Point layout optimization method for follow-up support head in mirror milling and follow-up support head

A point layout optimization method for a follow-up support head in mirror milling, the method is used to optimize and adjust the point layout of the follow-up support head in mirror milling in combination with specific working conditions, support points in the follow-up support head comprise a central support point and peripheral support points arranged circularly around the central support point, wherein the point layout optimization method comprises the following steps:

• S1:
• establishing a coupling vibration model of cutter, workpiece, and support head in mirror milling, comprising the following process:
• S11:
• defining a milling force acting on an axial direction of the workpiece as Fm(t), moving paths of a center point of a milling cutter are , and generating a milling excitation qm(x,y,t) by combining a Dirac function δ;
• S12:
• defining a total quantity of support points of the support head as n, where 1 support point is located at a center of the support head, and remaining n−1 support points are evenly distributed on a circle with a radius of r;
• n and r are characteristic parameters that characterize the point layout of the follow-up support head;
• S13:
• defining moving paths of the central support point as , and generating moving paths of each peripheral support point as (t), where i=2, 3 . . . n;
• S14:
• defining a total support force provided by the support head as Fs(t), and generating a support excitation qs(x,y,t) by combining the moving paths of each peripheral support point (t) and the Dirac function δ;
• and
• S15:
• defining a transverse deflection perpendicular to a machining surface in mirror milling as w(x,y,t), based on a Kirchhoff-Love hypothesis, establishing a coupled vibration model of an equal-thickness plate component under external excitation as follows:
• D
• ⁡
• (
• ∂
• 4
• w
• ∂
• x
• 4
• +
• 2
• ⁢
• ∂
• 4
• w
• ∂
• x
• 2
• ⁢
• ∂
• y
• 2
• +
• ∂
• 4
• w
• ∂
• y
• 4
• )
• +
• ρ
• ⁢
• h
• ⁢
• ∂
• 2
• w
• ∂
• t
• 2
• =
• q
• ⁡
• (
• x
• ,
• y
• ,
• t
• )
• where q(x,y,t) denotes an additional excitation on a unit area of the workpiece, the additional excitation is composed of the milling excitation qm(x,y,t) and the support excitation qs(x,y,t);
• D denotes a bending stiffness of the workpiece, h denotes the wall thickness of the workpiece;
• ρ denotes a density of the workpiece;
• S2:
• weighting a vibration peak ƒ1 of points at different positions on a coupling contact area at different times and a root mean square ƒ2 of a vibration of each point in an investigation period as an objective function ƒ to evaluate a vibration of a machining process, an optimization goal is as follows:
• min ƒ=α1ƒ1+α2ƒ2
• where α1 and α2 are weight coefficients of the vibration peak ƒ1 and the root mean square ƒ2 of each point vibration, and satisfy α1+α2=1;
• S3:
• combining spatial layouts and moving paths of the center support point and the peripheral support points of the follow-up support head, establishing a spatial constraint equation and a quantity constraint equation of the support points in the follow-up support head;
• S4:
• taking n and r as design variables, establishing a single-objective optimization model representing a current optimization problem combined with the coupled vibration model, objective function, and constraint equation;
• S5:
• solving the single-objective optimization model by a swarm intelligence optimization algorithm to obtain a globally optimal quantity of support points n and a radius of the distribution circle r;
• a solution strategy is as follows:
• (1) choosing any one of the swarm intelligence optimization algorithms as a dominant algorithm of the solution process;
• (2) according to the constraint equation established in S3, calculating an upper limit the quantity of support points n, and then determining m candidate values of discrete design variable n, then transforming a bivariate optimization process of an iterative optimization process into an optimization process of a parallel processing of a single variable r in m different populations;
• and
• (3) introducing a penalty function F to modify a fitness function fit of the swarm intelligence optimization algorithm when it is updated iteratively:
• fit=ƒ+F;
• and
• S6:
• according to preferred values of n and r, adjusting the quantity of support points in the follow-up support head and a distribution radius of the peripheral support points.