CN106197909B - A kind of harmonic speed reducer transmission stiffness test method - Google Patents
A kind of harmonic speed reducer transmission stiffness test method Download PDFInfo
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- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M5/00—Investigating the elasticity of structures, e.g. deflection of bridges or air-craft wings
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Abstract
The invention discloses a kind of harmonic speed reducer transmission stiffness test methods.The present invention is based on kinetic models and system identifying method, and in the case where carrying incentive action using the periodicity similar with the practical military service operating mode of product, band, the method for the invention can continuous, automatic, accurately test the motion transmission rigidity of harmonic speed reducer.Meanwhile the present invention is without being fixed harmonic speed reducer one end, also more loose to output torque measuring condition, therefore, the present invention directly can carry out online or off-line measurement using the field evidence of product, without specific experimental provision.
Description
Technical field
The present invention relates to harmonic speed reducer technical fields, and in particular to a kind of harmonic speed reducer transmission stiffness test method.
Background technology
Harmonic speed reducer is a kind of flexible deformation by flexible gear to realize retarder that power and movement are transmitted, because
This, alternatively referred to as " strain wave transmission device ".Harmonic speed reducer is made of three mutually independent components, i.e. wave producer, soft
Wheel and firm gear；In the case of correct assembly, three components can be rotated coaxially according to the transitive relation that transmission ratio determines.Generally
In the case of, it is fixed using firm gear, deceleration transmission form of the wave producer as input, flexbile gear as output.Wave producer is ellipse
Round member is mounted on inside flexbile gear, and forcing flexbile gear to generate radial deformation in longitudinal end according to certain rule becomes ellipticity；By
In flexbile gear 2 gear teeth fewer than firm gear, therefore, when wave producer rotation is turned around, flexbile gear retreats 2 tooth pitches with respect to firm gear, to
Realize big retarding than transmission.
Currently, the test of harmonic speed reducer transmission stiffness cannot be realized by promoting the calculation formula of ordinary gear, and
Experimental method is depended on to carry out；Main test method has the manual measurement method of load code-disc and optical measuring system cooperation
(Tan Li, from strong, harmonic speed reducer rigidity test technical research [J] vacuum and low temperature under the high and low temperature environments such as Wang Changsheng,
2013,19(2):117-120.) and using the servo motor being operated under torque control pattern coordinate with photoelectric code disk continuous
Mensuration (the firm gear gear teeth have the short cylinder flexible gear harmonic reducer and its transmission stiffness test device at inclination angle, CN102777546B).
The former needs artificial operation repeatedly, comparatively laborious, and obtained data are more discrete；The latter can more measure rapidly, continuously
The torsion stiffness characteristic of harmonic speed reducer.However, current either manual discrete measurement method or automatic continuous measurement method
Be carry out static or semi-static load, acquisition be harmonic speed reducer static rigidity, or in test fixed input terminal,
Then fixed output end loads static or quasi-static torsional load in the other end, then is obtained by measuring torsional deflection
Its transmission stiffness characteristic.
By experimental study (Tuttle T.D.Understanding and Modeling the Behavior of
aHarmonic Drive Gear TransmissionR.MIT Artificial Intelligence Laboratory,
1993.Report No.:AD-A259 610.) it is found that harmonic speed reducer shows in static rigidity and product actual moving process
There is some difference for dynamic rate out.Especially to harmonic wave drive speed reducer, due to its both by joint assembly pretightening power, be
The influence of the intrinsic factor of the frictional force and joint space etc. of uniting, and turned by actual loading, the speed of service, system resonance, wave producer
The influence of the use conditions such as angle, this species diversity can biggers.Tuttle draws a conclusion according to many experiments and points out, these factors can be led
It can be more than 30% to cause the difference fluctuating range between the static rigidity and dynamic rate of harmonic drive system.Practical implementation
Show：This species diversity often lead to the staring torque of actual product commonly greater than theoretical expectation values and model predication value, start or
Deboost phase, there is also step-out phenomenons, and there are certain deviations for the real response of dynamic operation and theoretical prediction response.
Invention content
In view of this, the present invention provides a kind of harmonic speed reducer transmission stiffness test method, can accurately obtain humorous
The dynamic rate of wave retarder driving joint.
A kind of harmonic speed reducer transmission stiffness test method, includes the following steps：
Step 1: using the product that harmonic speed reducer joint is constituted as object, using its control system, the output to product
End control, makes it make the reciprocating motion of rule；
Step 2: according to the test environment for the correlative factor and product for influencing transmission stiffness, the harmonic wave in product is established
The kinetic model of retarder joint transmission rigidity, and establish corresponding constraints；
Step 3: starting product to be measured, start to test：
According to stepper motor gain of parameter harmonic speed reducer joint input angle；Directly measure the output of harmonic speed reducer joint
Angle；Using difference algorithm, exported according to each moment harmonic speed reducer joint input angle and each moment harmonic speed reducer joint
Angle obtains input angular velocity and Output speed；Relative angle speed is obtained according to the input angular velocity of acquisition and Output speed
Degree；Relative angular displacement is obtained according to the input angle of acquisition and output angle；
N groups are tested altogether, obtain n group kinematics parameters；
Step 4: according to the n group kinematics parameters obtained in step 3, using Output speed information, using calculus of finite differences
Estimate output angle acceleration information, and place is filtered to the output angular acceleration data of gained using moving average filter
Reason, obtains filtered output angular acceleration；
Harmonic speed reducer joint output end inertia is multiplied with filtered output angular acceleration data, obtains harmonic reduction
Device joint exports end moment；And the average value of all relative angular displacements and joint output torque is sought, obtain average relative angular displacement
With average joints output torque；
Step 5: according to the parameter obtained in step 3 and step 4, the transmission stiffness power established in step 2 is substituted into
It learns in model, carries out stiffness parameters identification, and then obtain the final expression formula of transmission stiffness kinetic model；It is passed in actual test
When dynamic stiffness, the relative angular displacement of harmonic speed reducer is substituted into, you can obtain the output torque in harmonic speed reducer joint, and then really
Determine the relationship between output torque and relative angular displacement, i.e. transmission stiffness.
Preferably, when test condition allows using additional testing equipment, obtained in step 4 using torque sensor
Harmonic speed reducer joint output torque.
Preferably, in step 3, harmonic speed reducer joint output angle is directly measured using the photoelectric encoder in product.
Advantageous effect：
Based on kinetic model and system identifying method, the periodicity similar with the practical military service operating mode of product, band are being utilized
It carries under incentive action, the method for the invention can continuous, automatic, accurately test the motion transmission rigidity of harmonic speed reducer.
The case where difference fluctuating range between traditional static measurement method acquired results and dynamic rate may be more than 30% phase
Than the surveyed transmission stiffness of the present invention is the motion transmission rigidity in product actual task, and the two is with uniformity.Meanwhile this
Invention is without being fixed harmonic speed reducer one end, and also more loose to output torque measuring condition (output torque can lead to
Cross kinematics parameters estimation), therefore, the present invention directly can be carried out online or be surveyed offline using the field evidence of product
Amount, without specific experimental provision.This aspect can save Special testing device, greatly save cost, improve production
On the other hand product development efficiency it is dynamic can to measure harmonic speed reducer in real time according to task needs in the product difference military service stage
The situation of change of state transmission stiffness is product transmission accuracy, defeated to grasp the performance degradation rule during its practical military service
Go out torque accuracy to keep promoting offer guidance with reliability.It is also possible to providing harmonic speed reducer motion transmission
While stiffness parameters, the estimation in its gap (or return difference) is provided.
Description of the drawings
Fig. 1 is uniaxial driving antenna product composition schematic diagram；
Fig. 2 is harmonic speed reducer joint schematic diagram；
Fig. 3 is the in-orbit on-line identification result of harmonic speed reducer joint motion transmission load-deflection curve；
Fig. 4 is the in-orbit on-line identification result of harmonic speed reducer joint motion transmission rigidity linear term；
Fig. 5 is the in-orbit on-line identification result of harmonic speed reducer joint motion transmission linear Stiffness item；
Fig. 6 is the in-orbit on-line identification result of harmonic speed reducer joint space size；
Fig. 7 is harmonic speed reducer transmission stiffness ground experiment test 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 ontologies, 2- antenna extension bars, 3- antenna reflective faces, 4- stepper motors, 5- harmonic speed reducers, 6- photoelectricity
Encoder, 7- output shafts, 8- torque sensors, 9- inertia discs.
Specific implementation mode
The present invention will now be described in detail with reference to the accompanying drawings and examples.
The present invention provides a kind of harmonic speed reducer transmission stiffness test method, main thought is：
In order to avoid the error that the transmission stiffness measured under static state is brought, the present invention makes harmonic reduction by control
Device carries out the sinusoidal motion of rule under the conditions of with carrying, and later, by measuring its input, output angle can estimate rigidity and survey
The information such as torsional deflection and loading moment needed for amount in turn pass the harmonic speed reducer of structure using corresponding optimization algorithm
Dynamic stiffness kinetic model carries out parameter identification, can obtain the measurement result of transmission stiffness parameter, you can obtains harmonic reduction
The motion transmission rigidity of device.
Embodiment 1：For the acquisition methods of the on-line measurement transmission stiffness of in-orbit application product：
Step 1: configuration experiment test hardware system makes output end make rule by the control of driving mechanisms control system
Sinusoidal motion or product execute authentic task when reciprocating motion；
Wherein, given rule can be arranged or directly utilize product actually in commission reciprocal fortune by measuring excitation
Dynamic, this makes harmonic speed reducer transmission stiffness is measured can facilitate progress in product development and during being on active service.
As shown in Figure 1, the present embodiment is using spacecraft single shaft driving mechanism antenna product as object, it includes driving mechanism controls
System (in 1 side of spacecraft ontology, being not drawn into figure), antenna extension bar 2,5 joint of harmonic speed reducer and antenna reflective face processed
3。
Wherein, harmonic speed reducer joint is as shown in Fig. 2, by stepper motor 4, harmonic speed reducer 5, photoelectric encoder 6 and defeated
7 four part of shaft forms；
Wherein, driving mechanisms control system had not only been responsible for control antenna end by given rule movement, but also was responsible for harmonic reduction
The data processing work of device joint stiffness parameter identification process.
For simplicity, the components such as compression relieving mechanism, the cable for including in uniaxial driving mechanism antenna actual product do not have
Have and draws in Fig. 1.
Unlike traditional measurement method：Since harmonic speed reducer joint is in accurate static in conventional method measurement process
State, there are large errors with its actual transmission stiffness for the transmission stiffness obtained.In order to avoid there is the above problem, this hair
The bright actual movement rule according to harmonic speed reducer joint, and then it is rigid to obtain the transmission in harmonic speed reducer joint under motion state
Degree.Specially：
When practical progress motion transmission stiffness measurement, by harmonic speed reducer joint output shaft, antenna reflective face 3 and its holder
Load of the component as harmonic speed reducer；Harmonic speed reducer steel wheel and corresponding housing unit are fixed；Harmonic speed reducer wave
The output shaft of wave producer and stepper motor 4 is as input terminal.Input terminal makes output under the control of driving mechanisms control system
Make sinusoidal motion by formula (1) rule in end.
Wherein, θoutputFor output angle；tConFor system operation time；According to the actual conditions of spacecraft computing capability,
Control system uses PD control algorithm, controlling cycle 1ms.
Step 2: establishing the kinetic model of harmonic speed reducer joint transmission rigidity, and constraints is set.
S21, consider that the in-orbit limited measuring condition of spacecraft, the present invention are established as cube shown in formula (2) is multinomial
Kinetic model of the formula as harmonic speed reducer joint transmission rigidity, the model consider non-linear factor and the pass of transmission stiffness
Internode gap.
T=a1θ'+a2θ'3 (2)
Wherein,
Wherein, a1,a2For stiffness parameters to be estimated；T is the measured value of output torque；θ is the opposite of characterization dysarthrasis
Angular displacement (contains gap), is calculated and is obtained by the measured value of input/output angle；Δ is harmonic speed reducer joint space；θ ' is to close
The true strain amount (being free of gap) of section, i.e. joint torsion angle；In order to calculating process is continuous, conveniently, in actual test or application,
The piecewise function of characterization joint torsion angle can use hyperbolic function approximate in formula (2).
S22, based on the kinetic model established in S21, establish the constraints as shown in formula (3)；The constraints (is received
Hold back criterion) be system reality output data sequence and kinetic model predict output sequence the minimum identification of error sum of squares
Optimality Criteria；I.e.：It is practical minimum with simulation error；
Wherein,
f(θ'k)=a1θ'k+a2θ'k 3
In formula, θ 'k、θk、TkRespectively k-th of torsion angle, k-th of relative angular displacement and k-th of output torque value, L are number
According to length；f(θ'k) it is shape of the motion transmission rigidity identification model of formula (2) characterization after substituting into k-th of relative angular displacement data
Formula.
Step 3: test primary data, obtains kinematics parameters.
Since task execution process and harmonic speed reducer transmission stiffness measurement process are combined into one, to wait for that system is transported
Start the estimation work of stiffness parameters after row a period of time.Under normal conditions, according to the ability of above-mentioned control system, select to wait be
System operation starts stiffness parameters after 6~7 seconds and recognizes work.At this moment, the initial data for parameter identification of accumulation has 6000.
Therefore according to formula (5) to formula (8), 6000 groups of kinematics parameters are obtained altogether.The acquisition methods of specific kinematics parameters are as follows：
Harmonic speed reducer joint input angle θ is calculated using stepper motor parameterInput, see formula (5).
θInput=q θ0n (5)
In formula, q is the frequency of Stepping Motor Subdivision Driver, θ0For stepper motor step angle, n is sampling time internal control
The pulse number that system processed is sent out to stepper motor.
Harmonic speed reducer joint output angle θ is directly measured using photoelectric encoder 6output。
Using difference algorithm, by sampling time sequence, each moment harmonic speed reducer joint input angle and each moment harmonic wave
Retarder joint output angle calculates separately input angular velocityAnd Output speedDifference algorithm formula is as follows：
Wherein, θInput,k、θOutput,kRespectively k-th of input angle and output angle measured value,Point
Not Wei k-th of input angular velocity and Output speed value, L is data length；Times of the t between k-th and -1 data of kth
Interval.Since the time interval between each adjacent two data in uniform sampling is equal, hereafter t is collectively expressed as two
Time interval between adjacent data.
According to input angle and output angle angle value, the relative angular displacement θ of characterization dysarthrasis is obtainedkWith opposite angular speedSee formula (7), formula (8).Wherein, subscript indicates k-th of value.
In formula, N is harmonic speed reducer reduction ratio.
During actual test, driving mechanisms control system of the invention uses Nonlinear Least-Square Algorithm into Mobile state
The On-line Estimation of transmission stiffness.In order to obtain more accurate kinematics parameters, the present invention is provided with data sliding window,
Driving mechanisms control system reaches 6000 in raw measurement data and just starts stiffness parameters identification work later；Subsequently, with
The execution of control process constantly replaces earliest measurement by data sliding window using the kinematics parameters of newest measurement
Kinematics parameters, be 6000 to ensure the original motion parameter for identification always.
Step 4: according to the 6000 groups of kinematics parameters obtained in step 3, kinetic parameter is obtained.
Angular velocity information is output and input using in step 3, angular acceleration information is estimated using calculus of finite differences, and utilize
Moving average filter is filtered the angular acceleration data of gained.
Wherein,To export k-th of value of angular acceleration.
The sliding step of moving average filter generally may be selected to be 5, and Filtering Formula is shown in formula (10)：
Wherein,For k-th of moving average filter treated output angular acceleration values.
Using harmonic speed reducer joint output end inertia (known conditions), output end inertia and output angular acceleration are directly used
Data are multiplied, and obtain harmonic speed reducer joint output end moment Tk.Wherein, output end inertia in harmonic speed reducer joint is product
The sum of the inertia of payload and harmonic wave reducer output shaft module, that is, required loading moment is the practical fortune of product when testing
The moment of inertia that itself is generated during dynamic, without using additional loading equipemtn.
By relative angular displacement and joint output torque, calculates average relative angular displacement and joint is averaged output torque.Specifically
For：Minimum, the maximum value of relative angular displacement are first found out, it is then ascending to find out given relative angular displacement center at regular intervals
Corresponding all joint output torques and all relative angular displacements, then can find out it respectively by this two groups of data and put down near value
Mean value.
By relative angular displacement θkThe sequence processing of (k=3,4,5 ..., L) from small to large, meanwhile, it is corresponding defeated to obtain its
Go out torque Tk(k=3,4,5 ..., L), forms new queue, is respectively defined as：θkk(kk=3,4,5 ..., L) and Tkk(kk=
3,4,5,...,L).Then for k0To k0One group of relative angular displacement in+λ ranges and output torque data, can be in the hope of the data
Average relative angular displacement in range sectionWith average output torque
In formula, k0Value range be 3, λ+4,2 λ+5,3 λ+6 ..., its last one value are L- λ；λ characterizations are average
Data break size when processing, for the positive integer less than L, it is contemplated that the equilibrium of DATA REASONING number and average processing accuracy,
General recommendations value is 4；The count flag that subscript kNew is newly introduced, the value since natural number 1, maximum occurrences kNewmax
It is determined by L and λ, sees formula (13)：
Data length L and λ, which are value, must ensure kNewmaxFor positive integer.
Step 5: according to the parameter obtained in step 3 and step 4, to the kinetic model of the foundation in step 2 into
Row parameter identification obtains the estimated value of transmission stiffness kinetic model stiffness parameters, the i.e. measurement of harmonic speed reducer transmission stiffness
As a result.
After obtaining above-mentioned average relative angular displacement and average output torque sequence, motion transmission rigidity shown in formula (2)
Model can be rewritten as the form of formula (14).At this moment, the Nonlinear Least-Square Algorithm pair with data sliding window can be utilized
The model carries out parameter Estimation, to obtain the linear term a of harmonic speed reducer joint stiffness1With nonlinear terms a2And between joint
The estimated value of gap Δ.
Wherein,
Wherein,It is averaged torsion angle for joint.By the harmonic speed reducer joint stiffness linear term a of acquisition1, rigidity it is non-thread
Property item a2It is substituted into formula (2) with the estimated value of clearance delta, that is, obtains transmission stiffness kinetic model expression formula；In actual test
When transmission stiffness, the relative angular displacement of harmonic speed reducer is substituted into, you can obtain harmonic speed reducer joint output torque, and then really
Determine the relationship between output torque and relative angular displacement, i.e. transmission stiffness.
The harmonic speed reducer motion transmission rigidity result obtained using the above method is as shown in Figures 3 to 6.
Fig. 3 is the spy of the harmonic speed reducer joint transmission rigidity drawn according to the identification result of stiffness parameters and gap size
Linearity curve.Wherein, green solid lines be to the non-linear rigidity in harmonic speed reducer joint, hesitation, gap, non-linear friction,
6 kinds of non-linear factors such as low frequency movement error and damping carry out after accurately measuring, and the precise kinetic model of foundation provides dynamic
The ideal curve of state transmission stiffness (i.e. the best of product actual curve approaches value)；Blue real point be the present embodiment step 4 in,
The average output torque peace relative angular displacement data sequence provided according to kinematics parameters estimation；According to red dotted line
The stiffness curve that the motion transmission stiffness parameters and joint space value of identification provide.
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 rigidity linear term identification result in the identification process of border；Green straight line is rigid to be provided according to identification result
Spend the final measured value of the average value of linear term, the value i.e. harmonic speed reducer motion transmission rigidity linear term；Blue solid lines
(i.e. product actual characteristic is best for the ideal value provided for the high-precision kinetic model after the above-mentioned 6 kinds of non-linear factors of consideration
Approach value).Each curve meaning of Fig. 5 and Fig. 6 is similar with Fig. 4.
It can be seen from Fig. 3 to Fig. 6 the measurement process of harmonic speed reducer joint motion transmission rigidity with task execution
It can gradually tend towards stability；Value comparison is most preferably approached with product it is found that measuring the motion transmission rigidity model provided with identification process
Parameter a1,a2It is better than 94%, 92% and 85% 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 make output end make rule by the control of driving mechanisms control system
Sinusoidal motion：
For the acquisition methods of ground survey transmission stiffness, the device used is used when can be with in-orbit on-line measurement
Device it is identical, can also be according to structure as shown in Figure 7, using increasing the method for adding measuring apparatus：Due to being not necessarily to consider
The measuring condition of spacecraft, therefore in ground survey transmission stiffness, using the antenna reflective face 3 in 9 alternate embodiment 1 of inertia disc
And its bracket component measures hardware system and also adds torque sensor 8 and torque acquisition to simulate the inertia of payload
Card.
When practical progress 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 wave and stepping electricity
4 output shaft of machine is as input terminal.Input terminal makes output end by the formula of embodiment 1 under the control of driving mechanisms control system
(1) rule makees sinusoidal motion.
Step 2, the kinetic model for establishing harmonic speed reducer joint transmission rigidity, and constraints is set.
21st step considers that the more well-to-do measuring condition in ground, the present invention establish the harmonic speed reducer as shown in formula (15)
The kinetic model in joint, the model consider the non-linear factor of transmission stiffness, rigidity hesitation and joint space.
Wherein
Wherein, a1,a2, A, α, c is stiffness parameters to be identified；T is the measured value of output torque；Δ is harmonic speed reducer
Joint space；θ'、Respectively torsion angle and torsion angular speed；θ、Respectively characterize the relative angular displacement and phase of dysarthrasis
Angular velocity is calculated by measured values such as input/output angle, input/output angular speed, joint spaces and is obtained.A, α, c are characterization
3 stiffness parameters of harmonic speed reducer joint dynamic rate hesitation；
22nd step, the method according to S22 establish the constraints based on the kinetic model obtained in the 21st step.
Step 3 obtains relevant parameter using the method for step 3.
Step 4, for mounting torque sensor, torque sensor 8 can be used and measure that obtain harmonic speed reducer joint defeated
Go out torque.
Step 5, according to the parameter obtained in step 3 and step 4, the kinetic model of the foundation in step 2 is joined
Number identification, obtains the estimated value of kinetic model stiffness parameters, the i.e. measurement result of harmonic speed reducer transmission stiffness.
Using the particle swarm optimization algorithm of weighting coefficient (or compressibility factor), according to the kinetic simulation established in step 2
Type, in conjunction with the parameter obtained in step 3 and step 4, to motion transmission stiffness parameters a1,a2, A, α, c is estimated, and final generation
Enter the kinetic model established in step 2, finally obtains transmission stiffness in actually measuring.
The harmonic speed reducer motion transmission rigidity result obtained using the above method is as shown in Fig. 8 to Figure 14.
Fig. 8 is the spy of the harmonic speed reducer joint transmission rigidity drawn according to the identification result of stiffness parameters and gap size
Linearity curve.Wherein, blue real point be to the non-linear rigidity in harmonic speed reducer joint, hesitation, gap, non-linear friction,
6 kinds of non-linear factors such as low frequency movement error and damping carry out after accurately measuring, and the precise kinetic model of foundation provides dynamic
The ideal curve of state transmission stiffness (i.e. the best of product actual curve approaches value)；Red open circle is to be passed according to the dynamic of identification
The stiffness curve that dynamic stiffness parameter and joint space value provide.
Fig. 9 to Figure 13 is respectively the identification result of each parameter of motion transmission rigidity, wherein red dotted line is according to measurement
The identifier that data and kinetic model are obtained, blue solid lines are that the best of product actual curve approaches value.As seen from the figure, humorous
Wave retarder joint each parameter a of motion transmission rigidity1,a2, A, α, the identification precision of c is respectively 99.51%, 98.27%,
97.56%, 97.69%, 97.22%.
Figure 14 is the dynamic changing process of fitness function in particle cluster algorithm identification process.As seen from the figure, fitness letter
Number rapid decrease (the smaller the better) in identification process, and the final value that tends towards stability.Illustrate that identification process convergence is fast, identification process
Stablize.
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 the present invention's
Within protection domain.
Claims (3)
1. a kind of harmonic speed reducer transmission stiffness test method, which is characterized in that include the following steps：
Step 1: using the product that harmonic speed reducer joint is constituted as object, using its control system, the output end control to product
System, makes it make the sinusoidal motion of rule；
Step 2: according to the test environment for the correlative factor and product for influencing transmission stiffness, the harmonic reduction in product is established
The kinetic model of device transmission stiffness, and establish corresponding constraints；Wherein, the correlative factor includes that harmonic speed reducer closes
Non-linear rigidity, hesitation, gap, non-linear friction, low frequency movement error and the damping of section；
Step 3: starting product to be measured, start to test：
According to stepper motor gain of parameter harmonic speed reducer joint input angle；Directly measure harmonic speed reducer joint output angle
Degree；Using difference algorithm, according to each moment harmonic speed reducer joint input angle and each moment harmonic speed reducer joint output angle
Degree obtains input angular velocity and Output speed；Opposite angular speed is obtained according to the input angular velocity of acquisition and Output speed；
Relative angular displacement is obtained according to the input angle of acquisition and output angle；
N groups are tested altogether, obtain n group kinematics parameters；
Step 4: being estimated using calculus of finite differences using Output speed information according to the n group kinematics parameters obtained in step 3
Output angle acceleration information, and the output angle acceleration information of gained is filtered using moving average filter, it obtains
Obtain filtered output angular acceleration；
Harmonic speed reducer joint output end inertia is multiplied with filtered output angular acceleration, it is defeated to obtain harmonic speed reducer joint
Go out end moment；And the average value of all relative angular displacements and joint output torque is sought, obtain average relative angular displacement and average pass
Save output torque；
Step 5: according to the parameter obtained in step 3 and step 4, the transmission stiffness kinetic simulation established in step 2 is substituted into
In type, stiffness parameters identification is carried out, and then obtain the final expression formula of transmission stiffness kinetic model；It is rigid in actual test transmission
When spending, the relative angular displacement of harmonic speed reducer is substituted into, you can obtain the output torque in harmonic speed reducer joint, and then determination is defeated
Go out the relationship between torque and relative angular displacement, i.e. transmission stiffness.
2. harmonic speed reducer transmission stiffness test method as described in claim 1, which is characterized in that when test condition allows to make
When with additional testing equipment, the harmonic speed reducer joint output torque in step 4 is obtained using torque sensor.
3. harmonic speed reducer transmission stiffness test method as described in claim 1, which is characterized in that in step 3, utilize production
Photoelectric encoder in product directly measures harmonic speed reducer joint output angle.
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| CN102777546A (en) * | 2012-07-27 | 2012-11-14 | 哈尔滨工业大学 | Short tube flexible gear harmonic reducer of rigid wheel tooth dip angle and transmission rigidity testing device thereof |
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| CN106197909A (en) | 2016-12-07 |
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