An Unbalance Prediction Method for Large Rotary Equipment with Clearance Fit

Abstract

The present invention belongs to the technical field of engine assembly, and discloses an unbalance prediction method for a large rotary equipment with clearance fit. Step 1: Establish a pose matrix equation of the rotor; Step 2: Decompose the unbalance of each stage of the rotor onto two unbalance correction planes A and B based on the pose matrix equation in Step 1; Step 3: Further synthesize the unbalances on the two correction planes A and B based on Step 2 to obtain the initial unbalance after rotor assembly; Step 4: Rotate the rotors except the first layer to achieve the optimal local unbalance after assembly with the first-stage rotor. It is used to solve the problem of how to predict the unbalance of a large rotary equipment with clearance fit.

Description

Technical Field

[0001] The present invention belongs to the technical field of engine assembly; specifically, it relates to a method for predicting the unbalance of a large rotary equipment with clearance fit. Background Art

[0002] The measurement and assembly accuracy of an engine directly determine the reliability, stability, and comprehensive performance of the whole machine. The faults of an engine mainly stem from vibration and rubbing, and the occurrence of vibration and rubbing is mainly caused by factors such as misalignment of components at all levels and out-of-tolerance unbalance after assembly. Taking the F119 turbofan aeroengine equipped on the US Air Force's fifth-generation fighter F22 as an example, the core engine is the most complex core unit in engine assembly, and its assembly accuracy has a crucial impact on the performance and life of the engine. It is reported that within two years of the US Air Force, the cracks in the turbine seal rings of aeroengines caused by rubbing led to the crash of 4 F16 fighter jets, forcing 339 aeroengines to be grounded directly or indirectly.

[0003] The turbine of an aerospace power engine has the characteristics of a small structure and a large number of rotor stages. Dozens of rotor parts need to be installed on an axis less than one meter long. At the same time, multiple rotors have a clearance fit. The errors of each stage of rotors in a large rotary equipment will accumulate and be amplified rapidly during the installation process of the large rotary equipment. In addition, its installation randomness will also seriously affect the performance of the engine. As Figure 1 shown, the rotor of some models of engines is composed of more than thirty rotors stacked with clearance fit. It is most ideal when the axis of rotation of each component coincides with the axis of the entire engine during assembly. The turbine part of an aerospace power engine can reach 40,000 r / min during operation. The coaxiality error caused by misalignment of rotor assembly at ultra-high speeds will cause the vibration to be amplified by 100 to 1000 times during high-speed operation, significantly intensifying the friction between rotors. When the misalignment of a large rotary equipment during assembly is serious, blade rubbing, fracture, and even spacecraft crash and explosion will occur, causing irreparable major losses. Therefore, for a large rotary equipment with clearance fit, it is extremely important to predict its unbalance (to prevent subsequent problems) and then guide the assembly. Summary of the Invention

[0004] The present invention provides a method for predicting the unbalance of a large rotary equipment with clearance fit to solve the problem of how to predict the unbalance of a large rotary equipment with clearance fit.

[0005] The present invention is realized through the following technical solutions:

[0006] A method for predicting the unbalance of a large rotary equipment with clearance fit, the unbalance prediction method includes the following steps:

[0007] Step 1: Establish a pose matrix equation of the rotor;

[0008] Step 2: Decompose the unbalance of each stage of the rotor into two unbalance correction planes A and B based on the pose matrix equation in Step 1;

[0009] Step 3: Based on Step 2, synthesize the unbalances on the two correction planes A and B to obtain the initial unbalance after rotor assembly;

[0010] Step 4: Rotate the rotors except the first layer to achieve the optimal local unbalance after assembly with the first-stage rotor.

[0011] A method for predicting the unbalance of a large rotary equipment with clearance fit, characterized in that the specific process of establishing the pose matrix equation of the rotor in Step 1 is as follows: the pose matrix equation of the nth-stage rotor is as follows:

[0012]

[0013] where T c is the transformation matrix of the centroid of the nth-stage rotor, T ri is the transformation matrix between the joint surfaces of two-stage rotors, T zi is the eccentricity of the ideal center of the rotor i, T cli is the translation transformation matrix of the eccentricity of the reference plane clearance of the rotor i, T dzi is the eccentric translation transformation matrix caused by the machining error of the reference plane of the rotor i, T ori is the rotation transformation matrix from the reference plane of the rotor i to the rotation center of the assembly surface; S xi is the rotation matrix of the reference plane of the ith-stage rotor rotating θ xi angle around the X axis; S yi is the rotation matrix of the reference plane of the ith-stage rotor rotating θ yi angle around the Y axis, S ri is the rotation matrix of the ith-stage rotor rotating θ ri angle around the Z axis, S n c is the rotation matrix of the centroid of the nth-stage rotor; p i is the ideal position vector of the center of the radial measurement plane of the ith-stage rotor; dp i is the machining error vector of the position of the center of the radial measurement plane of the ith-stage rotor; dp′ i is the eccentric position vector caused by the clearance. In addition, the translation matrix of the centroid of the nth-stage rotor is dp n c .

[0014] A method for predicting the unbalance of a large rotary equipment with clearance fit. The pose matrix equation of the rotor is obtained from the rotor unbalance. Since the rotor unbalance is the product of the unbalanced mass and the distance of its centroid from the axis, it is necessary to first calculate the eccentric position of the rotor centroid. The specific eccentric position of the rotor centroid is as follows:

[0015]

[0016] Furthermore, after the assembly of the nth-stage rotor, the unbalance u of the nth-stage rotor is obtained n :

[0017]

[0018] In the formula, m n represents the mass of the nth-stage rotor;

[0019] dx 0-n c represents the cumulative centroid offset of the nth-stage rotor along the X-axis direction;

[0020] dy 0-n c represents the cumulative centroid offset of the nth-stage rotor along the Y-axis direction.

[0021] A method for predicting the unbalance of a large rotary equipment with clearance fit, characterized in that the nth-stage rotor is composed of multiple single-stage rotors, and the projection method of the unbalance of the single-stage rotor shape, that is, when the rotor itself is flat, its unbalance can be projected onto a single cross-section for characterization; when the rotor itself is cylindrical, its unbalance should be projected onto two cross-sections for characterization;

[0022] When the rotor itself is flat, the cumulative centroid eccentricity transfer matrix T of the single-stage rotor 0-1 c :

[0023]

[0024] In the formula, T i r represents the assembly phase matrix of the ith-stage rotor;

[0025] T i c represents the centroid eccentricity transfer matrix of the ith-stage rotor;

[0026] The assembly phase matrix T i r and the centroid eccentricity transfer matrix T i c The mathematical expressions are respectively:

[0027]

[0028]

[0029] In the formula, dR i r represents the 3×3 rotation transformation matrix of the center of the ith-stage rotor;

[0030] dR i c The 3×3 rotation transformation matrix representing the centroid of the i-th stage rotor

[0031] Dp i c The 3×1 position vector representing the centroid of the i-th stage rotor

[0032] When the rotor itself is cylindrical, the centroid cumulative eccentricity transfer matrix T of a single-stage rotor 0-1g c :

[0033]

[0034] Where T ig c Represents the centroid eccentricity transfer matrix of the j-th section of the i-th stage rotor; T ig c The mathematical expression is:

[0035]

[0036] Where dR ig c Represents the 3×3 rotation transformation matrix of the centroid of the i-th stage rotor at the g-th section;

[0037] dp ig c Represents the 3×1 position vector of the centroid of the i-th stage rotor at the g-th section.

[0038] An unbalance prediction method for a large rotary equipment with clearance fit. Substituting equations (2), (3) and (7) into equation (6), then:

[0039]

[0040] Where dR1 r Represents the identity matrix;

[0041] The rotation transformation matrix dR of the assembly phase of the i-th stage rotor i r The mathematical expression is:

[0042]

[0043] Where θ ri Represents the assembly phase of the i-th stage;

[0044] The center transformation matrix dR of the i-th stage rotor i o And the centroid transformation matrix dR i c Are shown in equations (10) and (11) respectively:

[0045]

[0046]

[0047] where θ ti represents the inclination angle of the fitting plane of the i-th stage rotor assembly surface relative to the horizontal plane;

[0048] θ li represents the angle between the direction from the center of the i-th stage rotor assembly surface to the lowest sampling point and the X-axis;

[0049] θ xi represents the angle of rotation of the i-th stage rotor centroid coordinate system relative to the reference coordinate system about the X-axis;

[0050] θ yi represents the angle of rotation of the i-th stage rotor centroid coordinate system relative to the reference coordinate system about the Y-axis;

[0051] θ zi represents the angle of rotation of the i-th stage rotor centroid coordinate system relative to the reference coordinate system about the Z-axis.

[0052] An unbalance prediction method for a large rotary equipment with clearance fit, characterized by including a center eccentricity translation transformation vector dp i o and a mass eccentricity translation transformation vector dp i c as shown in equations (12) and (13) respectively:

[0053]

[0054]

[0055] where dx i o represents the center offset of the i-th stage rotor along the X-axis;

[0056] dy i o represents the center offset of the i-th stage rotor along the Y-axis;

[0057] dz i o represents the center offset of the i-th stage rotor along the Z-axis;

[0058] dx i c represents the centroid offset of the i-th stage rotor along the X-axis;

[0059] dy i cRepresents the centroid offset of the i-th stage rotor in the Y-axis direction;

[0060] dz i c Represents the centroid offset of the i-th stage rotor in the Z-axis direction;

[0061] z i o Represents the ideal position of the center of the i-th stage rotor in the Z-axis direction;

[0062] z i c Represents the ideal position of the centroid of the i-th stage rotor in the Z-axis direction;

[0063] According to equations (8)-(13), the centroid offset after rotor assembly is obtained, and then the unbalance u2 of the second-stage rotor after assembly is obtained:

[0064]

[0065] In the formula, dx 0-2 c Represents the cumulative centroid offset of the second-stage rotor in the X-axis direction;

[0066] dy 0-2 c Represents the cumulative centroid offset of the second-stage rotor in the Y-axis direction.

[0067] An unbalance prediction method for a large rotary equipment with clearance fit, characterized by obtaining the centroid eccentricity transfer relationship of the k-th stage rotor after assembly of the n-stage rotor according to the derivation of the unbalance formula for the second-stage rotor assembly:

[0068]

[0069] Substitute equations (2), (3) and (7) into equation (15), then:

[0070]

[0071] According to equations (9)-(13) and equation (16), the cumulative centroid offset of the rotor can be obtained, and then the unbalance u of the k-th stage rotor after assembly of the n-stage rotor can be obtained k :

[0072]

[0073] In the formula, dx 0-k c Represents the cumulative centroid offset of the k-th stage rotor in the X-axis direction;

[0074] dy 0-k crepresents the cumulative offset of the centroid of the k-th stage rotor in the Y-axis direction;

[0075] According to Equation (17), the calculation of the unbalance of any stage rotor after the assembly of multi-stage rotors under a single projection section can be realized.

[0076] An unbalance prediction method for a large rotary equipment with clearance fit, characterized in that when the n-stage rotors are assembled and the unbalance of the k-th stage rotor needs to be characterized by projecting onto two sections, the centroid eccentricity transfer relationship of the i-th projection section is obtained as:

[0077]

[0078] Translation transformation vector dp kg c The mathematical expression is:

[0079]

[0080] In the formula, dx kg c represents the offset of the centroid of the k-th stage rotor on the g-th section in the X-axis direction;

[0081] dy kg c represents the offset of the centroid of the k-th stage rotor on the g-th section in the Y-axis direction;

[0082] dz kg c represents the offset of the centroid of the k-th stage rotor on the g-th section in the Z-axis direction;

[0083] z kg c represents the ideal position of the centroid of the k-th stage rotor on the g-th section in the Z-axis direction;

[0084] According to Equations (9)-(12), (18) and (19), the cumulative offset of the rotor centroid is obtained, and then the unbalance u of the k-th stage rotor on the g-th section after the assembly of the n-stage rotors is obtained kg :

[0085]

[0086] In the formula, dx 0-kg c represents the cumulative offset of the centroid of the k-th stage rotor on the g-th section in the X-axis direction;

[0087] dy 0-kg c represents the cumulative offset of the centroid of the k-th stage rotor on the g-th section in the Y-axis direction;

[0088] The calculation of the unbalance of any stage of the rotor after the assembly of the multi-stage rotor under the two projection sections can be realized by Equation (20).

[0089] An unbalance prediction method for a large rotary equipment with clearance fit, characterized in that the specific step 3 is to obtain the initial unbalance u after the assembly of the n-stage rotor:

[0090] u(θ rk ) = max{u A , u B}, k = 1, 2,..., n (23)

[0091] In the formula, u A represents the modulus of the combined unbalance of the correction plane A;

[0092] u B represents the modulus of the combined unbalance of the correction plane B.

[0093] The beneficial effects of the present invention are:

[0094] The present invention effectively adjusts the overall unbalance after the assembly of the large rotary equipment by rotating each stage of the rotor and changing the assembly phase of the rotor, so as to ensure the clearance fit and the assembly quality of the large rotary equipment of the aero-engine.

[0095] The present invention first installs the multi-stage clearance rotors with the central axis as the reference, and predicts the unbalance of the assembled rotor engine during the whole process, so as to minimize the overall unbalance of the rotor through phase adjustment, thus ensuring the assembly accuracy of the engine.

[0096] The present invention aims at the unbalance prediction model of the large rotary equipment with clearance fit to guide the precise assembly of the engine. Description of the Drawings

[0097] Att Figure 1 is a schematic diagram of the clearance fit of the engine rotor of the present invention.

[0098] Att Figure 2 is a diagram of the centroid eccentricity adjustment of the three-stage rotor assembly of the present invention. Among them, Figure (a) is the three-stage rotor, Figure (b) is the rotor without rotation, Figure (c) is the second-stage rotor rotated, and Figure (d) is the third-stage rotor rotated.

[0099] Att Figure 3 is a diagram of the relationship between the shape of the single-stage rotor and the unbalance projection section of the present invention. Among them, Figure 3 -(a) is a diagram of the relationship between the unbalance projection method of the flat rotor, Figure 3 -(b) is a diagram of the relationship between the unbalance projection method of the cylindrical rotor.

[0100] Att Figure 4It is the diagram of the imbalance transfer model of the two-stage rotor assembly of the present invention.

[0101] Appendix Figure 5 It is the simulation diagram of the imbalance of the second-stage rotor under different rotor tilt errors of the present invention.

[0102] Appendix Figure 6 It is the simulation diagram of the imbalance of the second-stage rotor under different rotor eccentricity errors of the present invention.

[0103] Appendix Figure 7 It is the diagram of the relationship between the initial imbalance of the two-stage rotor and the assembly angle of the present invention.

[0104] Appendix Figure 8 It is the diagram of the relationship between the initial imbalance of the three-stage rotor and the assembly angle of the present invention.

[0105] Appendix Figure 9 It is the vertical balancing machine for measuring the rotor imbalance of the present invention.

[0106] Appendix Figure 10 It is the horizontal balancing machine for measuring the imbalance of multi-stage rotors of the present invention. Detailed implementation manners

[0107] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0108] The rotor imbalance is the product of the unbalanced mass and the distance between its centroid and the axis of rotation. During the assembly process of multi-stage rotors, the imbalance of each stage of the rotor is not only related to the eccentricity of its own centroid, but also related to the geometric processing errors of the previous stages of rotors during the assembly process. The geometric processing errors of each stage of the rotor are accumulated and transferred through the connecting contact surfaces during the assembly process, affecting the centroid position of each stage of the rotor after assembly, and further affecting the overall initial imbalance of the rotor after assembly. In the actual assembly process, by rotating each stage of the rotor and changing the assembly phase of the rotor, the overall imbalance of the multi-stage rotor after assembly can be effectively adjusted. The assembly schematic diagram of the three-stage rotor is as Figure 2 shown.

[0109] As Figure 2 shown, C1, C2, and C3 are the centroids of the first, second, and third stage rotors respectively. By rotating the second and third stage rotors, the eccentricity between the centroids of the second and third stage rotors and the axis of rotation can be effectively reduced, thereby reducing the initial imbalance of the three-stage rotor after assembly.

[0110] An unbalance prediction method for a large rotary equipment with clearance fit. The unbalance prediction method includes the following steps:

[0111] Step 1: Establish the pose matrix equation of the rotor;

[0112] Step 2: Decompose the unbalance of each stage of the rotor into two unbalance correction planes A and B based on the pose matrix equation in Step 1;

[0113] Step 3: Based on Step 2, synthesize the unbalances on the two correction planes A and B to obtain the initial unbalance after rotor assembly;

[0114] Step 4: Rotate the second-stage rotor to change the initial unbalance in Step 3, so that the local unbalance is optimal after the second-stage rotor and the first-stage rotor are assembled;

[0115] It can be analyzed that: by rotating the second-stage rotor, the initial unbalance of the first two stages of the rotor can be changed, and the local unbalance is optimal after multi-stage rotor assembly. When the assembly phase of the second-stage rotor is 177°, the overall unbalance of the first two stages of the rotor reaches the minimum of 316 g·mm, which is the optimal assembly phase; when the assembly phase of the second-stage rotor is 357°, the unbalance of the first two stages of the rotor reaches the maximum of 457 g·mm, which is the worst assembly phase. Compared with the optimal and the worst, the unbalance is optimized by 31%. Figure 7 Analysis shows that: by rotating the second-stage rotor, the initial unbalance of the first two stages of the rotor can be changed, and the local unbalance is optimal after multi-stage rotor assembly. When the assembly phase of the second-stage rotor is 177°, the overall unbalance of the first two stages of the rotor reaches the minimum of 316 g·mm, which is the optimal assembly phase; when the assembly phase of the second-stage rotor is 357°, the unbalance of the first two stages of the rotor reaches the maximum of 457 g·mm, which is the worst assembly phase. Compared with the optimal and the worst, the unbalance is optimized by 31%.

[0116] Step 5: Rotate the second-stage rotor and the third-stage rotor to change the initial unbalance of the three rotors, so that the local unbalance is optimal after the third-stage rotor is assembled with the first-stage rotor and the second-stage rotor.

[0117] It can be analyzed that Figure 8 Analysis shows that the initial unbalance after the third-stage rotor is assembled is related to the rotation angles of the second and third-stage rotors. By rotating the second and third-stage rotors, the initial unbalance of the three rotors can be changed. When the assembly phase of the second-stage rotor is 180° and the assembly phase of the third-stage rotor is 352°, the initial unbalance reaches the minimum of 292 g·mm, which is the optimal assembly phase; when the assembly phase of the second-stage rotor is 355° and the assembly phase of the third-stage rotor is 349°, the initial unbalance reaches the maximum of 1831 g·mm, which is the worst assembly phase. Compared with the optimal and the worst, the unbalance is optimized by 84%.

[0118] An unbalance prediction method for a large rotary equipment with clearance fit, characterized in that, in Step 1, establishing the pose matrix equation of the rotor specifically is that the pose matrix equation of the nth-stage rotor is as follows:

[0119]

[0120] where T c is the transformation matrix of the centroid of the nth-stage rotor, Tri is the transformation matrix between the mating surfaces of the two-stage rotor, T zi is the eccentricity of the ideal center of the rotor i, T cli is the translation transformation matrix of the eccentricity of the reference plane clearance of the rotor i, T dzi is the eccentricity translation transformation matrix caused by the machining error of the reference plane of the rotor i, T ori is the rotation transformation matrix from the reference plane of the rotor i to the center of rotation of the assembly surface; S xi is the rotation matrix of the reference plane of the i-th stage rotor rotating by θ around the X-axis xi angle; S yi is the rotation matrix of the reference plane of the i-th stage rotor rotating by θ around the Y-axis yi angle, S ri is the rotation matrix of the i-th stage rotor rotating by θ around the Z-axis ri angle, S n c is the rotation matrix of the centroid of the n-th stage rotor; p i is the ideal position vector of the center of the radial measurement plane of the i-th stage rotor; dp i is the machining error vector of the position of the center of the radial measurement plane of the i-th stage rotor; dp′ i is the eccentricity position vector caused by the clearance. In addition, the translation matrix of the centroid of the n-th stage rotor is dp n c .

[0121] An unbalance prediction method for a large rotary equipment with clearance fit. The pose matrix equation of the rotor is obtained from the rotor unbalance. Since the rotor unbalance is the product of the unbalanced mass and the distance from its centroid to the axis, it is necessary to calculate the eccentric position of the rotor centroid first. The eccentric position of the rotor centroid is specifically

[0122]

[0123] Furthermore, after the assembly of the n-stage rotor, the unbalance u of the n-th stage rotor is obtained n :

[0124]

[0125] where m n represents the mass of the rotor n;

[0126] dx 0-n c represents the cumulative offset of the centroid of the n-th stage rotor in the X-axis direction;

[0127] dy 0-n c represents the cumulative offset of the centroid of the n-th stage rotor in the Y-axis direction.

[0128] An unbalance prediction method for a large rotary equipment with clearance fit, characterized in that single-stage rotors of aero-engines are all rotary parts. According to the ratio of diameter d to height h, they can be divided into two types: flat (d / h≥5) and cylindrical (d / h<5). As Figure 3 shown, the n-stage rotor is composed of multiple single-stage rotors. The projection method of the unbalance of the single-stage rotor shape, that is, when the rotor itself is flat, its unbalance can be projected onto a single cross-section for characterization; when the rotor itself is cylindrical, its unbalance should be projected onto two cross-sections for characterization;

[0129] When the rotor itself is flat, the centroid cumulative eccentricity transfer matrix T of the single-stage rotor 0-1 c :

[0130]

[0131] where T i r represents the assembly phase matrix of the i-th stage rotor;

[0132] T i c represents the centroid eccentricity transfer matrix of the i-th stage rotor;

[0133] The assembly phase matrix T i r and the centroid eccentricity transfer matrix T i c The mathematical expressions are respectively:

[0134]

[0135]

[0136] where dR i r represents the 3×3 rotation transformation matrix of the center of the i-th stage rotor;

[0137] dR i c represents the 3×3 rotation transformation matrix of the centroid of the i-th stage rotor;

[0138] Dp i c represents the 3×1 position vector of the centroid of the i-th stage rotor;

[0139] When the rotor itself is cylindrical, the centroid cumulative eccentricity transfer matrix T of the single-stage rotor 0-1g c :

[0140]

[0141] Where T ig c represents the centroid eccentricity transfer matrix of the j-th section of the i-th stage rotor; T ig c The mathematical expression is:

[0142]

[0143] Where dR ig c represents the 3×3 rotation transformation matrix of the centroid of the i-th stage rotor at the g-th section;

[0144] dp ig c represents the 3×1 position vector of the centroid of the i-th stage rotor at the g-th section.

[0145] For an unbalance prediction method of a large rotary equipment with clearance fit, substituting equations (2), (3) and (7) into equation (6), then:

[0146]

[0147] Where dR1 r represents the identity matrix;

[0148] The rotation transformation matrix dR of the assembly phase of the i-th stage rotor i r The mathematical expression is:

[0149]

[0150] Where θ ri represents the assembly phase of the i-th stage;

[0151] The center transformation matrix dR of the i-th stage rotor i o and the centroid transformation matrix dR i c are shown in equations (10) and (11) respectively:

[0152]

[0153]

[0154] Where θ ti represents the inclination angle of the fitting plane of the assembly surface of the i-th stage rotor relative to the horizontal plane;

[0155] θ li represents the angle between the direction from the center of the assembly surface of the i-th stage rotor to the lowest sampling point and the X-axis;

[0156] θ xirepresents the rotation angle of the centroid coordinate system of the i-th stage rotor relative to the reference coordinate system about the X-axis;

[0157] θ yi represents the rotation angle of the centroid coordinate system of the i-th stage rotor relative to the reference coordinate system about the Y-axis;

[0158] θ zi represents the rotation angle of the centroid coordinate system of the i-th stage rotor relative to the reference coordinate system about the Z-axis.

[0159] An unbalance prediction method for a large rotary equipment with clearance fit, characterized by including the center eccentricity translation transformation vector dp i o and the mass eccentricity translation transformation vector dp i c are respectively shown in formulas (12) and (13):

[0160]

[0161]

[0162] In the formula, dx i o represents the center offset of the i-th stage rotor along the X-axis direction;

[0163] dy i o represents the center offset of the i-th stage rotor along the Y-axis direction;

[0164] dz i o represents the center offset of the i-th stage rotor along the Z-axis direction;

[0165] dx i c represents the centroid offset of the i-th stage rotor along the X-axis direction;

[0166] dy i c represents the centroid offset of the i-th stage rotor along the Y-axis direction;

[0167] dz i c represents the centroid offset of the i-th stage rotor along the Z-axis direction;

[0168] z i o represents the ideal position of the center of the i-th stage rotor in the Z-axis direction;

[0169] z i c represents the ideal position of the centroid of the i-th stage rotor in the Z-axis direction;

[0170] According to formulas (8)-(13), the centroid offset after rotor assembly is obtained, and then the unbalance u2 after the second-stage rotor assembly is obtained:

[0171]

[0172] In the formula, dx 0-2 c represents the cumulative centroid offset of the second-stage rotor in the X-axis direction;

[0173] dy 0-2 c represents the cumulative centroid offset of the second-stage rotor in the Y-axis direction.

[0174] To analyze in detail the influence of tilt error and eccentricity error on the unbalance after rotor assembly, formula (14) is simulated. Assume that the mass of each stage of the rotor is 2000 g, the diameter is 150 mm, and the centroid offsets dx i c 、dy i c 、dz i c are all l (l = 0.04 mm). The offsets dx i o 、dy i o 、dz i o of the centers of each stage of the rotor in the X, Y, and Z axis directions are all 0.06 mm. The tilt angles θ ti of the fitting plane of the two-stage rotor assembly relative to the horizontal plane are taken as 1′, 20′, 40′, and 60′ respectively. The unbalance of the second-stage rotor under different rotor tilt errors is as Figure 6 shown.

[0175] From Figure 5 the analysis, it can be obtained that when the tilt error of the two-stage rotor assembly surface is certain, by rotating the second-stage rotor, the unbalance of the second-stage rotor can be changed. When θ t1 is 60′ and s = 0.06 mm, and the assembly phase of the second-stage rotor is 298°, the unbalance of the second-stage rotor reaches the minimum of 309 g·mm; when the assembly phase of the second-stage rotor is 118°, the unbalance of the second-stage rotor reaches the maximum of 536 g·mm. Compared with the best and the worst, the unbalance is optimized by 42%.

[0176] At the same time, from Figure 5It can be concluded that when the rotor eccentricity error is constant, as the rotor tilt angle increases, for the second-stage rotor with different assembly phases, the optimal unbalance first decreases and then increases. The decrease is because when the tilt angle is small, the unbalance caused by the eccentricity error is large, and due to the vector cancellation characteristic, the unbalance decreases. The increase is because as the tilt angle increases, the unbalance caused by the tilt angle dominates, so as the tilt angle increases, the unbalance increases. When the tilt angles of the rotor are 1′, 20′, 40′, and 60′ respectively, the corresponding optimal unbalances of the second-stage rotor are: 50 g·mm, 18 g·mm, 146 g·mm, and 309 g·mm.

[0177] The unbalances of the second-stage rotor under different rotor eccentricity errors are as Figure 6 shown. Assume that the tilt angle θ ti of the fitting plane of the assembly surfaces of the two-stage rotors relative to the horizontal plane is 40′, and the offsets dx i o , dy i o , and dz i o of the centers of each stage of the rotor in the X, Y, and Z axis directions are all l, and l takes 0.02, 0.06, 0.10, and 0.14 mm respectively, and other parameters are the same as those in the simulation of the rotor tilt error.

[0178] From Figure 6 the analysis, it can be obtained that when the rotor eccentricity error is constant, as the tilt angle increases, for the second-stage rotor with different assembly phases, the optimal unbalance first decreases and then increases. The decrease is because the eccentricity error is small and the unbalance caused by the tilt angle is large, and due to the vector cancellation characteristic, the unbalance decreases. The increase is because as the eccentricity error increases, the unbalance caused by the offset error dominates, so as the offset error increases, the unbalance increases. When the rotor eccentricity errors l are 0.02, 0.06, 0.10, and 0.14 mm respectively, the optimal unbalances of the second-stage rotor are: 199 g·mm, 146 g·mm, 136 g·mm, and 175 g·mm.

[0179] Based on Figure 5 and Figure 6 the conclusions, when the unbalances of the rotor caused by the rotor tilt angle θ t and the center offsets dx i o , dy i o , and dz i o are in the same order of magnitude, there is a certain interaction relationship between them. By changing the rotor assembly phase and using the vector cancellation characteristic of the unbalance, the unbalance after rotor assembly can be effectively reduced.

[0180] An unbalance prediction method for a large rotary equipment with clearance fit, characterized by, according to the derivation of the unbalance formula for the second-stage rotor assembly, obtaining the centroid eccentricity transfer relationship of the k-th rotor after the assembly of the n-th rotor as:

[0181]

[0182] Substituting equations (2), (3) and (7) into equation (15), then:

[0183]

[0184] Based on equations (9)-(13) and equation (16), the cumulative offset of the rotor centroid can be obtained, and further, after the assembly of the n-th rotor, the unbalance u of the k-th rotor k :

[0185]

[0186] In the formula, dx 0-k c represents the cumulative offset of the centroid of the k-th rotor in the X-axis direction;

[0187] dy 0-k c represents the cumulative offset of the centroid of the k-th rotor in the Y-axis direction;

[0188] Based on equation (17), the calculation of the unbalance of any rotor after the assembly of multiple-stage rotors under a single projection section can be realized.

[0189] An unbalance prediction method for a large rotary equipment with clearance fit, characterized by, when after the assembly of the n-th rotor and the unbalance of the k-th rotor needs to be characterized by projecting onto two sections, obtaining the centroid eccentricity transfer relationship of the i-th projection section as:

[0190]

[0191] The mathematical expression of the translation transformation vector dp kg c is:

[0192]

[0193] In the formula, dx kg c represents the offset of the centroid of the k-th rotor in the X-axis direction on the g-th section;

[0194] dy kg c represents the offset of the centroid of the k-th rotor in the Y-axis direction on the g-th section;

[0195] dz kg c It represents the offset of the centroid of the k-th stage rotor in the Z-axis direction on the g-th section;

[0196] z kg c It represents the ideal position of the centroid of the k-th stage rotor in the Z-axis direction on the g-th section;

[0197] According to equations (9)-(12), (18) and (19), the cumulative offset of the rotor centroid is obtained, and then the unbalance u of the k-th stage rotor on the g-th section after the assembly of the n-stage rotor is obtained kg :

[0198]

[0199] In the formula, dx 0-kg c It represents the cumulative offset of the centroid of the k-th stage rotor in the X-axis direction on the g-th section;

[0200] dy 0-kg c It represents the cumulative offset of the centroid of the k-th stage rotor in the Y-axis direction on the g-th section;

[0201] The calculation of the unbalance of any stage rotor after the assembly of the multi-stage rotor under two projection sections can be realized from equation (20).

[0202] A method for predicting the unbalance of a large rotary equipment with clearance fit, characterized in that, specifically in step 3, the initial unbalance u after the assembly of the n-stage rotor is obtained:

[0203] u(θ rk ) = max{u A , u B}, k = 1, 2,..., n (23)

[0204] In the formula, u A represents the modulus of the combined unbalance of the correction plane A;

[0205] u B represents the modulus of the combined unbalance of the correction plane B.

[0206] For a detailed analysis of the relationship between the initial unbalance of the multi-stage rotor assembly and the assembly phase, a simulation analysis is carried out on formula (23). Then the simulation results of the initial unbalance of the two-stage rotor and the initial unbalance of the three-stage rotor are as Figure 7 , Figure 8 shown.

[0207] In the simulation, the offsets dx i o and dy io , dz i o are all 0.1 mm; the mass m i are all 2000 g, and the diameters are all 150 mm; the unbalance projections of the first and third-stage rotors are characterized on two cross-sections, and the centroid offsets dx 1i c , dy 1i c , dz 1i c , dx 3i c , dy 3i c , dz 3i c are all 0.05 mm; the centroid offsets dx2 c , dy2 c , dz2 c are all 0.05 mm.

[0208] An unbalance prediction method for a large rotary equipment with clearance fit, characterized in that, specifically for step 4, rotate the second-stage rotor to change the initial unbalance in step 3, so that the local unbalance is optimal after the second-stage rotor is assembled with the first-stage rotor;

[0209] Rotate the second-stage rotor and the third-stage rotor to change the initial unbalance of the three rotors, so that the local unbalance is optimal after the third-stage rotor is assembled with the first-stage rotor and the second-stage rotor.

Claims

1. An unbalance prediction method for a large rotary equipment with clearance fit, characterized in that, The unbalance prediction method includes the following steps: Step 1: Establish the pose matrix equation of the rotor; Step 2: Decompose the unbalance of each stage of the rotor into two unbalance correction planes A and B based on the pose matrix equation in Step 1; Step 3: Based on Step 2, synthesize the unbalances on the two correction planes A and B to obtain the initial unbalance after rotor assembly; Step 4: Rotate the rotors except the first layer to achieve the optimal local unbalance after assembly with the first-stage rotor; Specifically, for Step 1 to establish the pose matrix equation of the rotor, the pose matrix equation of the nth-stage rotor is as follows: where T c is the transformation matrix of the centroid of the nth - stage rotor, T ri is the transformation matrix between the mating surfaces of the two - stage rotor, T zi is the eccentricity of the ideal center of the circle of rotor i, T cli is the translation transformation matrix of the eccentricity of the clearance of the reference plane of rotor i, T dzi is the eccentricity translation transformation matrix caused by the machining error of the reference plane of rotor i, T ori is the rotation transformation matrix from the reference plane of rotor i to the rotation center of the assembly surface; S xi is the rotation matrix of the reference plane of the ith - stage rotor rotating by θ xi angle about the X - axis; S yi is the rotation matrix of the reference plane of the ith - stage rotor rotating by θ yi angle about the Y - axis; S ri is the rotation matrix of the ith - stage rotor rotating by θ ri angle about the Z - axis; S n c is the rotation matrix of the centroid of the nth - stage rotor; p i is the ideal position vector of the center of the radial measurement plane of the ith - stage rotor; dp i is the machining error vector of the position of the center of the radial measurement plane of the ith - stage rotor; dp′ i is the eccentricity position vector caused by the clearance. In addition, the translation matrix of the centroid of the nth - stage rotor is dp n c ; The pose matrix equation of the rotor is obtained from the rotor unbalance. Since the rotor unbalance is the product of the unbalance mass and the distance from its centroid to the axis of rotation, it is necessary to first calculate the eccentricity position of the rotor centroid. Specifically, the eccentricity position of the rotor centroid is Furthermore, after the assembly of the nth-stage rotor, the unbalance amount u of the nth-stage rotor is obtained n : where m n represents the mass of the rotor n; dx 0-n c represents the cumulative centroid offset of the nth-stage rotor in the X-axis direction; dy 0-n c represents the cumulative centroid offset of the nth-stage rotor in the Y-axis direction; Specifically, for Step 3, obtain the initial unbalance u after assembly of the nth-stage rotor: u(θ rk ) = max{u A , u B}, k = 1, 2, ..., n (23) where u A represents the magnitude of the combined unbalance of the correction plane A; u B represents the modulus of the combined unbalance amount of the calibration plane B; Specifically, for Step 4, rotate the second-stage rotor to change the initial unbalance in Step 3 to make the local unbalance optimal after assembly of the second-stage rotor and the first-stage rotor; Rotate the second-stage rotor and the third-stage rotor to change the initial unbalance of the three rotors to make the local unbalance optimal after assembly of the third-stage rotor, the first-stage rotor, and the second-stage rotor.

2. The unbalance prediction method according to claim 1, characterized in that it includes, The nth-stage rotor is composed of multiple single-stage rotors. The projection method of the unbalance of the single-stage rotor shape, that is, when the rotor itself is flat, its unbalance can be projected onto a single cross-section for characterization; when the rotor itself is cylindrical, its unbalance should be projected onto two cross-sections for characterization; When the rotor itself is flat, the centroid cumulative eccentricity transfer matrix T of the single-stage rotor 0-1 c : In the formula represents the assembly phase matrix of the i-th stage rotor; Denote the eccentricity transfer matrix of the centroid of the i-th stage rotor; Assembly phase matrix Centroid eccentricity transfer matrix The mathematical expressions are respectively as follows: where is a 3×3 rotation transformation matrix representing the center of the i-th stage rotor; A 3×3 rotation transformation matrix representing the centroid of the i-th stage rotor A 3×1 position vector representing the centroid of the rotor at the i-th level; When the rotor itself is cylindrical, the centroid cumulative eccentricity transfer matrix T of the single-stage rotor 0-1g c : where T ig c represents the centroid eccentricity transfer matrix of the j-th section of the i-th stage rotor; T ig c The mathematical expression is: where dR ig c represents the 3×3 rotation transformation matrix of the centroid of the i-th stage rotor at the g-th section; dp ig c It represents the 3×1 position vector of the centroid of the i-th stage rotor at the g-th section.

3. The unbalance amount prediction method according to claim 2, wherein, Substitute Equations (2), (3), and (7) into Equation (6), then: where dR1 r represents the identity matrix; The rotation transformation matrix of the assembly phase of the i-th stage rotor The mathematical expression is as follows: where θ ri represents the assembly phase of the i-th stage; The centroid transformation matrix of the i-th stage rotor and the centroid transformation matrix are shown in equations (10) and (11) respectively: where θ ti represents the inclination angle of the fitting plane of the rotor assembly surface at the i-th stage relative to the horizontal plane; θ li represents the included angle between the direction from the center of the assembly surface of the i-th stage rotor to the lowest sampling point and the X-axis; θ xi represents the angle of rotation of the centroid coordinate system of the i-th stage rotor relative to the reference coordinate system about the X-axis; θ yi represents the angle of rotation of the centroid coordinate system of the i-th stage rotor relative to the reference coordinate system about the Y-axis; θ zi represents the angle of rotation of the centroid coordinate system of the i-th stage rotor relative to the reference coordinate system about the Z-axis.

4. The unbalance amount prediction method according to claim 3, wherein the features include, Center-of-circle eccentric translation transformation vector dp i o and mass eccentric translation transformation vector dp i c are respectively shown in Eqs. (12) and (13) as follows: where dx i o represents the offset of the center of the i-th stage rotor in the X-axis direction; dy i o represents the center offset of the i-th stage rotor in the Y-axis direction; dz i o It represents the offset of the center of the i-th stage rotor along the Z-axis direction; dx i c represents the centroid offset of the i-th stage rotor in the X-axis direction; dy i c represents the centroid offset of the i-th stage rotor in the Y-axis direction; dz i c represents the centroid offset of the i-th stage rotor in the Z-axis direction; z i o represents the ideal position in the Z-axis direction of the center of the i-th stage rotor; z i c represents the ideal position in the Z-axis direction of the centroid of the i-th stage rotor; According to Equations (8)-(13), obtain the centroid offset after rotor assembly, and then obtain the unbalance u2 after assembly of the second-stage rotor: where dx 0-2 c represents the cumulative centroid offset of the second-stage rotor in the X-axis direction; dy 0-2 c Represents the cumulative offset of the centroid of the second-stage rotor in the Y-axis direction.

5. The unbalance amount prediction method according to claim 4, wherein the features include, Based on the derivation of the unbalance formula for the second-stage rotor assembly, obtain the centroid eccentricity transfer relationship of the kth-stage rotor after assembly of the nth-stage rotor as: Substitute Equations (2), (3), and (7) into Equation (15), then: According to equations (9)-(13) and equation (16), the cumulative offset of the rotor's center of mass can be obtained, and further, after the assembly of the n-stage rotor, the unbalance amount u of the k-th stage rotor can be obtained k : where dx 0-k c represents the cumulative centroid offset of the k-th stage rotor in the X-axis direction; dy 0-k c represents the cumulative centroid offset of the k-th stage rotor in the Y-axis direction; According to Equation (17), the calculation of the unbalance of any stage of the rotor after multi-stage rotor assembly under a single projection cross-section can be realized.

6. The unbalance prediction method according to claim 5, characterized by comprising, When the nth-stage rotor is assembled and the unbalance of the kth-stage rotor needs to be projected onto two cross-sections for characterization, obtain the centroid eccentricity transfer relationship of the ith projection cross-section as: Translation transformation vector dp kg c The mathematical expression is as follows: where dx kg c represents the offset in the X-axis direction of the centroid on the g-th section of the k-th stage rotor; dy kg c It represents the offset of the centroid in the Y-axis direction of the g-th section of the k-th stage rotor. dz kg c It represents the offset of the centroid in the Z-axis direction of the g-th section of the k-th stage rotor. z kg c represents the ideal position in the Z-axis direction of the centroid on the g-th section of the k-th stage rotor; According to formulas (9)-(12), (18) and (19), the cumulative offset of the rotor centroid is obtained, and then the unbalance u on the g-th section of the k-th rotor after the assembly of the n-stage rotor is obtained. kg : where dx 0-kg c represents the cumulative offset of the centroid in the X-axis direction on the g-th section of the k-th stage rotor; dy 0-kg c represents the cumulative centroid offset along the Y-axis direction at the g-th section of the k-th stage rotor; From Equation (20), the calculation of the unbalance of any stage of the rotor after multi-stage rotor assembly under two projection cross-sections can be realized.

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