CN114036671A - Cutting force model modeling method considering spindle thermal error and cutter bounce - Google Patents

Abstract

The invention discloses a cutting force model modeling method considering spindle thermal error and cutter bounce, which comprises the following steps: 1) establishing a cutting force theoretical model under ideal conditions; 2) considering the cutter runout, solving the cutter shaft offset distance rho and the cutter shaft offset angle phi caused by the cutter runout_ro(ii) a 3) The thermal error of the main shaft is considered, and the offset distance rho and the offset angle phi of the cutter shaft are corrected by the thermal error of the main shaft in a thermal balance state_roObtaining the corrected offset distance rho of the cutter shaft₁Offset angle phi from cutter shaft_r1By the offset distance rho of the cutter shaft₁Offset angle phi from cutter shaft_r1And correcting the cutting force theoretical model to obtain a cutting force model considering cutter bounce and thermal errors. The invention relates to a cutting force model considering the thermal error of a main shaft and the jumping of a cutter and a modeling method thereof,the influence of the thermal error of the main shaft and the cutter bounce on the cutting force is considered, so that the actual machining condition can be better met.

Description

Cutting force model modeling method considering spindle thermal error and cutter bounce

Technical Field

The invention belongs to the technical field of machining, and particularly relates to a cutting force model modeling method considering spindle thermal error and cutter bounce.

Background

Existing cutting force studies are generally predicted under ideal conditions, namely: the shape of the tool is strictly centrosymmetric and rotates around its axis, and the material removal process does not have any effect on the tool shape. For example, the cutting force modeling method of the fine PCD milling cutter without the side edge relief angle disclosed in the chinese patent application with the publication number CN 113536543 a and the modeling method of the static milling force of the ball end mill based on the semi-analytical method disclosed in the chinese patent application with the publication number CN 113297696 a are all implemented under the ideal conditions of cutting, however, in actual machining, the cutter may jump, the spindle may also generate a thermal error after long-time operation, and both the cutter jump and the spindle thermal error may cause the cutter shaft to be cheap, thereby causing the cutting force to change.

Disclosure of Invention

In view of the above, the present invention provides a cutting force model modeling method considering spindle thermal error and tool run-out, which can better meet the actual machining conditions by considering the influence of the spindle thermal error and the tool run-out on the cutting force.

In order to achieve the purpose, the invention provides the following technical scheme:

a cutting force model modeling method considering spindle thermal error and cutter bounce comprises the following steps:

1) establishing a cutting force theoretical model under ideal conditions;

2) considering the cutter runout, solving the cutter shaft offset distance rho and the cutter shaft offset angle phi caused by the cutter runout_ro；

3) The thermal error of the main shaft is considered, and the offset distance rho and the offset angle phi of the cutter shaft are corrected by the thermal error of the main shaft in a thermal balance state_roObtaining the corrected offset distance rho of the cutter shaft₁Offset angle with cutter shaftφ_r1By the offset distance rho of the cutter shaft₁Offset angle phi from cutter shaft_r1And correcting the cutting force theoretical model to obtain a cutting force model considering cutter bounce and thermal errors.

Further, in the step 1), the modeling method of the cutting force theoretical model under the ideal condition is as follows:

dividing the cutter into M layers of infinitesimal cutting edges along the cutter shaft, decomposing the cutting force generated by any infinitesimal cutting edge into tangential cutting force, radial cutting force and axial cutting force, and then the cutting force model of the infinitesimal cutting edge is as follows:

wherein, K_te,K_re,K_aeExpressing the tangential, radial and secondary normal ploughing power cutting coefficients of the infinitesimal cutting edge, K_tc,K_rc,K_acRespectively representing the tangential, radial and secondary normal shearing force cutting coefficients of the infinitesimal cutting edge; dS and db respectively represent the length and width of the infinitesimal cutting edge; uct₀(φ, κ) represents the undeformed chip thickness, related to the infinitesimal point position angle ψ and infinitesimal point axial immersion angle κ of the infinitesimal cutting edge, and:

ψ＝θ+(i-1)φ_p-φ_z

wherein θ represents a cutting edge position angle measured at the tip; phi is a_zThe helical retardation angle, phi, of a cutting edge infinitesimal with respect to the position of the tip_z＝ztan(i₀)/R，i₀Representing a helix angle; phi is a_pIndicates the tool tip angle of the tool_p2 pi/N, wherein N is the number of cutter teeth; i denotes the i-th cutting edge;

uct₀(ψ,κ)＝n·f

n＝(sin(κ)sin(ψ),sin(κ)cos(ψ),cos(κ))^T

wherein i₀Representing a helix angle; n represents the normal at the surface of the infinitesimal cutting edge; dz represents the infinitesimal cutting edge thickness; f is a feed vector;

converting the cutting force model of the infinitesimal cutting edge into a tool coordinate system to obtain:

wherein dF_x、dF_yAnd dF_zRespectively representing the components of the cutting force of the infinitesimal cutting edge in the directions of X, Y and Z axis;

and (3) integrating and accumulating the cutting force of the infinitesimal cutting edge to obtain the cutting force of the cutter, namely a cutting force theoretical model:

wherein, F_x、F_yAnd F_zRepresenting the components of the tool cutting force in the X, Y and Z-axis directions, respectively.

Further, the cutter shaft offset distance ρ and the cutter shaft offset angle φ caused by the cutter shaft runout_roThe solving method comprises the following steps:

at a given position angle τ, the cutting force for one rotation of the tool is:

F(τ)＝F₀(τ)+ρA₁(τ)cos(φ_ro)+ρA₂(τ)sin(φ_ro)

wherein, F₀(τ) is the theoretical cutting force when the tool is free of runout; k is a radical of_ijThe cutting edge position angle of a layer j of infinitesimal cutting edge of the No. i cutting edge is represented; psi_ijThe axial immersion angle of a layer-j infinitesimal cutting edge of a No. i cutting edge is shown;

the difference in cutting force Δ F at positions between phase angles 2 π/N is:

ΔF＝F(τ)-F(τ-φ_p)＝ρ(a₁(τ)cos(φ_ro)+a₂(τ)sin(φ_ro))

a₁＝A₁(τ)-A₁(τ-φ_p)

a₂＝A₂(τ)-A₂(τ-φ_p)

then:

during one rotation of the tool, a series of tan (phi) values is obtained_ro) Using least square fitting method to obtain offset angle phi_ro(ii) a Will phi_roSubstituting the calculation formula of the cutting force difference delta F to obtain a group of data of the cutter shaft offset distance rho, and obtaining the cutter shaft offset distance rho by adopting a minimum quadratic fitting method.

Further, the cutter shaft offset distance ρ is obtained after the spindle generates a thermal error₁Offset angle phi from cutter shaft_r1Is about delta_y,ρ,φ_r0And:

wherein, delta_yIs the thermal drift of the principal axis in the Y direction;

the extra feed f of the tool is caused by both tool runout and spindle thermal error_r1Comprises the following steps:

f_r1＝(ρ₁sin(φ_r1+θ)-ρ₁sin(φ_r1+θ-φ_p),ρ₁cos(φ_r1+θ)-ρ₁cos(φ_r1+θ-φ_p),0)^T

additional micro-deformed chip thickness uct corrected by tool runout and spindle thermal error_r1Comprises the following steps:

uct_r1＝ρ₁sin(κ)cos(φ_r1+φ_z-(i-1)φ_p)-ρ₁sin(κ)cos(φ_r1+φ_z-(i-2)φ_p)

the cutting force model of the infinitesimal cutting edge considering the tool runout and the spindle thermal error is

And substituting the cutting force model of the infinitesimal cutting edge considering the tool run-out and the spindle thermal error into the cutting force theoretical model to obtain the cutting force model considering the tool run-out and the spindle thermal error.

The invention has the beneficial effects that:

according to the cutting force model modeling method considering the spindle thermal error and the cutter bounce, the theoretical model of the cutting force is corrected by researching the influence of the cutter bounce and the spindle thermal error on the cutter shaft offset distance and the cutter shaft offset angle respectively and jointly considering the cutter bounce and the cutter shaft offset distance and the cutter shaft offset angle after the spindle thermal error, so that the cutting force model considering the cutter bounce and the thermal error can be obtained, and the actual processing conditions can be better met.

Drawings

In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:

FIG. 1 is a flow chart of an embodiment of a cutting force model modeling method of the present invention that takes into account spindle thermal error and tool run-out;

FIG. 2 is a schematic diagram of a tool coordinate system;

FIG. 3 is a schematic structural view of a cutting edge contact segment of the ball end mill;

FIG. 4(a) is a schematic structural diagram of the layered discretization of the cutter;

FIG. 4(b) is a schematic diagram illustrating the calculation of the undeformed cut thickness;

FIG. 5 is a schematic view of undeformed cutting thickness taking into account tool run-out; (a) is a front view; (b) is a top view; (c) the influence of tool jumping on the undeformed cutting thickness;

FIG. 6 is a schematic view of a spindle thermal error detection apparatus;

FIG. 7 is a schematic diagram of spindle offset due to thermal error;

FIG. 8(a) is a schematic view of arbor offset taking into account tool run-out and spindle thermal error;

FIG. 8(b) is a schematic view of the effect of tool run-out and spindle thermal error on undeformed cut thickness;

Detailed Description

The present invention is further described with reference to the following drawings and specific examples so that those skilled in the art can better understand the present invention and can practice the present invention, but the examples are not intended to limit the present invention.

Fig. 1 is a flow chart of an embodiment of a cutting force modeling method of the present invention that takes into account spindle thermal error and tool run-out. The cutting force model modeling method considering the spindle thermal error and the cutter bounce comprises the following steps:

1) establishing a theoretical model of cutting force under ideal conditions

The milling force model is usually established based on a tool coordinate system, and as shown in fig. 2, the tool coordinate system setting method of the present embodiment is as follows:

origin of coordinates: setting the position of the tool nose point as the origin of coordinates of a tool coordinate system;

X_Tshaft: setting the projection direction of the tool feeding direction in the horizontal plane as the X of the tool coordinate system_TIn the positive direction of the axis, since the present embodiment deals with milling forces in high machining, the feed direction of the tool has been limited to that in the positive directionIn a horizontal plane perpendicular to the axis of the tool, i.e. the feed direction and X of the tool_TThe axial directions are parallel;

Z_Tshaft: setting the direction upward along the tool axis to Z_TThe positive direction of the axis;

Y_Tshaft: perpendicular to X_T,Z_TAnd (4) a plane.

Specifically, in order to predict the cutting force, the tool is divided into M layers of infinitesimal cutting edges along the tool axis, the cutting force generated by any infinitesimal cutting edge is decomposed into a tangential cutting force, a radial cutting force and an axial cutting force, and then the cutting force model of the infinitesimal cutting edge is:

wherein, K_te,K_re,K_aeExpressing the tangential, radial and secondary normal ploughing power cutting coefficients of the infinitesimal cutting edge, K_tc,K_rc,K_acRespectively representing the tangential, radial and secondary normal shearing force cutting coefficients of the infinitesimal cutting edge; dS and db respectively represent the length and width of the infinitesimal cutting edge; uct₀(φ, κ) represents the undeformed chip thickness, which is related to the infinitesimal point position angle ψ of the infinitesimal cutting edge and the infinitesimal point axial dip angle κ.

A typical constant lead spherical helix is shown in figure 3. The infinitesimal point position angle psi of the infinitesimal cutting edge is:

ψ＝θ+(i-1)φ_p-φ_z

wherein θ represents a cutting edge position angle measured at the tip; phi is a_zThe helical retardation angle, phi, of a cutting edge infinitesimal with respect to the position of the tip_z＝ztan(i₀)/R，i₀Representing a helix angle; phi is a_pIndicates the tool tip angle of the tool_p2 pi/N, wherein N is the number of cutter teeth; i represents … …;

as shown in fig. 4(b), the undeformed cut thickness can be expressed as:

uct₀(ψ,κ)＝n·f

n＝(sin(κ)sin(ψ),sin(κ)cos(ψ),cos(κ))^T

the length of the infinitesimal cutting edge is:

the width of the infinitesimal cutting edge is:

wherein, i₀Representing a helix angle; n represents the normal at the surface of the infinitesimal cutting edge; dz represents the infinitesimal cutting edge thickness; f is a feed vector; f is along X_TA directional feed vector.

Converting the cutting force model of the infinitesimal cutting edge into a tool coordinate system to obtain:

wherein dF_x、dF_yAnd dF_zRepresenting the components of the cutting force of the infinitesimal cutting edge in the X, Y and Z-axis directions, respectively.

And (3) integrating and accumulating the cutting force of the infinitesimal cutting edge to obtain the cutting force of the cutter, namely a cutting force theoretical model:

wherein, F_x、F_yAnd F_zRepresenting the components of the tool cutting force in the X, Y and Z-axis directions, respectively.

2) Considering the cutter runout, solving the cutter shaft offset distance rho and the cutter shaft offset angle phi caused by the cutter runout_ro

As shown in fig. 5, the tool runout can be regarded as the tool axis is offset by a distance ρ and an angle Φ_ro. When considering tool runout, the actual feed will include for each revolution of the toolTwo parts, because of the run-out from the geometric center O by the rotation axis₀To the actual centre of rotation O₁The offset induced feed and the original design feed per tooth. Thus, the effect of tool runout can be considered as an additional feed.

Extra feed caused by tool runout

Can be expressed as:

f_r＝(ρsin(φ_ro+θ)-ρsin(φ_ro+θ-φ_p),ρcos(φ_ro+θ)-ρcos(φ_ro+θ-φ_p),0)^T

the feed direction is perpendicular to the tool axis. Then, the corresponding additional undeformed cut thickness is obtained, namely:

uct_ro＝ρsin(κ)cos(φ_ro+φ_z-(i-1)φ_p)-ρsin(κ)cos(φ_ro+φ_z-(i-2)φ_p)

in the presence of tool runout, the cutting forces generated by the current tooth and the previous tooth will be different depending on the runout parameters ρ and φ_ro. By analyzing the cutting signal with the phase difference of 2 pi/N (the sharp angle of the cutter) in the machining of the three-axis machine tool, the offset distance rho and the angle phi generated by the cutter jumping can be obtained_ro。

Specifically, the cutter shaft offset distance ρ and the cutter shaft offset angle φ caused by cutter shaft runout_roThe solving method comprises the following steps:

the cutting force in any direction can be used to calculate the run-out parameter. Here, the edge X is used_TDirectional cutting forces are examples. At a given position angle τ, the cutting force for one rotation of the tool is:

uct will be mixed_roAfter substitution, we obtain:

F(τ)＝F₀(τ)+ρA₁(τ)cos(φ_ro)+ρA₂(τ)sin(φ_ro)

wherein, F₀(τ) is the theoretical cutting force when the tool is free of runout; kappa_ijThe cutting edge position angle of a layer j of infinitesimal cutting edge of the No. i cutting edge is represented; psi_ijThe axial immersion angle of a layer-j infinitesimal cutting edge of a No. i cutting edge is shown;

the difference in cutting force Δ F at positions between phase angles 2 π/N is:

ΔF＝F(τ)-F(τ-φ_p)＝ρ(a₁(τ)cos(φ_ro)+a₂(τ)sin(φ_ro))

a₁＝A₁(τ)-A₁(τ-φ_p)

a₂＝A₂(τ)-A₂(τ-φ_p)

then in the experimental data, as long as sufficiently large sample data is collected, various values of af can be collected. In each such set of data, one can obtain:

using the measured cutting force data, a series of tan (φ) values can be obtained during one revolution of the tool_ro) The deviation angle phi is obtained by adopting a least square fitting method_ro(ii) a Will phi_roSubstituting the calculation formula of the cutting force difference delta F to obtain a group of data of the cutter shaft offset distance rho, and obtaining the cutter shaft offset distance rho by adopting a least square fitting method.

3) The thermal error of the main shaft is considered, and the offset distance rho and the offset angle phi of the cutter shaft are corrected by the thermal error of the main shaft in a thermal balance state_roObtaining the corrected offset distance of the cutter shaftDistance rho₁Offset angle phi from cutter shaft_r1By the offset distance rho of the cutter shaft₁Offset angle phi from cutter shaft_r1And correcting the cutting force theoretical model to obtain a cutting force model considering cutter bounce and thermal errors.

In the machining process of the machine tool, under the condition of uneven heat distribution, the machine tool parts are subjected to uneven thermal deformation. In the vertical machining center spindle, the spindle deflects and drifts in the direction X, Y due to the deformation of other parts such as the spindle case.

In order to better detect the thermal effect of a spindle of a numerical control machine tool, according to ISO 230-3 international standards, equipment such as a displacement sensor is utilized, thermal effect deformation is determined according to actual requirements of comprehensive performance test and evaluation of spindle products of a five-axis milling machine, spindle deformation caused by temperature rise caused by spindle rotation is mainly detected, detected data is sorted, and a spindle deformation image caused by the thermal effect is obtained. In the embodiment, a spindle thermal error measuring system shown in FIG. 6 is constructed according to a five-point detection method in the ISO 230-3 standard. Studies have shown that the main effect on spindle distortion is distributed around the spindle head, so when thermally modeling the spindle, the temperature of the spindle head is mainly measured, and the temperature sensor mounting positions are shown in table 1.

TABLE 1 temperature sensor mounting location

	Placing position	Function of
			T1～T3	Main spindle box (Upper, lower, side)	Measuring spindle heating
T4～T5	Main shaft sleeve	Measuring spindle heating
			T6	Spindle motor	Measuring heating of an electric machine
T7	Machine tool shell	Measuring ambient temperature

As shown in FIG. 6, X₁，X₂The thermal drift of the main shaft mean line in the X direction is approximately replaced by the error measured by the displacement sensor in the X direction; y is₁，Y₂The thermal drift of the main shaft mean line in the Y direction is approximately replaced by the error measured by the displacement sensor in the Y direction; z is a thermal error measured by a Z-direction sensor and is a main shaft Z thermal elongation obtained by direct measurement;

as shown in FIG. 7, line A assumes that the check rod does not deform during operation of the machine tool₀B₀Checking the position of the stick for initial value, A₁B₁Spindle inspection stick position after thermal error for the spindle occurs. A. the_x，B_xSpindle inspection stick position A after thermal error₁B₁Projection in the X direction, for the same reason A_y，B_yIs A₁B₁Projected in the Y direction. Through the analysis of the geometric relationship, an accurate expression of the five-term error can be obtained. In the formula of_x，δ_yRespectively X, Y direction thermal drift. Alpha is alpha_x，α_yThermal tilts, delta, about axis Y, X, respectively_zIs Z-direction thermal elongation, X₁，X₂Is the variation value of the displacement sensor in the X direction. Y is₁，Y₂The variation value of the displacement sensor in the Y direction and the axial displacement of the main shaft in the Z directionThe change value of the sensor. H_x，H_yDistance between two sensors in direction X, Y, L_x，L_yX, Y distance of the direction end sensor from the end face of the spindle. In the trapezium formed in the figure, it is easy to ignore high order small quantities according to a simple geometrical relationship:

the thermal error of the main shaft can cause the thermal inclination of the main shaft, but the inclination angle alpha is very small, the influence on error compensation can be ignored, and the compensation value is irrelevant to the length of a cutter when the thermal error is compensated. In addition, the radial offset in the X direction is negligible, and because the present embodiment mainly considers the influence of the offset of the spindle in the X-Y plane and the tool runout on the spindle offset, thereby causing the change of the cutting force, the extension of the spindle in the Z direction caused by the thermal error is not considered temporarily. In summary, in the embodiment, when considering the influence of the thermal error on the cutting force, only the Y thermal drift δ needs to be considered_yThe value of (2) is sufficient.

According to the measured thermal error delta_yThe thermal error model can be established with the temperature T of the machine tool:

δ_y＝(T,V)

in the formula, T represents the measured temperature, and V represents the rotation speed of the spindle.

Specifically, the cutter shaft offset distance ρ caused by cutter shaft runout and spindle thermal error₁Cutter shaftOffset angle phi_r1The solving method comprises the following steps:

the thermal error is considered again on the basis of the tool runout, and the tool offset is shown in fig. 8(a) and 8 (b). After thermal errors are considered, the cutter shaft is offset by a distance rho and an angle phi_roWill become the offset distance ρ₁Angle phi of_r1. From the geometric relationship, ρ₁,φ_r1Is about delta_y,ρ,φ_r0And:

wherein, delta_yIs the thermal drift of the principal axis in the Y direction.

The extra feed f of the tool is caused by both tool runout and spindle thermal error_r1Comprises the following steps:

f_r1＝(ρ₁sin(φ_r1+θ)-ρ₁sin(φ_r1+θ-φ_p),ρ₁cos(φ_r1+θ)-ρ₁cos(φ_r1+θ-φ_p),0)^T

additional micro-deformed chip thickness uct corrected by tool runout and spindle thermal error_r1Comprises the following steps:

uct_r1＝ρ₁sin(κ)cos(φ_r1+φ_z-(i-1)φ_p)-ρ₁sin(κ)cos(φ_r1+φ_z-(i-2)φ_p)

wherein theta is a cutting edge position angle measured at the tool nose; phi is a_zHelical lag angle phi of cutting edge infinitesimal element relative to tool tip position_z＝ztan(i₀)/R，i₀Is the helix angle; phi is a_pIs the sharp angle of the cutter_p2 pi/N, and N is the number of teeth.

The cutting force model of the infinitesimal cutting edge considering the tool runout and the spindle thermal error is

And substituting the cutting force model of the infinitesimal cutting edge considering the tool run-out and the spindle thermal error into the cutting force theoretical model to obtain the cutting force model considering the tool run-out and the spindle thermal error.

In the cutting force model modeling method considering the spindle thermal error and the cutter runout, the theoretical cutting force model is corrected by researching the influence of the cutter runout and the spindle thermal error on the cutter shaft offset distance and the cutter shaft offset angle respectively and jointly considering the cutter shaft offset distance and the cutter shaft offset angle after the cutter runout and the spindle thermal error, so that the cutting force model considering the cutter runout and the thermal error can be obtained, and the actual processing conditions can be better met.

The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or the change made by the person skilled in the art on the basis of the present invention are within the protection scope of the present invention. The protection scope of the invention is subject to the claims.

Claims (4)

1. A cutting force model modeling method considering spindle thermal error and cutter bounce is characterized in that: the method comprises the following steps:

1) establishing a cutting force theoretical model under ideal conditions;

2) considering the cutter runout, solving the cutter shaft offset distance rho and the cutter shaft offset angle phi caused by the cutter runout_ro；

3) The thermal error of the main shaft is considered, and the offset distance rho and the offset angle phi of the cutter shaft are corrected by the thermal error of the main shaft in a thermal balance state_roObtaining the corrected offset distance rho of the cutter shaft₁Offset angle phi from cutter shaft_r1By the offset distance rho of the cutter shaft₁Offset angle phi from cutter shaft_r1And correcting the cutting force theoretical model to obtain a cutting force model considering cutter bounce and thermal errors.

2. The cutting force model modeling method taking into account spindle thermal error and tool run-out according to claim 1, characterized in that: in the step 1), the modeling method of the cutting force theoretical model under the ideal condition comprises the following steps:

dividing the cutter into M layers of infinitesimal cutting edges along the cutter shaft, decomposing the cutting force generated by any infinitesimal cutting edge into tangential cutting force, radial cutting force and axial cutting force, and then the cutting force model of the infinitesimal cutting edge is as follows:

wherein, K_te，K_re，K_aeExpressing the tangential, radial and secondary normal ploughing power cutting coefficients of the infinitesimal cutting edge, K_tc，K_rc，K_acRespectively representing the tangential, radial and secondary normal shearing force cutting coefficients of the infinitesimal cutting edge; dS and db respectively represent the length and width of the infinitesimal cutting edge; uct₀(φ, κ) represents the undeformed chip thickness, related to the infinitesimal point position angle ψ and infinitesimal point axial immersion angle κ of the infinitesimal cutting edge, and:

ψ＝θ+(i-1)φ_p-φ_z

wherein θ represents a cutting edge position angle measured at the tip; phi is a_zThe helical lag angle, phi, of a cutting edge infinitesimal element relative to the position of the tip_z＝ztan(i₀)/R，i₀Representing a helix angle; phi is a_pIndicates the tool tip angle of the tool_p2 pi/N, wherein N is the number of cutter teeth; i denotes the i-th cutting edge;

uct₀(ψ，κ)＝n·f

n＝(sin(κ)sin(ψ)，sin(κ)cos(ψ)，cos(κ))^T

wherein i₀Representing a helix angle; n represents the normal at the surface of the infinitesimal cutting edge; dz represents the infinitesimal cutting edge thickness; f is a feed vector;

converting the cutting force model of the infinitesimal cutting edge into a tool coordinate system to obtain:

wherein dF_x、dF_yAnd dF_zRespectively representing the components of the cutting force of the infinitesimal cutting edge in the directions of X, Y and Z axis;

and (3) integrating and accumulating the cutting force of the infinitesimal cutting edge to obtain the cutting force of the cutter, namely a cutting force theoretical model:

wherein, F_x、F_yAnd F_zRepresenting the components of the tool cutting force in the X, Y and Z-axis directions, respectively.

3. The cutting force model modeling method taking into account spindle thermal error and tool run-out according to claim 2, characterized in that: cutter shaft offset distance rho and cutter shaft offset angle phi caused by cutter shaft jumping_roThe solving method comprises the following steps:

at a given position angle τ, the cutting force for one rotation of the tool is:

F(τ)＝F₀(τ)+ρA₁(τ)cos(φ_ro)+ρA₂(τ)sin(φ_ro)

wherein, F₀(τ) is the theoretical cutting force when the tool is free of runout; kappa_ijThe position angle of a layer of infinitesimal cutting edge of a No. i cutting edge j is shown; psi_ijThe axial immersion angle of a layer-j infinitesimal cutting edge of a No. i cutting edge is shown;

the difference in cutting force Δ F at positions between phase angles 2 π/N is:

ΔF＝F(τ)-F(τ-φ_p)＝ρ(a₁(τ)cos(φ_ro)+a₂(τ)sin(φ_ro))

a₁＝A₁(τ)-A₁(τ-φ_p)

a₂＝A₂(τ)-A₂(τ-φ_p)

then:

during one rotation of the tool, a series of tan (phi) values is obtained_ro) Using least square fitting method to obtain offset angle phi_ro(ii) a Will phi_roSubstituting the calculation formula of the cutting force difference delta F to obtain a group of data of the cutter shaft offset distance rho, and obtaining the cutter shaft offset distance rho by adopting a least square fitting method.

4. The cutting force model modeling method taking into account spindle thermal error and tool run-out as claimed in claim 3, wherein: cutter shaft offset distance rho after main shaft generates thermal error₁Offset angle phi from cutter shaft_r1Is about delta_y，ρ，φ_r0And:

wherein, delta_yIs the thermal drift of the principal axis in the Y direction;

the extra feed f of the tool is caused by both tool runout and spindle thermal error_r1Comprises the following steps:

f_r1＝(ρ₁sin(φ_r1+θ)-ρ₁sin(φ_r1+θ-φ_p)，ρ₁cos(φ_r1+θ)-ρ₁cos(φ_r1+θ-φ_p)，0)^T

additional micro-deformed chip thickness uct corrected by tool runout and spindle thermal error_r1Comprises the following steps:

uct_r1＝ρ₁sin(κ)cos(φ_r1+φ_z-(i-1)φ_p)-ρ₁sin(κ)cos(φ_r1+φ_z-(i-2)φ_p)

the cutting force model of the infinitesimal cutting edge considering the tool runout and the spindle thermal error is

And substituting the cutting force model of the infinitesimal cutting edge considering the cutter bounce and the main shaft thermal error into the cutting force theoretical model to obtain the cutting force model considering the cutter bounce and the thermal error.

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