CN102262696B - Modeling method for cylindrical gear of straight tooth or helical tooth - Google Patents

Abstract

The invention provides a modeling method for a cylindrical gear of a straight tooth or helical tooth, comprising the following steps: (1) using a computer to create a tooth profile curve parameterization sketch module and finishing a sealing sketch and a dedendum circle sketch of a gear tooth; (2) creating an entity of the gear tooth in a component environment; (3) creating an entity of a dedendum circle cylinder in the component environment; (4) taking the entity of the dedendum circle cylinder as an entity of a reference annular array gear tooth; and (5) combining the entity of the gear tooth with the entity of the dedendum circuit cylinder, and finishing to obtain an integrated simulation entity of a virtual three-dimensional gear. The common modeling method for the cylindrical gear of the straight tooth or helical tooth provided by the invention is simple and easy to learn, is suitable for modeling three-dimensional entity models for the various cylindrical gears of the different straight teeth or helical teeth.

Description

Modeling method of standard involute straight tooth or helical tooth cylindrical gear

Technical Field

The invention relates to a modeling method of a transmission part, in particular to a modeling method of a standard involute straight tooth or helical tooth cylindrical gear by utilizing a powerful secondary development function of computer drawing software.

Background

Straight-tooth or helical-tooth cylindrical gears are one of the most basic parts for transmitting parallel shaft motion and power in the mechanical field, and are widely applied to various mechanical equipment such as mines, metallurgy, buildings, transportation and the like. With the rapid development of computer technology, the design and manufacture of gears is moving towards computer aided design, manufacture, analysis and measurement. Computer aided design is carried out, firstly, a three-dimensional geometric model of a gear is needed, the conventional modeling method of the straight-tooth or helical-tooth cylindrical gear is mainly completed by utilizing the conventional large commercial software or carrying out secondary development on the large commercial software, the modeling mode needs to carry out complicated mathematical calculation, each modeling can only establish a model for a single specific type of gear, and the modeling method cannot be used for establishing models of other different types of straight-tooth or helical-tooth cylindrical gears, for example, the method for establishing the model of the involute straight-tooth or helical-tooth cylindrical gear cannot be applied to modeling of the cycloid straight-tooth or helical-tooth cylindrical gear. In addition, each pair of cylindrical gears with different types of straight teeth or helical teeth is modeled, specific three-dimensional modeling is required according to actual specific requirements, so that a designer is required to have high professional knowledge in the aspects of gears and software, the work is complex and tedious, and the model is difficult to master. Therefore, unified and simple gear three-dimensional modeling methods are urgently needed.

Disclosure of Invention

The invention aims to solve the technical problem of providing a universal, simple and easy-to-learn modeling method for a standard involute straight-tooth or helical-tooth cylindrical gear, which is suitable for building three-dimensional solid models of various cylindrical gears with different straight teeth or helical teeth.

Technical scheme

A modeling method of a standard involute straight tooth or helical tooth cylindrical gear comprises the following steps:

(1) creating a tooth profile curve parameterization sketch module by using a computer to complete a closed sketch and a tooth root circle sketch of the gear teeth;

(2) creating an entity of a gear tooth in a component environment;

(3) under the environment of the component, creating an entity of a root cylinder;

(4) taking a tooth root round cylindrical entity as a reference annular array gear tooth entity;

(5) combining the gear tooth entity and the gear root cylindrical entity, and finishing to obtain a complete virtual three-dimensional gear simulation entity;

the method is characterized in that: when the computer is used for creating a tooth profile curve parameterized sketch module and finishing a closed sketch and a root circle sketch of one gear tooth, the closed sketch of one gear tooth is finished by selecting the following parameter equation:

z＝u+lcosγ

at the same time

cosγ＝tanβcosα，

$\cos \mathrm{\λ}=\frac{\cos \mathrm{\α}}{\sin \mathrm{\γ}},$

$u=\frac{r}{\tan \mathrm{\β}}\mathrm{\θ},$

x-the abscissa of a point on the tooth surface; y-ordinate of a point on the tooth surface;

z-the axial coordinate of a point on the tooth surface; r-is the gear pitch radius;

l-the tooth surface normal length; the direction angle of the alpha-tooth surface normal is more than or equal to 0 and less than or equal to pi;

the direction angle of the gamma-tooth surface normal is more than or equal to 0 and less than or equal to pi; beta-is the helical angle of the helical gear;

lambda-intermediate variable, 0 ≤ lambda ≤ 2 pi; τ -intermediate variable;

-a base parameter; θ — a base parameter;

u-basic reference variables.

In the above method, when β is 0, λ is α, γ is pi/2,

and the tooth profile obtained when u is z is a straight tooth.

In the method, the gear tooth closed sketch in the step (1) is manually input, intercepted and finished through a tooth profile curve parameter equation, or the tooth profile curve parameter equation is programmed by a computer language and used as a macro program, and the program is operated to obtain the gear tooth closed sketch, and the interception and finishing are finished.

In the above method, the steps (2), (3), (4) and (5) are completed by a series of Boolean logic operation commands.

Advantageous effects

The invention combines the modern computer aided design and the traditional machining industry and provides a three-dimensional solid model modeling method for a cylindrical gear with straight teeth or helical teeth. Different direction angle functions can be obtained for the gears with straight teeth or helical teeth, so that the rectangular coordinate of any point on the tooth-shaped curved surface is obtained, and the tooth-shaped curved surface is constructed. The top circle and the root circle of the gear are equidistant circles of pitch circles, and the gear tooth is applicable to gears with different straight teeth or helical teeth. The method can be suitable for three-dimensional solid modeling of various straight-tooth or helical-tooth cylindrical gears, is simple and easy to learn, can be mastered without high-depth gear and computer software knowledge, can create a gear tooth sketch accurately by using a parameterized equation, can truly reflect the tooth surface profile of the straight-tooth or helical-tooth cylindrical gears, can provide accurate coordinate parameters for numerical control processing of high-quality straight-tooth and helical-tooth cylindrical gears, and lays a good foundation for research on mechanical properties of various complex straight-tooth or helical-tooth cylindrical gears and the like.

Drawings

FIG. 1 is a schematic drawing of a first embodiment of a gear tooth and root according to the present invention.

Fig. 2 is a schematic physical representation of a first embodiment of a gear tooth in accordance with the present invention.

Fig. 3 is a schematic physical diagram of a first embodiment of a root cylinder of the present invention.

Fig. 4 is a schematic diagram of a first embodiment of an array gear tooth entity according to the present invention.

FIG. 5 is a schematic solid view of a standard involute spur gear according to a first embodiment of the present invention.

FIG. 6 is a sketch of a gear tooth and tooth root of a second embodiment of the present invention.

FIG. 7 is a schematic view of a standard involute helical gear entity according to a second embodiment of the present invention.

Detailed Description

The invention is further illustrated with reference to the following figures and specific examples.

The invention discloses a modeling method of a standard involute straight toothed spur gear, which comprises the following steps:

(1) and (3) creating a tooth profile curve parameterized sketch module, and finishing the drawing of the closed sketch of the gear teeth by selecting the following parameter equations:

z＝u+lcosγ

wherein,

cosγ＝tanβcosα,

$\cos \mathrm{\λ}=\frac{\cos \mathrm{\α}}{\sin \mathrm{\γ}},$

$u=\frac{r}{\tan \mathrm{\β}}\mathrm{\θ},$

taking alpha-lambda as 20 degrees, beta-theta as 0 degree, gamma as pi/2 degree,

the method is simplified to obtain:

z＝u

x-the abscissa of a point on the tooth surface; y-ordinate of a point on the tooth surface;

z-the axial coordinate of a point on the tooth surface; r-is the gear pitch radius;

l-the tooth surface normal length; the direction angle of the alpha-tooth surface normal is more than or equal to 0 and less than or equal to pi;

the direction angle of the gamma-tooth surface normal is more than or equal to 0 and less than or equal to pi; beta-is the helical angle of the helical gear;

lambda-intermediate variable, 0 ≤ lambda ≤ 2 pi; τ -intermediate variable;

-basic variables(ii) a θ — a base parameter;

u-basic reference variable;

manually inputting the tooth profile curve parameter equation, or programming by using a computer language and using the computer language as a macro program, wherein the gear module is 2, the tooth number is 20, and the program is operated to obtain a closed sketch and a tooth root circle sketch of the gear teeth, intercept and trim to obtain a graph as shown in the attached figure 1;

(2) under the environment of a part, finishing creating an entity of a gear tooth according to the gear tooth sketch obtained in the step (1), as shown in the attached figure 2;

(3) under the environment of a part, completing the creation of an entity of a tooth root cylinder according to the tooth root circle sketch obtained in the step (1), as shown in the attached figure 3;

(4) taking the root circle cylinder entity as a reference annular array gear tooth entity, as shown in figure 4;

(5) and combining the gear tooth entity and the tooth root cylindrical entity, finishing and obtaining a complete virtual three-dimensional standard involute straight toothed cylindrical gear simulation entity, as shown in the attached figure 5.

And (3) completing the steps (2), (3), (4) and (5) by using a series of Boolean logic operation commands.

Another embodiment of the modeling method is a modeling method of a standard involute helical gear, which comprises the following steps:

(1) creating a parameterized sketch module of a tooth profile curve of a standard involute helical gear, and drawing a closed sketch of the gear teeth by selecting the following parameter equation:

z＝u+lcosγ

wherein,

ctanγ＝tanβcosλ，

cosα＝sinγcosλ,

$\mathrm{\θ}=\frac{u\tan \mathrm{\β}}{r},$

x-the abscissa of a point on the tooth surface, y-the ordinate of a point on the tooth surface;

z-the axial coordinate of a point on the tooth surface, r-is the gear pitch circle radius;

l-the normal length of the tooth surface, and the direction angle of the alpha-the normal of the tooth surface, wherein alpha is more than or equal to 0 and less than or equal to pi;

the direction angle of the gamma-tooth surface normal is more than or equal to 0 and less than or equal to pi, and beta-is the helical angle of the helical gear;

lambda-intermediate variable, lambda is greater than or equal to 0 and less than or equal to 2 pi;

theta-a base parameter;

u-basic reference variables.

The tooth profile curve parameter equation is manually input, or is programmed by a computer language and used as a macro program, the program is operated to obtain a closed sketch of the gear teeth, and the graph shown in the attached figure 6 is obtained by cutting and trimming the closed sketch, wherein lambda is 20 degrees, beta is 10 degrees, a basic parameter 0 is more than u <20, the normal modulus is 2, and the number of teeth is 20. And then, according to the steps in the first embodiment, the three-dimensional entity modeling is carried out on the attached figure 6, and the complete virtual three-dimensional standard involute helical tooth cylindrical gear simulation entity figure 7 is obtained through trimming.

Claims (4)

1. A modeling method of a standard involute straight tooth or helical tooth cylindrical gear comprises the following steps:

(1) creating a tooth profile curve parameterization sketch module by using a computer to complete a closed sketch and a tooth root circle sketch of the gear teeth;

(2) creating an entity of a gear tooth in a component environment;

(3) under the environment of the component, creating an entity of a root cylinder;

(4) taking a tooth root round cylindrical entity as a reference annular array gear tooth entity;

(5) combining the gear tooth entity and the gear root cylindrical entity, and finishing to obtain a complete virtual three-dimensional gear simulation entity;

the method is characterized in that: when the computer is used for creating a tooth profile curve parameterized sketch module and finishing a closed sketch and a root circle sketch of one gear tooth, the closed sketch of one gear tooth is finished by selecting the following parameter equation:

z＝u+lcosγ

wherein,

cosγ＝tanβcosα，

$\cos \mathrm{\&lambda;}=\frac{\cos \mathrm{\&alpha;}}{\sin \mathrm{\&gamma;}},$

$u=\frac{r}{\tan \mathrm{\&beta;}}\mathrm{\&theta;},$

x-the abscissa of a point on the tooth surface; y-ordinate of a point on the tooth surface;

z-the axial coordinate of a point on the tooth surface; r-is the gear pitch radius;

l-the tooth surface normal length; the direction angle of the alpha-tooth surface normal is more than or equal to 0 and less than or equal to pi;

the direction angle of the gamma-tooth surface normal is more than or equal to 0 and less than or equal to pi; beta-is the helical angle of the helical gear;

lambda-intermediate variable, 0 ≤ lambda ≤ 2 pi; τ -intermediate variable;

-a base parameter; θ — a base parameter;

u-basic reference variables.

2. A method of modelling a standard involute spur or helical gear as claimed in claim 1 wherein: for the parametric equations described when β is 0, λ is α, γ is pi/2,

and the tooth profile obtained when u is z is a straight tooth.

3. A method of modelling a standard involute spur or helical gear as claimed in claim 1 wherein: and (2) manually inputting, intercepting and finishing the gear tooth closed sketch in the step (1) through a tooth profile curve parameter equation, or programming the tooth profile curve parameter equation by using a computer language and using the programmed tooth profile curve parameter equation as a macro program, operating the program to obtain the gear tooth closed sketch, and intercepting and finishing the gear tooth closed sketch.

4. A method of modelling a standard involute spur or helical gear as claimed in claim 1 wherein: and (3) completing the steps (2), (3), (4) and (5) by using a series of Boolean logic operation commands.

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