An optimization method for the pre-tightening force of the shaft end nut of a rotor system considering the influence of thermal deformation

Abstract

The present invention discloses an optimization method for the pre-tightening force of the shaft-end nut of a rotor system considering the influence of thermal deformation, comprising the following steps: Step 1, theoretically calculate the thread pre-tightening force of the shaft-end nut of the rotor system; Step 2, simulate the variation law of the pre-tightening force of the shaft-end nut of the rotor system; Step 3, correct the pre-tightening force model of the nut by solving the average value of the theoretical calculation value and the simulation value of the nut pre-tightening force at each temperature value point; Step 4, calculate the reliability of the pre-tightening force of the shaft-end nut of the rotor system under thermal deformation based on the result of Step 3; Step 5: Based on the result of Step 4, continuously adjust the upper and lower limit values of the pre-tightening force index until the pre-tightening force of the shaft-end nut during the operation of the rotor system meets the actual working requirements.

Description

Technical Field

[0001] The present invention relates to the technical field of thermal machinery, and particularly relates to an optimization method for the pre-tightening force of the shaft-end nut of a rotor system considering the influence of thermal deformation. Background Art

[0002] A certain type of turbofan engine is a thermal machinery that is used repeatedly under harsh environmental conditions such as heat, force, electricity, and magnetism for a long time. Among them, the rotor system is an important part of the engine, and the mass characteristics of the rotor system have an important impact on the performance of the engine. The pre-tightening force of the shaft-end nut of the rotor system is an important quality index for the assembly of the rotor system. The function of the shaft-end nut is to press three turbines onto the rotating shaft of the rotor. Excessive pre-tightening force accelerates the creep process of the nut material, resulting in the fracture of the thread. Insufficient pre-tightening force will directly cause the nut to loosen under the condition of engine vibration, and then cause rubbing damage between the rotating and stationary parts of the engine.

[0003] The extremely harsh working environment of the rotor system will cause the pre-tightening force of the shaft-end nut to change during use, especially the influence of temperature change is particularly obvious. When the engine is working, the rotor system rotates at high speed, and high-temperature and high-pressure air and gas flow in the flow passage, and the rotor is deformed by heat. When the dynamic value of the pre-tightening force of the shaft-end nut of the rotor system exceeds the boundary of the pre-tightening force index, problems such as loosening and rubbing of the rotor system will occur, resulting in damage to the engine structure. Therefore, in order to solve the problems of loosening and rubbing of the rotor system of a certain type of turbofan engine, studying the relationship between the thermal deformation of the rotor system and the pre-tightening force of the shaft-end nut, and ensuring that the pre-tightening force of the shaft-end nut meets the working requirements when the rotor system is working, is an important technical basic work to improve the assembly reliability of the rotor system.

[0004] At present, during the assembly process of the rotor system and the shaft-end nut, the pre-tightening force is achieved by controlling the tightening torque of the nut, without considering the influence of thermal deformation.

[0005] During the working process of the engine, under the combined action of thermal load and vibration, the pre-tightening force of the shaft-end nut of the rotor system will change. Especially for the start-stop working cycle that the engine has to go through many times during the ground test of the R & D engine, it is also easy to cause the change of the nut pre-tightening force, which may cause problems such as loosening and rubbing of the rotor, resulting in damage to the engine structure.

[0006] In view of the above problems, on the basis of the existing pre-tightening force control, it is necessary to study an optimization method for the pre-tightening force of the shaft-end nut of a rotor system considering the influence of thermal deformation. Summary of the Invention

[0007] In view of this, the present invention provides an optimization method for the pre-tightening force of the shaft-end nut of a rotor system considering the influence of thermal deformation, which can improve the reliability of the connection of the shaft-end nut of the rotor system and ensure that the pre-tightening force of the rotor system meets the requirements when the engine is working.

[0008] The technical solution of the present invention is: an optimization method for the pre-tightening force of the shaft-end nut of a rotor system considering the influence of thermal deformation, comprising the following steps:

[0009] Step 1: Theoretically calculate the thread pre-tightening force of the shaft-end nut of the rotor system;

[0010] Step 2: Simulate the variation law of the pre-tightening force of the shaft-end nut of the rotor system;

[0011] Step 3: Modify the nut pre-tightening force model by solving the average value of the theoretical calculation value and the simulation value of the nut pre-tightening force at each temperature value point;

[0012] Step 4: Calculate the reliability of the pre-tightening force of the shaft-end nut of the rotor system under thermal deformation based on the results of Step 3;

[0013] Step 5: Based on the results of Step 4, continuously adjust the upper and lower limit values of the pre-tightening force index until the pre-tightening force of the shaft-end nut during the operation of the rotor system meets the actual working requirements.

[0014] Preferably, in Step 1, the analytical algorithm for the thread pre-tightening force when not heated is:

[0015] In the thread connection body of the rotor shaft and the nut, the tightening torque T applied to the nut is equal to the sum of the frictional resistance torque T1 between the thread pairs and the frictional resistance torque T2 between the nut annular end face and the support surface of the connected part / washer, that is:

[0016] T = T1 + T2 (1)

[0017] Simplify the mechanical analysis of the thread pair into the mechanical calculation of an inclined wedge, and regard the nut as an inclined wedge block wound around the rotor shaft; when pre-tightening, the axial force received by the nut is F b , and the tangential force is U f . During the nut tightening process, according to the relationship of mechanical equilibrium, it can be obtained that:

[0018] U f cosβ - F b sinβ = μ s (U f sinβ + F b cosβ) (2)

[0019] Among them, β is the thread lead angle, and the friction coefficient is μ s ;

[0020] From formula (2), the following formula can be obtained:

[0021]

[0022] Among them, ρ is the thread surface friction angle;

[0023] During the loosening process of the nut, by changing the sign of β in Equation (3) to a negative sign, we can obtain:

[0024] U f = F b tan(ρ - β) (4)

[0025] Let the pitch diameter of the thread be d p , then the torque T1 when tightening the screw pair is:

[0026]

[0027] When the nut contacts the connecting structural member, due to the generation of friction, the nut needs to overcome the frictional torque of the nut support surface when it continues to be turned. The expression of T2 is as follows:

[0028]

[0029] Among them, μ w is the friction coefficient between the nut support surfaces, d w is the nominal diameter of the nut, and F f is the pressing force;

[0030] When the pressure on the nut support surface is evenly distributed, the area of the support surface is the circular area with the distance B between the opposite sides of the nut as the diameter. Let the diameter of the threaded hole be D, then there is:

[0031]

[0032] From this, the frictional torque between the nut and the support surface is:

[0033]

[0034] Substituting Equation (5) and Equation (8) into Equation (1) gives:

[0035]

[0036] Among them, F is the screw pre-tightening force, F = F b = F f ;

[0037] From Equation (9), it can be obtained that:

[0038]

[0039] Preferably, in the first step, the analytical algorithm for the screw pre-tightening force after heating is:

[0040] The change in the pre-tightening force of each part of the rotor system comes from two parts, namely: the elongation or shortening of the parts caused by the tension or compression of the parts of the rotor system and the expansion of the parts caused by the increase in temperature;

[0041] When only subjected to the thread pre-tightening force F, the elongation of the rotor shaft is calculated by the following formula:

[0042]

[0043] Where, ΔL y is the elongation of the rotor shaft when only subjected to the pre-tightening force, L is the effective length of the rotor shaft, s is the stress area of the rotor shaft, and E is the elastic modulus of the rotor shaft;

[0044] At this time, the parts installed on the rotor shaft are also compressed under the action of the thread pre-tightening force F, and the total compression deformation amount generated is:

[0045]

[0046] In the formula, ΔL yi is the compression deformation amount of each part under the action of the pre-tightening force, L i is the effective length of each part, s i is the force-bearing area of each part, E i is the elastic modulus of each installed part of the rotor shaft, and n is the total number of parts;

[0047] When only subjected to the thermal load, the elongation of the rotor shaft is calculated by the following formula:

[0048] ΔL r = α·L·(t - t0) (13)

[0049] In the formula, ΔL r is the elongation of the rotor shaft when only subjected to the thermal load, α is the thermal expansion coefficient of the rotor shaft, and (t - t0) is the temperature difference;

[0050] At this time, the parts installed on the rotor shaft are also expanded under the action of the thermal load, and the total elongation amount generated is:

[0051]

[0052] In the formula, ΔL ri is the elongation of each part under the action of the thermal load, L i is the effective length of each part, α i is the thermal expansion coefficient of each part;

[0053] At room temperature t0, when applying the torque T for pre-tightening, both the rotor shaft and the installed parts are compressed. According to Cook's law, the elongation ΔL of the rotor shaft and the compression amount of all the installed parts on it The relationship with the torque is expressed as:

[0054]

[0055]

[0056] Wherein, ΔL i is the compression amount of each mounting part, d is the diameter of the rotor shaft, S is the stress area of the rotor shaft, and S i is the stress area of each mounting part of the rotor shaft, is the elastic modulus of the rotor shaft at room temperature, is the elastic modulus of each mounting part of the rotor shaft at room temperature;

[0057] Thus, the length L' of the rotor shaft after applying torque and the sum of the lengths of the parts mounted thereon are expressed as:

[0058] L' = L - ΔL (17)

[0059]

[0060] When the entire rotor system is heated to temperature t, the elongation amount ΔL' of the rotor shaft caused by the temperature and the total elongation amount of all mounting parts are respectively:

[0061] ΔL' = αL'(t - t0) (19)

[0062]

[0063] Then, the length L'' of the rotor shaft and the sum of the lengths of all mounting parts at temperature t are:

[0064] L'' = L' + ΔL' (21)

[0065]

[0066] If the total elongation amount of all mounting parts after heating is greater than the elongation amount of the rotor shaft, the rotor pre-tightening force will further increase; otherwise, the pre-tightening force will decrease; due to the change of the pre-tightening force, elastic deformation will occur between the rotor shaft and each part. According to the deformation coordination relationship, the elongation amounts of the rotor shaft and each part should satisfy the relationship:

[0067]

[0068] Wherein, ΔL'' is the tensile amount of the rotor shaft caused by the increase of the pre-tightening force, is the total compression amount of all parts caused by the increase of the pre-tightening force;

[0069] Among them:

[0070]

[0071]

[0072] In the formula, ΔF is the change in the pre-tightening force of the shaft-end nut, and E t is the elastic modulus of the rotor shaft at temperature t, and E it is the elastic modulus of each component at temperature t;

[0073] Combining the above formulas, the change in the pre-tightening force of the thread when heated to temperature t is ΔF t :

[0074]

[0075] Then the pre-tightening force of the thread at the moment of heating to temperature t is:

[0076]

[0077] Preferably, in the second step, according to the elongation of the rotor system in the pre-tightened state obtained by simulation and the relationship between the elongation of the rotor system and the change in the pre-tightening force, the simulation result of the pre-tightening force of the shaft-end nut is obtained.

[0078] Preferably, in the fourth step, the calculation formula for the reliability of the pre-tightening force of the shaft-end nut is:

[0079]

[0080] In the above formula, δ is the reliability of the pre-tightening force of the shaft-end nut, F(t) is the change function of the pre-tightening force of the shaft-end nut with respect to temperature, t1 is the operating temperature when the pre-tightening force of the shaft-end nut is at the lower limit of the index requirement, and t2 is the operating temperature when the pre-tightening force of the shaft-end nut is at the upper limit of the index requirement.

[0081] Beneficial effects:

[0082] In the present invention, the change law of the pre-tightening force of the shaft-end nut of the rotor system under thermal load is obtained through theoretical calculation and finite element simulation. After model correction, by fitting the simulation curve of the pre-tightening force changing with temperature, the corresponding relationship curve between the pre-tightening force and temperature is obtained, and then the change of the pre-tightening force during engine operation can be predicted; by quantitatively calculating the reliability of the pre-tightening force of the shaft-end nut under the service conditions and according to the target value of the reliability of the pre-tightening force of the rotor system and the index requirements of the pre-tightening force of the rotor system, the upper and lower limit values of the pre-tightening force can be optimized, the connection reliability of the shaft-end nut of the rotor system can be improved, and it is ensured that the pre-tightening force of the shaft-end nut meets the working requirements during the operation of the rotor system; at the same time, this method considers the influence of thermal deformation on the pre-tightening force, and based on the relationship curve between thermal deformation and the pre-tightening force, the reliability of the pre-tightening force can be quantitatively calculated, which has certain guiding significance for improving the reliability of the assembly process; it provides technical support for the design and research and development of subsequent new products. Description of the drawings

[0083] Figure 1 Schematic diagram of the mechanical model of the thread pair involved in the present invention.

[0084] Figure 2 Schematic diagram of the finite element simulation process of the nut pre-tightening force.

[0085] Figure 3 Schematic diagram of the principle for calculating the reliability of the pre-tightening force in the present invention. Specific implementation manners

[0086] The present invention will be described in detail below with reference to the accompanying drawings and by way of examples.

[0087] This embodiment provides an optimization method for the pre-tightening force of the shaft-end nut of a rotor system considering the influence of thermal deformation, which can improve the reliability of the connection of the shaft-end nut of the rotor system and ensure that the pre-tightening force of the rotor system meets the requirements during the operation of the engine.

[0088] The pre-tightening force optimization method includes the following steps:

[0089] Step 1: Theoretically calculate the thread pre-tightening force of the shaft-end nut of the rotor system

[0090] 1. Analytical algorithm for the thread pre-tightening force when not heated

[0091] In the thread connection body of the rotor shaft and the nut, the tightening torque T applied to the nut is equal to the sum of the frictional resistance torque T1 between the thread pairs and the frictional resistance torque T2 between the nut annular end face and the supporting surface of the connected part (here it is the rotor shaft) / washer, that is:

[0092] T = T1 + T2 (1)

[0093] As Figure 1 shown, the mechanical analysis of the thread pair is simplified to the mechanical calculation of an inclined wedge, and the nut is regarded as an inclined wedge block wound around the rotor shaft; when pre-tightening, the axial force received by the nut is F b , and the tangential force is U f . During the tightening process of the nut, according to the relationship of mechanical equilibrium, it can be obtained:

[0094] U f cosβ - F b sinβ = μ s (U f sinβ + F b cosβ) (2)

[0095] where β is the thread lead angle and the friction coefficient is μ s ;

[0096] From formula (2), the following formula can be derived:

[0097]

[0098] Among them, ρ is the friction angle of the thread surface;

[0099] During the loosening process of the nut, by changing the sign of β in Equation (3) to a negative sign, we can obtain:

[0100] U f = F b tan(ρ - β) (4)

[0101] Let the pitch diameter of the thread be d p , then the torque T1 when tightening the thread pair is:

[0102]

[0103] When the nut starts to contact the connecting structural member (rotor shaft), due to the generation of friction, the nut needs to overcome the frictional torque of the nut support surface when it continues to be screwed. The expression of T2 is as follows:

[0104]

[0105] Among them, μ w is the friction coefficient between the nut support surfaces, d w is the nominal diameter of the nut, F f is the compressive force;

[0106] When the pressure on the nut support surface is evenly distributed, the area of the support surface is the circular area with the distance B between the opposite sides of the nut as the diameter. Let the diameter of the threaded hole be D, then it can be calculated by the following formula:

[0107]

[0108] From this, the frictional torque between the nut and the support surface can be obtained as:

[0109]

[0110] Substituting Equation (5) and Equation (8) into Equation (1) gives:

[0111]

[0112] Among them, F is the thread preload, F = F b = F f ;

[0113] From Equation (9), the general theoretical calculation formula for the thread preload can be obtained as:

[0114]

[0115] 2. Analytical algorithm for thread preload after heating

[0116] The change in the pre-tightening force of each part of the rotor system comes from two parts, namely: the elongation or shortening of the parts caused by tension or compression of the parts of the rotor system, and the expansion of the parts caused by temperature rise;

[0117] When only bearing the thread pre-tightening force F, the elongation of the rotor shaft can be calculated by the following formula:

[0118]

[0119] Among them, ΔL y is the elongation of the rotor shaft when only bearing the pre-tightening force, L is the effective length of the rotor shaft, s is the stress area of the rotor shaft, and E is the elastic modulus of the rotor shaft;

[0120] At this time, the parts installed on the rotor shaft (i.e., the turbine shaft, axial flow wheel, mixed flow wheel, high-pressure wheel, and two shaft sleeves) are also compressed by the thread pre-tightening force F, and the total compression deformation amount generated is:

[0121]

[0122] In the formula, ΔL yi is the compression deformation amount of each part under the pre-tightening force, L i is the effective length of each part, s i is the stress area of each part, E i is the elastic modulus of each part installed on the rotor shaft, and n is the total number of parts, which is 6 here;

[0123] When only bearing the thermal load, the elongation of the rotor shaft can be calculated by the following formula:

[0124] ΔL r = α·L·(t - t0) (13)

[0125] In the formula, ΔL r is the elongation of the rotor shaft when only bearing the thermal load, α is the thermal expansion coefficient of the rotor shaft, and (t - t0) is the temperature difference;

[0126] At this time, the parts installed on the rotor shaft, namely the turbine shaft, axial flow wheel, mixed flow wheel, high-pressure wheel, and two shaft sleeves, are also expanded by the thermal load, and the total elongation amount generated is:

[0127]

[0128] In the formula, ΔL ri is the elongation of each part under the thermal load, L i is the effective length of each part, α i is the thermal expansion coefficient of each part;

[0129] At room temperature \(t_0\), when a pre-tightening torque \(T\) is applied, both the rotor shaft and the mounting parts are compressed. According to Hooke's law, the elongation \(\Delta L\) of the rotor shaft and the compression of all the mounting parts on it The relationship with the torque can be expressed as:

[0130]

[0131]

[0132] where \(\Delta L\) i is the compression of each mounting part, \(d\) is the diameter of the rotor shaft, \(S\) is the stress area of the rotor shaft, and \(S\) i is the stress area of each mounting part of the rotor shaft, is the elastic modulus of the rotor shaft at room temperature, is the elastic modulus of each mounting part of the rotor shaft at room temperature;

[0133] From this, the length \(L'\) of the rotor shaft after applying the torque and the sum of the lengths of the mounting parts on it can be expressed as:

[0134] L' = L - \(\Delta L\) (17)

[0135]

[0136] When the entire rotor system is heated to temperature \(t\), the elongation \(\Delta L'\) of the rotor shaft and the total elongation of all the mounting parts due to the temperature are respectively:

[0137] \(\Delta L'\) = \(\alpha L'\)(t - \(t_0\)) (19)

[0138]

[0139] Then the length \(L''\) of the rotor shaft and the sum of the lengths of all the mounting parts at temperature \(t\) (due to the combined action of torque and temperature) is:

[0140] L'' = L' + \(\Delta L'\) (21)

[0141]

[0142] If the total elongation of all the mounting parts after heating is greater than the elongation of the rotor shaft, the pre-tightening force of the rotor will further increase; otherwise, the pre-tightening force will decrease; due to the change in the pre-tightening force, elastic deformation will occur between the rotor shaft and each part. According to the deformation compatibility relationship, the elongation of the rotor shaft and each part should satisfy the relationship:

[0143]

[0144] Where, ΔL″ is the tensile amount of the rotor shaft caused by the increase in the pre-tightening force, is the total compression amount of all parts caused by the increase in the pre-tightening force;

[0145] Among them:

[0146]

[0147]

[0148] Where, ΔF is the change amount of the pre-tightening force of the shaft end nut, and E t is the elastic modulus of the rotor shaft at temperature t, and E it is the elastic modulus of each part at temperature t;

[0149] Combining the above formulas, the change amount of the thread pre-tightening force when heated to temperature t is ΔF t :

[0150]

[0151] Then the thread pre-tightening force at the moment of heating to temperature t is:

[0152]

[0153] Step 2. Simulate the change law of the pre-tightening force of the shaft end nut of the rotor system

[0154] Tightening the shaft end nut is the last step in the assembly of the rotor system. In the actual operation process, the control of the pre-tightening force is realized by a torque measuring wrench; the magnitude of the pre-tightening force cannot be directly measured. After the engine is assembled, the operator needs to measure the elongation of the turbine shaft with a laser rangefinder and indirectly calculate the pre-tightening force with the help of a theoretical formula;

[0155] The simulation of the pre-tightening force will be completed in the commercial finite element analysis software ANSYS WORKBENCH, and the pre-tightening force of the bolt cannot be directly obtained by the finite element analysis method in this software; the elongation of the bolt under the stress state is only related to the stress of the bolt, and the influence of variable factors such as the friction coefficient, contact deformation, and deformation of the connected parts can be excluded; therefore, it is feasible in principle to indirectly calculate the pre-tightening force by measuring the elongation of the bolt; relevant literature shows that this method is widely used for the pre-tightening force control of bolt flange connections in important occasions, and if the measurement is correct, the calculation error of the pre-tightening force is about ±5%;

[0156] In this embodiment, the above method is used to simulate the change of the pre-tightening force of the shaft end nut of the rotor system, and the pre-tightening force of the shaft end thread of the rotor system is indirectly calculated by simulating the elongation of the rotor system under the pre-tightened state; with the help of the relevant knowledge of elasticity, the relationship between the elongation of the rotor system and the change of the pre-tightening force is shown in the following formula:

[0157]

[0158] Among them, ΔF is the change in the pre-tightening force of the shaft-end nut, L is the effective length of the rotor shaft, S is the stress area of the rotor shaft, and S i is the stress area of each installed part of the rotor shaft, E is the elastic modulus of the rotor shaft, and E i is the elastic modulus of each installed part of the rotor shaft;

[0159] As Figure 2 shown, the steps of the simulation are as follows:

[0160] 1) Simplify the rotor model; among them, the simplification contents to be carried out include: removing the blades, simplifying the mixed-flow wheel into a cone, simplifying the axial-flow wheel and the turbine disk into cylinders, removing the weight-reducing ring, shortening the turbine shaft, etc.; at the same time, a cylinder with a through-hole is used to replace the engine stator structure;

[0161] 2) Import the simplified rotor model into ANSYS WORKBENCH;

[0162] 3) Set the material parameters of each part;

[0163] 4) Set the contact mode between parts: set the contact modes of the shaft-end nut and the turbine shaft thread, and the shaft-end nut and the locking ring as "friction", and set other contact modes as "bonded";

[0164] 5) Mesh generation: set the mesh size of the shaft-end nut and the high-pressure shaft to 1 mm, and the mesh size of other structures to 3 mm;

[0165] 6) Fix the connected parts: add "Fix" constraints to parts such as the turbine disk, axial-flow wheel, and mixed-flow wheel; among them, Fix means fixed;

[0166] 7) Apply torque to the shaft-end nut;

[0167] 8) Calculate and obtain the part deformation results (including the elongation of the rotor shaft and the compression of the parts): add the post-processing option for deformation in the turbine shaft direction to view the elongation of the turbine shaft;

[0168] 9) Calculate the pre-tightening force according to the part deformation, and convert to obtain the pre-tightening force of the shaft-end nut according to Equation (11);

[0169] 10) Add thermal load (temperature load), set the load step, set the initial temperature of the system to 20 °C, and increase the temperature to 50 - 1000 °C at intervals of 50 °C to obtain the change of the pre-tightening force under different thermal loads;

[0170] 11) Obtain the pre-tightening force change curve: Solve, add the post-processing option for the deformation in the turbine shaft direction, and view the curve of the elongation of the turbine shaft changing with time in "Solution Information"; among them, Solution Information is the solution information.

[0171] 12) Solve the pre-tightening force: Convert the elongation of the turbine shaft into the pre-tightening force of the nut.

[0172] Step 3. Modify the nut pre-tightening force model based on the theoretical calculation results and simulation results

[0173] After Steps 1 and 2, the analytical curve and simulation curve of the pre-tightening force changing with temperature are obtained. In order to further reduce the model error and make the simulation results correct the theoretical calculation results of the pre-tightening force changing with temperature; for the sake of simplifying the calculation, in this embodiment, the method of taking the average value is used to obtain the modified model of the pre-tightening force changing with temperature, that is, at each temperature value point, the average value of the theoretical calculation value and the simulation value of the nut pre-tightening force is solved, and then the curve of the modified nut pre-tightening force changing with temperature is fitted for the subsequent calculation of the reliability of the nut pre-tightening force.

[0174] Step 4. Calculate the reliability of the shaft-end nut pre-tightening force of the rotor system under thermal deformation

[0175] After the above steps, the curve and analytical equation of the modified shaft-end nut pre-tightening force changing with temperature are obtained. When the upper and lower limits of the shaft-end nut pre-tightening force required to ensure the normal operation of the engine are known, the following formula can be used to calculate the reliability of the shaft-end nut pre-tightening force:

[0176]

[0177] In the above formula, δ is the reliability of the shaft-end nut pre-tightening force, F(t) is the function of the shaft-end nut pre-tightening force changing with temperature, t1 is the working temperature when the shaft-end nut pre-tightening force is at the lower limit of the index requirement, and t2 is the working temperature when the shaft-end nut pre-tightening force is at the upper limit of the index requirement; among them, as Figure 3 shown, the temperature domain is (t1, t2), USL is the upper limit of the pre-tightening force index requirement, and LSL is the lower limit of the pre-tightening force index requirement. In the temperature domain, the larger the area enclosed by F(t), USL, and LSL, the greater the reliability of the pre-tightening force.

[0178] Step 5: Optimization of the shaft-end nut pre-tightening force of the rotor system

[0179] According to Equation (29) in Step 4, the reliability of the pre-tightening force of the shaft end nut of the rotor system can be quantitatively calculated. According to the set reliability value of the pre-tightening force of the rotor system and the requirements for the pre-tightening force of the rotor system, by continuously adjusting the upper and lower limits of the pre-tightening force index until the pre-tightening force of the shaft end nut during the operation of the rotor system meets the actual working requirements, the connection reliability of the shaft end nut of the rotor system is improved.

[0180] In summary, the above are only the preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An optimization method for the pre-tightening force of the shaft-end nut of a rotor system considering the influence of thermal deformation, characterized in that, The following steps are involved: Step 1: Theoretically calculate the thread preload of the nut at the shaft end of the rotor system. The analytical algorithm for the thread preload when not heated is: In the threaded connection between the rotor shaft and the nut, the tightening torque T applied to the nut is equal to the sum of the friction resistance torque T1 between the thread pair and the friction resistance torque T2 between the annular end face of the nut and the supporting surface of the connected part / washer, that is: T=T1+T2 (1) Simplify the mechanical analysis of the screw pair into the mechanical calculation of an inclined wedge, and regard the nut as an inclined wedge block wound around the rotor shaft; when pre-tightening, the axial force received by the nut is F b , and the tangential force is U f , during the process of tightening the nut, according to the relationship of mechanical equilibrium, it can be obtained that: U f cosβ - F b sinβ = μ s (U f sinβ + F b cosβ)(2) where β is the lead angle of the thread and the coefficient of friction is μ s ; From formula (2), we can get the following formula: Where ρ is the friction angle of the thread surface; During the loosening process of the nut, the sign of β in formula (3) is replaced by a negative sign, and the following equation is obtained: U f = F b tan(ρ - β) (4) Let the pitch diameter of the thread be d p , then the torque T1 when tightening the screw pair is as follows: When the nut contacts the connecting structure, due to the friction force generated, the nut needs to overcome the friction torque of the nut support surface to continue to turn. The expression of T2 is as follows: Among them, μ w is the friction coefficient between the nut support surfaces, d w is the nominal diameter of the nut, F f is the pressing force; When the pressure on the nut support surface is evenly distributed, the area of ​​the support surface is the area of ​​a circle with the distance B from the opposite side of the nut as the diameter. If the diameter of the threaded hole is D, then: The friction torque between the nut and the supporting surface is obtained as follows: Substituting equation (5) and equation (8) into equation (1), we get: Among them, F is the thread pre-tightening force, F = F b = F f ; From formula (9), we can get: The analytical algorithm for the thread preload after heating is: The change in preload force of each part of the rotor system comes from two parts, namely: the elongation or shortening of the parts of the rotor system caused by tension or compression, and the expansion of the parts caused by temperature increase; When only the thread preload F is applied, the elongation of the rotor shaft is calculated by the following formula: Among them, ΔL y is the elongation of the rotor shaft when only the pre-tightening force is applied, L is the effective length of the rotor shaft, s is the stress area of the rotor shaft, and E is the elastic modulus of the rotor shaft; At this time, the parts installed on the rotor shaft are also compressed by the thread preload F, and the total compression deformation is: Where, ΔL yi is the compression deformation of each component under the action of the pre-tightening force, L i is the effective length of each component, s i is the stress area of each component, E i is the elastic modulus of each installation component of the rotor shaft, and n is the total number of components; When only thermal load is applied, the elongation of the rotor shaft is calculated as follows: ΔL r = α·L·(t - t0) (13) where ΔL r is the elongation of the rotor shaft under the condition of only thermal load, α is the thermal expansion coefficient of the rotor shaft, and (t - t0) is the temperature difference; At this time, the parts installed on the rotor shaft also expand due to the thermal load, and the total elongation generated is: Where, ΔL ri is the elongation of each component under thermal load, L i is the effective length of each component, and α i is the coefficient of thermal expansion of each component; At room temperature t0, when a pre-tightening torque T is applied, both the rotor shaft and the mounting parts are compressed. According to Hooke's law, the elongation ΔL of the rotor shaft and the compression of all mounting parts thereon The relationship with the torque is expressed as: Where ΔL i is the compression amount of each mounting part, d is the diameter of the rotor shaft, S is the stress area of the rotor shaft, and S i is the stress area of each mounting part of the rotor shaft, is the elastic modulus of the rotor shaft at room temperature, is the elastic modulus of each mounting part of the rotor shaft at room temperature; From this, the sum of the length L′ of the rotor shaft after the application of torque and the lengths of the components mounted thereon is expressed as: L′=L-ΔL (17) When the entire rotor system is heated to temperature t, the elongation ΔL′ of the rotor shaft caused by the temperature and the total elongation of all mounting parts are respectively: ΔL′=αL′(t-t0) (19) Then the length L″ of the rotor shaft at temperature t and the sum of the lengths of all the installed parts are as follows: L″=L′+ΔL′ (21) If the total elongation of the installed parts after heating is greater than the elongation of the rotor shaft, the rotor preload will increase further; otherwise, the preload will decrease. Due to the change in preload, the rotor shaft and the parts will undergo elastic deformation. According to the deformation coordination relationship, the elongation of the rotor shaft and the parts should satisfy the relationship: where ΔL″ is the elongation of the rotor shaft caused by the increase in the preload force, and is the total compression of all parts caused by the increase in the preload force; in: Where ΔF is the change in the pre-tightening force of the shaft-end nut, and E t is the elastic modulus of the rotor shaft at temperature t, and E it is the elastic modulus of each component at temperature t; Combining the above formulas, the change in the thread pre-tightening force when heated to temperature t is ΔF t : Then the thread preload at the time of heating to temperature t is: Step 2, simulating the change law of the preload force of the shaft end nut of the rotor system; Step 3: The nut preload model is modified by solving the average value of the theoretical calculated value and the simulation value of the nut preload at each temperature value point; Step 4: Calculate the reliability of the preload force of the nut at the shaft end of the rotor system under thermal deformation based on the result of step 3; Step 5: Based on the result of step 4, continuously adjust the upper and lower limits of the preload index until the preload of the shaft end nut during the operation of the rotor system meets the actual working requirements.

2. The optimization method for the pre-tightening force of the shaft end nut of the rotor system considering the influence of thermal deformation according to claim 1, characterized in that In the step 2, the simulation result of the preload force of the shaft end nut is obtained according to the elongation of the rotor system in the preload state obtained by simulation, and the relationship between the elongation of the rotor system and the change of the preload force.

3. The optimization method for the pre-tightening force of the shaft end nut of the rotor system considering the influence of thermal deformation according to claim 1 or 2, characterized in that In step 4, the calculation formula of the reliability of the shaft end nut preload force is: In the above formula, δ is the reliability of the pre-tightening force of the shaft-end nut, F(t) is the function of the change of the pre-tightening force of the shaft-end nut with respect to temperature, t1 is the working temperature when the pre-tightening force of the shaft-end nut is at the lower limit of the index requirement, and t2 is the working temperature when the pre-tightening force of the shaft-end nut is at the upper limit of the index requirement.

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