CN107179746B - A method of eliminating the moving platform fluctuation of speed of parallel architecture main tapping terminal - Google Patents
A method of eliminating the moving platform fluctuation of speed of parallel architecture main tapping terminal Download PDFInfo
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- CN107179746B CN107179746B CN201710470566.4A CN201710470566A CN107179746B CN 107179746 B CN107179746 B CN 107179746B CN 201710470566 A CN201710470566 A CN 201710470566A CN 107179746 B CN107179746 B CN 107179746B
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- speed
- moving platform
- main tapping
- parallel architecture
- terminal moving
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/41—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that path
- G05B19/4103—Digital interpolation
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/34—Director, elements to supervisory
- G05B2219/34169—Coarse interpolator, path calculator delivers position, speed, acceleration blocks
Abstract
The invention discloses a kind of methods for eliminating the moving platform fluctuation of speed of parallel architecture main tapping terminal, belong to machine tool technology field.This method initially sets up the constraint relationship between parallel architecture main tapping terminal moving platform expectation revolving speed and actual speed；The motion information of terminal moving platform is obtained according to universal numerical control code, and then establishes interpolation coordinate system, and each interpolation position of terminal moving platform during rotation is calculated；The transient speed calculation formula for further obtaining parallel architecture main tapping terminal moving platform, the actual speed of terminal moving platform is calculated using the formula；Then comparison actual speed and desired revolving speed optimize feed rate if being unsatisfactory for the constraint relationship to eliminate the fluctuation of speed of terminal moving platform.The present invention solves the problems, such as parallel architecture main tapping because of the terminal fluctuation of speed caused by nonlinear velocity transmission characteristic, effectively increases the speed stability in motion process.
Description
Technical field
The invention belongs to machine tool technology field, in particular to the velocity of rotation of parallel architecture main tapping terminal moving platform is stablized
Property problem.
Background technique
Relative to conventional serial mechanism, parallel institution theoretically has many advantages, such as higher rigidity mass ratio,
Better dynamic property and better Precision Potential.Based on these theory advantages, parallel institution is widely used in practical work
Industry wherein the parallel architecture main tapping based on parallel institution is the important equipment in current High-speed machining field, and has largely simultaneously
Connection configuration main tapping is designed, manufactured, but most of parallel architecture main tappings are unable to satisfy practical application request, it is therefore desirable into
One step promotes its comprehensive performance, and among these, how to eliminate the fluctuation of speed of parallel architecture main tapping terminal moving platform is one
Key technical problem urgently to be resolved.
No matter the stability of serial configured main tapping or parallel architecture main tapping, terminal moving platform movement velocity is direct
Determine the stability of tool motion speed.The rotary motion of parallel architecture main tapping terminal moving platform is by each drive shaft of joint space
Linear motion determine that but there are strong nonlinear velocity transmission characteristics between terminal moving platform and each drive shaft, therefore in reality
In the motion process on border, there is the apparent fluctuation of speed in parallel architecture main tapping terminal moving platform, and then causes process tool
The fluctuation of speed, workpiece surface quality is unqualified during eventually leading to processing curve, the processing of strong influence practical work piece
Effect.Conventional serial configuration main tapping is able to maintain the preferable velocity-stabilization of terminal moving platform by the optimization of simple feed rate
Property, but its speed transmission characteristic be it is linear, do not have nonlinear characteristic, therefore its feed rate optimization method is no longer desirable for
Parallel architecture main tapping.
Do not have a kind of effective solution method also for parallel architecture main tapping fluctuation of speed problem at present, is gone here and there using tradition
Connection configuration main tapping feed rate optimization method is unable to satisfy actual processing demand, therefore combines parallel architecture main tapping feature,
For its nonlinear velocity transmission characteristic, propose that one kind effectively eliminates the method for the terminal moving platform fluctuation of speed to promotion extensively
The movement velocity stability of parallel architecture main tapping is of great significance.
Summary of the invention
The purpose of the present invention is the movement velocity stability to improve parallel architecture main tapping, by proposing a kind of eliminate simultaneously
Join the method for the configuration main tapping terminal moving platform fluctuation of speed, to solve parallel architecture main tapping because nonlinear velocity transmitting is special
Fluctuation of speed problem caused by property.
Technical scheme is as follows:
A method of eliminating the moving platform fluctuation of speed of parallel architecture main tapping terminal, it is characterised in that this method includes such as
Lower step:
1) it establishes actual speed and it is expected the constraint relationship between revolving speed:
In formula,WithThe respectively actual speed of parallel architecture main tapping terminal moving platform and desired revolving speed；||||2For
Opposite direction measures mould, characterizes revolving speed size；τ % is the fluctuation of speed range allowed；
2) cartesian coordinate system O-XYZ is established, according to universal numerical control code, obtains the motion information [A of terminal moving platformi
Bi] and [Ae Be], wherein AiWith AeRespectively terminal moving platform movement starting is at the end of around the corner of OX axis direction, BiWith Be
Respectively terminal moving platform movement starting and at the end of around OY axis direction corner；
3) interpolation coordinate system o-x'y'z' is established, according to the motion information of terminal moving platform, is carried out in interpolation coordinate system
Interpolation operation:
In formula, n is interpolation points, tnFor interpolation cycle, θiWith θi-1The interpolation angle in respectively the i-th period and the (i-1)-th period
Degree；And then obtain corresponding interpolation vector are as follows:
Here OCiFor the interpolation vector in the i-th period；Ox', oy' and oz' are respectively three of interpolation coordinate system o-x'y'z'
Reference axis unit vector；
4) the transient speed calculation formula of parallel architecture main tapping terminal moving platform is established:
In formula,For the transient speed of parallel architecture main tapping terminal moving platform；F is drive shaft feed rate；Kd
It (k) is instantaneous velocity carry-over factor；And then calculate the actual speed of parallel architecture main tapping terminal moving platform during the motion
Are as follows:
In formula,For the velocity equivalent carry-over factor in motion process, n here be 3) in insert
Complement point number；
5) it will be calculatedWith desired revolving speedIt is compared, judges whether to meet the constraint in step 1) and close
System；If meeting the constraint relationship, protects drive shaft and hold that feed rate F is constant, otherwise recalculate to obtain new feed rate
F' are as follows:
Into after next motion process, step 1) -5 is repeated), parallel architecture main tapping terminal moving platform is eliminated to realize
The fluctuation of speed.
In the above method of the invention, interpolation coordinate system o-x'y'z' is established according to following steps:
1) it calculates the start vector in motion process and terminates vector are as follows:
OA=[- sin (Bi)cos(Ai) sin(Ai) -cos(Ai)cos(Bi)]T
OB=[- sin (Be)cos(Ae) sin(Ae) -cos(Ae)cos(Be)]T
In formula, OA and OB be respectively start vector in parallel architecture main tapping terminal moving platform motion process and terminate to
Amount；
2) three reference axis unit vectors of interpolation coordinate system o-x'y'z' are calculated are as follows:
Interpolation establishment of coordinate system is completed by calculating above three reference axis unit vector；
In the above method of the invention, instantaneous velocity carry-over factor is obtained according to following steps:
1) transitive relation between terminal moving platform transient speed and each drive shaft transient motion speed is established:
In formula,AndIt is terminal moving platform around the wink of OX axis direction, OY axis direction and OZ axis direction
When revolving speed；g11(k)、g12(k)、....、g33(k) element is transmitted for instantaneous velocity；WithFor each drive shaft transient motion
Speed；
2) calculation formula of instantaneous velocity carry-over factor are as follows:
In formula, gmi、gmjMiddle m=1,2,3, i=1,2,3, j=1,2,3；ΔZiWith Δ ZjIt is respectively driven for parallel architecture main tapping
The moving displacement increment of moving axis, i=1,2,3, j=1,2,3.
A kind of method for eliminating the fluctuation of speed of parallel architecture main tapping proposed by the present invention, has the following advantages that and high-lighting
Technical effect: the present invention initially set up parallel architecture main tapping terminal moving platform expectation revolving speed and actual speed between constraint close
System；The motion information of terminal moving platform is obtained according to universal numerical control code；And then interpolation coordinate system is established, obtain terminal moving platform
Each interpolation position during rotation；The transient speed for further establishing parallel architecture main tapping terminal moving platform calculates public affairs
Formula obtains the actual speed of terminal moving platform using the formula；Actual speed and desired revolving speed are compared, is closed if being unsatisfactory for constraint
System, then optimize feed rate.The fluctuation of speed for finally eliminating parallel architecture main tapping terminal moving platform, improves end
The movement velocity stability for holding moving platform, effectively improves the motion qualities of parallel architecture main tapping.
Detailed description of the invention
Fig. 1 is a kind of typical parallel architecture main tapping.
Fig. 2 is a kind of flow chart for the method for eliminating the fluctuation of speed of parallel architecture main tapping of the present invention.
Fig. 3 is the speed conditions of the parallel architecture main tapping terminal moving platform obtained using the present invention.
In Fig. 1: the first sliding block of 1-；The second sliding block of 2-；3- third sliding block；4- terminal moving platform；The first rod piece of 5-；6- second
Rod piece；7- third rod piece.
Specific embodiment
Below in conjunction with drawings and the specific embodiments, invention is further described in detail.
Fig. 1 show a kind of typical freedom degree parallel connection configuration main tapping, and the main tapping is sliding by the first sliding block 1, second
The movement of block 2 and third sliding block 3 drives the movement of terminal moving platform 4, and the first sliding block 1, the second sliding block 2 are with third sliding block 3 by phase
Motor driven is answered, is attached between terminal moving platform 4 and the first sliding block 1 by the first rod piece 5, terminal moving platform 4 and second is slided
It is attached between block 2 by the second rod piece 6, is attached between terminal moving platform 4 and third sliding block 3 by third rod piece 7；Sliding block
1 place axis is the first drive shaft, and 2 place axis of sliding block is the second drive shaft, and 3 place axis of sliding block is third drive shaft.
Fig. 2 show a kind of process for the method for eliminating the moving platform fluctuation of speed of parallel architecture main tapping terminal of the present invention
Figure.A kind of method of the solution parallel architecture main tapping fluctuation of speed proposed is applied to the parallel architecture main tapping, the party
Specific step is as follows for method:
1) in the present embodiment, it is expected that revolving speed sizeThe fluctuation of speed range of permission is 10%, is established
It is expected that the constraint relationship between revolving speed and actual speed is as follows:
In formula,For the actual speed of parallel architecture main tapping terminal moving platform；
2) as shown in Figure 1, establishing cartesian coordinate system O-XYZ, the universal numerical control code in embodiment is read in, obtains terminal
The motion information of moving platform are as follows: [Ai Bi- π/4]=[of-π/4] and [Ae Beπ/4]=[of π/4], wherein AiWith AeRespectively eventually
Hold moving platform movement starting at the end of around the corner of OX axis direction, BiWith BeRespectively terminal moving platform movement starting and end
When around OY axis direction corner；
3) as shown in Figure 1, establishing interpolation coordinate system o-x'y'z', according to the motion information of the terminal moving platform of acquisition, meter
It calculates the start vector obtained in motion process and terminates vector are as follows:
OA=[- sin (Bi)cos(Ai) sin(Ai) -cos(Ai)cos(Bi)]T (2)
OB=[- sin (Be)cos(Ae) sin(Ae) -cos(Ae)cos(Be)]T (3)
In formula, OA and OB be respectively start vector in parallel architecture main tapping terminal moving platform motion process and terminate to
Amount；
4) unit vector of three reference axis of interpolation coordinate system O-x'y'z' is as follows:
In formula, ox', oy' and oz' are respectively the unit vector of three reference axis of interpolation coordinate system O-x'y'z'；
5) it is as follows that interpolation operation is carried out in interpolation coordinate system O-x'y'z':
In formula, n is interpolation points, tnFor interpolation cycle, size 0.1s, θiWith θi-1Respectively the i-th period and (i-1)-th
The interpolation angle in period；And then obtain corresponding interpolation vector are as follows:
Here OCiFor the interpolation vector in the i-th period；
6) biography between the terminal moving platform transient speed of parallel architecture main tapping and each drive shaft transient motion speed is established
Pass relationship:
In formula,AndIt is terminal moving platform around the wink of OX axis direction, OY axis direction and OZ axis direction
When revolving speed；g11(k)、g12(k)、....、g33(k) element is transmitted for instantaneous velocity；WithFor each drive shaft transient motion
Speed；
7) instantaneous velocity carry-over factor calculation formula is obtained:
In formula, KdIt (k) is instantaneous velocity carry-over factor；gmi、gmjMiddle m=1,2,3, i=1,2,3, j=1,2,3；ΔZiWith
ΔZjFor the moving displacement increment of each drive shaft of parallel architecture main tapping, i=1,2,3, j=1,2,3；
8) the transient speed calculation formula of parallel architecture main tapping terminal moving platform is established:
In formula,For the transient speed of parallel architecture main tapping terminal moving platform；F is drive shaft feed rate,
Size is 90mm/min；
9) actual speed of parallel architecture main tapping terminal moving platform during the motion is calculated are as follows:
In formula,For the velocity equivalent carry-over factor in motion process；
10) basis is calculatedJudge whether it meets the constraint relationship shown in formula (1), if meeting the constraint
Relationship, then keep feed rate F constant, otherwise recalculates to obtain new feed rate F' are as follows:
Into after next motion process, step 1) -10 is repeated), to realize that elimination parallel architecture main tapping terminal is dynamic flat
The fluctuation of speed of platform.
Method to further illustrate a kind of elimination parallel architecture main tapping fluctuation of speed proposed, Fig. 3, which is shown, to be adopted
After this method, the rotation speed change situation of the parallel architecture main tapping terminal moving platform in entire working space, the cross of image
Coordinate represents pivot angle A variation range, and pivot angle A is changed to π/4 from-π/4 here, and ordinate represents pivot angle B variation range, puts here
Angle B is changed to π/4 from-π/4, and curve is the contour of parallel architecture main tapping terminal moving platform revolving speed in figure, and value is in song
It is marked on line, characterizes terminal moving platform revolving speed size, unit rad/s.See from result, after this method, entire
In working space, the revolving speed of parallel architecture main tapping terminal moving platform is respectively less than 1.1rad/s, and simultaneously greater than 0.9rad/s, full
The corresponding constraint condition of foot.Therefore, using a kind of method energy for eliminating the fluctuation of speed of parallel architecture main tapping proposed by the present invention
It effectively solves the problems, such as the parallel architecture main tapping fluctuation of speed, and then achievees the purpose that improve speed stability.
Claims (3)
1. a kind of method for eliminating the moving platform fluctuation of speed of parallel architecture main tapping terminal, it is characterised in that this method includes as follows
Step:
1) it establishes actual speed and it is expected the constraint relationship between revolving speed:
In formula,WithThe respectively actual speed of parallel architecture main tapping terminal moving platform and desired revolving speed；|| ||2For opposite direction
Mould is measured, revolving speed size is characterized；τ % is the fluctuation of speed range allowed；
2) cartesian coordinate system O-XYZ is established, according to universal numerical control code, obtains the motion information [A of terminal moving platformi Bi] and
[Ae Be], wherein AiWith AeRespectively terminal moving platform movement starting is at the end of around the corner of OX axis direction, BiWith BeRespectively
Terminal moving platform movement starting and at the end of around OY axis direction corner；
3) interpolation coordinate system o-x'y'z' is established, according to the motion information of terminal moving platform, interpolation is carried out in interpolation coordinate system
Operation:
In formula, n is interpolation points, tnFor interpolation cycle, θiWith θi-1The interpolation angle in respectively the i-th period and the (i-1)-th period；Into
And obtain corresponding interpolation vector are as follows:
Here OCiFor the interpolation vector in the i-th period；Ox', oy' and oz' are respectively three coordinates of interpolation coordinate system o-x'y'z'
Axis unit vector；
4) the transient speed calculation formula of parallel architecture main tapping terminal moving platform is established:
In formula,For the transient speed of parallel architecture main tapping terminal moving platform；F is drive shaft feed rate；Kd(k) it is
Instantaneous velocity carry-over factor；And then calculate the actual speed of parallel architecture main tapping terminal moving platform during the motion are as follows:
In formula,For the velocity equivalent carry-over factor in motion process, n here is inserting in step 3)
Complement point number；
5) it will be calculatedWith desired revolving speedIt is compared, judges whether to meet the constraint relationship in step 1)；Such as
Fruit meets the constraint relationship, then keeps drive shaft feed rate F constant, otherwise recalculates to obtain new feed rate F' are as follows:
Into after next motion process, step 1) -5 is repeated), turning for parallel architecture main tapping terminal moving platform is eliminated to realize
Speed fluctuation.
2. a kind of method for eliminating the moving platform fluctuation of speed of parallel architecture main tapping terminal according to claim 1, special
Sign is that interpolation coordinate system o-x'y'z' described in step 3) is established according to following steps:
1) it calculates the start vector in motion process and terminates vector are as follows:
OA=[- sin (Bi)cos(Ai) sin(Ai) -cos(Ai)cos(Bi)]T
OB=[- sin (Be)cos(Ae) sin(Ae) -cos(Ae)cos(Be)]T
In formula, OA and OB is respectively start vector and end vector in parallel architecture main tapping terminal moving platform motion process；
2) three reference axis unit vectors of interpolation coordinate system o-x'y'z' are calculated are as follows:
Interpolation establishment of coordinate system is completed by calculating above three reference axis unit vector.
3. a kind of method for eliminating the moving platform fluctuation of speed of parallel architecture main tapping terminal according to claim 1, special
Sign is that instantaneous velocity carry-over factor described in step 4) is obtained according to following steps:
1) transitive relation between terminal moving platform transient speed and each drive shaft transient motion speed is established:
In formula,AndTurn for terminal moving platform around the instantaneous of OX axis direction, OY axis direction and OZ axis direction
Speed；g11(k)、g12(k)、....、g33(k) element is transmitted for instantaneous velocity；WithFor each drive shaft transient motion speed
Degree；
2) calculation formula of instantaneous velocity carry-over factor are as follows:
In formula, gmi、gmjMiddle m=1,2,3, i=1,2,3, j=1,2,3；ΔZiWith Δ ZjFor each drive shaft of parallel architecture main tapping
Moving displacement increment, i=1,2,3, j=1,2,3.
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| US6865441B2 (en) * | 2002-12-19 | 2005-03-08 | National Instruments Corporation | Parallel trajectory generation, interpolation, and control in a motion control application |
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| JP2006105356A (en) * | 2004-10-08 | 2006-04-20 | Aisin Aw Co Ltd | Hydraulic control device for automatic transmission |
| CN101259617A (en) * | 2008-03-31 | 2008-09-10 | 浙江理工大学 | Fork four-freedom parallel connection robot mechanism |
| CN102722136A (en) * | 2012-06-29 | 2012-10-10 | 沈阳工业大学 | Device and method for controlling XY working platform of ultrasonic motor based on neural network |
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