CN110362929B - Assembly error transfer attribute analysis method for combined joint surface - Google Patents
Assembly error transfer attribute analysis method for combined joint surface Download PDFInfo
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Abstract
The invention discloses an assembly error transfer attribute analysis method of a combined joint surface, which comprises the following steps: step 1: acquiring the variation range of transferable error components of each combined surface; step 2: projecting the variation range of the transferable error components of each joint surface obtained in the step 1 onto a plane where the transferable rotation error components of the combined joint surfaces are located; and step 3: and calculating the rotation error component and the movement error component of the combined joint surface according to the plane in which the rotation error component which can be transmitted by the analytic geometry on the combined joint surface is located. The invention combines the tolerance zone with the analytic geometry, and converts the quantitative analysis problem of the error component into the analytic geometry solving problem, thereby being capable of quantitatively calculating the transferable error component of the combined joint surface simply and quickly.
Description
Technical Field
The invention belongs to the technical field of machining and manufacturing, and particularly relates to an analysis method for an assembly error transfer attribute of a combined joint surface.
Background
The assembly error of the mechanical product is formed by accumulated transmission of a plurality of local error sources according to the topological structure of the mechanical product, however, the complex mechanical product often comprises tens of thousands of parts. In order to simplify the analysis of the assembly error, according to an FMA (Function-motion-Action) structured decomposition method, a meta-motion concept is introduced into mechanical product assembly error modeling, so that the assembly precision modeling of the whole product is converted into the assembly precision modeling of a plurality of meta-motion units.
Meta-action Unit (MU): the whole formed by all parts realizing a certain meta-action according to the structural relationship is called a meta-action unit. The element action unit comprises five basic elements, namely a power input element, a power output element, an intermediate element, a fastening element and a supporting element.
Compared with a complex mechanical product, the number of parts in the element action unit is small, the type of the joint surface is simple, the joint surface is a pair of contact surfaces formed by mutually attaching two geometric elements on different parts according to a matching relation, and the joint surface is an accumulated node of geometric element errors of a pair of adjacent parts with the matching relation. According to the geometry of the joint surfaces, the main joint surfaces of the element action units can be divided into: a plane joint surface, a cylindrical surface joint surface, a thread joint surface and a special shape joint surface in the bearing. The threaded joint surface generally belongs to a fastener, and the part is kept unchanged in the positioning position in the element action unit and does not play a positioning role, so that the threaded joint surface can be ignored in the assembly error modeling; the error transfer characteristic of a special-shaped junction surface in the bearing is complex and needs to be specifically analyzed according to different conditions; plane and cylindrical junction surfaces are most common in meta-action units, and the corresponding geometric elements are planes, cylinders and cylindrical axes (derived geometric elements of cylinders).
In actual assembly, error variation of parts needs to be controlled according to the matching mode of the multiple joint surfaces, so that the assembly error transmission attribute of the parallel joint surfaces formed by matching the multiple joint surfaces is the basis for analyzing the unit assembly error of the element motion. The inventor firstly divides the parallel connection joint surfaces into two main types: the combined joint surface is matched with the common parallel joint surface. When the positioning geometric elements of the parts are small geometric elements relative to the positioning geometric elements, the combined joint surfaces are formed by matching the joint surfaces. When any positioning geometric element of the part is a large geometric element relative to the positioning geometric element, the multiple combining surfaces are matched to form a general parallel combining surface.
When the part is positioned through the non-combined joint surface, errors of two geometric elements which are matched with each other can be equally and equally transmitted to the positioned part through the joint surface, when the part is positioned through the combined joint surface, the error change of the part is commonly influenced by the joint surfaces, and the error change condition of the positioned part is complex.
Small Displacement momentum (SDT) theory was proposed and introduced by Bourdet in 1996 in the field of tolerance modeling, which is applicable to mathematical models representing tolerances of geometric elements. In the SDT tolerance model, the error of the actual geometric element of the part is expressed by a small rigid variation of the nominal surface, and the actual geometric element of the part is replaced by an ideal geometric element.
The small displacement rotation can describe a small variation of the geometric element in six degrees of freedom, and can be expressed as D ═ α, β, γ, u, v, w, where α, β, γ represent small amounts of rotation about the x, y, z axes, and u, v, w represent small amounts of movement in translation along the x, y, z axes. Within the scope of the present study, the respective amount of variation of the SDT is the error used to describe the geometric elements of the part.
According to the concept of constancy in the new generation of GPS standards, when a geometric element slightly varies in a certain degree of freedom, if the swept trajectory is unchanged from its own characteristic shape, it has a constancy in the direction of the degree of freedom. Therefore, the constancy is used to indicate that the pose variation of the geometric element in a specific direction has no effect on the characteristic shape of the geometric element, and the corresponding SDT component is zero. In the SDT tolerance model, the errors of the geometric elements are described by the non-zero components of the SDT. The common geometric elements in the meta-motion unit are a plane, a cylinder and a cylinder axis, and the present invention mainly studies the three geometric elements, as shown in table 1 below, which are SDT expressions of the plane, the cylinder and the cylinder axis.
TABLE 1 expression of geometry elements SDT commonly found in Meta action units
Table 1 SDT expressions of common geometric elements in Meta-action Units
In the SDT tolerance model, when geometric element errors are controlled by multiple tolerances, the position component of an ideal geometric element is controlled by a fixed tolerance band and the orientation is controlled by a translational tolerance. Because the floating tolerance band can not control the position and the direction of the geometric elements and has no constraint effect on each fluctuation quantity of the SDT, the representation of the SDT model on the floating tolerance band is not perfect enough, and the error accumulation effect of the floating tolerance band on the assembly body is relatively small, so that the coupling modeling is only carried out on the fixed tolerance band and the translation tolerance. The invention aims at analyzing the variation condition of common geometric element errors of plane, cylindrical surface and cylindrical axis in the element action unit under the tolerance coupling action, and establishes a corresponding SDT error model.
The common combined joint surfaces in the element action units include a plane combined joint surface and a cylindrical combined joint surface, although the qualitative analysis of the error transfer attribute of the combined joint surface can be obtained according to experience: the plane combined joint surface can transmit error components of alpha, beta and w or beta and w, and the cylindrical joint surface can transmit error components of alpha, beta, u and v, wherein alpha and beta respectively represent rotation error components around x and y axes, and u, v and w respectively represent translation error components along x, y and z axes.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an analysis method for the transmission attribute of the assembling error of the combined joint surface, which realizes the quantitative analysis of the transmission attribute of the error of the combined joint surface.
In order to solve the technical problems, the technical scheme of the invention is as follows: an assembly error transfer attribute analysis method of a combined joint surface comprises the following steps:
step 1: acquiring the variation range of transferable error components of each combined surface;
step 2: projecting the variation range of the transferable error components of each joint surface obtained in the step 1 onto a plane where the transferable rotation error components of the combined joint surfaces are located;
and step 3: and calculating the rotation error component and the movement error component of the combined joint surface according to the plane in which the rotation error component which can be transmitted by the analytic geometry on the combined joint surface is located.
Further, the range of variation of the transferable error component of the joint surface is obtained as follows:
step 1.1: acquiring tolerance zones of the positioning geometric elements and the positioned geometric elements of the joint surface, wherein the tolerance zones comprise a fixed tolerance zone and a translation tolerance zone;
step 1.2, respectively calculating the variation ranges of the error components of the positioning geometric elements and the positioned geometric elements according to the SDT error model;
step 1.3: the variation range of the error component corresponding to the error component deliverable by the joining surface, which is obtained from the variation range of the error component deliverable by the positioning geometric element, is summed with the variation range of the error component corresponding to the error component deliverable by the joining surface, which is obtained from the variation range of the error component deliverable by the positioning geometric element, to obtain the variation range of the error component deliverable by the joining surface.
Further, the SDT error models for the plane geometric element, the cylinder geometric element, and the cylinder axis geometric element are respectively as follows:
SDT error model of planar geometry:
wherein a represents the width of the plane and b represents the length of the plane; establishing a coordinate system by taking the geometric center of an ideal rectangular plane as the origin of the coordinate system, the normal direction of the coordinate system as the z axis, the length direction as the x axis and the width direction as the y axis, wherein alpha ' represents a rotation error component rotating around the x axis, beta ' represents a rotation error component rotating around the y axis, and w ' represents a movement error component moving along the z axis; t isPRepresenting a tolerance band of planar translation, TdRepresents a dimensional tolerance band of a plane;
SDT error model of cylindrical geometry:
wherein l represents the length of the cylinder; using the geometric center of the ideal cylinder as coordinateThe system origin point, the axis direction of the cylindrical surface is a z axis, the radial direction is an x axis and a y axis to establish a coordinate system, alpha 'represents a rotation error component rotating around the x axis, and u' represents a movement error component moving along the x axis; t isDRepresenting the dimensional tolerance band, T, of the cylinderRRepresenting a radial circle run-out tolerance band of the cylindrical surface;
SDT error model of cylinder axis geometry:
wherein l represents the length of the cylinder; establishing a coordinate system by taking the geometric center of an ideal axis as the origin of the coordinate system, taking the axis direction as the z axis, and taking the radial direction as the x axis and the y axis, wherein alpha 'represents a rotation error component rotating around the x axis, and u' represents a movement error component moving along the x axis; t isVTolerance zone, T, for perpendicularity of the axis of the cylinderCRepresenting the tolerance band of coaxiality of the cylindrical axis.
Further, when the joint surface is a plane-facet, the transferable error attribute is a movement error component moving along a z-axis, and the z-axis is perpendicular to the joint surface;
when the joint surface is a plane-narrow plane, transferable error attributes are a moving error component moving along a z-axis and a rotating error component rotating around an x-axis, wherein the z-axis is vertical to the joint surface, and the x-axis is the length direction of the joint surface;
when the joint surface is a cylindrical surface-short cylindrical surface, transferable error attributes are a movement error component moving along an x axis and a rotation error component rotating around a y axis, the z axis is an axial direction, and the x axis and the y axis are both radial directions.
Further, when the combined joint surface is a cylindrical combined joint surface consisting of two cylindrical-short cylindrical joint surfaces F1 and F2, the direction of the z axis is taken as the axial direction, the directions of the x axis and the y axis are taken as the radial directions, the z axis is parallel to the ideal cylindrical axis, and the origin o of the coordinate system is on the ideal cylindrical axis; the cylindrical surface combination joint surface can transmit error components T ═ alpha, beta, u, v ], wherein alpha and beta respectively represent rotation error components around x and y axes, and u and v respectively represent translation error components along x and y axes; the method comprises the following specific steps:
step s 1: obtaining the variation range of the error components which can be transmitted by the cylindrical surface-short cylindrical surface combination surfaces F1 and F2 respectively:
step s 2: variation range u of translation error component for moving cylindrical-short cylindrical joint surfaces F1 and F2 along x axis1、u2Respectively projecting the error components to an x-o-z plane to calculate error components beta and u which can be transmitted by a cylindrical surface joint surface; translation error component v for moving the cylinder-short cylindrical joint surfaces F1, F2 along the y-axis1、v2The variation ranges are respectively projected on a z-o-y plane to calculate error components alpha and v which can be transmitted by the cylindrical surface combination joint surface;
step s 3: according to the analytic geometry, error components beta, u, alpha and v are calculated according to the following formulas:
wherein L represents the length of the ideal cylinder axis, L1Representing the distance of the coordinate system origin o from the ideal cylinder axis end point along the z-axis.
Further, when the combined surface is a plane combined surface, the combined surface is simplified into a combined point for analysis; the geometric center of the positioned surface is used as a coordinate system origin o, the direction perpendicular to the positioned plane is used as a z-axis direction, the length direction of the positioned surface is used as an x-axis direction, and the width mode of the positioned surface is used as a y-axis direction.
Further, when the positioning surface in the plane combination combining and combining surface is 4 small planes symmetrically distributed on the positioned surface, the 4 combining surfaces are plane-small plane combining surfaces, a combining surface F1 is arranged at the upper left corner of the positioned surface, and the combining surfaces F1, F2, F3 and F4 are arranged in the clockwise direction; the plane combination joint surface can transmit error components T ═ alpha, beta, w ], wherein alpha and beta respectively represent rotation error components around x and y axes, and w represents a movement error component along the direction of the z axis; the specific calculation steps are as follows:
step a 1: variation ranges of movement error components in the z-axis direction of the 4 joint surfaces F1, F2, F3, and F4 are obtained: w is a1、w2、w3、w4；
Step a 2: projecting the variation ranges of the movement error components of the joint surfaces F1, F2, F3 and F4 along the z-axis direction to a z-o-y plane and a z-o-x plane respectively;
step a 3: the movement error component w is calculated on the z-axis:
the rotation error component α is calculated in the z-o-y plane from the analytic geometry:
wherein L is2Represents the distance between the two binding points in the y-axis direction;
the rotation error component β is calculated in the z-o-x plane from the analytic geometry:
wherein L is1Indicating the distance between the two points of engagement in the x-axis direction.
Further, when the positioning surface in the planar combination combining and combining surface is two narrow planes symmetrically distributed on the positioning surface, and the length direction of the narrow planes is parallel to the width direction of the positioning surface, each of the two combining surfaces F1 and F2 is simplified into two combining points respectively located at two ends of the positioning surface in the length direction; the plane combination joint surface can transmit error components T ═ alpha, beta, w ], wherein alpha and beta respectively represent rotation error components around x and y axes, and w represents a movement error component along the direction of the z axis; the specific calculation steps are as follows:
step b 1: obtaining the variation ranges of the movement error components of the F1 and the F2 in the z-axis direction respectively: w is a1、w2(ii) a Respectively acquiring the variation ranges of the rotation error components of the joint surfaces F1 and F2 rotating around the x axis: alpha is alpha1、α2；
Step b 2: projecting the variation ranges of the movement error components of the joint surfaces F1 and F2 in the z-axis direction onto a z-o-x plane respectively; projecting the variation ranges of the rotation error components of the joint surfaces F1 and F2 rotating around the x axis onto a z-o-y plane respectively;
step b 3: the movement error component w is calculated on the z-axis:
the rotation error component α is calculated in the z-o-y plane from the analytic geometry:
the rotation error component β is calculated in the z-o-x plane from the analytic geometry:
further, when the positioning surfaces in the plane combination combining surfaces are two small planes symmetrically distributed on the positioning surface, the 2 combining surfaces F1 and F2 are respectively simplified into two combining points; the plane combination joint surface can transmit an error component T ═ beta, w ], wherein beta represents a rotation error component around a y axis, and w represents a movement error component along a z axis; the specific calculation steps are as follows:
step c 1: obtaining the variation ranges of the movement error components of the joint surfaces F1 and F2 in the z-axis direction: w is a1、w2；
Step c 2: projecting the tolerance band of the movement error component of the joint surfaces F1 and F2 in the z-axis direction onto a z-o-x plane;
step c 3: the movement error component w is calculated on the z-axis:
the rotation error component β is calculated in the z-o-x plane from the analytic geometry:
where L represents the distance between two binding points.
Compared with the prior art, the invention has the following beneficial effects:
1. the tolerance zone is the range of variation given to the actual size, shape and position of the product by designers in the design stage of the product, and is also the basis for manufacturing and detecting parts. The invention combines the tolerance zone with the analytic geometry, and converts the quantitative analysis problem of the error component into the analytic geometry solving problem, thereby being capable of quantitatively calculating the transferable error component of the combined joint surface simply and quickly.
2. The invention provides an error transfer attribute analysis method for 4 specific types of combined joint surfaces, which are respectively 1 cylindrical surface combined joint surface and 3 plane combined joint surfaces and meet the main requirements in practical engineering application.
3. The proposal of the concept of the combined joint surface solves the problem that the error transfer characteristic is not clear when a plurality of small joint surfaces are used for positioning the part, and establishes an error transfer model of the small joint surfaces.
4. The invention researches the influence of the interaction of the combined joint surfaces on the error transmission attribute of each joint surface, and is an important component and basis for decoupling element action unit actual error transmission path and solving transmission error.
Drawings
FIG. 1 is a schematic diagram of modeling SDT errors for planar geometric elements under multi-tolerance coupling;
FIG. 2 is a schematic diagram of an SDT error model for establishing cylindrical geometric elements under the coupling action of a dimensional tolerance band and a radial circular run-out translational tolerance band;
FIG. 3 is a schematic diagram of an SDT error model for establishing cylindrical surface geometric elements under the coupling action of a dimensional tolerance zone and a radial circular run-out fixed tolerance zone;
FIG. 4 is a schematic diagram of modeling SDT errors for cylindrical axis geometry under multi-tolerance coupling;
FIG. 5 is a schematic view of a cylindrical combination bonding surface;
FIG. 6 is a schematic diagram of the error component solution for the cylindrical surface combination junction surface;
FIG. 7 is a schematic view of a class a planar composite bonding surface;
FIG. 8 is a schematic view of a class b planar composite bonding surface;
FIG. 9 is a schematic diagram of solving the narrow plane shift error component in the combined junction plane of the class b plane;
FIG. 10 is a schematic view of a class c planar composite bonding surface.
Detailed Description
To facilitate understanding within the present invention, the error transmission properties of common joint surfaces are first described: the joint surface is a pair of contact surfaces formed by mutually attaching two geometric elements on different parts according to a matching relation, and is an accumulated node of geometric element errors of a pair of adjacent parts with the matching relation; in the assembling process, the parts are positioned by applying a constraint action on the adjacent parts through the combining surface, and meanwhile, the error change of the parts has influence on the positioning state of the adjacent parts, so that the error transmission is realized. The error transfer property of the faying surface is closely related to the geometry of the faying surface. The planar joint surface and the cylindrical joint surface are two types of joint surfaces which are most common in the element action unit, and the error transmission attributes of the joint surfaces are shown in table 2.
TABLE 2 Joint surface error transfer Properties
Table 3.1 Joint Surface Error Transfer Properties
Facet: when the positioning geometric element and the positioned geometric element in the combined joint surface are both plane geometric elements, the positioning surface corresponding to the small area of the positioned part (the small degree of freedom is not limited in the rotation freedom degree of the part in each direction) is a small plane.
Narrow plane: when the positioning geometric element and the positioned geometric element in the combined joint surface are both planar geometric elements, the positioning surface is a narrow plane relative to the positioning surface when the length of the positioned part is narrow (the positioning surface is narrow so that the freedom of rotation in the length direction of the part is not limited).
Short cylindrical surface: when the positioning geometric element and the positioned geometric element in the combined joint surface are both cylindrical geometric elements, the positioning surface which is short relative to the part to be positioned when the length is short (short enough that the rotational freedom degree in the non-axial direction of the cylinder is not limited) is a short cylindrical surface.
In actual assembly, error variation of parts needs to be controlled according to the matching mode of the multiple joint surfaces, so that the assembly error transmission attribute of the parallel joint surfaces formed by matching the multiple joint surfaces is the basis for analyzing the unit assembly error of the element motion. The inventor firstly divides the parallel connection joint surfaces into two main types: the combined joint surface is matched with the common parallel joint surface. When the positioning geometric elements of the parts are small geometric elements relative to the positioning geometric elements, the combined joint surfaces are formed by matching the joint surfaces. When any positioning geometric element of the part is a large geometric element relative to the positioning geometric element, the multiple combining surfaces are matched to form a general parallel combining surface.
In order to realize the quantitative analysis of the assembly error transfer attribute of the combined joint surface, the invention combines a tolerance band with an analytic geometry and converts the quantitative analysis problem of an error component into an analytic geometry solving problem, and the adopted scheme is as follows:
an assembly error transfer attribute analysis method of a combined joint surface comprises the following steps:
step 1: acquiring the variation range of transferable error components of each combined surface;
step 2: projecting the variation range of the transferable error components of each joint surface obtained in the step 1 onto a plane where the transferable rotation error components of the combined joint surfaces are located;
and step 3: and calculating the rotation error component and the movement error component of the combined joint surface according to the plane in which the rotation error component which can be transmitted by the analytic geometry on the combined joint surface is located.
The variation range of the transferable error components of the binding surfaces in step 1 is obtained as follows:
step 1.1: acquiring tolerance zones of the positioning geometric elements and the positioned geometric elements of the joint surface, wherein the tolerance zones comprise a fixed tolerance zone and a translation tolerance zone;
step 1.2, respectively calculating the variation ranges of the error components of the positioning geometric elements and the positioned geometric elements according to the SDT error model;
step 1.3: the variation range of the error component corresponding to the error component deliverable by the joining surface, which is obtained from the variation range of the error component deliverable by the positioning geometric element, is summed with the variation range of the error component corresponding to the error component deliverable by the joining surface, which is obtained from the variation range of the error component deliverable by the positioning geometric element, to obtain the variation range of the error component deliverable by the joining surface.
Firstly, establishing an SDT error model of a plane, a cylindrical surface and a cylindrical axis
1.1 error modeling under planar multi-tolerance coupling
Taking the coupling effect of the dimensional tolerance and the parallelism tolerance of the plane positioning as an example, the error variation condition of the plane geometric elementThe analysis was performed to establish the planar tolerance band under the multi-tolerance coupling as shown in FIG. 1: and a plane with the length b and the width a takes the geometric center of the ideal rectangular plane as the origin of a coordinate system, the normal direction of the coordinate system is the Z axis, the length direction is the X axis, and the width direction is the Y axis, so that the coordinate system is established. T isDIndicating a tolerance band of the orientation dimension of the plane, oriented parallel to the reference plane, positioned at a distance L from the reference. T ispThe direction of the parallelism tolerance zone of the plane is parallel to the reference plane, and according to the product geometric technical specification (GPS), the direction tolerance zone is smaller than the position tolerance zone of the element, so that the position of the parallelism tolerance zone translates in two parallel planes with the size of TD dimension tolerance zone. In the SDT tolerance model, the actual plane is used as the ideal surface SSIndicating that the errors of the plane geometric elements are represented by the ideal surface SSThe variation of the three components α ', β ', w ' of (a), β ', w '. Dimensional tolerance control of ideal surface SSPosition component w ', parallelism tolerance control direction vector α ', β ', parallelism versus ideal surface SSHas no constraining force.
In summary, the SDT component variation of the planar geometric elements under the coupled effect of the dimensional tolerance and the flatness tolerance is not equal to:
to place the ideal surface within the coupling tolerance band, a constraint relationship should be added to the components in the SDT tolerance model:
-TDL≤w′+aα′+bβ′≤TDU (1.2)
the mathematical model is carried out by using two groups of mathematical inequality coupling tolerances, wherein the equation (1.1) is a variation inequality of the component parameters and represents a variation range allowed by a single component parameter of the plane geometric element. The formula (1.2) is a constraint inequality of variable parameters, describes the variation constraint relation among the component parameters of the plane geometric elements, and ensures the reasonability of the value of the component parameters.
1.2 SDT error model under cylindrical surface multi-tolerance coupling effect
Taking the dimensional tolerance of the diameter of the cylindrical surface and the radial circle run-out tolerance as an example, the error variation condition of the geometric elements of the cylindrical surface is analyzed, and the cylindrical surface tolerance band under the multi-tolerance coupling effect is established. The length of the cylinder is l, the diameter is 2d, the geometric center of the ideal cylinder is taken as the origin of a coordinate system, the axial direction of the cylinder is taken as the Z axis, and then the SDT error components of the cylinder have alpha ', beta', u 'and v'. Since the dimensional tolerance band and the radial run-out tolerance band have the same characteristics in radial properties, an ideal prime line in which the xoz plane of the coordinate system intersects the cylindrical surface and x >0, where the SDT components have β '═ α', u '═ v', can be selected as the object of study. Because the radial circle run-out tolerance zone can be divided into a translation tolerance zone taking the self cylindrical axis as a reference axis and a fixed tolerance zone taking the non-self cylindrical axis as a reference axis, the two conditions are discussed
As shown in fig. 2, the tolerance coupling condition is the dimensional tolerance band and the radial circular run-out translational tolerance band. T isDAnd representing the size tolerance zone of the cylindrical surface, wherein the direction and the position of the tolerance zone are determined relative to the reference axis line, the direction is parallel to the direction of the reference axis line, and the position is at a distance d from the reference axis line. T isRThe radial circle run-out tolerance zone of the cylindrical surface is represented, the direction of the radial circle run-out tolerance zone is parallel to the direction of the reference axis, and the position of the radial circle run-out tolerance zone radially translates in the size tolerance zone. According to the product geometric technical specification (GPS), the position tolerance zone is smaller than the run-out tolerance zone of the element, so that the radial circular run-out tolerance zone can not control the geometric element to change to the reference direction, and the dimensional tolerance controls the ideal element line S in the SDT modelSPosition component u 'and direction vector α', radial circular run-out to ideal prime line SSThe position and direction components have no constraining forces.
In summary, the variation of the SDT component of the cylindrical geometric element under the coupling effect of the dimensional tolerance and the radial circular run-out translational tolerance is not equal to:
to place the ideal surface within the coupling tolerance band, a constraint relationship should be added to the components in the SDT tolerance model:
as shown in fig. 3, the dimensional tolerance band is coupled with the radial run-out fixed tolerance band. Because the reference axis line of the circular run-out fixed tolerance zone is not coincident with the reference axis line of the size tolerance zone, the relative reference axis lines of the size tolerance zone and the radial circular run-out fixed tolerance zone are assumed to be parallel to each other, according to the analysis of the error transfer direction of the third chapter, the reference axis line of the circular run-out fixed tolerance zone is taken as a fixed reference, and then the size tolerance zone T is taken as a fixed referenceDIn the radial circle run-out fixed tolerance zone TRRadial translation, as shown, so that in the SDT model, radial run-out fixed tolerance controls the ideal prime line SSPosition component u ', dimensional tolerance control direction rotation alpha', dimensional tolerance to ideal prime line SSHas no constraining force.
In summary, the variation of the SDT component of the cylindrical geometric element under the coupling effect of the dimensional tolerance and the radial run-out fixed tolerance is different as follows:
to place the ideal surface within the coupling tolerance band, a constraint relationship should be added to the components in the SDT tolerance model:
1.3 SDT error model under cylindrical axis multi-tolerance coupling effect
The cylinder axis is a derivation factor, and the error thereof is finally reflected in the error variation of the cylinder. Taking the verticality tolerance and the coaxiality of the cylindrical axis as an example, the error variation condition of the geometric elements is analyzed, and the cylindrical axis tolerance band under the multi-tolerance coupling effect is established. The length of the axis is l, the midpoint of the ideal axis is taken as the origin of the coordinate system, the direction of the axis is taken as the z-axis, and the SDT error components of the geometric elements of the cylinder axis have alpha ', beta', u 'and v'. Since the tolerance band of perpendicularity and the tolerance band of axiality have the same characteristics of radial properties, a section xoz of the tolerance band can be selected as the subject of study, in which SDT components have β '═ α', u '═ v', as shown in fig. 4.
In FIG. 4, TcRepresenting the tolerance band of coaxiality of the cylindrical axis, the direction of the tolerance band being parallel to the axis of reference a, the position being at the axis of reference a. T isvAnd (3) representing a verticality tolerance zone of the cylindrical axis, wherein the direction of the tolerance zone is vertical to a reference B plane, and assuming that the axis of the reference A is vertical to the reference B plane, according to the product geometric technical specification (GPS), the direction tolerance zone is smaller than the position tolerance zone of the element, and the position of the verticality tolerance zone radially translates in the coaxiality tolerance zone. Thus, in the SDT model, the coaxiality tolerance controls the ideal axis SSPosition component u ', perpendicularity tolerance control direction rotation quantity alpha', perpendicularity tolerance to ideal axis SSHas no constraining force.
In summary, the variation of the SDT component of the geometric elements of the cylinder axis under the coupling effect of the verticality difference and the coaxiality tolerance is not equal to:
to place the ideal surface within the coupling tolerance band, a constraint relationship should be added to the components in the SDT tolerance model:
from the above analysis, the moving error component of the geometric element in the SDT model is determined by the fixed tolerance zone Ts, the rotating error component is determined by the translational tolerance zone Tt, and the error variation inequality can be expressed as:
the constraint equation can be expressed as:
TSmin≤f(α′,β′,γ′,u′,v′,w′)≤TSmax(1.10)
the different types of geometric element error variation inequalities and constraint inequalities are shown in table 3.
TABLE 3 error variation inequality and constraint inequality of geometric elements under the action of translational tolerance and fixed tolerance
Table 2.6 Error variation inequalities and constraint inequalities of geometric elements under the action of translational tolerance and fixed tolerance
Error transfer transmission attribute analysis of two-cylinder and cylindrical-surface combined surface
Fig. 5, a schematic diagram of a cylindrical combination bonding surface. The cylindrical surface combination joint surface consists of cylindrical surface-short cylindrical surface joint surfaces F1 and F2, and the variable range T1 of the transmissible error component of the joint surface F1 is [ u ]1，v1]Variation range T of error component transferable by joint surface F22＝[μ2，v2]The error transfer of the cylindrical surface combination joint surface is considered to be an error variation of the cylindrical axis, and the error component of the cylindrical axis is T ═ α, β, μ, v]. Since the error components of the axis have the same radial properties, the x-o-z cross section of the tolerance band can be selected as the object of study, as shown in fig. 6.
In FIG. 6, L is the length of the axis, and the origin o of the coordinate system is on the ideal cylinder axis, L from the right end of the axis1The z-axis direction is parallel to the ideal axis of the cylinder, and each error component of the cylinder axis can be obtained by the following equation:
similarly, when the tolerance band is projected onto the z-o-y plane, the translational error component v along the y-axis and the rotational error component α in the x-axis can be obtained by the following equation:
as can be seen from expressions (2.1) to (2.4), the cylindrical axis error component is determined by the position error component of the mating surface and the geometry of the part to be positioned, and is independent of the orientation error component of the mating surface.
Error transfer transmission attribute analysis of three-plane combined joint surface
When the combined surface is a plane combined surface, simplifying the positioning surface into positioning points for analysis; the geometric center of the positioned surface is used as a coordinate system origin o, the direction perpendicular to the positioned plane is used as a z-axis direction, the length direction of the positioned surface is used as an x-axis direction, and the width mode of the positioned surface is used as a y-axis direction.
(1) Error transfer attribute analysis of class a plane combination joint surface
Referring to fig. 7, when the positioning surface of the planar combination coupling surface is 4 small planes f1, f2, f3 and f4 symmetrically distributed on the positioned surface, the combination coupling surface is a type a planar combination coupling surface.
When the positioning surface in the plane combination combining and combining surface is 4 small planes which are symmetrically distributed on the positioned surface, the 4 combining surfaces are plane-small plane combining surfaces, the combining surface F1 is arranged at the upper left corner of the positioned surface, and the combining surfaces F1, F2, F3 and F4 are arranged in the clockwise direction; the plane combination joint surface can transmit error components T ═ alpha, beta, w ], wherein alpha and beta respectively represent rotation error components around x and y axes, and w represents a movement error component along the direction of the z axis; the specific calculation steps are as follows:
step a 1: variation ranges of movement error components in the z-axis direction of the 4 joint surfaces F1, F2, F3, and F4 are obtained: w is a1、w2、w3、w4；
Step a 2: projecting the variation ranges of the movement error components of the joint surfaces F1, F2, F3 and F4 along the z-axis direction to a z-o-y plane and a z-o-x plane respectively;
step a 3: the movement error component w is calculated on the z-axis:
the rotation error component α is calculated in the z-o-y plane from the analytic geometry:
wherein L is2Representing the distance between two locating points in the y-axis direction;
the rotation error component β is calculated in the z-o-x plane from the analytic geometry:
wherein L is1Indicating the distance between the two points of engagement in the x-axis direction.
As can be seen from the expressions (2.5) to (2.7), the error components of the plane combination joint surface are determined by the position error component of the combination surface and the geometric structure of the positioned part, and are independent of the direction error component of the combination surface.
(2) Error transfer attribute analysis of class b plane combination joint surface
Referring to the b-type plane combination combining surface shown in fig. 8, when the positioning surfaces F1 and F2 in the plane combination combining surface are two narrow planes symmetrically distributed on the positioning surface, and the length direction of the narrow planes is parallel to the width direction of the positioning surface, each of the two combining surfaces F1 and F2 is simplified into two combining points respectively located at two ends of the positioning surface in the length direction; the joint 1, 2, 3, 4 may transmit a movement error component in the z-axis direction, which may be set as w1’，w2’，w3' and w4’。
The y-o-z section of the tolerance band was selected as the study object, as shown in FIG. 9. L2 is the length of the narrow plane 1, and the rotation error component alpha of the narrow plane 11Error component at the joint 1
Can be obtained by the following equation:
therefore, the total error component at the joint point 1 is
The same applies to the other joints 2, 3, 4, so that the relationship between the movement error component of the joint and the error component transmissible by the joint can be expressed by equation (2.8).
The error transfer characteristic of the b-type plane combination surface is similar to that of the a-type plane combination surface, and each error component of the b-type plane combination surface can be deduced by combining equations (2.5) - (2.7).
The b-type plane combination joint surface can transmit error components T ═ alpha, beta, w ], wherein alpha and beta respectively represent rotation error components around x and y axes, and w represents a movement error component along the z-axis direction; the specific calculation steps are as follows:
step b 1: obtaining the variation ranges of the movement error components of the F1 and the F2 in the z-axis direction respectively: w is a1、w2(ii) a Respectively acquiring the variation ranges of the rotation error components of the joint surfaces F1 and F2 rotating around the x axis: alpha is alpha1、α2；
Step b 2: projecting the variation ranges of the movement error components of the joint surfaces F1 and F2 in the z-axis direction onto a z-o-x plane respectively; projecting the variation ranges of the rotation error components of the joint surfaces F1 and F2 rotating around the x axis onto a z-o-y plane respectively;
step b 3: the movement error component w is calculated on the z-axis:
the rotation error component α is calculated in the z-o-y plane from the analytic geometry:
the rotation error component β is calculated in the z-o-x plane from the analytic geometry:
(3) error transfer attribute analysis of c-type plane combination joint surface
Referring to the c-type plane combination surface shown in fig. 10, when the positioning surfaces F1, F2 in the plane combination surface are two small planes symmetrically distributed on the positioning surface, the 2 combination positioning surfaces F1, F2 are respectively simplified into two combination points.
The c-type plane combined joint surface can only restrain one rotation direction of a positioned plane, and the error component T which can be transmitted by the c-type plane combined joint surface is [ beta, w ], wherein beta represents a rotation error component around a y axis, and w represents a movement error component along a z axis; the specific calculation steps are as follows:
step c 1: obtaining the variation ranges of the movement error components of the joint surfaces F1 and F2 in the z-axis direction: w is a1、w2；
Step c 2: projecting the tolerance band of the movement error component of the joint surfaces F1 and F2 in the z-axis direction onto a z-o-x plane;
step c 3: the movement error component w is calculated on the z-axis:
the rotation error component β is calculated in the z-o-x plane from the analytic geometry:
where L represents the distance between two binding points.
Claims (7)
1. An assembly error transmission attribute analysis method of a combined joint surface is characterized by comprising the following steps:
step 1: acquiring the variation range of transferable error components of each combined surface;
step 2: projecting the variation range of the transferable error components of each joint surface obtained in the step 1 onto a plane where the transferable rotation error components of the combined joint surfaces are located;
and step 3: calculating the rotation error component and the movement error component of the combined joint surface according to the plane in which the rotation error component which can be transmitted by the analytic geometry on the combined joint surface is located;
when the combined joint surface is a cylindrical combined joint surface consisting of two cylindrical-short cylindrical joint surfaces F1 and F2, the direction of a z axis is taken as the axial direction, the directions of x and y axes are taken as the radial directions, the z axis is parallel to the ideal cylindrical axis, and the origin o of a coordinate system is on the ideal cylindrical axis; the cylindrical surface combination joint surface can transmit error components T ═ alpha, beta, u, v ], wherein alpha and beta respectively represent rotation error components around x and y axes, and u and v respectively represent translation error components along x and y axes; the method comprises the following specific steps:
step s 1: obtaining the variation range of the error components which can be transmitted by the cylindrical surface-short cylindrical surface combination surfaces F1 and F2 respectively:
step s 2: variation range u of translation error component for moving cylindrical-short cylindrical joint surfaces F1 and F2 along x axis1、u2Respectively projecting the error components to an x-o-z plane to calculate error components beta and u which can be transmitted by a cylindrical surface joint surface; translation error component v for moving the cylinder-short cylindrical joint surfaces F1, F2 along the y-axis1、v2The variation ranges are respectively projected on a z-o-y plane to calculate error components alpha and v which can be transmitted by the cylindrical surface combination joint surface;
step s 3: according to the analytic geometry, error components beta, u, alpha and v are calculated according to the following formulas:
wherein L represents the length of the ideal cylinder axis, L1Representing the distance of the coordinate system origin o from the ideal cylinder axis end point along the z-axis.
2. The method of claim 1, wherein the range of variation of the transferable error components of the combined faying surface is obtained as follows:
step 1.1: acquiring tolerance zones of the positioning geometric elements and the positioned geometric elements of the joint surface, wherein the tolerance zones comprise a fixed tolerance zone and a translation tolerance zone;
step 1.2, respectively calculating the variation ranges of the error components of the positioning geometric elements and the positioned geometric elements according to the SDT error model;
step 1.3: the variation range of the error component corresponding to the error component deliverable by the joining surface, which is obtained from the variation range of the error component deliverable by the positioning geometric element, is summed with the variation range of the error component corresponding to the error component deliverable by the joining surface, which is obtained from the variation range of the error component deliverable by the positioning geometric element, to obtain the variation range of the error component deliverable by the joining surface.
3. The method for analyzing the assembly error transmission property of a combined faying surface according to claim 2, wherein the SDT error models for the planar geometric elements, the cylindrical geometric elements and the cylindrical axis geometric elements are respectively as follows:
SDT error model of planar geometry:
wherein a represents the width of the plane and b represents the length of the plane; establishing a coordinate system by taking the geometric center of an ideal rectangular plane as the origin of the coordinate system, the normal direction of the coordinate system as the z axis, the length direction as the x axis and the width direction as the y axis, wherein alpha ' represents a rotation error component rotating around the x axis, beta ' represents a rotation error component rotating around the y axis, and w ' represents a movement error component moving along the z axis; t isPRepresenting a tolerance band of planar translation, TdRepresents a dimensional tolerance band of a plane;
SDT error of cylindrical geometryModel:
wherein l represents the length of the cylinder; establishing a coordinate system by taking the geometric center of an ideal cylindrical surface as the origin of the coordinate system, taking the axial direction of the cylindrical surface as the z axis, taking the radial direction as the x axis and the y axis, wherein alpha 'represents a rotation error component rotating around the x axis, and u' represents a movement error component moving along the x axis; t isDRepresenting the dimensional tolerance band, T, of the cylinderRRepresenting a radial circle run-out tolerance band of the cylindrical surface;
SDT error model of cylinder axis geometry:
wherein l represents the length of the cylinder; establishing a coordinate system by taking the geometric center of an ideal axis as the origin of the coordinate system, taking the axis direction as the z axis, and taking the radial direction as the x axis and the y axis, wherein alpha 'represents a rotation error component rotating around the x axis, and u' represents a movement error component moving along the x axis; t isVTolerance zone, T, for perpendicularity of the axis of the cylinderCRepresenting the tolerance band of coaxiality of the cylindrical axis.
4. The method for analyzing the assembly error transfer property of a combined joint surface according to claim 1, wherein when the combined joint surface is a planar combined joint surface, the joint surface is simplified into joint points for analysis; the geometric center of the positioned surface is used as a coordinate system origin o, the direction perpendicular to the positioned plane is used as a z-axis direction, the length direction of the positioned surface is used as an x-axis direction, and the width mode of the positioned surface is used as a y-axis direction.
5. The assembly error transmission attribute analysis method of the combined joint surface as claimed in claim 4, wherein when the positioning surface of the planar combined joint surface is 4 small planes symmetrically distributed on the positioned surface, the 4 joint surfaces are all plane-small plane joint surfaces, and the joint surface F1 is located at the upper left corner of the positioned surface, and the joint surfaces F1, F2, F3 and F4 are arranged in the clockwise direction; the plane combination joint surface can transmit error components T ═ alpha, beta, w ], wherein alpha and beta respectively represent rotation error components around x and y axes, and w represents a movement error component along the direction of the z axis; the specific calculation steps are as follows:
step a 1: variation ranges of movement error components in the z-axis direction of the 4 joint surfaces F1, F2, F3, and F4 are obtained: w is a1、w2、w3、w4；
Step a 2: projecting the variation ranges of the movement error components of the joint surfaces F1, F2, F3 and F4 along the z-axis direction to a z-o-y plane and a z-o-x plane respectively;
step a 3: the movement error component w is calculated on the z-axis:
the rotation error component α is calculated in the z-o-y plane from the analytic geometry:
wherein L is2Represents the distance between the two binding points in the y-axis direction;
the rotation error component β is calculated in the z-o-x plane from the analytic geometry:
wherein L is1Indicating the distance between the two points of engagement in the x-axis direction.
6. The method for analyzing the assembly error transmission property of the combined joint surfaces as claimed in claim 4, wherein when the positioning surfaces of the planar combined joint surfaces are two narrow planes symmetrically distributed on the positioning surface, and the length direction of the narrow planes is parallel to the width direction of the positioning surface, each of the two joint surfaces F1 and F2 is simplified into two joint points respectively located at two ends of the positioning surface in the length direction; the plane combination joint surface can transmit error components T ═ alpha, beta, w ], wherein alpha and beta respectively represent rotation error components around x and y axes, and w represents a movement error component along the direction of the z axis; the specific calculation steps are as follows:
step b 1: obtaining the variation ranges of the movement error components of the F1 and the F2 in the z-axis direction respectively: w is a1、w2(ii) a Respectively acquiring the variation ranges of the rotation error components of the joint surfaces F1 and F2 rotating around the x axis: alpha is alpha1、α2；
Step b 2: projecting the variation ranges of the movement error components of the joint surfaces F1 and F2 in the z-axis direction onto a z-o-x plane respectively; projecting the variation ranges of the rotation error components of the joint surfaces F1 and F2 rotating around the x axis onto a z-o-y plane respectively;
step b 3: the movement error component w is calculated on the z-axis:
the rotation error component α is calculated in the z-o-y plane from the analytic geometry:
the rotation error component β is calculated in the z-o-x plane from the analytic geometry:
7. the method for analyzing the assembly error transmission property of a combined joint surface as claimed in claim 4, wherein when the positioning surfaces of the planar combined joint surface are two small planes symmetrically distributed on the positioning surface, the 2 joint surfaces F1 and F2 are respectively simplified into two joint points; the plane combination joint surface can transmit an error component T ═ beta, w ], wherein beta represents a rotation error component around a y axis, and w represents a movement error component along a z axis; the specific calculation steps are as follows:
step c 1: obtaining the variation ranges of the movement error components of the joint surfaces F1 and F2 in the z-axis direction: w is a1、w2；
Step c 2: projecting the tolerance band of the movement error component of the joint surfaces F1 and F2 in the z-axis direction onto a z-o-x plane;
step c 3: the movement error component w is calculated on the z-axis:
the rotation error component β is calculated in the z-o-x plane from the analytic geometry:
where L represents the distance between two binding points.
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