CN102049572B - Design method for hob of cylindrical gear - Google Patents

Abstract

The invention relates to a design method for a hob of a cylindrical gear, in particular to a design method for a hob of a timing gear of an automobile engine. The coordinate point of a tooth form of the hob is obtained by machining the given coordinate point of a tooth form of the cylindrical gear. The hob designed by the method can machine all given coordinate points on the tooth form of the cylindrical gear, the machined tooth form is smooth, and singular points do not protrude, so that the quality of a cylindrical gear product is improved.

Description

A kind of method for designing of roller gear hobcutter

Technical field

The present invention relates to a kind of method for designing of roller gear hobcutter, relate in particular to a kind of method for designing of timing gear ofr automobile engine hobcutter.

Background technology

Gear drive part of a great variety just can be divided into involute, cycloid, circular arc line and various modification curves etc. on profile of tooth; On the kind of drive, can be divided into roller gear, bevel gear, worm and gear etc.; Processing technology mainly contains gear hobbing, gear shaping, powder metallurgy forming, hot investment casting etc. also in continuous progress.For roller gear, generally adopt hobcutter to process profile of tooth (the operation name is called gear hobbing), adopt shaving or roll flute to come the refine profile of tooth at last, the height of gear hobbing precision directly influences the final mass of roller gear.

For timing gears,, can't carry out the profile of tooth refine thereafter and handle, so the height of gear hobbing quality has directly determined the quality of product because the particularity of its tooth profile parameter is processed the final operation that profile of tooth is it with hobcutter.The main factor that influences timing gears and the belt cooperation transmission life-span is that tooth Shape Design is unreasonable and machining accuracy is not high.Improve the machining accuracy of timing gears, just need design hobcutter accurately, but because the timing gears drawing provides generally is the point coordinates that disperses, design difficulty is bigger, dyscalculia.The approximate processing of general employing profile of tooth replaces design tooth profile on the technology at present, and approximate profile of tooth off-design profile of tooth is bigger, and precision is relatively poor.The method of extensive use adopts powder metallurgy forming or hot investment casting etc. in addition in addition, but its manufacturing cost is high, and the accuracy of gear also is difficult to meet design requirement.

Summary of the invention

The objective of the invention is to have invented a kind of method for designing of roller gear hobcutter in order to solve the problems of the technologies described above.

1 technical problem that will solve

For the hobcutter design of gear, generally the formula according to mechanical design handbook calculates.If but the form of gear tooth that design of gears unit provides be modification curve or discrete after point coordinate data, then can't carry out the hobcutter design by mechanical design handbook; Also can't carry out the calculating of slope of a curve and curvature for single point coordinates, also can't be connected with consecutive points, to carry out the design of hobcutter also infeasible so use Principles of Gear Connection.

2 technical schemes

In order to solve the problems of the technologies described above, the present invention realizes through following technical method:

This method adopts cubic spline interpolation exactly; The point that each is discrete couples together with the curve fit method; Its slope and curvature are continuous everywhere on given characteristic point, to the profile of tooth analysis with calculate highly beneficially, have fundamentally solved hobcutter DESIGN THEORY problem fully.

Owing to take above-mentioned technical method, make the present invention have following advantage and effect:

The curve of cubic spline interpolation structure contains given point coordinates set fully; The most similar with the DESIGN THEORY teeth outline; Its slope and curvature are continuous everywhere on given point coordinates, to the profile of tooth analysis with calculate highly beneficial, and also very convenient for computer programming.Utilize the hobcutter of this method design can process whole coordinate points given on the roller gear profile of tooth accurately, the profile of tooth that processes is smooth-going smooth, does not have the singular point projection, has improved the machining accuracy of roller gear product; Because gear hobbing technology is simple, the manufacturing cost of roller gear product is also reduced greatly.

Description of drawings

The profile of tooth point coordinates figure that Fig. 1 provides for gear,

The profile of tooth point coordinates that the 1-gear is given.

Fig. 2 is the design flow diagram of timing gears hobcutter

2-gets whole point coordinates given on the profile of tooth

The 3-coordinate transform

4-confirms the point on the I section

5-confirms the point on the V section

6-confirms the point on the IV section

7-confirms the point on the II section

8-confirms the point on the III section

The match of 9-cubic spline interpolation

10-expands fitting result

11-defines reference frame

12-finds the solution the tangent slope of putting in the matched curve

The 13-iterative computation

The 14-linear transformation

All the other calculation of parameter of 15-

The design of 16-hobcutter is published picture

The specific embodiment

As shown in Figure 1, we at first carry out rough segmentation to the given profile of tooth point coordinates 1 of the gear in the drawing, generally can be divided into five sections curve: I, II, III, IV, V.

As shown in Figure 2, progressively confirm the coordinate points that each section on the given profile of tooth point coordinates 1 of Fig. 1 middle gear should comprise by the step of design flow diagram, promptly confirm the decomposition point of each section; Design simultaneously the point coordinates on the blade profile of tooth of hobcutter of each section of processing profile of tooth set by step.

I section described in Fig. 1 is the some set on the Gear Root circle, and the II section is the some set on the fillet curve, and the III section is the operating point set, and the IV section is the set of tooth top transition arc point, and the V section is the some set on the outside circle.

Because the not segmentation of point coordinates that provides in the gear drawing, the profile of tooth point coordinates 1 given at Fig. 1 middle gear also only carried out rough segmentation to profile of tooth, so need further to confirm the decomposition point of each section.

The flow chart step that concrete design provides by Fig. 2:

Step 1 is got whole point coordinates 2 given on the profile of tooth, sets up plane right-angle coordinate.

Step 2, coordinate transform 3 just transforms to all point coordinates in the plane right-angle coordinate first quartile shown in Figure 1, and initial point O is a gear centre.

Step 3 is confirmed the point 4 on the I section, and the point 4 among Fig. 1 on the I section is on the root circle of gear, and the radius vector value of available point is compared with the Gear Root radius of circle to confirm, according to given pitch circle radius, can be calculated the hobcutter outside pitch line length then.

Step 4 is confirmed the point 5 on the V section, and the point 5 among Fig. 1 on the V section is on the outside circle of gear, and the radius vector value of available point is compared with the gear teeth tips radius of circle to confirm, according to given pitch circle diameter, can be calculated the hobcutter inside pitch line length then.

Step 5 is confirmed the point 6 on the IV section, and the point 6 among Fig. 1 on the IV section is on the tooth top transition arc, because curve is short, available involute replaces, and precision meets design requirement fully, can calculate angle and the height dimension of hobcutter profile of tooth at the tooth root position then.

Step 6 is confirmed the point 7 on the II section, and the point 7 among Fig. 1 on the II section is on fillet curve, owing to do not participate in work, this section curve can be given by the recommendation of Tool Design handbook.The Fitting Calculation is carried out in the back for ease, can suppose that the hobcutter tooth top is the circular arc of certain diameter, and the epicycloid that calculating cutter tip circle arc forms on gear gets final product.

Step 7 is confirmed the point 8 on the III section, and through the calculating of front, final remaining point is exactly the point on the III section, supposes that quantity is m, and the curve that these points are formed is the operate as normal curve of gear.

Step 8 is carried out cubic spline interpolation match 9 to the point on the III section.Utilize the cubic spline interpolation method, can simulate n=m-1 section cubic spline curve, all corresponding monobasic cubic function independently of each section curve, each independent function all has the coefficient of four the unknowns, amounts to 4n unknown number.For any two neighboring sections curve, must satisfy following condition: the starting point of curve and terminal point equate with given point coordinates value; The terminal point coordinate value of leading portion curve equates (representative function is continuous at the node place) with the starting point coordinate value of back segment curve; The ending slope of leading portion curve equates (the representative function slope is continuous) with the starting slope of back segment curve; The terminal point curvature of front end curve equates (representative function curvature is continuous) with the starting point curvature of back segment curve; For two limit points of curve, adjacent with the two-end-point of a section III respectively point on our desirable section II of border and the section IV just.Utilize above relation promptly can obtain whole curvilinear equations of family of curves.

Step 9 can be expanded the calculating of fitting result 10.Just from these curves, arbitrarily obtain the parameter of point how arbitrarily, conveniently carry out more accurate research.

Step 10, definition reference frame 11 is convenient to study in great detail a little the characteristics of motion and engagement.Because the family of curves of match is the profile of tooth line segment III of timing gears, gear is done uniform speed rotation's (counterclockwise for just) around initial point O, and angular speed is constant, can be made as rotating coordinate system; Lathe can be made as fixedly rectangular coordinate system, and initial point also is O; Hobcutter is made as translate coordinate system, and initial point is on the intersection point of pitch radius and axis of ordinates.The axis of ordinates of original position three-coordinate overlaps.Hobcutter and gears engaged owing to be stable drive ratio motion, so in fixing rectangular coordinate system definition certain to put be the public instantaneous and fixed of each point on the profile of tooth.Defining public instantaneous point is pitch radius R to the distance of gear centre initial point ₀Take up an official post from family of curves and to get the motion state that any studies this point, at first can calculate the radius vector size R of this point ₂, velocity magnitude, with the forward angle of vertical coordinate axle, can calculate the point-to-point speed size of corresponding points on the hobcutter simultaneously.

Step 11 is found the solution the tangent slope of putting in the matched curve 12.Through finding the solution the first derivative of matched curve equation, can obtain the tangent slope of each point in the matched curve.

Based on Principles of Gear Connection, cross the common normal at public point of contact on the form of gear tooth and the hobcutter profile of tooth and must pass through instantaneous point.Suppose that any point in the form of gear tooth is rotated counterclockwise certain angle, the normal of this point is just in time through public instantaneous, and then postrotational point coordinates also is the point on the hobcutter profile of tooth simultaneously.Find the solution gear and the cutter velocity vector relation at public point of contact, can obtain the tangent slope at public point of contact, it and any point tangent slope before rotation differs an anglec of rotation.Obtain following equation through this relation:

$[K_2\×\cos \left({\mathrm{\α}}_2\right)+\mathrm{SIN}\left({\mathrm{\α}}_2\right)]\×[\cos \left({\mathrm{\φ}}_2\right)+\mathrm{SIN}\left({\mathrm{\φ}}_2\right)\×\mathrm{tg}\left({\mathrm{\φ}}_2\right)]$

$-\frac{K_2\×R_0}{R_2}-\frac{R_0\×\mathrm{Tg}}{R_2}=0$ (formula one)

In the formula: K ₂---the tangent slope of each point in the matched curve;

α ₂---before rotating to an angle, the angle of the line of each point and gear centre and vertical coordinate axle in the matched curve;

φ ₂---the anglec of rotation.

Unknown number in the following formula is anglec of rotation φ ₂, all corresponding unique anglec of rotation φ of each point in the matched curve ₂

Step 12 utilizes computer programming and iterative computation 13 can obtain φ accurately ₂

Step 13 is carried out linear transformation 14.The new coordinate that obtains after any point in the matched curve rotated to an angle transforms in the translate coordinate system again, just can obtain the profile of tooth point coordinates of hobcutter, and its accounting equation is:

$\left\{\begin{array}{c}{X}_1=X_2\×\mathrm{Cos}\left({\mathrm{\φ}}_2\right)-Y_2\×\mathrm{SIN}\left({\mathrm{\φ}}_2\right)+R_0\×{\mathrm{\φ}}_2\\ Y_1=X_2\×\mathrm{SIN}\left({\mathrm{\φ}}_2\right)+Y_2\×\mathrm{Cos}\left({\mathrm{\φ}}_2\right)-R_0\end{array}\right.$ (formula two)

In the formula: X ₁, Y ₁---the profile of tooth point abscissa of hobcutter, ordinate;

X ₂, Y ₂---abscissa, the ordinate put on the form of gear tooth;

So far, the point coordinates that is used on the hobcutter profile of tooth of Machining of Gear profile of tooth is all obtained.

Step 14 is carried out all the other calculation of parameter 15.According in the mechanical design handbook about the design part of hobcutter, can all the other structural parameters of roller gear hobcutter be decided.

Step 15 is carried out hobcutter at last and is designed Figure 16.

Claims (1)

1. the method for designing of a roller gear hobcutter; Mainly handle given roller gear profile of tooth coordinate points data through segmentation; Coordinate points The data cubic spline interpolation to the profile of tooth working portion carries out curve fitting, and utilizes the theory of engagement and linear transformation to draw the profile of tooth coordinate points of hobcutter again; After the curve match finishes, can on the curve of match, get more coordinate points and calculate, the hobcutter profile of tooth coordinate points quantity that draws so also will increase, for the hobcutter manufacturing provides more gross data; It is characterized in that to use following formula one to solve the accurate anglec of rotation of each coordinate points, and utilize the anglec of rotation finally to calculate whole coordinate points of tool-tooth profile;

The definition reference frame is convenient to study in great detail a little the characteristics of motion and engagement; Because the family of curves of match is the profile of tooth line segment of timing gears, gear is done the uniform speed rotation around initial point 0, and counterclockwise for just, angular speed is constant, so can be made as rotating coordinate system A; Lathe is made as fixedly rectangular coordinate system B, and initial point also is 0; Hobcutter is made as translate coordinate system C, and initial point is on the intersection point of pitch radius and axis of ordinates; The axis of ordinates of the original position of A, B, C three-coordinate overlaps; Hobcutter and gears engaged owing to be stable drive ratio motion, so in fixing rectangular coordinate system B definition certain to put be the public instantaneous and fixed of each point on the profile of tooth, defining public instantaneous point is pitch radius R to the distance of gear centre initial point ₀Take up an official post from family of curves and to get the motion state that any studies this point, at first can calculate the radius vector size R of this point ₂, velocity magnitude, with the forward angle of vertical coordinate axle ₂, the point-to-point speed that can calculate corresponding points on the hobcutter simultaneously is big or small; Through finding the solution the first derivative of matched curve equation, can access the tangent slope K of each point in the matched curve ₂

According to Principles of Gear Connection, cross the common normal at public point of contact on the form of gear tooth and the hobcutter profile of tooth and must pass through public instantaneous point; Suppose that any point in the form of gear tooth is rotated counterclockwise certain angle, the normal of this point is just in time through public instantaneous point, and then postrotational point coordinates also is the point on the hobcutter profile of tooth simultaneously; Find the solution gear and the cutter velocity vector relation at public point of contact, can access the tangent slope at public point of contact, the tangent line at public point of contact and any point tangent line before rotation differs an anglec of rotation; Obtain following equation through this relation:

Formula one:

$[K_2\×\mathrm{COS}\left({\mathrm{\α}}_3\right)+\mathrm{SIN}\left({\mathrm{\α}}_2\right)]\×[\mathrm{COS}\left({\mathrm{\φ}}_2\right)+\mathrm{SIN}\left({\mathrm{\φ}}_2\right)\×\mathrm{tg}\left({\mathrm{\φ}}_2\right)]$

$-\frac{K_2\×R_0}{R_2}-\frac{R_0\×\mathrm{tg}\left({\mathrm{\φ}}_2\right)}{R_2}=0$

In the formula: K ₂---the tangent slope of each point in the matched curve;

α ₂---before rotating to an angle, the forward angle of the line of each point and gear centre and vertical coordinate axle in the matched curve;

φ ₂---the anglec of rotation;

R ₀---pitch radius;

R ₂---the radius vector size;

Unknown number in the following formula is anglec of rotation φ ₂, all corresponding unique anglec of rotation φ of each point in the matched curve ₂

Utilize computer programming and iterative computation can obtain φ accurately ₂

Carry out linear transformation, the new coordinate that obtains after any point in the matched curve is rotated to an angle transforms among the translate coordinate system C again, just can access the profile of tooth point coordinates of hobcutter, and its accounting equation is:

$\left\{\begin{array}{c}{X}_1=X_2\×\mathrm{COS}\left({\mathrm{\φ}}_2\right)-Y_2\×\mathrm{SIN}\left({\mathrm{\φ}}_2\right)+R_0\×{\mathrm{\φ}}_2\\ Y_1=X_2\×\mathrm{SIN}\left({\mathrm{\φ}}_2\right)+Y_2\×\mathrm{COS}\left({\mathrm{\φ}}_2\right)-R_0\end{array}\right.$

In the formula: X ₁, Y ₁---the profile of tooth point abscissa of hobcutter, ordinate;

X ₂, Y ₂---abscissa, the ordinate put on the form of gear tooth;

So far, the point coordinates that is used on the hobcutter profile of tooth of Machining of Gear profile of tooth is all obtained;

According in the mechanical design handbook about the design part of hobcutter, can all the other structural parameters of roller gear hobcutter be decided.

Images