CN104239723A - Method for judging system stability in milling - Google Patents

Abstract

The invention discloses a method for judging system stability in milling operation. The stability of a system under a certain group of milling technological parameters is judged by calculating argument variation of a characteristic equation. The method comprises the following steps of (1) acquiring a group of experimental data of component force of tangential, radial and axial force of cutting force; (2) establishing an average cutting force model and a cutting force coefficient model according to an experimental data average measured in an experiment in the step (1), and calculating average cutting force and a cutting force coefficient, wherein C, calculating the average cutting force in a workpiece coordinate system, and D, calibrating the cutting force coefficient; (3) establishing a differential equation for describing a flutter problem of a power system in milling according to the cutting force coefficient obtained in the step (2), converting the equation into a neutral type matrix equation form, and obtaining the characteristic equation by utilizing Laplace transformation; (4) judging the system stability in milling by calculating the argument variation of the characteristic equation according to any group of technological parameters consisting of axial depth of cut, radial depth of cut, a spindle speed and a feed rate. The method has the beneficial effects that the method is simple in calculation, and a new stability judging method is provided for theoretical study of milling.

Description

The method of discrimination of system stability in a kind of Milling Process

Art

The present invention relates to the method for discrimination of system stability in the Milling Process in field of machining, particularly a kind of Criterion on stability of Flutter Problem in a kind of Milling Process.

Background technology

Along with present generation aircraft, the improving constantly of spacecraft performance requirement, the processing of all kinds of integral structure component to be carried out at a high speed, efficient, high precision processing.Metal cutting is a complex process, relates to the subjects such as elastic and plastic properties mechanics, tribology, thermodynamics, material science, mechanical kinetics.But in cutting process, one of most distinct issues are exactly the machining deformation of workpiece, and flutter is the very important factor affecting workpiece deformation.Flutter in process can make system of processing loses stability, affects machining precision and workpiece surface quality, reduces working (machining) efficiency, even causes workpiece to scrap.Therefore, flutter is the focal issue of process technology research to the research of cutting processing system stability always.

Study in processing in Flutter Problem, the stability Lobe figure of system of processing well can embody the stability of partial differential equation equilibrium point.At present, the method for structural stability figure mainly contains D curve method, timing departure method, semi-discrete method (Semi-discret ization method) and the approximate shceme method (Full-discretization method) that St é p á n proposes.The present invention utilizes Laplace to convert the secular equation obtaining system equation, is carried out the stability of discriminant equation by the argument variable quantity calculating secular equation, and the method calculates simple, and the theoretical research for cut provides a kind of new Convenient stable criterion.

Summary of the invention

The present invention seeks a kind of method of discrimination calculating simple and stable for the differential equation describing power system in Milling Process.Milling Process dynamical system time lag-magnetic hysteresis differential equation is changed into neutral type matrix form equation by the present invention, utilizes argument principle calculating argument variable quantity to propose a kind of Criterion on stability of Flutter Problem.For matrix equation, Laplace is utilized to convert, obtain its secular equation, by calculating the stability of argument variable quantity judgement system under certain group Milling Process technological parameter of secular equation, by calculating the stability under different Milling Process technological parameter, obtain the stability Lobe figure of power system.

The present invention realizes the step of the method: the method for discrimination of system stability in Milling Process.The method comprises the following steps:

(1), utilize and cut experimental provision earnestly, technological parameter group be made up of axially different cutting-in, radial cutting-in, the speed of mainshaft and feed rate by design one group, carries out orthogonal experiment scheme, obtains that one group of cutting force is tangential, the experimental data of radial direction, axial force component:

(2), (1) test the experimental data average recorded according to step, set up average cutting Force Model, Cutting Force Coefficient model, calculate average cutting force and Cutting Force Coefficient, be specifically calculated as follows:

A, definition of object co-ordinate systems XYZ and tool coordinate system X _ty _tz _t

B, set up flat-bottomed cutter infinitesimal cutting Force Model:

$\left[\begin{array}{c}{\mathrm{dF}}_t\\ {\mathrm{dE}}_r\\ {\mathrm{dF}}_a\end{array}\right]=\left[\begin{array}{c}{K}_{\mathrm{te}}\mathrm{dS}+K_{\mathrm{tc}}\·t_n\·\mathrm{db}\\ K_{\mathrm{re}}\mathrm{dS}+K_{\mathrm{rc}}\·t_n\·\mathrm{db}\\ K_{\mathrm{ae}}\mathrm{dS}+K_{\mathrm{ac}}\·t_n\·\mathrm{db}\end{array}\right]$

Wherein, F _t, F _r, F _abe respectively tangential, radial, the axial force component of cutting force.DS, t _n, db is respectively in FCN coordinate system and represents contact arc length infinitesimal, is not out of shape and cuts thick infinitesimal and cut wide infinitesimal;

The calculating of average cutting force in C, workpiece coordinate system:

By tool coordinate system X _ty _tz _tmiddle cutting force component $\left[\begin{array}{c}{\mathrm{dF}}_t\\ {\mathrm{dF}}_r\\ {\mathrm{dF}}_a\end{array}\right],$ Along contact blade integration, obtain the average cutting force three-component in tool coordinate system $\left[\begin{array}{c}{F}_{\mathrm{xt}}\\ F_{\mathrm{yt}}\\ F_{\mathrm{zt}}\end{array}\right],$ Then workpiece coordinate system is converted to $\left[\begin{array}{c}{F}_X\\ F_Y\\ F_Z\end{array}\right]:$

The demarcation of D, Cutting Force Coefficient:

Measure with dynamometer and obtain mean force signal, substitute into the average cutting force under the workpiece coordinate system of above-mentioned foundation $\left[\begin{array}{c}{F}_X\\ F_Y\\ F_Z\end{array}\right],$ Cutting Force Coefficient K to be calibrated is obtained by least square method _te, K _tc, K _re, K _rc, K _ae, K _ac.

(3) the Cutting Force Coefficient, according to step (2) obtained, sets up in Milling Process the differential equation describing power system Flutter Problem, this equation is transformed to a kind of neutral type matrix form equation, utilizes Laplace to convert, obtain its secular equation, be specifically calculated as follows:

$\stackrel{.}{X}\left(t\right)==\mathrm{AX}\left(t\right)+\mathrm{BX}(t-\mathrm{\τ})+p{\∫}_{-h}^{0}R\left(\mathrm{\θ}\right)X(t+\mathrm{\θ})\mathrm{d\θ}-p{\∫}_{-h}^{0}K\left(\mathrm{\θ}\right)X(t-\mathrm{\τ}+\mathrm{\θ})\mathrm{d\θ}---\left(1\right)$

Wherein utilize Laplace to convert, obtain its secular equation

$P\left(z\right)=\det [\mathrm{zI}-A-\stackrel{-}{B}-\stackrel{-}{R}\left(z\right)-\stackrel{-}{K\left(z\right)}]=0---\left(2\right)$

(4), according to the technological parameter of any one group of axial cutting-in, radial cutting-in, the speed of mainshaft and feed rate composition, by calculating the argument variable quantity of secular equation, to system in Milling Process under stability judge:

Whether the phase curve of A, secular equation P (z) and the imaginary axis have intersection point or whether comprise initial point o=(0,0), if the phase plane of P (z) and the imaginary axis do not have intersection point and do not comprise initial point, change at the RHP of phase plane, then Milling Process system stability:

The phase curve of B, secular equation P (z) and the imaginary axis have intersection point or comprise initial point, then system is unstable.

The invention has the beneficial effects as follows, the present invention utilizes Laplace to convert the secular equation obtaining system equation, carried out the stability of discriminant equation by the argument variable quantity calculating secular equation, the method calculates simple, and the theoretical research for cut provides a kind of new Convenient stable criterion.

Accompanying drawing explanation

Accompanying drawing 1 is workpiece coordinate system XYZ of the present invention and tool coordinate system X _ty _tz _tschematic diagram.

Accompanying drawing 2 is Milling Process system stability schematic diagram of the present invention.

Accompanying drawing 3 is the unstable schematic diagram of Milling Process system of the present invention.

Embodiment

The method of discrimination of system stability in a kind of Milling Process.The method comprises the following steps:

(1), utilize chip power experimental provision, by the technological parameter group that design one group is made up of axially different cutting-in, radial cutting-in, the speed of mainshaft and feed rate, carry out orthogonal experiment scheme respectively, obtain that one group of cutting force is tangential, radial, the experimental data of axial force component:

(2), (1) test the experimental data average recorded according to step, set up average cutting Force Model, Cutting Force Coefficient model, calculate average cutting force and Cutting Force Coefficient, be specifically calculated as follows:

A, definition of object co-ordinate systems XYZ and tool coordinate system X _ty _tz _t

Flat-bottomed cutter infinitesimal cutting Force Model is set up in B, (2):

$\left[\begin{array}{c}{\mathrm{dF}}_t\\ {\mathrm{dE}}_r\\ {\mathrm{dF}}_a\end{array}\right]=\left[\begin{array}{c}{K}_{\mathrm{te}}\mathrm{dS}+K_{\mathrm{tc}}\·t_n\·\mathrm{db}\\ K_{\mathrm{re}}\mathrm{dS}+K_{\mathrm{rc}}\·t_n\·\mathrm{db}\\ K_{\mathrm{ae}}\mathrm{dS}+K_{\mathrm{ac}}\·t_n\·\mathrm{db}\end{array}\right]$

Wherein, F _t, F _r, F _abe respectively tangential, radial, the axial force component of cutting force.DS, t _n, db is respectively in FCN coordinate system and represents contact arc length infinitesimal, is not out of shape and cuts thick infinitesimal and cut wide infinitesimal;

The calculating of average cutting force in C, workpiece coordinate system:

By tool coordinate system X _ty _tz _tmiddle cutting force component $\left[\begin{array}{c}{\mathrm{dF}}_t\\ {\mathrm{dF}}_r\\ {\mathrm{dF}}_a\end{array}\right],$ Along contact blade integration, obtain the average cutting force three-component in tool coordinate system $\left[\begin{array}{c}{F}_{\mathrm{xt}}\\ F_{\mathrm{yt}}\\ F_{\mathrm{zt}}\end{array}\right],$ Then workpiece coordinate system is converted to $\left[\begin{array}{c}{F}_X\\ F_Y\\ F_Z\end{array}\right]:$

The demarcation of D, Cutting Force Coefficient:

Measure with dynamometer and obtain mean force signal, substitute into the average cutting force under the workpiece coordinate system of above-mentioned foundation $\left[\begin{array}{c}{F}_X\\ F_Y\\ F_Z\end{array}\right],$ Cutting Force Coefficient K to be calibrated is obtained by least square method _te, K _tc, K _re, K _rc, K _ae, K _ac.

(3) the Cutting Force Coefficient, according to step (2) obtained, sets up in Milling Process the differential equation describing power system Flutter Problem, this equation is transformed to a kind of neutral type matrix form equation, utilizes Laplace to convert, obtain its secular equation, be specifically calculated as follows:

$\stackrel{.}{X}\left(t\right)==\mathrm{AX}\left(t\right)+\mathrm{BX}(t-\mathrm{\τ})+p{\∫}_{-h}^{0}R\left(\mathrm{\θ}\right)X(t+\mathrm{\θ})\mathrm{d\θ}-p{\∫}_{-h}^{0}K\left(\mathrm{\θ}\right)X(t-\mathrm{\τ}+\mathrm{\θ})\mathrm{d\θ}---\left(1\right)$

Wherein utilize Laplace to convert, obtain its secular equation

$P\left(z\right)=\det [\mathrm{zI}-A-\stackrel{-}{B}-\stackrel{-}{R}\left(z\right)-\stackrel{-}{K\left(z\right)}]=0---\left(2\right)$

(4), according to the technological parameter of any one group of axial cutting-in, radial cutting-in, the speed of mainshaft and feed rate composition, by calculating the argument variable quantity of secular equation, to system in Milling Process under stability judge:

Whether the phase curve of A, secular equation P (z) and the imaginary axis have intersection point or whether comprise initial point o=(0,0), if the phase plane of P (z) and the imaginary axis do not have intersection point and do not comprise initial point, change at the RHP of phase plane, then Milling Process system stability:

The phase curve of B, secular equation P (z) and the imaginary axis have intersection point or comprise initial point, then system is unstable.

In the embodiment of the present invention, by calculating the stability under different parameters, obtain the stability Lobe figure of power system, the differentiation carrying out Milling Process system stability of intuitive and convenient.

Claims (2)

1. the method for discrimination of system stability in a Milling Process.It is characterized in that: the method comprises the following steps:

(1), utilize chip power experimental provision, by the technological parameter group that design one group is made up of axially different cutting-in, radial cutting-in, the speed of mainshaft and feed rate, carry out orthogonal experiment scheme respectively, obtain that one group of cutting force is tangential, radial, the experimental data of axial force component:

(2), (1) test the experimental data average recorded according to step, set up average cutting Force Model, Cutting Force Coefficient model, calculate average cutting force and Cutting Force Coefficient, be specifically calculated as follows:

A, definition of object co-ordinate systems XYZ and tool coordinate system X _ty _tz _t

B, set up flat-bottomed cutter infinitesimal cutting Force Model:

$\left[\begin{array}{c}{\mathrm{dF}}_t\\ {\mathrm{dE}}_r\\ {\mathrm{dF}}_a\end{array}\right]=\left[\begin{array}{c}{K}_{\mathrm{te}}\mathrm{dS}+K_{\mathrm{tc}}\·t_n\·\mathrm{db}\\ K_{\mathrm{re}}\mathrm{dS}+K_{\mathrm{rc}}\·t_n\·\mathrm{db}\\ K_{\mathrm{ae}}\mathrm{dS}+K_{\mathrm{ac}}\·t_n\·\mathrm{db}\end{array}\right]$

Wherein, F _t, F _r, F _abe respectively tangential, radial, the axial force component of cutting force.DS, t _n, db is respectively in FCN coordinate system and represents contact arc length infinitesimal, is not out of shape and cuts thick infinitesimal and cut wide infinitesimal;

The calculating of average cutting force in C, workpiece coordinate system:

By tool coordinate system X _ty _tz _tmiddle cutting force component $\left[\begin{array}{c}{\mathrm{dF}}_t\\ {\mathrm{dF}}_r\\ {\mathrm{dF}}_a\end{array}\right],$ Along contact blade integration, obtain the average cutting force three-component in tool coordinate system $\left[\begin{array}{c}{F}_{\mathrm{xt}}\\ F_{\mathrm{yt}}\\ F_{\mathrm{zt}}\end{array}\right],$ Then workpiece coordinate system is converted to $\left[\begin{array}{c}{F}_X\\ F_Y\\ F_Z\end{array}\right]:$

The demarcation of D, Cutting Force Coefficient:

Measure with dynamometer and obtain mean force signal, substitute into the average cutting force under the workpiece coordinate system of above-mentioned foundation $\left[\begin{array}{c}{F}_X\\ F_Y\\ F_Z\end{array}\right],$ Cutting Force Coefficient K to be calibrated is obtained by least square method _te, K _tc, K _re, K _rc, K _ae, K _ac.

(3) the Cutting Force Coefficient, according to step (2) obtained, sets up in Milling Process the differential equation describing power system Flutter Problem, this equation is transformed to a kind of neutral type matrix form equation, utilizes Laplace to convert, obtain its secular equation, be specifically calculated as follows:

$\stackrel{.}{X}\left(t\right)==\mathrm{AX}\left(t\right)+\mathrm{BX}(t-\mathrm{\τ})+p{\∫}_{-h}^{0}R\left(\mathrm{\θ}\right)X(t+\mathrm{\θ})\mathrm{d\θ}-p{\∫}_{-h}^{0}K\left(\mathrm{\θ}\right)X(t-\mathrm{\τ}+\mathrm{\θ})\mathrm{d\θ}---\left(1\right)$

Wherein utilize Laplace to convert, obtain its secular equation

$P\left(z\right)=\det [\mathrm{zI}-A-\stackrel{-}{B}-\stackrel{-}{R}\left(z\right)-\stackrel{-}{K\left(z\right)}]=0---\left(2\right)$

(4), according to the technological parameter of any one group of axial cutting-in, radial cutting-in, the speed of mainshaft and feed rate composition, by calculating the argument variable quantity of secular equation, to system in Milling Process under stability judge:

Whether the phase curve of A, secular equation P (z) and the imaginary axis have intersection point or whether comprise initial point o=(0,0), if the phase plane of P (z) and the imaginary axis do not have intersection point and do not comprise initial point, change at the RHP of phase plane, then Milling Process system stability:

The phase curve of B, secular equation P (z) and the imaginary axis have intersection point or comprise initial point, then system is unstable.

2. the method for discrimination of system stability in a kind of Milling Process according to claim 1, is characterized in that: by calculating the stability under different parameters, obtains the stability Lobe figure of power system, carries out the differentiation of Milling Process system stability.