CN104570933A - Flying shear control method based on high-order curve - Google Patents

Abstract

The invention provides a flying shear control method based on a high-order curve. A flying shear controls the movement of scissors of the flying shear through the quintic curve, the angle of a scissors-following knife roll of the flying shear is obtained, and the synchronization between the flying shear rotation angle and the movement distance of conveyed materials is achieved. The flying shear movement track synchronization algorithm oriented to the constant acceleration and deceleration tracking algorithm is abandoned, the flying shear movement track synchronization control method based on the quintic curve is put forward, the speed, the accelerated speed and the accelerated speed smooth transition of the flying shear rotation movement are ensured, and meanwhile the short cutting and long cutting track planning of batched machining can be achieved and the higher shearing accuracy and the higher production efficiency can be obtained.

Description

A kind of flying shearing machine control method based on luminance curve

Technical field

The invention belongs to fields of numeric control technique, particularly relate to the control of flying shearing machine, for a kind of based on the flying shearing machine control method of luminance curve.

Background technology

Along with developing rapidly of high power AC servomotor and Numeric Control Technology, the simple rotary flying shear of structure is developed, and horizontal cutting off in spiral is at home and abroad widely used.

In shearing system, pay-off is all the time with the speed at the uniform velocity feeding strip of sheet material of setting, and do not have acceleration and deceleration and stand-by time in shear history, shear precision and throughput rate significantly improve.

Flying shear control system domestic at present still adopts constant acceleration and deceleration to follow the mode of feeding.This tracing of the movement algorithm due to its acceleration and acceleration unsmooth, cause that moving component is stressed easily has sudden change, the wearing and tearing of mechanical part are comparatively large, affect the serviceable life of equipment; Also affect the model-following control effect of servo-drive system simultaneously, shear precision is reduced.

Summary of the invention

The technical problem to be solved in the present invention is: the control of tracing of the movement algorithm to flying shearing machine that the flying shear control system of prior art uses is unsmooth, causes the wearing and tearing of mechanical part comparatively large, affects service life of a machine, reduce the precision of shearer.

Technical scheme of the present invention is: a kind of flying shearing machine control method based on luminance curve, flying shearing machine control the motion in acceleration region and decelerating area of flying shearing machine scissors by quintic curve, make in flying shearing machine retaining zone, flying shear angular velocity of rotation is with transmitting the synchronous of material movement speed, and described quintic curve is:

f(u)＝Au ⁵+Bu ⁴+Cu ³+Du ²+Eu+F

In formula, u is the length of feeding, and f (u) follows the angle of rotor motion, i.e. the flying shear anglec of rotation for flying shearing machine scissors, is flying shearing machine rotor position by flying shear anglec of rotation f (u) conversion, and then controls flying shearing machine motion, is specially:

With rotor center for initial point sets up coordinate system, if two of flying shearing machine retaining zone end points are respectively: retaining zone starting point coordinate (u ₁, p ₁) and retaining zone terminal point coordinate (u ₀, p ₀), quintic curve to the single order of u and second derivative is:

$\frac{\mathrm{df}\left(u\right)}{\mathrm{du}}=5A{u}^4+4B{u}^3+3C{u}^2+2\mathrm{Du}+E$

$\frac{d^{2}f\left(u\right)}{d{u}^2}=20A{u}^3+12B{u}^2+6Cu+2D$

Its coefficient obtains from Matrix Calculating below:

$\left|\begin{array}{cccccc}{u_0}^5& {u_0}^4& {u_0}^3& {u_0}^2& {u_0}^1& 1\\ {u_1}^5& {u_1}^4& {u_1}^3& {u_1}^2& {u_1}^1& 1\\ 5{u_0}^4& 4{u_0}^3& 3{u_0}^2& 2u_0& 1& 0\\ 5{u_1}^4& 4{u_1}^3& 3{u_1}^2& 2u_1& 1& 0\\ 20{u_0}^3& 12{u_0}^2& 6u_0& 2& 0& 0\\ 20{u_1}^3& 12{u_1}^2& 6u_1& 2& 0& 0\end{array}\right|\left\{\begin{array}{c}A\\ B\\ C\\ D\\ E\\ F\end{array}\right\}=\left\{\begin{array}{c}{p}_0\\ p_1\\ \frac{d{p}_0}{\mathrm{du}}\\ \frac{d{p}_1}{\mathrm{du}}\\ \frac{d^2{p}_0}{d{u}^2}\\ \frac{d^2{p}_1}{d{u}^2}\end{array}\right\}$

Utilize retaining zone starting point (L, p ₁), retaining zone terminal (0, p ₀), first order derivative and second derivative six conditions try to achieve six coefficient solutions of quintic curve:

$A=\frac{1}{{u_1}^5}[6(p_1-p_0)-3(\frac{{\mathrm{dp}}_1}{\mathrm{du}}+\frac{{\mathrm{dp}}_0}{\mathrm{du}})u_1+\frac{1}{2}(\frac{d^2{p}_1}{d{u}^2}-\frac{d^2{p}_0}{d{u}^2}){u_1}^2]$

$B=\frac{1}{{u_1}^4}[-15(p_1-p_0)+(7\frac{{\mathrm{dp}}_1}{\mathrm{du}}+8\frac{{\mathrm{dp}}_0}{\mathrm{du}})u_1-(\frac{d^2{p}_1}{d{u}^2}-\frac{3}{2}\frac{d^2{p}_0}{d{u}^2}){u_1}^2]$

$C=\frac{1}{{2u_1}^3}[20(p_1-p_0)-4(2\frac{{\mathrm{dp}}_1}{\mathrm{du}}+3\frac{{\mathrm{dp}}_0}{\mathrm{du}})u_1+(\frac{d^2{p}_1}{d{u}^2}-3\frac{d^2{p}_0}{d{u}^2}){u_1}^2]$

$D=\frac{1}{2}\frac{d^2{p}_0}{d{u}^2}$

$E=\frac{d{p}_0}{\mathrm{du}}$

F＝p ₀。

Control when flying shearing machine run is specially: establish P ₁for retaining zone starting point, P ₀for retaining zone terminal,

First time is when shearing, scissors rotates 180 ° and arrives clipped position C from start and stop position, initial velocity, initial acceleration are all 0, realize level and smooth startup, the starting point of quintic curve is start and stop position, enter the scissors angle position of retaining zone and the final position of quintic curve, after entering retaining zone, the horizontal range s that scissors is walked is:

s＝sin(θ ₀/2)R-sin(θ ₀/2-θ)R

θ in formula ₀for retaining zone angle, be set by the user; θ is the anglec of rotation after scissors enters retaining zone; R is the effective radius of rotor; S for material enter retaining zone after the distance walked;

The anglec of rotation θ obtaining scissors is:

θ＝θ ₀/2-2arcsin((sin(θ ₀/2)R-s)/R) (1)

Formula (1) carries out first derivation to s, and the relative angle speed obtaining scissors is:

$\frac{\mathrm{d\θ}}{\mathrm{ds}}=\frac{1}{\cos ({\mathrm{\θ}}_0/2-\mathrm{\θ})R}=\frac{1}{\sqrt{R^2-{(\sin ({\mathrm{\θ}}_0/2)R-s)}^2}}---\left(2\right)$

Formula (2) carries out first derivation again to s, and the relative angle acceleration obtaining scissors is:

$\frac{d^2\mathrm{\θ}}{d{s}^2}=\frac{(\sin ({\mathrm{\θ}}_0/2)R-s}{{(R^2-{(\sin ({\mathrm{\θ}}_0/2)R-s)}^2)}^{\frac{3}{2}}}---\left(3\right)$

Make s=0, obtain at P ₁the relative angle speed of scissors and angular acceleration during point:

$\frac{\mathrm{d\θ}}{\mathrm{ds}}{|}_{s=0}=\frac{1}{\cos ({\mathrm{\θ}}_0/2)R}---\left(4\right)$

$\frac{d^2\mathrm{\θ}}{d{s}^2}{|}_{s=0}=\frac{\sin ({\mathrm{\θ}}_0/2)R}{{\left(\cos ({\mathrm{\θ}}_0/2)R\right)}^3}---\left(5\right)$

In first time shearing, initial velocity, initial acceleration are all 0, the starting point feed length of quintic curve is 0, terminal is sheared length L, the relative angle speed that convolution (4) and (5) obtain and angular acceleration, brought into the equations of 6 coefficients of quintic curve by these 6 boundary conditions, wherein the relative angle speed of the start position of quintic curve corresponds to the relative angle acceleration of the start position of quintic curve corresponds to corresponding to the angular velocity in the final position of quintic curve corresponding to the angular velocity in the final position of quintic curve obtain the coefficient to the quintic curve sheared next time, before controlling to shear, in acceleration region, cutter rod drives the rotation of scissors next time;

The follow-up continuous shear stress that second time starts, from clipped position C, speed still calculates by the length velocity relation of retaining zone, has been the terminal P of retaining zone always ₀point, from retaining zone symmetry, the now starting point P of quintic curve ₀speed and the accekeration of point are:

$\frac{\mathrm{d\θ}}{\mathrm{ds}}=\frac{1}{\cos ({\mathrm{\θ}}_0/2)R}---\left(6\right)$

$\frac{d^2\mathrm{\θ}}{d{s}^2}=-\frac{\sin ({\mathrm{\θ}}_0/2)R}{{\left(\cos ({\mathrm{\θ}}_0/2)R\right)}^3}---\left(7\right)$

The boundary condition of quintic curve terminal was sheared with first time, obtained the coefficient to the quintic curve sheared next time thus;

According to the quintic curve equation sheared each time, substitute into corresponding feed length u, calculate the angle that rotor followed by flying shearing machine scissors, realize controlling the operation of flying shearing machine.

Further, before flying shearing machine run, calculate maximum chopped length Lp, namely flying shearing machine are the permission maximum shear length not occurring reversing, and when actual shearing length is greater than maximum chopped length Lp, processes, be specially quintic curve:

1) quintic curve coefficient method for solving is utilized to adopt process of iteration to try to achieve at the null maximum chopped length Lp of start and stop position and speed, and the coefficient of quintic curve during corresponding Lp;

2) to maximum chopped length Lp, when calculating scissors arrival start and stop position, the length L0 of feeding;

3) cut in moving calculation process at actual (tube) length, by step 1) quintic curve that calculates punishes section at feed length L0, and insert and wait for section, that is:

When feed length u is less than or equal to L0, call the anglec of rotation that quintic curve calculates scissors;

When feed length u is greater than L0 and is less than or equal to L-Lp-2L0, never call the anglec of rotation that quintic curve calculates scissors, scissors speed remains 0;

When feed length is greater than L-Lp-2L0, again call the anglec of rotation that quintic curve function calculates scissors.

The present invention abandons the flying shear movement locus synchronized algorithm based on constant acceleration and deceleration track algorithm, proposes a kind of flying shear movement locus synchronisation control means based on high order curve.The present invention is while ensureing the speed of flying shear rotary motion, acceleration and acceleration smooth excessiveness, and what can realize lots processed shortly to cut, longly cut trajectory planning, obtains higher shear precision and production efficiency.

Accompanying drawing explanation

Fig. 1 is the principle of work schematic diagram of flying shearing machine.

Fig. 2 is the coordinate schematic diagram of flying shearing machine.

Fig. 3 is the quintic curve that the present invention grows when cutting untreated.

Fig. 4 is the embodiment of the present invention 1 flying shear angle and angle velocity chart, and (a) is flying shear angle, and (b) is flying shear angular velocity.

Fig. 5 is the embodiment of the present invention 2 flying shear angle and angle velocity chart, and (a) is flying shear angle, and (b) is flying shear angular velocity.

Fig. 6 is the embodiment of the present invention 3 flying shear angle and angle velocity chart, and (a) is flying shear angle, and (b) is flying shear angular velocity.

Fig. 7 is the embodiment of the present invention 4 flying shear angle and angle velocity chart, and (a) is flying shear angle, and (b) is flying shear angular velocity.

Embodiment

Fig. 1 is existing flying shearing machine fundamental diagram, and flying shear is waited in start and stop position and being sheared, and material testing apparatus detects feed length, and when the length of feeding meets acceleration environment, Acceleration of starting runs; The travelling speed that after entering retaining zone, the component velocity of its horizontal direction is expected with transmission is all the time equal, namely synchronously, has sheared after leaving retaining zone, slows down and gets back to start and stop position, waits for and shearing next time.Because scissors moves with rotor, control the rotation that scissors is equivalent to control rotor.

The parameter of user to the input of flying shearing machine comprises: effective girth, sheared length, the retaining zone angle of rotor, be synchronized with the movement coefficient and cutter head quantity.

Quintic curve of the present invention controls flying shearing machine scissors after completing once shearing, scissors is in the motion of acceleration region and decelerating area, make in continuous shear stress, in flying shearing machine retaining zone, flying shear angular velocity of rotation is with transmitting the synchronous of material movement speed, ensure the smooth excessiveness of speed, acceleration and acceleration that flying shear rotates, thus make flying shear rotate the level and smooth of pursuit movement.Described quintic curve is:

f(u)＝Au ⁵+Bu ⁴+Cu ³+Du ²+Eu+F

In formula, u is the length of feeding, i.e. the feed length of pick-up unit detection, counting down to sheared length L from 0, is a variable, the angle that f (u) follows for scissors.

There are 6 parameters in above-mentioned quintic curve, need 6 boundary conditions to go to calculate.These conditions comprise retaining zone starting point P ₁coordinate (u ₁, p ₁) and retaining zone terminal P ₀coordinate (u ₀, p ₀), as shown in Figure 2, set up coordinate system with rotor center, here the p of ordinate ₀and p ₁value be different, Fig. 2 is schematic diagram, and symmetrical physically derivation curved boundary conditions has identical characteristic just under connecting and cutting situation, is in fact asymmetric from numerically saying.

4 boundary conditions are also had to be p ₀and p ₁first order derivative and second derivative quintic curve to the single order of u and second derivative is:

$\frac{\mathrm{df}\left(u\right)}{\mathrm{du}}=5A{u}^4+4B{u}^3+3C{u}^2+2\mathrm{Du}+E$

$\frac{d^{2}f\left(u\right)}{d{u}^2}=20A{u}^3+12B{u}^2+6Cu+2D$

Its coefficient can obtain from Matrix Calculating below:

$\left|\begin{array}{cccccc}{u_0}^5& {u_0}^4& {u_0}^3& {u_0}^2& {u_0}^1& 1\\ {u_1}^5& {u_1}^4& {u_1}^3& {u_1}^2& {u_1}^1& 1\\ 5{u_0}^4& 4{u_0}^3& 3{u_0}^2& 2u_0& 1& 0\\ 5{u_1}^4& 4{u_1}^3& 3{u_1}^2& 2u_1& 1& 0\\ 20{u_0}^3& 12{u_0}^2& 6u_0& 2& 0& 0\\ 20{u_1}^3& 12{u_1}^2& 6u_1& 2& 0& 0\end{array}\right|\left\{\begin{array}{c}A\\ B\\ C\\ D\\ E\\ F\end{array}\right\}=\left\{\begin{array}{c}{p}_0\\ p_1\\ \frac{d{p}_0}{\mathrm{du}}\\ \frac{d{p}_1}{\mathrm{du}}\\ \frac{d^2{p}_0}{d{u}^2}\\ \frac{d^2{p}_1}{d{u}^2}\end{array}\right\}$

Utilize u ₀=0, u1=L, i.e. (L, p ₁), (0, p ₀), first order derivative and second derivative six conditions try to achieve six coefficient solutions of quintic curve:

$A=\frac{1}{{u_1}^5}[6(p_1-p_0)-3(\frac{{\mathrm{dp}}_1}{\mathrm{du}}+\frac{{\mathrm{dp}}_0}{\mathrm{du}})u_1+\frac{1}{2}(\frac{d^2{p}_1}{d{u}^2}-\frac{d^2{p}_0}{d{u}^2}){u_1}^2]$

$B=\frac{1}{{u_1}^4}[-15(p_1-p_0)+(7\frac{{\mathrm{dp}}_1}{\mathrm{du}}+8\frac{{\mathrm{dp}}_0}{\mathrm{du}})u_1-(\frac{d^2{p}_1}{d{u}^2}-\frac{3}{2}\frac{d^2{p}_0}{d{u}^2}){u_1}^2]$

$C=\frac{1}{{2u_1}^3}[20(p_1-p_0)-4(2\frac{{\mathrm{dp}}_1}{\mathrm{du}}+3\frac{{\mathrm{dp}}_0}{\mathrm{du}})u_1+(\frac{d^2{p}_1}{d{u}^2}-3\frac{d^2{p}_0}{d{u}^2}){u_1}^2]$

$D=\frac{1}{2}\frac{d^2{p}_0}{d{u}^2}$

$E=\frac{d{p}_0}{\mathrm{du}}$

F＝p ₀。

In order to solve the parameter in above formula, need to solve curve two end points P ₁, P ₀first order derivative and second derivative.Calculate according to the operation of flying shearing machine when solving.

The scissors number installed for one week is for 1.Fig. 2 is flying shear coordinate schematic diagram, and in flying shearing machine, take tool roller axis as axial line, clipped position is 0 °, and start stop bit is set to 180 °.First time shears, scissors 180 ° from start and stop position startup, and run to 360 ° from 180 ° and need only rotate 180 ° and just can realize shearing once, now the starting point of quintic curve is start and stop position, and terminal is P ₁; And second time scissors needs with initial velocity when shearing is that synchronous speed starts, and rotate a circle from 0 ° and just can get back to clipped position and realize shearing once, now quintic curve starting point is P ₀, terminal is P ₁, because flying shear is synchronous with feeding in retaining zone, initial velocity here refers to the speed transmitting material.Therefore first time shears different with the quintic curve parameter of continuous shear stress below.

When first time shears, initial velocity, initial acceleration are all 0, realize smoothly starting; Enter the angle position of retaining zone and the final position of quintic curve, final position is quintic curve end point, and the angle entering retaining zone refers to the angle position of scissors, and quintic curve controls the scissor motion only covering specification region.After entering retaining zone, the scissors anglec of rotation and speed will calculate according to feeding speed.As shown in Figure 2, the horizontal range s that scissors is walked is:

s＝sin(θ ₀/2)R-sin(θ ₀/2-θ)R

θ in formula ₀for retaining zone angle, be set by the user; θ is the anglec of rotation after scissors enters retaining zone; R is the effective radius of rotor; S also for material enter retaining zone after the distance walked.

The anglec of rotation θ going out scissors according to above formula reverse is

θ＝θ ₀/2-2arcsin((sin(θ ₀/2)R-s)/R) (1)

Formula (1) carries out first derivation to s, and the relative angle speed obtaining scissors is

$\frac{\mathrm{d\θ}}{\mathrm{ds}}=\frac{1}{\cos ({\mathrm{\θ}}_0/2-\mathrm{\θ})R}=\frac{1}{\sqrt{R^2-{(\sin ({\mathrm{\θ}}_0/2)R-s)}^2}}---\left(2\right)$

Formula (2) carries out first derivation again to s, and the relative angle acceleration obtaining scissors is

$\frac{d^2\mathrm{\θ}}{d{s}^2}=\frac{(\sin ({\mathrm{\θ}}_0/2)R-s}{{(R^2-{(\sin ({\mathrm{\θ}}_0/2)R-s)}^2)}^{\frac{3}{2}}}---\left(3\right)$

Make s=0, obtain at the relative angle speed of P1 point and angular acceleration

$\frac{\mathrm{d\θ}}{\mathrm{ds}}{|}_{s=0}=\frac{1}{\cos ({\mathrm{\θ}}_0/2)R}---\left(4\right)$

$\frac{d^2\mathrm{\θ}}{d{s}^2}{|}_{s=0}=\frac{\sin ({\mathrm{\θ}}_0/2)R}{{\left(\cos ({\mathrm{\θ}}_0/2)R\right)}^3}---\left(5\right)$

The relative angle speed of being tried to achieve by formula (4) and formula (5) and angular acceleration are two boundary conditions of quintic curve terminal, quintic curve played spot speed and acceleration 0, and starting point feed length 0 and terminal are sheared coefficient that 6 conditions such as terminal velocity that feed length L and formula (4) and formula (5) obtain and acceleration bring quintic curve into and are solved formula and can try to achieve first time and shear all quintic curve parameter coefficients.

When wherein first time shears, the relative angle speed of the start position of quintic curve corresponds to the relative angle acceleration of the start position of quintic curve corresponds to corresponding to the angular velocity in the final position of quintic curve corresponding to the angular velocity in the final position of quintic curve s is angular velocity in order to calculate the quintic curve final position moment and angular acceleration and the intermediate quantity introduced, without the need to calculating its concrete value.

During the follow-up shearing that second time starts, from clipped position C, speed still calculates by the length velocity relation of retaining zone, has been retaining zone P always ₀point, now P ₀point is the starting point of quintic curve, and terminal is still for entering the P of retaining zone ₁point.From retaining zone symmetry, the starting point P of quintic curve ₀speed and accekeration be

$\frac{\mathrm{d\θ}}{\mathrm{ds}}=\frac{1}{\cos ({\mathrm{\θ}}_0/2)R}---\left(6\right)$

$\frac{d^2\mathrm{\θ}}{d{s}^2}=-\frac{\sin ({\mathrm{\θ}}_0/2)R}{{\left(\cos ({\mathrm{\θ}}_0/2)R\right)}^3}---\left(7\right)$

The boundary condition of terminal was sheared with first time.Be specially: (adopting formula (6)) corresponds to corresponding to the relative angle speed of the start position of quintic curve (adopting formula (7)) corresponds to corresponding to the relative angle speed of the start position of quintic curve (adopting formula (4)) is corresponding to the angular velocity in the final position of quintic curve (adopting formula (5)) is corresponding to the angular velocity in the final position of quintic curve obtain the quintic curve of the follow-up continuous shear stress that second time starts, control the motion of flying shearing machine.

As shown in Figure 3, when sheared length is longer, the quintic curve as calculated according to starting point and end points boundary condition just there will be scissors first rotate over 180 ° to a certain angle after again reversing return back to another angle, this is unallowed in practical engineering application.Therefore the maximum length sheared when not occurring reversing to be calculated in advance, i.e. maximum chopped length Lp.When actual shearing length is greater than maximum chopped length, will process quintic curve, and wait in initial position and do not reverse when ensureing long cutting, the flatness of speed and acceleration will be ensured simultaneously.

Long computing method of cutting and computation process as follows:

1) coefficient of the quintic curve in the null maximum chopped length Lp of initial position speed and correspondence is utilized above-mentioned short quintic curve parameter acquiring method when cutting to adopt process of iteration to approach to try to achieve;

2) to maximum chopped length, scissors is calculated when arriving clipped position place, the length L0 of feeding that check point detects, i.e. now u=L0;

3) cut in moving calculation process at actual (tube) length, by step 1) quintic curve that calculates is divided into two sections at feed length L0 (namely in start and stop position), waits for sections, that is: in two intersegmental insertions

The anglec of rotation that quintic curve function calculates scissors is called when feed length is less than or equal to L0;

When feed length is greater than L0 and is less than or equal to length L-Lp-2L0, never call the anglec of rotation that quintic curve function calculates scissors, scissors rests on start and stop position, and speed remains 0;

When feed length is greater than L-Lp-2L0, again call the anglec of rotation that quintic curve function calculates scissors.

By step 3) process after, scissors there will not be the phenomenon of reversing, and operation curve transitions smooth.

The flying shear quintic curve movement locus that speed according to flying shear motion of the present invention and acceleration relation are tried to achieve, can realize the smooth motion of flying shear and high-precision synchronous orbit tracking movement; Shearing system according to the sheared length of user's input, can calculate the length needing to wait for feeding in start and stop position automatically, automatically realizes long cutting and cuts with short; The horizontal component velocity of flying shear and the speed sync of feeding can be realized in the nonlinear velocity motion of retaining zone application flying shear, thus ensure that high-precision shearing and smooth shearing area; When retaining zone, different curves can also be switched to, realize a batch shearing.

Below in conjunction with instantiation, the present invention is elaborated.Major parameter is as follows:

Rotary/shaft encoder resolution: 3600 × 4 pulses/turn;

Transmission shaft encoder resolution: 0.05mm/ pulse;

The effective girth of rotor: 800mm.

1) shortly cut, sheared length is less than or equal to maximum chopped length Lp:

Shear parameters: cutter head quantity 1; Sheared length 1000mm; Synchronous angle 30 °; Shearing point is to the distance 500mm of material tests point.

Fig. 4 and Fig. 5 for the coefficient that is synchronized with the movement be respectively 0.9 and 1.1 time, the angle of flying shear and angular velocity curve.Flying shear is the continuous shear stress to be achieved such as not in start and stop position, does not namely drop to 180 ° of place's speed that 0 realization is short continuously cuts, and (b) of Fig. 4 and Fig. 5 is angle velocity chart, and the angular velocity of two figure does not all drop to 0, and whole service process rate curve is level and smooth.Fig. 5 is at the angular velocity of retaining zone faster than Fig. 4 20%.Flying shear angular range (0 in Fig. 4, Fig. 5,15) and (345,360) be retaining zone, cause because synchronization factor is different when Fig. 5 speed is faster, the coefficient that is synchronized with the movement refers to that flying shear enters the angular velocity of synchronization zone and the proportionate relationship of material velocity.

2) length is cut, and sheared length is more than or equal to maximum chopped length Lp:

Shear parameters: cutter head quantity 2; Sheared length 1000mm; Synchronous angle 30 °; Shearing point is to the distance 500mm of material tests point.

Fig. 6 and Fig. 7 for be synchronized with the movement coefficient respectively 0.9 and 1.1 time, the speed of flying shear and angular velocity curve.This to be cutter head quantity be 2 situation, when cutter head is 2,90 ° is start and stop position, and flying shear reduces to 0 in start and stop position (90 °) place's speed, waits for a period of time to restart to shear next time, and realize long cutting, whole service process rate curve is level and smooth.Fig. 7 is at the angular velocity of retaining zone faster than Fig. 6 20%.

Claims (3)

1. the flying shearing machine control method based on luminance curve, it is characterized in that flying shearing machine control the motion in acceleration region and decelerating area of flying shearing machine scissors by quintic curve, make in flying shearing machine retaining zone, flying shear angular velocity of rotation is with transmitting the synchronous of material movement speed, and described quintic curve is:

f(u)＝Au ⁵+Bu ⁴+Cu ³+Du ²+Eu+F

In formula, u is the length of feeding, and f (u) follows the angle of rotor motion, i.e. the flying shear anglec of rotation for flying shearing machine scissors, is flying shearing machine rotor position by flying shear anglec of rotation f (u) conversion, and then controls flying shearing machine motion, is specially:

With rotor center for initial point sets up coordinate system, if two of flying shearing machine retaining zone end points are respectively: retaining zone starting point coordinate (u ₁, p ₁) and retaining zone terminal point coordinate (u ₀, p ₀), quintic curve to the single order of u and second derivative is:

$\frac{\mathrm{df}\left(u\right)}{\mathrm{du}}=5{\mathrm{Au}}^4+4{\mathrm{Bu}}^3+3{\mathrm{Cu}}^2+2\mathrm{Du}+E$

$\frac{d^{2}f\left(u\right)}{{\mathrm{du}}^2}=20{\mathrm{Au}}^3+12{\mathrm{Bu}}^2+6\mathrm{Cu}+2D$

Its coefficient obtains from Matrix Calculating below:

$\left|\begin{array}{cccccc}{u_0}^5& {u_0}^4& {u_0}^3& {u_0}^2& {u_0}^1& 1\\ {u_1}^5& {u_1}^4& {u_1}^3& {u_1}^2& {u_1}^1& 1\\ 5{u_0}^4& 4{u_0}^3& 3{u_0}^2& 2u_0& 1& 0\\ 5{u_1}^4& 4{u_1}^3& 3{u_1}^2& 2u_1& 1& 0\\ 20{u_0}^3& 12{u_0}^2& 6u_0& 2& 0& 0\\ 20{u_1}^3& 12{u_1}^2& 6u_1& 2& 0& 0\end{array}\right|\left\{\begin{array}{c}A\\ B\\ C\\ D\\ E\\ F\end{array}\right\}\left\{\begin{array}{c}{p}_0\\ p_1\\ \frac{d{p}_0}{\mathrm{du}}\\ \frac{d{p}_1}{\mathrm{du}}\\ \frac{d^2{p}_0}{{\mathrm{du}}^2}\\ \frac{d^2{p}_1}{{\mathrm{du}}^2}\end{array}\right\}$

Utilize retaining zone starting point (L, p ₁), retaining zone terminal (0, p ₀), first order derivative and second derivative six conditions try to achieve six coefficient solutions of quintic curve:

$A=\frac{1}{{u_1}^5}[6(p_1-p_0)-3(\frac{{\mathrm{dp}}_1}{\mathrm{du}}+\frac{{\mathrm{dp}}_0}{\mathrm{du}})u_1+\frac{1}{2}(\frac{d^2{p}_1}{{\mathrm{du}}^2}-\frac{d^2{p}_0}{{\mathrm{du}}^2}){u_1}^2]$

$B=\frac{1}{{u_1}^4}[-15(p_1-p_0)+(7\frac{{\mathrm{dp}}_1}{\mathrm{du}}+8\frac{{\mathrm{dp}}_0}{\mathrm{du}})u_1-(\frac{d^2{p}_1}{{\mathrm{du}}^2}-\frac{3}{2}\frac{d^2{p}_0}{{\mathrm{du}}^2}){u_1}^2]$

$C=\frac{1}{2{u_1}^3}[20(p_1-p_0)-4(2\frac{{\mathrm{dp}}_1}{\mathrm{du}}+3\frac{{\mathrm{dp}}_0}{\mathrm{du}})u_1+(\frac{d^2{p}_1}{{\mathrm{du}}^2}-3\frac{d^2{p}_0}{{\mathrm{du}}^2}){u_1}^2]$

$D=\frac{1}{2}\frac{d^2{p}_0}{{\mathrm{du}}^2}$

$E=\frac{d{p}_0}{\mathrm{du}}$

F＝p ₀。

2. a kind of flying shearing machine control method based on luminance curve according to claim 1, is characterized in that control when flying shearing machine run is specially: establish P ₁for retaining zone starting point, P ₀for retaining zone terminal,

First time is when shearing, scissors rotates 180 ° and arrives clipped position C from start and stop position, initial velocity, initial acceleration are all 0, realize level and smooth startup, the starting point of quintic curve is start and stop position, enter the scissors angle position of retaining zone and the final position of quintic curve, after entering retaining zone, the horizontal range s that scissors is walked is:

s＝sin(θ ₀/2)R-sin(θ ₀/2-θ)R

θ in formula ₀for retaining zone angle, be set by the user; θ is the anglec of rotation after scissors enters retaining zone; R is the effective radius of rotor; S for material enter retaining zone after the distance walked;

The anglec of rotation θ obtaining scissors is:

θ＝θ ₀/2-2arcsin((sin(θ ₀/2)R-s)/R) (1)

Formula (1) carries out first derivation to s, and the relative angle speed obtaining scissors is:

$\frac{\mathrm{d\θ}}{\mathrm{ds}}=\frac{1}{\cos ({\mathrm{\θ}}_0/2-\mathrm{\θ})R}=\frac{1}{\sqrt{R^2-{(\sin ({\mathrm{\θ}}_0/2)R-s)}^2}}---\left(2\right)$

Formula (2) carries out first derivation again to s, and the relative angle acceleration obtaining scissors is:

$\frac{d^2\mathrm{\θ}}{{\mathrm{ds}}^2}=\frac{(\sin ({\mathrm{\θ}}_0/2)R-s}{{(R^2-{(\sin ({\mathrm{\θ}}_0/2)-R-s)}^2)}^{\frac{3}{2}}}---\left(3\right)$

Make s=0, obtain at P ₁the relative angle speed of scissors and angular acceleration during point:

${\frac{\mathrm{d\θ}}{\mathrm{ds}}|}_{s=0}=\frac{1}{\cos ({\mathrm{\θ}}_0/2)R}---\left(4\right)$

${\frac{d^2\mathrm{\θ}}{{\mathrm{ds}}^2}|}_{s=0}=\frac{\sin ({\mathrm{\θ}}_0/2)R}{{\left(\cos ({\mathrm{\θ}}_0/2)R\right)}^3}---\left(5\right)$

In first time shearing, initial velocity, initial acceleration are all 0, the starting point feed length of quintic curve is 0, terminal sheared length L, the relative angle speed that convolution (4) and (5) obtain and angular acceleration, brought into the equations of 6 coefficients of quintic curve by these 6 boundary conditions, wherein the relative angle speed of the start position of quintic curve corresponds to the relative angle acceleration of the start position of quintic curve corresponds to corresponding to the angular velocity in the final position of quintic curve corresponding to the angular velocity in the final position of quintic curve obtain the coefficient to the quintic curve sheared next time, before controlling to shear, in acceleration region, cutter rod drives the rotation of scissors next time;

The follow-up continuous shear stress that second time starts, from clipped position C, speed still calculates by the length velocity relation of retaining zone, has been the terminal P of retaining zone always ₀point, from retaining zone symmetry, the now starting point P of quintic curve ₀speed and the accekeration of point are:

$\frac{\mathrm{d\θ}}{\mathrm{ds}}=\frac{1}{\cos ({\mathrm{\θ}}_0/2)R}---\left(6\right)$

$\frac{d^2\mathrm{\θ}}{{\mathrm{ds}}^2}=-\frac{\sin ({\mathrm{\θ}}_0/2)R}{{\left(\cos ({\mathrm{\θ}}_0/2)R\right)}^3}---\left(7\right)$

The boundary condition of quintic curve terminal was sheared with first time, obtained the coefficient to the quintic curve sheared next time thus;

According to the quintic curve equation sheared each time, substitute into corresponding feed length u, calculate the angle that rotor followed by flying shearing machine scissors, realize controlling the operation of flying shearing machine.

3. a kind of flying shearing machine control method based on luminance curve according to claim 1 and 2, it is characterized in that calculating maximum chopped length Lp before flying shearing machine run, namely flying shearing machine are the permission maximum shear length not occurring reversing, when actual shearing length is greater than maximum chopped length Lp, quintic curve is processed, is specially:

1) quintic curve coefficient method for solving is utilized to adopt process of iteration to try to achieve at the null maximum chopped length Lp of start and stop position and speed, and the coefficient of quintic curve during corresponding Lp;

2) to maximum chopped length Lp, when calculating scissors arrival start and stop position, the length L0 of feeding;

3) cut in moving calculation process at actual (tube) length, by step 1) quintic curve that calculates punishes section at feed length L0, and insert and wait for section, that is:

When feed length u is less than or equal to L0, call the anglec of rotation that quintic curve calculates scissors;

When feed length u is greater than L0 and is less than or equal to L-Lp-2L0, never call the anglec of rotation that quintic curve calculates scissors, scissors speed remains 0;

When feed length is greater than L-Lp-2L0, again call the anglec of rotation that quintic curve function calculates scissors.