CN116484531A - Tooth profile design and shape modification method for internal gear - Google Patents
Tooth profile design and shape modification method for internal gear Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/08—Profiling
- F16H55/0806—Involute profile
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/08—Profiling
- F16H55/088—Profiling with corrections on tip or foot of the teeth, e.g. addendum relief for better approach contact
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
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Abstract
The invention discloses a tooth profile design and modification method of an internal meshing gear, which relates to the technical field of gear design, and utilizes the intersection point of the addendum circle and the instantaneous center line of two gears of internal meshing transmission to construct an elliptic meshing line; setting elliptical half-axis parameters based on elliptical characteristics; based on the constructed elliptic meshing line, constructing a rack tooth profile equation by using a plane meshing principle and utilizing the meshing theorem of the elliptic meshing line and the rack tooth profile; constructing a conjugate tooth profile curve meshed with the rack according to a conjugate equation, wherein the conjugate tooth profile curve is an internal gear tooth top tooth profile curve and an external gear tooth top tooth profile curve; the conjugate principle is used to construct the tooth profile conjugate to the addendum profile curve and the gear profile modification scheme is obtained by changing the elliptical half-axis parameters. The invention not only avoids the difficulty of parameter selection in the traditional shape modification method, but also avoids the problems of unstable transmission, impact, interference and the like in the shape modification design due to the conformity with the plane meshing transmission characteristic.
Description
Technical Field
The invention relates to the technical field of gear design, in particular to a tooth profile design and shape modification method for an internal gear.
Background
The ring gear transmission is widely used in industrial production as a transmission mode. The internal gear transmission efficiency is high and can reach more than 90%; the axial lead distance of the transmission is relatively short, high-power transmission can be completed in a smaller space, and under the same condition, the internal engaged gear transmission is lighter and more compact than other types of transmission. The diameter of the gear of the internal gear transmission is larger, and the tooth width of the gear is wider, so that the bearing capacity of the internal gear transmission is very strong, and the internal gear transmission can bear larger load, so that the mechanical operation is more stable and reliable.
The internal gear has higher requirements on the tooth profile transmission performance of the gear, but the tooth profile of the internal gear in the market at present is designed by involute tooth profile and cycloidal tooth profile, and the tooth profile is relatively fixed when the gear is designed for given transmission ratio, modulus and other parameters, so that the transmission performance is still to be improved. For the traditional internally-meshed gears, most of the gears are shaped by adopting curves such as parabolas, circular arc lines, involute curves and the like, the tooth profile is directly shaped, the difficulty in selecting the shaping quantity is large, and the shaping effect is poor in controllability; sometimes even the adverse effects of tooth form interference and meshing impact occur.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention aims to provide a method for modifying the tooth profile design of an internal meshing gear, which utilizes the characteristics of smoothness, continuity and adjustability of an elliptic meshing line, derives a gear conjugate tooth profile curve by changing elliptic half-shaft parameters according to the gear meshing principle, and modifies, designs and optimizes the original tooth profile. The method not only avoids the difficulty of parameter selection in the traditional shape modification method, but also avoids the problems of unstable transmission, impact, interference and the like in the shape modification design due to the fact that the method accords with the plane meshing transmission characteristic.
In order to achieve the above object, the present invention is realized by the following technical scheme:
the embodiment of the invention provides a tooth profile design modification method for an internal gear, which comprises the following steps:
an elliptic meshing line is constructed by utilizing the intersection point of the addendum circles and the instantaneous center line of the two gears of the internal meshing transmission; setting elliptical half-axis parameters based on elliptical characteristics;
based on the constructed elliptic meshing line, constructing a rack tooth profile equation by using a plane meshing principle and utilizing the meshing theorem of the elliptic meshing line and the rack tooth profile;
constructing a conjugate tooth profile curve meshed with the rack according to a conjugate equation, wherein the conjugate tooth profile curve is an internal gear tooth top tooth profile curve and an external gear tooth top tooth profile curve;
the conjugate principle is used to construct the tooth profile conjugate to the addendum profile curve and the gear profile modification scheme is obtained by changing the elliptical half-axis parameters.
As a further implementation manner, the method for constructing the elliptic meshing line comprises the following steps: and constructing an addendum circle and an instantaneous center line of the internal meshing gear, solving an intersection point of the addendum circles of the two meshing gears and the instantaneous center line, and constructing an elliptic arc line as a gear meshing line.
As a further implementation mode, given elliptical half-axis parameters, different elliptical arc meshing lines are obtained along with the change of elliptical arc half-axis parameters;
and solving the other half axial length A of the ellipse and the polar coordinate parameter theta of the elliptical arc according to the geometric principle for the set elliptical half axial parameter B to obtain an expression of the meshing line of the elliptical arc.
As a further implementation manner, the expression of the elliptical arc meshing line is:
as a further implementation mode, an internal meshing gear conjugate tooth top profile curve meeting the design of an elliptic meshing line is constructed, a meshing line equation is substituted into a conjugate equation to obtain a corresponding relation between the elliptic meshing line and a conjugate tooth profile curve, and the conjugate tooth profile curve meeting the elliptic meshing line is obtained through coordinate transformation and calculation.
As a further implementation, the internal gear tooth top profile curve is expressed as:
the external gear tooth top profile curve is expressed as:
wherein,,
as a further implementation, the tooth profile curves of the internal gear and the external gear are constructed, and the relative motion relationship of the internal gear, the external gear and the tooth profile curves thereof is known, and according to the conjugation principle, the tooth profile curves of the external gear conjugated to the tooth profile curves of the internal gear and the tooth profile curves of the internal gear conjugated to the tooth profile curves of the external gear are respectively constructed.
As a further implementation, the external gear root profile curve is expressed as:
wherein,,
r1 is the radius of the external gear, R2 is the radius of the internal gear, and ha1 and ha2 are the tooth top coefficients respectively.
As a further implementation mode, the meshing line is modified by changing the half-axis parameter of the elliptic meshing line, and the tooth profile of the internal meshing gear is deduced, so that the design shape modifying effect of the original tooth shape is obtained.
As a further implementation, the conjugate tooth profile is determined using a tooth form normal method.
The beneficial effects of the invention are as follows:
compared with the traditional gear shaping, the invention directly shapes the tooth profile by adopting curves such as parabola, arc line, involute and the like, has the defects of large difficulty in selecting the shaping quantity and poor controllability of the shaping effect, utilizes the characteristics of smoothness, continuity and adjustability of an elliptic meshing line, derives a gear conjugate tooth profile curve by changing elliptic half-axis parameters according to the gear meshing principle, and performs shaping design optimization on the original tooth profile;
the invention not only avoids the difficulty of parameter selection of the traditional shape modification method, but also avoids the problems of unstable transmission, impact, interference and the like in the shape modification design due to the conformity with the plane meshing transmission characteristic, and provides a simple and efficient design method for the shape modification design of the internal meshing transmission gear.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
FIG. 1 is a flow diagram in accordance with one or more embodiments of the invention;
FIG. 2 is a schematic view of elliptical meshing lines for different half-axis parameters in accordance with one or more embodiments of the present invention;
FIG. 3 is a schematic view of the construction of an elliptical meshing line in accordance with one or more embodiments of the present invention;
FIG. 4 is a parametric schematic of an elliptical meshing line in accordance with one or more embodiments of the present invention;
FIG. 5 is a schematic view of a meshing line derived rack profile according to one or more embodiments of the present invention;
FIG. 6 is a schematic illustration of the instantaneous centerline and tooth profile engagement of an ring gear according to one or more embodiments of the present invention;
FIG. 7 is a schematic illustration of a known tooth profile conjugate thereto in accordance with one or more embodiments of the present invention;
FIG. 8 is a schematic illustration of a meshing line for a half-axis parameter of 80 in accordance with one or more embodiments of the present invention;
FIG. 9 is a schematic illustration of meshing lines for half-shaft parameters 140 in accordance with one or more embodiments of the present invention;
FIG. 10 is a schematic diagram of tooth profiles with half-axis parameters 80, 140 according to one or more embodiments of the present invention;
fig. 11 is a graph of the elliptical meshing line shaping effect of the present invention in accordance with one or more embodiments.
Detailed Description
Embodiment one:
the embodiment provides a method for designing and modifying the tooth profile of an internal engaged gear, as shown in fig. 1, an elliptic meshing line is constructed by utilizing the intersection point of the addendum circles and instantaneous center lines of two gears of internal engaged transmission, elliptic half-shaft parameters are set based on elliptic characteristics, and a rack tooth profile equation is constructed by utilizing the meshing theorem of the meshing line and the tooth profile of a rack through a plane meshing principle based on the constructed meshing line; constructing a conjugate tooth profile curve meshed with the rack according to a conjugate equation, wherein the conjugate tooth profile curve is an internal gear tooth top tooth profile curve and an external gear tooth top tooth profile curve; the conjugate principle is used to construct the tooth profile conjugate to the addendum profile curve and the modification of the gear profile is achieved by varying the elliptical half-axis parameters.
Specifically, the method comprises the following steps:
step one, constructing an addendum circle and an instantaneous center line of an internal meshing gear, solving an intersection point of the addendum circles and the instantaneous center line of the two meshing gears, constructing an elliptical arc line as a gear meshing line, establishing a tooth profile equation based on the elliptical arc line according to a plane meshing principle, and establishing a conjugate equation of internal meshing gear transmission on the basis:
constructing an internal meshing gear conjugate tooth top profile curve meeting the design of an elliptic meshing line, substituting a meshing line equation into the conjugate equation to obtain a corresponding relation between the elliptic meshing line and a conjugate tooth profile curve, and obtaining the conjugate tooth profile curve meeting the elliptic meshing line through coordinate transformation and calculation, wherein only the tooth top profile participates in meshing because the elliptic meshing line is positioned between a tooth top circle and an instantaneous center line, so that the obtained conjugate tooth profile curve is an internal gear tooth top profile curve and an external gear tooth top profile curve;
constructing tooth root profile curves of the internal gear and the external gear, and respectively constructing a tooth root profile curve of the external gear conjugate to the tooth root profile curve of the internal gear and the tooth root profile of the external gear conjugate to the tooth profile of the external gear according to a conjugate principle by knowing the tooth root profile curves of the internal gear and the external gear and the relative motion relation between the tooth root profile curves of the external gear and the external gear;
and fourthly, modifying the meshing line by changing the half-shaft parameter of the elliptic meshing line, and deducing the tooth profile of the internal meshing gear on the basis of the modification to achieve the design modification effect of the original tooth shape. Because the tooth profile obtained by this method is derived on the basis of the meshing line, no interference occurs.
Further, the construction process of the meshing line is as follows:
the corresponding gear tooth profile is formed by a given meshing line. During gear transmission, as the contact point slides on the meshing line, the track drawn on the gear coordinate system is the gear tooth profile curve participating in meshing. For the mesh line shape of an equal ratio gear pair, a corresponding pair of conjugate tooth forms is required. The speed vector of the two tooth profiles at the contact point is mutually perpendicular to the normal vector of the meshing line, so that stable and effective operation of gear transmission can be ensured.
As shown in fig. 2, an elliptical arc passing through the intersection point of the instantaneous line of the ring gear and the intersection point of the addendum circle is constructed, and the semi-axis parameters of the ellipse are given, so that different elliptical arc meshing lines can be obtained along with the change of the semi-axis parameters of the elliptical arc.
Further, an elliptical arc connecting the intersection points of the tooth top circles of the internal gear and the external gear and the instantaneous center line is used as a meshing line of the internal gear. As shown in fig. 3 and 4, P is the intersection point of the instantaneous line of the internal gear and the external gear, Q is the intersection point of the addendum circle of the internal gear and the external gear, PQ is a section of circular arc with the center connecting the points P and Q on the Y0 axis, for a given elliptical half-axis parameter a, according to the geometric principle, the other half-axis length B of the ellipse and the polar coordinate parameter θ of the elliptical arc can be conveniently solved, and the equation expression of the obtained elliptical arc meshing line on the coordinate system S0 is:
as shown in FIG. 4, O is the center of ellipse, and the length of OS is the parameter A, the length of OP can be represented by B because the modulus, tooth number and tooth crest coefficient of the internal and external gears are already determined, O 1 P、O 2 P、O 1 Q，O 2 The value of Q can be obtained by a parameter calculation formula of the gear.
In triangle O 1 O 2 The length of three sides in P is known, so that the value of any angle can be obtained;
the geometrical relationship of each side of the triangle can be known:
TQ, TP are the x, y coordinates of point Q in the fixed coordinate system, respectively, and therefore:
because the modulus and the tooth number of the inner gear and the outer gear are determined, the tooth crest coefficient is determined, and for any given elliptical half-axis parameter A, the unique determined B can be calculated by the formula (4) to form an ellipse, then the ellipse is an arcI.e. a uniquely defined line of engagement.
Further, the derivation of the new tooth profile includes the derivation of the rack tooth profile and the derivation of the gear tooth profile;
the deduction process of the tooth profile of the rack comprises the following steps:
first, as shown in fig. 5, S0 (P-X, Y) is a fixed coordinate system with the node P as the origin, sc (o-X, Y) is a coordinate system fixedly connected to the rack, and at the initial position, the two coordinate systems are coincident.
Let the expression of the meshing line on the rectangular coordinate system S0 be:
y＝f(x) (5)
further assume that the rack profile corresponding to the meshing line is expressed in the coordinate system Sc (o-X, Y) as
Y＝f(X) (6)
In the initial position, the rack tooth form is shown at solid line I and intersects with the meshing line at point A, which has a coordinate of (x 0 ＝X 0 ,y 0 ＝Y 0 ) According to the tooth engagement basic theorem, the normal to the tooth form y=f (X) at point a must pass through point P, i.e., its tangent at point a must be perpendicular to PA. Let the angle between PA and axis be alpha 0 Then the following must be satisfied:
it is also known from the basic theorem of tooth engagement that the normal to tooth form I at point B must also pass through point P, while the normal to tooth form I at point B and the tooth formThe normal at point B is parallel, i.e. it should also be at an angle α to the X axis, or:
from the formulae (7) and (8):
and because the ordinate of the point B is equal to that of the point B, the following can be obtained:
the expression of the rack profile is:
where C is an integral constant which may be dependent on the condition of the starting position (i.e., x=x 0 ,y＝y 0 When x=x 0 ,Y＝Y 0 ) And (5) determining. Since the meshing line passes through the node, the position of the rack tooth profile passing through the point P can be generally used as the starting position, namely, the condition is that x=x=0 and y=y=0, and the calculation is convenient.
If the meshing line is known as a polar expression:
dy＝(rcosθ+r′sinθ)dθ (13)
the rack profile expression is:
substituting the parameter expression of the elliptic equation to obtain the tooth profile of the elliptic meshing line rack:
a series of coordinate transformations are carried out according to the plane meshing principle, and the tooth profile of the elliptic meshing line rack can be further obtained, so that a gear tooth profile equation based on the elliptic meshing line can be obtained.
Further, the gear tooth profile derivation process includes elliptic meshing line-based gear tooth top tooth profile derivation, elliptic meshing line-based gear tooth root profile derivation;
the gear tooth top tooth profile deduction process based on the ellipse meshing line comprises the following steps:
assuming that the rotation center of the sun gear is O1, the rotation center of the inner gear is O2, a rectangular coordinate system S1: { O1, X1, Y1}, S2: { O2, X2, Y2} is fixedly connected with the sun gear and the inner gear respectively, a coordinate system S0: { O0, X0, Y0} is a fixed coordinate system, and P (O0) is a node, and then O0 is on a gear meshing action line.
Let phi 1, phi 2 be the rotation angle of the sun gear and the ring gear respectively, the transmission ratio is m12=phi 1/phi 2=z2/z 1, z2 be the number of teeth of the sun gear and the ring gear respectively, R1, R2 be the pitch radii of the sun gear and the ring gear respectively.
The equation expression of the elliptic arc meshing line on the coordinate system S0 is as follows:
since the elliptical arc meshing line is located between the tip circles and the instantaneous lines of the internal and external gears, only the tip tooth profiles participate in meshing, and the conjugate tooth profile constructed by the elliptical arc meshing line is the tip tooth profile of the internal and external gears.
Let the center of the sun gear 1 be fixedly connected with the gear 1 in the coordinate system 01 (x 1, y 1) in fig. 6, and the pitch circle radius of the gear is t. In the starting position, the tooth form of the tooth form is tangent to the rack at the point A on the meshing line, and when the rack moves leftwards by L distance, the central gear 1 rotates anticlockwise by phi 1 to be tangent to the rack at the point B on the meshing line, so that the tooth form is obtained:
the vector of the locus of the conjugate point on the meshing line on the rectangular coordinate system S1 is expressed as:
wherein M is 10 Is a rectangular coordinate system S 0 To S 1 Is a coordinate transformation matrix of (a).
Conjugate point on meshing line is in rectangular coordinate system S 2 The vector of the trace above is expressed as:
wherein M is 20 Is a rectangular coordinate system S 0 To S 2 Is a coordinate transformation matrix of (a).
Substituting the elliptic arc meshing line rack equation into the formula (17) to obtain:
order theThe expression of the conjugate addendum profile curve internal gear and the external gear of the elliptical arc meshing line obtained in the expression (18) and the expression of the addendum profile curve of the external gear are correspondingly substituted in the expression (22) and the expression (23):
it should be noted that r (θ) is a mathematical hidden function expression, and represents a parameter expression driven by the polar coordinate θ.
Given that the tooth top profile curves of the external gear and the internal gear are Γa1, Γa2, respectively, assuming that the external gear tooth root profile curve conjugated to the internal gear tooth top profile curve Γa2 is Γd1 (d is the tooth root profile) and the internal gear tooth root profile curve conjugated to the external gear tooth top profile curve Γa1 is Γd2, the equation for the external gear tooth root profile curve Γd1 may be expressed as:
further, the gear tooth root profile derivation process based on the elliptic meshing line is:
the tooth profile normal method finds the conjugate tooth profile, as shown in fig. 7, the instantaneous center line of the gear 1 is an arc of R1 with a radius, P is an instantaneous center point, and its position in the fixed coordinate system (P-x, y) is constant. Known tooth form a-a and coordinate system (O 1 -x 1 ,y 1 ) Together, in the starting position shown. If the normal to point M on a-a passes exactly through point P, it is a point of contact at this time. Assuming that the intersection point of the normal line of the other point M1 on the tooth form and the pitch circle is P1, in order to make M1 a contact point, the gear 1 and the tooth form a-a must be rotated together to reach the position of the broken line, and P reaches the position of the node P1, and at this time, the contact point position is M1. The rotation angle of the gear 1 is positive in the clockwise direction.
Likewise, m 'on a-a' 1 The intersection point of the normal line of the point and the pitch circle is p' 1 When the gear rotatesAngle p' 1 When turning to P, m' 1 The point becomes the contact point, since the gear is now rotated clockwise, therefore +.>The angle being negativeA kind of electronic device.
Set any point m on tooth form a-a 1 (x 1 ,y 1 ) Tangent to x 1 The included angle of the axes is gamma, and O 1 M is taken as 1 p 1 And is set with O 1 p 1 As can be seen from fig. 7, the included angle is ψ:
the a-a tooth form can be given by the equation for the corresponding calculated gamma angle in several different ways as follows:
the coordinates of any point on tooth form a-a are determined, the included angle gamma between the tangent line and x, axis of the point is calculated by (29), and the required rotation when the point becomes the contact point can be obtained by the formula (29)And (5) corners. Calculated Zhongzhi->The angle is positive and the tooth form is shown to be rotated counter-clockwise from the starting position to bring the point to the contact point position.
Substituting the conjugate top tooth profile curve equation of the internal gear and the external gear of the elliptic arc meshing line into (29) to solve gamma to obtain:
substituting the formulas (30), (31) into the formula (29) to obtain the external gear gamma 1 Analytical expression of corner (32):
will gamma 1 The analytic substitution of the angle (2-2-13) can be obtained by trigonometric function reductionValues of (2)
Wherein R is a constant corresponding to a particular half-axis parameter
Wherein R1 is the radius of the external gear, R2 is the radius of the internal gear, and ha1 and ha2 are the tooth top coefficients respectively. Internal gear gamma can be found in the same way 2 The expression:
substituting formulas (36), (37) into formula (29) to obtain internal gear gamma 2 Analytical expression for angle (39):
will gamma 2 The analysis of the angle is substituted (39) and is simplified by trigonometric function to obtainIs the value of (1):
to be calculatedSubstituting the values into formula (27) to obtain a corresponding transformation matrix, substituting the corresponding transformation matrix into formula (26) to obtain an internal gear tooth root profile curve Γd2 conjugated with the external gear tooth top profile curve Γa1, and simplifying the internal gear tooth root profile curve Γd2 by the following formula (41):
the same applies to the internal gear tooth root profile curve Γd1 conjugate to the external gear tooth top profile curve Γa2, and the internal gear tooth root profile curve Γd1 is reduced by the following formula (42):
as can be seen from fig. 11, compared with the conventional gear shaping which directly shapes the tooth profile by adopting curves such as parabola, arc line, involute and the like, the method has the defects of large difficulty in selecting the shaping quantity and poor controllability of the shaping effect, and the embodiment uses the characteristic of smooth and continuous oval meshing line and adjustability, derives the curve of the conjugated tooth profile of the gear by changing the oval half-axis parameter according to the gear meshing principle, and performs shaping design optimization on the original tooth profile; the method not only avoids the difficulty of parameter selection of the traditional shape modification method, but also avoids the problems of unstable transmission, impact, interference and the like in the shape modification design due to the conformity with the plane meshing transmission characteristics, and provides a simple and efficient design method for the shape modification design of the internal meshing transmission gear.
Embodiment two:
the present embodiment is based on the scheme described in the first embodiment, and is described by taking as an example a ring gear having the teeth number z1=38, z2=58, and m=5:
the half-axis parameter of the ellipse is selected to be 80, and the specific parameters are shown in table 1:
TABLE 1
Step one, constructing an elliptic meshing line of an inner meshing gear:
designing an elliptical arc, wherein the semi-axis parameter of the arc obtained according to the geometric principle is B=80 mm, and the radian maximum value of A= 98.0761mm is theta max = 0.83171rad, the equation is:
the pitch circle radius of the external gear and the internal gear is R 1 ＝z 1 ×m/2，R 2 ＝z 2 X m/2, according to the deduction, the corresponding relation between points on the elliptic meshing line and contact points on the conjugate tooth profile curve is obtained:
step two, constructing tooth profile curves of tooth tops of the inner gear and the outer gear:
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constructing tooth root profile curves of the external gear and the internal gear:
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the oval meshing line with the half-axis parameter 80 shown in fig. 8 is obtained through the steps.
Modifying the half-axis parameters of the ellipse to 140:
designing an elliptical arc, wherein the semi-axis parameter of the arc obtained according to the geometric principle is B=140mm, and the radian maximum value of A= 124.6384mm is theta max = 0.62066rad, the equation is:
and the other group of gear tooth profile parameter coordinates can be obtained by the same method:
/>
the ellipse meshing line is obtained when the half-axis parameter shown in fig. 9 is 140, and the tooth profiles of the half-axis parameters 80 and 140 are shown in fig. 10.
As can be seen from fig. 11, the gear transmission error is significantly improved after the elliptical meshing line is modified.
The foregoing description is only of the preferred embodiments of the present application and is not intended to limit the same, but rather, various modifications and variations may be made by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.
Claims (10)
1. A method of modifying a tooth profile design of an internally meshed gear, comprising:
an elliptic meshing line is constructed by utilizing the intersection point of the addendum circles and the instantaneous center line of the two gears of the internal meshing transmission; setting elliptical half-axis parameters based on elliptical characteristics;
based on the constructed elliptic meshing line, constructing a rack tooth profile equation by using a plane meshing principle and utilizing the meshing theorem of the elliptic meshing line and the rack tooth profile;
constructing a conjugate tooth profile curve meshed with the rack according to a conjugate equation, wherein the conjugate tooth profile curve is an internal gear tooth top tooth profile curve and an external gear tooth top tooth profile curve;
the conjugate principle is used to construct the tooth profile conjugate to the addendum profile curve and the gear profile modification scheme is obtained by changing the elliptical half-axis parameters.
2. The method for modifying the tooth profile design of an internally meshed gear according to claim 1, wherein the method for constructing the elliptical meshing line is as follows: and constructing an addendum circle and an instantaneous center line of the internal meshing gear, solving an intersection point of the addendum circles of the two meshing gears and the instantaneous center line, and constructing an elliptic arc line as a gear meshing line.
3. The method for designing and shaping the tooth profile of the internal gear according to claim 2, wherein given the semi-axis parameters of the ellipse, different elliptical arc meshing lines are obtained along with the change of the semi-axis parameters of the elliptical arc;
and solving the other half axial length A of the ellipse and the polar coordinate parameter theta of the elliptical arc according to the geometric principle for the set elliptical half axial parameter B to obtain an expression of the meshing line of the elliptical arc.
4. The method for modifying the tooth profile design of a ring gear according to claim 3, wherein the elliptic arc meshing line has the expression:
5. the method for designing and modifying the tooth profile of the internal engaged gear according to claim 1, wherein an internal engaged gear conjugate tooth top tooth profile curve meeting the design ellipse meshing line is constructed, a meshing line equation is substituted into a conjugate equation to obtain a corresponding relation between the ellipse meshing line and the conjugate tooth profile curve, and the conjugate tooth profile curve meeting the ellipse meshing line is obtained through coordinate transformation and calculation.
6. The ring gear tooth profile design modification method according to claim 1 or 5, wherein the internal gear tooth top profile curve is expressed as:
the external gear tooth top profile curve is expressed as:
wherein,,
7. the method of claim 1 wherein the tooth profile curves of the internal and external gears are constructed, the relative movement relationship of the internal and external gears and their tooth profile curves being known, and the tooth profile curves of the external gear and the tooth profile of the internal gear being conjugate to the tooth profile of the external gear being constructed separately according to the principle of conjugation.
8. The method of claim 1 or 7, wherein the external gear tooth profile curve is expressed as:
wherein,,
r1 is the radius of the external gear, R2 is the radius of the internal gear, and ha1 and ha2 are the tooth top coefficients respectively.
9. The method for modifying the tooth profile design of a ring gear according to claim 1, wherein the tooth profile of the ring gear is modified by changing the half-axis parameters of the elliptic meshing line, and the tooth profile of the ring gear is derived to obtain the original tooth profile design modification effect.
10. The method for modifying the tooth profile design of a ring gear according to claim 9, wherein the conjugate tooth profile is determined by a tooth form normal method.
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| CN117407989A (en) * | 2023-10-24 | 2024-01-16 | 辽宁工业大学 | Internal gear shaping design method based on meshing line with variable circle center |
| CN117407989B (en) * | 2023-10-24 | 2024-06-28 | 辽宁工业大学 | Internal gear shaping design method based on meshing line with variable circle center |
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