A method for measuring and evaluating stress concentration in cage-type elastic supports

Abstract

This invention provides a method for measuring and evaluating stress concentration in a cage-type elastic support, belonging to the field of measurement and testing technology. The method includes the following steps: First, determining the stiffness of the elastic support through calibration tests; second, calculating the stress distribution formula of the cage bars based on their structural dimensions; third, obtaining the analytical solution for stress concentration using the multivariate function extremum method; fourth, obtaining the theoretical solution for the strain gauge measurement range using the area integral method; and fifth, measuring, evaluating, and correcting the stress concentration to obtain the measured value of the stress concentration in the cage bars. This invention solves the problem of inaccurate measurement location and data in existing technologies when measuring stress concentration at the root of the cage bars, providing accurate data support for the structural strength design and fatigue life estimation of elastic supports.

Description

Technical Field

[0001] This invention belongs to the field of measurement and testing technology, specifically relating to a method for measuring and evaluating stress concentration in cage-type elastic supports. Background Technology

[0002] The cage-type elastic support is an annular slotted structure used to adjust the critical speed of an aero-engine. It secures the aero-engine rotor to the casing, and its stiffness can be altered by adjusting structural parameters such as the number and spacing of the cage bars. When the engine accelerates to its operating speed after startup, it needs to surpass the critical speed. This causes resonance in the casing-elastic support-rotor system. The elastic support is subjected to alternating loads generated by the rotor's rotation. The magnitude and direction of these loads change with rotor rotation and are called whirl loads. Whirl loads cause significant stress concentration at the root of the cage bars. After a certain number of whirl load cycles, the cage bars are prone to fatigue fracture, leading to engine failure. Therefore, the stress concentration effect of the elastic support is one of the key issues to consider in engine design.

[0003] Existing technologies typically use bonded strain gauges to measure stress concentration at the root of cage bars. This method has several drawbacks: First, strain measurement is affected by the structural shape: strain gauges are generally bonded to relatively flat areas, while stress concentration in cage bars often occurs at transitions, chamfers, etc., resulting in a discrepancy between the strain measurement location and the actual stress concentration location. Second, fatigue fracture of cage bars is the process of initiation and propagation of the crack tip plastic zone caused by stress concentration. The stress concentration area is much smaller than the measurement range of the strain gauge, and the stress gradient in the stress concentration area is large. The strain gauge measurement result is the average stress within the strain gauge range, which cannot accurately measure stress concentration. Third, unlike general static stress concentration measurement methods, eddy loads change continuously in magnitude and direction, exhibiting high frequency and high amplitude characteristics. The stress distribution and stress concentration location at the root of the cage bars also change continuously with the load. Therefore, time-varying analysis is required for the selection of strain measurement locations and the evaluation of measurement results, which the bonded strain gauge method cannot meet.

[0004] In summary, the existing method of attaching strain gauges has shortcomings in assessing the variation of stress concentration areas, the accuracy of measurement areas, and the validity of data under vortex loading of elastic supports, and needs to be improved. Summary of the Invention

[0005] This invention provides a method for measuring and evaluating stress concentration in cage-type elastic supports. The purpose is to solve the problem that existing technologies are inaccurate in measuring the stress concentration at the root of the cage bars, resulting in inaccurate measurement locations and data, and thus failing to meet the requirements of time-varying analysis.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A method for measuring and evaluating stress concentration in a cage-type elastic support includes the following steps:

[0008] The first step is to determine the stiffness of the elastic support through calibration tests;

[0009] The second step is to calculate the stress distribution formula of the elastic support cage bar based on its structural dimensions.

[0010] The third step is to obtain the analytical solution of stress concentration using the multivariate function extremum method.

[0011] Step 4: Obtain the theoretical solution for the strain gauge measurement range using the area integral method;

[0012] The fifth step is to measure, evaluate, and correct the stress concentration to obtain the measured values ​​of stress concentration in the cage bars.

[0013] As a preferred approach, in the step of determining the stiffness of the elastic support through calibration tests, static calibration is performed along any direction of the eddy load position to obtain the load-displacement relationship. The eddy load F rotates around the central axis O of the elastic support. i Let be the i-th cage-shaped central axis, and let vortex load F be equal to OO. i The included angle formed by the connecting lines is φ i ; along any OO i A static calibration test is performed in the direction, and the parameter k is determined according to the following formula:

[0014]

[0015] in,

[0016] The meanings of each parameter are as follows: K S For calibrating the stiffness of the elastic support, E is the elastic modulus of the material, L is the length of the cage bar, a is the inner width of the cage bar, b is the outer width of the cage bar, h is the thickness of the cage bar, n is the number of cage bars, and i is the cage bar number. Let be the angle between the i-th cage bar and the external force.

[0017] As a preferred embodiment, in the step of calculating the stress distribution formula of the cage bar based on the structural dimensions of the elastic support cage bar, the stress distribution formula σ of the i-th cage bar section is... i (p,q,t,l) is:

[0018]

[0019] Where (p,q) are the local coordinates of any point on the cage bar section, l is the section height, t is the loading time, F is the vortex loading load, ω=2πf, and f is the vortex loading frequency.

[0020] As a preferred approach, the stress distribution formula σ of the i-th cage bar section is obtained in the step of obtaining the analytical solution of stress concentration using the multivariate function extremum method. i The extreme values ​​of (p,q,t,l) are the analytical solutions σ of the stress concentration. m (t) is obtained by the multivariate function extremum method according to the following formula:

[0021]

[0022] in,

[0023]

[0024] As a preferred approach, in the step of obtaining the theoretical solution for the strain gauge measurement range using the area integral method, the measured theoretical value is obtained by the following formula:

[0025]

[0026] Among them, l x and l y Let x and y be the side dimensions of the strain gauge in the strain gauge, and l be the side dimensions of the strain gauge. x and l y The variables are: x is the local coordinate of the strain gauge along the normal direction, y is the local coordinate of the strain gauge along the axis direction, and l... x l is the x-axis length of the strain gauge. y Let y be the length of the strain gauge.

[0027] As a preferred approach, in the theoretical solution step of obtaining the strain gauge measurement range using the area integral method, if the strain gauge is a square with side length d, i.e., l x =l y =d, then the strain value σ S3 for:

[0028]

[0029] strain value σ S4 for:

[0030]

[0031] strain value σ S3 and σ S4 The strain value σ of the half-bridge group SΔ for:

[0032]

[0033] As a preferred option, in the stress concentration measurement, evaluation, and correction steps, the measured strain value of the half-bridge assembly is: Compared with the theoretical strain value σ SΔThe bending coefficient ξ is:

[0034]

[0035] Theoretical strain value σ of half-bridge group SΔ With the analytical solution σ of stress concentration m The stress evaluation coefficient η for (t) is:

[0036]

[0037] Measured values ​​of stress concentration Obtained through the following formula:

[0038]

[0039] By correcting the measured strain results using the above formula, the measured stress concentration value of the cage bars can be obtained.

[0040] As a preferred option, in the stress concentration measurement, evaluation and correction steps, the calculated bending coefficient ξ is used to evaluate the bending stress state of the cage structure. The closer ξ is to 1, the closer the measured stress result is to the theoretical value, and the closer the measurement position is to the pure bending state.

[0041] As a preferred approach, during the stress concentration measurement, evaluation, and correction steps, the theoretical strain value σ of the half-bridge group is... SΔ With the analytical solution σ of stress concentration m The stress assessment coefficient η of (t) is used to describe the relative relationship between the strain gauge measurement value and the stress concentration value. The value range of the stress assessment coefficient η is (0,1). The closer the value is to 1, the closer the strain measurement location is to the stress concentration area, and the more accurate the measurement result is.

[0042] The beneficial technical effects achieved by this invention are:

[0043] To address the measurement requirements of vortex loading stress concentration in the elastic support structure of aero-engines, a bridge-based measurement method is adopted. A strain measurement method for the stress concentration region at the root of the elastic support cage bars and a numerical theoretical calculation method for stress concentration points are proposed. An evaluation index for the strain measurement results relative to the actual stress concentration is also presented. The analytical results are obtained based on the actual structural dimensions and loading conditions, demonstrating strong theoretical foundation, wide applicability, and high reliability. Experimental data can be compared and verified with theoretical results using two evaluation coefficients, improving the accuracy and reliability of vortex load testing of elastic supports. This allows for the acquisition of more precise stress concentration results, providing data support for the structural strength design and fatigue life estimation of elastic supports. It solves the problems existing in current technologies and possesses outstanding substantive features and significant progress. Attached Figure Description

[0044] Figure 1 This is a flowchart of the measurement and evaluation process according to one specific embodiment of the present invention;

[0045] Figure 2 This is a schematic diagram of the isometric structure of a cage-type elastic support according to one specific embodiment of the present invention;

[0046] Figure 3 yes Figure 2 The main view;

[0047] Figure 4 yes Figure 3 Top view;

[0048] Figure 5 This is a schematic diagram of the parameters of a cage-type elastic support structure according to one specific embodiment of the present invention;

[0049] Figure 6 yes Figure 5 A schematic diagram of the local structural parameters at point A in the middle;

[0050] Figure 7 yes Figure 6 A schematic diagram of the local structural parameters of the mid-section section;

[0051] Figure 8 This is a schematic diagram of the strain gauge region according to one specific embodiment of the present invention;

[0052] Figure 9 yes Figure 8 A schematic diagram of the local structural parameters at point B;

[0053] Reference numerals: 1. Flange edge; 2. Cage bar; 3. Location of vortex load. Detailed Implementation

[0054] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection claimed by the present invention.

[0055] like Figure 1 As shown, a specific embodiment of a method for measuring and evaluating stress concentration in a cage-type elastic support is presented. This method employs an eddy load-based approach. First, the stiffness of the elastic support is determined through calibration tests. Then, the stress distribution formula of the cage 2 is calculated based on its structural dimensions. An analytical solution for stress concentration is obtained using the multivariate function extremum method. A theoretical solution for the strain gauge measurement range is obtained using the area integral method. Finally, a method for measuring, evaluating, and correcting stress concentration is proposed, specifically including the following steps:

[0056] The first step is to determine the stiffness k of the elastic support through calibration tests.

[0057] The upper and lower sides of the cage bar 2 structure are connected to the bottom flange edge 1 and the eddy load position 3 respectively through transition fillets. The eddy load F is transmitted to each cage bar 2 through the connected positions. The cage bar 2 is equivalent to the upper and lower ends being fixed boundary states, and the stress distribution formula at any position S of the cage bar 2 can be obtained.

[0058] like Figures 2-7 As shown, in this specific embodiment, the elastic support structure is annularly symmetrical. The flange 1 at the bottom of the structure is fixed, and the eddy load position 3 is located at the engine rotor bearing. The cage bar 2 deforms under the action of the eddy load. Static calibration is performed along any direction of the eddy load position 3 to obtain the load-displacement relationship. The eddy load F rotates around the central axis O of the elastic support. i Let the centroidal axis of the i-th cage bar be 2, and let the vortex load F be equal to OO. i The included angle formed by the connecting lines is φ i Along any OO i A static calibration test was conducted in the direction, and the parameter k was determined according to equation (1):

[0059]

[0060] in,

[0061] like Figures 5-7 As shown, the meanings of the other parameters in equation (1) are as follows: K S For calibrating the stiffness of the elastic support, E is the elastic modulus of the material, L is the length of the cage bar, a is the inner width of the cage bar, b is the outer width of the cage bar, h is the thickness of the cage bar, n is the number of cage bars, and i is the cage bar number. Let O be the angle between the i-th cage bar and the external force, and let O be the central axis of the elastic support. i Let F be the i-th cage-shaped mandrel, F be the eddy load, and φ be the vortex load. i Let be the eddy load angle, l be the section height, S be the location of any point, p be the coordinates of point S along the diameter direction, q be the coordinates of point S along the normal direction, S1 be the first stress concentration location, and S2 be the second stress concentration location.

[0062] The second step is to calculate the stress distribution formula σ of cage bar 2 based on the structural dimensions of the elastic support cage bar. i (p,q,t,l)

[0063] According to equation (1), the stress distribution formula for the i-th cage bar section 2 is σ. i (p,q,t,l) is:

[0064]

[0065] Where (p,q) are the local coordinates of any point on the cross section of cage bar 2, l is the cross section height, t is the loading time, F is the vortex loading load, ω=2πf, and f is the vortex loading frequency.

[0066] The third step is to obtain the analytical solution σ of stress concentration using the multivariable function extremum method. m (t)

[0067] The extreme value of equation (2) is the analytical solution σ of stress concentration. m (t), in this specific embodiment, the extreme value of equation (2) is obtained by the multivariate function extremum method, which is equation (3):

[0068]

[0069] in,

[0070]

[0071] Based on the structural parameters, the stress concentration location at the root of cage bar 2 is determined. According to the structural parameters, the stress maximum value is either point S1 (p1, q1) or point S2 (p2, q2).

[0072] Step 4: Calculate the theoretical solution for strain gauge measurements.

[0073] Strain gauges are attached to the centerline positions on the inner and outer sides of the base of the cage bars, according to the strain gauge size l. x and l y The theoretical solution for the strain gauge measurement range is obtained through the area integral method. In this specific embodiment, the theoretical measurement value is obtained according to equation (4):

[0074]

[0075] Among them, l x and l y Let x and y be the side dimensions of the strain gauge in the strain gauge, and l be the side dimensions of the strain gauge. x and l y The variables are determined by the positions of strain gauges S3 and S4 attached to the roots of the inner and outer widths of cage bar 2, as shown in the figure. Figures 8-9 As shown in the figure, the meanings of the markings are as follows: x is the local coordinate of the strain gauge along the normal direction, y is the local coordinate of the strain gauge along the axis direction, and l is the coordinate of the strain gauge along the axis. x l is the x-axis length of the strain gauge. y Let y be the length of the strain gauge.

[0076] If the strain gauge is a square with side length d, i.e. l x =l y =d, then the strain value σ S3 σ S4The strain value σ of the half-bridge group composed of the two SΔ for:

[0077]

[0078]

[0079]

[0080] Strain gauges are attached along the neutral axis of cage bar 2, with a strain gauge size of d. Based on equation (4), the theoretical stress solutions for regions S3 / S4 are obtained as follows: σ S3 (t) and σ S4 (t), the two together form a half-bridge with a value of σ. SΔ (t).

[0081] Step 5: Measure, assess, and correct for stress concentration.

[0082] The measured strain values ​​of the half-bridge assembly are as follows: Compared with the theoretical strain value σ SΔ The bending coefficient ξ is:

[0083]

[0084] The closer ξ is to 1, the closer the measured stress result is to the theoretical value, and the closer the measurement location is to a pure bending state.

[0085] In this specific embodiment, equation (7) and the measured half-bridge strain values ​​are used. The bending coefficient ξ is calculated according to formula (8), which can be used to evaluate the bending stress state of the cage bar 2 structure.

[0086] Theoretical strain value σ of half-bridge group SΔ With the analytical solution σ of stress concentration m The stress evaluation coefficient η for (t) is:

[0087]

[0088] The value of η ranges from (0,1). The closer the value is to 1, the closer the strain measurement location is to the stress concentration region, and the more accurate the measurement result. The stress assessment coefficient η describes the relative relationship between the strain gauge measurement value and the stress concentration value.

[0089] Measured values ​​of stress concentration It can be obtained through the following formula:

[0090]

[0091] By correcting the measured strain results using equation (10), the measured stress concentration value of cage bar 2 can be obtained.

[0092] The beneficial technical effects achieved by this specific embodiment are:

[0093] To address the measurement requirements of vortex loading stress concentration in the elastic support structure of aero-engines, a bridge-based measurement method is adopted. A strain measurement method for the stress concentration region at the root of the elastic support cage bars and a numerical theoretical calculation method for stress concentration points are proposed. An evaluation index for the strain measurement results relative to the actual stress concentration is also presented. The analytical results are obtained based on the actual structural dimensions and loading conditions, demonstrating strong theoretical foundation, wide applicability, and high reliability. Experimental data can be compared and verified with theoretical results using two evaluation coefficients, improving the accuracy and reliability of vortex load testing of elastic supports. This allows for the acquisition of more precise stress concentration results, providing data support for the structural strength design and fatigue life estimation of elastic supports. It solves the problems existing in current technologies and possesses outstanding substantive features and significant progress.

Claims

1. A method of measuring and evaluating stress concentration of a springing with a cage bar, characterized by, It comprises the following steps: First, determine the elastic support stiffness through calibration test; Static calibration is performed along any direction of the eddy load position to obtain the load-displacement relationship. The eddy load F rotates about the central axis O of the elastic support. i Let be the i-th cage-shaped central axis, and let vortex load F be equal to OO. i The included angle formed by the connecting lines is φ i ; along any OO i A static calibration test is performed in the direction, and the parameter k is determined according to the following formula: wherein The meanings of the parameters are as follows: K S K is the calibrated stiffness of the elastic support, E is the elastic modulus of the material, L is the length of the cage bar, a is the inner width of the cage bar, b is the outer width of the cage bar, h is the thickness of the cage bar, n is the number of cage bars, and i is the cage bar number, is the angle between the ith cage bar and the external force. Second, calculate the stress distribution formula of the cage strip according to the structural size of the elastic support cage strip; The formula for the stress distribution in the cross-section of the ith cage bar σ i (p, q, t, l) are: Wherein, (p, q) is the local coordinates of any point of the cage strip section, l is the section height, t is the loading time, F is the vortex loading load, ω = 2πf, f is the vortex loading frequency; Third, obtain the stress concentration analytical solution through the multivariate function extreme value method; The stress distribution formula of the ith cage strip section σ i The maximum and minimum of (p, q, t, l) is the analytical solution of stress concentration σ m (t) is obtained by the extreme value method of multivariate function as follows: wherein, Fourth, obtain the theoretical solution of the strain gauge measurement range through the area integral method; The measurement theoretical value is obtained according to the following formula: wherein, l x and l y is the length of the strain gage in the x direction, l x and l y is the length of the strain gage in the y direction; x is the coordinate of the local strain gage in the normal direction, y is the coordinate of the local strain gage in the axial direction, l x is the length of the strain gage in the x direction, l y is the length of the strain gage in the y direction; If the strained gate is a square with side length d, i.e. l x = l y = d, then the strain value σ S3 is: Strain value σ S4 is: Strain value σ S3 And σ S4 The half-bridge group bridge strain value σ SΔ Is: Fifth, measure, evaluate and correct the stress concentration to obtain the actual measured value of the stress concentration of the cage strip; The measured strain value of the half-bridge group is The bending coefficient ξ of the measured strain value σ SΔ is: Theoretical strain value σ of half-bridge group SΔ With the analytical solution σ of stress concentration m The stress evaluation coefficient η for (t) is: Stress concentration measured value Obtained by the formula: The measured strain results are corrected through the above formula, and the actual measured value of the stress concentration of the cage strip is obtained.

2. The cage spring stress concentration measurement and evaluation method according to claim 1, characterized in that In the step of measuring, evaluating and correcting the stress concentration, the calculated bending coefficient ξ is used to evaluate the bending stress state of the cage strip structure, and the closer ξ is to 1, the closer the stress measurement result is to the theoretical value, and the closer the measurement position is to the pure bending state.

3. The cage spring stress concentration measurement and evaluation method according to claim 2, characterized in that In the stress concentration measurement, evaluation, and correction steps, the theoretical strain value σ of the half-bridge group... SΔ With the analytical solution σ of stress concentration m The stress assessment coefficient η of (t) is used to describe the relative relationship between the strain gauge measurement value and the stress concentration value. The value range of the stress assessment coefficient η is (0,1). The closer the value is to 1, the closer the strain measurement location is to the stress concentration area, and the more accurate the measurement result is.

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