support during bearing whirl, the contact relationship between the bearing, bearing housing, and elastic support needs to be established. An elastic ring with an inner diameter equal to the outer diameter of the elastic support is used to simulate the bearing, and an elastic ring with an outer diameter equal to the inner diameter of the elastic support is used to simulate the bearing housing. In this example, the outer diameter of the elastic support is 45.6 mm, and the inner diameter is 40 mm.

[0051] Step 4, 1) Read material mechanical property data. Automatically read the material properties of the elastic support, elastic shaft, and elastic bearing ring. These material properties must include elastic modulus, density, Poisson's ratio, yield strength, and ductile properties. These material properties are necessary input conditions for this optimization program.

[0052] 2) Setting Assembly Requirements. Based on the actual operating environment, the elastic support contacts both the bearing and the bearing support simultaneously. To reduce wear between the elastic support and the bearing and bearing support under turbine vortex action, interference fit is generally used at both contact points for installation. This interference will cause pre-deformation of the elastic ring, thus changing the support stiffness of the elastic support. A small interference is given as an input condition in the initial calculation, and this interference is used as an optimization parameter in the later optimization design iterations. In this example, the interference at both the inner and outer sides is initially set to 0.01 mm.

[0053] 3) Boundary Conditions and Loads. Constrain all degrees of freedom of the outer wall surface of the elastic bearing housing; constrain the axial rotation, axial displacement, and radial rotation degrees of freedom of the elastic circular shaft; constrain the axial displacement degree of freedom of the elastic support, and set the interference contact relationship between the elastic support, the elastic circular shaft, and the elastic bearing housing. Generally, this contact is set to frictional, and the friction coefficient is set to 0-0.2. To simulate the whirl displacement generated during the rotor's design operation, it is assumed that the rotor undergoes circular whirl, thereby applying two mutually perpendicular radial (x, y) displacement loads to the elastic circular shaft. The load values ​​can vary between 0-1 mm, and these two displacement loads need to satisfy the requirement that the trajectory is circular. Examples of load input variations can be seen in Table 1.

[0054] Table 1. Calculation Results of Input Load, Deformation, and Elastic Support Stiffness

[0055]

[0056]

[0057] 4) Automatically solve for the support reaction force of the elastic support on the elastic circular shaft under the current parameters, and obtain the stiffness value of the elastic support from the displacement load and support reaction force. Write the stress, strain, mass, and stiffness values ​​of the elastic support into the file scratch;

[0058] 5) Direct optimization is performed using finite element zero-order optimization, first-order optimization, or second-order optimization algorithms. In the optimization analysis step, the scratch file in step 4.5 is called and the design variables, objective function, and constraint variables are read. The stiffness value and the internal stress value of the elastic support are used as the judgment criteria. The optimization path is searched and iterated until the result converges.

[0059] Step 5, 1) Research shows that for cantilevered rotors, the support stiffness of the bearings near the turbine has a significant impact on the dynamic characteristics of the turbine rotor. Furthermore, the distance between the two support bearings has a significant impact on the rotor's dynamic characteristics and structural design. The finite element model of the turbine rotor is imported, and bearing elements are established near the turbine bearing mounting position. These elements are assigned a series stiffness value combining the elastic support and bearing stiffness, while bearings farther from the turbine are assigned their original stiffness. The axial displacement and axial rotational degrees of freedom of the rotor are constrained, and modal and critical speed analyses are performed.

[0060] 2) Analyze the first and second critical speeds of the rotor bending mode, and determine the speed margin between the current critical speed, the cut-off speed, and the long-term operating speed. Generally, this margin is ±20%.

[0061] Step 6: If the critical speed of the rotor does not meet the speed margin requirement under the current parameters, change the stiffness design requirements and iterate through steps 3-5 again. In this example, the first-order critical speed of the turbine rotor with optimized elastic supports is 20508 RPM, which meets the vibration margin requirement.

[0062] It should be noted that the above description is only a preferred embodiment of the present invention; any part not described in detail is considered to be prior art or conventional implementation means; it should also be noted that for those skilled in the art, several modifications and improvements can be made without departing from the principle of the present invention, and these should also be considered to fall within the protection scope of the present invention.

Claims

1. A method for optimizing the design of an elastic support for an air turbine starter rotor, characterized in that, The optimization method includes the following steps: Step S1: Obtain the radial and axial dimensions of the turbine bearing and the bearing support stiffness to obtain the bearing design parameters; select the bearing according to the actual load and life requirements of the bearing, and obtain the bearing design parameters, which include at least: structural parameters and bearing stiffness parameters; structural parameters include inner diameter, outer diameter, and width; Step S2: Based on the turbine rotor structure characteristics and support position, call the bearing structure parameters and bearing stiffness parameters mentioned in step S1, calculate the rotor mode and critical speed under this condition, and determine the adjustment direction and range of rotor bearing stiffness. Step S3: Establish a parametric model of the elastic support assembly, using an elastic shaft to simulate the bearing and an elastic ring to simulate the bearing mounting base; Step S4: Use finite element software to automatically read material properties, assembly relationships, solve calculations, obtain calculation results, find optimization paths, and iterate to obtain an elastic support structure under a certain stiffness. Step S5: Load the turbine model, start the rotor dynamics analysis module, and use the series stiffness of the elastic support stiffness corresponding to the elastic support structure obtained in step S4 and the bearing stiffness in step S1 as the overall stiffness to carry out rotor critical speed analysis. Step S6: Analyze the current rotor critical speed. If it does not meet the design requirements, repeat steps S3-S5 until the design requirements are met.

2. The method for optimizing the design of an elastic support for an air turbine starter rotor as described in claim 1, characterized in that, Step S2 includes the following steps: 1) Obtaining turbine rotor support position parameters; 2) Obtaining material parameters; 3) Establishing a preliminary finite element analysis model; 4) Performing calculations based on the finite element model to obtain the rotor's vibration modes and critical speed Campbell's diagram, evaluating the first-order critical speed of the rotor's bending mode, and obtaining preliminary calculation results; 5) Determining the speed points at which the air turbine starter rotor needs to operate for a long time and the disengagement speed points based on actual usage requirements, and determining the adjustment direction and range of rotor bearing stiffness based on evaluation standards and actual critical speed values.

3. The method for optimizing the design of the elastic support for the turbine rotor of an air turbine starter as described in claim 2, characterized in that, In step S2, establishing the finite element analysis model involves importing the air turbine starter turbine rotor model into the finite element software, constraining the axial rotation and axial displacement degrees of freedom of the bearing mounting position in the rotor model, replacing the bearing with a spring element, and assigning the bearing stiffness parameters obtained in step S1 to the spring element.

4. The method for optimizing the design of the elastic support for the turbine rotor of an air turbine starter as described in claim 2, characterized in that, When determining the operating speed and disengagement speed of the air turbine starter rotor, the first and second critical speeds should be at least ±20% away from the operating speed and disengagement speed. The adjustment direction and range of the support stiffness should be determined based on the evaluation criteria and the actual critical speed value.

5. The method for optimizing the design of the elastic support for the turbine rotor of an air turbine starter as described in claim 1, characterized in that, Step S3 includes the following steps: 1) Selecting the basic type of elastic support; 2) Establishing a parametric model of the elastic support; 3) Establishing a finite element model for stiffness analysis of the elastic support.

6. The method for optimizing the design of the elastic support for the turbine rotor of an air turbine starter as described in claim 5, characterized in that, When establishing the parametric model of the elastic support, the design is carried out based on the finite element software ANSYS APDL language, which contains all structural information of the elastic support.

7. The method for optimizing the design of the elastic support for the turbine rotor of an air turbine starter as described in claim 5, characterized in that, When establishing the finite element model for stiffness analysis of the elastic support, an elastic ring simulating the bearing with the inner diameter of the elastic support being the outer diameter is established, and an elastic ring simulating the bearing housing with the outer diameter of the elastic support being the inner diameter is established.

8. The method for optimizing the design of the elastic support for the turbine rotor of an air turbine starter as described in claim 1, characterized in that, Step S4 is executed as follows: 1) Read material mechanical property data; automatically read the material properties of the elastic support, elastic shaft, and elastic bearing ring. These material properties need to include elastic modulus, density, Poisson's ratio, yield strength, and plasticity; 2) Based on the actual usage environment, the elastic support is in contact with both the bearing and bearing support. To reduce wear between the elastic support and the bearing and bearing support under turbine vortex action, an initial interference of 0.01mm is given as an input condition, and the interference is used as an optimization parameter in the later optimization design iteration; 3) Constrain all degrees of freedom of the outer wall surface of the elastic bearing housing; constrain the axial rotation, axial displacement, and radial rotation degrees of freedom of the elastic circular shaft; Constrain the axial displacement degree of freedom of the elastic support, and set the interference contact relationship between the elastic support and the elastic circular shaft and the elastic bearing housing. To simulate the whirl displacement generated during the rotor design process, assume that the rotor performs circular whirl, and thus apply two mutually perpendicular radial (x, y) displacement loads to the elastic circular shaft; the load value varies between 0-1mm, and these two displacement loads need to meet the requirement that the trajectory is circular; 4) Automatically solve the support reaction force of the elastic support on the elastic circular shaft under the current parameters, and obtain the stiffness value of the elastic support from the displacement load and support reaction force; write the stress, strain, mass, and stiffness values ​​of the elastic support into the file scratch; 5) Use the finite element zero-order optimization, first-order optimization, or second-order optimization algorithm for direct optimization. In the optimization analysis step, call the scratch file in step 4) and read the design variables, objective function, and constraint variables, using the stiffness value and the internal stress value of the elastic support as the judgment criteria; search for the optimization path and iterate until the result converges.

9. The method for optimizing the design of the elastic support for the turbine rotor of an air turbine starter as described in claim 1, characterized in that, When analyzing the critical speed of the rotor, the first and second critical speeds of the rotor bending mode are analyzed to determine the speed margin between the current critical speed and the cut-off speed and the long-term operating speed.

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