CN-121980731-A - Stress and rigidity analysis method for multi-waveform membrane disc under angular load

CN121980731ACN 121980731 ACN121980731 ACN 121980731ACN-121980731-A

Abstract

The invention discloses a stress and rigidity analysis method under multi-waveform membrane disc angular load, which comprises the steps of defining geometric and working condition parameters, constructing a segmented deflection model, establishing a non-axisymmetric stress analysis model and pushing an angular rigidity analysis formula, wherein the analysis method is based on a plate shell theory, and deduces a deflection expression of a maximum deformation section by carrying out segmented treatment on a corrugated molded line and setting displacement, slope and curvature continuous conditions; and carrying out circumferential integral on the infinitesimal bending moment and shearing force to obtain total bending moment and calculating angular rigidity, thereby realizing integral analysis and solving of deflection, stress and rigidity. The method realizes high-precision prediction of the angular mechanical behavior of the complex corrugated film disc, has high calculation efficiency and stable and consistent result, can effectively replace a large number of finite element iterations, and provides a reliable tool for structural optimization and engineering design of the film disc coupler.

Inventors

CAO ANGANG
HAO YONGXING
ZHOU JUNJUN
DOU JIANQIANG
JIANG SHIQUAN
Jin Huiting

Assignees

郑州科技学院

Dates

Publication Date: 20260505
Application Date: 20251202

Claims (10)

1. The method for analyzing the stress and the rigidity of the multi-waveform membrane disc under the angular load is characterized by comprising the following steps of: Defining geometrical parameters and working condition parameters of a multi-waveform membrane disc, and establishing a geometrical feature set based on the radial dimension of the membrane disc, a corrugated molded line, a connecting hub and a rim structure for constructing a mechanical analysis model under angular load; secondly, carrying out deflection function assumption on the maximum deformation section of the multi-waveform membrane disc under the action of angular load based on a plate shell theory, carrying out sectional treatment on the membrane disc according to the periodicity of the corrugated structure, and deducing a vertical deflection analysis expression of the maximum deformation section by combining the continuity conditions of an inner ring boundary, an outer ring boundary and a sectional boundary; Establishing a non-axisymmetric bending-torsion coupling mechanical model for the multi-waveform membrane disc based on a cylindrical coordinate system, and obtaining analytic expressions of radial stress, circumferential stress and tangential stress of the membrane disc under the action of angular load through a geometric equation and a physical equation to form a stress distribution prediction model under the angular load; And step four, based on the bending moment balance relation and the shearing force balance relation of the infinitesimal membrane disc, establishing a total bending moment-deflection angle equation, and deducing an angular rigidity analysis formula of the membrane disc under the action of an angular load.
2. The method for analyzing stress and rigidity under angular load of multi-waveform membrane disc according to claim 1, wherein in the first step, the defined geometric parameters include a molded line inner radius b, a molded line outer radius a, a ripple thickness H, a ripple amplitude H, a hub thickness H1, a rim thickness H2, a hub transition fillet radius r2, a rim transition fillet radius r3, a membrane disc inner radius r0, a membrane disc outer radius r1, and the working condition parameters include a membrane disc number m and a working rotation speed r.
3. The method for analyzing stress and stiffness under angular load of multi-waveform film tray according to claim 1, wherein in the second step, when the corrugated line is segmented, the corrugation is divided into at least two sections in the radial direction, each section respectively establishes a deflection hypothesis function v1, v2, and the conditions of continuous displacement, continuous slope and continuous curvature are satisfied at the segment boundary.
4. The method for analyzing stress and stiffness under angular load of a multi-waveform film disc according to claim 2, wherein in the second step, after the piecewise flexibility functions v1 and v2 of the first segment and the second segment are established, the method is respectively provided with: the boundary condition of the inner ring is that the vertical deflection v1=t, t is the displacement of the inner ring, and the bending moment M=0; the segmentation boundary conditions are v1=v2, dv 1/dr=dv 2/dr, d 2 v1/dr 2 =d 2 v2/dr 2 ; The boundary condition of the outer ring is that the vertical deflection v2=0 and the dv 2/dr=0; The concave-convex constraint points are arranged in the segmented interval and used for determining that the second derivative of the corrugated segment is zero.
5. The method for analyzing stress and rigidity under angular load of multi-waveform membrane disc according to claim 1, wherein in the third step, a cylindrical coordinate system with Z axis coincident with symmetry axis of membrane disc is adopted, a non-axisymmetric mechanical model is established by taking radius r and circumference rotation angle θ as variables, and based on deflection function v (r), its spatial variation relationship and angle phi between the normal of ripple and symmetry axis of membrane disc, geometric equations of radial strain epsilonr, circumference strain epsilonθ and tangential strain γrθ are deduced, so that non-axisymmetric deformation of membrane disc under angular load is commonly characterized by deflection curve, deformation gradient and ripple inclination angle.
6. The method for analyzing stress and stiffness under angular load of a multi-waveform membrane disc according to claim 5, wherein in the third step, the radial strain εr, the circumferential strain εθ, and the tangential strain γr θ are substituted into Hooke's law to create a physical equation, so as to be converted into radial stress σr, circumferential stress σθ, and tangential stress τrθ, respectively, to obtain a stress expression capable of reflecting the multi-directional mechanical response of the membrane disc under the angular load, wherein: Radial stress σr=e/(1- μ 2 ) and (εr+μεθ); circumferential stress σθ=e/(1- μ 2 ) and (εθ+μσr); Shear stress τrθ=e/(2 (1+μ)), γrθ; e is the elastic modulus and μ is the Poisson's ratio.
7. The method for analyzing stress and stiffness under angular load of multi-waveform membrane disc according to claim 1, wherein in the fourth step, the total bending moment M is obtained by performing circumferential integration on the bending moment and shearing force of the membrane disc micro-element body, and the angular stiffness K is calculated based on the relation between the total bending moment and the angular deflection angle α: K=M/α。
8. The method for analyzing stress and rigidity under angular load of multi-waveform membrane disc according to claim 7, wherein the calculation of the total bending moment M comprises circumferential integration of horizontal bending moment Mr, circumferential bending moment mθ, torque Mr θ and shearing force Qr of membrane disc primordial, and establishing an integral static equation by combining force balance relation of qr= (mr+ ∂ Mr/∂ r+mθ)/R, so that the total bending moment M is calculated by superposition of ≡ (0-2pi) Mr, cosθ,2θ, and ≡ (0-2pi) Qr, where h is equal to R, and is equal to d θ.
9. The method for analyzing stress and rigidity under angular load of multi-waveform film disc according to any one of claims 1-8, wherein the analytical calculation in the second to fourth steps is realized by MATLAB programming.
10. The method for analyzing stress and rigidity of a multi-waveform membrane disc under angular load according to claim 9, further comprising the step of obtaining reference data of deflection, stress and rigidity of the multi-waveform membrane disc by adopting a numerical simulation method, and comparing the reference data with an analysis calculation result to verify model accuracy.

Description

Stress and rigidity analysis method for multi-waveform membrane disc under angular load Technical Field The invention belongs to the technical field of mechanical transmission part design and mechanical property analysis, in particular to a mechanical property analysis technology of a multi-waveform membrane disc, which is a core element of a flexible coupling, and is particularly suitable for stress distribution prediction and angular rigidity calculation of the multi-waveform membrane disc under the action of angular load under the working conditions of high power density and high rotating speed (such as an aeroengine, a high-speed pump and a compressor transmission system). Background The flexible coupling is used as a key connecting element in a rotary mechanical transmission system, is widely applied to aeroengines, high-speed compressors, high-speed centrifugal pumps and other high-speed high-power density equipment, and has the main functions of transmitting torque and compensating relative displacement between two shafts, including radial offset, axial movement, angular deviation and the like, caused by installation errors, thermal deformation or dynamic vibration. With the continuous development of aerospace, energy equipment and high-speed transmission equipment in the directions of higher power, higher rotating speed and lighter weight, the flexible coupling has higher angular compensation capability, higher torque bearing capability and longer fatigue life while ensuring transmission efficiency and reliability, and more stringent requirements on mechanical properties are put forward. The types of flexible couplings commonly used in the industry today mainly include diaphragm couplings and membrane disc couplings. The traditional diaphragm coupling generally adopts a mode of overlapping and connecting a plurality of groups of film sheets, and displacement compensation is realized through in-plane stretching and out-of-plane bending of the diaphragm. The planar membrane structure has the advantages of simple processing, convenient installation and the like, but is limited by the thickness, diameter and material performance of the membrane, has limited out-of-plane bending capacity, is easy to generate local stress concentration under the action of larger angular deviation, and leads to the reduction of fatigue life. Along with the continuous promotion of transmission system power and rotational speed, traditional plane diaphragm is when bearing big moment of torsion and big angular compensation operating mode, and its stress and deformation level are close the material limit, are difficult to satisfy high-end equipment to the demand of lightweight, high bearing. The membrane disc coupling is used as another common high-performance flexible coupling, and the torque transmission capacity and the compensation performance are improved to a certain extent by introducing an annular membrane disc structure. However, the traditional flat membrane disc structure still has inherent design limitations that an effective bearing area is mainly concentrated near the inner and outer connecting rings of the membrane disc, the torque (torque diameter ratio) which can be transmitted in unit radial dimension is difficult to further improve, meanwhile, the membrane disc is single in shape and limited in elastic deformation capacity, the problem of obvious stress concentration still can occur under the working condition of large angular deviation, and the fatigue life has bottlenecks. Furthermore, in practical use, the stress distribution of flat membrane discs is highly dependent on geometric dimensions and assembly deviations, the sensitivity to manufacturing and assembly accuracy of which makes the space for structural optimization limited. In order to break through the limitations of the membrane and the membrane disc coupling in terms of compensation capability and bearing efficiency, various structural improvement schemes are proposed in the prior art, such as changing the thickness of the membrane, increasing the number of membrane discs, adopting a local chamfer or equal thickness area structure and the like, so as to improve the stress concentration condition. However, most of these improvements are still made on the basis of the traditional planar structure, the compensation performance is limited, and the requirements of higher performance are still difficult to meet in terms of structure weight reduction and stress uniform distribution. Meanwhile, in order to adapt to the working condition of high rotation speed, some technologies propose means such as material reinforcement and a novel lamination structure, but the integral structure of the planar membrane or the flat membrane disc is not enough in large-angle compensation. In recent years, in order to adapt to high-load and high-deviation working conditions, researches have been made on using a corrugated diaphragm, a corrugated diaphragm disc or other e