CN-121996883-A - Function expression method of milling aviation aluminum alloy stress wave in real number domain

CN121996883ACN 121996883 ACN121996883 ACN 121996883ACN-121996883-A

Abstract

The invention discloses a function expression method of milling aviation aluminum alloy stress waves in a real number domain, relates to the technical field of aviation aluminum alloy milling, and aims to solve the problems that an existing three-dimensional stress wave model is complex in solving, time-consuming and difficult to guarantee in accuracy. The method comprises the steps of judging the contact condition of an end mill and a workpiece, calculating the thickness of a milling micro-element instantaneous cutting layer by utilizing the cutter tooth instantaneous contact relation, calculating the size of a milling stress wave excitation source by combining the obtained thickness of the cutting layer based on a one-dimensional stress wave theory, constructing a longitudinal wave equation by using a Lame-Navier equation, and solving a partial differential equation by using a Laplace transformation method to obtain a function expression of a stress wave in a real domain. The method simplifies the stress wave solving process, improves the calculation precision and efficiency, and provides a basic calculation method for milling aviation aluminum alloy high-stability processing and stress wave related research.

Inventors

Zhao Peidie
WU HONGYANG
JIANG BIN
OUYANG YIJIE

Assignees

哈尔滨理工大学

Dates

Publication Date: 20260508
Application Date: 20251029

Claims (9)

1. The method for expressing the function of the milling aviation aluminum alloy stress wave in the real number domain is characterized by comprising the following steps: S1, milling infinitesimal instantaneous cutting layer thickness calculation Judging whether the end mill is in contact with the machined aviation aluminum alloy workpiece, if so, analyzing and solving the instantaneous cutting layer thickness h D (t,z),h D (t, z) of the milling micro-element by utilizing the instantaneous contact relation between the cutter tooth and the workpiece, and calculating according to the following formula: Wherein t is time, z is the z-axis direction in the cutting coordinate system, and A x 、A y is respectively Relative to A distance of movement in the feed direction and the width-cutting direction; Respectively the rotation centers of the axially highest tool tip points of the cutter teeth i and the cutter teeth i-1, wherein theta t is the included angle of the rotation radii of the cutter teeth in the direction of projection lines along the depth cutting direction, theta i 、θ i-1 is the milling micro-element instantaneous position angle of the cutter teeth i and the cutter teeth i-1, and r i and r i-1 are the cutter tooth radii of the cutter teeth i and the cutter teeth i-1; The inclination angles caused by milling vibration of the cutter teeth i and the cutter teeth i-1 are respectively shown; s2, calculating the size of milling stress wave excitation source Based on the milling infinitesimal instantaneous cutting layer thickness h D (t, z) obtained in the step S1, under a one-dimensional stress wave theoretical model, calculating the size of a milling stress wave excitation source according to the stress condition of a workpiece, wherein the size of the excitation source is represented by stress sigma i (t) born by an i point, and the calculation formula is as follows: Wherein dF i (t, dz) is the micro-element milling force, dz is the micro-element axial milling depth, and h D (t, dz) is the thickness of the cutter tooth milling micro-element instantaneous cutting layer; S3, solving stress wave real number domain function expression Based on the size of the milling stress wave excitation source obtained in the step S2, constructing a longitudinal wave equation by utilizing a Lame-Navier equation, and solving a partial differential equation by adopting a Laplace transformation method to obtain a function expression of the stress wave in a real number domain, wherein the function expression is as follows: Where L -1 is an inverse laplace transformation symbol, σ i (t) is a uniformly distributed load applied to the workpiece surface in the x direction, s is a laplace variable, x is a coordinate of the stress wave propagation path direction, and c is a wave equation of the longitudinal wave.
2. The method for expressing functions of milling aviation aluminum alloy stress waves in real number domain according to claim 1, wherein in step S1, when the cutter tooth i for the next cutting reaches the same position as the cutter tooth i-1 for the last cutting, the included angle theta t of turning radius of the two cutter teeth in the projection line direction along the depth direction is calculated by the following formula: wherein, theta i is the milling infinitesimal instantaneous position angle of the cutter tooth i, r i-1 is the cutter tooth radius of the cutter tooth i-1, and delta i-1 is the inclination angle caused by milling vibration of the cutter tooth i-1.
3. The method for expressing functions of milling aviation aluminum alloy stress waves in real number domain according to claim 2, wherein in step S1, the instantaneous position angle theta i (t, z) of milling micro-elements is calculated by the following formula: wherein beta is the helix angle of the cutting edge of the milling cutter, R i is the cutter tooth radius of cutter tooth i, and z is the coordinate of milling infinitesimal in the axial direction of the cutter.
4. A method for expressing a function of a stress wave of a milled aviation aluminum alloy in a real number domain according to claim 3, wherein in step S1, the distance A x that o j i moves in the feeding direction and the distance that o j i-1 moves in the tangential direction are calculated by the following formulas: A x ＝f z +A x (t 1 )+A x (t 2 ); A y ＝A y (t 1 )+A y (t 2 ); Wherein f z represents the feeding amount per tooth, t 1 、t 2 is the time when the cutter tooth i and the cutter tooth i-1 reach the cutting position, A x (t 1 ) is the vibration displacement of the cutter tooth i along the feeding direction at the time t 1 , A x (t 2 ) is the vibration displacement of the cutter tooth i along the feeding direction at the time t 2 , A y (t 1 ) is the vibration displacement of the cutter tooth i along the width cutting direction at the time t 1 , and A y (t 2 ) is the vibration displacement of the cutter tooth i along the width cutting direction at the time t 2 .
5. The method for expressing functions of milling aviation aluminum alloy stress waves in real number domain according to claim 1, wherein in step S2, under a one-dimensional stress wave theoretical model, the included angle alpha (t) between the connecting line of the point i and the center of the milling cutter and the vertical direction is calculated by the following formula: a e is the radial depth of cut width, n is the milling cutter rotational speed, t is time, r is the milling cutter turning radius, and a st is the maximum angle that can be reached by the included angle α (t).
6. The method of expressing a function of a stress wave of a milled aviation aluminum alloy in a real number domain according to claim 5, wherein in step S2, an included angle beta (t) between an x-direction force F' x applied by a workpiece and a resultant force F i applied by a point i is calculated by the following formula: wherein F' y is the y-direction force applied by the tool to the workpiece.
7. The method for expressing a function of a stress wave of a milled aviation aluminum alloy in a real number domain according to claim 1, wherein in step S3, the expression of the Lame-Navier equation is: Wherein the method comprises the steps of Is a Laplacian operator; Wherein: λ=Eν/[(1+ν)(1-2ν)]; μ=G=E/[2(1+ν)]; Wherein, theta t is the included angle of the turning radius, mu and lambda are Ramey constants, E, v and G are respectively the elastic modulus, poisson ratio and shear modulus of the aviation aluminum alloy material, theta is the volume strain, i represents three directions in three-dimensional coordinates, u i represents the displacement of particles in the x, y and z directions, The second derivative of u i with respect to time t represents acceleration, and ρ is the density of the aviation aluminum alloy material.
8. The method for expressing the function of the milling aviation aluminum alloy stress wave in the real domain according to claim 7, wherein in the step S3, the wave equation of the longitudinal wave is derived by setting the displacement field of the medium to be a non-rotating field and combining the Lame-Navier equation to derive the wave equation of the longitudinal wave as follows: Wherein ρ is the density of the medium; stress gradient, positive stress, coordinate of propagation path direction, and wave equation of longitudinal wave.
9. The method for expressing the function of the milling aviation aluminum alloy stress wave in the real number domain according to claim 8, wherein in step S3, the specific process of solving the partial differential equation by using the Laplace transformation method comprises the following steps: s31 wave equation for longitudinal wave Expression of x-direction stress sigma (x, t) Boundary conditions Taking Laplace transformation for time t, we get: ∑ x (x,s)| x＝0 ＝∑ i (s),∑ x (x,s)| x＝+∞ =0; Wherein U x (x,s)、Σ i (s)、Σ x (x, s) are Laplace transforms of U x (x,t)、σ i (t), sigma (x, t) with respect to t, respectively, s is a Laplace variable; step S32, solving the transformed longitudinal wave equation to obtain a general solution of the longitudinal wave equation: Wherein A, B is the undetermined coefficient in the general solution; step S33, determining a coefficient A, B to be determined by combining the transformed boundary conditions, substituting A, B into the transformed x-direction stress expression to obtain a transformed stress expression: S34, performing Laplace inverse transformation on the transformed stress expression, and obtaining a function expression of the stress wave in a real number domain according to a delay property L -1 [∑ i (s)e -sr ]＝∑ i (t-tau) u (t-tau); wherein u (t) is a unit step function, e -sr is a delay factor, and τ is a lag time.

Description

Function expression method of milling aviation aluminum alloy stress wave in real number domain Technical Field The invention belongs to the technical field of milling of aviation aluminum alloy, and particularly relates to a function expression method of milling aviation aluminum alloy stress waves in a real number domain. Background The aviation aluminum alloy has the comprehensive advantages of low density, high specific strength, good corrosion resistance and excellent processability, can meet the manufacturing requirements of complex aviation parts, becomes one of aviation industry core structural materials, has important influence on the application performance of aviation aluminum alloy workpieces due to the cutting stability and processing quality, and breaks the initial equilibrium state of particles of the workpieces when the aviation aluminum alloy workpieces are milled due to the milling force, so that the particles are separated from the initial equilibrium position, and the disturbance is transmitted to the particles on the subsurface layer to generate a fluctuation phenomenon to finally form milling stress waves, so that plastic deformation of the workpieces is caused. In both brittle and plastic materials, stress waves can cause certain damage and impact to the material. The existing research is less for stress wave research generated in the milling process, the mathematical model related to the three-dimensional stress wave model is complex, more mathematical variables are introduced, the solving process is too complex and time-consuming, the solving accuracy is difficult to ensure, and in the actual wave equation solving process, the wave equation is a partial differential equation and is very complex to directly solve in a real number domain, so that the function expression of the stress wave in the real number domain is necessary to solve. Aiming at the stable cutting processing requirement of the milling aviation aluminum alloy workpiece, the invention provides a calculation method of the milling micro-element instantaneous cutting layer thickness of the cutter tooth under the influence of milling vibration, provides a calculation method of the size of a milling stress wave excitation source under the effect of the milling vibration, and obtains a function expression method of the stress wave in a real domain. Disclosure of Invention The invention aims to solve the technical problems that in the prior art, a three-dimensional stress wave model for solving and milling an aviation aluminum alloy stress wave is complex in mathematic, time-consuming and difficult to guarantee in solving due to multiple variables, and a wave equation (partial differential equation) is directly solved in a real number domain. In order to achieve the above purpose, the present invention provides the following technical solutions: a function expression method of milling aviation aluminum alloy stress waves in a real number domain comprises the following steps: S1, milling infinitesimal instantaneous cutting layer thickness calculation Judging whether the end mill is in contact with the machined aviation aluminum alloy workpiece, if so, analyzing and solving the instantaneous cutting layer thickness h D(t,z),hD (t, z) of the milling micro-element by utilizing the instantaneous contact relation between the cutter tooth and the workpiece, and calculating according to the following formula: ; Wherein t is time, z is the z-axis direction in the cutting coordinate system, and A x、Ay is respectively Relative toA distance of movement in the feed direction and the width-cutting direction;、 Respectively the rotation centers of the axially highest tool tip points of the cutter teeth i and the cutter teeth i-1, the included angle of the rotation radius of the cutter teeth in the projection line direction along the depth cutting direction, the included angle of the rotation radius of the cutter teeth theta t, the included angle of the rotation radius of the cutter teeth theta i, Milling micro-element instantaneous position angles of cutter tooth i and cutter tooth i-1 respectively, and r i andCutter tooth radii of the cutter tooth i and the cutter tooth i-1 respectively;、 The inclination angles caused by milling vibration of the cutter teeth i and the cutter teeth i-1 are respectively shown; s2, calculating the size of milling stress wave excitation source Based on the milling infinitesimal instantaneous cutting layer thickness h D (t, z) obtained in the step S1, under a one-dimensional stress wave theoretical model, calculating the size of a milling stress wave excitation source according to the stress condition of a workpiece, wherein the size of the excitation source is stressed by an i pointThe expression, the calculation formula is: ; Wherein, the For the purpose of a micro-component milling force,H D (t, dz) is the thickness of a cutter tooth milling micro-element instantaneous cutting layer; S3, solving stress wave