CN105234743A - Deflection error compensation method for five-axis machining center tool - Google Patents

Abstract

The invention discloses a tool deformation error compensation method of a five-axis machining center. The method includes: calculating the magnitude of the milling force according to the established five-axis machining milling force model; Benchmark; calculate the tool deformation error caused by the milling force at the current tool position according to the tool deformation; perform mirror image anti-deformation compensation on the current tool position point and tool axis vector, and obtain a new tool position point and tool axis vector based on the tool deformation error calculation ;Calculate the new tool deformation error based on the compensated tool position point data, and judge whether the new error is true; if the requirements are met, stop the calculation and save the tool position point information; sort out the compensation tool corresponding to the tool path position from 1 to N Position data information, and then get the compensated tool position trajectory, and generate the compensated NC machining program through the post-processing software.

Description

A Compensation Method for Tool Deformation Error of Five-axis Machining Center

technical field

The invention relates to the technical field of numerical control machining, in particular to a tool deformation error compensation method for a five-axis machining center.

Background technique

In the actual processing process, the milling system is generally composed of machine tools, tools, fixtures, and workpieces. The rigidity of the machine tools and fixtures is generally considered to be sufficient, and the deformation of the workpiece (non-thin-walled parts) is relatively small. The rigidity of the tool is relatively fragile, and the deformation of the tool in the milling system is an unavoidable problem, especially when using a "slender rod" tool for processing, the deformation of the tool cannot be ignored, and it is prone to bending under the action of cutting force Deformation is the main factor causing the geometric error of the machined surface. Five-axis linkage CNC technology has unique advantages in the processing of complex shapes and surfaces, that is, it can maintain the optimal cutting state of the tool and avoid tool interference by adjusting the position and posture of the tool, thereby improving the processing and manufacturing accuracy of the part. Therefore, it is of great significance to analyze tool deformation and study error compensation methods during five-axis machining.

(1) RaoVS and RaoPVM proposed a tool deformation error compensation method caused by cutting force through the analysis of tool deformation during machining. (See RaoVS, RaoPVM (2006) Tooldeflection compensation in peripheral milling of curved geometries. Int J Mach Tools Manuf 46 (15): 2036-2043).

(2) BeraTC, DesaiKA and RaoPVM analyzed the comprehensive influence of tool deformation and thin-walled part deformation on machining errors during milling, and compensated the errors by changing the tool path during machining, and the laboratory verified this method feasibility. (See Bera TC, Desai KA, Rao PVM (2011) Error compensation inflexible end milling of tube large geometries. Journal of Materials Processing Technology 211 (1): 24-34).

(3) ZhuS, DingG, QinS, LeiJ, ZhuangL and YanK used a ballbar to identify the geometric errors of five-axis machine tools, and established a machining error compensation model caused by machine tool errors. (See ZhuS, DingG, QinS, LeiJ, ZhuangL, YanK (2012) Integrated geometry error modeling, identification and compensation of CNC machine tools. IntJ MachToolsManuf52 (1): 24-29).

The tool deformation error compensation method proposed in literature (1) (2) is mainly for three-axis machining, and it is not applicable to tool deformation error compensation for five-axis machining.

The error compensation model established in literature (3) considers the geometric error during the machine tool motion process, but does not involve the tool deformation error during the five-axis machine tool machining process.

Contents of the invention

The invention provides a tool deformation error compensation method for a five-axis machining center. The invention analyzes the amount of tool deformation in the five-axis machining process and considers the influence of the tool deformation on the machining profile, and proposes a method for five-axis machining The advanced tool deformation error compensation method provides a theory for high-precision machining of complex curved surface parts. See the description below for details:

A five-axis machining center tool deformation error compensation method, the error compensation method includes the following steps:

Establish the mutual conversion relationship between the tool coordinate system, workpiece coordinate system and machine tool coordinate system, and obtain the motion parameters of the machine tool during five-axis machining;

In the tool coordinate system, obtain the deformation of the tool; read the theoretical tool position trajectory data file automatically generated by the CAM software;

Calculate the milling force according to the established five-axis machining milling force model; use the theoretical tool position point and tool axis vector as the benchmark for mirror image anti-deformation compensation;

Calculate and obtain the tool deformation error caused by the milling force at the current tool position according to the tool deformation;

Perform mirror image anti-deformation compensation on the current tool position point and tool axis vector, and calculate new tool position point and tool axis vector according to the tool deformation error;

Calculate the new tool deformation error based on the compensated tool position point data, and judge whether the new error is true; if it meets the requirements, stop the calculation and save the tool position point information;

Organize the data information of the compensated tool position points corresponding to the position of the tool path from 1 to N, and then obtain the compensated tool position trajectory, and generate the compensated NC machining program through the post-processing software.

The beneficial effect of the technical solution provided by the invention is that the invention establishes a tool deformation model in a five-axis machining process based on the cantilever beam theory. Before the actual processing, the error amount caused by the machining surface of the workpiece is obtained through the calculation of the established tool force deformation model, the tool position trajectory file automatically generated by the CAM software is modified, and the theoretical tool position trajectory is offset along the surface of the processed part. Set the same error amount to achieve error compensation, and finally use the modified tool path file in the actual machining process, thereby improving the manufacturing accuracy of five-axis machining. Finally, the effectiveness of the method is verified by cutting experiments.

Description of drawings

Figure 1 is a motion diagram of a five-axis machining center;

Figure 2 is a schematic diagram of tool deformation;

3 is a schematic diagram of an error compensation method;

Fig. 4 is a reference base diagram for tool axis vector compensation;

Figure 5 is a reference map for tool point compensation;

Fig. 6 is a processing part diagram;

Figure 7 Error distribution comparison chart;

Fig. 8 is a flow chart of a tool deformation error compensation method for a five-axis machining center.

detailed description

In order to make the purpose, technical solution and advantages of the present invention clearer, the implementation manners of the present invention will be further described in detail below.

The specific implementation of the embodiment of the present invention will be described in detail below in conjunction with the accompanying drawings, taking the milling of the ball end of the five-axis linkage machine tool with the B swing head and the C turntable as an example.

101: Establish the mutual conversion relationship between the tool coordinate system, workpiece coordinate system and machine tool coordinate system, and obtain the motion parameters of the machine tool during five-axis machining;

The embodiment of the present invention takes a five-axis CNC machine tool with C turntable and B swing head structure as an example, analyzes the kinematic relationship between coordinates, and establishes the conversion relationship between the tool coordinate system, the workpiece coordinate system and the machine tool coordinate system.

In order to facilitate the description of the tool's trajectory during the five-axis machine tool machining process, the coordinate system shown in Figure 1 is established. In the initial state of the machine tool, the workpiece coordinate system [O _w , X _w , Y _w , Z _w ] is in the same direction as the machine tool coordinate system [O _m , X _m , Y _m , Z _m ], and the origin of the workpiece coordinate system and the machine tool coordinate system origin Coincident; the origin of the tool coordinates [O _c , X _c , Y _c , Z _c ] is at the tool tip, and the direction of its coordinate system is consistent with the machine tool coordinate system; [O _m1 , X _m1 , Y _m1 , Z _m1 ] are the rotation coordinates system, the rotation angle of the tool around the axis Y _m1 is θ _B (counterclockwise is positive), and its coordinate system direction is consistent with the machine tool coordinate system; [O _m2 , X _m2 , Y _m2 , Z _m2 ] is the rotary coordinate system, and the workpiece The rotation angle of axis Z _m2 is θ _C (counterclockwise is positive), and the direction of its coordinate system is consistent with that of the machine tool coordinate system. In the initial state of the machine tool, the distance between O _c O _m1 is L, the distance between O _w O _m2 is H, and the initial state of the translation axis of the machine tool is in Respectively represent the initial position of X, Y, Z axes of the machine tool. Any point in the tool coordinate system can be converted to the workpiece coordinate system, and the coordinate transformation matrix T is:

T＝T ₅ T ₄ T ₃ T ₂ T ₁ (1)

${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; L</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; L</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; h</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$

${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}& {\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}& {\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$

In formula (1), T ₁ , T ₃ and T ₅ are translation matrices, and T ₂ and T ₄ are rotation matrices.

In the tool coordinate system, the position vector of any point q can be expressed as The direction vector of the directed line segment formed by point q and the origin of tool coordinates can be expressed as In the workpiece coordinate system, the corresponding position vector of point q can be expressed as The direction vector of the directed line segment formed by point q and the origin of workpiece coordinates can be expressed as Therefore, the conversion relation of any point in the tool coordinate system relative to the workpiece coordinate system is:

${<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&rsqb;</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; T</span>}{<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&rsqb;</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

${<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&rsqb;</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&rsqb;</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Expand formulas (2) and (3) to get:

$<span\; class="notranslate">\; \{</span>\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; L</span>}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}\\ {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; L</span>}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}\\ {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; L</span>}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}\\ {\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}\\ {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In five-axis NC programming, the tool trajectory generated by CAD/CAM software is generally calculated based on the CAD model of the workpiece to obtain the position vector and direction vector of the tool tip point relative to the workpiece. Therefore, the position vector and direction vector of the tool nose point in the tool coordinate system can be expressed as and Substitute into formula (4) to get:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; L</span>}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}\\ {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; L</span>}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}\\ {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; L</span>}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}\\ {\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}\\ {\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}\\ {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

The motion parameters of the machine tool in the five-axis machining process can be obtained by formula (5).

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; L</span>}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}\\ {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}\\ {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; L</span>}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; L</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

102: Under the tool coordinate system, obtain the deformation δx ^C , δy ^C of the tool in the X _c , Y _c directions;

The tool deformation is calculated according to the cantilever beam theory, as shown in Figure 2. In the tool coordinate system, the tool is stretched or compressed due to the cutting force acting on the axial direction _Zc , and the cutting force in the direction of _Xc and _Yc causes it to bend and deform, and it is generally considered that the rigidity of the tool in the direction of _Zc Larger, the influence on the error of the milling profile is very small, and it is generally ignored. Therefore, the bending deformation generated by the tool in the X _c and Y _c directions is mainly considered. In the tool coordinate system, the deformation δx ^C , δy ^C in the direction of X _c , Y _c can be expressed as:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&delta;x</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 6</span>}\mathrm{<span\; class="notranslate">\; E.</span>}\mathrm{<span\; class="notranslate">\; I</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&delta;y</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; Y</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 6</span>}\mathrm{<span\; class="notranslate">\; E.</span>}\mathrm{<span\; class="notranslate">\; I</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

In the formula, Respectively represent the component force in the direction of X _c , Y _c ; D is the overhang length of the tool rod; a _p is the cutting depth; E is the elastic modulus of the tool material; I is the moment of inertia of the tool _; Location.

Five-axis machining tool deformation error compensation is mainly divided into two aspects: tool position point compensation and tool axis vector compensation. As shown in Figure 3.

103: Read the theoretical tool position trajectory data file automatically generated by the CAM software, the coordinates of the i-th tool position point are The tool axis vector is i∈(1,N), N is the number of tool positions;

104: The initialization cycle starts, i=1; calculate the magnitude of the milling force according to the established five-axis machining milling force model;

105: Use the theoretical tool position point and tool axis vector as the benchmark for mirror image anti-deformation compensation;

106: Calculate and obtain the tool deformation error E ₁ caused by the milling force at the current tool position according to the tool deformation;

107: Perform mirror image anti-deformation compensation on the current tool position point and tool axis vector, and calculate and obtain new tool position point and tool axis vector according to the tool deformation error E ₁ ;

108: Calculate the new tool deformation error E ₂ according to the compensated tool position point data, and judge whether the new error E ₂ <ε (tolerance) is established;

If the requirements are met, then stop the operation, save the tool location point information, and execute step 109; otherwise, go to step 106 until the requirements are met;

109: Organize the data information of the compensated tool position point corresponding to the position of the tool path from 1 to N, and then obtain the compensated tool position trajectory, and generate the compensated NC machining program through the post-processing software.

According to the cantilever beam deformation theory, the deformation of the tool in the axial direction is an arc. Therefore, if the error compensation reference standard is selected unreasonably, it will lead to "overcut" or "undercut" in the compensation process, especially in the process of side milling, the compensation effect will be seriously affected, thus The machining error after compensation is larger than that before compensation. For this reason, it is necessary to select a reasonable reference datum for error compensation of the tool axis vector and the tool position point.

As shown in Figure 4, the position vector and direction vector of any point P in the theoretical tool position trajectory are and In the process of CNC machine tool processing, due to the action of milling force, the tool is deformed by force to form a new tool position point and tool vector and It can be seen from Figure 4 that when the tool axis vector is changed, the vector parallel to vector Therefore, the error compensation reference datum of the tool axis vector can be defined as point to The points form the direction vector of the directed line segment can be expressed as:

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\\ {\mathrm{<span\; class="notranslate">\; j</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\\ {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\\ {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\\ {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

in

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\\ {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\\ {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\\ \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; T</span>}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}\\ {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}\\ {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}\\ \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$

As shown in Figure 5, the error compensation reference datum of the tool position point Can be expressed as:

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\\ {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\\ {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\\ {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\\ {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

in

$\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; W</span>}}\\ \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; T</span>}\left[\begin{array}{c}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;x</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;x</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}\\ <span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;y</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;y</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}\\ {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; C</span>}}\\ \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$

In the formula, Respectively represent the maximum and minimum force deformation of the tool in the tool coordinate system.

Experimental verification

In order to verify the feasibility of this scheme, the uncompensated tool path and the compensated tool path are used to process the surface 1 and surface 2 of the parts shown in Fig. 6, respectively, and the error of the parts after processing is measured. The overall error of profile 2 has decreased significantly compared with profile 1, which verifies the feasibility of this compensation method, as shown in Figure 7.

Those skilled in the art can understand that the accompanying drawing is only a schematic diagram of a preferred embodiment, and the serial numbers of the above embodiments of the present invention are only for description, and do not represent the advantages and disadvantages of the embodiments.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection of the present invention. within range.

Claims (2)

1. a Five-axis NC Machining Center cutter distortion error compensating method, is characterized in that, described error compensating method comprises the following steps:

Set up tool coordinate system, Conversion Relations between workpiece coordinate system and lathe coordinate system three, obtain the kinematic parameter of lathe in five-axis robot process;

Under tool coordinate system, obtain the deflection of cutter; Read the theoretical cutter location data file automatically generated by CAM software;

Milling Force size is calculated according to the five-axis robot Milling Force Model set up; Using the benchmark that theoretical cutter location and generating tool axis vector compensate as mirror image reversible deformation;

The cutter distortion error obtaining current tool position and caused by Milling Force is calculated according to cutter distortion gauge;

Mirror image reversible deformation compensation is carried out to current cutter location and generating tool axis vector, obtains new cutter location and generating tool axis vector according to cutter distortion error calculation;

Calculate new cutter distortion error according to the cutter location data after compensating, judge whether new error is set up; If met the demands, then stop computing, preserve cutter location information.

2. a kind of Five-axis NC Machining Center cutter distortion error compensating method according to claim 1, it is characterized in that, described error compensating method also comprises:

Arrange cutter path position from 1 to N, corresponding compensation cutter location data message, and then the Path after being compensated, the nc program after being compensated by postpositive disposal Software Create, N is cutter location number.