CN110502866A - A kind of connecting rod mechanism movement analysis method for reliability considering error originated from input - Google Patents
A kind of connecting rod mechanism movement analysis method for reliability considering error originated from input Download PDFInfo
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- CN110502866A CN110502866A CN201910812348.3A CN201910812348A CN110502866A CN 110502866 A CN110502866 A CN 110502866A CN 201910812348 A CN201910812348 A CN 201910812348A CN 110502866 A CN110502866 A CN 110502866A
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Abstract
The present invention discloses a kind of connecting rod mechanism movement analysis method for reliability for considering error originated from input, applied to mechanism kinematic reliability analysis model field, in order to solve of the existing technology not consider driving link error originated from input, causing analysis result, there are relatively large deviations, and do not consider the problems of pair clearance error in different operating scene；Effective bar that the present invention is calculated separately out according to effective length theory in the case of continuous type contact contacts two kinds with discrete is long；Effective bar in the case of contacting two kinds using continuous type contact and discrete is long long instead of the practical bar in slider displacement error expression caused by scale error, the slider displacement error as caused by scale error and pair clearance error is obtained, according to the slider displacement error calculation offset slider-crank mechanism movement reliability as caused by scale error and pair clearance error；Method of the invention comprehensively, more can accurately reflect the kinetic characteristic of the offset slider-crank mechanism of engineering in practice.
Description
Technical field
The invention belongs to mechanism kinematic fail-safe analysis field, in particular to a kind of consideration driving link error originated from input, bar are long
The offset slider-crank mechanism kinematic accuracy analysis model of scale error and the effective length analysis for considering pair clearance error
Model.
Background technique
The processing is simple, easily reach the higher accuracy of manufacture, can be realized multi-motion track due to having for link mechanism
The features such as curve and the characteristics of motion, is widely used in various mechanical and instrument.Slider-crank mechanism belongs to planar linkage mechanism
A kind of evolution forms.
The characteristics of motion of practical set-up is the geometry and size, quality, material property by constituting each component of mechanism
And act on what the factors such as driving force and working resistance in mechanism determined.For same class mechanism, due to foozle, assembly
Error, working resistance when use, the differences such as power source and maintenance exist, their kinematic parameter is not quite similar；Even if
It is also a variable to same mechanism, place to use, environment and using the variation of time.So above-mentioned influence factor be with
In the case where machine variable, the output parameter of mechanism kinematic rule is also a polytomy variable.
Mechanism kinematic reliability refer to mechanism system or component under regulation use condition, it is specified that in the time complete rule
Determine the ability of motor function, i.e., is specified under conditions of the given mechanism driving link characteristics of motion, in research institution a certain on component
The displacement of point, velocity and acceleration, the various influence factors the effects of under, reach specified value, or general in prescribed limit
Rate.
Compare in previous reliability consideration and pay attention to its intensity or reliability of service life, to the research of motion credibility compared with
It is few.But the problem of motion credibility, is also very important during machine work.For example, on flexible manufacturing equipment, if
Between each moving component cannot mutual co-ordination or each component cannot reach predetermined position before the deadline, it will
It is unable to run the entire production line.
The main task of mechanism kinematic fail-safe analysis is set up mechanism performance output parameter and influence mechanism performance output
The mathematical model of function or correlativity between the main random variable of Parameters variation.
Slider-crank mechanism is a kind of typical link mechanism, and for slider-crank mechanism, mechanism kinematic is reliable
Property is mainly influenced by two kinds of errors.The first error is scale error, and processing and manufacturing scale error including rod piece was assembled
Journey bring error in mounting position and long time running cause error caused by component wear etc..Second of error is hinge knot
In structure, since mismachining tolerance and assembly deflections cause pin shaft that can not tightly be bonded with axle sleeve, there are gaps between kinematic pair, that is, transport
Dynamic auxiliary air gap error.The presence of the above-mentioned two classes error of slider-crank mechanism, will lead to the reduction of whole system kinematic accuracy even
Motor function failure, so to slider-crank mechanism carry out Kinematic Reliability modeling be very it is necessary to.
There are following two main problems for existing connecting rod mechanism movement Reliability Modeling:
(1) existing modeling method generally has ignored driving link error originated from input, that is, has ignored the output error of hydraulic cylinder, do not have
The influence for considering this key factor causes analysis result and engineering is practical relatively large deviation.
(2) conventional motion auxiliary air gap error separation fail separate consider high speed operation scene (continuous type contact) with it is low
The difference of pair clearance error in fast operative scenario (discrete contact).
Summary of the invention
In order to solve the above technical problems, the present invention proposes a kind of connecting rod mechanism movement fail-safe analysis for considering error originated from input
Method comprehensively considers driving mechanism error and pair clearance error.
The technical solution adopted by the present invention are as follows: a kind of connecting rod mechanism movement analysis method for reliability for considering error originated from input,
The mean value and variance for calculating the slider displacement error as caused by scale error and pair clearance error, according to obtained sliding block position
The mean value and variance of shift error calculate offset slider-crank mechanism movement reliability.
Further, the calculating process of the slider displacement error as caused by scale error and pair clearance error are as follows:
A1, the displacement expression formula in Driven by Hydraulic Cylinder sliding block is established according to geometry；
A2, scale error is obtained according to the displacement expression formula of sliding block caused by slider displacement error expression；
A3, calculated separately out according to effective length theory continuous type contact and discrete contact two kinds in the case of it is effective
Bar is long；
A4, sliding block described in step A2 is replaced using effective bar in the case of two kinds of continuous type contact and discrete contact is long
Practical bar in displacement error expression formula is long, obtains the slider displacement error as caused by scale error and pair clearance error.
Further, the scale error includes: rod length error, error in mounting position, Driven by Hydraulic Cylinder error；It is described
Rod length error includes: crank length error and length of connecting rod error.
Further, the long relationship long with practical bar of effective bar in the case of continuous type contact and discrete contact two kinds
Formula are as follows:
Wherein, R is that effective bar is long, and r is that practical bar is long, xG、yGIt is the transverse and longitudinal coordinate of local coordinate, local coordinate is with axle sleeve
Sets of holes center is coordinate origin, using connecting rod direction as positive direction of the x-axis, using upwards vertically with the direction of connecting rod as positive direction of the y-axis, and G
For pair clearance.
Further, it includes effective crank length and effective length of connecting rod that effective bar is long.
Further, it includes actual crank length and actual length of connecting rod that practical bar is long.
Further, described practical using the long replacement of effective bar in the case of two kinds of continuous type contact and discrete contact
Bar is long, specifically: actual crank length is replaced using effective crank length, is replaced using effective length of connecting rod actual
Length of connecting rod.
Beneficial effects of the present invention: the present invention has comprehensively considered shadow brought by scale error and pair clearance error
It rings, and has used different effective length models according to operative scenario difference；It is compared with the traditional method, method of the invention can
Comprehensively, accurately reflect the kinetic characteristic of the offset slider-crank mechanism of engineering in practice.
Detailed description of the invention
Fig. 1 is offset slider-crank mechanism schematic diagram；
Fig. 2 is pair clearance schematic diagram；
Fig. 3 is discrete contact model schematic diagram；
Fig. 4 is that discrete contacts effective long model schematic of bar；
Fig. 5 is continuous type contact model schematic diagram；
Fig. 6 is that continuous type contacts effective long model schematic of bar.
Specific embodiment
The present invention will be further explained below with reference to the attached drawings and specific examples.
As shown in Figure 1, it is known that input parameter: the sum of hydraulic cylinder natural length and stroke a；Structural parameters: hydraulic cylinder two
End is respectively b and c, crank length r at a distance from crank terminal AABLength of connecting rod is rBC, offset distance e；Output is sliding block position
Move s.It is required that the limit error of slider displacement s is no more than δ.In above-mentioned parameter, b, c are constant, and other parameters include error, point
Cloth is assumed to normal distribution, known to mean variance.A kind of offset slider-crank mechanism movement of additional consideration driving error is reliable
Property analysis model, comprising steps of
Step 1. establishes the displacement expression formula s in Driven by Hydraulic Cylinder sliding block C according to mechanism geometrical relationship.By geometrical relationship
Known to
S=rAB cosα+rBC cosθ (1)
From the cosine law
Step 2. carries out Taylor expansion to the displacement expression formula s of sliding block C, is decomposed into displacement ideal value s*With by scale error
Caused slider displacement error amount Δ s.
Sliding block C displacement-type can be write as
S=F (rAB,rBC,e,a,b,c) (4)
It is available since b, c are constant
S=F (rAB,rBC,e,a) (5)
It is available after Taylor expansion
" * " indicates it as ideal value in above formula, and " Δ " indicates it for error amount.ΔrAB、ΔrBCIt is rod length error, Δ e
It is error in mounting position, Δ a is Driven by Hydraulic Cylinder error.Four be scale error.
Overall size error is in above formula
According to geometrical relationship Shi Ke get
Wherein
Step 3. calculates mean value E (Δ s) and variance D (the Δ s) of the slider displacement error amount Δ s as caused by scale error.
Formula 8 is brought into formula (7), the expression formula of scale error in the motion process of available sliding block
Wherein
The scale error mean value of generation is
In above formula
The scale error variance of generation is
In above formula
Step 4. calculates separately out continuous type contact according to effective length theory and discrete contacts in the case of two kinds
The long expression formula R of effective bar.
Be illustrated in figure 2 pair clearance schematic diagram: pin shaft moves among axle sleeve sets of holes.The circle of uncertainty is pin shaft and axle sleeve
Sets of holes keep center of circle motion profile when inscribe, and a diameter of axle sleeve covers the difference of the diameter of bore dia and pin shaft.It follows that pin
The eternal movement in the axis center of circle is on the circle of uncertainty or in circle.
In terms of hinge movement auxiliary air gap research, two kinds of movement moulds are divided into according to the size of the height of movement velocity, stress
Type；That is discrete contact model and continuous type contact model.
(1) discrete contact model
Noncontinuity contact model is mainly used in that mechanism kinematic speed is low, the smaller scene of stress.In this scene
A possibility that movement, pin shaft and axle sleeve sets of holes separate in hinge movement pair, is bigger, i.e., the pin shaft center of circle is random in the circle of uncertainty
Distribution, as shown in Figure 3.
Effective length model is introduced at this time, and discrete contact effective long model of bar such as Fig. 4 shows.
(2) continuous type contact model
Continuity contact model is mainly used in mechanism kinematic speed height, the bigger scene of stress.It is transported in this scene
Dynamic, pin shaft and axle sleeve sets of holes are kept for a possibility that continuously contacting with bigger in hinge movement pair, i.e. the pin shaft center of circle is in the circle of uncertainty
Upper random distribution, as shown in Figure 5.
Effective length model is introduced at this time, and it is as shown in Figure 6 that continuous type contacts effective long model of bar.
In above two model, circle T is the circle of uncertainty, and T point is axle sleeve sets of holes center, and K point is pin shaft center.Connecting rod PT long
For r.Due to the presence of hinge movement auxiliary air gap, sets of holes center T, pin shaft center K two o'clock is caused not to be overlapped.Therefore between consideration radial direction
Effective bar length of gap should be PK, be indicated with R
X in formulaG、yGIt is the local coordinate of pin shaft center K.Local coordinate is using T point as coordinate origin, using PT as x-axis pros
To with vertical 90 ° upwards for positive direction of the y-axis.G is pair clearance, i.e. error-circuit
Step 5. calculates the local coordinate x of pin shaft center K point in pair clearance analysis modelG、yGMean value E (xG)、E
(yG) and variance expression formula D (xG)、D(yG)。
(1) discrete contact model
The kinetic characteristic contacted from discrete
Due to pin shaft center K among the circle of uncertainty T random distribution, push away to obtain xG、yGWith it is identical with error-circuit G with
Machine.
It is assumed that being normal distribution, due to xG、yGSymmetry, mean value is
The x known to 3 σ principles of normal distributionGStandard deviation be
For a collection of mechanism, G is statistical value.The mean value and variance of G be respectively
It is obtained by formula (16)
It can be obtained according to the property of variance
Simultaneous formula (19) and formula (20) can obtain xGAnd yGVariance be
(2) continuous type contact model
The kinetic characteristic contacted from continuous type
I.e.
Assuming that G Normal Distribution, φ obeys being uniformly distributed for (- π, π) known to analysis.
I.e.θ~U (- π, π), the two is mutually indepedent.
Thus pin shaft center K local coordinate x is pushed away to obtainG、yGMean value be
Write formula (22) as variance form
Because of pin shaft center K random distribution and x on the circle of uncertaintyG、yGWith symmetry, so xG、yGRandom character phase
Together, it can obtain
According to the property of variance, local coordinate xG、yGVariance be
Simultaneous formula (24), formula (26) and formula (27) can obtain xGAnd yGVariance be
Step 6. replaces the long r of practical bar with the long R of effective bar, is updated in displacement error value Δ s, respectively obtains and continuously contact with
With the slider displacement error expression Δ S in the case of two kinds of discontinuous contact.The expression formula has comprehensively considered scale error
With pair clearance error.
Effective long R of bar and the corresponding relationship of the long r of practical bar are
According to theory herein, in formula (2), the long r of practical bar is replaced with the long R of effective bar
Substituting into the long scale error of effective bar is
Wherein
Step 7. calculates the mean value E for comprehensively considering the slider displacement error amount Δ S of scale error and pair clearance error
(Δ S) and variance D (Δ S).
The randomness that effective bar is long and practical bar is long can be expressed as
R=R*+ΔR (32)
R=r*+Δr (33)
The two ideal value is equal
R*=r* (34)
From inference in step 5
E(xG)=E (yG) (35)
Since the long error delta R of effective bar is established on the basis of practical bar long error delta r, and local coordinate xG、yGNo
Influence the mean value of Δ R.Available conclusion: the long introducing of effective bar will not bring the variation of error mean.I.e.
Wherein
(1) discrete contact model is applied
After substituting into effective length, the L-expression of sliding block is
S=F (rAB,rBC,e,xG1,xG2,xG3,yG1,yG2,yG3,a) (37)
Square difference of displacement can indicate are as follows:
Because
Have
2RABσRAB=2 (rAB+xG1)σrAB (40)
By RAB、rABAnd xG1Use mean valueWithIt substitutes into
And because
It can similarly obtain
With
It can equally be obtained by the above method
With
With
According to the scale error and pair clearance error relationship derived, synthesis can be obtained
Wherein
(2) continuous type contact model is applied
Similar with discrete contact model, the slider displacement error variance that may be accounted continuous type contact model is
Wherein
Step 8. calculates the probability that slider displacement error amount Δ S is no more than given limit of error value δ, which is exactly inclined
Set slider-crank mechanism movement reliability.
For sliding block, displacement error should be not more than allowable error δ, i.e.,
ΔS≤δ (45)
The limit state function of slider displacement is at this time
Z=δ-| Δ S | (46)
For same a collection of slider-crank mechanism, the dimensions length and pair clearance size of each component are stochastic variable,
And general Normal Distribution.Therefore, slider displacement error also Normal Distribution.Slider displacement reliability is
To sum up, compared to conventional method, the present invention has comprehensively considered brought by scale error and pair clearance error
It influences, and has used different effective length models according to operative scenario difference；Method of the invention is more comprehensively than conventional method
Ground reflects the kinetic characteristic of the offset slider-crank mechanism of engineering in practice, and reliability calculating result is compared to conventional method
It is more accurate, so also can accurately reflect the kinetic characteristic of the offset slider-crank mechanism of engineering in practice.
Those of ordinary skill in the art will understand that the embodiments described herein, which is to help reader, understands this hair
Bright principle, it should be understood that protection scope of the present invention is not limited to such specific embodiments and embodiments.For ability
For the technical staff in domain, the invention may be variously modified and varied.All within the spirits and principles of the present invention, made
Any modification, equivalent substitution, improvement and etc. should be included within scope of the presently claimed invention.
Claims (7)
1. a kind of connecting rod mechanism movement analysis method for reliability for considering error originated from input, which is characterized in that calculate by scale error
With the mean value and variance of slider displacement error caused by pair clearance error, according to the mean value of obtained slider displacement error and
Variance calculates offset slider-crank mechanism movement reliability.
2. a kind of connecting rod mechanism movement analysis method for reliability for considering error originated from input according to claim 1, feature
It is, the calculating process of the slider displacement error as caused by scale error and pair clearance error are as follows:
A1, the displacement expression formula in Driven by Hydraulic Cylinder sliding block is established according to geometry；
A2, scale error is obtained according to the displacement expression formula of sliding block caused by slider displacement error expression；
A3, calculated separately out according to effective length theory continuous type contact and discrete contact two kinds in the case of effective bar
It is long；
A4, slider displacement described in step A2 is replaced using effective bar in the case of two kinds of continuous type contact and discrete contact is long
Practical bar in error expression is long, obtains the slider displacement error as caused by scale error and pair clearance error.
3. a kind of connecting rod mechanism movement analysis method for reliability for considering error originated from input according to claim 2, feature
It is, the scale error includes: rod length error, error in mounting position, Driven by Hydraulic Cylinder error；The rod length error includes:
Crank length error and length of connecting rod error.
4. a kind of connecting rod mechanism movement analysis method for reliability for considering error originated from input according to claim 3, feature
It is, the long relational expression long with practical bar of effective bar in the case of two kinds of continuous type contact and discrete contact are as follows:
Wherein, R is that effective bar is long, and r is that practical bar is long, xG、yGIt is the transverse and longitudinal coordinate of local coordinate, local coordinate is with axle sleeve sets of holes
Center is coordinate origin, using connecting rod direction as positive direction of the x-axis, using upwards vertically with the direction of connecting rod as positive direction of the y-axis, G is fortune
Dynamic auxiliary air gap.
5. a kind of connecting rod mechanism movement analysis method for reliability for considering error originated from input according to claim 4, feature
It is, long effective bar includes effective crank length and effective length of connecting rod.
6. a kind of connecting rod mechanism movement analysis method for reliability for considering error originated from input according to claim 5, feature
It is, long practical bar includes actual crank length and actual length of connecting rod.
7. a kind of connecting rod mechanism movement analysis method for reliability for considering error originated from input according to claim 5, feature
It is, it is described to replace practical bar long using effective bar in the case of two kinds of continuous type contact and discrete contact is long, specifically:
Actual crank length is replaced using effective crank length, actual length of connecting rod is replaced using effective length of connecting rod.
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