CN109241553A - A kind of joint of mechanical arm Real-time dynamics modeling method - Google Patents
A kind of joint of mechanical arm Real-time dynamics modeling method Download PDFInfo
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Abstract
The present invention discloses a kind of joint of mechanical arm Real-time dynamics modeling method, comprising the following steps: 1, establish the kinetic model of joint of mechanical arm；The kinetic model is motor torque and motor rotary inertia, frictional force and load torque equilibrium equation；2, above-mentioned kinetic parameters are measured: 3, constructing the torsion stiffness linear model of joint of mechanical arm；4, the moment of friction model of fit of joint of mechanical arm is constructed；5, substituting into the model in step 3 and step 4 in step 1 can be completed real time implementation modeling, and the present invention can reduce joint power model and calculate the time, realize the real-time simulation of mechanical arm.
Description
Technical field
The invention belongs to dynamic modeling and simulation fields, and in particular to a kind of joint of mechanical arm Real-time dynamics modeling side
Method, the method for the present invention are suitable for large space mechanical arm Real-time Dynamics Simulation, semi-physical simulation and test, are both meeting in real time
Under the premise of property, and dynamic analysis precision is not lost.
Background technique
Space station mechanical arm is one of the key technology of China's manned space flight successive projects, for ensureing that space station exists
Safe and reliable operation during the rail service life, space station assemble construction, maintenance and repair, auxiliary spacefarer's extravehicular activity, support space
Using etc. tasks, be guarantee Chinese Space station engineering critical equipment.
Due to space station mechanical arm layout, envelope, in terms of propose more harsh constraint condition, lead to machine
Tool arm has the characteristics that draw ratio is big, flexible obvious, and in addition the in-orbit task of mechanical arm is various, operation object is more, load variation is big
The characteristics of, task verifying can not be carried out by physical prototyping on the ground according to the mechanical arm of steric requirements design, so that mechanical
The verifying of arm task becomes one of mechanical arm product design and the main problem of application.Mathematical simulation and semi-physical simulation are to solve
The main means of this problem, the development process of the mechanical arm of the states such as the U.S., Canada show the modeling of mechanical arm, emulation
Important function is all played in the design of mechanical arm, use and the development of follow-up work with verifying work.
Semi-physical system refers to the analogue system for not only including mathematical model but also including actual hardware product, space station machine
Tool arm semi-physical system generally uses the mechanical part of space station mechanical arm (i.e. the kinetic characteristics of space station mechanical arm)
Mathematical model description, electronics, logical gate (such as joint control, central controller) are substituted with actual hardware product, together
When, in order to support the use of actual hardware product, the calculating cycle of mathematical model must be in the communication cycle of actual hardware product
And calculated result is correct, i.e., mathematical model must meet the requirement of real-time and accuracy.
Based on considerations above, the exploitation of Chinese Space station mechanical arm has urgent need to mechanical arm Real-time dynamics model
It asks.Space mechanism shoulder joint is to provide power, perceived position and realizes the important component that armed lever room machine connects, and is to guarantee machinery
The key of arm motion range, kinematic accuracy and robust motion, generally using multi-stage planetary gear transmission system (such as Fig. 1 institute
Show), the accuracy of kinetic model directly determines the accuracy of whole arm model.
Canadian SPAR company is in research SRMS joint power " Structural Flexibility of the
Shuttle Remote Manipulator System Mechanical Arm》、《Upgrade of the SRMS Math
Model To Support the Orbiter Tile Repair Maneuver " when, joint is reduced to a non-linear torsion
Spring (as shown in Figure 2), joint-friction moment model are reduced to Coulomb friction model, ignore damping.Japanese aerospace research is opened
The joint JEMRMS is also reduced to such spring-Frictional model " Development of Japanese by hair mechanism
Experiment Module Remote Manipulator System ", it is more that this model is now widely used for space manipulator
In body dynamics modeling.
However, rigidity-Frictional model is since it is with apparent nonlinear characteristic, when joint motions speed is lower,
It takes and judges joint-friction torque type at quarter, more calculated performance is expended in logical operation, pass can not be applied directly to
It saves in Real-time dynamics model.
Summary of the invention
In view of this, it is dynamic to can reduce joint the present invention provides a kind of joint of mechanical arm Real-time dynamics modeling method
Mechanical model calculates the time, realizes the real-time simulation of mechanical arm.
Realize that technical scheme is as follows:
A kind of joint of mechanical arm Real-time dynamics modeling method, comprising the following steps:
Step 1, the kinetic model for establishing joint of mechanical arm；The kinetic model is that motor torque and motor rotate
Inertia, frictional force and load torque equilibrium equation；
Step 2, the above-mentioned kinetic parameters of measurement:
Step 3, the torsion stiffness linear model for constructing joint of mechanical arm；
Step 4, the moment of friction model of fit for constructing joint of mechanical arm；
Real time implementation modeling will can be completed in the model substitution step 1 in step 3 and step 4 in step 5.
Further, the torsion stiffness linear model are as follows:
K=a0+a1Δθ+a2Δθ2+a3Δθ3
Wherein: K is joint stiffness, and Δ θ is joint torsional deflection, aiFor stiffness coefficient, i=0,1,2,3.
Further, the moment of friction model of fit are as follows:
Wherein: fcFor dynamic friction torque, fvFor viscous friction coefficient, k is amplification coefficient, and v is joint angular speed
The utility model has the advantages that
(1) rigidity model in the present invention and moment of friction model can effectively fit non-linear rigidity and Coulomb frictions
Power effect, through analyzing, the two error is lower than 1%, and the model in the present invention is continuous function, effectively removes hardware logic
Calculating demand.
(2) joint power of the invention model can take into account the computational accuracy and computational efficiency of joint model.
(3 present invention can effectively support the real time implementation of the whole arm kinetic model of space manipulator, support half object of space manipulator
Manage the work such as test and validation.
Detailed description of the invention
Fig. 1 is certain space manipulator joint gear transmission system.
Fig. 2 is flexibility of joint model schematic.
Fig. 3 is coulomb+stickiness friction model schematic diagram.
Fig. 4 is joint nonlinear rigidity model schematic diagram.
Fig. 5 is joint mechanics deformation curve schematic diagram.
Fig. 6 is joint-friction torque test curve schematic diagram.
Fig. 7 is final fitting stiffness curve and test data curve synoptic diagram.
Fig. 8 is the joint-friction moment model comparison schematic diagram of different amplification coefficients.
Fig. 9 is flow chart of the present invention.
Specific embodiment
The present invention will now be described in detail with reference to the accompanying drawings and examples.
The present invention provides a kind of joint of mechanical arm Real-time dynamics modeling methods, as shown in figure 9, the present invention specifically includes
Following steps:
Step 1, the kinetic model for establishing joint of mechanical arm；The kinetic model is that motor torque and motor rotate
Inertia, frictional force and load torque equilibrium equation；
Space mechanism shoulder joint is usually multi-stage planetary gear train and driving motor composition, and joint model mainly includes closing
Return difference model, joint stiffness model, load effect and joint-friction model are saved, is converted motor output end information to by them
The information at joint end.Its kinetic model is general as described in formula (1), mainly normal including joint motor inertia, reduction ratio, electric current
The parameters such as number, non-linear rigidity, joint-friction torque, different types of joint model are slightly different.Motor torque T and motor turn
Dynamic inertia, moment of friction and load torque equilibrium equation are as follows:
In formula, θmFor motor position corner,For motor position corner angular speed,For the acceleration of motor position corner angle
Degree, J are driving assembly rotary inertia；frFor viscous friction coefficient；TjFor joint loads torque；N is joint reduction ratio.
The load and friction acted on joint passes to motor, formula (1) by the reduction ratio between joint and motor shaft
Middle joint loads torque can be calculated by following formula.
Tj=K (θm/N-θj) (2)
Wherein: N is joint reduction ratio；θjFor joint output angle；K is joint stiffness.
Load effect is the input of joint end load, and payload size has a larger impact to control, but it is for joint model
It is intended only as an extraneous input variable to have an impact controller, does not need separately to build complicated mathematical model.Joint-friction mould
Type generally uses coulomb+stickiness friction model, as shown in figure 3, its expression formula is as follows:
Wherein: f0For static friction torque, fcFor dynamic friction torque, fvFor viscous friction coefficient, v is joint angular speed.
Step 2, the above-mentioned kinetic parameters of measurement:
The parameter of required measurement include the following:
1) articulation inertia measures: articulation inertia refers to the used of joint housing, joint tooth train and bearing portions
It measures and all parts must be considered wherein when measuring articulation inertia.
For the complicated joint of multi-stage planetary gear transmission system, rotary inertia need to include joint housing and joint gear
The inertia of train.Relative to joint output end, articulation inertia is measured specifically such as formula (4)
J=Jk+Jjij 2(j=1,2...N) (4)
J in formulak--- joint housing rotary inertia；Jj--- j-th stage planetary gear rotation inertia；ij--- jth and planet
Reduction ratio of the gear relative to output end.
The modeling ability and modeling accuracy of the d solid modelings softwares such as current Pro/e are very high, and therefore, measurement joint turns
When dynamic inertia, directly it can analyze to obtain using software.
2) joint reduction ratio measures: joint reduction ratio measurement refers to the revolving speed at measurement joint motor end and joint output end
Than.Joint motor end angle can be effectively measured by measuring joint motor end code-disc, joint motor end angle speed can be obtained after difference
DegreeJoint output end angular speed can similarly be measuredThen joint reduction ratio
3) joint torsion stiffness measure: joint torsion stiffness have it is biggish non-linear (as shown in Figure 4 and Figure 5), therefore
When measuring joint torsion stiffness, joint stiffness measurement and the analysis at small deformation must be paid special attention to, it is non-linear just in measurement joint
When spending, joint motor end must be locked, be loaded in joint output end, read joint torsional deflection, joint moment-change can be drawn
Shape curve.Multi-stage planetary gear driving joint hysteretic characteristic is obvious, need to repeatedly measure and be averaged.
4) joint-friction torgue measurement: as the torsion stiffness of joint, joint-friction torque also have it is biggish it is non-linear (such as
Shown in Fig. 6), also need the joint-friction torque for paying special attention to small deformation section.Different angular speed are measured on the dynamic test stand of joint
Corresponding joint-friction torque when hypozygal steady-state operation, due to controlling the presence of equal error, what different control parameters adapted to
Speed interval is also different, and the part of joint steady-state operation must be chosen when measuring joint-friction torque.
Step 3, the torsion stiffness linear model for constructing joint of mechanical arm；
Joint real time analysis: during solution formula (1), the combined effect of joint space and rigidity causes to close
Rigidity is saved in apparent non-linear, is tested through joint stiffness, specific stiffness curve is as shown in Figure 5, it is clear that, stiffness curve is basic
Symmetrically, when dysarthrasis is smaller, joint stiffness very little.
The joint model known to Fig. 5, Fig. 6 must not stop to carry out logic judgment when calculating joint moment to determine joint-friction
The occurrence of torque, joint stiffness, causes solving speed to be greatly reduced, and test shows this in real-time simulation platform LABVIEW
Model is lower or when stress is smaller is unable to satisfy to calculate in real time and require in speed, cause its communicate with hardware product occur losing walk or
Phenomena such as dislocation.
The joint stiffness model known to Fig. 4,5 is more conform with polynomial curve, as shown in Figure 5 joint forward direction force-deflection
Curve and negative sense force-deflection curve almost symmetry, the positive and negative expression formula to force-deflection is same, and the present invention is passed through to Fig. 5
Shown in joint non-linear rigidity construct a continuous model, to substitute above-mentioned non-linear rigidity, as shown in formula (5), institute
State torsion stiffness linear model are as follows:
K=a0+a1Δθ+a2Δθ2+a3Δθ3 (5)
Wherein: K is joint stiffness, and Δ θ is joint torsional deflection, aiFor stiffness coefficient, i=0,1,2,3.
The measurement data measured by joint torsion stiffness in step (2), obtains joint mechanics-change by the measurement data
A in formula (5) can be obtained using least square method fitting in shape curveiCoefficient (as shown in Figure 7).
Step 4, the moment of friction model of fit for constructing joint of mechanical arm；
Fig. 6 is a kind of typical joint-friction torque measured curve, reflects moment of friction shown in formula (3) substantially
Model, the present invention construct a continuous function, for the simulation to Coulomb friction torque, are specifically shown in formula (6).
The moment of friction model of fit are as follows:
Wherein: fcFor dynamic friction torque, fvFor viscous friction coefficient, k is amplification coefficient, and v is joint angular speed.
It is fitted to obtain joint dynamic friction torque f through data processingcFor 121.44Nm, viscous friction coefficient fvFor
41.451Nms/ °, by optimizing algorithm, most suitable amplification coefficient k is found, friction model shown in formula (5) can be made more
Approach actual curve.The simulation curve of different amplification coefficients and actual curve are as shown in Figure 8.It obviously, can be effective when k=100
Simulation space manipulator complexity joint-friction moment model.It is at this time full curve shown in formula (6), is effectively reduced
The calculation amount of joint-friction moment model is able to satisfy space manipulator joint power model real time implementation requirement.
Real time implementation modeling will can be completed in the model substitution step 1 in step 3 and step 4 in step 5.
Model above can be used to real-time emulation system, in PXI real-time emulation system, to substitute joint in kind, use
Zero-g test, joint control, the test of central controller semi physical etc. are tieed up to complete whole arm 6, it can also be used to it is real to establish whole arm
When kinetic model for completing mechanical arm simulator carry out the whole arm number accompanying flying work of mechanical arm.
In conclusion the above is merely preferred embodiments of the present invention, being not intended to limit the scope of the present invention.
All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in of the invention
Within protection scope.
Claims (3)
1. a kind of joint of mechanical arm Real-time dynamics modeling method, which comprises the following steps:
Step 1, the kinetic model for establishing joint of mechanical arm；The kinetic model is that motor torque and motor rotation are used
Amount, frictional force and load torque equilibrium equation；
Step 2, the above-mentioned kinetic parameters of measurement:
Step 3, the torsion stiffness linear model for constructing joint of mechanical arm；
Step 4, the moment of friction model of fit for constructing joint of mechanical arm；
Real time implementation modeling will can be completed in the kinetic model of the model substitution step 1 in step 3 and step 4 in step 5.
2. a kind of joint of mechanical arm Real-time dynamics modeling method as described in claim 1, which is characterized in that the torsion is rigid
Spend linear model are as follows:
K=a0+a1Δθ+a2Δθ2+a3Δθ3
Wherein: K is joint stiffness, and Δ θ is joint torsional deflection, aiFor stiffness coefficient, i=0,1,2,3.
3. a kind of joint of mechanical arm Real-time dynamics modeling method as described in claim 1, which is characterized in that the frictional force
Square model of fit are as follows:
Wherein: fcFor dynamic friction torque, fvFor viscous friction coefficient, k is amplification coefficient, and v is joint angular speed.
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