CN105425723A - Rapid flexible mechanical beam end positioning algorithm for point-to-point small displacement translation - Google Patents

Abstract

The invention discloses a rapid flexible mechanical beam end positioning algorithm for point-to-point small displacement translation. The algorithm comprises: S1, a vibration period T0 of mechanical beam is calculated; S2, time of one period for point-to-point motion is divided into n equal parts equally, wherein the value of the n is equal to T0; S3, a speed vi at each equal part point is calculated; S4, the number Wi of pulses sent by a servo motor is calculated; and S5, interpolation computation of the pulse number Wn at the last equal part point n is carried out. Therefore, the system controller becomes simple and the operation becomes easy and reliable; because no extra hardware structure needs to be added, the system cost is reduced correspondingly and the post maintenance becomes easy. The algorithm can be widely applied to system equivalent to the flexible beam structure; and rapid and accurate positioning control of the point-to-point displacement translation can be realized.

Description

For the flexible mechanical beam end fast locating algorithm of point-to-point thin tail sheep translation

Technical field

The invention belongs to the technical field that numerically-controlled machine controls, be specifically related to a kind of flexible mechanical beam end fast locating algorithm for the translation of point-to-point thin tail sheep.

Background technology

At present, in high-speed numeric control Punching Machine Feeding mechanism, in high speed placement system and high speed sealed in unit, compliant motion mechanism end can be considered that translation flexible mechanical girder system is united, it is done at a high speed, the motion of high plus/minus speed time can be treated to: mechanical beams is planar done fast, the thin tail sheep motion of point-to-point frequently, and requires that beam end mass is at impact point place hi-Fix.Not only can reach high-speed motion to the requirement of high speed flexible beam with translation system, and require instantaneously to reach at a high speed, instantaneous accurate stopping, so require very large acceleration and very high positioning precision.Traditional way is that (1) adopts the non-contact measurement such as image technique or laser technology mode, measures the motion state of mechanical beams end, to form closed-loop system, controls beam end location; (2) elastic deformation of piezoelectric ceramics to mechanical beams is used to compensate, to reach the positioning control of beam end.

Due in the Practical Project of simulating in mechanical beams, system is generally all difficult to installation detecting device accurately to obtain the response of beam end; In addition, in (1) scheme, add the sensor measuring beam end state, while cost increases, due to adding of feedback detecting element, also can bring corresponding interference to Precision Position Location System, therefore can not implement (1) scheme.If adopting traditional scheme to make translation girder system unite instantaneously reaches at a high speed, beam end instantaneously can stop at impact point place, (2) scheme will be adopted, but piezoelectric ceramics has certain compensation ability to effect during the component vibration compensation that bendind rigidity is close, and when the bendind rigidity of component is greater than piezoelectric ceramics, its compensation effect significantly weakens, and due to piezoelectric ceramics be hard brittle material, it is also limited to the compensation range of respective members, therefore cannot meet unlike material mechanical beams motion time its end quick position control.

Therefore, need to design new, the practical flexible mechanical beam end quick position control algolithm for the translation of point-to-point thin tail sheep.

Above-mentioned discussion content object be to reader introduce may to below by the various aspects of technology relevant for the various aspects of the present invention be described and/or advocate, believe that this discussion content contributes to for reader with background's information, to be conducive to understanding various aspects of the present invention better, therefore, should be appreciated that it is discuss to read these with this angle, instead of admit prior art.

Summary of the invention

The object of the invention is to avoid deficiency of the prior art and provide a kind of flexible mechanical beam end fast locating algorithm for the translation of point-to-point thin tail sheep, it can carry out quick position to flexible mechanical beam end.

Object of the present invention is achieved through the following technical solutions:

There is provided a kind of flexible mechanical beam end fast locating algorithm for the translation of point-to-point thin tail sheep, wherein mechanical beams is by driven by servomotor, comprises the steps:

S1, according to following formulae discovery machinery vibration of beam cycle T ₀

$T_0=2\mathrm{\π}\sqrt{\frac{{\mathrm{ml}}^3}{3{\mathrm{EI}}_Z}}---\left(1\right)$

Wherein, m is the gross mass of mechanical beams and end mass, and l is the beam length of mechanical beams, and E is the Young modulus of mechanical beams material, I _zfor the cross sectional moment of inertia of mechanical beams;

S2, the time of point-to-point motion one-period is divided into n equal portions, the value of n is:

n＝T ₀(2)

S3, calculate the speed v at every Along ent place _i

Mechanical beams is done in the period of motion of a quick point-to-point, the speed v at each Along ent i (0≤i≤n-1) place _ias follows according to following formulae discovery:

$v_i=\left\{\begin{array}{cc}\frac{8s}{n^2}i,& i\∈\[0,\frac{n}{4}\]\\ \frac{4s}{n}-\frac{8s}{n^2}i,& i\∈(\frac{n}{4},\frac{n}{2}\]\\ \frac{8s}{n^2}i-\frac{4s}{n},& i\∈(\frac{n}{2},\frac{3n}{4}\]\\ \frac{8s}{n}-\frac{8s}{n^2}i,& i\∈(\frac{3n}{4},n\]\end{array}\right.,\left(i\∈Z,0\≤i\≤n-1\right)---\left(3\right)$

Wherein, s be mechanical beams from starting point to the displacement of impact point, v _ifor mechanical beams is from the 0th Along ent to the speed of (n-1) Along ent;

The umber of pulse W that S4, calculating servomotor send _i

At each Along ent place, pulsatile once sent out by servomotor, the umber of pulse W sent _iaccording to following formulae discovery be:

$W_i=\frac{1}{2}(v_i+v_{i+1})\×\frac{p}{1000}---\left(4\right)$

Wherein, W _ibe the umber of pulse that the i-th Along ent place servomotor sends, p is the umber of pulse that the transmission of 1mm needs walked by servomotor;

S5, calculate the umber of pulse W at last Along ent n place according to following formula interpolation _n

$W_n=p\×s\×1000-\underset{i=1}{\overset{n-1}{\Σ}}{W}_i---\left(5\right)$

Wherein, W _nit is the umber of pulse that the n-th Along ent place servomotor sends.

Wherein, in step s 2, mechanical beams system planar does the thin tail sheep motion fast, frequently from starting point to impact point, the motion of this section of thin tail sheep is regarded as a period of motion.

Owing to have employed above-mentioned structure, beneficial effect of the present invention: it is simpler that the present invention not only can make system controller realize, operation is more prone to reliable, and due to without the need to increasing extra hardware configuration, system cost can reduce accordingly, later stage also more easy care, can be widely used in the system that can be equivalent to flexible beam structure, does the quick and precisely positioning control of point-to-point thin tail sheep motion.

Accompanying drawing explanation

The invention will be further described to utilize accompanying drawing, but the embodiment in accompanying drawing does not form any limitation of the invention, for those of ordinary skill in the art, under the prerequisite not paying creative work, can also obtain other accompanying drawing according to the following drawings.

Fig. 1 is the structure vertical view of translation flexible mechanical girder system system.

Fig. 2 is mechanical beams control system block diagram.

Fig. 3 is the process flow diagram of algorithm of the present invention.

Embodiment

Technical scheme of the present invention is understood better in order to make those skilled in the art, below in conjunction with the drawings and specific embodiments, the present invention is described in further detail, it should be noted that, when not conflicting, the feature in the embodiment of the application and embodiment can combine mutually.

As shown in Figure 1, in the translation flexible mechanical girder system system of the present invention's application, slide block O side-to-side movement along the horizontal plane, mechanical beams one end is fixed on slide block, the other end is seamless connection one mass body.When slide block does the thin tail sheep motion of quick point-to-point in the horizontal direction, sill bolt end mass and is also moved in the horizontal direction thereupon, and produces vibration relative to slide block.The power source of whole system is servomotor, and control objectives point is at mechanical beams end mass.As shown in Figure 2, in mechanical beams control system, slide block O in servomotor Direct driver mechanical beams system, mechanical beams mechanism is also had between slide block O and end mass, when system therefore will be made to do the motion of point-to-point thin tail sheep, end mass accurately stops at impact point place, must carry out the design of control algolithm to servomotor.

As shown in Figure 3, control algolithm of the present invention comprises the steps:

The vibration period T of S1, mechanical beams ₀calculating:

$T_0=2\mathrm{\π}\sqrt{\frac{{\mathrm{ml}}^3}{3{\mathrm{EI}}_Z}}---\left(1\right)$

Wherein, m is the gross mass of beam and end mass; L is the beam length of mechanical beams; E is the Young modulus of mechanical beams material; I _zfor the cross sectional moment of inertia of mechanical beams.

S2, the time of point-to-point motion one-period is carried out decile

Mechanical beams system planar does the thin tail sheep motion fast, frequently from starting point to impact point, and the motion of this section of thin tail sheep is regarded as a period of motion, the time of this period of motion is divided into n equal portions, the value of n is:

n＝T ₀(2)

S3, calculate the speed v at every Along ent place _i

Mechanical beams system is done in the period of motion of a quick point-to-point, and the speed at each Along ent i (0≤i≤n-1) place is calculated as follows:

$v_i=\left\{\begin{array}{cc}\frac{8s}{n^2}i,& i\∈\[0,\frac{n}{4}\]\\ \frac{4s}{n}-\frac{8s}{n^2}i,& i\∈(\frac{n}{4},\frac{n}{2}\]\\ \frac{8s}{n^2}i-\frac{4s}{n},& i\∈(\frac{n}{2},\frac{3n}{4}\]\\ \frac{8s}{n}-\frac{8s}{n^2}i,& i\∈(\frac{3n}{4},n\]\end{array}\right.,\left(i\∈Z,0\≤i\≤n-1\right)---\left(3\right)$

Wherein, s be mechanical beams from starting point to the displacement of impact point, v _ifor mechanical beams system is from the 0th Along ent to the speed of (n-1) Along ent.

The umber of pulse W that S4, each step of calculating servomotor send _i

Mechanical beams system is by driven by servomotor, and at each Along ent place, pulsatile once sent out by servomotor, the umber of pulse W sent _ibe calculated as:

$W_i=\frac{1}{2}(v_i+v_{i+1})\×\frac{p}{1000}---\left(4\right)$

Wherein, W _ibe the umber of pulse that the i-th Along ent place servomotor sends, p is the umber of pulse that the transmission of 1mm needs walked by servomotor.

S5, interpolation calculate the umber of pulse W at last Along ent n place _n

$W_n=p\×s\×1000-\underset{i=1}{\overset{n-1}{\Σ}}{W}_i---\left(5\right)$

Wherein, W _nit is the umber of pulse that the n-th Along ent place servomotor sends.

Set forth a lot of detail in description above so that fully understand the present invention, but the present invention can also adopt other to be different from other modes described here and implement, and therefore, can not be interpreted as limiting the scope of the invention.

In a word; those skilled in the art although the present invention illustrates above-mentioned preferred implementation, should illustrate, although can carry out various change and remodeling; unless such change and remodeling deviate from scope of the present invention, otherwise all should be included in protection scope of the present invention.

Claims (2)

1., for a flexible mechanical beam end fast locating algorithm for point-to-point thin tail sheep translation, wherein mechanical beams is by driven by servomotor, it is characterized in that, comprises the steps:

S1, according to following formulae discovery machinery vibration of beam cycle T ₀

$T_0=2\mathrm{\π}\sqrt{\frac{{\mathrm{ml}}^3}{3{\mathrm{EI}}_Z}}---\left(1\right)$

Wherein, m is the gross mass of mechanical beams and end mass, and l is the beam length of mechanical beams, and E is the Young modulus of mechanical beams material, I _zfor the cross sectional moment of inertia of mechanical beams;

S2, the time of point-to-point motion one-period is divided into n equal portions, the value of n is:

n＝T ₀(2)

S3, calculate the speed v at every Along ent place _i

Mechanical beams is done in the period of motion of a quick point-to-point, the speed v at each Along ent i (0≤i≤n-1) place _ias follows according to following formulae discovery:

$v_i=\left\{\begin{array}{cc}\frac{8s}{n^2}i,& i\∈\[0,\frac{n}{4}\]\\ \frac{4s}{n}-\frac{8s}{n^2}i,& i\∈(\frac{n}{4},\frac{n}{2}\]\\ \frac{8s}{n^2}i-\frac{4s}{n},& i\∈(\frac{n}{2},\frac{3n}{4}\]\\ \frac{8s}{n}-\frac{8s}{n^2}i,& i\∈(\frac{3n}{4},n\]\end{array}\right.,\left(i\∈Z,0\≤i\≤n-1\right)---\left(3\right)$

Wherein, s be mechanical beams from starting point to the displacement of impact point, v _ifor mechanical beams is from the 0th Along ent to the speed of (n-1) Along ent;

The umber of pulse W that S4, calculating servomotor send _i

At each Along ent place, pulsatile once sent out by servomotor, the umber of pulse W sent _iaccording to following formulae discovery be:

$W_i=\frac{1}{2}(v_i+v_{i+1})\×\frac{p}{1000}---\left(4\right)$

Wherein, W _ibe the umber of pulse that the i-th Along ent place servomotor sends, p is the umber of pulse that the transmission of 1mm needs walked by servomotor;

S5, calculate the umber of pulse W at last Along ent n place according to following formula interpolation _n

$W_n=p\×s\×1000-\underset{i=1}{\overset{n-1}{\Σ}}{W}_i---\left(5\right)$

Wherein, W _nit is the umber of pulse that the n-th Along ent place servomotor sends.

2. the flexible mechanical beam end fast locating algorithm for the translation of point-to-point thin tail sheep according to claim 1, it is characterized in that: in step s 2, mechanical beams system planar does the thin tail sheep motion fast, frequently from starting point to impact point, the motion of this section of thin tail sheep is regarded as a period of motion.