Rotor initial unbalance prediction method considering assembly deviation of stop and measurement error

Abstract

The application discloses a rotor initial unbalance prediction method considering joint assembly deviation and measurement error, and belongs to the field of aero-engine assembly. The method comprises the following steps: a finite element simulation model of a joint temperature difference assembly process is established, an end face normal vector and a cylindrical centroid coordinate vector of a lower joint of an upper disc are extracted; joint assembly deviation parameters between two-stage discs are determined; two times of unbalance measurement are performed on a single-stage disc, and a system of linear equations is solved to eliminate measurement error caused by tool assembly clearance, and mass deviation characteristics are obtained; joint fitting surface run-out data are measured, geometric deviation parameters are determined, a coordinate transformation matrix is constructed, and the mass deviation characteristics are converted to a unified coordinate system; mass deviation characteristics of each disc are transferred stage by stage, and unbalance amount and unbalance phase of a rotor assembly on two correction planes are solved based on a vector superposition and a torque balance principle. The application can effectively improve the prediction precision of the initial unbalance amount of the aero-engine rotor, and meets high reliable assembly requirements.

Description

Technical Field

[0001] This invention belongs to the field of aero-engine assembly technology, specifically relating to a method for predicting rotor initial imbalance, and more specifically to a method for predicting rotor initial imbalance that considers stop assembly deviation and measurement error. Background Technology

[0002] Rotor assembly is a critical step in aero-engine manufacturing, and its quality directly affects the engine's performance and service life. Initial imbalance is a core indicator for evaluating the assembly quality of rotor components. If this imbalance is too large, it will generate complex vibrations and noise during high-speed rotor rotation, and in severe cases, may even threaten the engine's operational safety. Therefore, it is necessary to effectively predict and control the initial imbalance before assembly.

[0003] Currently, there are three main prediction models based on error propagation: the first is a prediction model that transforms the two-sided imbalance result into a single value by taking the maximum value or vector summation; the second is a two-sided imbalance prediction model based on the torque balance principle (i.e., the two-mass model); and the third is a prediction model based on the skew distribution of the principal axis of inertia. The first two models are equivalent unbalanced mass models. The former has lower prediction accuracy because it ignores the influence of the unbalanced torque; the latter, although considering the influence of the unbalanced torque, can only identify imbalances on two specified cross-sections. Therefore, neither is suitable for analyzing the mass distribution of complex rotor systems. The third model improves prediction accuracy to some extent compared to the first two models, but it assumes the rotor is a rigid stack and does not consider the morphology of the mating surfaces and assembly deformation, resulting in insufficient prediction accuracy for the initial imbalance of complex rotor assemblies, making it difficult to meet the requirements of high-reliability assembly. Summary of the Invention

[0004] The purpose of this invention is to solve the problem of low prediction accuracy in existing rotor initial imbalance prediction methods, and to propose a method to improve prediction accuracy by quantifying stop assembly deviation through simulation, improving tooling compensation measurement, and unifying coordinate transmission error.

[0005] To achieve the above objectives, the technical solution provided by this invention is:

[0006] A method for predicting the initial imbalance of a rotor, taking into account assembly deviations and measurement errors, is provided, including the following steps:

[0007] Step 1: Establish a finite element simulation model of the temperature difference assembly process of the stop. Using the surface morphology data of the stop mating and the assembly process parameters as input, perform contact simulation calculations and extract the normal vector of the lower stop end face of the upper wheel disk used to characterize the skewing of the stop assembly and the centroid coordinate vector of the lower stop cylinder surface of the upper wheel disk used to characterize the eccentricity of the stop assembly.

[0008] Step 2: Based on the end face normal vector and cylindrical centroid coordinate vector extracted in Step 1, determine the stop assembly deviation parameters between the two-stage wheel disks. The stop assembly deviation parameters include the rotation transformation matrix from the upper wheel disk coordinate system to the lower wheel disk upper stop fitting plane coordinate system, and the translation vector of the lower stop centroid of the upper wheel disk relative to the upper stop centroid of the lower wheel disk.

[0009] Step 3: Perform unbalance measurement on the single-stage wheel to obtain its own mass deviation characteristics. This includes: taking two measurements with the wheel and balancing fixture in the initial assembly state and the assembly state after a 180-degree relative rotation in the circumferential direction, respectively. During each measurement, obtain the cylindrical runout data of the wheel stop and the overall unbalance data measured by the dynamic balancing machine. Based on the data from the two measurements, solve for the measurement error caused by the tooling assembly gap to obtain the centroid offset vector and the inertial principal axis tilt vector relative to the coordinate system of the wheel's head and tail.

[0010] Step 4: Measure the runout data of the mating surface of the single-stage wheel, determine the geometric deviation parameters of the single-stage wheel, and based on the geometric deviation parameters, construct a coordinate transformation matrix from the upper stop fitting plane coordinate system of the wheel to its single-stage wheel coordinate system; through coordinate transformation, transform the mass deviation characteristics obtained in Step 3 from the end-to-end line coordinate system to the single-stage wheel coordinate system to obtain the transformed mass deviation characteristics.

[0011] Step 5: Using the single-stage disk coordinate system of the first-stage disk as the assembly coordinate system, the mass deviation characteristics of subsequent disks after transformation in Step 4 are sequentially transferred to the assembly coordinate system through the stop assembly deviation parameters determined in Step 2 and the coordinate transformation matrix constructed in Step 4. Then, the mass deviation characteristics of each disk in the first-to-last line coordinate system are obtained through coordinate transformation. Based on the mass and moment of inertia of each disk, and based on the principles of vector superposition and torque balance, the unbalance quantity and unbalance phase of the rotor assembly on the two correction planes are solved, which serve as the initial unbalance prediction results of the multi-stage rotor assembly.

[0012] Furthermore, in step 1, the temperature difference assembly process of the stop includes four processes: heating and expansion of the concave stop or cooling and contraction of the convex stop, contact of the pre-compression end face during assembly, contact of the cylindrical surface during temperature recovery, and contact of the bolt tightening end face.

[0013] Furthermore, in step 1, the finite element simulation model is automatically parametrically simulated by Matlab and Ansys. Matlab is used to construct the three-dimensional geometric model of the concave and convex stop containing the surface topography data of the mating surfaces and to generate the node and mesh data of the finite element model. Ansys is used to call the data file to perform contact deformation analysis and to achieve parametric updates through the APDL command stream.

[0014] Further, in step 1, the end face normal vector is obtained by fitting the end face displacement data of the lower stop of the upper wheel, and the cylindrical centroid coordinate vector is obtained by fitting the cylindrical displacement data of the lower stop of the upper wheel. Then, the stop assembly skew angle, stop assembly skew phase, stop assembly eccentricity and stop assembly eccentricity phase are calculated.

[0015] Furthermore, in step 2, the rotation transformation matrix is ​​determined by coordinate rotation transformation based on the end face normal vector. Specifically, the end face normal vector is used as the fitting plane coordinate system of the upper stop of the lower-level wheel. In the axial direction, calculate the revolution around the axis based on the components of the normal vector of the end face. shaft and The rotation angle of the axis is used to construct a rotation matrix, which is then inverted to obtain the rotation transformation matrix from the upper wheel coordinate system to the lower wheel upper stop fitting plane coordinate system; the translation vector adopts the cylindrical centroid coordinate vector, and its axial component is ignored.

[0016] Furthermore, in step 3, the thin disk and the thick disk are distinguished according to the length-to-diameter ratio of the disk. When the length-to-diameter ratio is greater than 0.2, it is a thick disk. The double-calibration surface balance measurement and the corresponding equation set are used to eliminate the measurement error caused by the tooling assembly gap. Otherwise, it is a thin disk. The single-calibration surface balance measurement and the corresponding equation set are used to eliminate the measurement error caused by the tooling assembly gap.

[0017] Furthermore, in step 4, the geometric deviation parameters include the centroid offset vector and the end face tilt normal vector.

[0018] Further, in step 4, the coordinate transformation matrix is ​​determined as follows: a single-level wheel coordinate system is established with the lower stop centroid as the origin, and an upper stop fitting plane coordinate system is established with the upper stop fitting centroid as the origin. The centroid coordinate vector of the upper stop in the single-level wheel coordinate system is obtained by measurement. and end face normal vector The coordinate transformation matrix from the fitted plane coordinate system at the upper stop to the single-stage wheel coordinate system is determined by the end face normal vector. Calculate the winding based on its components. shaft and The rotation angle of the axis is obtained by constructing the rotation matrix and then taking its inverse; the transformation matrix used to transform the mass deviation characteristics obtained in step 3 from the head-to-tail coordinate system to the single-level wheel coordinate system is derived from the centroid coordinate vector. Calculate the winding based on its components. shaft and The rotation angle of the axis is obtained by constructing a rotation matrix and then taking its inverse.

[0019] Furthermore, in step 5, the step-by-step transfer is achieved in the following way: the mass deviation characteristics of each wheel are transformed from the single-stage wheel coordinate system to the assembly coordinate system, and then to the coordinate system of the beginning and end of the rotor assembly. The static unbalance vector and the moment unbalance vector of each wheel are calculated respectively. Then, according to the principle of vector superposition and moment balance, the unbalance vector of the rotor assembly on the two correction planes is obtained. Finally, it is transformed into the unbalance quantity and unbalance phase in the polar coordinate system.

[0020] The advantages of this invention are:

[0021] 1. This invention establishes a high-fidelity finite element simulation model that simulates the actual assembly process of the stop surface due to temperature differences. By incorporating the rotor surface morphology and deformation generated during the assembly process, it achieves quantitative calculation of the eccentricity and skewness of the stop assembly and introduces them as error sources into the assembly error propagation model. This improvement overcomes the shortcomings of existing models that treat the rotor as a rigid stack and ignore the morphology of the mating surfaces and assembly deformation, making the prediction of the initial imbalance more closely resemble the actual assembly state and fundamentally improving the prediction accuracy.

[0022] 2. This invention improves the tooling compensation method for rotor imbalance measurement. By performing two measurements—one with the part and the balancing fixture in their initial assembly state and the other with a 180-degree relative circumferential rotation—and solving a system of equations using the cylindrical runout and imbalance data from both measurements, the interference of the assembly clearance between the part and the fixture on the measurement results is effectively eliminated. This yields the true mass deviation data (center of mass shift and principal axis tilt) of the part in the actual rotating coordinate system. This compensation strategy ensures the accuracy and reliability of the mass characteristic data input into the prediction model, improving prediction accuracy from the source.

[0023] 3. This invention uses the centroid offset vector and the principal axis tilt vector to describe the mass deviation characteristics of a single-stage rotor, and describes these mass characteristics and geometric error characteristics in a unified coordinate system through coordinate transformation. Compared with the existing two-sided unbalance prediction model based on the torque balance principle, this description method based on the rigid body six-degree-of-freedom spatial pose more completely reflects the actual mass distribution of the rotor assembly and is suitable for complex multi-stage rotor stacking systems. Based on this, through step-by-step error propagation and solving based on vector superposition and the torque balance principle, the initial unbalance and unbalance phase of the multi-stage rotor assembly on the two correction planes can be accurately calculated.

[0024] 4. Experimental verification results show that the prediction error of the initial imbalance of the rotor assembly predicted by the method of this invention is significantly reduced compared with the traditional method, basically controlled within 15%, and the predicted results of the imbalance phase are closer to the measured results. Therefore, this invention can effectively meet the requirements of high-reliability assembly of aero-engine rotors, providing a scientific and reliable technical means for accuracy prediction and pre-control before assembly. Attached Figure Description

[0025] The above and other features and advantages of the present invention will become more readily understood from the following description with reference to the accompanying drawings, in which:

[0026] Figure 1 This is a flowchart of a rotor initial imbalance prediction method considering stop assembly deviation and measurement error according to an embodiment of the present invention;

[0027] Figure 2 This is a schematic diagram of the process of forming eccentricity and deviation in the assembly of the stop in this embodiment of the invention;

[0028] Figure 3 This is a flowchart of the automated parametric simulation of interference fit assembly in an embodiment of the present invention;

[0029] Figure 4 This is a schematic diagram of the eccentricity and skewness error model of the stop assembly under contact equilibrium state in an embodiment of the present invention;

[0030] Figure 5 This is a schematic diagram of the mass deviation characteristics of a single-stage wheel in an embodiment of the present invention;

[0031] Figure 6 This is a schematic diagram of the geometric error model of a single-stage wheel in an embodiment of the present invention;

[0032] Figure 7 This is a schematic diagram of the unbalanced feature coordinate transformation process in an embodiment of the present invention;

[0033] Figure 8 This is a schematic diagram of a two-stage wheel stack in an embodiment of the present invention;

[0034] Figure 9 This is a schematic diagram of a three-dimensional model of the rotor assembly in an embodiment of the present invention.

[0035] In the diagram: 1 - Lower stop of the upper-level wheel; 2 - Upper stop of the lower-level wheel. Detailed Implementation

[0036] The present invention will now be described in detail with reference to the accompanying drawings and exemplary embodiments thereof. It should be noted that the following detailed description of the present invention is for illustrative purposes only and is not intended to limit the scope of the invention.

[0037] This invention provides a rotor initial imbalance prediction method that considers stop assembly deviation and measurement error, which is used to predict and optimize the assembly accuracy of multi-stage wheel rotor assemblies of aero-engines, thereby improving the reliability and consistency of rotor assembly.

[0038] Reference Figure 1 The rotor initial imbalance prediction method considering stop assembly deviation and measurement error, as an exemplary embodiment of the present invention, includes the following steps: Step S1, establishing an automatic parameterized simulation model simulating the actual stop temperature difference assembly process; Step S2, establishing a stop assembly deviation model between two-stage rotor disks; Step S3, obtaining rotor mass deviation data in the actual rotating coordinate system; Step S4, establishing a single-stage rotor disk geometric error model and unifying the coordinate system; Step S5, establishing a rotor assembly error propagation model and calculating the initial imbalance of the multi-stage rotor assembly. The steps are described in detail below with reference to the accompanying drawings.

[0039] Step S1: Establish a finite element simulation model of the temperature difference assembly process at the stop.

[0040] This step begins by examining the rotor assembly process to explore the formation principles of eccentricity and misalignment in the stop assembly. For example... Figure 2 As shown, the temperature difference assembly process of the interference fit-bolt connection structure mainly includes four processes: (1) heating expansion of the concave stop or cooling contraction of the convex stop; (2) assembly pre-compression end face contact process; (3) temperature recovery cylindrical surface contact process; (4) bolt tightening end face contact process. If the coupling effect of end face contact and cylindrical surface contact is ignored, the skew amount after assembly is mainly determined by processes (2) and (4), and the eccentricity is mainly determined by process (3).

[0041] Figure 2 (a) illustrates the pre-compression end-face contact stage of the assembly. In this stage, the cylindrical surfaces of the concave stop (after heating) (or the convex stop (after cooling) do not contact; only the end faces contact. During the press-fitting force... Under the equivalent spring force of a series of contact points on the mating end face, a contact equilibrium state is reached. Macroscopically, this is manifested as a spatial angle between the lower stop 1 of the upper wheel and the upper stop 2 of the lower wheel in the absolute coordinate system. This is the first stage of skew formation.

[0042] Figure 2 (b) illustrates the temperature recovery cylinder contact stage. Under the pressure of the press, the mating cylinders gradually come into contact as the temperature changes; this is the centering process. After the temperature recovers to room temperature, the mating cylinders reach equilibrium under the action of the equivalent spring force and end-face friction at the contact point. Macroscopically, this is represented by the centroid of the lower stop 1 (i.e., the convex stop) of the upper wheel. The centroid of the upper stop 2 (i.e., the concave stop) relative to the lower-level wheel disk There is eccentricity This is the process of eccentricity formation.

[0043] Figure 2 (c) shows the bolt tightening end face contact stage. After the cylindrical surface is centered, the pressing force is removed, the bolt is installed and tightened, and the mating end face is under bolt preload. Under the combined action of cylindrical friction and contact point reaction force, another equilibrium state is reached. Macroscopically, this is manifested as an skew angle between the lower stop 1 of the upper wheel and the upper stop 2 of the lower wheel. This is the second stage of deflection formation. At this point, the contact state of the mating surfaces is the final state after assembly.

[0044] To simulate the above process with high fidelity, the finite element method was employed, using Matlab and Ansys to achieve automated parametric simulation. This allowed for the investigation of the impact of variations in assembly process parameters such as installation phase, pressing force, and preload on the initial imbalance of the rotor. The simulation process is as follows: Figure 3 As shown. First, in Matlab software, the centroid of the fitting edge on the lower-level wheel is taken as the origin, and the direction of the jump measurement starting point is taken as... In the positive direction of the axis, with the end face normal vector as In the axial direction, a geometric coordinate system was established according to the right-hand rule to construct three-dimensional geometric models of the concave and convex stops, and measured surface topography data of the mating surfaces were superimposed to generate the node and mesh data files of the finite element model of the stop connection structure. Next, an APDL command stream file was written to implement model data file calling, stop contact deformation analysis, and result output and saving. SOLID 185 was used as the element type; the contact surface of the concave stop was treated as the target surface using TARGE 170 elements, and the contact surface of the convex stop was treated as the contact surface using CONTA 174 elements, with the friction coefficient precisely set to 0.15. To avoid the influence of bolt deformation due to temperature differences, two forces of equal magnitude and opposite direction were applied to the stop end face region in contact with the bolt end face to simulate bolt preload. Different preloads were applied to different bolt connections for finite element calculations. Then, MATLAB read the APDL command file to update the assembly parameters and submitted it to the Ansys solver for simulation. After the simulation, the displacement data of the end face and cylindrical surface of the lower stop of the upper wheel were retrieved using MATLAB, and the normal vector of the end face of the lower stop of the upper wheel, which characterizes the assembly misalignment of the stop, was obtained through fitting. and the cylindrical centroid coordinate vector of the lower stop of the upper wheel used to characterize the eccentricity of the stop assembly. The locating angle of the stop assembly can then be calculated using the following formula. skew phase eccentricity and off-center phase :

[0045]

[0046] In the formula, , and The normal vectors of the end face of the lower stop of the upper wheel in the geometric coordinate system are respectively... , and Components in direction, , and The coordinate vectors of the centroid of the upper wheel's lower stop in the geometric coordinate system are respectively... , and Components in direction.

[0047] The simulation model described above can quantify the influence of the surface morphology of the stop and the assembly process parameters on the assembly deviation, providing accurate input for subsequent error transmission.

[0048] Step S2: Establish a model for the assembly deviation of the stop between the two-stage wheel discs.

[0049] Based on the simulation results of step S1, the upper-level roulette wheel, i.e., the first one, can be fitted. The lower stop of the first-level wheel is on the next-level wheel, i.e., the first... The end face normal vector in the fitted plane coordinate system of the upper stop of the stage wheel and the coordinate vector of the centroid of the cylinder .

[0050] like Figure 4 As shown, the first Centroid of the lower stop of the stage wheel It can be regarded as being caused by the first The centroid of the stop on the stage wheel is fitted. Along vector Formed by translation. Since minute axial deviations have little impact on the overall coaxiality error of the rotor, .

[0051] To describe the relative pose between the two-stage wheels, it is necessary to establish a starting point from the first stage. Level 1 roulette coordinate system To the Fitting Plane Coordinate System to the Upper Stop of the Stage Wheel The rotation transformation matrix is ​​as follows: Using the first... In the fitted plane coordinate system of the upper stop of the stage wheel, the first Normal vector of the lower stop face of the stage wheel As the first The level wheel coordinate system In the axial direction, the direction around the axis is calculated based on the three components of the vector. shaft and The rotation angle of the shaft, another The rotation angles are calculated using the following formulas:

[0052]

[0053] In the formula, For the new coordinate system in the original coordinate system Axial direction vector; and They are respectively around the original coordinate system shaft and The angle of rotation of the axis; , and They are vectors In the original coordinate system , and Components in direction.

[0054] Construction around Rotation matrix of axis and around Rotation matrix of axis Then the rotation matrix ,Right now:

[0055]

[0056] From the Level 1 roulette coordinate system to the 1st Rotation transformation matrix of the fitting plane coordinate system at the stop of the stage wheel for:

[0057]

[0058] At the same time, the translation vector directly adopts the coordinate vector of the centroid of the cylinder. And ignore its axial component (let) Thus, the stop assembly deviation model fully describes the eccentricity (translation) and skewness (rotation) errors between the two-stage discs caused by the stop fit.

[0059] This model simplifies the complex stop contact state into a six-degree-of-freedom spatial pose transformation, which not only preserves the main error characteristics but also facilitates coordinate transfer in subsequent multi-level stacking.

[0060] Step S3: Obtain rotor mass deviation data in the actual rotating coordinate system.

[0061] The mass deviation characteristics of a single-stage wheel are measured using a dynamic balancing machine. For example... Figure 5 As shown, the direction of the calibration screw hole is defined as zero phase, with the centroid of the lower stop of the part as the origin of the coordinate system, and the line connecting the centroids of the beginning and end of the part is... for The axis and zero phase direction are Establish a coordinate system for the line connecting the beginning and end of the part along the positive axis. The picture Represents the center of mass of the part.

[0062] To eliminate measurement errors introduced by the assembly clearance between the measured part and the balancing fixture, the following compensation strategy is adopted: Measurements are performed twice, once in the initial assembly state and once when the wheel and balancing fixture are rotated 180 degrees relative to each other circumferentially. During each measurement, the cylindrical runout of the wheel's stop is measured, and an unbalanced measurement coordinate system is fitted to obtain the result. Centroid coordinate vectors at both ends of the middle part and Simultaneously, the overall imbalance data measured by the dynamic balancing machine is recorded. Based on the two sets of cylindrical runout data and imbalance data obtained from the two measurements, the pre-set set of equations is solved to eliminate the influence of tooling imbalance and assembly clearance, and obtain the true quality deviation characteristics relative to the coordinate system connecting the beginning and end of the part.

[0063] Different balancing measurement methods are used for thin and thick disks. The disk is distinguished based on its length-to-diameter ratio: when the ratio is greater than 0.2, it is a thick disk, and a double-calibration-plane balancing measurement and corresponding equations are used; otherwise, it is a thin disk, and a single-calibration-plane balancing measurement and corresponding equations are used. The center of mass of the part is known. to the centroid The axial distance is By solving the system of equations, the offset vector of the part's centroid relative to the coordinate system connecting the beginning and end of the part can be obtained. and the tilt vector of the principal axis of inertia (For thin plates, ).

[0064] The specific system of equations is as follows:

[0065] For single-calibration plane balancing measurements (thin disk), the equation set is as follows:

[0066]

[0067] For double-calibration plane balancing measurements (thick disk), the equation set is as follows:

[0068]

[0069] In the formula, "~" indicates that the first two rows of the matrix or vector are extracted; the subscripts "0" and "180" represent the initial assembly state of the tooling and the part and the assembly state after rotating 180 degrees circumferentially, respectively. The variables corresponding to the subscripts are obtained from the corresponding measurement states. To measure from an unbalanced coordinate system coordinate system connecting the beginning and end of the part The rotation matrix, m is the mass of the part; , and These represent the part imbalance vector measured on a single calibration plane, the tooling imbalance vector, and the overall imbalance vector directly measured by the balancing machine. , , ,in, Given quantities, the subscripts "x" and "y" represent the vector in the unbalanced measurement coordinate system, respectively. and Components in direction; subscripts “a” and “b” represent the left and right calibration planes in dual calibration plane measurement, respectively, and the variables corresponding to the subscripts are the values ​​on the corresponding calibration planes; and These are the distances from the part's centroid to the left and right correction surfaces, respectively. and These are the rotational inertia of the part's diameter and its polar rotational inertia, respectively.

[0070] This compensation method can effectively eliminate interference from tooling assembly gaps and tooling imbalances, and obtain the true mass distribution data of the parts themselves.

[0071] Step S4: Establish a geometric error model for a single-stage wheel and unify the coordinate system.

[0072] Due to machining errors, the center of the fitted circle on the upper stop cylindrical surface is offset from the ideal center, and the fitted plane of the upper stop end face is tilted relative to the reference plane. Therefore, as Figure 6 As shown, the following stop centroid The origin of the coordinate system is at the th position. Establish a single-stage wheel coordinate system at the lower stop of the stage wheel. The above stops are fitted to the centroid. Establish a local coordinate system at the upper stop fitting plane of the single-stage wheel, with the origin of the coordinate system as the origin. Both coordinate systems use the origin pointing towards the circumferential measurement zero point direction as the coordinate system. The positive direction of the axis, with the plane normal vector as the reference direction. The axis direction, and follows the right-hand rule.

[0073] The geometric deviation parameters of a single-stage wheel are obtained by measuring the reference error correction, that is, the first... Centroid coordinate vector of the stop on the stage wheel and end face normal vector ,in This refers to the centroid offset vector of the upper and lower stops of the wheel at this level in the geometric deviation parameters (reflecting eccentricity). This refers to the end face inclination normal vector of the upper and lower stops of the wheel in the geometric deviation parameters (reflecting the skew). The upper stop is fitted to a plane coordinate system. It can be viewed as a single-level wheel coordinate system First along the vector Translate, then rotate Axis rotation Angle, then around Axis rotation The angle is obtained.

[0074] Coordinate transformation matrix from the upper stop fitting plane coordinate system to the single-level wheel coordinate system It can be obtained from the end face normal vector Following the same rotation transformation method as step S2 (i.e., first calculate the rotation angle, then construct the rotation matrix and inverse it), we obtain:

[0075]

[0076] in, It is the end face normal vector The rotation matrix is ​​constructed according to the method in step S2.

[0077] To describe the quality deviation characteristics and geometric error characteristics in a unified coordinate system, it is necessary to use the first step obtained in step S3. centroid offset vector of the roulette wheel and the tilt vector of the principal axis of inertia From the Coordinate system connecting the beginning and end of the roulette wheel Transform to a single-level wheel coordinate system In the middle. For example Figure 7 As shown, among them The centroid of the i-th level roulette wheel is represented by the transformation matrix derived from the centroid coordinate vector. We obtain the following by constructing and inverting the same rotational transformation:

[0078]

[0079] Then the transformed first centroid offset vector of the roulette wheel and the tilt vector of the principal axis of inertia Calculate using the following formula:

[0080]

[0081] Through this coordinate transformation, the centroid offset vector and the principal axis tilt vector relative to the single-level wheel coordinate system are obtained, realizing a unified expression of mass characteristics and geometric characteristics.

[0082] Step S5: Establish a rotor assembly error propagation model and calculate the initial imbalance of the multi-stage rotor assembly.

[0083] This step uses the single-level wheel coordinate system of the first-level wheel as the assembly coordinate system, and sequentially transforms the mass deviation characteristics (centroid offset vector) of subsequent wheel levels after step S4. and the tilt vector of the principal axis of inertia The stop assembly deviation parameters (rotation transformation matrix) determined in step S2 and vectors as translation vectors The coordinate transformation matrix constructed in step S4 and the coordinate transformation matrix The mass deviation characteristics of each stage of the rotor assembly are then transferred to the assembly coordinate system and transformed to obtain the mass deviation characteristics of each stage of the rotor assembly in the coordinate system connecting the beginning and end. Based on the mass and moment of inertia of each stage of the rotor assembly, and based on the principles of vector superposition and torque balance, the unbalance quantity and unbalance phase of the rotor assembly on the two correction planes are calculated, serving as the initial unbalance prediction results for the multi-stage rotor assembly.

[0084] Specifically, such as Figure 8 As shown, the error propagation process is illustrated using a two-stage wheel stack as an example. During the stacking assembly process, the first-stage wheel remains stationary by default, and the single-stage wheel coordinate system established at its lower stop is used as the assembly coordinate system. Align the calibration screw holes of the second-stage wheel with those of the first-stage wheel, and define the assembly phase of the second-stage wheel as zero at this point.

[0085] for The stacked wheel is in the assembly system coordinate system, the first... centroid offset vector of the roulette wheel ( This can be represented as:

[0086]

[0087] in, and In the assembly system coordinate system, the first... The centroid offset vectors of the upper and lower stops of the first-stage wheel assembly, the first The lower stop of the first stage wheel is relative to the centroid of the first stage wheel. The centroid offset vector of the stop on the first-stage wheel and the first The offset vector of the centroid of the stage wheel relative to the centroid of its lower stop; Stop assembly eccentricity vector (i.e. From the first The rotation transformation matrix for transforming the fitting plane coordinate system of the upper stop of the stage wheel to the assembly coordinate system. For the first The centroid offset vector of the upper and lower stops of the stage wheel (i.e., The rotation transformation matrix from the single-stage wheel reference coordinate system to the assembly coordinate system. The rotation matrix, which takes into account the phase change during assembly, is calculated by the following formula:

[0088]

[0089] in, For the first The first roulette wheel relative to the second The circumferential mounting phase of the stage wheel (counterclockwise is positive).

[0090] Similarly, the first The inertial principal axis tilt vector of the roulette wheel It can be represented as:

[0091]

[0092] After obtaining the centroid offset vector and principal axis tilt vector of each wheel in the assembly system coordinate system, it is necessary to transform them to the coordinate system of the rotor assembly's beginning and end lines. Let the first... The coordinate vector of the centroid of the upper stop of the stage wheel in the assembly system coordinate system is: Taking the center of the lower stop of the component as the origin, and connecting the centers of the first and last ends... for Establish a coordinate system connecting the beginning and end of the rotor assembly along the axial direction. The transformation matrix from the assembly system coordinate system to this coordinate system is:

[0093]

[0094] In the coordinate system connecting the beginning and end of the rotor assembly, the first... centroid offset vector of the roulette wheel and the tilt vector of the principal axis of inertia They are respectively:

[0095]

[0096] In the formula, , and They are respectively In the coordinate system connecting the beginning and end of the rotor assembly , and Components in direction, , and They are respectively In the coordinate system connecting the beginning and end of the rotor assembly , and Components in direction.

[0097] Then, based on the quality of each level of roulette wheel... Diameter Moment of Inertia Polar moment of inertia Calculate the first The static unbalance vector of the cyclone Moment imbalance vector :

[0098]

[0099] In the formula, and They are respectively In the coordinate system connecting the beginning and end of the rotor assembly and Components in direction, and They are respectively In the coordinate system connecting the beginning and end of the rotor assembly and Components in direction.

[0100] Finally, based on the vector superposition method and the torque balance principle, the unknown unbalance vectors on the two correction planes are listed. and The torque balance equations:

[0101]

[0102] In the formula, , , Let $\mathbf{ ... and Finally, the unbalance vector in the Cartesian coordinate system is transformed into the unbalance quantity and unbalance phase in the polar coordinate system, which is the initial unbalance prediction result of the multi-stage rotor assembly.

[0103] As described above, this invention quantifies the assembly deviation of the stop by establishing a temperature difference assembly simulation model, eliminates the measurement error caused by tooling clearance through two measurement compensations, unifies the quality and geometric characteristics through coordinate transformation, and solves the initial imbalance of the rotor assembly through step-by-step error propagation and torque balance. This can effectively improve the prediction accuracy and meet the requirements of high-reliability assembly of aero-engine rotors.

[0104] In this embodiment, the cross-sectional view of the three-dimensional model of the assembled rotor assembly is as follows: Figure 9As shown, an assembly coordinate system is established at the lower stop of the 5&6 level discs, and assembly is carried out from bottom to top. The 5&6 level discs and the 4 level discs are connected by 40 evenly distributed bolts.

[0105] First, the runout and imbalance data of the 4th-level disk and the 5th & 6th-level disks were measured. The 4th-level disk underwent single-calibration plane balancing measurement, while the 5th & 6th-level disks underwent double-calibration plane balancing measurement. The centroid offset vectors of the two-level disks and the inertial principal axis tilt vectors of the 5th & 6th-level disks were obtained and are listed in Table 1.

[0106] Table 1 Quality characteristics of wheel parts and assemblies

[0107]

[0108] Then, the wheel is assembled by heat fitting, pre-pressing, and applying torque. The assembly deviation results of the stop at 0° and 108° are obtained by simulation calculation (including the stop assembly skew angle, skew phase, eccentricity, and eccentric phase). The results are shown in Table 2.

[0109] Table 2. Assembly deviation results of the stop at the 0° and 108° installation phases.

[0110]

[0111] Using these data as input, the unbalance of the rotor assembly is predicted according to the model proposed in this invention, and the prediction results are compared with those of the traditional two-mass prediction model and the measured results. The comparison results are shown in Table 3.

[0112] Table 3 Comparison of Predicted and Measured Results of Component Imbalance

[0113]

[0114] Comparative results show that the prediction method proposed in this invention has higher accuracy in predicting imbalance compared to traditional prediction methods, with a prediction error generally within 15%, and the predicted imbalance phase is closer to the measured results. This fully verifies the accuracy and superiority of the method proposed in this invention.

[0115] Finally, it should be noted that the features mentioned and / or shown in the above description of exemplary embodiments of the present invention can be combined in the same or similar manner with one or more other embodiments, combined with or substituted for corresponding features in other embodiments. These combined or substituted technical solutions should also be considered to be included within the scope of protection of the present invention.

Claims

1. A method for predicting initial rotor imbalance considering assembly deviation and measurement error, characterized in that, Includes the following steps: Step 1: Establish a finite element simulation model of the temperature difference assembly process of the stop. Using the surface morphology data of the stop mating and the assembly process parameters as input, perform contact simulation calculations and extract the normal vector of the lower stop end face of the upper wheel disk used to characterize the skewing of the stop assembly and the centroid coordinate vector of the lower stop cylinder surface of the upper wheel disk used to characterize the eccentricity of the stop assembly. Step 2: Based on the end face normal vector and cylindrical centroid coordinate vector extracted in Step 1, determine the stop assembly deviation parameters between the two-stage wheel disks. The stop assembly deviation parameters include the rotation transformation matrix from the upper wheel disk coordinate system to the lower wheel disk upper stop fitting plane coordinate system, and the translation vector of the lower stop centroid of the upper wheel disk relative to the upper stop centroid of the lower wheel disk. Step 3: Perform unbalance measurement on the single-stage wheel to obtain its own mass deviation characteristics. This includes: taking two measurements with the wheel and balancing fixture in the initial assembly state and the assembly state after a 180-degree relative rotation in the circumferential direction, respectively. During each measurement, obtain the cylindrical runout data of the wheel stop and the overall unbalance data measured by the dynamic balancing machine. Based on the data from the two measurements, solve for the measurement error caused by the tooling assembly gap to obtain the centroid offset vector and the inertial principal axis tilt vector relative to the coordinate system of the wheel's head and tail. Step 4: Measure the runout data of the mating surface of the single-stage wheel, determine the geometric deviation parameters of the single-stage wheel, and based on the geometric deviation parameters, construct a coordinate transformation matrix from the upper stop fitting plane coordinate system of the wheel to its single-stage wheel coordinate system; through coordinate transformation, transform the mass deviation characteristics obtained in Step 3 from the end-to-end line coordinate system to the single-stage wheel coordinate system to obtain the transformed mass deviation characteristics. Step 5: Using the single-stage disk coordinate system of the first-stage disk as the assembly coordinate system, the mass deviation characteristics of subsequent disks after transformation in Step 4 are sequentially transferred to the assembly coordinate system through the stop assembly deviation parameters determined in Step 2 and the coordinate transformation matrix constructed in Step 4. Then, the mass deviation characteristics of each disk in the first-to-last line coordinate system are obtained through coordinate transformation. Based on the mass and moment of inertia of each disk, and based on the principles of vector superposition and torque balance, the unbalance quantity and unbalance phase of the rotor assembly on the two correction planes are solved, which serve as the initial unbalance prediction results of the multi-stage rotor assembly.

2. The rotor initial imbalance prediction method according to claim 1, characterized in that, In step 1, the temperature difference assembly process of the stop includes four processes: heating and expanding the concave stop or cooling and contracting the convex stop, contact of the pre-compression end face during assembly, contact of the cylindrical surface during temperature recovery, and contact of the bolt tightening end face.

3. The rotor initial imbalance prediction method according to claim 1, characterized in that, In step 1, the finite element simulation model is automatically parametrically simulated by Matlab and Ansys. Matlab is used to construct the three-dimensional geometric model of the concave and convex stop containing the morphological data of the mating surface and to generate the node and mesh data of the finite element model. Ansys is used to call the data file to perform contact deformation analysis and to achieve parametric updates through the APDL command stream.

4. The rotor initial imbalance prediction method according to claim 1, characterized in that, In step 1, the end face normal vector is obtained by fitting the end face displacement data of the lower stop of the upper wheel, and the cylindrical centroid coordinate vector is obtained by fitting the cylindrical displacement data of the lower stop of the upper wheel. Then, the stop assembly skew angle, stop assembly skew phase, stop assembly eccentricity and stop assembly eccentricity phase are calculated.

5. The rotor initial imbalance prediction method according to claim 1, characterized in that, In step 2, the rotation transformation matrix is ​​determined by coordinate rotation transformation based on the end face normal vector. Specifically, the end face normal vector is used as the fitting plane coordinate system of the upper stop of the lower-level wheel. In the axial direction, calculate the revolution around the axis based on the components of the normal vector of the end face. shaft and The rotation angle of the axis is used to construct a rotation matrix, which is then inverted to obtain the rotation transformation matrix from the upper wheel coordinate system to the lower wheel upper stop fitting plane coordinate system; the translation vector adopts the cylindrical centroid coordinate vector, and its axial component is ignored.

6. The rotor initial imbalance prediction method according to claim 1, characterized in that, In step 3, the thin and thick disks are distinguished according to the length-to-diameter ratio of the disk. When the length-to-diameter ratio is greater than 0.2, it is a thick disk. The double-calibration surface balance measurement and the corresponding equation set are used to eliminate the measurement error caused by the tooling assembly gap. Otherwise, it is a thin disk. The single-calibration surface balance measurement and the corresponding equation set are used to eliminate the measurement error caused by the tooling assembly gap.

7. The rotor initial imbalance prediction method according to claim 1, characterized in that, In step 4, the geometric deviation parameters include the centroid offset vector and the end face tilt normal vector.

8. The rotor initial imbalance prediction method according to claim 1, characterized in that, In step 4, the coordinate transformation matrix is ​​determined as follows: a single-level wheel coordinate system is established with the lower stop centroid as the origin, and an upper stop fitting plane coordinate system is established with the upper stop fitting centroid as the origin. The centroid coordinate vector of the upper stop in the single-level wheel coordinate system is obtained by measurement. and end face normal vector The coordinate transformation matrix from the fitted plane coordinate system at the upper stop to the single-stage wheel coordinate system is determined by the end face normal vector. Calculate the winding based on its components. shaft and The rotation angle of the axis is obtained by constructing the rotation matrix and then taking its inverse. The transformation matrix used to convert the quality deviation characteristics obtained in step 3 from the head-to-tail coordinate system to the single-level wheel coordinate system is composed of the centroid coordinate vector. Calculate the winding based on its components. shaft and The rotation angle of the axis is obtained by constructing a rotation matrix and then taking its inverse.

9. The rotor initial imbalance prediction method according to any one of claims 1 to 8, characterized in that, In step 5, the step-by-step transfer is achieved in the following way: the mass deviation characteristics of each wheel are transformed from the single-stage wheel coordinate system to the assembly coordinate system, and then to the coordinate system of the beginning and end of the rotor assembly. The static unbalance vector and moment unbalance vector of each wheel are calculated respectively. Then, according to the principle of vector superposition and torque balance, the unbalance vector of the rotor assembly on the two correction planes is obtained. Finally, it is transformed into the unbalance quantity and unbalance phase in the polar coordinate system.

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