CN112859746A - Complex curved surface residual height calculation method based on isoparametric curve method - Google Patents

Abstract

The invention discloses a method for calculating the residual height of a complex curved surface based on an isoparametric curve method, which is mainly used for calculating the residual height of the curved surface when a ball-end milling cutter is used for processing the complex curved surface. The method comprises the steps of parameterizing a free curved surface, generating a processing tool path track through an isoparametric curve method, dispersing the processing tool path track into a plurality of scattered points according to uv of the curved surface, and then projecting and transforming the coordinates of the scattered points on one track to obtain the surface of a workpiece on a two-dimensional plane. And (3) fitting the coordinate points of the surface of the workpiece by adopting a polynomial to obtain a characterization function equation, performing mathematical modeling on the process of cutting the surface of the curved surface by the cutter, and calculating to obtain the relation between the surface residual height and the line spacing. When the method is applied to the ball end milling cutter for processing the complex curved surface, the calculation of the residual height of the curved surface under different processing line distances is calculated, and a certain guiding function is played for the selection of the line distances in the processing process, so that the processing efficiency is improved as much as possible while the processing precision is ensured.

Description

Complex curved surface residual height calculation method based on isoparametric curve method

Technical Field

The invention belongs to the field of CAD/CAM, and particularly relates to a method for calculating residual height under the current machining line spacing based on a parameter line of a curved surface when a ball end mill is used for machining a complex curved surface.

Background

The free-form surface is different from a regular surface, the shape of the free-form surface is often difficult to represent through a mathematical expression, but a part designed based on the free-form surface has excellent performances such as fluid dynamics, aerodynamics and the like. The machining of the free-form surface is closely related to the multi-axis numerical control technology, and the machining precision of the free-form surface can greatly influence the performance of the part, so that how to obtain the free-form surface part with good surface quality becomes one of the research hotspots of a plurality of scholars.

In multi-axis numerical control machining, a ball end milling cutter is mostly adopted for curved surface machining. The tool path planning of the ball end mill comprises parameter settings of a machining step length and a machining step pitch, and the machining step pitch can influence the residual height of a machined surface, so that the surface precision of the machined surface is influenced. At present, when the numerical value of the residual height in the machining is calculated, the surfaces of the workpieces in two adjacent tracks are equivalent to straight lines or fixed-curvature arcs, however, the curvature of the surface of an actual free-form surface is complex, and an accurate residual height numerical value is difficult to obtain by using an equivalent mode.

Disclosure of Invention

The invention aims to further characterize the relation between the residual height and the processing line distance and calculate the influence of the processing line distance under the surface of any workpiece on the residual height. A method for calculating the residual height of a complex curved surface based on an isoparametric curve method is provided. The specific technical scheme is as follows:

a method for calculating the residual height of a complex curved surface based on an isoparametric curve method comprises the following steps:

and S1, parameterizing the free-form surface, and describing the surface F (u, v) by uv two parameters.

S2, selecting any curve F (v) in the curved surfaces_j) Dispersing the curve into a plurality of scattered points according to the UV parameters, and generating a tool path track by adopting an isoparametric line method on the curved surface, wherein the line spacing is a curve F (v)_j) Point F (u) on_i，v_j) And point F (u)_i+1，v_j) The distance between them.

S3, making a passing point F (u)₁，v_j) About a perpendicular to the v-direction, and curve F (v)_j) Point ofProjecting along the normal direction of the perpendicular line to obtain a straight line F (v)_jL)。

S4, straight line F (v) at this time_jL) Coordinate points in coordinate point set A above can be represented by the parametric equation F (x (u)_i，v_jL)，y(u_i，v_jL)，z(u_i，v_jL) Is expressed) and coordinate-transforms coordinate points in the coordinate point set so that their coordinates x (u) in the x direction_i，v_jL) Are equal, and the equation of the coordinate point set A becomes F (x (u)_i′，v_jL′)，y(u_i′，v_jL′)，z(u_i′，v_jL′))。

And S5, performing polynomial fitting on the coordinate points in the coordinate point set A to obtain a curve parallel to the YZ plane, and converting the curve in the three-dimensional space into a curve in the two-dimensional plane. The curve equation can be simplified to F' (y (u)_i′，v_jL′)，z(u_i′，v_jL′) Replace y (u) in the original equation with x_i′，v_jL′) Replacing z (u) in the original equation with y_i′，v_jL′) And converting the equation of the curve into F' (x, y), namely, the function expression of the surface of the processed curved surface.

S6, performing mathematical modeling on the process of cutting the curved surface by the cutter, and assuming that the cutter contact point of the ith machining track is CC_i(x_cci，y_cci，i_cci，j_cci) Wherein x is_cci，y_cciAs coordinates of the knife contact, i_cci，j_cciIs the knife axis vector of the knife contact. CL_i(x_cli，y_cli) The coordinates of the knife location point. T is_i(x_ti，y_ti) And T_i+1(x_ti+1，y_ti+1) And (4) an envelope equation of the ith machining path tool and the (i + 1) th machining path tool. L is_iAnd (3) the line spacing between the ith machining track and the (i + 1) th machining track, and r is the radius of the ball end mill cutter. The relationship shown in the following formula can be established

x_cli＝x_cci+i_ccir

y_cli＝y_cci+j_ccir

T_i＝(x-x_cci)²+(y-y_cci)²-r²

T_i+1＝(x-x_cci+1)²+(y-y_cci+1)²-r²

Two point coordinates required for solving the residual height are respectively set as RS_i1(x_rsi1，y_rsi1) And RS_i2(x_rsi2，y_rsi2) The equation of the straight line of these two points is RS (x, y). The following expression can be established corresponding to the relationship between the variables

RS can be obtained from the above two equations_i1And RS_i2The residual height is the distance between two points.

The method for making the v-direction perpendicular line equation in the step S3 is as follows:

curve F (v)_j) Can be expressed as a parametric equation F (v) for u_j(t)), the tangent vector of the curve at a certain point is:

x is the normal vector representing the solved perpendicular.

And repeating the steps S2-S5, and traversing all curves on the free-form surface to obtain an accurate value of the residual height left by the tool path track.

Compared with the prior art, the invention has the beneficial effects that: according to the method, after the free-form surface part is parameterized, the curve is fitted, so that the surface of the part which is more accurate than that of the part which is obtained by the traditional method and is equivalent to a plane or a cambered surface between two machining tracks is obtained, and the calculation of the residual height of the workpiece is more accurate.

Drawings

FIG. 1 is an overall flow chart of the process

FIG. 2 is a graph showing the result of parameterization of a free-form surface to be machined

FIG. 3 is a processing trace diagram generated by isoparametric line generation

FIG. 4 is a plurality of scatter plots of the discretized surface after parameterization

FIG. 5 shows a transition point F (u)₁，v_j) Making a perpendicular to curve F (v)_j) Vertical line drawing of

FIG. 6 is a mathematical modeling diagram of a process

FIG. 7 is a diagram illustrating the calculation result of the residual height

Detailed Description

The embodiments of the present invention will be described in detail below with reference to the accompanying drawings:

as shown in fig. 1, a method for calculating the residual height of a complex curved surface based on an isoparametric curve method includes the following steps:

s1, parameterize the free form surface as shown in fig. 2, and describe the surface F (u, v) by uv two-parameter.

S2, as shown in fig. 3 and 4, selecting any one curve F (v) in the curved surfaces_j) Dispersing the curve into a plurality of scattered points according to the UV parameters, and generating a tool path track by adopting an isoparametric line method on the curved surface, wherein the line spacing is a curve F (v)_j) Point F (u) on_i，v_j) And point F (u)_i+1，v_j) The distance between them.

S3, as shown in FIG. 5, a point F (u) is reached₁，v_j) About a perpendicular to the v-direction, and curve F (v)_j) The point on the surface is projected along the normal direction of the perpendicular line direction to obtain a straight line F (v)_jL)。

S4, straight line F (v) at this time_jL) Coordinate points in coordinate point set A above can be represented by the parametric equation F (x (u)_i，v_jL)，y(u_i，v_jL)，z(u_i，v_jL) Is expressed) and coordinate-transforms coordinate points in the coordinate point set so that their coordinates x (u) in the x direction_i，v_jL) Are equal, and the equation of the coordinate point set A becomes F (x (u)_i′，v_jL′)，y(u_i′，v_jL′)，z(u_i′，v_jL′))。

And S5, performing polynomial fitting on the coordinate points in the coordinate point set A to obtain a curve parallel to the YZ plane, and converting the curve in the three-dimensional space into a curve in the two-dimensional plane. The curve equation can be simplified to F' (y (u)_i′，v_jL′)，z(u_i′，v_jL′) Replace y (u) in the original equation with x_i′，v_jL′) Replacing z (u) in the original equation with y_i′，v_jL′) And converting the equation of the curve into F' (x, y), namely, the function expression of the surface of the processed curved surface.

S6, performing mathematical modeling on the process of cutting the curved surface by the cutter, and assuming that the cutter contact point of the ith machining track is CC_i(x_cci，y_cci，i_cci，j_cci) Wherein x is_cci，y_cciAs coordinates of the knife contact, i_cci，j_cciIs the knife axis vector of the knife contact. CL_i(x_cli，y_cli) The coordinates of the knife location point. T is_i(x_ti，y_ti) And T_i+1(x_ti+1，y_ti+1) And (4) an envelope equation of the ith machining path tool and the (i + 1) th machining path tool. L is_iAnd (3) the line spacing between the ith machining track and the (i + 1) th machining track, and r is the radius of the ball end mill cutter. The relationship shown in the following formula can be established

x_cli＝x_cci+i_ccir

y_cli＝y_cci+j_ccir

T_i＝(x-x_cci)²+(y-y_cci)²-r²

T_i+1＝(x-x_cci+1)²+(y-y_cci+1)²-r²

Two point coordinates required for solving the residual height are respectively set as RS_i1(x_rsi1，y_rsi1) And RS_i2(x_rsi2，y_rsi2) The equation of the straight line of these two points is RS (x, y). The following expression can be established corresponding to the relationship between the variables

RS can be obtained from the above two equations_i1And RS_i2The residual height is the distance between two points.

The method for making the v-direction perpendicular line equation in the step S3 is as follows:

curve F (v)_j) Can be expressed as a parametric equation F (v) for u_j(t)), the tangent vector of the curve at a certain point is:

x is the normal vector representing the solved perpendicular.

Example of the implementation

The coordinates of the points on the surface of the curved surface to be processed are shown in the following table

CLS files of the processing tracks are shown in the following table

Serial number	X(mm)	Y(mm)	Z(mm)	i	j	k
								1	30	87.1719	87.4046	0.1960035	0.6267468	0.7541692
2	30	89.9692	85.1514	0.1908968	0.6038797	0.7738784
							3	30	92.8132	83.0028	0.1854803	0.5798698	0.7933146
4	30	95.7753	80.9112	0.1796095	0.5541014	0.812842
							5	30	98.8128	78.9146	0.1733604	0.526937	0.8320358
6	30	101.8925	77.037	0.1668055	0.4987096	0.8505673
							7	30	105.016	75.2775	0.159953	0.4694661	0.8683413
8	30	108.185	73.6351	0.1528142	0.4392654	0.8852648
							9	30	111.4014	72.1092	0.1454036	0.4081777	0.9012485
10	30	114.6671	70.6996	0.1377387	0.3762846	0.9162085
							11	30	117.9831	69.4064	0.1298427	0.3436883	0.9300641
12	30	121.3443	68.2322	0.1217566	0.3105615	0.9427231
							13	30	124.7497	67.1773	0.1135145	0.277044	0.9541285
14	30	128.1993	66.2417	0.1051497	0.2432705	0.9642422
							15	30	131.6932	65.4255	0.0966968	0.2093773	0.9730421
16	30	135.2313	64.7286	0.0881909	0.1754999	0.9805214
							17	30	138.8136	64.151	0.0796666	0.14177	0.9866887
18	30	142.4041	63.6968	0.0712418	0.1086429	0.9915248
							19	30	145.9542	63.3659	0.0630545	0.0766428	0.9950628
20	30	149.5107	63.1483	0.0550173	0.045409	0.9974523
							21	30	153.1209	63.04	0.0470466	0.0146061	0.9987859

The fitting equation of the workpiece surface is shown as the following formula

F′(x，y)＝1.1909*10^-7*x⁴-8.1165*10^-5*x³+0.024869*x²-3.6304*x-y+261.78

The radius of the processing cutter is 5mm, and the processing step distance is 8.5 mm.

The obtained processing residue heights are shown in the following table

Serial number	Residual height (mm)
		1	0.224867423
2	0.222858028
		3	0.238573742
4	0.245649715
		5	0.246407903
6	0.248437479
		7	0.251501121
8	0.255376524
		9	0.260042588
10	0.265325583
		11	0.270120007
12	0.275410961
		13	0.281471589
14	0.288490106
		15	0.296487021
16	0.305356495
		17	0.308266072
18	0.302542971
		19	0.304912373
20	0.314587565

Claims (2)

1. A method for calculating the residual height of a complex curved surface based on an isoparametric curve method is characterized by comprising the following steps of:

s1, parameterizing the free curved surface, and describing the curved surface F (u, v) through uv two parameters;

s2, selecting any curve F (v) in the curved surfaces_j) Dispersing the curve into a plurality of scattered points according to the UV parameters, and generating a tool path track by adopting an isoparametric line method on the curved surface, wherein the line spacing is a curve F (v)_j) Point F (u) on_i，v_j) And point F (u)_i+1，v_j) The distance between them;

s3, making a passing point F (u)₁，v_j) About a perpendicular to the v-direction, and curve F (v)_j) The point on the surface is projected along the normal direction of the perpendicular line direction to obtain a straight line F (v)_jL)；

S4, straight line F (v) at this time_jL) Coordinate points in coordinate point set A above can be represented by the parametric equation F (x (u)_i，v_jL)，y(u_i，v_jL)，z(u_i，v_jL) Is expressed) and coordinate-transforms coordinate points in the coordinate point set so that their coordinates x (u) in the x direction_i，v_jL) Are all equal to each other, thisThe equation of the time coordinate point set A becomes F (x (u)_i′，v_jL′)，y(u_i′，v_jL′)，z(u_i′，v_jL′))；

S5, performing polynomial fitting on coordinate points in the coordinate point set A to obtain a curve parallel to a YZ plane, and converting the curve in a three-dimensional space into a curve in a two-dimensional plane; the curve equation can be simplified to F' (y (u)_i′，v_jL′)，z(u_i′，v_jL′) Replace y (u) in the original equation with x_i′，v_jL′) Replacing z (u) in the original equation with y_i′，v_jL′) Converting the equation of the curve into F' (x, y), namely a function expression of the surface of the processed curved surface;

and S6, performing mathematical modeling on the process of cutting the curved surface by the cutter, and calculating to obtain the relation between the surface residual height and the line spacing.

2. The method of claim 1, wherein the step S6 is performed by mathematically modeling the process of the tool cutting the curved surface as follows: suppose the contact point of the cutter of the ith processing track is CC_i(x_cci，y_cci，i_cci，j_cci) Wherein x is_cci，y_cciAs coordinates of the knife contact, i_cci，j_cciIs the knife axis vector of the knife contact; CL_i(x_cli，y_cli) The coordinates of the knife location point; t is_i(x_ti，y_ti) And T_i+1(x_ti+1，y_ti+1) An envelope equation of the ith and (i + 1) th machining track cutters is obtained; l is_iThe line spacing between the ith and (i + 1) th processing tracks is defined, and r is the radius of the ball end mill cutter; the relationship shown in the following formula is established

x_cli＝x_cci+i_ccir

y_cli＝y_cci+j_ccir

T_i＝(x-x_cci)²+(y-y_cci)²-r²

T_i+1＝(x-x_cci+1)²+(y-y_cci+1)²-r²

Two point coordinates required for solving the residual height are respectively set as RS_i1(x_rsi1，y_rsi1) And RS_i2(x_rsi2，y_rsi2) The equation of the straight line where the two points are located is RS (x, y); the following expression can be established corresponding to the relationship between the variables

RS can be obtained from the above two equations_i1And RS_i2The residual height is the distance between two points;

the method for making the v-direction perpendicular line equation in the step S3 is as follows:

curve F (v)_j) Can be expressed as a parametric equation F (v) for u_j(t)), the tangent vector of the curve at a certain point is:

x is the normal vector representing the solved perpendicular.

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