CN106197909A - A kind of harmonic speed reducer transmission stiffness method of testing - Google Patents

Abstract

The invention discloses a kind of harmonic speed reducer transmission stiffness method of testing.The present invention is based on kinetic model and system identifying method, and under utilizing the similar periodicity of military service operating mode actual with product, band load incentive action, the method for the invention can test the motion transmission rigidity of harmonic speed reducer continuously, automatically, exactly.Meanwhile, the present invention is without being fixed harmonic speed reducer one end, the loosest to output torque measuring condition, and therefore, the present invention can directly utilize the field evidence of product and carry out online or off-line measurement, and without specific experimental provision.

Description

A kind of harmonic speed reducer transmission stiffness method of testing

Technical field

The present invention relates to harmonic speed reducer technical field, be specifically related to a kind of harmonic speed reducer transmission stiffness method of testing.

Background technology

Harmonic speed reducer be a kind of elastic deformation relying on flexible gear to realize power and the decelerator of motion transmission, because of This, it is possible to it is referred to as " strain wave actuating device ".Harmonic speed reducer is made up of three separate parts, i.e. wave producer, soft Wheel and just wheel；In the case of correct assembling, three parts all can rotate coaxially according to the transitive relation that gear ratio determines.Typically In the case of, use just wheel fixing, wave producer as input, flexbile gear as the deceleration transmission form of output.Wave producer is ellipse Round member, is arranged on inside flexbile gear, and forcing flexbile gear to produce radial deformation according to certain rule in longitudinal end becomes ellipticity；By Just taking turns few 2 gear teeth in flexbile gear ratio, therefore, when wave producer rotation is turned around, flexbile gear has the most just taken turns 2 tooth pitches of retrogressing, thus Realize big retarding and compare transmission.

At present, the test to harmonic speed reducer transmission stiffness can not be realized by the computing formula promoting ordinary gear, and Depend on laboratory method to carry out；Main method of testing has the manual measurement method that loading code-disc coordinates with optical measuring system (Tan Li, from by force, Wang Changsheng etc. harmonic speed reducer rigidity test technical research [J] under high and low temperature environment. vacuum and low temperature, 2013,19 (2): 117-120.) and utilize that the servomotor that is operated under Torque Control pattern coordinates with photoelectric code disk continuous Measurement method (just the wheel gear teeth have short cylinder flexible gear harmonic reducer and transmission stiffness test device, the CN102777546B at inclination angle). The former needs artificial repeatable operation, comparatively laborious, and the data obtained are the most discrete；The latter can measure the most rapidly, continuously The torsional rigidity characteristic of harmonic speed reducer.But, the most no matter it is manual discrete measuring method, or Automatic continuous measuring method All be by static state or semi-static load, acquisition be the static rigidity of harmonic speed reducer, when test otherwise fixing input, Fixing outfan, then loads static or quasistatic torsional load at the other end, then obtains by measuring torsional deflection Its transmission stiffness characteristic.

By experimentation (Tuttle T.D.Understanding and Modeling the Behavior of aHarmonic Drive Gear TransmissionR.MIT Artificial Intelligence Laboratory, 1993.Report No.:AD-A259 610.) understand, harmonic speed reducer performance in static rigidity and product actual moving process There is some difference for dynamic rate out.Particularly to harmonic wave drive speed reducer, due to it both by joint assembly pretightening power, be The impact of intrinsic factor such as system frictional force and joint space etc., is turned by actual loading, the speed of service, system resonance, wave producer again Angles etc. use the impact of condition, and this species diversity can be bigger.Tuttle reaches a conclusion according to great many of experiments and points out, these factors can be led Causing the difference fluctuating margin between static rigidity and the dynamic rate of harmonic drive system can be more than 30%.Practical implementation is also Show: this species diversity often lead to the staring torque of actual product commonly greater than theoretical expectation values and model predication value, startup or Deboost phase there is also step-out phenomenon, and the real response of dynamic operation and theoretical prediction response exist certain deviation.

Summary of the invention

In view of this, the invention provides a kind of harmonic speed reducer transmission stiffness method of testing, it is possible to obtain humorous exactly The dynamic rate of ripple decelerator driving joint.

A kind of harmonic speed reducer transmission stiffness method of testing, comprises the steps:

Step one, the product constituted using harmonic speed reducer joint, as object, utilize its control system, the output to product End controls so that it is make the reciprocating motion of rule；

Step 2, test environment according to the correlative factor and product affecting transmission stiffness, set up the harmonic wave in product The kinetic model of decelerator joint transmission rigidity, and set up corresponding constraints；

Step 3, start product to be measured, start test:

According to motor gain of parameter harmonic speed reducer joint input angle；Directly measure the output of harmonic speed reducer joint Angle；Utilize difference algorithm, export according to each moment harmonic speed reducer joint input angle and each moment harmonic speed reducer joint Angle, it is thus achieved that input angular velocity and Output speed；Relative angle speed is obtained according to the input angular velocity obtained and Output speed Degree；Relative angular displacement is obtained according to the input angle obtained and output angle；

Test n group altogether, it is thus achieved that n group kinematics parameters；

Step 4, according to the n group kinematics parameters obtained in step 3, utilize Output speed information, employing calculus of finite differences Estimate output angle acceleration information, and utilize moving average filter that the output angle acceleration information of gained is filtered place Reason, it is thus achieved that filtered output angle acceleration；

Harmonic speed reducer joint outfan inertia is multiplied with filtered output angle acceleration information, it is thus achieved that harmonic reduction Device joint outfan moment；And ask all relative angular displacements and the meansigma methods of joint output torque, it is thus achieved that average relative angular displacement With average joints output torque；

Step 5, according to the parameter obtained in step 3 and step 4, substitute into the transmission stiffness power set up in step 2 Learn in model, carry out stiffness parameters identification, and then obtain the final expression formula of transmission stiffness kinetic model；Pass in reality test During dynamic stiffness, the relative angular displacement of harmonic speed reducer is substituted into, can obtain the output torque in harmonic speed reducer joint, and then really Determine the relation between output torque and relative angular displacement, i.e. transmission stiffness.

It is preferred that when test condition allows to use additional testing equipment, utilize torque sensor to obtain in step 4 Harmonic speed reducer joint output torque.

It is preferred that in step 3, utilize the photoelectric encoder in product directly to measure harmonic speed reducer joint output angle.

Beneficial effect:

Based on kinetic model and system identifying method, utilizing the similar periodicity of military service operating mode actual with product, band Carrying under incentive action, the method for the invention can test the motion transmission rigidity of harmonic speed reducer continuously, automatically, exactly. May situation phase more than 30% with the difference fluctuating margin between traditional static measuring method acquired results and dynamic rate Ratio, the surveyed transmission stiffness of the present invention is i.e. the motion transmission rigidity in product actual task, and both have concordance.Meanwhile, originally Invention is without being fixed harmonic speed reducer one end, and to output torque measuring condition, the most loosely (output torque can be led to Cross kinematics parameters to estimate), therefore, the present invention can directly utilize the field evidence of product and carry out online or off-line survey Amount, and without specific experimental provision.On the one hand this can save Special testing device, is greatly saved cost, improves and produce Product development efficiency, on the other hand can measure harmonic speed reducer in the product difference military service stage move according to task needs in real time The situation of change of state transmission stiffness, thus grasp its actual be on active service during performance degradation rule, for product transmission accuracy, defeated Go out torque accuracy to keep promoting to provide with reliability instructing.It is also possible to providing harmonic speed reducer motion transmission While stiffness parameters, provide the estimation of its gap (or return difference).

Accompanying drawing explanation

Fig. 1 is that single shaft drives antenna product composition schematic diagram；

Fig. 2 is harmonic speed reducer joint schematic diagram；

Fig. 3 is harmonic speed reducer joint motion transmission load-deflection curve on-line identification result in-orbit；

Fig. 4 is harmonic speed reducer joint motion transmission rigidity linear term on-line identification result in-orbit；

Fig. 5 is harmonic speed reducer joint motion transmission linear Stiffness item on-line identification result in-orbit；

Fig. 6 is harmonic speed reducer joint space size on-line identification result in-orbit；

Fig. 7 is that harmonic speed reducer transmission stiffness ground experiment tests device；

Fig. 8 is harmonic speed reducer joint motion transmission load-deflection curve ground off-line identification result；

Fig. 9 is harmonic speed reducer joint motion transmission rigidity linear term ground off-line identification result；

Figure 10 is harmonic speed reducer joint motion transmission rigidity cube item ground off-line identification result；

Figure 11 is the ground off-line identification result of harmonic speed reducer joint motion transmission rigidity sluggishness item parameter A；

Figure 12 is the ground off-line identification result of harmonic speed reducer joint motion transmission rigidity sluggishness item parameter alpha；

Figure 13 is the ground off-line identification result of harmonic speed reducer joint motion transmission rigidity sluggishness item parameter c；

Figure 14 is identification process fitness function change curve.

1-spacecraft body, 2-antenna extension bar, 3-antenna reflective face, 4-motor, 5-harmonic speed reducer, 6-photoelectricity Encoder, 7-output shaft, 8-torque sensor, 9-inertia disc.

Detailed description of the invention

Develop simultaneously embodiment below in conjunction with the accompanying drawings, describes the present invention.

The invention provides a kind of harmonic speed reducer transmission stiffness method of testing, its main thought is:

The error brought in order to avoid the transmission stiffness measured under static state, the present invention makes harmonic reduction by control Device carries out the sinusoidal motion of rule under the conditions of band carries, and afterwards, by measuring its input, output angle just can estimate rigidity and survey The information such as torsional deflection needed for amount and loading moment, and then, utilize the corresponding optimized algorithm harmonic speed reducer to building to pass Dynamic stiffness kinetic model carries out parameter identification, just can obtain the measurement result of transmission stiffness parameter, can obtain harmonic reduction The motion transmission rigidity of device.

Embodiment 1: for the acquisition methods of the on-line measurement transmission stiffness of application product in-orbit:

Step one, configuration experiment test hardware system, by the control of driving mechanisms control system, make outfan make rule Sinusoidal motion or product perform authentic task time reciprocating motion；

Wherein, measure excitation both to have arranged given rule, the actual in commission reciprocal fortune of product can also be directly utilized Dynamic, this makes the measurement of harmonic speed reducer transmission stiffness all can conveniently carry out during product development and military service.

As it is shown in figure 1, the present embodiment is with spacecraft single shaft drive mechanism antenna product as object, it comprises drive mechanism control System processed (in spacecraft body 1 side, be not drawn in figure), antenna extension bar 2, harmonic speed reducer 5 joint and antenna reflective face 3。

Wherein, harmonic speed reducer joint is as in figure 2 it is shown, by motor 4, harmonic speed reducer 5, photoelectric encoder 6 and defeated Shaft 7 four part forms；

Wherein, driving mechanisms control system is both responsible for controlling antenna end and is pressed given regular movement, is responsible for again harmonic reduction The data processing work of device joint stiffness parameter identification process.

For simplicity's sake, the parts such as the compression relieving mechanism that comprises in single shaft drive mechanism antenna actual product, cable do not have Have and draw in FIG.

Unlike traditional measurement method: during measuring due to traditional method, harmonic speed reducer joint is in accurate static State, there is bigger error with the transmission stiffness of its reality in its transmission stiffness obtained.In order to avoid the problems referred to above occur, this The bright actual movement rule according to harmonic speed reducer joint, and then it is firm to obtain the transmission in harmonic speed reducer joint under kinestate Degree.Particularly as follows:

Actual when carrying out motion transmission stiffness measurement, by harmonic speed reducer joint output shaft, antenna reflective face 3 and support thereof Assembly is as the load of harmonic speed reducer；Harmonic speed reducer steel wheel and corresponding housing unit are fixed；Harmonic speed reducer ripple The output shaft of wave producer and motor 4 is as input.Input, under the control of driving mechanisms control system, makes output End makees sinusoidal motion by formula (1) rule.

Wherein, θ_outputFor output angle；t_ConFor system operation time；According to the practical situation of spacecraft computing capability, Control system uses PD control algolithm, control cycle to be 1ms.

Step 2, set up the kinetic model of harmonic speed reducer joint transmission rigidity, and constraints is set.

S21, in view of the most limited measuring condition of spacecraft, the cube that the present invention sets up as shown in formula (2) is multinomial Formula is as the kinetic model of harmonic speed reducer joint transmission rigidity, and this model considers non-linear factor and the pass of transmission stiffness Internode gap.

T=a₁θ'+a₂θ'³ (2)

Wherein,

${\mathrm{\&theta;}}^{\&prime;}=\left\{\begin{array}{cc}\mathrm{\&theta;}-\mathrm{\&Delta;},& \mathrm{\&theta;}>\mathrm{\&Delta;}\\ 0,& \left|\mathrm{\&theta;}\right|\&le;\mathrm{\&Delta;}\\ \mathrm{\&theta;}+\mathrm{\&Delta;},& \mathrm{\&theta;}<-\mathrm{\&Delta;}\end{array}\right.$

Wherein, a₁,a₂For stiffness parameters to be estimated；T is the measured value of output torque；θ is the relative of sign joint deformity Angular displacement (containing gap), is calculated by the measured value of input/output angle and obtains；Δ is harmonic speed reducer joint space；θ ' is for closing The true strain amount (without gap) of joint, i.e. joint torsion angle；In order to calculate process continuously, conveniently, in actual test or application, The piecewise function characterizing joint torsion angle in formula (2) can approximate with hyperbolic function.

S22, based on the kinetic model set up in S21, set up constraints as shown in formula (3)；This constraints (is received Hold back criterion) it is the actual output data sequence of system and the minimum identification of error sum of squares of kinetic model prediction output sequence Optimality Criteria；That is: actual minimum with simulation error；

$J\left({\mathrm{\&theta;}}^{\&prime;}\right)=\underset{k=1}{\overset{L}{\&Sigma;}}{\&lsqb;T_k-f\left({{\mathrm{\&theta;}}^{\&prime;}}_k\right)\&rsqb;}^2---\left(3\right)$

Wherein,

${{\mathrm{\&theta;}}^{\&prime;}}_k==\left\{\begin{array}{cc}{\mathrm{\&theta;}}_k-\mathrm{\&Delta;},& {\mathrm{\&theta;}}_k>\mathrm{\&Delta;}\\ 0,& \left|{\mathrm{\&theta;}}_k\right|\&le;\mathrm{\&Delta;}\\ {\mathrm{\&theta;}}_k+\mathrm{\&Delta;},& {\mathrm{\&theta;}}_k<-\mathrm{\&Delta;}\end{array}\right.---\left(4\right)$

f(θ'_k)=a₁θ'_k+a₂θ'_k ³

In formula, θ '_k、θ_k、T_kBeing respectively kth torsion angle, kth relative angular displacement and kth output torque value, L is number According to length；f(θ'_k) it is the motion transmission rigidity identification model that characterizes of formula (2) shape after substituting into kth relative angular displacement data Formula.

Step 3, test primary data, it is thus achieved that kinematics parameters.

Measuring process due to tasks carrying process and harmonic speed reducer transmission stiffness to unite two into one, therefore, system to be treated is transported The estimation work of stiffness parameters is started after row a period of time.Under normal circumstances, according to the ability of above-mentioned control system, select to wait be System starts stiffness parameters identification work after running 6～7 seconds.At this moment, the initial data being available for parameter identification of accumulation has 6000. Therefore according to formula (5) to formula (8), obtain 6000 groups of kinematics parameters altogether.The acquisition methods of concrete kinematics parameters is as follows:

Motor parameter is utilized to calculate harmonic speed reducer joint input angle θ_Input, see formula (5).

θ_Input=q θ₀n (5)

In formula, q is the frequency of Stepping Motor Subdivision Driver, θ₀For motor step angle, n is sampling time internal control The pulse number that system processed sends to motor.

Photoelectric encoder 6 is utilized directly to measure harmonic speed reducer joint output angle θ_output。

Utilize difference algorithm, by sampling time sequence, each moment harmonic speed reducer joint input angle and each moment harmonic wave Decelerator joint output angle calculates input angular velocity respectivelyAnd Output speedDifference algorithm formula is as follows:

$\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{Input,k}=\frac{{\mathrm{\&theta;}}_{Input,k}-{\mathrm{\&theta;}}_{Input,k-1}}{t},k=2,3,4,\mathrm{...},L\\ {\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{Output,k}=\frac{{\mathrm{\&theta;}}_{Output,k}-{\mathrm{\&theta;}}_{Output,k-1}}{t},k=2,3,4,\mathrm{...},L\end{array}---\left(6\right)$

Wherein, θ_Input,k、θ_Output,kIt is respectively kth input angle and output angle measured value,Point Not Wei kth input angular velocity and Output speed value, L is data length；T is the time between kth and-1 data of kth Interval.Owing to the time interval between adjacent two data each in uniform sampling is equal, therefore, hereafter t is collectively expressed as two Time interval between adjacent data.

According to input angle and output angle angle value, it is thus achieved that characterize the relative angular displacement θ of joint deformity_kWith relative angle speedSee formula (7), formula (8).Wherein, subscript represents kth value.

${\mathrm{\&theta;}}_k={\mathrm{\&theta;}}_{Output,k}-\frac{{\mathrm{\&theta;}}_{Input,k}}{N},k=2,3,4,\mathrm{...},L---\left(7\right)$

${\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_k={\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{Output,k}-\frac{{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{Input,k}}{N},k=2,3,4,\mathrm{...}L---\left(8\right)$

In formula, N is harmonic speed reducer speed reducing ratio.

In actual test process, the driving mechanisms control system of the present invention uses Nonlinear Least-Square Algorithm to carry out dynamically The On-line Estimation of transmission stiffness.In order to obtain kinematics parameters more accurately, the present invention is provided with data sliding window, Driving mechanisms control system just starts stiffness parameters identification work after raw measurement data reaches 6000；Follow-up, along with The execution of control process, by data sliding window, constantly utilizes the kinematics parameters of up-to-date measurement to replace measurement the earliest Kinematics parameters, thus guarantee all the time for the original motion parameter of identification be 6000.

Step 4, according in step 3 obtain 6000 groups of kinematics parameters, it is thus achieved that kinetic parameter.

Utilize the input in step 3 and Output speed information, use calculus of finite differences to estimate angular acceleration information, and utilize The angular acceleration data of gained is filtered processing by moving average filter.

${\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{Output,k}=\frac{{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{Output,k}-{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{Output,k-1}}{t},k=3,4,...,L---\left(9\right)$

Wherein,Kth value for output angle acceleration.

The sliding step of moving average filter typically may be selected to be 5, and its Filtering Formula is shown in formula (10):

${\stackrel{\&OverBar;}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}}_{Output,3}={\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{Output,3}$

${\stackrel{\&OverBar;}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}}_{Output,4}=\frac{{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{Output,3}+{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{Output,4}+{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{Output,5}}{3}$

${\stackrel{\&OverBar;}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}}_{Output,k}=\frac{{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{Output,k-2}+{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{Output,k-1}+{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{Output,k}+{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{Output,k+1}+{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{Output,k+2}}{5},k=5,6,7,\mathrm{...},L-2---\left(10\right)$

Wherein,Output angle accekeration after processing for kth moving average filter.

Utilize harmonic speed reducer joint outfan inertia (known conditions), directly with outfan inertia and output angle acceleration Data are multiplied, it is thus achieved that harmonic speed reducer joint outfan moment T_k.Wherein, outfan inertia in harmonic speed reducer joint is product Payload and the inertia sum of harmonic wave reducer output shaft module, i.e. required during test loading moment is the actual fortune of product The moment of inertia that during Dong, self produces, it is not necessary to use extra loading equipemtn.

$T_k=J{\stackrel{\&OverBar;}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}}_{Output,k}---\left(11\right)$

By relative angular displacement and joint output torque, calculate average relative angular displacement and the average output torque in joint.Specifically For: first find out the minimum of relative angular displacement, maximum, the most ascending find out given relative angular displacement center at regular intervals All joints output torque corresponding near value and all relative angular displacements, then can be obtained it respectively by these two groups of data and put down Average.

By relative angular displacement θ_k(k=3,4,5 ..., L) sequence from small to large processes, simultaneously, it is thus achieved that its correspondence defeated Go out moment T_k(k=3,4,5 ..., L), form new queue, be respectively defined as: θ_kk(kk=3,4,5 ..., L) and T_kk(kk= 3,4,5,...,L).Then for k₀To k₀One group of relative angular displacement in the range of+λ and output torque data, can be in the hope of these data Average relative angular displacement in range sectionWith average output torque

$\begin{array}{c}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_{kNew}=\frac{\underset{kk=k_0}{\overset{k_0+\mathrm{\&lambda;}}{\&Sigma;}}{\mathrm{\&theta;}}_{kk}}{\mathrm{\&lambda;}+1}\\ {\stackrel{\&OverBar;}{T}}_{kNew}=\frac{\underset{kk=k_0}{\overset{k_0+\mathrm{\&lambda;}}{\&Sigma;}}{T}_{kk}}{\mathrm{\&lambda;}+1}\end{array}---\left(12\right)$

In formula, k₀Span be 3, λ+4,2 λ+5,3 λ+6 ..., its last value is L-λ；λ characterizes average Data break size during process, for the positive integer less than L, it is contemplated that DATA REASONING number and the equilibrium of average processing accuracy, General recommendations value is 4；The count flag that subscript kNew is newly introduced, starts value from natural number 1, its maximum occurrences kNew_max Determined by L and λ, see formula (13):

${\mathrm{kNew}}_{max}=\frac{L-2}{\mathrm{\&lambda;}+1}---\left(13\right)$

Data length L and λ is that value must guarantee kNew_maxFor positive integer.

Step 5, according in step 3 and step 4 obtain parameter, the kinetic model of the foundation in step 2 is entered Line parameter identification, it is thus achieved that the estimated value of transmission stiffness kinetic model stiffness parameters, the i.e. measurement of harmonic speed reducer transmission stiffness Result.

After obtaining above-mentioned average relative angular displacement and average output torque sequence, the motion transmission rigidity shown in formula (2) Model can be rewritten as the form of formula (14).At this moment, it is possible to use the Nonlinear Least-Square Algorithm pair of band data sliding window This model carries out parameter estimation, thus obtains the linear term a of harmonic speed reducer joint stiffness₁With nonlinear terms a₂, and close internode The estimated value of gap Δ.

${\stackrel{\&OverBar;}{T}}_{kNew}=a_1{{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}^{\&prime;}}_{kNew}+a_2{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}^{\&prime;}{{}_{kNew}}^3,kNew=1,2,3,...,\frac{L-2}{\mathrm{\&lambda;}+1}---\left(14\right)$

Wherein,

${{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}^{\&prime;}}_{kNew}=\left\{\begin{array}{cc}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_{kNew}-\mathrm{\&Delta;},& {\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_{kNew}>\mathrm{\&Delta;}\\ 0,& \left|{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_{kNew}\right|\&le;\mathrm{\&Delta;}\\ {\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_{kNew}+\mathrm{\&Delta;},& {\stackrel{\&OverBar;}{\mathrm{\&theta;}}}_{kNew}<-\mathrm{\&Delta;}\end{array}\right.$

Wherein,For the average torsion angle in joint.The harmonic speed reducer joint stiffness linear term a that will obtain₁, rigidity non-thread Property item a₂Substitute in formula (2) with the estimated value of clearance delta, i.e. obtain transmission stiffness kinetic model expression formula；Test in reality During transmission stiffness, the relative angular displacement of harmonic speed reducer is substituted into, can obtain harmonic speed reducer joint output torque, and then really Determine the relation between output torque and relative angular displacement, i.e. transmission stiffness.

Utilize the harmonic speed reducer motion transmission rigidity result that said method obtains as shown in Figures 3 to 6.

Fig. 3 is the spy of the harmonic speed reducer joint transmission rigidity that the identification result according to stiffness parameters and gap length draws Linearity curve.Wherein, green solid lines be the non-linear rigidity to harmonic speed reducer joint, hesitation, gap, non-linear friction, After 6 kinds of non-linear factors such as low frequency movement error and damping are accurately measured, it is dynamic that the precise kinetic model of foundation is given The ideal curve of state transmission stiffness (i.e. product actual curve most preferably approach value)；Blue real point is in the present embodiment step 4, The average output torque peace all relative angular displacement data sequence be given are estimated according to kinematics parameters；According to red dotted line The stiffness curve that the motion transmission stiffness parameters of identification and joint space value are given.

Fig. 4 is harmonic speed reducer joint motion transmission rigidity linear term a₁Identification result.Wherein, red dotted line is real The actual change curve of the rigidity linear term identification result in the identification process of border；Green straight line be according to identification result be given firm The meansigma methods of degree linear term, this value i.e. the final measured value of harmonic speed reducer motion transmission rigidity linear term；Blue solid lines (i.e. product actual characteristic is optimal for the ideal value be given for the high accuracy kinetic model after considering above-mentioned 6 kinds of non-linear factors Approach value).Fig. 5 with Fig. 6 each bar curve implication is similar with Fig. 4.

By Fig. 3 to Fig. 6 it can be seen that the measurement process of harmonic speed reducer joint motion transmission rigidity is along with the execution of task Can gradually tend towards stability；Most preferably approach value contrast to understand with product, measure the motion transmission rigidity model provided with identification process Parameter a₁,a₂94%, 92% and 85% it is better than respectively with the stable state accuracy of harmonic speed reducer joint space Δ.

Embodiment 2: for the acquisition methods of ground survey transmission stiffness:

Step 1, configuration experiment test hardware system, by the control of driving mechanisms control system, make outfan make rule Sinusoidal motion:

For the acquisition methods of ground survey transmission stiffness, its device used can with on-line measurement in-orbit time used Device identical, it is also possible to according to structure as shown in Figure 7, use the method increasing additional measurement equipment: due to without considering The measuring condition of spacecraft, therefore when ground survey transmission stiffness, use the antenna reflective face 3 in inertia disc 9 alternate embodiment 1 And carriage assembly, to simulate the inertia of payload, it is measured hardware system and also add torque sensor 8 and moment collection Card.

Actual when carrying out motion transmission stiffness measurement, using inertia disc and harmonic speed reducer joint output shaft as harmonic reduction The load of device；Harmonic speed reducer steel wheel and corresponding housing unit are fixed；The wave producer of harmonic speed reducer ripple and stepping electricity Machine 4 output shaft is as input.Input, under the control of driving mechanisms control system, makes outfan by the formula of embodiment 1 (1) rule makees sinusoidal motion.

Step 2, set up the kinetic model of harmonic speed reducer joint transmission rigidity, and constraints is set.

21st step, considering the well-to-do measuring condition in ground, the present invention sets up the harmonic speed reducer as shown in formula (15) The kinetic model in joint, this model considers the non-linear factor of transmission stiffness, rigidity hesitation and joint space.

$T=a_1\left({\mathrm{\&theta;}}^{\&prime;}\right)+a_2{\left({\mathrm{\&theta;}}^{\&prime;}\right)}^3+sign\left({\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}^{\&prime;}\right)\frac{A}{\mathrm{\&alpha;}}+sign\left({\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}^{\&prime;}\right){\mathrm{ce}}^{-sign\left({\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}^{\&prime;}\right){\mathrm{\&alpha;\&theta;}}^{\&prime;}}$

Wherein

Wherein, a₁,a₂, A, α, c are stiffness parameters to be identified；T is the measured value of output torque；Δ is harmonic speed reducer Joint space；θ'、It is respectively torsion angle and torsion angle speed；θ、It is respectively relative angular displacement and the phase characterizing joint deformity Angular velocity, is calculated by measured values such as input/output angle, input/output angular velocity, joint spaces and obtains.A, α, c are for characterizing 3 stiffness parameters of harmonic speed reducer joint dynamic rate hesitation；

22nd step, method according to S22, set up constraints based on the kinetic model obtained in the 21st step.

Step 3, the method for employing step 3 obtain relevant parameter.

Step 4, for mounting torque sensor, can use torque sensor 8 measure obtain harmonic speed reducer joint defeated Go out moment.

Step 5, according in step 3 and step 4 obtain parameter, the kinetic model of the foundation in step 2 is joined Number identification, it is thus achieved that the estimated value of kinetic model stiffness parameters, the i.e. measurement result of harmonic speed reducer transmission stiffness.

Use the particle swarm optimization algorithm of weight coefficient (or claiming compressibility factor), according to the kinetic simulation set up in step 2 Type, the parameter obtained in integrating step 3 and step 4, to motion transmission stiffness parameters a₁,a₂, A, α, c estimate, and final generation Enter the kinetic model set up in step 2, in reality is measured, finally obtain transmission stiffness.

Utilize the harmonic speed reducer motion transmission rigidity result that said method obtains as shown in Fig. 8 to Figure 14.

Fig. 8 is the spy of the harmonic speed reducer joint transmission rigidity that the identification result according to stiffness parameters and gap length draws Linearity curve.Wherein, blue real point be the non-linear rigidity to harmonic speed reducer joint, hesitation, gap, non-linear friction, After 6 kinds of non-linear factors such as low frequency movement error and damping are accurately measured, it is dynamic that the precise kinetic model of foundation is given The ideal curve of state transmission stiffness (i.e. product actual curve most preferably approach value)；Red open circle is the dynamic biography according to identification The stiffness curve that dynamic stiffness parameter and joint space value are given.

Fig. 9 to Figure 13 is respectively the identification result of each parameter of motion transmission rigidity, wherein measures according to red dotted line The identifier that data and kinetic model are obtained, blue solid lines be product actual curve most preferably approach value.As seen from the figure, humorous Ripple decelerator joint each parameter a of motion transmission rigidity₁,a₂, the identification precision of A, α, c is respectively 99.51%, 98.27%, 97.56%, 97.69%, 97.22%.

Figure 14 is in particle cluster algorithm identification process, the dynamic changing process of fitness function.As seen from the figure, fitness letter Number rapid decrease (the smaller the better) in identification process, and the value that finally tends towards stability.Illustrate that identification process convergence is fast, identification process Stable.

In sum, these are only presently preferred embodiments of the present invention, be not intended to limit protection scope of the present invention. All within the spirit and principles in the present invention, any modification, equivalent substitution and improvement etc. made, should be included in the present invention's Within protection domain.

Claims (3)

1. a harmonic speed reducer transmission stiffness method of testing, it is characterised in that comprise the steps:

Step one, the product constituted using harmonic speed reducer joint, as object, utilize its control system, the outfan control to product System so that it is make the reciprocating motion of rule；

Step 2, test environment according to the correlative factor and product affecting transmission stiffness, set up the harmonic reduction in product The kinetic model of device joint transmission rigidity, and set up corresponding constraints；

Step 3, start product to be measured, start test:

According to motor gain of parameter harmonic speed reducer joint input angle；Directly measure harmonic speed reducer joint output angle Degree；Utilize difference algorithm, according to each moment harmonic speed reducer joint input angle and each moment harmonic speed reducer joint output angle Degree, it is thus achieved that input angular velocity and Output speed；Relative angle speed is obtained according to the input angular velocity obtained and Output speed； Relative angular displacement is obtained according to the input angle obtained and output angle；

Test n group altogether, it is thus achieved that n group kinematics parameters；

Step 4, according to the n group kinematics parameters obtained in step 3, utilize Output speed information, use calculus of finite differences estimation Output angle acceleration information, and utilize moving average filter to be filtered the output angle acceleration information of gained processing, obtain Obtain filtered output angle acceleration；

Harmonic speed reducer joint outfan inertia is multiplied with filtered output angle acceleration information, it is thus achieved that harmonic speed reducer closes Joint outfan moment；And ask all relative angular displacements and the meansigma methods of joint output torque, it is thus achieved that average relative angular displacement peace All joint output torques；

Step 5, according to the parameter obtained in step 3 and step 4, substitute into the transmission stiffness kinetic simulation set up in step 2 In type, carry out stiffness parameters identification, and then obtain the final expression formula of transmission stiffness kinetic model；Firm in reality test transmission When spending, the relative angular displacement of harmonic speed reducer is substituted into, the output torque in harmonic speed reducer joint can be obtained, and then determine defeated Go out the relation between moment and relative angular displacement, i.e. transmission stiffness.

2. harmonic speed reducer transmission stiffness method of testing as claimed in claim 1, it is characterised in that when test condition allows to make During with additional testing equipment, torque sensor (8) is utilized to obtain the harmonic speed reducer joint output torque in step 4.

3. harmonic speed reducer transmission stiffness method of testing as claimed in claim 1, it is characterised in that in step 3, utilize and produce Harmonic speed reducer joint output angle directly measured by photoelectric encoder (6) in product.