CN110008433A - A kind of metaaction cell parts Tolerance Distribution Method based on state space equation - Google Patents
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Abstract
The invention discloses the present invention provides a kind of metaaction cell parts Tolerance Distribution Methods based on state space equation;The transmitting of metaaction unit build-up tolerance is construed to the additive process of the dimensional tolerance and geometric tolerance of each part under different fit forms by the structural model for analyzing metaaction unit;Each component assembly sequence of metaaction unit and the correlated parts geometrical characteristic of each mating feature has been determined, and each part geometry feature space pose is expressed with thin tail sheep spinor according to tolerance Model, the small transformation of the assembly features attained pose after every step assembly is calculated;According to build-up tolerance differential vector, the output tolerance vector of power output member after being assembled, to obtain the state space equation of metaaction unit assembling process;By iterative calculation, the part geometry tolerance of meet demand is fitted, realizes the distribution of metaaction cell parts tolerance.
Description
Technical field
The invention belongs to mechanical tolerance distribution techniques, especially accuracy Design technical field, and in particular to one kind is based on shape
The metaaction cell parts Tolerance Distribution Method of state space equation.
Background technique
Tolerance assignment problem is the top priority that Design Stage needs to solve, and effective, accurate Tolerance assignment mould
Type is the basis of reasonable distribution part processing precision.Engineering goods are usually formed by hundreds of or thousands of component assemblies, right
In product tolerance assignment problem, if the TRANSFER MODEL between directly researching part can cause to calculate because of the huge of number of parts
The problems such as process is cumbersome, error calculated is big.Traditional Tolerance assignment model mainly considers the subordinate between part and product
Relationship can not reflect the transitive relation of the relative motion state and kinematic error between part.Complex mechanical product is by zero
Interaction (including power, torque, friction, abrasion, vibration, kinematic accuracy etc.) between component, according to " movement-movement-function
Can " mode realize the function and performance of complete machine, therefore, University Of Chongqing proposes a kind of new engineering goods FMA
(Function-Movement-Action), FMA structural method in sufficiently prominent engineering goods structure " movement " and
" movement " the two key concepts, and applied the (mission reliability based on metaaction unit in reliability prediction analysis
Expectancy analysis method, publication number: CN 107038321A) and assembly technology in (it is a kind of based on metaaction decompose pallet exchange frame
Assembly technology, publication number: CN 107097169A).After metaaction theory is introduced into Tolerance assignment, it is with basic motion unit
Research object pay close attention to motion layer analysis so that modeling granularity refinement, model it is more acurrate, distinguish metaaction unit in and metaaction
Relational model between unit, while considering the relative positional accuracy between metaaction unit, relative motion precision, contact precision and member
Parts size precision accumulation in motor unit assembling process solves conventional tolerance TRANSFER MODEL and only considers static assembly precision
The problem of, a more effective, more accurate method is provided for mechanical product tolerance distribution research.Metaaction Element Theory at present
It is only applied in reliability field, the part tolerance distribution method about metaaction unit is not yet established.
Summary of the invention
In view of the above shortcomings of the prior art, the technical problems to be solved by the present invention are: how to provide it is a kind of meet it is defeated
The metaaction cell parts Tolerance Distribution Method based on state space equation of required precision out.
In order to solve the above-mentioned technical problem, present invention employs the following technical solutions:
A kind of metaaction cell parts Tolerance Distribution Method based on state space equation, which is characterized in that including as follows
Step:
S1, according to the composed structure of metaaction unit, determine metaaction unit component part include power input, in
Between part, fastener, supporting element and power output member;
The correlated parts geometrical characteristic of S2, the crucial mating feature for determining metaaction and each mating feature: according to metaaction
The assembly sequence of each component part of unit will directly or indirectly influence power output member according to assemble sequence in assembling process
Spatial pose mating feature as the crucial mating feature for influencing metaaction unit output accuracy, it is special to extract each crucial cooperation
Levy M=(M1,M2,…,Mn), M1~MnIndicate the mating feature code name in n installation step;
Using the geometric dimension of two component part contact surfaces mutually matched in crucial mating feature or geometric tolerance as
The correlated parts geometrical characteristic of crucial mating feature determines that the correlated parts geometrical characteristic of each crucial mating feature is respectively as follows: M1
=(M11,M12,…,M1a) ..., Mn=(Mn1,Mn2,…,Mnz), wherein M11Indicate mating feature M1In part geometry feature 1,
Other code meanings are identical;
S3, power output member theoretical coordinate system and assembly features ideal coordinates system are established: in the geometry of power output member
The heart is that coordinate origin establishes power output member theoretical coordinate system, using the crucial mating feature of assembling stage as assembly features, and
Assembly features ideal coordinates system is established with each assembly features geometric center;
S4, each part geometry feature tolerances value is set, and indicates tolerance value with thin tail sheep spinor, is i.e. the actual bit of part
Minor shifts amount of the appearance relative to theoretical pose, wherein υ=(dx, dy, dz)TIndicate the small variations vector on moving direction, θ
=(δ α, δ β, δ γ)TIndicate the small variations vector in rotation direction;By each offset summation of geometric tolerances in mating feature
Obtain Δ xi、Δyi、ΔziAssembly features attained pose is to the small flat of assembly features ideal coordinates system after indicating the assembly of the i-th step
Move transformation, Δ αi、Δβi、ΔγiAssembly features attained pose is to the micro- of assembly features ideal coordinates system after indicating the assembly of the i-th step
Small rotation transformation;
S5, the differential tolerance vector d for calculating the assembly of the i-th stepiAnd δi, expression formula is as follows:
di=m1iΔxi+m2iΔyi+m3iΔzi+m4iΔαi+m5iΔβi+m6iΔγi
δi=m7iΔαi+m8iΔβi+m9iΔγi
Wherein m1i、m2i、m3i、m4i、m5i、m6iTo translate tolerance transformation vectors from the 3 × 1 of the (i-1)-th step to the i-th step, and by
The translation transformation vector of part known to formula is codetermined by translation tolerance and rotation tolerance;m7i、m8i、m9iFor the (i-1)-th step to
3 × 1 rotation tolerance transformation vectors of i step, the rotation transformation vector of part known to formula are only determined by rotation tolerance;Wherein:
S6, Computing Meta motor unit the power output member real space pose relative theory coordinate system when kth is walked and assembled
Differential translation vector dkWith differential rotating vector δk, expression formula is as follows:
Wherein Ri-1For the (i-1)-th step after the assembly is completed assembly features attained pose to the 3 of power output member theoretical coordinate system ×
3 spin matrixs, Pi-1For the (i-1)-th step after the assembly is completed assembly features attained pose to power output member theoretical coordinate system 3 × 1
Translation vector;
S7,6 × 1 tolerance vectors for calculating the i-th step assembly power output memberExpression formula are as follows:
Further it is written as:
Wherein Δ x, Δ y, the column vector of N × 1 that Δ z is mating feature translation transformation, Δ α, Δ β, Δ γ are mating feature
The column vector of the N of rotation transformation × 1, above-mentioned column vector is by obtained by design tolerance or measurement error, and Δ x=(Δ x1,Δ
x2,…,Δxk)T, Δ y=(Δ y1,Δy2,…,Δyk)T, Δ z=(Δ z1,Δz2,…,Δzk)T, Δ α=(Δ α1,Δ
α2,…,Δαk)T, Δ β=(Δ β1,Δβ2,…,Δβk)T, Δ γ=(Δ γ1,Δγ2,…,Δγk)T;W1i、W2i、W3i、
W4i、W5i、W6i、W7i、W8i、W9iFor 3XN matrix, and W1i=Ri-1m1i, W2i=Ri-1m2i, W3i=Ri-1m3i, W4i=Ri-1m4i+Pi-1
×{Ri-1m7i, W5i=Ri-1m7i, W6i=Ri-1m5i+Pi-1×{Ri-1m8i, W7i=Ri-1m8i, W8i=Ri-1m6i+Pi-1×{Ri- 1m9i, W9i=Ri-1m9i;
S8, according to the state space equation of metaaction unit assembling process:
WhereinFor 6 × 1 vectors, indicate the mating feature real space pose of the i-th step assembly relative to mating feature
The deviation of theoretical coordinate system;A (k) is unit matrix;F (k) is that metaaction unit kth walks assembly features tolerance from assembly features reason
By coordinate system to 6 × 6 tolerance transfer matrixes of power output member theoretical coordinate system;C (k) is that obtain metaaction unit complete for measurement
Exporting tolerance matrix at the r × 6 of assembly indicates, wherein r is output tolerance variable number;
The gross tolerance that power output member adds up under theoretical coordinate system after the i-th step is assembled is calculatedAnd become
The state input quantity of+1 step of kth assembly;And the output vector of r × 1 indicates that metaaction unit power output member exports geometrical characteristic
Tolerance
The gross tolerance that power output member after the assembly is completed adds up under theoretical coordinate system is that the output of metaaction unit is public
Difference.
S9, judge metaaction unit output tolerance whether meet demand, each geometry of output element is public if meet demand
Poor apportioning cost resets each part geometry feature tolerances value in step S4 if being unsatisfactory for demand, and repeats step S4~S9,
Until metaaction unit exports tolerance meet demand.
In conclusion the present invention is based on the output tolerance stack mistakes that metaaction cellular construction feature establishes metaaction assembly
Journey expresses part space error with thin tail sheep spinor by constantly iterating to calculate, and fits and meets the output of metaaction unit
Each part geometry Tolerance assignment value of tolerance, calculating process accurate and effective, and can be added in an iterative process according to practical
The apportioning cost of work ability and each geometric tolerances of economy reasonable coordination mentions to guarantee the machining accuracy of part for Tolerance assignment
A kind of new method is supplied.
Detailed description of the invention
Fig. 1 is flow chart of the invention.
Fig. 2 is metaaction unit structure model figure.
Specific embodiment
Below with reference to embodiment, the present invention is described in further detail.
When specific implementation: as depicted in figs. 1 and 2,
1, according to the composed structure of metaaction unit, as shown in Fig. 2, obtaining the power input of metaaction unit, centre
Part, fastener, supporting element, power output member.The output accuracy of metaaction unit can regard that the geometric dimension of each part is logical as
It crosses assembly to be finally added on power output member, is presented as pose of the power output member on the six degree of freedom direction of space, wherein
Moving along reference axis in x, y, z representation space rectangular coordinate system, α, β, γ indicate the rotation around reference axis.
2, the assembly sequence for establishing each part of metaaction unit, extracting according to assemble sequence influences the output of metaaction unit
The crucial mating feature M=(M of precision1,M2,…,Mn), M1~MnIndicate the mating feature code name in n installation step;And it determines
The tolerance code name M of the correlated parts geometrical characteristic of each mating feature1=(M11,M12,…,M1a) ..., Mn=(Mn1,Mn2,…,
Mnz), wherein M11Indicate mating feature M1In part geometry feature 1, other code meanings are identical.Crucial mating feature depends on
Whether the spatial pose of power output member can directly or indirectly be influenced in assembling process, and correlated parts geometrical characteristic is to cooperate two
The geometric dimension or geometric tolerance in feature contacts face.
3, power output member theoretical coordinate system is established by coordinate origin of power output member geometric center, with each assembly features
Geometric center establishes assembly features ideal coordinates system.
4, each part geometry feature tolerances value is set, and indicates tolerance value with thin tail sheep spinor, is i.e. the actual bit of part
Minor shifts amount of the appearance relative to theoretical pose, wherein υ=(dx, dy, dz)TIndicate the small variations vector on moving direction, θ
=(δ α, δ β, δ γ)TIndicate the small variations vector in rotation direction.In view of the microcosmos geometric shape in geometrical characteristic face is all
It is irregular, it calculates for convenience, each spinor parameter takes maximum value in tolerance domain, to obtain M according to table 11To MnEach tolerance
Spinor parameter value, wherein T be tolerance value.Then it sums each offset of geometric tolerances in mating feature to obtain Δ xi、Δ
yi、ΔziIndicate the i-th step assembly after small translation transformation of the assembly features attained pose to assembly features ideal coordinates system, Δ αi、
Δβi、ΔγiIndicate the i-th step assembly after small rotation transformation of the assembly features attained pose to assembly features ideal coordinates system.
The common tolerance Model of table 1
5, it calculates the i-th step and assembles differential tolerance vector diAnd δi, expression formula is as follows:
di=m1iΔxi+m2iΔyi+m3iΔzi+m4iΔαi+m5iΔβi+m6iΔγi
δi=m7iΔαi+m8iΔβi+m9iΔγi
Wherein m1i、m2i、m3i、m4i、m5i、m6iTo translate tolerance transformation vectors from the 3 × 1 of the (i-1)-th step to the i-th step, and by
The translation transformation vector of part known to formula is codetermined by translation tolerance and rotation tolerance.m7i、m8i、m9iFor the (i-1)-th step to
3 × 1 rotation tolerance transformation vectors of i step, the rotation transformation vector of part known to formula are only determined by rotation tolerance.And:
6, differential translation of the Computing Meta motor unit kth step assembly power output member real space pose to theoretical coordinate system
Vector dkWith differential rotating vector δk, expression formula is as follows:
Wherein Ri-1For the (i-1)-th step after the assembly is completed assembly features attained pose to the 3 of power output member theoretical coordinate system ×
3 spin matrixs, Pi-1For the (i-1)-th step after the assembly is completed assembly features attained pose to power output member theoretical coordinate system 3 × 1
Translation vector.
7,6 × 1 tolerance vectors of the i-th step assembly power output member are calculatedExpression formula are as follows:
Further it is written as:
Wherein Δ x, Δ y, the column vector of N × 1 that Δ z is mating feature translation transformation, Δ α, Δ β, Δ γ are mating feature
The column vector of the N of rotation transformation × 1, these column vectors are by obtained by design tolerance or measurement error, and Δ x=(Δ x1,Δ
x2,…,Δxk)T, Δ y=(Δ y1,Δy2,…,Δyk)T, Δ z=(Δ z1,Δz2,…,Δzk)T, Δ α=(Δ α1,Δ
α2,…,Δαk)T, Δ β=(Δ β1,Δβ2,…,Δβk)T, Δ γ=(Δ γ1,Δγ2,…,Δγk)T。W1i、W2i、W3i、
W4i、W5i、W6i、W7i、W8i、W9iFor 3 × N matrix, and W1i=Ri-1m1i, W2i=Ri-1m2i, W3i=Ri-1m3i, W4i=Ri-1m4i+
Pi-1×{Ri-1m7i, W5i=Ri-1m7i, W6i=Ri-1m5i+Pi-1×{Ri-1m8i, W7i=Ri-1m8i, W8i=Ri-1m6i+Pi-1×
{Ri-1m9i, W9i=Ri-1m9i
8, according to the state space equation of metaaction unit assembling process:
WhereinIndicate that the mating feature real space pose of the i-th step assembly is managed relative to mating feature for 6 × 1 vectors
By the deviation of coordinate system;A (k) is unit matrix;F (k) is that metaaction unit kth walks assembly features tolerance from assembly features theory
6 × 6 tolerance transfer matrixes of the coordinate system to power output member theoretical coordinate system;C (k) obtains metaaction unit for measurement and is completed
The r of assembly × 6 exports tolerance matrix and indicates, wherein r is output tolerance variable number.
The gross tolerance that power output member adds up under theoretical coordinate system after the i-th step is assembled is calculatedAnd become
The state input quantity of+1 step of kth assembly;And the output vector of r × 1 indicates that metaaction unit power output member exports geometrical characteristic
Tolerance
The gross tolerance that power output member after the assembly is completed adds up under theoretical coordinate system is that the output of metaaction unit is public
Difference.
9, judge metaaction unit output tolerance whether meet demand, each geometric tolerances of output element if meet demand
Apportioning cost resets each part geometry feature tolerances value in step 4 if being unsatisfactory for demand, and repeats step 4~9, until
Until metaaction unit exports tolerance meet demand.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not limitation with the present invention, all in essence of the invention
Made any modifications, equivalent replacements, and improvements etc., should all be included in the protection scope of the present invention within mind and principle.
Claims (1)
1. a kind of metaaction cell parts Tolerance Distribution Method based on state space equation, which is characterized in that including walking as follows
It is rapid:
S1, according to the composed structure of metaaction unit, determine that the component part of metaaction unit includes power input, centre
Part, fastener, supporting element and power output member;
The correlated parts geometrical characteristic of S2, the crucial mating feature for determining metaaction and each mating feature: according to metaaction unit
The assembly sequence of each component part the sky of power output member will be directly or indirectly influenced in assembling process according to assemble sequence
Between pose mating feature as the crucial mating feature for influencing metaaction unit output accuracy, extract each crucial mating feature M
=(M1,M2,…,Mn), M1~MnIndicate the mating feature code name in n installation step;
Using the geometric dimension of two component part contact surfaces mutually matched in crucial mating feature or geometric tolerance as key
The correlated parts geometrical characteristic of mating feature determines that the correlated parts geometrical characteristic of each crucial mating feature is respectively as follows: M1=
(M11,M12,…,M1a) ..., Mn=(Mn1,Mn2,…,Mnz), wherein MnzIndicate mating feature MnIn part geometry feature z;
S3, power output member theoretical coordinate system and assembly features ideal coordinates system are established: is with the geometric center of power output member
Coordinate origin establishes power output member theoretical coordinate system, using the crucial mating feature of assembling stage as assembly features, and with each
Assembly features geometric center establishes assembly features ideal coordinates system;
S4, each part geometry feature tolerances value is set, and indicates tolerance value with thin tail sheep spinor, is i.e. the attained pose phase of part
For the minor shifts amount of theoretical pose, wherein υ=(dx, dy, dz)TIndicate the small variations vector on moving direction, θ=(δ
α,δβ,δγ)TIndicate the small variations vector in rotation direction;Each offset of geometric tolerances in mating feature is summed to obtain
Δxi、Δyi、ΔziAssembly features attained pose becomes the small translation of assembly features ideal coordinates system after indicating the assembly of the i-th step
It changes, Δ αi、Δβi、ΔγiIndicate the i-th step assembly after small rotation of the assembly features attained pose to assembly features ideal coordinates system
Transformation is changed;
S5, the differential tolerance vector d for calculating the assembly of the i-th stepiAnd δi, expression formula is as follows:
di=m1iΔxi+m2iΔyi+m3iΔzi+m4iΔαi+m5iΔβi+m6iΔγi
δi=m7iΔαi+m8iΔβi+m9iΔγi
Wherein m1i、m2i、m3i、m4i、m5i、m6iTo translate tolerance transformation vector from the 3 × 1 of the (i-1)-th step to the i-th step, and by formula
Know that the translation transformation vector of part is codetermined by translation tolerance and rotation tolerance;m7i、m8i、m9iFor the (i-1)-th step to the i-th step
3 × 1 rotation tolerance transformation vectors, only determined by rotation tolerance by the rotation transformation vector of part known to formula;Wherein:
The differential of S6, Computing Meta motor unit power output member real space pose relative theory coordinate system when kth is walked and assembled
Translation vector dkWith differential rotating vector δk, expression formula is as follows:
Wherein Ri-1For 3 × 3 rotations of the assembly features attained pose to power output member theoretical coordinate system after the assembly is completed of the (i-1)-th step
Torque battle array, Pi-1For 3 × 1 translations of the assembly features attained pose to power output member theoretical coordinate system after the assembly is completed of the (i-1)-th step
Vector;
S7,6 × 1 tolerance vectors for calculating the i-th step assembly power output memberExpression formula are as follows:
Further it is written as:
Wherein Δ x, Δ y, the column vector of N × 1 that Δ z is mating feature translation transformation, Δ α, Δ β, Δ γ are mating feature rotation
The column vector of the N of transformation × 1, above-mentioned column vector is by obtained by design tolerance or measurement error, and Δ x=(Δ x1,Δx2,…,
Δxk)T, Δ y=(Δ y1,Δy2,…,Δyk)T, Δ z=(Δ z1,Δz2,…,Δzk)T, Δ α=(Δ α1,Δα2,…,Δ
αk)T, Δ β=(Δ β1,Δβ2,…,Δβk)T, Δ γ=(Δ γ1,Δγ2,…,Δγk)T;W1i、W2i、W3i、W4i、W5i、
W6i、W7i、W8i、W9iFor 3 × N matrix, and W1i=Ri-1m1i, W2i=Ri-1m2i, W3i=Ri-1m3i, W4i=Ri-1m4i+Pi-1×{Ri- 1m7i, W5i=Ri-1m7i, W6i=Ri-1m5i+Pi-1×{Ri-1m8i, W7i=Ri-1m8i, W8i=Ri-1m6i+Pi-1×{Ri-1m9i, W9i
=Ri-1m9i;
S8, according to the state space equation of metaaction unit assembling process:
WhereinFor 6 × 1 vectors, indicate that the mating feature real space pose of the i-th step assembly is sat relative to mating feature theory
Mark the deviation of system;A (k) is unit matrix;F (k) is that metaaction unit kth walks assembly features tolerance from assembly features theoretical coordinate
It is 6 × 6 tolerance transfer matrixes to power output member theoretical coordinate system;C (k) obtains metaaction unit for measurement and assembly is completed
R × 6 export tolerance matrix indicate, wherein r be output tolerance variable number;
The gross tolerance that power output member adds up under theoretical coordinate system after the i-th step is assembled is calculatedAnd become kth+1
Walk the state input quantity of assembly;And the output vector of r × 1 indicates that metaaction unit power output member exports geometrical characteristic tolerance
The gross tolerance that power output member after the assembly is completed adds up under theoretical coordinate system is metaaction unit output tolerance;
S9, judge metaaction unit output tolerance whether meet demand, each geometric tolerances of output element point if meet demand
With value, each part geometry feature tolerances value in step S4 is reset if being unsatisfactory for demand, and repeat step S4~S9, until
Until metaaction unit exports tolerance meet demand.
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