Interpolation of linear of much axis linkage reachs his " S adds decelerate " the program is algorithmic

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Summary: The article adds the S curve of speed law of decelerate compasses be to one's profit to be used at interpolation of linear of much axis linkage before add decelerate to handle. Derivation interpolation iteration is formulary, gave out to realize algorithm. In the numerical control system that uses this program algorithm at twister of fiber of much coordinate linkage, the effect is very good. The linear interpolation of linkage of 1 preface much axis reachs his to add decelerate algorithm is the core technology of system of high-grade numerical control. Decelerate is added before adding decelerate to treat branch decelerate processing is added after processing is mixed. Decelerate processing is added to be before interpolation before, its advantage depends on undertaking controlling to resultant velocity, do not affect positional precision, but want those who undertake decelerate is nodded to forecast. Decelerate is added to be used normally before add decelerate point-blank. Decelerate is being added after is to each interpolation the axis undertakes decelerate is controlled adding respectively, because there is harmonious relationship between each axis, accordingly, synthetic position may be not exact. S curve adds decelerate to be used after to add decelerate to handle normally, when the twister of fiber of much coordinate linkage that we are based on system of open mode numerical control in development, apply its at before add decelerate processing, obtained very good result. The linear interpolation S of linkage of 2 much axes adds decelerate S curve to add decelerate to plan is to point to when adding decelerate, make the derivative of its acceleration (Jerk) Da/dt is constant, reduce the impact that causes to mechanical system through coming to utmost ground to imposing the control that Jerk is worth. Additional, pass pair of acceleration and Jerk the parameter set of two physical quantity or process designing set, can come true flexible impose decelerate control, in order to get used to the operating mode of different and phyletic machine tool. Set in program of numerical control of interpolation of N dimension linear, data of a paragraph of interpolation is random | P1, p2, ... , pn, f | Among them: F is resultant velocity, p1 ～ Pn is each interpolation axis current paragraph displacement. According to linear interpolation principle, the displacement of each interpolation axis is as equal as speed comparing, have should the cent speed at each interpolation axis. Your | Pi | =P=TSEPi=1, 2, ... , NFiF(1) graph 1 " S adds decelerate " program principle is schematic in: P=(Pi2)½ expresses to synthesize displacement; TSEP expresses this linear interpolation paragraph each axis arrives at terminal place to need time at the same time; F1 ～ F2 is resultant velocity correspondence the cent speed at each interpolation axis. Your Ki=Pii=1, 2, ... , NP(2) criterion Fi=KiFi=1, 2, ... , when N(3) adds decelerate to handle afore, undertake planning to giving rate, if the graph is shown 1 times, whole add decelerate process cent to be 3 paragraphs, quicken namely paragraph (1, 2, 3 areas) , divide evenly fast paragraph (4 areas) and fast paragraph (4, 5, 6 areas) . Quickening paragraph with decelerate paragraph, include to change respectively again add decelerate division (1, 3, 5, 7 areas) add decelerate division with constant (2, 6 areas) : Change add decelerate division, | Da/dt | =J, jerk is constant value; Constant adds decelerate division, | A | =A, acceleration is constant value, divide evenly fast paragraph (4 areas) speed is worth Vc for constant. The athletic parameter of each axis becomes scale to nod power series to spread out in Te to the resultant velocity V(t) that already planned, your T=t-tx, v(t)=v(tx)+a(tx)t+½J(te)t2(4) is the same as manage, each interpolation axis is corresponding. Nod speed Vi(t)=vi(te)+ai(te)t+½Ji(tx)t2Fi=1, 2, ... , n(5) basis is linear interpolation principle, resultant velocity and speed of each interpolation axis have following scale concern: Vi(t)=Kiv(t)Fi=1, 2, ... , n(6) to above identity, due Vi(tx)=Kiv(tx) , ai(tx)=Kia(tx) , ji(tx)=KiJ(tx)(7) is random as a result of Tx a bit, this type makes clear paragraph inside the speed of each interpolation axis in adding decelerate process, acceleration and Jerk part to become scale with compound rate, acceleration and Jerk correspondence. When planning by S curve to resultant velocity, each interpolation axis is in assure dimensional contrail while, also undertake adding decelerate by S curve, namely S curve adds decelerate to be able to be used at before impose decelerate control. In the meantime, afore-mentioned relations can be used at the limiting value examination of the speed of each interpolation axis, acceleration and Jerk. S adds the interpolation recurrence formula of decelerate to set interpolation cycle to be T, be in K the synthetic displacement Sk when interpolation cycle ends is K of T(vk-1+ak-1t+½Jt2)dt=Sk-1+vk-1T+½ak-1T2+(1/6)JT300tk-10(8) of ∫ of Tk-1+Tv(t)dt=Sk-1 of ∫ of Tk-1v(t)dt+ of ∫ of Sk= ∫ Tkv(t)dt= the synthetic displacement increment inside interpolation cycle notices for Sk=vk-1T+(1/2)ak-1T2+(1/6)JT3=vk-1T+(1/2)(ak-1+(1/3)JT)T2=vk-1+(1/2)akT2=(vk-1+(1/2)akT)=vkT(9)ak=ak-1+(1/3)JT(10)vk=vk-1+(1/2)akT(11) , partition gets used to afore-mentioned recurrence formula, namely J={J, t ∈ [T0, t1] ∪ T6, t70, t ∈ (T1, t2) ∪ (T3, t4) ∪ (T5, t6)-J, t ∈ [T2, t3] ∪ [T4, t5](12) wants initiative condition Ak-1 and Vk-1 to give only, can push derive each interpolation synthesizes displacement increment periodicly. Get each interpolation shaft then the displacement increment inside interpolation cycle, the differentiate that its formula is Pik=PiSk=KiSkP(13) interval paragraph inside when adding decelerate, speed of electromotor of every block servo always should be decreased 0 hind carry out below one block again. Accordingly its are quickened paragraph with decelerate paragraph displacement is equal, see a picture 1. 1 area (the initiative speed of T0-t1) and initiative acceleration are 0, be in the displacement Pti=(1/6)Jt13 of T1 hour, its acceleration A1=A=Jts, speed Vt1=(1/2)At12=(1/2)Ats, criterion Ts=t1=A/J(14) by the graph 1 medium acceleration graph line can see V=(1/2)Ats+Atl+(1/2)Ats=A(ts+tl)(15) criterion Tl=(V/A)-(A/J)(16)ta=2ts+tl=(V/A)+(A/J)(17) by Ts, Tl, Tm the time of T7 of calculable ～ giving T0, undertake interval differentiate with this. S of distance of terminal differentiate terminus and Si of distance of each wheelbase terminus pursue algorithm of 1(19)3 of ∑ of 1(18)Si=Pi-kPik of ∑ of S=P-kSk of block diagram of flow of 2 interpolation computation describes the program that adds decelerate to undertake in interpolation pretreatment. Read in A, J, V, Pi. Computational Ki, the speed of each axis that computation gives and acceleration will be compared with the limiting value of each axis, if exceed limiting value, correction V. K of scanning speed fold, your V=KV. Initialization, t0=O, si=Pi. Speed plans, computational Tl, Ts, Tm. Buy speed plans to finish a mark. Interpolation. The computational flow block diagram of interpolation is shown 2 times like the graph, of interpolation pretreatment in adding decelerate to plan, already reached the time limits of each area, need to judge current interpolation cycle to be in interval only when interpolation, can give the displacement increment that each interpolation axis and career program get used to by computation of interpolation iteration formula, come true thereby its add decelerate. 4 epilogue the interpolation iteration that the article gave out to be based on speed S curve to add decelerate to plan is algorithmic, apply at before add decelerate processing. Although considered only usually paragraph inside add decelerate, but its thought and method are right more complex paragraph inside add decelerate and paragraph add decrease still applicable. The algorithm that the article gives out can use acceleration and acceleration derivative process designing, can the treatment operating mode that utmost ground gets used to machine tool of of all kinds numerical control, in the meantime, this algorithm is very concise also and come true easily. CNC Milling