CN114580099A - Method for accurately creating worm wheel digifax - Google Patents
Method for accurately creating worm wheel digifax Download PDFInfo
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- CN114580099A CN114580099A CN202210149760.3A CN202210149760A CN114580099A CN 114580099 A CN114580099 A CN 114580099A CN 202210149760 A CN202210149760 A CN 202210149760A CN 114580099 A CN114580099 A CN 114580099A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
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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
- F16H55/22—Toothed members; Worms for transmissions with crossing shafts, especially worms, worm-gears
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
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Abstract
The invention belongs to the technical field of computer digital-analog creation, and particularly relates to a method for precisely creating a worm wheel digital-analog, which comprises the steps of determining basic parameters of a worm wheel, then taking a default coordinate system of a system as a modeling coordinate system of the worm wheel, laying out the position of the worm wheel, and creating a cross section profile of a worm wheel tooth blank based on the layout of the position of the worm wheel; generating a gear blank of a worm wheel for a rotating surface based on the cross section profile of the gear blank; based on the layout of the position of the worm gear, a tooth space right tooth profile and a tooth space left tooth profile are created, and a tooth space profile is further created; and finally, forming a first tooth socket on the tooth blank based on the tooth socket profile, taking the worm wheel axis L as the center, and forming other tooth sockets on the tooth blank according to a tooth number z circular array, namely finishing the creation of the worm wheel digifax. In the technical scheme, the worm gear tooth profile curve is strictly determined according to the definition of an involute, the generated gear tooth profile is accurate in shape, no theoretical error exists, all calculation and graphic drawing are automatically completed by a macro program, the use is convenient, and manual operation errors can be avoided.
Description
Technical Field
The invention belongs to the technical field of computer digital-analog creation, and particularly relates to a method for precisely creating a worm wheel digital-analog.
Background
The worm gear and worm transmission is applied to transmission of motion and power between 90-degree staggered shafts, has a large transmission ratio and stable motion, and is the most basic mechanical part. With the rapid development and application of computer technology and three-dimensional design software, part design rapidly develops from two-dimensional to three-dimensional. The worm and gear transmission is equivalent to gear and rack transmission in the main section, the tooth profile curve of the worm gear in the main section is an involute, and the tooth space direction of the worm gear is a spiral line, so that the problem that a digital-analog is abnormally difficult to create in three-dimensional design software is solved.
The prior related patent is as disclosed in an invention patent with application number 201210443297.X named as 'a precise modeling method for worm wheel': the tooth profile curve is obtained by intercepting the worm teeth with a number of planes parallel along the main section of the worm wheel, each section being replicated in a fixed value array, creating a reference point for the array profile edge and connecting to a tooth profile curve, and then fitting the tooth profile curves on a number of such sections to the tooth slot surface. The conversion mathematical relationship involved in this method is quite complex and is difficult for the skilled person to understand, and the accuracy of the tooth flanks of the wheel is determined by the number of sections selected.
The prior related patent is as disclosed in the invention patent with application number 201910190492.8 and name 'a three-dimensional modeling method for extended involute worm gear hobbing': a three-dimensional digital model of the hob blade track is established by simulating the machining motion of the gear hobbing of the worm gear, and Boolean operation is carried out on the three-dimensional digital model and the digital model of the worm gear tooth blank to obtain the tooth socket of the worm gear. The method needs to establish a digital model of the hob and indirectly establishes the tooth socket.
The prior related patent, namely the invention patent with the application number of 201811564419.4 and the name of 'a modeling method of worm gear and worm', discloses a technical scheme which has the following problems: a) the number of auxiliary lines to be established is large, the operation is complex, and if a base circle and a reference circle are required to be established; b) the involute can be created only by manually using a 'regular curve' functional module provided by three-dimensional software, so that the possibility of realizing the involute by using a computer secondary development program is limited, and the manual operation efficiency is low; c) as in the previous patent, the physical characteristics of part of gear teeth of the worm are generated, and then Boolean operation (difference) is carried out on the gear teeth and a gear blank of the worm gear to obtain a gear tooth groove, so as to indirectly create the tooth groove; d) when the radius of the root circle of the worm wheel is smaller than that of the base circle, the generated involute does not intersect with the root circle, the method cannot generate the scanning characteristic of the worm gear teeth, and the tooth socket of the worm wheel cannot be created through Boolean operation.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for accurately creating a worm wheel digital-analog, which is a method for accurately and directly creating the worm wheel digital-analog in the three-dimensional environment of a computer.
The invention is realized by the following technical scheme:
a method of accurately creating a worm digifax, comprising the steps of:
s1, determining basic parameters of the worm wheel, including a modulus m, a tooth number z, a tooth profile angle alpha, a tooth blank thickness H, a worm reference circle diameter d1 and a worm head number z 1; the modulus m and the tooth profile angle alpha are selected according to the standard, and other parameters are determined by structural design;
s2, in the three-dimensional environment of the part design, the coordinate system of the default system is taken as the modeling coordinate system of the worm gear, and the position of the worm gear is laid out based on the modeling coordinate system, wherein the position comprises the determination of the worm gear axis L;
s3, in the three-dimensional environment of the part design, based on the layout of the worm gear positions in the step S2, a worm gear blank section outline is created;
s4, in a three-dimensional environment of part design, calling a rotator command, rotating by 360 degrees by taking a worm gear axis L as a rotation center and taking a tooth blank section outline as a rotation surface, and generating a tooth blank of the worm gear;
s5, respectively creating a tooth space right tooth profile and a tooth space left tooth profile based on the layout of the worm wheel positions in the step S2 in the three-dimensional environment of the part design;
s6, in a three-dimensional environment of part design, creating a tooth space profile based on a tooth space right tooth profile line and a tooth space left tooth profile line;
and S7, in a three-dimensional environment of part design, opening a first tooth socket on the tooth blank based on the tooth socket outline, taking the worm wheel axis L as the center, and forming the rest tooth sockets on the tooth blank according to a tooth number z circular array, namely completing the creation of a worm wheel digifax.
Preferably, in step S2, the step of laying out the positions of the worm gears includes the steps of:
s2-1, taking the coordinate origin O of the modeling coordinate system as the central point of the worm wheel;
s2-2, taking the intersection line of the xy plane and the yz plane as the worm wheel axis L;
s2-3, taking zx plane as the main section of the worm wheel;
s2-4, a worm axis Lc is created in the main cross-section parallel to the xy-plane and perpendicular to the worm wheel axis L.
Preferably, in step S2, the distance between the worm wheel axis L and the worm axis Lc is the worm wheel-worm center distance a, and a = (d1+ mz)/2.
Preferably, in the step 3, the step of creating the cross-sectional profile of the worm gear blank comprises the following steps:
s3-1, determining a modeling size based on the basic parameters;
s3-2, establishing an excircle bus CD, a side bus DA, a side bus BC and a bottom line AB of the worm wheel in a yz plane by combining basic parameters and modeling dimensions;
s3-3, combining the basic parameters and the modeling size, and creating a worm wheel throat circle by taking the worm axis Lc as the center of a circle in the yz plane;
and S3-4, finishing the excircle generatrix CD, the side generatrix DA, the side generatrix BC, the bottom line AB and the worm wheel throat circle by combining basic parameters and modeling dimensions to form a closed worm wheel gear blank section profile.
Preferably, the modeled dimensions in step S3-1 include a worm wheel outer circle radius rc and a worm wheel throat circle radius rg;
wherein, for the outer circle radius rc of the worm wheel:
when z1=1, rc = m (z + 4)/2;
when z1= 2-3, rc = m (z + 3.5)/2;
when z1=4~6, rc = m (z + 3)/2;
for the worm wheel throat radius rg, rg = a- (mz +2m)/2, and a represents the center distance of the worm wheel and worm.
Preferably, in the step S3-4, the outer circle bus CD, the side bus DA, the bottom line AB and the side bus BC are sequentially connected end to end and are in rectangular distribution; the bottom line AB is superposed with the axis L of the worm wheel, and the length of the bottom line AB is equal to the thickness H of the gear blank; the origin O is the midpoint of the bottom line AB.
Preferably, the step S5 of creating the tooth slot right tooth profile line and the tooth slot left tooth profile line includes the steps of:
s5-1, taking a coordinate origin O of a modeling coordinate system as a base circle center of the tooth profile involute, and continuously creating discrete points on n involutes on a zx plane on the basis of an X axis and a Z axis of the modeling coordinate system, wherein the value of n is 16-32;
s5-2, connecting the n discrete points into a smooth involute curve in sequence according to a spline command;
s5-3, in a zx plane, rotating the smooth involute curve clockwise around a worm wheel axis L by a certain angle theta to obtain a tooth space right tooth profile; wherein θ =3.1415/(4 × z) - (tan (α) - α);
and S5-4, in a zx plane, taking a yz plane as a symmetrical neutral plane, and mirroring the right tooth profile of the tooth socket to obtain the left tooth profile of the tooth socket.
Preferably, in step S5-2, the creating of the discrete point is to determine the coordinates (Xi, 0, Zi) of the discrete point, and the calculation formulas of Xi and Zi are as follows:
radius of reference circle r = mz/2;
radius rb = r × cos (α) of the base circle of the involute;
roll angle ω i = (i-1) × 0.05;
z value Zi = rb sin (ω i) -rb ω i cos (ω i) at point i;
the X value Xi = rb × cos (ω i) + rb × ω i sin (ω i) -r at the point i;
wherein i takes on the value of 1-n.
Preferably, in step S6, the step of creating the tooth slot profile includes the following steps:
s6-1, in a zx plane, establishing a root circle by taking a coordinate origin O of a modeling coordinate system as a circle center; wherein the root circle radius rf = mz/2-1.2 × m;
s6-2, comparing the radius rf of the tooth root circle with the radius rb of the involute base circle, and creating a tooth space profile according to the comparison result, specifically:
when Rf is more than or equal to rb, the upper vertexes of the tooth groove left tooth profile and the tooth groove right tooth profile are linearly connected, and the tooth groove left tooth profile, the tooth groove right tooth profile and the tooth root circle are matched to jointly enclose a closed tooth groove profile;
when rf is less than rb, respectively creating a tangent line pointing to the direction of the origin of coordinates O through the lower end points of the tooth space left tooth profile line and the tooth space right tooth profile line on a zx plane, wherein the tangent line penetrates through a tooth root circle; taking the created tangent as a tooth profile transition line in an involute base circle; the upper vertexes of the straight tooth groove left tooth profile and the tooth groove right tooth profile are adopted to cooperate with the tooth groove left tooth profile, the tooth groove right tooth profile, the tooth root circle and the tooth profile transition line to jointly enclose a closed tooth groove profile.
Preferably, in step S7, the step of forming the first tooth slot includes the steps of:
s7-1, intersecting the throat circle of the worm wheel with the zx plane to obtain an intersection point;
s7-2, calling a spiral line command, taking the worm axis Lc as the central line of the spiral line, taking the worm rotation direction as the rotation direction of the spiral line, and creating the spiral line with the pitch p of the spiral line through a crossing point; wherein the pitch of the helix p =3.1415 m z 1;
and S7-3, calling a slotting command in a three-dimensional environment of part design, taking the tooth socket outline as a tooth socket and slot body model, taking the spiral line as a slotted central curve, matching the tooth socket outline with the spiral line, and forming a tooth socket from the tooth blank.
Preferably, all the non-illustrated angles involved in the steps are in radian measure, and the basic parameters in step S1 are determined manually and input manually.
Preferably, the steps S1-S7 are programmed by computer language and then used as a macro program in three-dimensional design software to automatically run to obtain the required worm wheel digifax.
Preferably, the system is a three-dimensional design software CATIA, UG or PROE containing a three-dimensional environment required for modeling.
The invention has the following beneficial effects:
1) according to the technical scheme, a complete worm wheel digifax creating flow is designed according to the overall structure of the worm wheel, the local structures of the worm wheel are established one by one according to the structural characteristics of the worm wheel, the method is clear, simple and easy to operate, the worm wheel digifax is not required to be generally simplified and processed when being created, the finally created worm wheel digifax can not only present clear appearance, but also can meet the analysis requirements during subsequent use.
2) Compared with the prior art, the technical scheme has the advantages that the mathematical relation among the local sizes of the worm wheel is established according to the structure of the worm wheel, and the method is simple and easy to understand;
3) according to the technical scheme, firstly, a spiral line and a tooth space profile are established according to the structural characteristics of the worm gear, and the tooth blank is grooved in a mode of matching the tooth space profile with the spiral line, so that compared with the prior art, the technical scheme has no theoretical error and the shape of the gear tooth is more accurate;
4) compared with the prior art, the technical scheme adopts a mode of directly establishing the tooth socket without establishing a hob digifax, so that the worm wheel establishing work is simpler; '
5) In the technical scheme, the worm gear tooth profile curve is strictly determined according to the definition of an involute, and the generated gear profile is accurate in shape and free of theoretical error; the steps of generating the gear blank and the gear slot are encapsulated into a computer macro program, all calculation and drawing are automatically completed by the macro program, errors caused by manual operation are avoided, and the method is convenient for common personnel to use.
Drawings
FIG. 1 is a schematic diagram of a modeled reference coordinate system structure;
FIG. 2 is a schematic cross-sectional profile structure of the resulting tooth blank;
FIG. 3 is a schematic view of the resulting tooth blank structure;
FIG. 4 is a schematic view of the structure of creating discrete points on n involutes (hidden tooth blank);
FIG. 5 is a schematic view of the structure of connecting discrete points on n involutes into an involute curve (hidden tooth blank);
FIG. 6 is a schematic view of the tooth slot right tooth profile configuration resulting from rotation of the involute curve (hidden tooth blank);
FIG. 7 is a schematic view of a tooth slot left tooth profile line structure (hidden tooth blank) obtained by mirroring the tooth slot right tooth profile;
FIG. 8 is a schematic view of the resulting tooth slot profile structure (hidden tooth blank);
FIG. 9 is a schematic view of the intersection of the worm wheel throat circle and the zx plane (hidden tooth blank);
FIG. 10 is a schematic view of the helical structure being generated (hidden tooth blank);
FIG. 11 is a schematic view of a first tooth slot cut in the tooth blank;
FIG. 12 is a schematic view of a circular array of tooth slots in a tooth blank;
in the figure:
1. an xy plane; 2. zx plane; 3. a worm axis Lc; 4. the yz plane; 5. a worm gear axis L; 6. a coordinate origin O; 7. point A; 8. a point D; 9. a worm wheel throat circle; 10. point C; 11. the cross section profile of the gear blank; 12. point B; 13. a tooth blank; 14. a point on the involute; 15 involute curves, 16 tooth space right tooth profiles; 17. a tooth slot left tooth profile; 18. root circle; 19. a gullet profile; 20. a point of intersection; 21. a helical line; 22. and (6) grooving.
Detailed Description
The invention is further described in the following with reference to the drawings and examples, but it should not be understood that the invention is limited to the examples below, and variations and modifications in the field of the invention are intended to be included within the scope of the appended claims without departing from the spirit of the invention.
The present embodiment discloses a method for accurately creating a worm wheel digifax, and as a preferred embodiment of the present invention, a right-handed worm wheel with a module m =3.15, a number of teeth z =40, a tooth profile angle α =0.349(20 °), a thickness H =30 of a tooth blank 13, a worm pitch circle diameter d1=35.5, and a number of worm heads z1=1 is taken as an example (all unexplained angles are in radian system), and is programmed in a computer language and then used as a macro program in three-dimensional design software, and automatically runs to obtain a required worm wheel digifax. The method specifically comprises the following steps:
and S1, determining basic parameters of the worm wheel, including a module m =3.15, the number of teeth z =40, a tooth profile angle alpha 0.349, the thickness H =30 of the gear blank 13, the pitch circle diameter d1=35.5 of the worm and the number of heads z1= 1. Further, the aforementioned basic parameters are manually determined and manually input.
S2, as shown in FIG. 1, in the three-dimensional environment of the part design, the default coordinate system of the system (the system is the three-dimensional design software CATIA, UG or PROE containing the three-dimensional environment required for modeling) is taken as the modeling coordinate system of the worm gear, and the position of the worm gear is laid out based on the modeling coordinate system, wherein the determination of the worm gear axis L5 is included. Specifically, the method comprises the following steps:
s2-1, taking the coordinate origin O6 of the modeling coordinate system as the central point of the worm wheel;
s2-2, taking the intersection line of the xy plane 1 and the yz plane 4 as a worm wheel axis L5;
s2-3, taking zx plane 2 as the main section of the worm wheel;
s2-4, a worm axis Lc3 is created in the main section plane parallel to the xy-plane 1 and perpendicular to the worm wheel axis L5.
Wherein, the distance between the worm wheel axis L5 and the worm axis Lc3 is the worm wheel-worm center distance a, and a = (d1+ mz)/2= 80.75.
S3, creating a cross-sectional profile 11 of the worm gear blank based on the layout of the positions of the worm gears in step S2, as shown in fig. 2, in a three-dimensional environment of the part design; specifically, the method comprises the following steps:
s3-1, determining modeling dimensions based on basic parameters, including the radius rc of the outer circle of the worm wheel and the radius rg of the throat circle 9 of the worm wheel;
wherein, for the outer circle radius rc of the worm wheel:
when z1=1, rc = m (z + 4)/2;
when z1= 2-3, rc = m (z + 3.5)/2;
when z1=4~6, rc = m (z + 3)/2;
in this embodiment, when z1=1, rc = m (z +4)/2= 69.3;
for the radius rg of the wheel throat 9, rg = a- (mz +2m)/2= 14.6.
S3-2, combining basic parameters and modeling dimensions, creating an excircle bus CD (formed by connecting a point C10 and a point D8), a side bus DA (formed by connecting a point D8 and a point A7), a side bus BC (formed by connecting a point B12 and a point C10) and a bottom line AB (formed by connecting a point A7 and a point B12) of the worm wheel in the yz plane 4;
s3-3, combining basic parameters and modeling dimensions, and creating a worm wheel throat circle 9 in the yz plane 4 by taking the worm axis Lc3 as the center of a circle;
and S3-4, finishing the excircle generatrix CD, the side generatrix DA, the side generatrix BC, the bottom line AB and the worm wheel throat circle 9 by combining basic parameters and modeling dimensions to form a closed worm wheel gear blank section outline 11. Further, the outer circle bus CD, the side bus DA, the bottom line AB and the side bus BC are sequentially connected end to end and are matched to be in rectangular distribution; the bottom line AB coincides with the worm wheel axis L5, and the length of the bottom line AB is equal to the thickness H of the gear blank 13; the origin O is the midpoint of the bottom line AB.
S4, in the three-dimensional environment of the part design, a rotator command is called to rotate 360 ° with the worm wheel axis L5 as the rotation center and the tooth blank cross-sectional profile 11 as the rotation plane, to produce the tooth blank 13 of the worm wheel, as shown in fig. 3.
S5, in the three-dimensional environment of the part design, the tooth-space right-tooth profile line and the tooth-space left-tooth profile line 17 are created based on the layout of the worm wheel positions in step S2, respectively. Specifically, the method comprises the following steps:
s5-1, taking a coordinate origin O6 of a modeling coordinate system as a base circle center of the tooth profile involute, and continuously creating discrete points on n involutes on a zx plane 2 on the basis of an X axis and a Z axis of the modeling coordinate system, as shown in FIG. 4, wherein the value of n is 16-32;
s5-2, sequentially connecting the n discrete points to form a smooth involute curve according to a spline command, as shown in fig. 5, that is, determining coordinates (Xi, 0, Zi) of the discrete points, wherein the calculation formulas of Xi and Zi are as follows:
radius of reference circle r = mz/2= 63;
radius rb = r × cos (α) =59.2 of the base circle of the involute;
roll angle ω i = (i-1) × 0.05;
z value Zi = rb sin (ω i) -rb ω i cos (ω i) at point i;
the X value Xi = rb × cos (ω i) + rb × ω i sin (ω i) -r at the point i;
wherein i takes values of 1-n, n takes values of 18, and i takes values of 1-18.
S5-3, in zx plane 2, rotating the smooth involute curve clockwise around the worm wheel axis L5 by a certain angle theta to obtain a tooth space right tooth profile, as shown in FIG. 6; wherein θ =3.1415/(4 × z) - (tan (α) - α) = 0.019635;
s5-4, in zx plane 2, with yz plane 4 as the neutral plane of symmetry, mirroring the tooth slot right profile to obtain tooth slot left profile 17, as shown in FIG. 7.
S6, creating a tooth slot profile 19 based on the tooth slot right tooth profile and the tooth slot left tooth profile 17 in a three-dimensional environment of the part design. Specifically, the method comprises the following steps:
s6-1, in zx plane 2, taking coordinate origin O6 of the modeling coordinate system as a center of a circle, and creating a root circle 18; wherein the root circle 18 radius rf = mz/2-1.2 m = 59.22;
s6-2, comparing the radius rf of the tooth root circle 18 with the radius rb of the involute base circle, and creating a tooth space profile 19 according to the comparison result, as shown in FIG. 8, specifically:
when Rf is more than or equal to rb, the upper vertexes of the tooth space left tooth profile line 17 and the tooth space right tooth profile line are connected linearly, and the tooth space left tooth profile line 17, the tooth space right tooth profile line and the tooth root circle 18 are matched to enclose a closed tooth space outline 19 together;
when rf is less than rb, the tooth space left tooth profile line 17 and the tooth space right tooth profile line do not intersect with the tooth root circle 18, and a closed tooth profile cannot be formed, on the zx plane 2, a tangent line pointing to the direction of the coordinate origin O6 is created through the lower end points of the tooth space left tooth profile line 17 and the tooth space right tooth profile line respectively, and the tangent line penetrates through the tooth root circle 18; taking the created tangent as a tooth profile transition line in an involute base circle; a closed tooth space profile 19 is defined by matching the tooth space left tooth profile line 17, the tooth space right tooth profile line, the tooth root circle 18 and the tooth space transition line together by adopting the upper vertexes of the straight tooth space left tooth profile line 17 and the tooth space right tooth profile line.
In the embodiment, the radius rf =59.22 of the root circle 18 is greater than the radius rb =59.2 of the base circle, the upper vertexes of the tooth groove left tooth profile line 17 and the tooth groove right tooth profile line are connected in a straight line, and the tooth groove left tooth profile line 17, the tooth groove right tooth profile line and the root circle 18 are matched to form a closed tooth groove profile 19 together.
And S7, in a three-dimensional environment of part design, opening a first tooth slot on the tooth blank 13 based on the tooth slot profile 19, taking the worm wheel axis L5 as the center, and circularly arraying the rest tooth slots on the tooth blank 13 according to the tooth number z =40, namely completing the creation of a worm wheel digifax, as shown in FIG. 12. Specifically, the step of forming the first tooth groove comprises the following steps:
s7-1, intersecting the worm wheel throat circle 9 with the zx plane 2 to obtain an intersection point 20, as shown in FIG. 9;
s7-2, calling a spiral line 21 command, taking a worm axis Lc3 as a center line of the spiral line 21, taking a worm rotation direction as a rotation direction of the spiral line 21, and creating the spiral line 21 through an intersection point 20 at a pitch p of the spiral line 21, as shown in FIG. 10; wherein the pitch p =3.1415 m z1=9.896 of the helix 21;
s7-3, in a three-dimensional environment of part design, calling a slotting command, taking the tooth socket outline 19 as a tooth socket and slot body model, taking the spiral line 21 as a central curve of slotting, matching the tooth socket outline 19 with the spiral line 21, and slotting from the tooth blank 13, as shown in FIG. 11. Specifically, the tooth space profile 19 rotates around the spiral line 21 and moves on the spiral track of the spiral line 21, so that the first tooth space is formed on the tooth blank.
The above examples are only for illustrating the present invention and are not intended to limit the scope of the present invention.
Claims (13)
1. A method of accurately creating a worm digifax, comprising the steps of:
s1, determining basic parameters of the worm wheel, including a modulus m, a tooth number z, a tooth profile angle alpha, a tooth blank (13) thickness H, a worm reference circle diameter d1 and a worm head number z 1; wherein, the modulus m and the tooth form angle alpha are selected according to the standard, and other parameters are determined by the structural design;
s2, in the three-dimensional environment of the part design, the coordinate system of the default system is the modeling coordinate system of the worm gear, and the position of the worm gear is arranged based on the modeling coordinate system, wherein the position comprises the determination of the worm gear axis L (5);
s3, in the three-dimensional environment of the part design, based on the layout of the worm gear position in the step S2, creating a worm gear tooth blank section outline (11);
s4, in a three-dimensional environment of part design, calling a rotator command, rotating 360 degrees by taking a worm wheel axis L (5) as a rotation center and taking a tooth blank section outline (11) as a rotation surface, and generating a tooth blank (13) of the worm wheel;
s5, respectively creating a tooth space right tooth profile and a tooth space left tooth profile (17) based on the layout of the worm wheel positions in the step S2 in the three-dimensional environment of the part design;
s6, creating a tooth slot profile (19) based on the tooth slot right tooth profile and the tooth slot left tooth profile (17) in a three-dimensional environment of part design;
s7, in a three-dimensional environment of part design, a first tooth groove is formed in the tooth blank (13) based on the tooth groove profile (19), the worm wheel axis L (5) is taken as the center, and the rest tooth grooves are circularly arrayed on the tooth blank (13) according to the tooth number z, namely the creation of a worm wheel digifax is completed.
2. The method for accurately creating the worm-gear digital-analog as claimed in claim 1, wherein: in step S2, the step of laying out the positions of the worm wheels includes the steps of:
s2-1, taking a coordinate origin O (6) of the modeling coordinate system as a central point of the worm wheel;
s2-2, taking the intersection line of the xy plane (1) and the yz plane (4) as the worm wheel axis L (5);
s2-3, taking a zx plane (2) as the main section of the worm wheel;
s2-4, a worm axis Lc (3) is created in the main cross section plane parallel to the xy-plane (1) and perpendicular to the worm wheel axis L (5).
3. The method for accurately creating the worm-gear digital-analog as claimed in claim 2, wherein: in step S2, the distance between the worm wheel axis L (5) and the worm axis Lc (3) is the worm wheel-worm center distance a, and a = (d1+ mz)/2.
4. The method for accurately creating the worm-gear digital-analog as claimed in claim 2, wherein: in the step 3, the step of creating the cross-sectional profile (11) of the worm gear blank comprises the following steps:
s3-1, determining a modeling size based on the basic parameters;
s3-2, creating an excircle bus CD, a side bus DA, a side bus BC and a bottom line AB of the worm wheel in a yz plane (4) by combining basic parameters and modeling dimensions;
s3-3, combining basic parameters and modeling dimensions, and creating a worm wheel throat circle (9) in a yz plane (4) by taking a worm axis Lc (3) as a center of a circle;
and S3-4, finishing the excircle generatrix CD, the side generatrix DA, the side generatrix BC, the bottom line AB and the worm wheel throat circle (9) by combining basic parameters and modeling dimensions to form a closed worm wheel gear blank section profile (11).
5. The method for accurately creating the worm-gear digital-analog as claimed in claim 4, wherein: the modeled dimensions in the step S3-1 include a worm wheel outer circle radius rc and a worm wheel throat circle (9) radius rg;
wherein, for the outer circle radius rc of the worm wheel:
when z1=1, rc = m (z + 4)/2;
when z1= 2-3, rc = m (z + 3.5)/2;
when z1=4~6, rc = m (z + 3)/2;
for the radius rg of the worm wheel throat circle (9), rg = a- (mz +2m)/2, and a represents the center distance of the worm wheel and the worm.
6. The method for accurately creating the worm-gear digital-analog as claimed in claim 4, wherein: in the step S3-4, the excircle bus CD, the side bus DA, the bottom line AB and the side bus BC are sequentially connected end to end and are matched to be in rectangular distribution; the bottom line AB is superposed with the worm wheel axis L (5), and the length of the bottom line AB is equal to the thickness H of the gear blank (13); the origin O is the midpoint of the bottom line AB.
7. The method for accurately creating the worm-gear digital-analog as claimed in claim 4, wherein: in step S5, creating a tooth slot right tooth profile and a tooth slot left tooth profile (17) comprises the steps of:
s5-1, taking a coordinate origin O (6) of a modeling coordinate system as a base circle center of a tooth profile involute, and continuously creating discrete points on n involutes on a zx plane (2) on the basis of an X axis and a Z axis of the modeling coordinate system, wherein the value of n is 16-32;
s5-2, connecting the n discrete points into a smooth involute curve in sequence according to a spline command;
s5-3, in a zx plane (2), rotating the smooth involute curve clockwise around a worm wheel axis L (5) by a rotation angle theta to obtain a tooth space right tooth profile; wherein θ =3.1415/(4 × z) - (tan (α) - α);
s5-4, in the zx plane (2), taking the yz plane (4) as a symmetrical neutral plane, and mirroring the tooth space right tooth profile to obtain the tooth space left tooth profile (17).
8. The method for accurately creating a worm digifax as recited in claim 7, wherein: in step S5-2, the step of creating the discrete point is to determine the coordinates (Xi, 0, Zi) of the discrete point, and the calculation formulas of Xi and Zi are as follows:
radius of reference circle r = mz/2;
radius rb = r × cos (α) of the base circle of the involute;
roll angle ω i = (i-1) × 0.05;
z value Zi = rb sin (ω i) -rb ω i cos (ω i) at point i;
the X value Xi = rb × cos (ω i) + rb × ω i sin (ω i) -r at the point i;
wherein i takes a value of 1-n.
9. The method for accurately creating a worm digifax as recited in claim 8, wherein: in step S6, creating a tooth slot profile (19) includes the steps of:
s6-1, in a zx plane (2), taking a coordinate origin O (6) of a modeling coordinate system as a center, and creating a root circle (18); wherein the root circle (18) has a radius rf = mz/2-1.2 × m;
s6-2, comparing the radius rf of the tooth root circle (18) with the radius rb of the involute base circle, and creating a tooth space profile (19) according to the comparison result, specifically:
when Rf is more than or equal to rb, the upper vertexes of the tooth space left tooth profile (17) and the tooth space right tooth profile are linearly connected, and the tooth space left tooth profile (17), the tooth space right tooth profile and the tooth root circle (18) are matched to jointly enclose a closed tooth space profile (19);
when rf is less than rb, respectively passing through the lower end points of the left tooth profile line (17) and the right tooth profile line of the tooth socket on the zx plane (2) to create a tangent line pointing to the direction of a coordinate origin O (6), wherein the tangent line runs through a root circle (18); taking the created tangent as a tooth profile transition line in an involute base circle; a closed tooth space profile (19) is defined by adopting the upper vertexes of the left tooth space profile (17) and the right tooth space profile of the linear tooth space and matching the left tooth space profile (17), the right tooth space profile, the root circle (18) and the tooth space transition line of the tooth space.
10. The method of accurately creating a worm digifax as recited in claim 9, wherein: in step S7, the step of forming the first tooth slot includes the steps of:
s7-1, intersecting the throat circle (9) of the worm wheel with the zx plane (2) to obtain an intersection point (20);
s7-2, calling a spiral line (21) command, taking a worm axis Lc (3) as a central line of the spiral line (21), taking a worm rotation direction as a rotation direction of the spiral line (21), and creating the spiral line (21) through an intersection point (20) according to a pitch p of the spiral line (21); wherein the pitch p =3.1415 m z1 of the helix (21);
s7-3, in a three-dimensional environment of part design, calling a slotting command, taking a tooth socket profile (19) as a tooth socket and slot body model, taking a spiral line (21) as a central curve of slotting, matching the tooth socket profile (19) with the spiral line (21), and slotting from a tooth blank (13).
11. A method of accurately creating a worm digifax as claimed in any one of claims 1-10, wherein: the non-illustrated angles involved in all steps are in the radian measure, and the basic parameters in step S1 are manually determined and manually input.
12. A method of accurately creating a worm digifax as claimed in any one of claims 1-10, wherein: and S1-S7 are programmed by computer language and then used as a macro program in three-dimensional design software to automatically run to obtain the required worm wheel digifax.
13. A method of accurately creating a worm digifax as claimed in any one of claims 1-10, wherein: the system is three-dimensional design software CATIA, UG or PROE which contains three-dimensional environment required by modeling.
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| CN117786900B (en) * | 2024-02-28 | 2024-05-17 | 烟台环球机床装备股份有限公司 | Mathematical physical method for modeling worm |
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