CN102136021B - Milling force modeling method for titanium alloy TC18 milling process - Google Patents

Abstract

The invention discloses a milling force modeling method for titanium alloy TC18 milling process, which is used for solving the technical problem that equal phase width non-zero milling force produced in titanium alloy TC18 milling process with cutter eccentricity can not be effectively simulated when milling force modeling for titanium alloy TC18 milling process in the prior art is carried out. In the technical scheme, the effect of a side blade and a bottom blade on milling force is considered when the side blade participates in cutting, the effect of the bottom blade on the milling force is also considered when the side blade quits cutting, and the disadvantage that the equal phase width non-zero milling force produced in titanium alloy TC18 milling process with cutter eccentricity can not be effectively simulated in the prior art is overcome; as bottom blade milling force coefficient can be expressed as exponential function of chipping width, the disadvantage that the size effect in the bottom edge cutting process can not be simulated in the prior art is overcome.

Description

Titanium alloy T C18 milling process Milling Force modeling method

Technical field

The present invention relates to a kind of Milling Force modeling method, particularly a kind of titanium alloy T C18 milling process Milling Force modeling method.

Background technology

Document 1 " Y.Altintas, Manufacturing Automation, Cambridge University Press, 2000. " discloses a kind of average Milling Force Model of considering tack slotting cutter side edge cutting effect, and its basic modeling procedure is:

(1), and asks the mean value of surveying Milling Force in the integer cycle through dynameter test Milling Force;

(2), set up the functional relation between average Milling Force and the Milling Force coefficient through theoretical derivation according to the technology geometric relationship between side edge and the workpiece;

(3) in (2) step of average Milling Force substitution that step (1) is obtained, find the solution and obtain the Milling Force coefficient.

Document 2 " M.Wan; W.H.Zhang; G.H.Qin, G.Tan, Efficient calibration of instantaneouscutting force coefficients and runout parameters for general end mills; Int.J.Mach.ToolsManuf.47 (2007) 1767-1776 " discloses a kind of Instantaneous Milling Force Model of considering tack slotting cutter side edge cutting effect, and its basic modeling procedure is:

(1) through dynameter test Milling Force;

(2), set up the functional relation between Instantaneous Milling Force and the Milling Force coefficient through theoretical derivation according to the technology geometric relationship between side edge and the workpiece;

(3) in (2) step of Instantaneous Milling Force substitution that step (1) is obtained, find the solution and obtain the Milling Force coefficient.

The typical feature of above document is: because the technology geometric relationship between cutting edge and the workpiece can not effectively be simulated the phenomenon such as mutually wide non-zero Milling Force such as grade that occurs in the band cutter deflection titanium alloy T C18 milling process to the influence of Milling Force when only having considered that side edge is participated in cutting.

Summary of the invention

In order to overcome prior art when carrying out the modeling of titanium alloy T C18 milling process Milling Force; Can not effectively simulate the deficiency of the mutually wide non-zero Milling Force such as grade that occurs in the band cutter deflection titanium alloy T C18 milling process; The present invention provides a kind of titanium alloy T C18 milling process Milling Force modeling method; Side edge and the influence of shear blade to Milling Force when both considering that side edge is participated in cutting consider that also side edge withdraws from when cutting shear blade the Instantaneous Milling Force forecast model is set up in the influence of Milling Force; Can realize that this method has also been considered the size effect of Milling Force coefficient to effective simulation of the mutually wide Milling Force such as grade that occurs in the band cutter deflection titanium alloy T C18 milling process.

The technical solution adopted for the present invention to solve the technical problems is: a kind of titanium alloy T C18 milling process Milling Force modeling method is characterized in may further comprise the steps:

(1) selected slotting cutter parameter comprises that radius R, helixangle, the cutter tooth of slotting cutter counted N _fSet cutting

Parameter: monodentate amount of feeding f, axial cutting depth Rz, radial cutting degree of depth Rr, speed of cutter spindle.

(2) milling cutter is divided into N vertically and waits the jowar section, act on i cutter constantly at t through computes

Tangential Milling Force F on the tooth on j side edge unit _{T, F, i, j}(t) and radially Milling Force F _{R, F, i, j}(t):

F _{T，F，i，j}(t)＝K _{T，F，i，j}h _F，i，j(t)w _z

F _{R，F，i，j}(t)＝K _R，F，jh _F，i，j(t)w _z

In the formula, K _{T, F, i, j}Be tangential Milling Force coefficient corresponding to j side edge unit on i the cutter tooth, K _{R, F, i, j}Be radially Milling Force coefficient corresponding to j side edge unit on i the cutter tooth, w _zExpression is corresponding to the axial height of j side edge unit on i the cutter tooth, h _{F, i, j}(t) be illustrated in the t instantaneous undeformed chip thickness of j side edge unit on i cutter tooth constantly.

(3) Milling Force on the side edge unit is transformed into X and Y direction and summation:

$F_{X,F}\left(t\right)=\underset{i,j}{\mathrm{\Σ}}[-F_{T,F,i,j}\left(t\right)\cos {\mathrm{\θ}}_{i,j}\left(t\right)-F_{R,F,i,j}\left(t\right)\sin {\mathrm{\θ}}_{i,j}\left(t\right)]$

$F_{Y,F}\left(t\right)=\underset{i,j}{\mathrm{\Σ}}[F_{T,F,i,j}\left(t\right)\sin {\mathrm{\θ}}_{i,j}\left(t\right)-F_{R,F,i,j}\left(t\right)\cos {\mathrm{\θ}}_{i,j}\left(t\right)]$

In the formula, θ _{I, j}(t) be the cutter anglec of rotation

J cutting angle that the side edge unit is corresponding on place and i the cutter tooth, be defined as from Y to clockwise to i the cutter tooth the angle that mid point turned over of j side edge unit.

(4) calculating acts on the radially Milling Force F on the shear blade constantly at t _{T, B, i}(t) and tangential Milling Force F _{R, B, i}(t)

1. when side edge is participated in cutting,

F _T，B，i(t)＝K _T，B，iA _B，i(t)

F _R，B，i(t)＝K _R，B，iA _B，i(t)

In the formula, K _{T, B, i}Be tangential Milling Force coefficient corresponding to i shear blade, K _{R, B, i}Be radially Milling Force coefficient corresponding to i shear blade, A _{B, i}(t) be and i the chipload area that shear blade is corresponding.

2. withdraw from when cutting when side edge,

F _T，B，i(t)＝K _T，B，ib _i(t)

F _R，B，i(t)＝K _R，B，ib _i(t)

In the formula, K _{T, B, i}Be tangential Milling Force coefficient corresponding to i shear blade, K _{R, B, i}Be radially Milling Force coefficient corresponding to i shear blade, b _i(t) be and i the chip width that shear blade is corresponding.

(5) Milling Force on the shear blade is transformed into X and Y direction

F _X，B(t)＝-F _T，B，i(t)cosθ _i，0(t)-F _R，B，i(t)sinθ _i，0(t)

F _Y，B(t)＝F _T，B，i(t)sinθ _i，0(t)-F _R，B，i(t)cosθ _i，0(t)

In the formula, θ _{I, 0}(t) be the cutter anglec of rotation

Place and i the cutting angle that shear blade is corresponding are defined as the angle between this blade direction and the Y axle positive dirction.

The Milling Force that (6) will act on each shear blade and side edge is sued for peace, and obtains total Milling Force:

$F\left(t\right)=\left[\begin{array}{c}{F}_{X,F}\left(t\right)\\ F_{Y,F}\left(t\right)\end{array}\right]+\left[\begin{array}{c}{F}_{X,B}\left(t\right)\\ F_{Y,B}\left(t\right)\end{array}\right]$

(7) confirm K through following method _{T, F, i, j}, K _{R, F, i, j}, K _{T, B, i}, K _{R, B, i}, A _{B, i}(t), K _{T, B, i}, K _{R, B, i}And b _i(t), and repeated execution of steps (1) arrives (6) in a cutter swing circle, obtains the interior Milling Force distribution plan of one-period.

1) selected slotting cutter and workpiece parameter comprise that radius R, helixangle, the cutter tooth of slotting cutter counted N _f,, the workpiece geometric parameter; Set the cutting parameter of rating test, monodentate amount of feeding f, axial cutting depth Rz, radial cutting degree of depth Rr, speed of cutter spindle.Require: workpiece is to satisfy the rectangular parallelepiped piece that dynamometer is installed.

2) cutting parameter of setting according to step 1) is also surveyed Milling Force, requires the workpiece machined surface vertical with tool axis.Expression will be designated as

and corresponding to the Instantaneous Milling Force of

corresponding to the phase angle of n sampled point in m cutter tooth cutting cycle with

3) according to step 2) Milling Force that records demarcates cutter deflection parameter ρ and λ.

4) in each sampling transient state; According to the coordinate transform relational expression; With step 2) Instantaneous Milling Force that records is transformed into local coordinate system from cartesian coordinate system, just

and

is transformed into component

and

under the local coordinate system

5) according to the result of step 4), use

With

Divided by h _{F, i, j}(t) w _z, obtain one group and h _{F, i, j}(t) w _zCorresponding discrete value should be organized discrete value and fit to h _{F, i, j}(t) w _zLinear function, the slope of this linear function is exactly to demarcate the tangential Milling Force COEFFICIENT K corresponding with all side edge unit obtain _{T, F, i, j}Milling Force COEFFICIENT K radially _{R, F, i, j}

6) according to the result of step 3) and step 5), at first calculate the X corresponding to Milling Force F with side edge according to (1) step and (2) step _{X, F}(t) and Y to Milling Force F _{Y, F}(t), then through computes step 2) the Milling Force component corresponding in the Milling Force that records with shear blade

7) confirm the smear metal parameter A _{B, i}(t) and b _i(t)

1. when side edge is participated in cutting, b _i(t) the instantaneous undeformed chip thickness of the side edge corresponding with the position of tool tip place equates, under this situation, through computes A _{B, i}(t)

$A_{B,i}\left(t\right)=\frac{{[b_i\left(t\right)/\cos \mathrm{\η}]}^2}{2\tan (\mathrm{\β}+\mathrm{\η})}$

In the formula, β representes the side edge helix angle, η be with longitudinal cross-section that tool axis overlaps in the drift angle of shear blade and cutter radial.

2. withdraw from when cutting, b when side edge _i(t) calculate through following steps:

(a) in the cycle, calculate the equation C of the rotational trajectory corresponding at two continuous cutters tooth with each point of a knife _{N, u}(n=1,2 ..., N _f, u=1,2), the track of current cutter tooth i is regarded as the last item track in the selected cycle.

(b) the equation L of line between the track center of the current cutter tooth i of calculating and the point of a knife _i

(c) calculate L _iWith all track C _{N, u}Between intersection point Z _{N, u}=(x _{N, u}, y _{N, u}).

(d) through computes Z _{I, 2}With other Z _{N, u}Direct distance

In the formula, n ≠ i when u=2.

(e) through computes b _i(t)

b _i(t)＝max[0，min(l _n，u)]

8), confirm tangential cutting force coefficient corresponding and Milling Force coefficient radially with shear blade according to the result of step 6) and step 7).

1. when side edge is participated in cutting, use F _{B, M}(t) divided by A _{B, i}(t), obtain one group of discrete data, should organize data fitting and become following and shear blade chip width b _i(t) corresponding exponential function relation formula promptly obtains the mathematical model of shear blade cutting force coefficient.

$K_{T,B,i}\left(t\right)=k_{T,B}{\left[b_i\left(t\right)\right]}^{-m_{T,B}}$

$K_{R,B,i}\left(t\right)=k_{R,B}{\left[b_i\left(t\right)\right]}^{-m_{R,B}}$

k _{T, B}, m _{T, B}, k _{R, B}And m _{R, B}It is the normal value coefficient that match obtains.

2. when side edge withdraws from cutting, use F _{B, M}(t) divided by b _i(t), obtain one group of discrete data, should organize data fitting and become following and shear blade chip width b _i(t) corresponding exponential function relation formula promptly obtains the mathematical model of shear blade cutting force coefficient.

$K_{T,B,i}\left(t\right)=k_{T,B}{\left[b_i\left(t\right)\right]}^{-m_{T,B}}$

$K_{R,B,i}\left(t\right)=k_{R,B}{\left[b_i\left(t\right)\right]}^{-m_{R,B}}$

k _{T, B}, m _{T, B}, k _{R, B}And m _{R, B}It is the normal value coefficient that match obtains.

The invention has the beneficial effects as follows: since when both having considered that side edge is participated in cutting side edge and shear blade to the influence of Milling Force; Considered that also shear blade had overcome prior art and can not effectively simulate the deficiency of being with the phenomenon such as mutually wide non-zero Milling Force such as grade that occurs in the cutter deflection titanium alloy T C18 milling process the influence of Milling Force when side edge withdrawed from cutting; Because shear blade Milling Force coefficient table is shown as the exponential function of chip width, overcome the deficiency that prior art can't be simulated the size effect in the shear blade working angles.

Below in conjunction with accompanying drawing and embodiment the present invention is elaborated.

Description of drawings

Fig. 1 is the synoptic diagram that calculates shear blade chip width after side edge withdraws from cutting in the titanium alloy T C18 milling process Milling Force modeling method of the present invention.

Fig. 2 is the prediction Milling Force and actual measurement Milling Force comparison diagram among the inventive method embodiment one.

Fig. 3 is the prediction Milling Force and actual measurement Milling Force comparison diagram among the inventive method embodiment two.

Among the figure, the track C of the current cutter tooth i of 1- _{I, 2}, the track C of 2-cutter tooth i-1 _I-12, the track C of 3-cutter tooth i-2 _I-22, the track center of the current cutter tooth i of 4-, 5-Z _{I, 2}, 6-b _i(t), 7-Z _I-12, 8-Z _I-22, the equation L of line between the track center of the current cutter tooth i of 9-and the point of a knife _i10-surveys Milling Force, and 11-adopts prediction Milling Force of the present invention, and 12-adopts the prediction Milling Force of document 2 methods; 13-Y direction Milling Force component; The non-zero Milling Force that 14-X direction Milling Force component, 15-adopt the prediction of document 2 methods to obtain is mutually wide, and 16-adopts non-zero Milling Force that the inventive method prediction obtains and that the test actual measurement obtains mutually wide.

Embodiment

With reference to accompanying drawing 1～3, titanium alloy milling process Milling Force modeling method of the present invention is that example specifies modeling method with titanium alloy T C18.Lathe is vertical three-dimensional milling machine.

Embodiment one:

(1) selected slotting cutter parameter: tool radius R is that 6mm, helixangle are that 37 degree, shear blade inclination angle η are 3 degree, the cutter number N of teeth _fBe 4; Milling mode: climb cutting.Set cutting parameter: speed of cutter spindle is 600RPM, monodentate amount of feeding 0.0625mm/ tooth, and axially cutting depth Rz equals 0.4mm, and radial cutting degree of depth Rr equals 2mm.

(2) milling cutter is divided into 400 vertically and waits the jowar sections, act on i the cutter tooth tangential Milling Force F on j the side edge unit constantly at t through computes _{T, F, i, j}(t) and radially Milling Force F _{R, F, i, j}(t):

F _{T，F，i，j}(t)＝K _{T，F，i，j}h _F，i，j(t)w _z

F _{R，F，i，j}(t)＝K _{R，F，j，j}h _F，i，j(t)w _z

In the formula, K _{T, F, i, j}Be tangential Milling Force coefficient corresponding to j side edge unit on i the cutter tooth, K _{R, F, i, j}Be radially Milling Force coefficient corresponding to j side edge unit on i the cutter tooth, w _zExpression is corresponding to the axial height of j side edge unit on i the cutter tooth, h _{F, i, j}(t) be illustrated in the t instantaneous undeformed chip thickness of j side edge unit on i cutter tooth constantly.

(3) Milling Force on the side edge unit is transformed into X and Y direction and summation:

$F_{X,F}\left(t\right)=\underset{i,j}{\mathrm{\Σ}}[-F_{T,F,i,j}\left(t\right)\cos {\mathrm{\θ}}_{i,j}\left(t\right)-F_{R,F,i,j}\left(t\right)\sin {\mathrm{\θ}}_{i,j}\left(t\right)]$

$F_{Y,F}\left(t\right)=\underset{i,j}{\mathrm{\Σ}}[F_{T,F,i,j}\left(t\right)s{\mathrm{in\θ}}_{i,j}\left(t\right)-F_{R,F,i,j}\left(t\right)\cos {\mathrm{\θ}}_{i,j}\left(t\right)]$

In the formula, θ _{I, j}(t) be the cutter anglec of rotation

J cutting angle that the side edge unit is corresponding on place and i the cutter tooth, be defined as from Y to clockwise to i the cutter tooth the angle that mid point turned over of j side edge unit.

(4) calculating acts on the radially Milling Force F on the shear blade constantly at t _{T, B, i}(t) and tangential Milling Force F _{R, B, i}(t) 1. when side edge is participated in cutting,

F _T，B，i(t)＝K _T，B，iA _B，i(t)

F _R，B，i(t)＝K _R，B，iA _B，i(t)

In the formula, K _{T, B, i}Be tangential Milling Force coefficient corresponding to i shear blade, K _{R, B, i}Be radially Milling Force coefficient corresponding to i shear blade, A _{B, i}(t) be and i the chipload area that shear blade is corresponding.

2. withdraw from when cutting when side edge,

F _T，B，i(t)＝K _T，B，ib _i(t)

F _R，B，it)＝K _R，B，ib _i(t)

In the formula, K _{T, B, i}Be tangential Milling Force coefficient corresponding to i shear blade, K _{R, B, i}Be radially Milling Force coefficient corresponding to i shear blade, b _i(t) be and i the chip width that shear blade is corresponding.

(5) Milling Force on the shear blade is transformed into X and Y direction

F _X，B(t)＝-F _T，B，i(t)cosθ _i，0(t)-F _R，B，i(t)sinθ _i，0(t)

F _Y，B(t)＝F _T，B，i(t)sinθ _i，0(t)-F _R，B，i(t)cosθ _i，0(t)

In the formula, θ _{I, 0}(t) be the cutter anglec of rotation

Place and i the cutting angle that shear blade is corresponding are defined as the angle between this blade direction and the Y axle positive dirction.

The Milling Force that (6) will act on each shear blade and side edge is sued for peace, and obtains total Milling Force:

$F\left(t\right)=\left[\begin{array}{c}{F}_{X,F}\left(t\right)\\ F_{Y,F}\left(t\right)\end{array}\right]+\left[\begin{array}{c}{F}_{X,B}\left(t\right)\\ F_{Y,B}\left(t\right)\end{array}\right]$

(7) will be through the definite tangential Milling Force COEFFICIENT K of following method corresponding to j side edge unit on i the cutter tooth _{T, F, i, j}, corresponding to the radially Milling Force COEFFICIENT K of j side edge unit on i the cutter tooth _{R, F, i, j}, corresponding to the tangential Milling Force COEFFICIENT K of i shear blade _{T, B, i}, corresponding to the radially Milling Force COEFFICIENT K of i shear blade _{R, B, i}, with i the chipload area A that shear blade is corresponding _{B, i}(t) and with i the chip width b that shear blade is corresponding _i(t) in the above formula of substitution, repeated execution of steps (1) can obtain the Milling Force distribution plan in the one-period to (5) in a cutter swing circle.

1) cutting parameter of setting rating test, speed of cutter spindle is 600RPM, monodentate amount of feeding 0.083mm/ tooth, axially cutting depth Rz equals 0.5mm, and radial cutting degree of depth Rr equals 2.5mm.Require: workpiece is to satisfy the rectangular parallelepiped piece that dynamometer is installed.

2) cutting parameter of setting according to step 1) is also surveyed Milling Force, requires the workpiece machined surface vertical with tool axis.Expression will be designated as

and

corresponding to the Instantaneous Milling Force of corresponding to the phase angle of n sampled point in m cutter tooth cutting cycle with

3) according to step 2) Milling Force that records; Adopt the method in the document 2 " M.Wan; W.H.Zhang, G.H.Qin, G.Tan; Efficient calibration of instantaneous cutting force coefficients and runout parametersfor general end mills, Int.J.Mach.Tools Manuf.47 (2007) 1767-1776 " to demarcate cutter deflection parameter ρ and λ then.Calibration result is: ρ=18.51 μ m, λ=96.06 °.

4) in each sampling transient state; According to the coordinate transform relational expression; With step 2) Instantaneous Milling Force that records is transformed into local coordinate system from cartesian coordinate system, just and

is transformed into component

and

under the local coordinate system

5) according to the result of step 4), use

With Divided by h _{F, i, j}(t) w _z, obtain one group and h _{F, i, j}(t) w _zCorresponding discrete value should be organized discrete value and fit to h _{F, i, j}(t) w _zLinear function, the slope of this linear function is exactly to demarcate the tangential Milling Force COEFFICIENT K corresponding with all side edge unit obtain _{T, F, i, j}Milling Force COEFFICIENT K radially _{R, F, i, j}, the result is: K _{T, F, i, j}=2199.6N/mm ²And K _{R, F, i, j}=4090.7N/mm ²

6) according to the result of step 3) and step 5), at first calculate the X corresponding to Milling Force F with side edge according to (1) step and (2) step _{X, F}(t) and Y to Milling Force F _{Y, F}(t), then through computes step 2) the Milling Force component corresponding in the Milling Force that records with shear blade

7) confirm the smear metal parameter A _{B, i}(t) and b _i(t)

1. when side edge is participated in cutting, b _i(t) the instantaneous undeformed chip thickness of the side edge corresponding with the position of tool tip place equates, under this situation, through computes A _{B, i}(t)

$A_{B,i}\left(t\right)=\frac{{[b_i\left(t\right)/\cos \mathrm{\η}]}^2}{2\tan (\mathrm{\β}+\mathrm{\η})}$

In the formula, β representes the side edge helix angle, η be with longitudinal cross-section that tool axis overlaps in the drift angle of shear blade and cutter radial.

2. withdraw from when cutting, b when side edge _i(t) calculate through following steps:

(a) in the cycle, calculate the equation C of the rotational trajectory corresponding at two continuous cutters tooth with each point of a knife _{N, u}(n=1,2 ..., N _f, u=1,2), the track of current cutter tooth i is regarded as the last item track in the selected cycle.

(b) the equation L of line between the track center of the current cutter tooth i of calculating and the point of a knife _i

(c) calculate L _iWith all track C _{N, u}Between intersection point Z _{N, u}=(x _{N, u}, y _{N, u}).

(d) through computes Z _{I, 2}With other Z _{N, u}Direct distance

In the formula, n ≠ i when u=2.

(e) through computes b _i(t)

b _i(t)＝max[0，min(l _n，u)]

8), confirm tangential cutting force coefficient corresponding and Milling Force coefficient radially with shear blade according to the result of step 6) and step 7).

1. when side edge is participated in cutting, use F _{B, M}(t) divided by A _{B, i}(t), obtain one group of discrete data, should organize data fitting and become following and shear blade chip width b _i(t) corresponding exponential function relation formula promptly obtains the mathematical model of shear blade cutting force coefficient.

K _T，B，i(t)＝85.79[b _i(t)] ^-2.03，N/mm ²

K _R，B，j(t)＝99.98[b _i(t)] ^-2.07，N/mm ²

2. when side edge withdraws from cutting, use F _{B, M}(t) divided by b _i(t), obtain one group of discrete data, should organize data fitting and become following and shear blade chip width b _i(t) corresponding exponential function relation formula promptly obtains the mathematical model of shear blade cutting force coefficient.

K _T，B，i(t)＝58.65[b _i(t)] ^-0.755，N/mm

K _R，B，i(t)＝78.10[b _i(t)] ^-0.816，N/mm

Through above step, prediction Milling Force that obtains and the comparison diagram of surveying Milling Force are like Fig. 2.

Embodiment two:

(1) selected slotting cutter parameter: tool radius R is that 6mm, helixangle are that 37 degree, shear blade inclination angle η are 3 degree, the cutter number N of teeth _fBe 4; Milling mode: climb cutting.Set cutting parameter: speed of cutter spindle is 800RPM, monodentate amount of feeding 0.03125mm/ tooth, and axially cutting depth Rz equals 0.4mm, and radial cutting degree of depth Rr equals 2.5mm.

(2) milling cutter is divided into 400 vertically and waits the jowar sections, act on i the cutter tooth tangential Milling Force F on j the side edge unit constantly at t through computes _{T, F, i, j}(t) and radially Milling Force F _{R, F, i, j}(t):

F _{T，F，i，j}(t)＝K _{T，F，i，j}h _F，i，j(t)w _z

F _{R，F，i，j}(t)＝K _{R，F，i，j}h _F，i，j(t)w _z

In the formula, K _{T, F, i, j}Be tangential Milling Force coefficient corresponding to j side edge unit on i the cutter tooth, K _{R, F, i, j}Be radially Milling Force coefficient corresponding to j side edge unit on i the cutter tooth, w _zExpression is corresponding to the axial height of j side edge unit on i the cutter tooth, h _{F, i, j}(t) be illustrated in the t instantaneous undeformed chip thickness of j side edge unit on i cutter tooth constantly.

(3) Milling Force on the side edge unit is transformed into X and Y direction and summation:

$F_{X,F}\left(t\right)=\underset{i,j}{\mathrm{\Σ}}[-F_{T,F,i,j}\left(t\right)\cos {\mathrm{\θ}}_{i,j}\left(t\right)-F_{R,F,i,j}\left(t\right)\sin {\mathrm{\θ}}_{i,j}\left(t\right)]$

$F_{Y,F}\left(t\right)=\underset{i,j}{\mathrm{\Σ}}[F_{T,F,i,j}\left(t\right)\sin {\mathrm{\θ}}_{i,j}\left(t\right)-F_{R,F,i,j}\left(t\right)\cos {\mathrm{\θ}}_{i,j}\left(t\right)]$

In the formula, θ _{I, j}(t) be the cutter anglec of rotation

J cutting angle that the side edge unit is corresponding on place and i the cutter tooth, be defined as from Y to clockwise to i the cutter tooth the angle that mid point turned over of j side edge unit.

(4) calculating acts on the radially Milling Force F on the shear blade constantly at t _{T, B, i}(t) and tangential Milling Force F _{R, B, i}(t)

1. when side edge is participated in cutting,

F _T，B，i(t)＝K _T，B，iA _B，i(t)

F _R，B，i(t)＝K _R，B，iA _B，i(t)

In the formula, K _{T, B, i}Be tangential Milling Force coefficient corresponding to i shear blade, K _{R, B, i}Be radially Milling Force coefficient corresponding to i shear blade, A _{B, i}(t) be and i the chipload area that shear blade is corresponding.

2. withdraw from when cutting when side edge,

F _T，B，i(t)＝K _T，B，ib _i(t)

F _R，B，i(t)＝K _R，B，ib _i(t)

In the formula, K _{T, B, i}Be tangential Milling Force coefficient corresponding to i shear blade, K _{R, B, i}Be radially Milling Force coefficient corresponding to i shear blade, b _i(t) be and i the chip width that shear blade is corresponding.

(5) Milling Force on the shear blade is transformed into X and Y direction

F _X，B(t)＝-F _T，B，i(t)cosθ _i，0(t)-F _R，B，i(t)sinθ _i，0(t)

F _Y，B(t)＝F _T，B，i(t)sinθ _i，0(t)-F _R，B，i(t)cosθ _i，0(t)

In the formula, θ _{I, 0}(t) be the cutter anglec of rotation Place and i the cutting angle that shear blade is corresponding are defined as the angle between this blade direction and the Y axle positive dirction.

The Milling Force that (6) will act on each shear blade and side edge is sued for peace, and obtains total Milling Force:

$F\left(t\right)=\left[\begin{array}{c}{F}_{X,F}\left(t\right)\\ F_{Y,F}\left(t\right)\end{array}\right]+\left[\begin{array}{c}{F}_{X,B}\left(t\right)\\ F_{Y,B}\left(t\right)\end{array}\right]$

(7) will be through the definite tangential Milling Force COEFFICIENT K of following method corresponding to j side edge unit on i the cutter tooth _{T, F, i, j}, corresponding to the radially Milling Force COEFFICIENT K of j side edge unit on i the cutter tooth _{R, F, i, j}, corresponding to the tangential Milling Force COEFFICIENT K of i shear blade _{T, B, i}, corresponding to the radially Milling Force COEFFICIENT K of i shear blade _{R, B, i}, with i the chipload area A that shear blade is corresponding _{B, i}(t) and with i the chip width b that shear blade is corresponding _i(t) in the above formula of substitution, repeated execution of steps (1) can obtain the Milling Force distribution plan in the one-period to (5) in a cutter swing circle.

1) cutting parameter of setting rating test, speed of cutter spindle is 600RPM, monodentate amount of feeding 0.083mm/ tooth, axially cutting depth Rz equals 0.5mm, and radial cutting degree of depth Rr equals 2.5mm.Require: workpiece is to satisfy the rectangular parallelepiped piece that dynamometer is installed.

2) cutting parameter of setting according to step 1) is also surveyed Milling Force, requires the workpiece machined surface vertical with tool axis.Expression will be designated as

and

corresponding to the Instantaneous Milling Force of

corresponding to the phase angle of n sampled point in m cutter tooth cutting cycle with

3) according to step 2) Milling Force that records; Adopt the method in the document 2 " M.Wan; W.H.Zhang, G.H.Qin, G.Tan; Efficient calibration of instantaneous cutting force coefficients and runout parametersfor general end mills, Int.J.Mach.Tools Manuf.47 (2007) 1767-1776 " to demarcate cutter deflection parameter ρ and λ then.Calibration result is: ρ=18.51 μ m, λ=96.06 °.

4) in each sampling transient state; According to the coordinate transform relational expression; With step 2) Instantaneous Milling Force that records is transformed into local coordinate system from cartesian coordinate system, just

and

is transformed into component

and

under the local coordinate system

5) according to the result of step 4), use

With

Divided by h _{F, i, j}(t) w _z, obtain one group and h _{F, i, j}(t) w _zCorresponding discrete value should be organized discrete value and fit to h _{F, i, j}(t) w _zLinear function, the slope of this linear function is exactly to demarcate the tangential Milling Force COEFFICIENT K corresponding with all side edge unit obtain _{T, F, i, j}Milling Force COEFFICIENT K radially _{R, F, i, j}, the result is: K _{T, F, i, j}=2199.6N/mm ²And K _{R, F, i, j}=4090.7N/mm ²

6) according to the result of step 3) and step 5), at first calculate the X corresponding to Milling Force F with side edge according to (1) step and (2) step _{X, F}(t) and Y to Milling Force F _{Y, F}(t), then through computes step 2) the Milling Force component corresponding in the Milling Force that records with shear blade

7) confirm the smear metal parameter A _{B, i}(t) and b _i(t)

1. when side edge is participated in cutting, b _i(t) the instantaneous undeformed chip thickness of the side edge corresponding with the position of tool tip place equates, under this situation, through computes A _{B, i}(t)

$A_{B,i}\left(t\right)=\frac{{[b_i\left(t\right)/\cos \mathrm{\η}]}^2}{2\tan (\mathrm{\β}+\mathrm{\η})}$

In the formula, β representes the side edge helix angle, η be with longitudinal cross-section that tool axis overlaps in the drift angle of shear blade and cutter radial.

2. withdraw from when cutting, b when side edge _i(t) calculate through following steps:

(a) in the cycle, calculate the equation C of the rotational trajectory corresponding at two continuous cutters tooth with each point of a knife _{N, u}(n=1,2 ..., N _f, u=1,2), the track of current cutter tooth i is regarded as the last item track in the selected cycle.

(b) the equation L of line between the track center of the current cutter tooth i of calculating and the point of a knife _i

(c) calculate L _iWith all track C _{N, u}Between intersection point Z _{N, u}=(x _{N, u}, y _{N, u}).

(d) through computes Z _{I, 2}With other Z _{N, u}Direct distance

In the formula, n ≠ i when u=2.

(e) through computes b _i(t)

b _i(t)＝max[0，min(l _n，u)]

8), confirm tangential cutting force coefficient corresponding and Milling Force coefficient radially with shear blade according to the result of step 6) and step 7).

1. when side edge is participated in cutting, use F _{B, M}(t) divided by A _{B, i}(t), obtain one group of discrete data, should organize data fitting and become following and shear blade chip width b _i(t) corresponding exponential function relation formula promptly obtains the mathematical model of shear blade cutting force coefficient.

K _T，B，i(t)＝85.79[b _i(t)] ^-2.03，N/mm ²

K _R，B，i(t)＝99.98[b _i(t)] ^-2.07，N/mm ²

2. when side edge withdraws from cutting, use F _{B, M}(t) divided by b _i(t), obtain one group of discrete data, should organize data fitting and become following and shear blade chip width b _i(t) corresponding exponential function relation formula promptly obtains the mathematical model of shear blade cutting force coefficient.

K _T，B，i(t)＝58.65[b _i(t)] ^-0.755，N/mm

K _R，B，i(t)＝78.10[b _i(t)] ^-0.816，N/mm

Through above step, prediction Milling Force that obtains and the comparison diagram of surveying Milling Force are like Fig. 3.

In order to verify the prediction effect of the inventive method; Disclosed predicted results in the list of references 2 " M.Wan; W.H.Zhang, G.H.Qin, G.Tan; Efficient calibration of instantaneous cutting force coefficients and runout parametersfor general end mills, Int.J.Mach.Tools Manuf.47 (2007) 1767-1776 " also is drawn among Fig. 2 and Fig. 3 compares.Can find out from Fig. 2 and Fig. 3:

(a) Milling Force that adopts the inventive method prediction to obtain, its non-zero Milling Force is mutually wide, tracing pattern, peak value size can better be coincide with the actual measurement Milling Force.

(b) because considering side edge, document 2 do not withdraw from of the influence of cutting back shear blade to cutting force; Exist between the mutually wide and measured value of the prediction of its non-zero Milling Force than large deviation; For the less test 2 of the monodentate amount of feeding, also bigger corresponding to the peak value and the deviation between the trial value of the prediction Milling Force of the 4th cutter tooth.

More than predict the outcome and show with test findings: prior art is the Milling Force in the titanium alloy T C18 milling process accurately, and especially the non-zero Milling Force is mutually wide, yet that the inventive method can be simulated the non-zero Milling Force that reflects actual conditions is mutually wide.

Claims (1)

1. titanium alloy T C18 milling process Milling Force modeling method is characterized in that may further comprise the steps:

(1) selected slotting cutter parameter comprises that radius R, helixangle, the cutter tooth of slotting cutter counted N _fSet cutting parameter, comprise monodentate amount of feeding f, axial cutting depth Rz, radial cutting degree of depth Rr, speed of cutter spindle;

(2) milling cutter is divided into N vertically and waits the jowar section, act on i the cutter tooth tangential Milling Force F on j the side edge unit constantly at t through computes _{T, F, i, j}(t) and radially Milling Force F _{R, F, i, j}(t):

F _{T，F，i，j}(t)＝K _{T，F，i，j}h _F，i，j(t)w _z

F _{R，F，i，j}(t)＝K _{R，F，i，j}h _F，i，j(t)w _z

In the formula, K _{T, F, i, j}Be tangential Milling Force coefficient corresponding to j side edge unit on i the cutter tooth, K _{R, F, i, j}Be radially Milling Force coefficient corresponding to j side edge unit on i the cutter tooth, w _zExpression is corresponding to the axial height of j side edge unit on i the cutter tooth, h _{F, i, j}(t) be illustrated in the t instantaneous undeformed chip thickness of j side edge unit on i cutter tooth constantly;

(3) Milling Force on the side edge unit is transformed into X and Y direction and summation:

In the formula, θ _{I, j}(t) be the cutter anglec of rotation J cutting angle that the side edge unit is corresponding on place and i the cutter tooth, be defined as from Y to clockwise to i the cutter tooth the angle that mid point turned over of j side edge unit;

(4) calculating acts on the radially Milling Force F on the shear blade constantly at t _{T, B, i}(t) and tangential Milling Force F _{R, B, i}(t);

1. when side edge is participated in cutting,

F _T，B，i?(t)＝K _T，B，iA _B，i(t)

F _R，B，i(t)＝K _R，B，iA _B，i(t)

In the formula, K _{T, B, i}Be tangential Milling Force coefficient corresponding to i shear blade, K _{R, B, i}Be radially Milling Force coefficient corresponding to i shear blade, A _{B, i}(t) be and i the chipload area that shear blade is corresponding;

2. withdraw from when cutting when side edge,

F _T，B，i(t)＝K _T，B，ib _i(t)

F _R，B，i(t)＝K _R，B，ib _i(t)

In the formula, K _{T, B, i}Be tangential Milling Force coefficient corresponding to i shear blade, K _{R, B, i}Be radially Milling Force coefficient corresponding to i shear blade, b _i(t) be and i the chip width that shear blade is corresponding;

(5) Milling Force on the shear blade is transformed into X and Y direction

F _X，B(t)＝-F _T，B，i(t)cosθ _i，0(t)-F _R，B，i(t)sinθ _i，0(t)

F _Y，B(t)＝F _T，B，i(t)sinθ _i，0(t)-F _R，B，i(t)cosθ _i，0(t)

In the formula, θ _{I, 0}(t) be the cutter anglec of rotation

Place and i the cutting angle that shear blade is corresponding are defined as the angle between this blade direction and the Y axle positive dirction;

The Milling Force that (6) will act on each shear blade and side edge is sued for peace, and obtains total Milling Force:

(7) confirm K through following method _{T, F, i, j}, K _{R, F, i, j}, K _{T, B, i}, K _{R, B, i}, A _{B, i}(t), K _{T, B, i}, K _{R, B, i}And b _i(t), and repeated execution of steps (1) arrives (6) in a cutter swing circle, obtains the interior Milling Force distribution plan of one-period;

1) selected slotting cutter parameter comprises that radius R, helixangle, the cutter tooth of slotting cutter counted N _f, selected workpiece geometric parameter; Set the cutting parameter of rating test, monodentate amount of feeding f, axial cutting depth Rz, radial cutting degree of depth Rr, speed of cutter spindle; Require: workpiece is to satisfy the rectangular parallelepiped piece that dynamometer is installed;

2) parameter of setting according to step 1) is also surveyed Milling Force, requires the workpiece machined surface vertical with tool axis; Expression will be designated as

and corresponding to the Instantaneous Milling Force of

corresponding to the phase angle of n sampled point in m cutter tooth cutting cycle with

3) according to step 2) Milling Force that records demarcates cutter deflection parameter ρ and λ;

4) in each sampling transient state; According to the coordinate transform relational expression; With step 2) Instantaneous Milling Force that records is transformed into local coordinate system from cartesian coordinate system, just

and is transformed into component

and

under the local coordinate system

5) according to the result of step 4), use

With Divided by h _{F, i, j}(t) w _z, obtain one group and h _{F, i, j}(t) w _zCorresponding discrete value should be organized discrete value and fit to h _{F, i, j}(t) w _zLinear function, the slope of this linear function is exactly to demarcate the tangential Milling Force COEFFICIENT K corresponding with all side edge unit obtain _{T, F, i, j}Milling Force COEFFICIENT K radially _{R, F, i, j}

6) according to the result of step 3) and step 5), at first calculate the X corresponding to Milling Force F with side edge according to step (1) and step (2) _{X, F}(t) and Y to Milling Force F _{Y, F}(t), then through computes step 2) the Milling Force component corresponding in the Milling Force that records with shear blade,

7) confirm the smear metal parameter A _{B, i}(t) and b _i(t), 1. when side edge is participated in cutting, b _i(t) the instantaneous undeformed chip thickness of the side edge corresponding with the position of tool tip place equates, under this situation, through computes A _{B, i}(t)

In the formula, β representes the side edge helix angle, η be with longitudinal cross-section that tool axis overlaps in the drift angle of shear blade and cutter radial;

2. when side edge withdraws from cutting, calculate b through following steps _i(t):

(a) in the cycle, calculate the equation C of the rotational trajectory corresponding at two continuous cutters tooth with each point of a knife _{N, u}, n=1,2 ..., N _f, u=1,2; The track of current cutter tooth i is regarded as the last item track in the selected cycle;

(b) the equation L of line between the track center of the current cutter tooth i of calculating and the point of a knife _i

(c) calculate L _iWith all track C _{N, u}Between intersection point Z _{N, u}=(x _{N, u}, y _{N, u});

(d) through computes Z _{I, 2}With other Z _{N, u}Direct distance

In the formula, n ≠ i when u=2;

(e) through computes b _i(t)

b _i(t)＝max[0，min(l _n，u)]

8), confirm tangential cutting force coefficient corresponding and Milling Force coefficient radially with shear blade according to the result of step 6) and step 7);

1. when side edge is participated in cutting, use F _{B, M}(t) divided by A _{B, i}(t), obtain one group of discrete data, should organize data fitting and become following and shear blade chip width b _i(t) corresponding exponential function relation formula promptly obtains the mathematical model of shear blade cutting force coefficient;

In the formula, K _{T, B}, m _{T, B}, k _{R, B}And m _{R, B}It is the normal value coefficient that match obtains;

2. when side edge withdraws from cutting, use F _{B, M}(t) divided by b _i(t), obtain one group of discrete data, should organize data fitting and become following and shear blade chip width b _i(t) corresponding exponential function relation formula obtains the mathematical model of shear blade cutting force coefficient;

In the formula, k _{T, B}, m _{T, B}, k _{R, B}And m _{R, B}It is the normal value coefficient that match obtains.

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