CN109626044A - A kind of sheet-fed press transfer suction nozzle motion profile optimum design method - Google Patents

A kind of sheet-fed press transfer suction nozzle motion profile optimum design method Download PDF

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CN109626044A
CN109626044A CN201811364889.6A CN201811364889A CN109626044A CN 109626044 A CN109626044 A CN 109626044A CN 201811364889 A CN201811364889 A CN 201811364889A CN 109626044 A CN109626044 A CN 109626044A
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section
suction nozzle
acceleration
motion profile
length
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CN109626044B (en
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王伟
高文林
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Fuzhou University
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Fuzhou University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B65—CONVEYING; PACKING; STORING; HANDLING THIN OR FILAMENTARY MATERIAL
    • B65H—HANDLING THIN OR FILAMENTARY MATERIAL, e.g. SHEETS, WEBS, CABLES
    • B65H5/00—Feeding articles separated from piles; Feeding articles to machines
    • B65H5/22—Feeding articles separated from piles; Feeding articles to machines by air-blast or suction device
    • B65H5/222—Feeding articles separated from piles; Feeding articles to machines by air-blast or suction device by suction devices

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)

Abstract

The present invention relates to a kind of sheet-fed press transfer suction nozzle motion profile optimum design methods, it is characterized in that using hyperelliptic curve transition between the segmentation of geometric locus, the horizontal proportion coefficient and vertical scale factors of introducing trajectory segment determine equation of locus according to track regions, period.According to the length in total period and trajectory segment, determines the time of segmentation, establish segment movement journey time multinomial.By equation of locus and movement travel time polynomial, displacement, the speed, acceleration of track are calculated.Using horizontal proportion coefficient, vertical scale factors and hyperelliptic curve order as design variable, the maximum resultant acceleration in whole section of track is designed as optimization design target.The trajectory design method design parameter is few, track changeover portion line smoothing, and suction nozzle movement is steady, impact vibration is small.

Description

A kind of sheet-fed press transfer suction nozzle motion profile optimum design method
Technical field
The present invention relates to press structure design fields, and in particular to a kind of suction nozzle of paper-feeding mechanism suction nozzle motion profile Optimum design method.
Background technique
Traditional suction nozzle of paper-feeding mechanism suction nozzle motion profile is divided into four sections of design, although can be realized transfer function, Biggish velocity perturbation is generated at horizontal displacement turning point, is used circular curve transition in corner changeover portion, is easy to produce larger Acceleration, certain vibration is easy to produce for mechanism, reduces the service life of machine, increases printing cost.
Summary of the invention
In view of this, subtracting the purpose of the present invention is to provide a kind of feeding mechanism suction nozzle motion profile optimum design method Small traditional design bring mechanical shocks, reduce the vibration of mechanism, and it is smooth to have obtained shape transition, steady efficient movement Track.
To achieve the above object, the present invention adopts the following technical scheme:
A kind of feeding mechanism suction nozzle motion profile optimum design method, includes the following steps:
Step S1: according to working region length, period, the equation of locus of curved transition section is determined；
Step S2: changeover portion arc length is calculated to changeover portion march line integral, acquires the length of uniform rectilinear's section, and is established Movement travel time polynomial；
Step S3: according to obtained equation of locus and movement travel time polynomial, the trajectory shape of movement is calculated The characteristics of motion figure changed over time with displacement, speed, acceleration；
Step S4: by vertical scale factors, horizontal proportion coefficient and hyperelliptic curve order are as design variable, and whole section most Big resultant acceleration is optimized as design object, and at any time according to the trajectory shape of movement and displacement, speed, acceleration Between the characteristics of motion figure that changes, obtain optimal motion track and characteristics of motion figure that displacement, speed, acceleration change over time.
Further, the step S1 specifically:
Step S11: motion profile is divided into eight sections；
Step S12: it is required according to transfer suction nozzle technique, determines that track total kilometres horizontal distance L1, backhaul ascent stage are vertical Distance L2, paper ascent stage vertical range L3, backhaul descending branch second half section horizontal distance L4, track cycle T are taken；
Step S13: vertical scale factors λ is introduced1, horizontal proportion coefficient lambda2, hyperelliptic order m determines curved transition section Equation of locus.
Further, it includes: that take paper ascent stage ABC, AB be front half section that the movement, which is divided into eight sections, and BC is the second half section；
Transfer section CD；Backhaul ascent stage DEF, front half section DE, second half section EF；Reverse-running section FG；Backhaul descending branch GHA, first half Section GH, second half section HA；Wherein transfer section and reverse-running section use straightway.Paper ascent stage, backhaul ascent stage, backhaul descending branch is taken to adopt With hyperelliptic curve transition.
Further, the step S2 specifically:
Step S21: changeover portion arc length is calculated to changeover portion march line integral, and acquires the length of uniform rectilinear's section；
Step S22: it according to total period and every section of length, determines every of time, considers every section of first and last position displacement, speed Journey time multinomial is established in the constraint of degree, acceleration, jerk
Further, the step S3 specifically:
Step S31: will be divided into N number of micro- section the period, determine every section of differential duration, right according to movement travel time polynomial It answers duration that total kilometres are accordingly divided into micro- section of N, determines every section of differential length；
Step S32: by equation of locus x, the relationship of y calculates each micro- section of x under local coordinate, the displacement of the direction y, speed Degree, acceleration.And it is converted by coordinate translation；
Step S33: converting whole coordinate for local coordinate, obtains motion profile shape, and displacement, speed, acceleration The characteristics of motion figure changed over time.
Further, the step S4 specifically:
Step S41: by vertical scale factors λ1, horizontal proportion coefficient lambda2With hyperelliptic curve order m as design variable, Whole section of maximum resultant acceleration is as design object；
Step S42: building m- λ1-λ2-amaxFigure；
Step S43: according to m- λ1-λ2-amaxFigure calculates the corresponding length ratio coefficient lambda of minimum acceleration1And λ2, super ellipse Circle order m obtains optimal motion profile shape, and the characteristics of motion figure that displacement, speed, acceleration change over time.
Compared with the prior art, the invention has the following beneficial effects:
1, the present invention retouches transfer suction nozzle motion profile by five parameters of four zone lengths and a cycle It states, it is excessive to solve traditional design parameter, and track describes bad, designs cumbersome problem；
2, the present invention suction nozzle of paper-feeding mechanism suction nozzle motion profile is segmented again, by track geometry size with The characteristics of motion combines and synchronizes design, reduces in traditional design that the two is uncoordinated, and caused kinematics performance is bad；
3, the present invention carries out transition processing using hyperelliptic curve in six corners, and carries out to hyperelliptic curve parameter Optimization reduces the high acceleration excessively that arc transition in traditional design generates, effectively reduces the vibration of mechanism, increase machine Service life, reduce printing cost.
Detailed description of the invention
Fig. 1 is Its Track Design size and changeover portion parameter schematic diagram in the embodiment of the present invention；
Fig. 2 is differential process schematic diagram in the embodiment of the present invention；
Fig. 3 is m- λ in the embodiment of the present invention1-λ2-amaxFigure；
Fig. 4 is optimal travel-time map in the embodiment of the present invention；
Fig. 5 is optimal motion trajectory diagram in the embodiment of the present invention；
Fig. 6 is that optimal trajectory corresponds to transfer suction nozzle characteristics of motion figure in the embodiment of the present invention.
Specific embodiment
The present invention will be further described with reference to the accompanying drawings and embodiments.
Fig. 1 is please referred to, the present invention provides a kind of sheet-fed press transfer suction nozzle motion profile optimum design method, according to Following steps are realized:
Step S1: according to zone length, period.Working region shape is abstracted, motion profile is divided into eight sections, with super ellipse Circular curve transition introduces vertical scale factors λ1, horizontal proportion coefficient lambda2, hyperelliptic order m determines the track of curved transition section Equation.
The present embodiment takes L1=70mm, L2=11mm, L3=4mm, L4=7mm, T=3s；
The value of hyperelliptic changeover portion order m is followed successively by 2,4,6；
Vertical scale factors value interval λ1Value interval be [0.2,0.7]；
Horizontal proportion coefficient value section λ2Value interval be [0.01,0.06].
According to initial designs area of space size, vertical scale factors λ is used1, horizontal proportion coefficient lambda2, to determine transition Section two-semiaxle size a, b, motion profile is divided into eight sections using hyperelliptic curve changeover portion and straightway, to changeover portion into Row curve integral calculation changeover portion arc length, and the length scale of uniform rectilinear's section is acquired, it prepares for polynomial foundation；
If Fig. 1, AB sections are paragraph 1, BC sections are the 2nd section, and CD sections are the 3rd section, and DE sections are the 4th section, and EF sections are the 5th section, FG It is the 6th section, GH is the 7th section, and HA is the 8th section.Except the 3rd, 6 section is uniform rectilinear's section, remaining each section is the super of certain movement rule Oval segmental arc.1st, 2 section of lagging half axle length having the same, the 4th, 5,6 lagging half axle length having the same, the 4th, 5 have phase With vertical half shaft length.8th section of lagging half axle length is L4Size.
Changeover portion parameter a, b, m calculation method:
Paragraph 1:b1=L3×λ1；m1=m；
2nd section: a2=a1；b2=L3×(1-λ1)；m2=m；
4th section:m4=m；
5th section: a5=a4；m5=m；
7th section: a7=a4；b7=(L2+L3)×(1-λ1)；m7=m；
8th section: a8=L4；b8=(L2+L3)×λ1；m8=m；
Each section of parameter is brought intoDetermine the equation of locus of curved transition section.
Step S2: calculating changeover portion arc length to changeover portion march line integral, and acquire the length of uniform rectilinear's section, according to Total period and every section of length determine every of time, consider every section of first and last position displacement, speed, acceleration, the pact of jerk Beam establishes journey time multinomial；
1) changeover portion curve arc long calculates:
Hyperelliptic equation:
Wherein, a is lagging half axle length, and b is vertical half shaft length, and m is that hyperelliptic order is with local coordinate system first quartile Example:
(if two or three four-quadrant curves, then taking corresponding tangent value)
First derivative is sought to x (θ), y (θ), this section of arc length are as follows:
2) uniform rectilinear's segment length calculates:
l3=L1-L4-a4；
l6=L1-2×a4；
3) each time is calculated:
The velocity magnitude of each section of duration and straightway is calculated according to total cycle T using each segment length as weight；
Ti- the i-th section of duration, the track T- total period, liEach section of path length, L- total trajectory length.
3rd, 6 section of velocity magnitude:
Wherein, δ1, δ2For straightway velocity coeffficient, shuttle speed size can be adjusted according to actual requirement, value is in this example 1；
4) movement travel time polynomial:
Using the method for seven order polynomials, the first and last distance of every section of movement is considered, speed, acceleration, the constraint of jerk builds Found every section of characteristics of motion s (t)；
S (t)=a0+a1×t+a2×t2+a3×t3+a4×t4+a5×t5+a6×t6+a7×t7；
Boundary condition:
Paragraph 1:
S (0)=0；S'(0)=0；S " (0)=0；S " ' (0)=0；
s(T1)=l1；s'(T1)=0；s"(T1)=0；s"'(T1)=0；
2nd section:
S (0)=0；S'(0)=0；S " (0)=0；S " ' (0)=0；
s(T2)=l2；s'(T2)=v3；s"(T2)=0；s"'(T2)=0；
4th section:
S (0)=0；S'(0)=v3；S " (0)=0；S " ' (0)=0；
s(T4)=l4；s'(T4)=0；s"(T4)=0；s"'(T4)=0；
5th section:
S (0)=0；S'(0)=0；S " (0)=0；S " ' (0)=0；
s(T5)=l5；s'(T5)=v6；s"(T5)=0；s"'(T5)=0；
7th section:
S (0)=0；S'(0)=v6；S " (0)=0；S " ' (0)=0；
s(T7)=l7；s'(T7)=0；s"(T7)=0；s"'(T7)=0；
8th section:
S (0)=0；S'(0)=0；S " (0)=0；S " ' (0)=0；
s(T8)=l8；s'(T8)=0；s"(T8)=0；s"'(T8)=0；
Acquire the journey time multinomial s of changeover portion1(t)、s2(t)、s4(t)、s5(t)、s7 (t)、s8(t).Straightway is adopted With the mode of linear uniform motion, by its straight length divided by this section of time calculating speed, and its journey time multinomial is obtained s3(t)、s6(t)；
Step S3: being divided into N number of micro- section for whole cycle, determine every section of differential duration, corresponding according to characteristics of motion multinomial Total kilometres are accordingly divided into micro- section of N by duration, determine every section of differential length.Pass through equation of locus x, the relationship of y.Calculate local coordinate Under each micro- section of x, the direction y displacement, speed, acceleration.And converted by coordinate translation, whole seat is converted by local coordinate Mark, the trajectory shape moved, and the characteristics of motion figure that displacement, speed, acceleration change over time；
Such as Fig. 2, by taking local coordinate system first quartile as an example:
Micro- Duan Shichang:
Differential arc length are as follows: u (i+1)=s (ti+1)-s(ti)；
Equation of locus:
Derivation:
The direction y increment:
The direction y displacement: yi+1=yi+Δyi+1；
The displacement of the direction x:
The direction x increment: Δ xi+1=xi+1-xi；
When | x'(yi) | > | y'(xi) | when
The direction x increment:
The direction x displacement: xi+1=xi+Δxi+1
The displacement of the direction y:
The direction y increment: Δ yi+1=yi+1-yi；
The direction each node x, y speed is calculated in the following ways.
Each node x, y directional acceleration is calculated in the following ways.
Other changeover portions can similarly obtain the trajectory shape size under local coordinate system by loop iteration.Coordinate translation transformation X under global coordinate system, the coordinate of y, i.e. trajectory shape, such as Fig. 5 can be obtained.By displacement, speed, acceleration is corresponding with the time obtains To the characteristics of motion figure of motion profile changed over time.
Step S4: by vertical scale factors λ1, horizontal proportion coefficient lambda2With hyperelliptic curve order m as design variable, Whole section of maximum resultant acceleration is optimized as design object, in m- λ1-λ2-amaxMinimum resultant acceleration pair is found in figure The vertical scale factors λ answered1, horizontal proportion coefficient lambda2With the size of hyperelliptic curve order m value, obtain optimal motion track and Characteristics of motion figure.
1) optimized parameter is found:
Acceleration array is established at every section, will be stored in array by every section of resulting acceleration of circulation every time, and be obtained m, λ1、λ2、 amaxCorresponding data list.Data are exported from data list, as Fig. 3 establishes λ1-λ2-m-amaxFigure, finds minimum acceleration pair The length ratio coefficient lambda answered1And λ2, hyperelliptic order m；
Such as Fig. 3 a), as m=2, motion profile resultant acceleration shows Minimum Area.Region of search is reduced, m=2 is taken, By λ1、λ2It as variable, calculates each subparameter and corresponds to resultant acceleration size, such as Fig. 3 b), that is, work as m=2, λ1=0.6, λ2=0.02 When have minimum resultant acceleration, 9.05m/s2, such as Fig. 6 d).That is optimal design result.With the resultant acceleration under other proportionality coefficients into Row comparison is optimal design result.
2) design result is obtained:
Export m=2, λ1=0.6, λ2Suction nozzle movement travel time polynomial under=0.02 correspondence, such as Fig. 4；Optimal motion Track, Fig. 5；Optimal trajectory corresponds to transfer suction nozzle displacement-speed-accelerating curve, such as Fig. 6.It is provided for the reverse design of mechanism Important references.
The foregoing is merely presently preferred embodiments of the present invention, all equivalent changes done according to scope of the present invention patent with Modification, is all covered by the present invention.

Claims (6)

1. a kind of suction nozzle of paper-feeding mechanism suction nozzle motion profile optimum design method, which comprises the steps of:
Step S1: according to working region length, period, the equation of locus of curved transition section is determined;
Step S2: changeover portion arc length is calculated to changeover portion march line integral, acquires the length of uniform rectilinear's section, and establishes movement Journey time multinomial;
Step S3: according to obtained equation of locus and movement travel time polynomial, trajectory shape and the position of movement is calculated It moves, the characteristics of motion figure that speed, acceleration changes over time；
Step S4: by vertical scale factors, horizontal proportion coefficient and hyperelliptic curve order are as design variable, whole section of maximum conjunction Acceleration is optimized as design object, and is become at any time according to the trajectory shape of movement and displacement, speed, acceleration The characteristics of motion figure of change obtains optimal motion track and characteristics of motion figure that displacement, speed, acceleration change over time.
2. a kind of suction nozzle of paper-feeding mechanism suction nozzle motion profile optimum design method according to claim 1, it is characterised in that: The step S1 specifically:
Step S11: motion profile is divided into eight sections；
Step S12: it is required according to transfer suction nozzle technique, determines track total kilometres horizontal distance L1, backhaul ascent stage vertical range L2, paper ascent stage vertical range L3, backhaul descending branch second half section horizontal distance L4, track cycle T are taken；
Step S13: vertical scale factors are introduced, horizontal proportion coefficient, hyperelliptic order m determines the track of curved transition section Equation.
3. a kind of suction nozzle of paper-feeding mechanism suction nozzle motion profile optimum design method according to claim 2, it is characterised in that: It includes: that take paper ascent stage ABC, AB be front half section that the movement, which is divided into eight sections, and BC is the second half section；
Transfer section CD；Backhaul ascent stage DEF, front half section DE, second half section EF；Reverse-running section FG；Backhaul descending branch GHA, front half section GH, Second half section HA；Wherein transfer section and reverse-running section use straightway；Take paper ascent stage, backhaul ascent stage, backhaul descending branch using super Elliptic curve transition.
4. a kind of suction nozzle of paper-feeding mechanism suction nozzle motion profile optimum design method according to claim 1, it is characterised in that: The step S2 specifically:
Step S21: changeover portion arc length is calculated to changeover portion march line integral, and acquires the length of uniform rectilinear's section;
Step S22: according to total period and every section of length, determining every of time, consider every section of first and last position displacement, speed, Journey time multinomial is established in the constraint of acceleration, jerk.
5. a kind of suction nozzle of paper-feeding mechanism suction nozzle motion profile optimum design method according to claim 1, it is characterised in that: institute State step S3 specifically:
Step S31: will be divided into N number of micro- section the period, determine every section of differential duration, according to movement travel time polynomial, to it is corresponding when Total kilometres are accordingly divided into micro- section of N by length, determine every section of differential length;
Step S32: by equation of locus x, the relationship of y calculates each micro- section of x under local coordinate, the displacement of the direction y, speed, acceleration Degree；And it is converted by coordinate translation；
Step S33: converting whole coordinate for local coordinate, obtains motion profile shape, and displacement, speed, acceleration are at any time Between the characteristics of motion figure that changes.
6. a kind of suction nozzle of paper-feeding mechanism suction nozzle motion profile optimum design method according to claim 2, it is characterised in that: The step S4 specifically:
Step S41: by vertical scale factors, horizontal proportion coefficientWith hyperelliptic curve order m as design variable, whole section Maximum resultant acceleration is as design object;
Step S42: building m---amaxFigure；
Step S43: according to m---amaxFigure calculates the corresponding length ratio coefficient of minimum accelerationWith, hyperelliptic rank Secondary m obtains optimal motion profile shape, and the characteristics of motion figure that displacement, speed, acceleration change over time.
CN201811364889.6A 2018-11-16 2018-11-16 Optimized design method for motion trail of paper transfer suction nozzle of sheet-fed printing machine Active CN109626044B (en)

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CN114476864A (en) * 2022-01-13 2022-05-13 北京精密机电控制设备研究所 Control method of electromechanical servo flexible cable driving device

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CN114476864B (en) * 2022-01-13 2024-05-10 北京精密机电控制设备研究所 Control method of electromechanical servo flexible cable driving device

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