CN105945311A - Numerically-controlled machine tool feed system speed regulation method based on power prediction - Google Patents

Abstract

The invention relates to a numerically-controlled machine tool feed system speed regulation method based on power prediction. During a rough turning process of a numerically-controlled machine tool, the minimum feed speed is generally set according to the maximum cutting depth, and machining is performed by taking the minimum feed speed as a constant feed speed. However, the problem of low efficiency caused by constant-speed machining is especially acute in case of a large amount of rough turning operation and a large machining batch. Aiming at the problem, the invention provides the numerically-controlled machine tool feed system speed regulation method based on power prediction. The method comprises the following steps: Step 1, acquiring power signals and inputting the power signals to a neural network to predict a power value of next moment; Step 2, calculating a deviation ratio of preset power and predicted power to judge whether speed regulation is needed; and Step 3, predicting a back cutting depth, and finishing speed regulation control over a feed system through combination of the back cutting depth and a preset power value. The method effectively solves the problem of lagging of speed regulation under different cutting conditions, reduces the machining cost and greatly improves the utilization rate and cutting efficiency of the machine tool.

Description

A kind of NC machine tool feed system speed regulating method based on power prediction

Technical field

The present invention is applicable to Digit Control Machine Tool manufacture field and uses, a kind of Digit Control Machine Tool based on power prediction Feed system speed regulating method.

Background technology

Rough turn is a kind of simply processing blank or the technical process of primary processing, and its main purpose is excision blank Surplus, makes approximation part by blank.The rough turn prescription to finished surface is the highest, and working (machining) efficiency is its emphasis paid close attention to. Therefore, the biggest amount of feeding and cutting depth are the most all set when roughing, in order in the shortest time inscribe Except chip as much as possible.For machine tool, rough turn mainly by operator's foundation operation technique, fulfil assignment by rule of thumb Task.But, for Digit Control Machine Tool, its course of processing and technological parameter are operated according to programmed values.One Denier programming completes, and Digit Control Machine Tool is just carried out with constant feed speed according to the technological parameter set in cutting operation Cutting.During programming, destroy because cutter, workpiece and lathe are produced by machining overload to be avoided, must be according to negative The operating mode selection machined parameters that the lotus upper limit is interval.But, in whole cutting operation, it is this that cutting output is in the cutting depth upper limit Operating mode the most only accounts for about the 5% of whole operation, and feed speed is operated according to programmed values always, and this is the most greatly Reduce working (machining) efficiency.In the case of, manufacturing batch more in rough turn operation is relatively big, the problem that rough turn working (machining) efficiency is low is the most aobvious Obtain especially prominent.

The key problem controlling feed speed is to be analyzed cutting feed power and control.Obtain centripetal force mainly have from Line simulation analysis and two kinds of methods of on-line checking.The subject matter that off-line simulation analysis exists is can not dynamic response practice processing Working conditions change, simulation analysis result needs to combine actual condition and is modified, and makeover process is complex.By to entering in real time It is optimized to power and controls to realize the control to feed speed, being allowed to the change along with actual cutting operating mode and occur Change, has greater advantage on the high-efficient cutting realizing Digit Control Machine Tool and even running.Centripetal force can be by special in real time Dynamometry instrument is measured, and what application was more at present is resistance-strain type of dynamometer instrument.But this measuring method measures inconvenience, And process system can be produced impact, and weaken the rigidity of lathe, also the installation to workpiece and cutter causes difficulty, and price The highest.On the other hand, owing to the speed regulation process of Machine Tool Feeding System performs by mechanical transmission mechanism, response time is relatively Long.Therefore, use conventional feedback easily to occur producing overload impact because speed governing is delayed, to cutter, parts and Lathe produces the problems such as destruction.So feed system being carried out speed governing suitably combine forecast Control Algorithm.

From energy-balance equation and the energy consumption characteristics of lathe, energy consumption can respond rapidly to load change.For numerical control For the feed system of lathe, although the power consumption link of system is numerous, and energy stream is complicated, studies have found that feed system There is quadratic function relation in energy input and centripetal force.Meanwhile, the changed power during lathe is rough turn easily detects and distinguishes Know.In consideration of it, this patent proposes a kind of NC machine tool feed system method for control speed based on power prediction, realize feeding The speed regulating control of system.

Summary of the invention

It is an object of the invention to provide a kind of NC machine tool feed system speed regulating method based on power prediction, the method Low for the rough turn process efficiency under constant low speed feed speed processing conditions, the speed regulation process response time of Machine Tool Feeding System Longer, that real-time is poor deficiency.By predicting the power of actual condition subsequent time, set up the function of power and back engagement of the cutting edge Relation, carries out the processing mode cut, it is achieved the rough turn mistake of lathe with constant feed speed during change Digit Control Machine Tool is rough turn The optimization of the speed governing of journey feed system, not only achieves the control of feed speed, more effectively solves speed governing lag issues, improves Machine tool utilization rate and stock-removing efficiency.

For reaching above-mentioned purpose, the present invention provides following technical scheme:

A kind of NC machine tool feed system speed regulating method based on power prediction, comprises the following steps:

Step one: prediction subsequent time performance number:

It is respectively mounted voltage sensor, current sensor and power sensor and gathers the voltage of feeding input end of motor, electricity Stream and performance number.The data collected are filtered respectively, singular value is processed；Then to the voltage collected and electricity Flow valuve carries out computing, merges the performance number calculated with the performance number detected, to improve power detection precision.

The power stream of feed system servomotor comprises stator copper loss, iron loss, and mechanical loss, stray loss and driving are negative The output etc. carried, in conjunction with the steady state voltage equation of AC servo motor, servomotor power can be expressed as:

$P_{ax}=3R{I}_s^2+\frac{{\mathrm{\ω}}_e^2({\mathrm{\ψ}}_d^2+{\mathrm{\ψ}}_q^2)}{R}+{\mathrm{\ω}}_e{K}_e{i}_q---\left(1\right)$

Wherein, R is stator winding resistance；I_sFor stator phase currents virtual value；ω_eFor Electromagnetic Field angular velocity；ψ_dFor magnetic Flux direct-axis component；ψ_qFor magnetic flux quadrature axis component；K_eFor electric torque coefficient；i_qFor stator current quadrature axis component.Incorporation engineering Practice, can be obtained feed system power equation by formula (1):

$\begin{array}{c}{P}_{ax}=(3{{\mathrm{RB}}_m^{\′}}^2+K_T{B}_m^{\′}){\mathrm{\ω}}_m^2+(6{\mathrm{RB}}_m^{\′}+K_T)\·\[K_{eq}^{\′}(M_t+M_{load})\\ +T_0^{\′}+T_c\]{\mathrm{\ω}}_m+3R{\[K_{eq}^{\′}(M_t+M_{load})+T_0^{\′}+T_c\]}^2\end{array}---\left(2\right)$

Wherein,K_TFor turning round Moment coefficient；B_mFor motor damping coefficient；P is the pitch of ball-screw；μ_vFor viscosity friction coefficient；K_gGear ratio for shaft coupling； ω_mFor feeding motor rotational shaft speed；μ_cFor Coulomb friction coefficient；M_tQuality for workbench；M_loadFor loaded work piece matter on workbench Amount；T₀For motor internal loss torque；F_extFor adding power on the table.

Using the performance number after process as input, build training sample (x_k, y), input neural network, the output valve of acquisition Y, is the predictive value of k+1 moment power.Power prediction refers to according to detected t_mPower data (P before moment_m, P_m-1...), to t_m+hPerformance number P in moment_m+h(h ＞ 0) estimates.Realizing this process is to historical data (P_m, P_m-1...) carry out nonlinear function approximation, generate a time-varying function P about variable t_m(t), and P_m+1Function P_m(t) it Between there are mapping relations, i.e. P_m+1=F [P_m(t)].Therefore, by functional F [] is fitted, it is possible to P_m+h(h ＞ 0) Value estimate.

Step 2: calculate pre-power scale and predetermined power deviation ratio, it may be judged whether need speed governing:

By obtain prediction performance number, can Digit Control Machine Tool based on power prediction rough turn during feed system speed governing Equation is:

$\frac{P_{\exp }-P_{ax}}{P_{\exp }}\≤\mathrm{\δ}---\left(3\right)$

Wherein, P_expAccording to processing reality preset feeding power of motor expected value, δ is power deviation rate.Calculate and preset Power and the power deviation rate of pre-power scale, if deviation ratio is less than setting value, then need not speed governing, proceed power prediction； If deviation ratio is more than setting value, then need prediction by bite, it is also desirable to feed speed is adjusted.

Step 3: prediction back engagement of the cutting edge value, realizes speed governing by predetermined power value and back engagement of the cutting edge:

According to the performance number of step one prediction, and system power equation and centripetal force empirical formula, obtain motor Input power and feed speed and the functional relationship of back engagement of the cutting edge, and then the back engagement of the cutting edge under actual condition is predicted.

Centripetal force F_xIt is the component bigger on NC machine tool feed system impact.After lathe is stable, act on workbench On power equal with centripetal force, according to engineering about the empirical formula of centripetal force, i.e. In like manner can calculate main cutting force F_z, the power P of consumption when simultaneously can cut_m=F_zv；Feeding motor rotational shaft speed ω_m=K_g ω_ls, wherein ω_lsFor ball-screw rotating speed.Relation between table feed speed v and ball-screw rotating speed is Cutting speedWherein ω is the speed of mainshaft, and d is major axis diameter.For material coefficient；For power correction factor； For back engagement of the cutting edge modified index；For amount of feeding modified index；For cutting speed modified index；Table feed speed with Relation between the amount of feeding isBy above various substitution (2) formula, can be by power input to machine P_axWith feeding Speed v is to back engagement of the cutting edge a_pIt is predicted, it may be assumed that

$\begin{array}{c}{P}_{ax}=(3{{\mathrm{RB}}_m^{\′}}^2+K_T{B}_m^{\′}){\left(\frac{2{\mathrm{\πK}}_{g}v}{P}\right)}^2+(6{\mathrm{RB}}_m^{\′}+K_T)\·\[K_{eq}^{\′}(M_t+M_{load})+T_0^{\′}\\ +\frac{9.81{\mathrm{PC}}_{F_x}{a}_p^{x_{F_x}}{\left(\frac{2\mathrm{\π}}{\mathrm{\ω}}v\right)}^{y_{F_x}}{\left(\frac{\mathrm{\ω}d}{2\mathrm{\π}}\right)}^{n_{F_x}}{K}_{F_{x}x}}{K_{T}2{\mathrm{\πK}}_g}\]\frac{2{\mathrm{\πK}}_{g}v}{P}+3R\[K_{eq}^{\′}(M_t+M_{load})\\ +T_0^{\′}+\frac{9.81{\mathrm{PC}}_{F_x}{a}_p^{x_{F_x}}{\left(\frac{2\mathrm{\π}}{\mathrm{\ω}}v\right)}^{y_{F_x}}{\left(\frac{\mathrm{\ω}d}{2\mathrm{\π}}\right)}^{n_{F_x}}{K}_{F_{x}x}}{K_{T}2{\mathrm{\πK}}_g}{\]}^2\end{array}---\left(4\right)$

(4) formula can be to be designated as following form:

P_ax=Av²+Bv+Cva_p+D(a_p)²+Ea_p+H (5)

When operating mode changes, back engagement of the cutting edge a_pCan change therewith, need to adjust feed speed v.By prediction Performance number is measurable by bite, will be taken back by bite predictive value in (5) formula, according to actual predetermined power, can be needed Feed speed to be adjusted to, and then the speed regulation process of completion system.

P can be made_axWith a_pChange and keep constant.

The beneficial effects of the present invention is:

The method by setting up the functional relationship of power and back engagement of the cutting edge, during utilizing lathe rough turn main transmission and Feed system power carries out real-time prediction to back engagement of the cutting edge, is allowed to according to actual cutting operating mode, optimizes feeding speed in real time Degree, it is achieved the control of feed speed.The method not only change Digit Control Machine Tool rough turn during carry out with constant feed speed The processing mode of cutting, is allowed to optimize feed speed in real time according to actual cutting operating mode, also efficiently solves speed governing delayed Problem, substantially increase machine tool utilization rate and stock-removing efficiency.

Accompanying drawing explanation

In order to make the purpose of the present invention, technical scheme and beneficial effect clearer, the present invention provides drawings described below to carry out Illustrate:

Fig. 1 is the schematic flow sheet of the method for the invention；

Fig. 2 is cutting stress and cutting parameter schematic diagram；

Fig. 3 is working angles power measured curve and the comparison diagram of prediction curve in embodiment；

Fig. 4 is that embodiment medium velocity controls simulation result；

Detailed description of the invention

Below in conjunction with accompanying drawing, the preferred embodiments of the present invention are described in detail.

Fig. 1 is the schematic flow sheet of the method for the invention, as it can be seen, number based on power prediction of the present invention Feed system speed regulating method during control lathe is rough turn, comprises the following steps: step one: prediction subsequent time performance number；Step Two: calculate pre-power scale and predetermined power deviation ratio, it may be judged whether need speed governing；Step 3: according to predetermined power and back of the body penetration of a cutting tool Amount, to feed system speed regulating control.

Prediction subsequent time performance number:

It is respectively mounted voltage sensor, current sensor and power sensor and gathers the voltage of feeding input end of motor, electricity Stream and performance number.The data collected are filtered respectively, singular value is processed；Then to the voltage collected and electricity Flow valuve carries out computing, merges the performance number calculated with the performance number detected, to improve power detection precision.

The power stream of feed system servomotor comprises stator copper loss, iron loss, and mechanical loss, stray loss and driving are negative The output etc. carried, in conjunction with the steady state voltage equation of AC servo motor, servomotor power can be expressed as:

$P_{ax}=3R{I}_s^2+\frac{{\mathrm{\ω}}_e^2({\mathrm{\ψ}}_d^2+{\mathrm{\ψ}}_q^2)}{R}+{\mathrm{\ω}}_e{K}_e{i}_q---\left(1\right)$

Wherein, R is stator winding resistance；I_sFor stator phase currents virtual value；ω_eFor Electromagnetic Field angular velocity；ψ_dFor magnetic Flux direct-axis component；ψ_qFor magnetic flux quadrature axis component；K_eFor electric torque coefficient；i_qFor stator current quadrature axis component.Incorporation engineering Practice, can be obtained feed system power equation by formula (1):

Wherein,K_TFor turning round Moment coefficient；B_mFor motor damping coefficient；P is the pitch of ball-screw；μ_vFor viscosity friction coefficient；K_gGear ratio for shaft coupling； ω_mFor feeding motor rotational shaft speed；μ_cFor Coulomb friction coefficient；M_tQuality for workbench；M_loadFor loaded work piece matter on workbench Amount；T₀For motor internal loss torque；F_extFor adding power on the table.

Using the performance number after process as input, build training sample (x_k, y), input neural network, the output valve of acquisition Y, is the predictive value of k+1 moment power.Power prediction refers to according to detected t_mPower data (P before moment_m, P_m-1...), to t_m+hPerformance number P in moment_m+h(h ＞ 0) estimates.The theoretical basis realizing this process is to history number According to (P_m,P_m-1...) carry out nonlinear function approximation, generate a time-varying function P about variable t_m(t), and P_m+1Function P_mThere are mapping relations, i.e. P between (t)_m+1=F [P_m(t)].Therefore, by functional F [] is fitted, it is possible to P_m+h The value of (h ＞ 0) is estimated.This method uses the three-layer neural network of single hidden layer to be predicted performance number, the god chosen Through network model it is:

Wherein v_i1For the i-th hidden neuron connection weights to output, the data amount check that n was gathered by certain moment, K is Time series number, ω before the k+1 moment_kiFor the input neuron in the kth moment connection weights to i-th hidden neuron, x_k For the input in kth moment, θ is the threshold values of hidden neuron.

Calculate pre-power scale and predetermined power deviation ratio, it may be judged whether need speed governing:

By obtain prediction performance number, can Digit Control Machine Tool based on power prediction rough turn during feed system speed governing Equation is:

$\frac{P_{\exp }-P_{ax}}{P_{\exp }}\≤\mathrm{\δ}---\left(3\right)$

Wherein, P_expAccording to processing reality preset feeding power of motor expected value, δ is power deviation rate.Calculate and preset Power and the power deviation rate of pre-power scale, if deviation ratio is less than setting value, then need not speed governing, proceed power prediction； If deviation ratio is more than setting value, then need prediction by bite, it is also desirable to feed speed is adjusted.

Prediction back engagement of the cutting edge value, realizes speed governing by predetermined power value and back engagement of the cutting edge

According to the performance number of step one prediction, and system power equation and centripetal force empirical formula, draw motor Input power and feed speed and the functional relationship of back engagement of the cutting edge, and then the back engagement of the cutting edge under actual condition is predicted.

Fig. 2 is cutting stress and cutting parameter schematic diagram.Metal is under the effect of cutter rake face, and the generation that is squeezed is cut Cut power.Cutting force can be analyzed to three orthogonal cutting component: (1) cutting force F_z: total cutting force is on direction of primary motion Orthographic projection；(2) centripetal force F_x: total cutting force orthographic projection in feed direction；(3) back force F_y: total cutting force is in vertical work Make the component in plane.(4) back engagement of the cutting edge a_p: the vertical dimension between machined surface and work surface；(5) amount of feeding f: Cutter on direction of feed motion relative to the displacement of workpiece；Cutting speed v_c: on cutting edge, Chosen Point is relative to workpiece master The instantaneous velocity of motion.

Centripetal force F_xIt is the component bigger on NC machine tool feed system impact.After lathe is stable, act on work Power on platform is equal with centripetal force, according to engineering about the empirical formula of centripetal force, i.e. In like manner can calculate main cutting force F_z, the power P of consumption when simultaneously can cut_m=F_zv；Feeding motor rotational shaft speed ω_m=K_g ω_ls, wherein ω_lsFor ball-screw rotating speed.Relation between table feed speed v and ball-screw rotating speed is Cutting speedWherein ω is the speed of mainshaft, and d is major axis diameter；For material coefficient；For power correction factor； For back engagement of the cutting edge modified index；For amount of feeding modified index；For cutting speed modified index table feed speed with enter To the relation between amount it isBy above various substitution (2) formula, can be by power input to machine P_axWith feeding speed Degree v is to back engagement of the cutting edge a_pIt is predicted, it may be assumed that

$\begin{array}{c}{P}_{ax}=(3{{\mathrm{RB}}_m^{\′}}^2+K_T{B}_m^{\′}){\left(\frac{2{\mathrm{\πK}}_{g}v}{P}\right)}^2+(6{\mathrm{RB}}_m^{\′}+K_T)\·\[K_{eq}^{\′}(M_t+M_{load})+T_0^{\′}\\ +\frac{9.81{\mathrm{PC}}_{F_x}{a}_p^{x_{F_x}}{\left(\frac{2\mathrm{\π}}{\mathrm{\ω}}v\right)}^{y_{F_x}}{\left(\frac{\mathrm{\ω}d}{2\mathrm{\π}}\right)}^{n_{F_x}}{K}_{F_{x}x}}{K_{T}2{\mathrm{\πK}}_g}\]\frac{2{\mathrm{\πK}}_{g}v}{P}+3R\[K_{eq}^{\′}(M_t+M_{load})\\ +T_0^{\′}+\frac{9.81{\mathrm{PC}}_{F_x}{a}_p^{x_{F_x}}{\left(\frac{2\mathrm{\π}}{\mathrm{\ω}}v\right)}^{y_{F_x}}{\left(\frac{\mathrm{\ω}d}{2\mathrm{\π}}\right)}^{n_{F_x}}{K}_{F_{x}x}}{K_{T}2{\mathrm{\πK}}_g}{\]}^2\end{array}---\left(4\right)$

Speed governing is realized by performance number and back engagement of the cutting edge

(4) formula can be to be designated as following form:

P_ax=Av²+Bv+Cva_p+D(a_p)²+Ea_p+H (5)

When operating mode changes, back engagement of the cutting edge a_pCan change therewith, need to adjust feed speed v.By prediction Performance number is measurable by bite, will be taken back by bite predictive value in (5) formula, according to actual predetermined power, can be needed Feed speed to be adjusted to, and then the speed regulation process of completion system.

Embodiment:

In the present embodiment, the feed speed control method that the method validation using test to combine with emulation is proposed Feasibility.When formulating proof scheme, owing to failing to obtain the control interface of the Digit Control Machine Tool used by experiment, so authenticated Journey is divided into two parts.First, by the working angles of Digit Control Machine Tool is tested, verify the feasible of power forecasting method Property；Then, the performance number using actual measurement carries out STATIC SIMULATION analysis as data source, the control to feed speed.

(1) power prediction test

Experimental test is carried out, the base of this Machine Tool Feeding System with numerically controlled lathe (C2-6136HK/1) Z axis feed system This parameter is as shown in table 1, and experimental condition is as shown in table 2.

The power-related parameter (Z axis) of table 1 numerically controlled lathe C26136HK/1 feed system

Table 2 NC machine tool feed system experimental condition

After lathe is stable, the contrast of working angles power measured curve and prediction curve is as it is shown on figure 3, wherein power Sampling period is about 40ms.It can be seen that prediction curve is higher to measured curve degree of fitting from comparison diagram, this just demonstrates merit The feasibility of rate Forecasting Methodology.

(2) speed regulating control emulation

Speed regulating control basic procedure is as follows:

If t₀Moment lathe is stable, and working angles starts.Now v=v₀, a_p=a_p0, P_ax=P₀, and at [t₀-t_i) Interval satisfiedBeing failure to actuate at this range restraint device, feed speed keeps v₀Constant.

t_iMoment,At this moment a is described_piChange, and make power deviation rate more than setting value δ.Now, System will be according to P_i, v₀Calculate a_pi.And then according to P_exp, a_piCalculate v_i.Meanwhile, speed setting controller action, make feed speed reach v_i。

At the beginning of controller designs, accelerate and slow down all to use PID to control.From simulation curve, control effect very Good.But by speed change curves is analyzed, it has been found that when accelerating speed governing, the existence of differentiation element so that response Time shortens, and in the actual course of processing, if the change of accelerator medium velocity is excessively violent, easily produces impact shock.Cause Control method is modified by this, accelerates to change into PI control, slows down and uses PID to control.Speed controlling simulation result such as Fig. 4 institute Showing, the Controlling model proposed can realize the control to speed, and velocity variations is more mild, and performance number is basically stable at setting Value.

Finally illustrate, preferred embodiment above only in order to technical scheme to be described and unrestricted, although logical Cross above preferred embodiment the present invention to be described in detail, it is to be understood by those skilled in the art that can be In form and it is made various change, without departing from claims of the present invention limited range in details.

Claims (1)

1. feed system speed regulating method during a Digit Control Machine Tool based on power prediction is rough turn, it is characterised in that: include with Lower step:

Step one: prediction subsequent time performance number:

Be respectively mounted voltage sensor, current sensor and power sensor gather the voltage of feeding input end of motor, electric current and Performance number.The data collected are filtered respectively, singular value is processed.Using the performance number after process as input, Build training sample (x_k, y), input neural network, output valve y of acquisition, it is the predictive value of k+1 moment power.This method Performance number is predicted by the three-layer neural network using single hidden layer, and the neural network model chosen is:Wherein v_i1For the i-th hidden neuron connection weights to output, n is certain moment The data amount check gathered, K is time series number before the k+1 moment, ω_kiFor the input neuron in kth moment to i-th hidden layer The connection weights of neuron, x_kFor the input in kth moment, θ is the threshold values of hidden neuron.

Step 2: calculate pre-power scale and predetermined power deviation ratio, it may be judged whether need speed governing:

By obtain prediction performance number, obtain Digit Control Machine Tool based on power prediction rough turn during feed system speed governing equation For:

$\frac{P_{\exp }-P_{ax}}{P_{\exp }}\≤\mathrm{\δ}---\left(1\right)$

Wherein, P_expAccording to processing reality preset feeding power of motor expected value, δ is power deviation rate.Calculate predetermined power With the power deviation rate of pre-power scale, if deviation ratio is less than setting value, then need not speed governing, proceed power prediction；If partially Rate is more than setting value, then need to predict by bite, and then be adjusted feed speed.

Step 3: prediction back engagement of the cutting edge value, realizes speed governing by predetermined power value and back engagement of the cutting edge:

According to the performance number of step one prediction, and system power equation and centripetal force empirical formula, available motor is defeated Enter power shown with the anticipation function such as formula (2) of feed speed and back engagement of the cutting edge, power input to machine P_axWith feed speed v and the back of the body Bite a_pThere is quadratic function relation.

P_ax=Av²+Bv+Cva_p+D(a_p)²+Ea_p+H (2)

Wherein, A, B, C, D, E are respectively the correlation coefficient of quadratic function, and H is constant.

Back engagement of the cutting edge and the quadratic function relation of feed speed of prediction can be obtained by (2) formula.Keeping, power is constant Under premise, when operating mode changes, back engagement of the cutting edge a_pCan change therewith.Adjust feed speed v, P can be made_axWith a_p's Change and keep constant.