CN112182804B - Sliding bearing shape and position error modeling method based on SDT theory - Google Patents

Abstract

The invention discloses a method for modeling the shape and position error of a sliding bearing based on the SDT theory, including: S1: taking any one of the shape and position errors of the sliding bearing as a selected element to establish a shape error model; S2: according to the element Degree of freedom, obtain the screw parameters based on SDT theory; S3: Solve the screw parameters according to the known tolerance domain; S4: Select the extreme points of the ideal surface of the sliding bearing, consider the extreme motion situation on the basis of the SDT theory, and obtain the extreme point movement to The position of the new point; S5: According to the limit position and boundary conditions of the known tolerance domain, the inequality constraints are established in combination with the error model; the generalized equation derived based on the SDT theory of the present invention can not only represent a shape error, but also represent Any shape and position error on the journal.

Description

A Modeling Method of Sliding Bearing Shape Error Based on SDT Theory

technical field

The invention relates to the technical field of manufacturing error analysis, in particular to a modeling method for shape and position errors of sliding bearings based on SDT theory.

Background technique

At present, sliding bearing rotor systems are widely used in large-scale high-speed and heavy-load studies of manufacturing errors and their interactions. From a manufacturing point of view, the stability of sliding bearings is crucial to the design of modern bearing-rotor systems.

However, the sliding bearing rotor system model constructed based on Sommerfeld coefficients discusses the influence of shape and position errors on operating characteristics by describing the geometric shape, but it can only reveal the general law of the influence of shape and position errors on operating characteristics, and does not The in-depth construction of the relationship between the operating characteristics and the subsequent tolerance optimization only describes the shape and position errors of the errors macroscopically, which has relatively large limitations.

Therefore, how to provide a sliding bearing shape error modeling method that can solve the above problems is an urgent problem to be solved by those skilled in the art.

Contents of the invention

In view of this, the present invention provides a sliding bearing shape error modeling method based on SDT theory, which realizes the tolerance semantic description of the error model in the analysis of the operating characteristics of the sliding bearing rotor system, and the established SDT-based error model is oriented to sliding bearing parts At the level, the result of a single error effect or multiple error coupling effects can be considered.

In order to achieve the above object, the present invention adopts the following technical solutions:

A method for modeling the shape and position error of sliding bearings based on SDT theory, including:

S1: Take any one of the shape and position errors of the sliding bearing as a selected element to establish a shape and position error model;

S2: According to the degree of freedom of the elements, the screw parameters are obtained based on the SDT theory;

S3: Solve the screw parameters according to the known tolerance domain;

S4: Select the extreme point of the ideal surface of the sliding bearing, consider the extreme motion situation on the basis of SDT theory, and obtain the position of the extreme point moving to a new point;

S5: According to the limit positions and boundary conditions of the known tolerance domain, combine the error model to establish inequality constraints.

Preferably, the step S3 specifically includes:

S31: judging whether the size error and the shape error exist at the same time;

S32: If yes, obtain the boundary of the tolerance domain, if not, obtain the variation equation;

S33: Obtain corresponding constraints;

S44: Obtain the variation range of the screw parameter.

Preferably, in the step S1, the expression of the shape error model is:

In the formula, x, y and z are the coordinates of any point on the journal surface of the sliding bearing, d _x , d _y , is the error parameter, r is the nominal radius of the journal of the sliding bearing, /> is the tolerance domain.

Preferably, the error parameters meet the following constraints:

In the formula, 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 sliding bearing, /> is the tolerance domain.

Preferably, the shape and position error is any one of cylindricity, roundness, coaxiality, perpendicularity and position.

It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a method for modeling position error of sliding bearings based on SDT theory. The generalized equation derived based on SDT theory can not only represent a form error , it can also indicate that any shape and position error on the journal can use the specified 6 small displacement screws to more accurately represent the ability of the journal shape and position error in a three-dimensional state; the established SDT-based error model is oriented to the level of sliding bearing parts , the result of a single error effect or multiple error coupling effects can be considered. In addition, the proposed modeling method starts from the actual working conditions and introduces the uncertainty of shape and position errors into the error description.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only It is an embodiment of the present invention, and those skilled in the art can also obtain other drawings according to the provided drawings without creative work.

Accompanying drawing of Fig. 1 is the flow chart of the form and position error modeling method provided by the present invention;

Accompanying drawing of Fig. 2 is the flowchart of step S3 of the present invention solving screw parameter;

Figure 3 is a schematic diagram of the error between the ideal journal and the error journal in Embodiment 2 of the present invention.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

Example 1

Referring to accompanying drawing 1, embodiment 1 of the present invention discloses a kind of sliding bearing shape error modeling method based on SDT theory, including:

S1: Take any one of the shape and position errors of the sliding bearing as a selected element to establish a shape and position error model;

S2: According to the degree of freedom of the elements, the screw parameters are obtained based on the SDT theory;

S3: Solve the screw parameters according to the known tolerance domain;

S4: Select the extreme point of the ideal surface of the sliding bearing, consider the extreme motion situation on the basis of SDT theory, and obtain the position of the extreme point moving to a new point;

S5: According to the limit positions and boundary conditions of the known tolerance domain, combine the error model to establish inequality constraints.

Specifically, the degree of invariance (n) refers to the number of movements or rotations that a given geometric element remains unchanged when it moves along a certain coordinate axis or rotates around a certain coordinate axis, such as a cylindrical surface that rotates around its axis or rotates along its axis When moving in the direction, the axial small displacement screw will remain unchanged, so the invariance of the cylindrical surface is the rotation around the axis and the translation along the axis.

The degree of freedom corresponds to the degree of invariance, and refers to the sum n+ d=6, and there is no intersection between invariant degrees and degrees of freedom.

Specifically, the determination process of the extreme point in step S4 is: any point on the ideal surface of the journal of the ideal sliding bearing is selected, and under the action of SDT, it moves to the position of the new point according to the established motion rules, and the selection of the specific point and It is not randomly selected, but the extreme point of the analysis position of the part is selected, because the deviation caused by the movement of the extreme point is the largest. If the extreme point meets the condition, then other points must meet the condition.

The process of determining the position of the new point is: any point on the ideal surface of the journal of the ideal sliding bearing is taken, and under the action of SDT, it moves to the position of the new point according to the established motion rules. In the sliding bearing system, the new point The reason for the position of the journal is that the shape and position errors such as roundness and cylindricity will rotate together during the movement of the journal, so the selected point will move to the new point position according to the established motion rules with the movement of the journal.

Referring to Figure 2, in a specific embodiment, step S3 specifically includes:

S31: judging whether the size error and the shape error exist at the same time;

S32: If yes, obtain the boundary of the tolerance domain, if not, obtain the variation equation;

S33: Obtain corresponding constraints;

S44: Obtain the variation range of the screw parameter.

In a specific embodiment, in the step S1, the expression of the shape error model is:

In the formula, x, y and z are the coordinates of any point on the journal surface of the sliding bearing, d _x , d _y , is the error parameter, r is the nominal radius of the journal of the sliding bearing, /> is the tolerance domain.

Among them, dimensional tolerance refers to the actual deviation from the theoretical size of the part due to the existence of manufacturing errors during the manufacturing process.

Parts have dimensional errors and shape errors at the same time, and the principle of dealing with the relationship between the two is the "tolerance principle". The principle of independence is the basic principle followed by the relationship between size error and shape error. It requires that each size, shape, and position requirements given by the sliding bearing pattern are independent and should meet the requirements separately. If there are specific requirements for the relationship between size and shape, size and position, it should be specified on the drawing. When the principle of independence is followed, the dimensional tolerance only controls the variation of the element size, but does not control its own shape and position error, and the shape and position error has nothing to do with the change of the element size. For elements that follow the principle of independence, the shape and position tolerance domain can only change within the area formed by the minimum entity boundary and the maximum entity boundary or the maximum entity effective boundary.

In a specific embodiment, the error parameters meet the following constraints:

In the formula, 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 sliding bearing, /> is the tolerance domain.

In a specific embodiment, the shape and position error is any one of cylindricity, roundness, coaxiality, perpendicularity and position.

Based on the SDT theory, the shape error modeling can make a correct interpretation of the error variation elements that meet the tolerance, that is, how the error variation elements change within the tolerance range. Based on mathematical definitions, the relationship between error variation elements and tolerances can be described rigorously with variation inequalities and constraint inequalities, and different types of shape and position error mathematical models can be established, and then the geometric elements can be determined according to the studied shape and position errors Create its equation.

Specifically, the common tolerance models and SDT screw parameters corresponding to common shape and position errors are shown in Table 1.

Table 1 Comparison table of shape and position error and SDT screw parameter

Example 2

Referring to the accompanying drawing 3, this embodiment 2 takes the cylindricity of the sliding bearing as an example, according to the geometric invariance of the cylindricity, the screw parameter d _z in the direction of the constant degree is eliminated, d _x ,d _y ,/> Both are variable screw parameters, so the cylindricity error model can use the formula

express,

In the formula, x, y and z are the coordinates of any point on the journal surface of the sliding bearing, r is the nominal radius of the journal of the sliding bearing, is the tolerance domain, and all shape error parameters conform to the following equations:

After converting from the Cartesian coordinate system to the cylindrical coordinate system, the cylindricity error model can be transformed into:

In the formula,

All infinitesimal displacement screws should be within the specified tolerance range, r(θ,z) is the radius of the journal with shape and position error at the point (θ,z) in the cylindrical coordinate system, and finally solve the variation range.

d _x : the infinitesimal moving screw along the x-axis in the coordinate plane yz

d _y : the infinitesimal moving screw along the y-axis in the coordinate plane xz

: the infinitesimal rotation screw about the x-axis

: an infinitesimal rotation spinor about the y-axis

Each embodiment in this specification is described in a progressive manner, each embodiment focuses on the difference from other embodiments, and the same and similar parts of each embodiment can be referred to each other. As for the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and for the related part, please refer to the description of the method part.

The above description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the invention. Implement these. Various modifications to the examples will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other examples without departing from the spirit or scope of the invention. Therefore, the present invention will not 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.