CN101412196A - Turning force prediction method based on cutting-tool angle and cutting amount parametric variation - Google Patents

Abstract

The invention discloses a method for predicting a turning force based on cutter angle and parameter variation of cutting data. The method comprises the following steps: using a dynamometer to measure a cutting force distributed along a coordinate axis of a coordinate system in one-time turning, calculating a three-way turning force coefficient of the cutting force in a converted coordinate system through converting the coordinate system, and calculating and obtaining the predicted turning force according to the factor of the cutting force, so as to achieve prediction of a three-way turning force for processing work pieces made from the same material and having the same heat treating state under the same cutting and lubricating conditions of the cutters made from the same material at any cutter angle parameter and cutting data parameter. The method for predicting the turning force needs little workload for cutting experiments, and the obtained cutting force models have wider application application, have predicting precision meeting actual demand, and are convenient to popularize and apply.

Description

Turning force prediction method based on cutting-tool angle and the variation of cutting data parameter

Technical field

The invention belongs to machinery manufacturing technology field, relate to a kind of Forecasting Methodology of Cutting Force, particularly a kind of turning force prediction method based on cutting-tool angle and the variation of cutting data parameter.

Background technology

In Cutting Parts processing, cutting force not only has a significant impact the surface quality of wearing and tearing, durability and the part to be processed of cutter, and has influence on the performance and the stock-removing efficiency of lathe.Therefore, it is significant to rationally choosing with Machine Tool design of tool sharpening, cutting parameter to estimate cutting force.

Cutting Force is subjected to influence of various factors, and as the material of cutting-tool angle, cutter material, cutting data condition, cutting fluid, machined material and heat-treat condition thereof etc., in these influence factors, some factor can quantitative expression, and some factor can only qualitative description.Therefore, set up accurate, general Cutting Force model and have certain degree of difficulty.

The Cutting Force forecasting model that uses mainly contains following four kinds at present:

1) based on the complete empirical model of experimental data.This model need be done a large amount of cutting experiments, generally find relation between cutting force and the cutting data parameter by the exponential curve fitting method, therefore can only be applicable to that the cutting data parameter changes, and the prediction of the Cutting Force under certain specific machining condition such as cutting-tool angle parameter, cutter material, workpiece material and lubricating condition, its versatility is relatively poor.

2) based on the physical model of cutting scheme and material constitutive relation.This model is mainly considered the material yield flow behavior of main shear zone and the friction behavior between cutter rake face and the smear metal, need do a large amount of experiments to set up the material constitutive model of material under high temperature, high strain environment, the experiment difficulty is big, and only is applicable to that fixed cutting tool and machined material reach fixedly machining condition scope (cutting-tool angle parameter, cutter material, workpiece material, lubricating condition etc. are certain).In addition, the friction behavior between cutter and the smear metal is very complicated, need do many simplification and handle, and influences modeling accuracy.This model is mainly used in FInite Element prediction cutting force, uses also inconvenience, needs the operator to possess FInite Element knowledge preferably.

3) unit cutting Force Model.Main cutting force on the cutting Force Model unit of being meant of the unit area of cut, this model is to measure main cutting force by cutting experiment, uses main cutting force divided by the area of cut then, the unit's of obtaining cutting force.During use, with the area of cut unit of multiply by cutting force, obtain main cutting force again.The limitation of this model is to be only applicable to the main cutting force prediction of different cutting data parameters; When the cutting-tool angle parameter changed, the unit cutting Force Model need rebulid.

4) based on the prediction of Turning Force with Artificial model of artificial intelligence.Mainly contain neural network model, Grey System Model etc.This model can be considered multiple quantitative and qualitative factor, utilizes this method will set up the cutting Force Model with certain versatility, must do a large amount of typical cutting experiments, so that abundant training pattern sample to be provided.The defective of this model is that to set up the required experimental data workload of cutting Force Model with certain versatility too big, and its scope of application is mainly in its machining condition scope.For neural network model, the validity of its model also depends on the topological structure of neutral net, and versatility is high more, and the neural network training model efficiency is lower, needs a large amount of training time of cost.

In sum, existing turning force prediction method need be done a large amount of cutting experiments, could obtain the Cutting Force forecast model that uses within the specific limits; And the required precision of forecast model is good more, the scope of application requires widely more, and the cutting experiment amount that need do is big more, and the difficulty that causes setting up this forecast model is also big more.In addition, existing Cutting Force forecast model also mainly is applicable to the situation that the cutting data parameter changes.As everyone knows, cutting experiment need expend a large amount of man power and materials, especially for some workpiece that adopts precious materials and exotic material to make, permits no. a large amount of cutting experiments and predicts its cutting force, therefore adopts conventional method almost to be difficult to realize.

Summary of the invention

The purpose of this invention is to provide a kind of turning force prediction method based on cutting-tool angle and the variation of cutting data parameter, this Forecasting Methodology can be set up the prediction of Turning Force with Artificial model by experiment number seldom, and the forecast model of being set up has the scope of application of broad.

The technical solution adopted in the present invention is, a kind of turning force prediction method based on cutting-tool angle and the variation of cutting data parameter, by the data that turning experiment obtains, the Cutting Force prediction when carrying out different cutting-tool angles, different cutting data parameter, this method is carried out according to the following steps:

Step 1: with lathe tool 1 turner 2, be the origin of coordinates, set up three-dimensional system of coordinate UVW, utilize three-dimensional dynamometer, measure the three-dimensional Cutting Force value F that distributes along the reference axis of this three-dimensional system of coordinate UVW with the point of a knife of lathe tool 1 _u, F _v, F _w, the cutting-tool angle parameter of lathe tool 1 is anterior angle γ ₀, cutting edge inclination λ _s, actual tool cutting edge angle Kr and actual auxiliary angle K _r', the cutting data parameter is cutting depth t and amount of feeding f;

Step 2: according to the three-dimensional system of coordinate UVW that step 1 is set up, keep coordinate origin and V axle constant, the plane of U axle and W axle formation is clockwise rotated the angle of the complementary angle of actual tool cutting edge angle Kr around the V axle, set up three-dimensional system of coordinate U ₁V ₁W ₁

Step 3: according to the three-dimensional system of coordinate U of step 2 foundation ₁V ₁W ₁, keep coordinate origin and U ₁Axle is constant, with V ₁Axle and W ₁The plane that axle constitutes is around U ₁Axle clockwise rotates cutting edge inclination λ _sAngle, set up three-dimensional system of coordinate U ₂V ₂W ₂

Step 4: according to the three-dimensional system of coordinate U of step 3 foundation ₂V ₂W ₂, keep coordinate origin and W ₂Axle is constant, with V ₂Axle and U ₂The plane that axle constitutes is around W ₂Axle clockwise rotates anterior angle γ ₀Angle, set up three-dimensional system of coordinate U ₃V ₃W ₃

Step 5: the three-dimensional cutting force F that records according to step 1 _u, F _vAnd F _w, by following formula with this three-dimensional cutting force F _u, F _vAnd F _wBe converted to the three-dimensional system of coordinate U that step 4 is set up ₃V ₃W ₃In three-dimensional cutting force F _U3, F _V3And F _W3:

$\left\{\begin{array}{c}{F}_{u3}\\ F_{v3}\\ F_{w3}\end{array}\right\}=T^{-1}\·\left\{\begin{array}{c}{F}_u\\ F_v\\ F_w\end{array}\right\}---\left(1\right)$

In the formula, T is to three-dimensional system of coordinate U by three-dimensional system of coordinate UVW ₃V ₃W ₃Coordinate conversion matrix;

Step 6: the three-dimensional cutting force F that obtains according to step 5 _U3, F _V3And F _W3, calculate three-dimensional cutting force COEFFICIENT K u according to the following equation ₃, K _V3, K _W3:

$\left\{\begin{array}{c}{K}_{u3}\\ K_{v3}\\ K_{w3}\end{array}\right\}=1/S\left\{\begin{array}{c}{F}_{u3}\\ F_{v3}\\ F_{w3}\end{array}\right\}---\left(2\right)$

In the formula, S is the effective area of cut on the lathe tool rake face;

Step 7: Cutting Force prediction and calculation

The three-dimensional cutting force COEFFICIENT K that obtains according to step 6 _U3, K _V3, K _W3, when going out lathe tool 1 cutting workpiece 2 of any given cutting-tool angle and cutting data parameter by the following formula prediction and calculation, the three-dimensional Cutting Force F under three-dimensional system of coordinate UVW _u, F _v, F _w:

$\left\{\begin{array}{c}{F}_{u3}\\ F_{v3}\\ F_{w3}\end{array}\right\}=S\left\{\begin{array}{c}{K}_{u3}\\ K_{v3}\\ K_{w3}\end{array}\right\}---\left(3\right)$

$\left\{\begin{array}{c}{F}_u\\ F_v\\ F_w\end{array}\right\}=T\·\left\{\begin{array}{c}{F}_{u3}\\ F_{v3}\\ F_{w3}\end{array}\right\}---\left(4\right)$

The qualitative influence factor that Forecasting Methodology of the present invention will influence in the multiple factor of Cutting Force is expressed in the mode of cutting force coefficient, and quantitative effect factor is wherein characterized with the variable format in the formula, experiment number by seldom is measurable Cutting Force, and scope of application broad.The cutter that is applicable to same material is using under the same cutting fluid or the condition without cutting fluid, when processing the workpiece of material of the same race and identical condition of heat treatment, to the Cutting Force prediction of different cutting data parameters and different cutting-tool angle parameters.

Description of drawings

Fig. 1 is the distribution schematic diagram of three-dimensional Cutting Force in the three-dimensional system of coordinate set up of Forecasting Methodology of the present invention and this coordinate system;

Fig. 2 is the schematic diagram of the various computing coordinate system of Forecasting Methodology foundation of the present invention;

Fig. 3 is the schematic diagram that Forecasting Methodology of the present invention is calculated the effective area of cut of lathe tool.

Among the figure, 1. lathe tool, 2. workpiece.

The specific embodiment

The present invention is described in detail below in conjunction with the drawings and specific embodiments.

The cutting force of lathe tool is subjected to influence of various factors, and in these influence factors, some can quantitative expression, as cutting-tool angle parameter and cutting data parameter; Some can only qualitative description, as the material and the condition of heat treatment thereof of cutter material, cutting fluid, machined material.

The qualitative influence factor that the inventive method will influence in the multiple factor of Cutting Force is expressed in the mode of cutting force coefficient, and the quantitative effect factor is characterized with the variable format in the formula, make to adopt Cutting Force model that the inventive method sets up applicable to the cutter of material of the same race under cutting fluid of the same race or condition without cutting fluid, when processing the workpiece of material of the same race and identical condition of heat treatment, the Cutting Force under different cutting data parameters and the different cutting-tool angle parameter condition is predicted.

Existing Cutting Force experimental study shows: under the medium cutting speed condition, cutting speed is little to the Cutting Force influence.The inventive method is when setting up the Cutting Force forecast model, do not consider the influence of cutting speed, the main consideration cutting amount of feeding, cutting depth parameter, simultaneously, lathe tool for sharpening sharp (new sharpening), do not consider the influence of its wear of the tool flank, therefore parameters such as the anterior angle of main consideration cutter, cutting edge inclination, tool cutting edge angle, auxiliary angle in the angle parameter of cutter.So the inventive method will be got rid of " anterior angle of cutting depth, the amount of feeding, cutter, cutting edge inclination, tool cutting edge angle, auxiliary angle " factor that influences Cutting Force in addition, consider with the cutting force coefficient of three directions, and set up the Cutting Force forecast model based on this.

Turning force prediction method of the present invention, specifically undertaken by following step:

Step 1: lathe tool 1 is installed on the dynamometer, workpiece 2 is cut, point of a knife with lathe tool 1 is the origin of coordinates, set up three-dimensional system of coordinate UVW as shown in Figure 1, utilize three-dimensional dynamometer, when measuring lathe tool 1 turner 2, the three-dimensional Cutting Force value F that the reference axis of the three-dimensional system of coordinate UVW that the edge is set up produces _u, F _v, F _w, because of instantaneous Cutting Force has fluctuation, this three-dimensional Cutting Force value is averaged.The angle of lathe tool 1 is anterior angle γ as shown in Figure 2 ₀, cutting edge inclination λ _s, actual tool cutting edge angle K _rWith the actual auxiliary angle K shown in Fig. 3 _r', selected cutting output is cutting depth t shown in Fig. 3 and amount of feeding f;

Step 2: according to the three-dimensional system of coordinate UVW that step 1 is set up, keep coordinate origin and V axle constant, the plane of U axle and W axle formation is clockwise rotated actual tool cutting edge angle K around the V axle _rThe angle of complementary angle, set up three-dimensional system of coordinate U ₁V ₁W ₁, as shown in Figure 2;

Step 3: according to the three-dimensional system of coordinate U of step 2 foundation ₁V ₁W ₁, keep coordinate origin and U ₁Axle is constant, with V ₁Axle and W ₁The plane that axle constitutes is around U ₁Axle clockwise rotates cutting edge inclination λ _sAngle, set up three-dimensional system of coordinate U ₂V ₂W ₂, as shown in Figure 2;

Step 4: according to the three-dimensional system of coordinate U of step 3 foundation ₂V ₂W ₂, keep coordinate origin and W ₂Axle is constant, with V ₂Axle and U ₂The plane that axle constitutes is around W ₂Axle clockwise rotates anterior angle γ ₀Angle, set up three-dimensional system of coordinate U ₃V ₃W ₃, as shown in Figure 2;

Step 5: the three-dimensional cutting force F that records according to step 1 _u, F _vAnd F _w, by following formula with this three-dimensional cutting force F _u, F _vAnd F _wBe converted to the three-dimensional system of coordinate U that step 4 is set up ₃V ₃W ₃In three-dimensional cutting force F _U3, F _V3And F _W3:

$\left\{\begin{array}{c}{F}_{u3}\\ F_{v3}\\ F_{w3}\end{array}\right\}=T^{-1}\·\left\{\begin{array}{c}{F}_u\\ F_v\\ F_w\end{array}\right\}---\left(1\right)$

In the formula, T is to coordinate system U from coordinate system UVW ₃V ₃W ₃Coordinate conversion matrix, its computing formula is as follows:

T＝T ₁·T ₂·T ₃

$T_1=\left[\begin{array}{ccc}\sin \left(\mathrm{Kr}\right)& 0& -\cos \left(\mathrm{Kr}\right)\\ 0& 1& 0\\ \cos \left(\mathrm{Kr}\right)& 0& \sin \left(\mathrm{Kr}\right)\end{array}\right]$

$T_2=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \left(\mathrm{\λs}\right)& \sin \left(\mathrm{\λs}\right)\\ 0& -\sin \left(\mathrm{\λs}\right)& \cos \left(\mathrm{\λs}\right)\end{array}\right]$

$T_3=\left[\begin{array}{ccc}\cos \left({\mathrm{\γ}}_0\right)& \sin \left({\mathrm{\γ}}_0\right)& 0\\ -\sin \left({\mathrm{\γ}}_0\right)& \cos \left({\mathrm{\γ}}_0\right)& 0\\ 0& 0& 1\end{array}\right].$

Step 6: the three-dimensional cutting force F that obtains according to step 5 _U3, F _V3And F _W3, calculate three-dimensional cutting force COEFFICIENT K according to the following equation _U3, K _V3, K _W3:

$\left\{\begin{array}{c}{K}_{u3}\\ K_{v3}\\ K_{w3}\end{array}\right\}=1/S\left\{\begin{array}{c}{F}_{u3}\\ F_{v3}\\ F_{w3}\end{array}\right\}---\left(2\right)$

In the formula, S is the effective area of cut on the lathe tool rake face, i.e. the projected area of the area of quadrangle BCDE on rake face among Fig. 3, promptly

$S=\frac{S_{\mathrm{BCDE}}}{\cos \left({\mathrm{\γ}}_0\right)\·\cos \left({\mathrm{\λ}}_S\right)}$

$S_{\mathrm{BCDE}}=f\·t-\frac{f^2\·\sin \left(\mathrm{Kr}\right)\·\sin (\mathrm{Kr}\′)}{2\sin (\mathrm{Kr}+\mathrm{kr}\′)}$

Lathe tool 1 cuts on the surface of workpiece 2, and its cutting depth is t; The residing location point of lathe tool 1 point of a knife is A, and after the cutting of doing amount of feeding f distance, point of a knife arrives the B point along workpiece spindle; At this moment, arrive the C point with the intersection point of workpiece 2 green surfaces by the D point on lathe tool 1 main cutting edge; The intersection point of the front cutting edge when line segment AD and lathe tool 1 point of a knife arrive the B point is made as E, and as shown in Figure 3, the projected area of quadrangle BCDE on rake face is the effective area of cut S on the lathe tool rake face;

Step 7: Cutting Force prediction and calculation

The three-dimensional cutting force COEFFICIENT K that obtains according to step 6 _U3, K _V3, K _W3, when going out lathe tool 1 cutting workpiece 2 of any given cutting-tool angle parameter and cutting data parameter by the following formula prediction and calculation, the three-dimensional Cutting Force F under three-dimensional system of coordinate UVW _u, F _v, F _w:

$\left\{\begin{array}{c}{F}_{u3}\\ F_{v3}\\ F_{w3}\end{array}\right\}=S\left\{\begin{array}{c}{K}_{u3}\\ K_{v3}\\ K_{w3}\end{array}\right\}---\left(3\right)$

$\left\{\begin{array}{c}{F}_u\\ F_v\\ F_w\end{array}\right\}=T\·\left\{\begin{array}{c}{F}_{u3}\\ F_{v3}\\ F_{w3}\end{array}\right\}---\left(4\right)$

Embodiment

Adopt Switzerland to produce Kistler9257B dynamometer, Kistler5070A charge amplifier and Kistler9403 knife rest, carry out three-dimensional Cutting Force real time record by computer Cutting Force data collecting system.Adopt the lathe tool of two new sharpenings, and for doing cutting.Table 1 is the tool geometrical parameter of two lathe tools.

The tool geometrical parameter of two lathe tools of table 1

	Material	Anterior angle	Tool cutting edge angle	Auxiliary angle	Cutting edge inclination	Relief angle
							No. 1 cutter	YT15	12°	45°	60°	6°	8°
No. 2 cuttves	YT15	3°	83°	20°	0°	13°

(1) get cutter No. 1, it is installed on the knife rest, selected cutting data parameter is: speed of mainshaft n=475r/min, amount of feeding f=0.16mm/r, cutting depth t=1.0mm; Workpiece is cut, obtain three-dimensional cutting force F by dynamometer _u, F _v, F _wValue, calculate three-dimensional cutting force COEFFICIENT K respectively according to this value _U3, K _V3, K _W3Three-dimensional cutting force is as shown in table 2 with the corresponding three-dimensional cutting force coefficient that calculates.

The Cutting Force and corresponding three-dimensional cutting force coefficient unit: the N of table 2:1 cutter

Still adopt lathe tool No. 1, selected another kind of cutting data parameter: speed of mainshaft n=475r/min, amount of feeding f=0.33mm/r, cutting depth t=0.85mm cuts above-mentioned workpiece again, obtains actual three-dimensional Cutting Force value by dynamometer; Simultaneously, the three-dimensional Cutting Force that obtains predicting according to the three-dimensional cutting force coefficient of aforesaid No. 1 cutter; The Cutting Force of this actual measurement three-dimensional Cutting Force and prediction is as shown in table 3.

The predicted value and the measured value contrast of table 3:1 cutter Cutting Force

	Fu	Fv	Fw
				Actual value (N)	226.7	609.4	305.2
Predicted value (N)	232.6	624.7	312.9
				Relative error (%)	2.52	2.45	2.45

Can draw actual three-dimensional Cutting Force and by the maximum relative error 2.52% between the Cutting Force of the inventive method prediction by table 3.

(2) get cutter No. 2, it is installed on the knife rest, selected cutting data parameter: speed of mainshaft n=475r/min, amount of feeding f=0.28mm/r, cutting depth t=1.0mm cut above-mentioned workpiece again.Obtain actual three-dimensional Cutting Force by dynamometer; Simultaneously, test resulting three-dimensional cutting force coefficient based on an above-mentioned lathe tool, prediction and calculation goes out the three-dimensional Cutting Force of No. 2 cuttves; The contrast of this prediction three-dimensional Cutting Force and actual measurement three-dimensional Cutting Force is as shown in table 4.

The predicted value of No. 2 cutter Cutting Force of table 4 and measured value contrast

	Fu	Fv	Fw
				Experiment value (N)	488.6	591.2	197.2
Predicted value (N)	468.4	626.2	215.7
				Relative error (%)	4.29	5.59	8.56

Show in the table 4 that Cutting Force that adopts Forecasting Methodology of the present invention to predict to obtain and the maximum relative error between the actual three-dimensional Cutting Force are 8.56%.Generation is to be the basis with the three-dimensional cutting force coefficient that No. 1 lathe tool obtained than the main cause of mistake, the three-dimensional Cutting Force of No. 2 lathe tools of prediction, and the material and the condition of heat treatment of two kinds of lathe tools there are differences.

Forecasting Methodology of the present invention under same cutting lubricating condition, when processing the workpiece of material of the same race and identical condition of heat treatment, predicts to have degree of precision to the Cutting Force of any cutting-tool angle parameter and cutting data parameter for the cutter of material of the same race.The general cutting at one time of only need doing is tested, and can obtain the three-dimensional cutting force coefficient of cutter, so the cutting experiment least number of times, and cutter is not had specific (special) requirements.

Claims (3)

1. turning force prediction method that changes based on cutting-tool angle and cutting data parameter, test the data that obtain by a turning, Cutting Force prediction when carrying out different cutting-tool angles, different cutting data parameter is characterized in that this method is carried out according to the following steps:

Step 1: with lathe tool (1) turner (2), be the origin of coordinates, set up three-dimensional system of coordinate UVW, utilize three-dimensional dynamometer, measure the three-dimensional Cutting Force value F that distributes along the reference axis of this three-dimensional system of coordinate UVW with the point of a knife of lathe tool (1) _u, F _v, F _w, the cutting-tool angle parameter of lathe tool (1) is anterior angle γ ₀, cutting edge inclination λ _s, actual tool cutting edge angle K _rWith actual auxiliary angle

, the cutting data parameter is cutting depth t and amount of feeding f;

Step 2: according to the three-dimensional system of coordinate UVW that step 1 is set up, keep coordinate origin and V axle constant, the plane of U axle and W axle formation is clockwise rotated actual tool cutting edge angle K around the V axle _rThe angle of complementary angle, set up three-dimensional system of coordinate U ₁V ₁W ₁

Step 3: according to the three-dimensional system of coordinate U of step 2 foundation ₁V ₁W ₁, keep coordinate origin and U ₁Axle is constant, with V ₁Axle and W ₁The plane that axle constitutes is around U ₁Axle clockwise rotates cutting edge inclination λ _sAngle, set up three-dimensional system of coordinate U ₂V ₂W ₂

Step 4: according to the three-dimensional system of coordinate U of step 3 foundation ₂V ₂W ₂, keep coordinate origin and W ₂Axle is constant, with V ₂Axle and U ₂The plane that axle constitutes is around W ₂Axle clockwise rotates anterior angle γ ₀Angle, set up three-dimensional system of coordinate U ₃V ₃W ₃

Step 5: the three-dimensional cutting force F that records according to step 1 _u, F _vAnd F _w, by following formula with this three-dimensional cutting force F _u, F _vAnd F _wBe converted to the three-dimensional system of coordinate U that step 4 is set up ₃V ₃W ₃In three-dimensional cutting force F _U3, F _V3And F _W3:

$\left\{\begin{array}{c}{F}_{u3}\\ F_{v3}\\ F_{w3}\end{array}\right\}=T^{-1}\·\left\{\begin{array}{c}{F}_u\\ F_v\\ F_w\end{array}\right\}---\left(1\right)$

In the formula, T is to three-dimensional system of coordinate U by three-dimensional system of coordinate UVW ₃V ₃W ₃Coordinate conversion matrix;

Step 6: the three-dimensional cutting force F that obtains according to step 5 _U3, F _V3And F _W3, calculate three-dimensional cutting force COEFFICIENT K according to the following equation _U3, K _V3, K _W3:

$\left\{\begin{array}{c}{K}_{u3}\\ K_{v3}\\ K_{w3}\end{array}\right\}=1/S\left\{\begin{array}{c}{F}_{u3}\\ F_{v3}\\ F_{w3}\end{array}\right\}---\left(2\right)$

In the formula, S is the effective area of cut on the lathe tool rake face;

Step 7: Cutting Force prediction and calculation

The three-dimensional cutting force COEFFICIENT K that obtains according to step 6 _U3, K _V3, K _W3, when going out lathe tool (1) cutting workpiece (2) of any given cutting-tool angle and cutting data parameter by the following formula prediction and calculation, the three-dimensional Cutting Force F under three-dimensional system of coordinate UVW _u, F _v, F _w:

$\left\{\begin{array}{c}{F}_{u3}\\ F_{v3}\\ F_{w3}\end{array}\right\}=S\left\{\begin{array}{c}{K}_{u3}\\ K_{v3}\\ K_{w3}\end{array}\right\}---\left(3\right)$

$\left\{\begin{array}{c}{F}_u\\ F_v\\ F_w\end{array}\right\}=T\·\left\{\begin{array}{c}{F}_{u3}\\ F_{v3}\\ F_{w3}\end{array}\right\}---\left(4\right)$

2. according to the described turning force prediction method of claim 1, it is characterized in that in the described step 5, the computing formula of coordinate conversion matrix T is:

T＝T ₁·T ₂·T ₃

$T_1=\left[\begin{array}{ccc}\sin \left(\mathrm{Kr}\right)& 0& -\cos \left(\mathrm{Kr}\right)\\ 0& 1& 0\\ \cos \left(\mathrm{Kr}\right)& 0& \sin \left(\mathrm{Kr}\right)\end{array}\right]$

$T_2=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \left(\mathrm{\λs}\right)& \sin \left(\mathrm{\λs}\right)\\ 0& -\sin \left(\mathrm{\λs}\right)& \cos \left(\mathrm{\λs}\right)\end{array}\right]$

$T_3=\left[\begin{array}{ccc}\cos \left({\mathrm{\γ}}_0\right)& \sin \left({\mathrm{\γ}}_0\right)& 0\\ -\sin \left({\mathrm{\γ}}_0\right)& \cos \left({\mathrm{\γ}}_0\right)& 0\\ 0& 0& 1\end{array}\right].$

3. according to the described turning force prediction method of claim 1, it is characterized in that the computing formula of the effective area of cut S in the described step 6 is:

$S=\frac{S_{\mathrm{BCDE}}}{\cos \left({\mathrm{\γ}}_0\right)\·\cos \left({\mathrm{\λ}}_S\right)}$

$S_{\mathrm{BCDE}}=f\·t-\frac{f^2\·\sin \left(\mathrm{Kr}\right)\·\sin (\mathrm{Kr}\′)}{2\sin (\mathrm{Kr}+\mathrm{kr}\′)}$

T is the cutting depth that lathe tool (1) cuts on workpiece (2) surface, and f is the amount of feeding.

Images