CN110362929A - A kind of rigging error transitive attribute analysis method combining faying face - Google Patents
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Abstract
The invention discloses a kind of rigging error transitive attribute analysis methods for combining faying face, comprising the following steps: step 1: obtaining the mobility scale of the transferable error component of each faying face in combination faying face；Step 2: the mobility scale of the transferable error component of each faying face obtained in step 1 is projected in the plane where combining the transferable rotation error component of faying face；Step 3: the rotation error component and displacement error component that combination faying face is calculated in the plane where the transferable rotation error component of faying face are being combined according to analytic geometry.The present invention combines tolerance range with analytic geometry, converts analytic geometry Solve problems for the quantitative analysis problem of error component, and the transferable error component of combination faying face is calculated so as to simple and quick quantifying.
Description
Technical field
The invention belongs to be machined manufacturing technology field more particularly to a kind of rigging error transmitting for combining faying face to belong to
The analysis method of property.
Background technique
The rigging error of engineering goods is the topological structure accumulation transmitting shape by multiple local error sources according to engineering goods
At, however thousands of a parts up to ten thousand are usually contained for complicated engineering goods.In order to simplify the analysis to rigging error, root
According to FMA (Function-Movement-Action, FMA) structuring decomposition method, metaaction concept is introduced into engineering goods dress
With error modeling, the assembly precision of several metaaction units is built so that being converted into the assembly precision modeling of product complete machine
Mould.
Metaaction unit (Meta-action Unit, MU): realize that all parts of some metaaction are closed according to structure
It is the entirety constituted, referred to as metaaction unit.Metaaction unit should include five big fundamentals, be power input respectively, move
Power output, middleware, fastener and supporting element.
Compared to complicated engineering goods, number of parts is few in metaaction unit, and faying face type is simple, and faying face refers to
Two geometric elements on different parts are with matching relationship according to a pair of of contact surface that matching relationship mutually fits and is formed
A pair of of adjacent parts geometric element error accumulation node.According to the geometry of faying face, metaaction unit it is main
Faying face can be divided into: plane faying face, is screwed special shape faying face in face and bearing at cylinder faying face.Wherein, spiral shell
Line faying face belongs to fastener under normal circumstances, and part is made to keep its position location constant in metaaction unit, does not play positioning
Effect, therefore rigging error modeling in can ignore；Special shape faying face error propagation characteristic is complex in bearing, needs
It to be made a concrete analysis of according to different situations；Plane faying face and cylinder faying face are most commonly seen in metaaction unit, corresponding several
What element is plane, cylinder and cylinder axis (the export geometric element of cylinder).
In practical set, the form cooperated according to multiple faying faces is needed to control the error of part and change, therefore more
The rigging error transitive attribute for the faying face in parallel that a faying face cooperatively forms is the basis of analysis elements action potential rigging error.
Faying face in parallel is divided into two major classes for the first time by inventor: combination faying face cooperates with general faying face in parallel.When the positioning of part
When geometric element is relative to being all small geometric element by positioning geometric element, multiple faying faces cooperatively form combination faying face.When
When any one positioning geometric element of part is relative to being big geometric element by positioning geometric element, multiple faying faces cooperate shape
At general faying face in parallel.
When part is positioned by non-combined faying face, mutually matched two geometric elements error can pass through faying face equivalent
It is transmitted in the same direction by locating element, when part is positioned by combining faying face, the error of itself is changed by multiple combinations
Face joint effect, it is complex by locating element error change conditions.
Thin tail sheep spinor (Small Displacement Torsor, SDT)) theory is suggested, and is existed by Bourdet
Introducing tolerance mathemodel field in 1996, the theory are suitable for indicating the mathematical model of geometric element tolerance.In SDT tolerance Model
In, the error of the practical geometric element of part is changed by the small rigidity of the one kind on nominal surface to indicate, and several with ideal
What element replaces the practical geometric element of actual parts, and in SDT tolerance Model, physical plane is assumed to be ideal plane, and
The small variations that physical plane generates then are expressed as to the small variations of local coordinate system.
Thin tail sheep spinor can describe the small variations of geometric element six-freedom degree, be represented by D=(α, beta, gamma, u,
V, w), wherein α, β, γ represent the minor rotation amount around the rotation of x, y, z axis, and u, v, w represent along the translation of x, y, z axis
Micro-amount of movement.In this paper research range, each variation of SDT is the error for describing part geometry element.
Concept according to invariance degree in new generation GPS standard is it is found that when geometric element generates small change in some freedom degree
When dynamic, if no change has taken place compared with its own character shape for its swept track, there is the freedom degree direction
On invariance degree.Therefore, invariance degree is used to indicate that the pose of geometric element in particular directions changes the feature to geometric element
Shape does not influence, and corresponding SDT component is zero.In SDT tolerance Model, wanted by the nonzero component of SDT to describe geometry
The error of element.Common geometric element has plane, cylinder and a cylinder axis in metaaction unit, the present invention also mainly to this three
Kind geometric element is studied, and is that the SDT of plane, cylinder and cylinder axis is expressed as shown in table 1 below.
Common geometric element SDT expression in 1 metaaction unit of table
Table1 SDT expressions of common geometric elements in Meta-action
Units
In SDT tolerance Model, when geometric element error is by multinomial allowance control, the location components of ideal geometric element
By fixed tolerance range control, direction is by translation allowance control.Since the tolerance range of floating not can control geometric element position and side
To there is no effect of contraction to each variation of SDT, therefore SDT model is perfect not enough to the expression of the tolerance range of floating, and float
Tolerance range it is relatively small to the error accumulation of assembly effect, therefore tolerance of only fixing and be translatable to tolerance range herein couples
Modeling.Text of the invention is coupled for plane, cylinder and cylinder axis geometric element error common in metaaction unit in tolerance
Change conditions under effect are analyzed, and corresponding SDT error model is established.
Common combination faying face has plane combination faying face and cylinder combination faying face in metaaction unit, although combination
The qualitative analysis of faying face error propagation attribute can be obtained rule of thumb: the transferable error component of plane combination faying face be α,
β, w or β, w, the transferable error component of cylinder faying face are α, β, u, v, wherein α, β respectively indicate the rotation mistake around x, y-axis
Difference component, u, v, w respectively indicate the translation error component along x, y, z axis, but how special to the error propagation of combination faying face
Property carry out quantitative analysis or the problem of urgent need to resolve.
Summary of the invention
In view of the above shortcomings of the prior art, the present invention provides a kind of rigging error transitive attribute analysis for combining faying face
Method realizes the quantitative analysis to combination faying face error propagation attribute.
In order to solve the above technical problems, technical scheme is as follows: a kind of rigging error transmitting for combining faying face
Property analysis method, comprising the following steps:
Step 1: obtaining the mobility scale of the transferable error component of each faying face in combination faying face；
Step 2: the mobility scale of the transferable error component of each faying face obtained in step 1 is projected into combination knot
In plane where the transferable rotation error component in conjunction face；
Step 3: calculating group in the plane where the transferable rotation error component of faying face is being combined according to analytic geometry
Close the rotation error component and displacement error component of faying face.
Further, the mobility scale of the transferable error component of faying face obtains as follows:
Step 1.1: obtaining the positioning geometric element of faying face and by the tolerance range of positioning geometric element, including fixed tolerance
Band and translation tolerance range；
Step 1.2 is calculated separately according to SDT error model positions geometric element and by the error component of positioning geometric element
Mobility scale；
Step 1.3: can with faying face by what is obtained from the mobility scale of the positioning transferable error component of geometric element
The mobility scale of the corresponding error component of the error component of transmitting, and from by the change of the transferable error component of positioning geometric element
The mobility scale of the error component corresponding with the transferable error component of faying face obtained in dynamic range is summed, thus
To the mobility scale of the transferable error component of faying face.
Further, for the SDT error model of plane geometry element, cylinder geometric element and cylinder axis geometric element
It is as follows respectively:
The SDT error model of plane geometry element:
In formula, a indicates that the width of plane, b indicate the length of plane；Using the geometric center of ideal rectangle plane as coordinate system
Origin, coordinate system normal direction are z-axis, and length direction is x-axis, and width direction is y-axis, establish coordinate system, and α ' expression turns around x-axis
Dynamic rotation error component, the rotation error component that β ' expression is rotated around y-axis, the displacement error component that w ' expression is moved along the z-axis；
TPIndicate the translation degree tolerance range of plane, TdIndicate the tolerance zone of plane；
The SDT error model of cylinder geometric element:
In formula, l indicates body length；Using the geometric center of ideal cylinder as coordinate origin, the axis direction of cylinder is Z
Axis, radial direction x, y-axis establish coordinate system, the rotation error component that α ' expression is rotated around x-axis, and u ' expression moves along the x-axis
Displacement error component；TDIndicate the tolerance zone of cylinder, TRIndicate the radial run-out tolerance range of cylinder；
The SDT error model of cylinder axis geometric element:
In formula, l indicates body length；Using the geometric center of ideal axis as coordinate origin, axis direction is Z axis, diameter
It is that x, y-axis establish coordinate system, the rotation error component that α ' expression is rotated around x-axis, the mobile mistake that u ' expression moves along the x-axis to direction
Difference component；TVIndicate the squareness tolerance band of cylinder axis, TCIndicate the concentricity tolerance band of cylinder axis.
Further, when faying face is plane-facet, transferable error properties are the mobile mistake being moved along the z-axis
Difference component, z-axis is perpendicular to faying face；
When faying face is plane-narrow plane, transferable error properties be the displacement error component that is moved along the z-axis with around
The rotation error component of x-axis rotation, for z-axis perpendicular to faying face, x-axis is faying face length direction；
When faying face is cylinder-short column face, transferable error properties be the displacement error component that moves along the x-axis with around
The rotation error component of y-axis rotation, z-axis is axis direction, and x, y-axis are radial direction.
Further, when combination faying face is to combine combination by the cylinder that two cylinders-short column face faying face F1, F2 is formed
When face, using z-axis direction as axis direction, using x, y-axis direction as radial direction, and z-axis is parallel to ideal cylinder axis, coordinate
It is origin o on ideal cylinder axis；Cylinder combines the transferable error component T=[α, β, u, v] of faying face, wherein α, β points
The translation error component along x, y-axis Biao Shi not be respectively indicated around x, the rotation error component of y-axis, u, v；Specific step is as follows:
Step s1: cylinder-short column face faying face F1, F2 transferable error component mobility scale is obtained respectively:
Step s2: by the mobility scale u of cylinder-short column face faying face F1, F2 translation error component moved along the x-axis1、u2
It is projected in x-o-z plane respectively, to calculate cylinder faying face transferable error component β, u；By cylinder-short column face faying face
The translation error component v that F1, F2 are moved along y-axis1、v2Mobility scale projected in z-o-y plane respectively, to calculate cylinder cells
Close faying face transferable error component α, v；
Step s3: according to analytic geometry, error component β, u, α, v are calculated as follows respectively:
Wherein, L indicates the length of ideal cylinder axis, L1Indicates coordinate system origin o is along the ideal cylindrical shaft line end of z-axis distance
The distance of point.
Further, when combining faying face is plane combination faying face, faying face is reduced to binding site to analyze；And
Using by the geometric center of positioning surface as coordinate origin o, using perpendicular to by the direction of positioning plane as z-axis direction, to be determined
The length direction of plane be x-axis direction, using by the width mode of positioning surface as y-axis direction.
Further, when the positioning surface in plane combination faying face is 4 symmetrical facets on by positioning surface
When, 4 faying faces are plane-facet faying face, if faying face F1 is located at by the positioning surface upper left corner, faying face F1, F2, f3
It is arranged in the direction of the clock with F4；The transferable error component T=[α, β, w] of plane combination faying face, wherein α, β points
Displacement error component along the z-axis direction Biao Shi not be indicated around x, the rotation error component of y-axis, w；Steps are as follows for specific calculating:
Step a1: 4 faying faces F1, F2, F3 and F4 are obtained respectively in the variation model of the displacement error component in z-axis direction
It encloses: w1、w2、w3、w4；
Step a2: the mobility scale of the displacement error component of faying face F1, F2, F3 and F4 along the z-axis direction is projected respectively
To z-o-y plane, and z-o-x plane is projected to respectively；
Step a3: displacement error component w is calculated in z-axis:
Rotation error component α is calculated in z-o-y plane according to analytic geometry:
Wherein, L2Indicate the distance in two binding sites in the y-axis direction；
Rotation error component β is calculated in z-o-x plane according to analytic geometry:
Wherein, L1Indicate the distance in two binding sites in the direction of the x axis.
Further, it is symmetrically distributed in when the positioning surface in plane combination faying face is two by the narrow plane on positioning surface
When, and the length direction of narrow plane is parallel to by the width direction of positioning surface, then by each knot in two basic change face F1, F2
Conjunction face is reduced to two binding sites for being located at positioning surface length direction both ends；The transferable mistake of plane combination faying face
Difference component T=[α, β, w], wherein α, β respectively indicate the rotation error component around x, y-axis, and w indicates mobile mistake along the z-axis direction
Difference component；Steps are as follows for specific calculating:
Step b1: F1, F2 are obtained respectively in the mobility scale of the displacement error component in z-axis direction: w1、w2；Knot is obtained respectively
The rotation error component mobility scale that conjunction face F1, F2 are rotated around x-axis: α1、α2；
Step b2: faying face F1, F2 are projected into z-o-x in the mobility scale of the displacement error component in z-axis direction respectively
In plane；Faying face F1, F2 are projected in z-o-y plane respectively around the mobility scale for the rotation error component that x-axis rotates；
Step b3: displacement error component w is calculated in z-axis:
Rotation error component α is calculated in z-o-y plane according to analytic geometry:
Rotation error component β is calculated in z-o-x plane according to analytic geometry:
Further, it is symmetrically distributed in when the positioning surface in plane combination faying face is two by the facet in positioning
When, 2 faying faces F1, F2 are reduced to two basic change point respectively；The transferable error component T=of plane combination faying face
[β, w], wherein β indicates that the rotation error component around y-axis, w indicate displacement error component along the z-axis direction；It is specific to calculate step
It is as follows:
Step c1: faying face F1, F2 are obtained respectively in the mobility scale of the displacement error component in z-axis direction: w1、w2；
Step c2: faying face F1, F2 are projected in z-o-x plane in the tolerance range of the displacement error component in z-axis direction；
Step c3: displacement error component w is calculated in z-axis:
Rotation error component β is calculated in z-o-x plane according to analytic geometry:
Wherein, L indicates the distance between two basic change point.
Compared with prior art, the invention has the following advantages:
1, tolerance range is product in the design phase, and designer gives product actual size, shape and the variation of position model
It encloses and part manufacturing and the foundation of detection.The present invention combines tolerance range with analytic geometry, by quantitative point of error component
Analysis problem is converted into analytic geometry Solve problems, calculates the transferable of combination faying face so as to simple and quick quantifying
Error component.
It 2, is a kind respectively the present invention provides the error propagation property analysis method of the combination faying face of 4 kinds of concrete types
Cylinder combines faying face and 3 kinds of plane combination faying faces, meets the major demands in practical engineering application.
3, the proposition for combining faying face concept solves by multiple small combinations when in face of part positioning error propagation characteristic not
Clear problem establishes the Error Propagation Model of small faying face.
4, the present invention has studied the influence that combination faying face interacts to each faying face error propagation attribute, is decoupling member
Motor unit actual error transmission path and the important component and foundation for solving transmission error.
Detailed description of the invention
Fig. 1 is the schematic diagram of the SDT error model for the plane geometry element established under more tolerance couplings；
Fig. 2 is the cylinder geometric element established under tolerance zone and radial run-out translation tolerance range coupling
The schematic diagram of SDT error model；
Fig. 3 is the cylinder geometric element established under tolerance zone and the fixed tolerance range coupling of radial run-out
The schematic diagram of SDT error model；
Fig. 4 is the schematic diagram of the SDT error model for the cylinder axis geometric element established under more tolerance couplings；
Fig. 5 is the schematic diagram of cylinder combination faying face；
Fig. 6 is cylinder combination faying face error component resolution principle figure；
Fig. 7 is the schematic diagram of a class plane combination faying face；
Fig. 8 is the schematic diagram of b class plane combination faying face；
Fig. 9 is narrow plane displacement error component resolution principle figure in b class plane combination faying face；
Figure 10 is the schematic diagram of c class plane combination faying face.
Specific embodiment
In order to make to easily facilitate understanding in the present invention, the error propagation attribute of common faying face is illustrated first: knot
Conjunction face refers to that two geometric elements on different parts are to have according to a pair of of contact surface that matching relationship mutually fits and is formed
The accumulation node of the geometric element error of a pair of of adjacent parts of matching relationship；In assembling process, part passes through faying face pair
Adjacent parts apply effect of contraction and are allowed to position, while have an impact part error variation to the positioning states of adjacent parts,
So that error propagation is achieved.The error propagation attribute of faying face and the geometry of faying face are closely bound up.Plane
Faying face and cylinder faying face are the most common two classes faying faces in metaaction unit, their faying face error propagation attribute is such as
Shown in table 2.
2 faying face error propagation attribute of table
Table3.1 Joint Surface Error Transfer Properties
Facet: when positioning geometric element in combination faying face and being all plane geometry element by positioning geometric element,
In relative to by the positioning of locating element area when smaller (small unrestricted in part all directions rotational freedom to freedom degree)
Face is facet.
Narrow plane: when positioning geometric element in combination faying face and being all plane geometry element by positioning geometric element,
In relative to by the positioning surface of locating element length when relatively narrow (be too narrow to rotational freedom unrestricted) on part length direction
For narrow plane.
Short column face: when positioning geometric element in combination faying face and being all cylinder geometric element by positioning geometric element,
In relative to by the positioning of locating element length when shorter (be short to rotational freedom unrestricted) on the non axial direction of cylinder
Face is short column face.
In practical set, the form cooperated according to multiple faying faces is needed to control the error of part and change, therefore more
The rigging error transitive attribute for the faying face in parallel that a faying face cooperatively forms is the basis of analysis elements action potential rigging error.
Faying face in parallel is divided into two major classes for the first time by inventor: combination faying face cooperates with general faying face in parallel.When the positioning of part
When geometric element is relative to being all small geometric element by positioning geometric element, multiple faying faces cooperatively form combination faying face.When
When any one positioning geometric element of part is relative to being big geometric element by positioning geometric element, multiple faying faces cooperate shape
At general faying face in parallel.
In order to realize the quantitative analysis of the rigging error transitive attribute to combination faying face, the present invention is by tolerance range and parses
Geometry combines, and converts analytic geometry Solve problems for the quantitative analysis problem of error component, the scheme of use is as follows:
A kind of rigging error transitive attribute analysis method combining faying face, comprising the following steps:
Step 1: obtaining the mobility scale of the transferable error component of each faying face in combination faying face；
Step 2: the mobility scale of the transferable error component of each faying face obtained in step 1 is projected into combination knot
In plane where the transferable rotation error component in conjunction face；
Step 3: calculating group in the plane where the transferable rotation error component of faying face is being combined according to analytic geometry
Close the rotation error component and displacement error component of faying face.
The mobility scale of the transferable error component of faying face in step 1 obtains as follows:
Step 1.1: obtaining the positioning geometric element of faying face and by the tolerance range of positioning geometric element, including fixed tolerance
Band and translation tolerance range；
Step 1.2 is calculated separately according to SDT error model positions geometric element and by the error component of positioning geometric element
Mobility scale；
Step 1.3: can with faying face by what is obtained from the mobility scale of the positioning transferable error component of geometric element
The mobility scale of the corresponding error component of the error component of transmitting, and from by the change of the transferable error component of positioning geometric element
The mobility scale of the error component corresponding with the transferable error component of faying face obtained in dynamic range is summed, thus
To the mobility scale of the transferable error component of faying face.
One, the SDT error model of plane, cylinder and cylinder axis is established
Error modeling under the more tolerance couplings of 1.1 planes
By taking the coupling of plane positioning size tolerance and parallelism tolerance as an example, the error of plane geometry element is changed
Situation is analyzed, and flatness allowance band under more tolerance couplings long b as shown in Figure 1:, the plane of wide a, with ideal square are established
The geometric center of shape plane is coordinate origin, and coordinate system normal direction is Z axis, and length direction is X-axis, and width direction is Y-axis,
Establish coordinate system.TDThe location dimension tolerance range for indicating plane, is oriented parallel to datum plane, position is in distance in benchmark L
Place.TpThe parallelism tolerance band for indicating plane, is oriented parallel to datum plane, according to Geometry Product Specification (GPS), side
It is less than the position of related features band of the element to tolerance range, therefore the position of parallelism tolerance band is that TD tolerance zone two is parallel in size
Translation in plane.In SDT tolerance Model, by physical plane ideal surfaced SSIt indicates, plane geometry element error is by ideal
Surface SSα ', three components of β ', w ' variation description.Dimensional tolerance controls ideal surfaced SSLocation components w ', parallelism tolerance
Direction spinor α ' is controlled, β ', the depth of parallelism is to ideal surfaced SSLocation components w ' do not have restraining force.
It to sum up analyzes, under dimensional tolerance and flatness tolerance coupling, the SDT component of plane geometry element changes not
Deng are as follows:
To be located at ideal surfaced in coupling tolerances band, the component coped in SDT tolerance Model adds the constraint relationship:
-TDL≤w′+aα′+bβ′≤TDU (1.2)
Mathematical model is carried out using two groups of Mathematical inequalities coupling tolerances, formula (1.1) is the variation inequality of component parameters,
It indicates the permitted mobility scale of the single component parameters of plane geometry element.Formula (1.2) is the constraint inequality of variable parameter,
It describes the variation the constraint relationship between each component parameters of plane geometry element, it is ensured that the reasonability of component parameters value.
SDT error model under the more tolerance couplings of 1.2 cylinders
By taking cylinder diameter dimension tolerance and radial run-out tolerance as an example, to the error change conditions of cylinder geometric element into
Row analysis, establishes the cylinder tolerance range under more tolerance couplings.Body length is l, diameter 2d, with the geometry of ideal cylinder
Center is coordinate origin, and the axis direction of cylinder is Z axis, then the SDT error component of cylinder has α ', β ', u ' and v '.Due to ruler
Very little tolerance range has the characteristics that radial nature is identical with radial run-out tolerance range, thus can choose the xoz plane of coordinate system with
The plain line of the ideal of cylinder intersection and x > 0 is as research object, and wherein SDT component has β '=α ', u '=v '.Due to radial run-out
Tolerance range can be divided by itself cylindrical axis for the translation tolerance range of benchmark axial line and on the basis of non-self cylindrical axis
The fixation tolerance range of axial line, therefore discuss in two kinds of situation
As shown in Fig. 2, for tolerance zone and radial run-out translation tolerance range tolerance coupling condition.TDIndicate cylinder
Tolerance zone, the direction and position of tolerance range are all determining, direction and benchmark direction of axis line with respect to its benchmark axial line
In parallel, position is in distance at benchmark axial line d.TRIndicate the radial run-out tolerance range of cylinder, direction and benchmark axle center
Line direction is parallel, and position is radially translatable in tolerance zone.According to Geometry Product Specification (GPS), position of related features band is small
In the run-out tolerance band of the element, therefore radial run-out tolerance range not can control geometric element and change to reference direction, therefore in SDT
In model, dimensional tolerance controls ideal plain line SSLocation components u ' and direction spinor α ', radial run-out is to ideal plain line SSPosition
Setting does not have restraining force with durection component.
To sum up analyze, under dimensional tolerance and radial run-out translation tolerance coupling, SDT points of cylinder geometric element
Amount, which changes, to be differed are as follows:
To be located at ideal surfaced in coupling tolerances band, the component coped in SDT tolerance Model adds the constraint relationship:
As shown in figure 3, for tolerance zone and the fixed tolerance range coupling condition of radial run-out.It is beated due to circle and fixes public affairs
The benchmark axial line of difference band is not overlapped with the benchmark axial line of tolerance zone, it is now assumed that tolerance zone and radial run-out are solid
Determine the opposite benchmark axial line of tolerance range to be parallel to each other, according to chapter 3 error propagation Orientation, is beated with circle and fix tolerance
The benchmark axial line of band is fixed reference, then tolerance zone TDIn the fixed tolerance range T of radial run-outRInterior radial translation, such as schemes
It is shown, therefore in SDT model, radial run-out fixes the ideal plain line S of allowance controlSLocation components u ', dimensional tolerance control
Direction spinor α ', dimensional tolerance is to ideal plain line SSLocation components u ' do not have restraining force.
To sum up analyze, under dimensional tolerance and the fixed tolerance coupling of radial run-out, SDT points of cylinder geometric element
Amount, which changes, to be differed are as follows:
To be located at ideal surfaced in coupling tolerances band, the component coped in SDT tolerance Model adds the constraint relationship:
SDT error model under the more tolerance couplings of 1.3 cylinder axis
Cylinder axis is export element, and the error that error is finally reflected cylinder changes.With the vertical of cylinder axis
It spends for tolerance and concentricity, the error change conditions of geometric element is analyzed, the circle under more tolerance couplings is established
Mast axis tolerance range.Axial length is l, and using the midpoint of ideal axis as coordinate origin, axis direction is Z axis, then cylindrical shaft
The SDT error component of line geometry element has α ', β ', u ' and v '.Since squareness tolerance band and concentricity tolerance band have radial direction
The identical feature of property, therefore the section xoz that can choose tolerance range is research object, wherein wherein SDT component has β '=α ', u '
=v ', as shown in Figure 4.
In Fig. 4, TcIndicate the concentricity tolerance band of cylinder axis, the direction of tolerance range is parallel with the axis of benchmark A, position
At the axis of benchmark A.TvIndicate the squareness tolerance band of cylinder axis, the direction of tolerance range is vertical with benchmark B plane, existing vacation
If the axis of benchmark A is vertical with benchmark B plane, according to Geometry Product Specification (GPS), orientation of related features band is less than the element
Position of related features band, then squareness tolerance band position is radially translatable in concentricity tolerance band.Therefore in SDT model, concentricity is public
Difference controls ideal axis SSLocation components u ', squareness tolerance control direction spinor α ', and squareness tolerance is to ideal axis SS's
Location components u ' does not have restraining force.
It to sum up analyzes, under perpendicularity difference and concentricity tolerance coupling, the SDT component of cylinder axis geometric element becomes
It is dynamic to differ are as follows:
To be located at ideal surfaced in coupling tolerances band, the component coped in SDT tolerance Model adds the constraint relationship:
By above-mentioned analysis it is found that geometric element displacement error component in SDT model is determined by fixing tolerance range Ts, turn
Dynamic error component is determined that error, which changes inequality, may be expressed as: by translation tolerance range Tt
Constraint equation may be expressed as:
TS min≤f(α′,β′,γ′,u′,v′,w′)≤TS max (1.10)
Different types of geometric element error changes inequality and constraint inequality is as shown in table 3.
The translation tolerance of table 3 and fixed tolerance act on the error variation inequality and constraint inequality of lower geometric element
Table 2.6 Error variation inequalities and constraint inequalities of
geometric elements under the action of translational tolerance and fixed
tolerance
Two, the error propagation transitive attribute analysis of cylinder combination faying face
Such as Fig. 5, cylinder combines faying face schematic diagram.Cylinder combines faying face by cylinder-short column face faying face F1 and F2 group
At the mobility scale T1=[u of the transferable error component of faying face F11, v1], the change of the transferable error component of faying face F2
Dynamic range T2=[μ2, v2], the error that the error propagation of cylinder combination faying face is regarded as cylinder axis changes, if cylindrical shaft
The error component of line is T=[α, β, μ, v].Since the error component of axis has the characteristics that radial nature is identical, therefore can select
The section x-o-z for selecting tolerance range is research object, as shown in Figure 6.
In Fig. 6, L is the length of axis, and the origin o of coordinate system is on ideal cylinder axis, away from axis right end L1Place, z-axis side
To parallel with cylinder ideal axis, each error component of cylinder axis can be obtained by the following formula:
Similarly, when tolerance range projects to z-o-y plane, the translation error component v along y-axis and the rotation in x-axis are missed
Difference component α can be obtained by the following formula:
From (2.1)~(2.4) expression formula can be seen that cylinder axis error component by the location error component of combinatorial surface with
And determined by locating element geometry, it is unrelated with the deflection error component of combinatorial surface.
Three, the error propagation transitive attribute analysis of plane combination faying face
When combining faying face is plane combination faying face, positioning surface is reduced to anchor point to analyze；And to be positioned
The geometric center in face as coordinate origin o, using perpendicular to by the direction of positioning plane as z-axis direction, by the length of positioning surface
Degree direction be x-axis direction, using by the width mode of positioning surface as y-axis direction.
(1) the error propagation transitive attribute analysis of a class plane combination faying face
Refering to what is shown in Fig. 7, the positioning surface in the plane combination faying face is 4 symmetrical small flat on by positioning surface
When f1, f2, f3 and the f4 of face, which is a class plane combination faying face.
When the positioning surface in plane combination faying face is 4 facets symmetrical on by positioning surface, 4 combinations
Face is plane-facet faying face, if faying face F1 is located at by the positioning surface upper left corner, faying face F1, F2, f3 and F4 press up time
The arrangement of needle direction；The transferable error component T=[α, β, w] of plane combination faying face, wherein α, β are respectively indicated around x, y
The rotation error component of axis, w indicate displacement error component along the z-axis direction；Steps are as follows for specific calculating:
Step a1: 4 faying faces F1, F2, F3 and F4 are obtained respectively in the variation model of the displacement error component in z-axis direction
It encloses: w1、w2、w3、w4；
Step a2: the mobility scale of the displacement error component of faying face F1, F2, F3 and F4 along the z-axis direction is projected respectively
To z-o-y plane, and z-o-x plane is projected to respectively；
Step a3: displacement error component w is calculated in z-axis:
Rotation error component α is calculated in z-o-y plane according to analytic geometry:
Wherein, L2Indicate the distance in two anchor points in the y-axis direction；
Rotation error component β is calculated in z-o-x plane according to analytic geometry:
Wherein, L1Indicate the distance in two binding sites in the direction of the x axis.
From (2.5)~(2.7), expression formula can be seen that each error component of plane combination faying face and be missed by the position of combinatorial surface
It difference component and is determined by locating element geometry, it is unrelated with the deflection error component of combinatorial surface.
(2) the error propagation transitive attribute analysis of b class plane combination faying face
With reference to b class plane combination faying face shown in Fig. 8, when positioning surface f1, f2 in plane combination faying face are two
When being symmetrically distributed in by narrow plane on positioning surface, and the length direction of narrow plane is parallel to by the width direction of positioning surface,
Each faying face in two basic change face F1, F2 is then reduced to two combinations for being located at positioning surface length direction both ends
Point；Binding site 1,2,3,4, which can transmit displacement error component along the z-axis direction, can be set as w1', w2', w3' and w4’。
The section y-o-z for selecting tolerance range is research object, as shown in Figure 9.L2 is the length of narrow plane 1, narrow plane 1
Rotation error component α1Error component at binding site 1It can be obtained by the following formula:
So the overall error component at binding site 1 is
Other binding sites 2,3,4, are all herewith managed, therefore the displacement error component of binding site and the transferable error of faying face point
The relationship of amount can be indicated by formula (2.8).
B class plane combination faying face error propagation characteristic is similar with a class error propagation characteristic, in conjunction with formula (2.5)~
(2.7) each error component of b class plane combination faying face can be derived.
B class plane combination faying face transferable error component T=[α, β, w], wherein α, β are respectively indicated around x, y-axis
Rotation error component, w indicate displacement error component along the z-axis direction；Steps are as follows for specific calculating:
Step b1: F1, F2 are obtained respectively in the mobility scale of the displacement error component in z-axis direction: w1、w2；Knot is obtained respectively
The rotation error component mobility scale that conjunction face F1, F2 are rotated around x-axis: α1、α2；
Step b2: faying face F1, F2 are projected into z-o-x in the mobility scale of the displacement error component in z-axis direction respectively
In plane；Faying face F1, F2 are projected in z-o-y plane respectively around the mobility scale for the rotation error component that x-axis rotates；
Step b3: displacement error component w is calculated in z-axis:
Rotation error component α is calculated in z-o-y plane according to analytic geometry:
Rotation error component β is calculated in z-o-x plane according to analytic geometry:
(3) the error propagation transitive attribute analysis of c class plane combination faying face
With reference to c class plane combination faying face shown in Fig. 10, when positioning surface f1, f2 in plane combination faying face are two
When being symmetrically distributed in the facet positioned, it is reduced to two basic change point respectively in conjunction with plane F1, F2 by 2.
C class plane combination faying face can only be constrained by one rotation direction of positioning plane, and c class plane combination faying face can pass
The error component T=[β, w] passed, wherein β indicates that the rotation error component around y-axis, w indicate displacement error point along the z-axis direction
Amount；Steps are as follows for specific calculating:
Step c1: faying face F1, F2 are obtained respectively in the mobility scale of the displacement error component in z-axis direction: w1、w2；
Step c2: faying face F1, F2 are projected in z-o-x plane in the tolerance range of the displacement error component in z-axis direction；
Step c3: displacement error component w is calculated in z-axis:
Rotation error component β is calculated in z-o-x plane according to analytic geometry:
Wherein, L indicates the distance between two basic change point.
Claims (9)
1. a kind of rigging error transitive attribute analysis method for combining faying face, which comprises the following steps:
Step 1: obtaining the mobility scale of the transferable error component of each faying face in combination faying face；
Step 2: the mobility scale of the transferable error component of each faying face obtained in step 1 is projected into combination faying face
In plane where transferable rotation error component；
Step 3: calculating combination knot in the plane where the transferable rotation error component of faying face is being combined according to analytic geometry
The rotation error component and displacement error component in conjunction face.
2. the rigging error transitive attribute analysis method of combination faying face according to claim 1, which is characterized in that in conjunction with
The mobility scale of the transferable error component in face obtains as follows:
Step 1.1: obtain the positioning geometric element of faying face with by the tolerance range of positioning geometric element, including fixed tolerance range with
Be translatable tolerance range；
Step 1.2 is calculated separately according to SDT error model positions geometric element and by the change of the error component of positioning geometric element
Dynamic range；
Step 1.3: can be transmitted what is obtained from the mobility scale of the positioning transferable error component of geometric element with faying face
The corresponding error component of error component mobility scale, and from by the variation model of the transferable error component of positioning geometric element
The mobility scale for enclosing the error component corresponding with the transferable error component of faying face of middle acquisition is summed, to be tied
The mobility scale of the transferable error component in conjunction face.
3. the rigging error transitive attribute analysis method of combination faying face according to claim 2, which is characterized in that for
Plane geometry element, cylinder geometric element and the SDT error model difference of cylinder axis geometric element are as follows:
The SDT error model of plane geometry element:
In formula, a indicates that the width of plane, b indicate the length of plane；Using the geometric center of ideal rectangle plane as coordinate system original
Point, coordinate system normal direction are z-axis, and length direction is x-axis, and width direction is y-axis, establish coordinate system, and α ' expression is rotated around x-axis
Rotation error component, the rotation error component that β ' expression is rotated around y-axis, the displacement error component that w ' expression is moved along the z-axis；TP
Indicate the translation degree tolerance range of plane, TdIndicate the tolerance zone of plane；
The SDT error model of cylinder geometric element:
In formula, l indicates body length；Using the geometric center of ideal cylinder as coordinate origin, the axis direction of cylinder is Z axis,
Radial direction is x, y-axis establishes coordinate system, the rotation error component that α ' expression is rotated around x-axis, the movement that u ' expression moves along the x-axis
Error component；TDIndicate the tolerance zone of cylinder, TRIndicate the radial run-out tolerance range of cylinder；
The SDT error model of cylinder axis geometric element:
In formula, l indicates body length；Using the geometric center of ideal axis as coordinate origin, axis direction is Z axis, radial direction side
Coordinate system, the rotation error component that α ' expression is rotated around x-axis, the displacement error that u ' expression moves along the x-axis point are established to for x, y-axis
Amount；TVIndicate the squareness tolerance band of cylinder axis, TCIndicate the concentricity tolerance band of cylinder axis.
4. the rigging error transitive attribute analysis method of combination faying face according to claim 1, which is characterized in that work as knot
When conjunction face is plane-facet, transferable error properties are the displacement error component being moved along the z-axis, and z-axis is perpendicular to combination
Face；
When faying face is plane-narrow plane, transferable error properties be the displacement error component that is moved along the z-axis with around x-axis
The rotation error component of rotation, for z-axis perpendicular to faying face, x-axis is faying face length direction；
When faying face is cylinder-short column face, transferable error properties be the displacement error component that moves along the x-axis with around y-axis
The rotation error component of rotation, z-axis are axis direction, and x, y-axis are radial direction.
5. according to the rigging error transitive attribute analysis method of combination faying face described in claim 1, which is characterized in that work as combination
Faying face is when combining faying face by the cylinder that two cylinders-short column face faying face F1, F2 is formed, using z-axis direction as axis side
To using x, y-axis direction as radial direction, and z-axis is parallel to ideal cylinder axis, and coordinate origin o is in ideal cylinder axis
On；Cylinder combines the transferable error component T=[α, β, u, v] of faying face, wherein α, β respectively indicate the rotation mistake around x, y-axis
Difference component, u, v respectively indicate the translation error component along x, y-axis；Specific step is as follows:
Step s1: cylinder-short column face faying face F1, F2 transferable error component mobility scale is obtained respectively:
Step s2: by the mobility scale u of cylinder-short column face faying face F1, F2 translation error component moved along the x-axis1、u2Respectively
It projects in x-o-z plane, to calculate cylinder faying face transferable error component β, u；By cylinder-short column face faying face F1,
The translation error component v that F2 is moved along y-axis1、v2Mobility scale projected in z-o-y plane respectively, with calculate cylinder combination knot
Conjunction face transferable error component α, v；
Step s3: according to analytic geometry, error component β, u, α, v are calculated as follows respectively:
Wherein, L indicates the length of ideal cylinder axis, L1Indicates coordinate system origin o is along the ideal cylinder axis endpoint of z-axis distance
Distance.
6. the rigging error transitive attribute analysis method of combination faying face according to claim 1, which is characterized in that work as group
When conjunction faying face is plane combination faying face, faying face is reduced to binding site to analyze；And by the geometric center of positioning surface
As coordinate origin o, using perpendicular to by the direction of positioning plane as z-axis direction, using by the length direction of positioning surface as x-axis side
To, using by the width mode of positioning surface as y-axis direction.
7. the rigging error transitive attribute analysis method of combination faying face according to claim 6, which is characterized in that when flat
It is 4 in facet symmetrical on by positioning surface that the positioning surface in faying face is combined in face, and 4 faying faces are plane-
Facet faying face, if faying face F1 is located at by the positioning surface upper left corner, faying face F1, F2, F3 and F4 are arranged in the direction of the clock；
The transferable error component T=[α, β, w] of plane combination faying face, wherein α, β respectively indicate the rotation mistake around x, y-axis
Difference component, w indicate displacement error component along the z-axis direction；Steps are as follows for specific calculating:
Step a1: 4 faying faces F1, F2, F3 and F4 are obtained respectively in the mobility scale of the displacement error component in z-axis direction: w1、
w2、w3、w4；
Step a2: the mobility scale of the displacement error component of faying face F1, F2, F3 and F4 along the z-axis direction is projected into z- respectively
O-y plane, and z-o-x plane is projected to respectively；
Step a3: displacement error component w is calculated in z-axis:
Rotation error component α is calculated in z-o-y plane according to analytic geometry:
Wherein, L2Indicate the distance in two binding sites in the y-axis direction；
Rotation error component β is calculated in z-o-x plane according to analytic geometry:
Wherein, L1Indicate the distance in two binding sites in the direction of the x axis.
8. the rigging error transitive attribute analysis method of combination faying face according to claim 6, which is characterized in that when flat
Positioning surface in face combination faying face is two when being symmetrically distributed in by narrow plane on positioning surface, and the length side of narrow plane
To being parallel to by the width direction of positioning surface, then each faying face in two basic change face F1, F2 is reduced to two difference positions
Binding site in positioning surface length direction both ends；The transferable error component T=[α, β, w] of plane combination faying face,
In, α, β respectively indicate the rotation error component around x, y-axis, and w indicates displacement error component along the z-axis direction；It is specific to calculate step
It is as follows:
Step b1: F1, F2 are obtained respectively in the mobility scale of the displacement error component in z-axis direction: w1、w2；Faying face is obtained respectively
The rotation error component mobility scale that F1, F2 are rotated around x-axis: α1、α2；
Step b2: faying face F1, F2 are projected into z-o-x plane in the mobility scale of the displacement error component in z-axis direction respectively
On；Faying face F1, F2 are projected in z-o-y plane respectively around the mobility scale for the rotation error component that x-axis rotates；
Step b3: displacement error component w is calculated in z-axis:
Rotation error component α is calculated in z-o-y plane according to analytic geometry:
Rotation error component β is calculated in z-o-x plane according to analytic geometry:
9. the rigging error transitive attribute analysis method of combination faying face according to claim 6, which is characterized in that when flat
When positioning surface in face combination faying face is symmetrically distributed in the facet positioned for two, 2 faying faces F1, F2 are distinguished
It is reduced to two basic change point；The transferable error component T=[β, w] of plane combination faying face, wherein β is indicated around y-axis
Rotation error component, w indicate displacement error component along the z-axis direction；Steps are as follows for specific calculating:
Step c1: faying face F1, F2 are obtained respectively in the mobility scale of the displacement error component in z-axis direction: w1、w2；
Step c2: faying face F1, F2 are projected in z-o-x plane in the tolerance range of the displacement error component in z-axis direction；
Step c3: displacement error component w is calculated in z-axis:
Rotation error component β is calculated in z-o-x plane according to analytic geometry:
Wherein, L indicates the distance between two basic change point.
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