CN112182804B - Sliding bearing shape and position error modeling method based on SDT theory - Google Patents
Sliding bearing shape and position error modeling method based on SDT theory Download PDFInfo
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Abstract
The invention discloses a sliding bearing shape and position error modeling method based on an SDT theory, which comprises the following steps: s1: taking any one of the shape and position errors of the sliding bearing as a selected element, and establishing a shape and position error model; s2: acquiring a rotation parameter based on an SDT theory according to the degree of freedom of the element; s3: solving the rotation parameters according to a known tolerance domain; s4: selecting an extreme point of an ideal surface of the sliding bearing, taking limit movement conditions into consideration on the basis of an SDT theory, and acquiring the position of the extreme point moving to a new point; s5: establishing inequality constraint conditions according to the limit positions and boundary conditions of the known tolerance domains and combining an error model; the generalized equation derived based on the SDT theory can not only represent a form and position error, but also represent any form and position error on the journal.
Description
Technical Field
The invention relates to the technical field of manufacturing error analysis, in particular to a sliding bearing shape and position error modeling method based on an SDT theory.
Background
At present, the sliding bearing rotor system is widely used for large-scale high-speed heavy-duty research on manufacturing errors and interaction thereof, and the problem of the working stability of the sliding bearing is crucial to the design of the modern bearing rotor system from the viewpoint of manufacturing.
However, the sliding bearing rotor system model constructed based on the Sommerfeld coefficient discusses the influence of the shape and position errors on the operation characteristics through the description of the geometric morphology, but only reveals the general rule of the influence of the shape and position errors on the operation characteristics, does not deeply construct the relation between the operation characteristics and the subsequent tolerance optimization, only macroscopically describes the shape and position errors, and has great limitation.
Therefore, how to provide a sliding bearing shape and position error modeling method capable of solving the above problems is a problem that needs to be solved by those skilled in the art.
Disclosure of Invention
In view of the above, the invention provides a sliding bearing shape and position error modeling method based on SDT theory, which realizes the tolerance semantic description of an error model in the analysis of the running characteristics of a sliding bearing rotor system, and the established SDT error model-based sliding bearing part-oriented layer can consider the result of single error action or multiple error coupling action.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a sliding bearing shape and position error modeling method based on SDT theory comprises the following steps:
s1: taking any one of the shape and position errors of the sliding bearing as a selected element, and establishing a shape and position error model;
s2: acquiring a rotation parameter based on an SDT theory according to the degree of freedom of the element;
s3: solving the rotation parameters according to a known tolerance domain;
s4: selecting an extreme point of an ideal surface of the sliding bearing, taking limit movement conditions into consideration on the basis of an SDT theory, and acquiring the position of the extreme point moving to a new point;
s5: and establishing inequality constraint conditions according to the limit positions and boundary conditions of the known tolerance domains and combining an error model.
Preferably, the step S3 specifically includes:
s31: judging whether the size error and the shape and position error exist simultaneously or not;
s32: if yes, acquiring a boundary of a tolerance domain, and if not, acquiring a change equation;
s33: acquiring corresponding constraint conditions;
s44: and acquiring the variation range of the rotation parameter.
Preferably, in the step S1, the expression of the shape and position error model is:
where x, y and z are the coordinates of any point on the journal surface of the plain bearing, d x ,d y ,Is the error parameter, r is the nominal radius of the journal of the plain bearing,/-)>Is a tolerance domain.
Preferably, the error parameter meets the following constraint:
where l is the length of the journal of the sliding bearing, d x ,d y ,Is the error parameter, r is the nominal radius of the journal of the plain bearing,/-)>Is a tolerance domain.
Preferably, the shape and position error is any one of cylindricity, roundness, coaxiality, perpendicularity and positional accuracy.
Compared with the prior art, the sliding bearing shape and position error modeling method based on the SDT theory is provided, and a generalized equation derived based on the SDT theory can not only represent a shape and position error, but also represent the capacity that any shape and position error on a journal can more accurately represent the shape and position error of the journal in a three-dimensional state by using specified 6 small displacement rotations; the established SDT-based error model is oriented to the sliding bearing part level, the result of single error action or multiple error coupling action can be considered, and in addition, the modeling method introduces uncertainty of shape and position errors into error description from the actual working condition.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a shape and position error modeling method provided by the invention;
FIG. 2 is a flow chart of the step S3 of solving the spin parameter according to the present invention;
FIG. 3 is a diagram showing the error of an ideal journal and an error journal according to example 2 of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
Referring to fig. 1, embodiment 1 of the invention discloses a sliding bearing shape and position error modeling method based on SDT theory, comprising:
s1: taking any one of the shape and position errors of the sliding bearing as a selected element, and establishing a shape and position error model;
s2: acquiring a rotation parameter based on an SDT theory according to the degree of freedom of the element;
s3: solving the rotation parameters according to a known tolerance domain;
s4: selecting an extreme point of an ideal surface of the sliding bearing, taking limit movement conditions into consideration on the basis of an SDT theory, and acquiring the position of the extreme point moving to a new point;
s5: and establishing inequality constraint conditions according to the limit positions and boundary conditions of the known tolerance domains and combining an error model.
Specifically, the invariance (n) refers to the constant movement or rotation number of a given geometric element when moving along a certain coordinate axis or rotating around a certain coordinate axis, for example, the axial small displacement rotation of the cylindrical surface when rotating around the axial direction or moving along the axial direction of the cylindrical surface is kept unchanged, so that the invariance of the cylindrical surface is the rotation around the axial direction and the translation along the axial direction.
The degree of freedom corresponds to the degree of invariance, meaning that when the feature translates (or rotates) along (or around) X, Y and the Z axis, the sum of the number n of invariance degrees and the number d of degrees of freedom is n+d=6, and the invariance degrees and the degrees of freedom do not intersect.
Specifically, the determining process of the extreme point in step S4 is as follows: taking a point on the ideal surface of the journal of the ideal sliding bearing, moving to a new point position according to a set movement rule under the action of SDT, selecting a specific point not randomly, selecting an extreme point of a part analysis position, wherein the extreme point has the largest deviation generated by movement, and if the extreme point meets the condition, other points must meet the condition.
The location determination process of the new point is: in the sliding bearing system, the shape and position errors such as roundness, cylindricity and the like of the journal can rotate along with the journal during the movement due to the position of the new point, so that the selected point can move to the position of the new point along with the movement of the journal according to the set movement rule.
Referring to fig. 2, in a specific embodiment, step S3 specifically includes:
s31: judging whether the size error and the shape and position error exist simultaneously or not;
s32: if yes, acquiring a boundary of a tolerance domain, and if not, acquiring a change equation;
s33: acquiring corresponding constraint conditions;
s44: and acquiring the variation range of the rotation parameter.
In a specific embodiment, in the step S1, the expression of the shape and position error model is:
where x, y and z are the coordinates of any point on the journal surface of the plain bearing, d x ,d y ,Is the error parameter, r is the nominal radius of the journal of the plain bearing,/-)>Is a tolerance domain.
The dimensional tolerance refers to the actual deviation of the part from the theoretical dimension due to the existence of manufacturing errors in the manufacturing process.
The parts have both dimensional errors and form and position errors, and the principle of dealing with the relationship between the two is the "tolerance principle". The independent principle is the basic principle followed by the interrelationship of dimensional errors and shape and position errors. It requires that each size and shape and position requirement given by the plain bearing pattern be independent and should meet the requirements separately. Specific requirements for size and shape, interrelationships between size and position should be specified on the pattern. When the independent principle is followed, the dimensional tolerance only controls the variation of the element size, but not the shape and position error of the dimensional tolerance, and the shape and position error is irrelevant to the variation of the element size. For elements that follow independent principles, the form and position tolerance domain can only vary within the area formed by the minimum physical boundary and the maximum physical boundary or the maximum physical effective boundary.
In a specific embodiment, the error parameter meets the following constraints:
where l is the length of the journal of the sliding bearing, d x ,d y ,Is the error parameter, r is the nominal radius of the journal of the plain bearing,/-)>Is a tolerance domain.
In a specific embodiment, the shape and position error is any one of cylindricity, roundness, coaxiality, verticality and positional accuracy.
The form and position error modeling based on the SDT theory can accurately explain error variation factors meeting the tolerance, namely how the error variation factors vary within the tolerance range. The relation between the error variation element and the tolerance can be strictly described by using a variation inequality and a constraint inequality based on mathematical definition, different types of shape and position error mathematical models are established, geometric elements are determined according to the studied shape and position errors, and an equation is established.
Specifically, the common tolerance model and SDT rotation parameters corresponding to the common form and position errors are shown in table 1.
TABLE 1 form and position error and SDT spin parameter comparison Table
Example 2
Referring to FIG. 3, in example 2, the cylindricity of the sliding bearing is taken as an example, and the rotation parameter d in the direction of the cylindricity is eliminated according to the geometric constancy of the cylindricity z ,d x ,d y ,/>All are variable rotation parameters, so that the cylindricity error model can use a formula
The representation is made of a combination of a first and a second color,
where x, y and z are the coordinates of any point on the journal surface, r is the nominal radius of the journal,is a tolerance domain, and all shape error parameters conform to the following equation:
after being converted into a cylindrical coordinate system by a Cartesian coordinate system, the cylindricity error model can be converted into:
in the method, in the process of the invention,
all infinitesimal displacement rotations should be within a prescribed tolerance range, r (θ, z) is the journal radius with shape and position errors at the point (θ, z) under the cylindrical coordinate system, and finally the variation range is solved.
d x : infinitesimal movement rotations along x-axis in coordinate plane yz
d y : infinitesimal movement rotations along y-axis in coordinate plane xz
: infinitely small rotational rotations about the x-axis
: infinitely small rotational rotations about the y-axis
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. These implementations are performed. Various modifications to the examples will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (3)
1. The sliding bearing shape and position error modeling method based on the SDT theory is characterized by comprising the following steps of:
s1: taking any one of the shape and position errors of the sliding bearing as a selected element, and establishing a shape and position error model;
s2: acquiring a rotation parameter based on an SDT theory according to the degree of freedom of the element;
s3: solving the rotation parameters according to a known tolerance domain;
s4: selecting an extreme point of an ideal surface of the sliding bearing, taking limit movement conditions into consideration on the basis of an SDT theory, and acquiring the position of the extreme point moving to a new point;
s5: establishing inequality constraint conditions according to the limit positions and boundary conditions of the known tolerance domains and combining an error model;
in the step S1, the expression of the shape and position error model is:
where x, y and z are the coordinates of any point on the journal surface of the plain bearing,is the error parameter, r is the nominal radius of the journal of the plain bearing,/-)>Is a tolerance domain;
the error parameter meets the following constraint conditions:
where l is the length of the journal of the sliding bearing,is the error parameter, r is the nominal radius of the journal of the plain bearing,/-)>Is a tolerance domain.
2. The sliding bearing shape and position error modeling method based on the SDT theory according to claim 1, wherein the step S3 specifically includes:
s31: judging whether the size error and the shape error of the sliding bearing exist simultaneously or not;
s32: if the tolerance domains exist simultaneously, acquiring boundaries of the tolerance domains, and if the tolerance domains do not exist simultaneously, acquiring a change equation;
s33: acquiring corresponding constraint conditions;
s44: and acquiring the variation range of the rotation parameter.
3. The method for modeling a sliding bearing shape and position error based on SDT theory according to any one of claims 1 to 2, wherein the shape and position error is any one of cylindricity, roundness, coaxiality, verticality and positional accuracy.
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| CN106529045A (en) * | 2016-11-15 | 2017-03-22 | 西北工业大学 | Spinor-based multi-axis milling tool axis modeling method |
| CN109933920A (en) * | 2019-03-18 | 2019-06-25 | 西南交通大学 | A kind of error vector modeling method of rotary shaft position deviation |
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| CN106529045A (en) * | 2016-11-15 | 2017-03-22 | 西北工业大学 | Spinor-based multi-axis milling tool axis modeling method |
| CN109933920A (en) * | 2019-03-18 | 2019-06-25 | 西南交通大学 | A kind of error vector modeling method of rotary shaft position deviation |
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