CN102513614A - Manufacturing method of worm gear pair - Google Patents
Manufacturing method of worm gear pair Download PDFInfo
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- CN102513614A CN102513614A CN2011104143458A CN201110414345A CN102513614A CN 102513614 A CN102513614 A CN 102513614A CN 2011104143458 A CN2011104143458 A CN 2011104143458A CN 201110414345 A CN201110414345 A CN 201110414345A CN 102513614 A CN102513614 A CN 102513614A
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Abstract
The invention relates to a manufacturing method of a worm gear pair, comprising steps as follows: step A, optimizing and simulating a planar secondary enveloping ring-surface worm gear pair, which comprises specific steps as follows: (A1) inputting basic parameters of the worm gear pair, such as the central distance a, the head number of the worm z1, and the gear number of the worm z2; (A2) leading the data of the previous step into a target function formula to perform parameter calculation; employing iteration and approximation of a complex method in the target function calculation process to obtain geometric parameters and technological parameters of the ring-surface worm gear pair, wherein the geometric parameters and the technological parameters are configured in a matched manner; and the target function formula is represented by FORMULA in which f(x) is a target function, Ai is a weighting coefficient, epsilon is a convergence coefficient, and K is an optimized parameter; and (A3) generating a three-dimensional graph of the worm; affirming that the worm has no undercutting and gear tip sharpening according to the three-dimensional graph of the worm; and step B, separately processing and manufacturing the worm and the gear of the worm gear pair according to the geometric parameters and the technological parameters.
Description
Technical Field
The invention belongs to the field of mechanical transmission, and relates to a method for manufacturing a worm gear pair, in particular to a method for manufacturing a planar double-enveloping worm gear pair. The invention can be applied to a worm transmission device, in particular to a screw-down device of a wide and thick plate rolling mill, and plays a role in pressing down a roller of the rolling mill.
Background
The worm transmission is a transmission device commonly used in mechanical equipment, wherein the enveloping worm transmission has the advantages of large bearing capacity, high transmission efficiency and long service life. Generally, a worm pair with a center distance of more than 500mm is called a large-center-distance worm pair; the number of the worm heads is more than 2, and the worm is called a multi-start worm pair.
In the initial stage, the application range of the ring surface is basically limited to the original linear enveloping ring surface worm, the reverse slope modification is used as a basic form, and the modification is a technology for purposefully changing the tooth thickness of the ring surface worm according to a certain rule so as to improve the performance of the worm pair (such as the bearing capacity of the ring surface worm pair). For a long time, the modification is an important measure for the processing and manufacturing of the enveloping worm and a key technology for improving the quality of the enveloping worm. The basis of the slope modification is to completely apply the concept of involute gear modification so as to reduce the adverse effects caused by manufacturing and installation errors and deformation caused by stress and temperature rise when the worm gear is meshed, and improve the bearing capacity by improving the transmission stability. The tooth profile of the original type enveloping worm is characterized in that: the tooth profile in the axial section of the worm is a straight line, and the tooth pitch and the tooth thickness on the concentric circle of the pitch circle of the worm wheel are equal. The original enveloping worm has a limit line on the tooth surface of the worm wheel, so that the meshing area is very small, and the exertion of the capacity of the enveloping worm is severely limited.
The invention relates to a 'plane two-in-one' worm gear pair, which is a novel ring surface worm gear pair invented by engineering technicians in China in the last 70 th century. It has better performance than original ring surface worm gear and common cylindrical worm gear.
The existing 'plane two-pack' worm pair has better performance under the condition of large transmission ratio (the transmission ratio is more than 35), and under the condition of a multi-head worm (medium and small transmission ratio), if parameters are not optimized, the performance can be greatly influenced. There is no reasonable tooth flank shape at all other than the root cause of undercut and tooth tip tapering. The grinding wheel with other shapes is used for grinding the worm instead of a plane grinding wheel in domestic exploration, certain progress is made, the problems of undercut and tooth crest sharpening are solved, and however, no obvious progress is made in the aspect of improving the bearing capacity.
In recent years, although some technical documents in the design and manufacture of the flat enveloping worm gear appear, for example, chinese patent: ZL 200610023387.8A three-dimensional solid modeling method for a toroidal worm; processing method of enveloping worm of ZL200810101196.8 hard tooth surface enveloping worm involute gear pair; ZL201020250672.5 is a numerical control grinder for double-conical enveloping worm, but still does not fundamentally solve the problems that a worm pair is designed by experiments and experiences and the transmission performance of a multi-head worm pair is unstable.
The above reasons cause the design and manufacture of the enveloping worm to be difficult, in particular to the design and manufacture of a large-center-distance multi-head plane secondary enveloping worm pair.
In the existing design literature of the enveloping worm, the essence of enveloping worm modification in journal 2004, 6 th year, of mechanical transmission, together with the difference between involute gear modification, is described in < article number: 1004-.
The curvature tooth form is an advanced enveloping worm tooth form proposed according to a great deal of experiments, practices and deep theoretical research. Based on the space meshing principle, the reasonable tooth form of the enveloping worm in the relative motion direction is explored and found, and the problem of optimal design of a plane secondary enveloping worm pair is solved. The performance of the 'plane two-pack' worm pair can be greatly improved. According to a comparison experiment, compared with the traditional enveloping worm, the curvature tooth-shaped enveloping worm can improve the bearing capacity by 10-20%.
Complete description of the curvature modification principle:
(1) the tooth form of the tooth surface of the enveloping worm relative to the motion direction is a main factor influencing the meshing performance of the worm pair.
(2) The reasonable tooth profile curve of the tooth surface of the enveloping worm in the relative motion direction is the curvature radius change curve of the tooth surface method of the worm.
(3) The three elements of the worm tooth profile (the extreme point, the rate of change, and the amount of inlet thinning) directly affect the position of the contact line on the worm gear tooth flank.
Disclosure of Invention
The object of the present invention is to provide a method for producing a worm gear in order to reduce or avoid the aforementioned problems.
In particular, the object of the invention is to provide a method for producing a worm gear, the parameters of which are optimized so that the performance of the produced worm gear is improved.
The technical scheme of the invention comprises the following steps:
a method of manufacturing a worm gear set comprising the steps of:
A. the optimized design and simulation of the planar double-enveloping ring surface worm gear pair comprise the following steps:
a1, inputting basic parameters of worm pair, center distance a and number z of worm heads1Number of teeth of worm gear z2；
A2, importing the data of the previous step into an objective function formula for parameter calculation, and obtaining the geometric parameters and the technological parameters of the enveloping worm pair by adopting iteration and approximation of a complex shape method in the objective function calculation process, wherein the geometric parameters and the technological parameters are set in a matching way,
the objective function formula is:
wherein f (x) is an objective function,
ai is a weighting coefficient, epsilon is a convergence coefficient, and k is an optimization parameter;
a3, generating a three-dimensional solid figure of the worm, and confirming that the worm does not have undercut and tooth top sharpening through the three-dimensional solid figure of the worm;
B. and respectively machining and manufacturing the worm and the worm wheel of the worm pair according to the geometrical parameters and the technological parameters.
In a preferred embodiment, in the step B, the worm is manufactured by a center distance displacement method, a transmission ratio displacement method, a variable center distance method, a variable transmission ratio method, or a composite method, based on the calculated geometric parameters and process parameters.
In a preferred embodiment, the tooth profile of the tooth flanks of the worm in the direction of relative movement meets the following condition:
de＝λdρ λ≥0
in the above formula:
de-the differential, or rate of change, of the amount of thinning of the tooth flanks of the worm;
dp is the differential, or rate of change, of the radius of curvature of the worm tooth surface method;
λ -coefficient.
In a preferred embodiment, the worm is a curved-tooth-shaped plane enveloping toroidal worm.
In a preferred embodiment, in the step B, the worm wheel is machined based on the calculated geometric parameters and the process parameters by using a hob having a tooth surface shape corresponding to the tooth surface shape of the worm, and the number of teeth of the process worm wheel is equal to the actual number of teeth of the worm wheel.
The embodiment of the invention has the following characteristics and advantages:
1. the manufacturing method of the worm pair optimizes the geometric parameters and the process parameters of the curvature tooth shape and the multi-head large-center-distance plane secondary enveloping worm pair device, and solves the problems of design and calculation of the geometric parameters and the process parameters of the curvature tooth shape and the multi-head large-center-distance plane secondary enveloping worm pair device; the reliability of the parameters is ensured, and the parameters are more advanced and reasonable than those obtained by experience or experiments, so that the reliability of the performance of the worm pair is ensured.
2. The three-dimensional graph, the distribution condition of the contact line and the undercut curve and the tooth-shaped curve of the worm can be obtained through computer simulation. Under the condition of medium and small transmission ratio, undercut and tooth top pointing are avoided.
3. The tooth surface of a hob of a processed worm gear is consistent with the tooth surface of a worm, and the tooth number of a process worm gear is the same as the actual tooth number of the worm (zero-tooth-difference process worm gear). The tooth surface of the worm is consistent with the ideal tooth shape without running in, and simultaneously, the conjugate relation between the worm wheel and the worm is ensured.
4. The bearing capacity of the worm gear of the embodiment of the invention is improved by 10-20% compared with that of a common plane enveloping ring surface worm gear under the condition of a multi-start worm (with a medium-small transmission ratio); the efficiency is improved by 3-6%.
Drawings
The drawings are only for purposes of illustrating and explaining the present invention and are not to be construed as limiting the scope of the present invention. Wherein,
fig. 1 is a schematic view of a worm gear arrangement of an embodiment of the present invention.
Fig. 2 is a graph of the radius of curvature of a tooth surface of a worm according to an embodiment of the present invention.
Detailed Description
In order to more clearly understand the technical features, objects, and effects of the present invention, embodiments of the present invention will now be described with reference to the accompanying drawings. Wherein like parts are given like reference numerals.
Some technical terms in this document are first described as follows:
a worm inlet: the worm is a driving part, and the tooth surface of the worm is firstly contacted with one end of the worm wheel.
A worm outlet: the worm is a driving part, and the tooth surface of the worm is finally separated from the end of the tooth surface of the worm wheel.
Center distance displacement: the center distance is different when the worm and the worm wheel are machined, but the center distance is not changed during machining.
The transmission ratio is changed: the gear ratio is different when the worm and the worm wheel are machined, but the gear ratio is not changed during machining.
The center distance is changed: when the worm is machined, the center distance is not a fixed value and changes at any time according to technological parameters.
And (3) changing the transmission ratio: when the worm is machined, the transmission ratio is not a fixed value and changes at any time according to technological parameters.
The compounding method comprises the following steps: the center distance displacement method, the transmission ratio displacement method, the variable center distance method and the variable transmission ratio method are combined randomly.
Root cutting: the abnormal concave area appears on the tooth root during the worm processing.
Tooth top sharpening: the tooth top widths of the two ends of the worm or worm gear hob are smaller than a specified value, and the using effect of the worm or hob is influenced.
The relation between the tooth profile of the worm and the curvature radius of the tooth surface is deduced according to the space meshing principle by the curvature modification principle, the optimal tooth profile of the enveloping worm is theoretically proved, and the optimal tooth profile is completely consistent with actual test and use results. The worm pair with excellent performance can be obtained only by processing the enveloping worm according to the curvature tooth form.
Different processing methods are adopted for different enveloping worms, and different geometric parameters and technological parameters are required. For a plane enveloping worm, special geometric parameters and technological parameters are needed to obtain an ideal curvature tooth form. Fig. 2 is a curvature profile according to an embodiment of the present invention.
In order to obtain the curvature tooth form, the invention provides a method for manufacturing a worm gear pair, which comprises the following steps:
A. the optimized design and simulation of the planar double-enveloping toroidal worm gear pair can be realized by adopting computer optimized design software, for example, the optimized design and simulation of the planar double-enveloping toroidal worm gear pair comprises the following steps:
a1, inputting basic parameters of worm pair, center distance a and number z of worm heads1Number of teeth of worm gear z2；
A2, importing the data of the previous step into an objective function formula for parameter calculation, and obtaining the geometric parameters and the technological parameters of the enveloping worm pair by adopting iteration and approximation of a complex shape method in the objective function calculation process, wherein the geometric parameters and the technological parameters are set in a matching way,
the objective function formula is:
wherein f (x) is an objective function,
ai is a weighting coefficient, epsilon is a convergence coefficient, and k is an optimization parameter;
a3, generating a three-dimensional solid figure of the worm, and confirming that the worm does not have undercut and tooth top sharpening through the three-dimensional solid figure of the worm;
B. and respectively machining and manufacturing the worm and the worm wheel of the worm pair according to the geometrical parameters and the technological parameters.
The worm pair manufacturing method of the embodiment of the invention solves the design and manufacturing problems of a curvature tooth shape, multi-head large-center-distance plane secondary enveloping worm pair device; the reliability of the performance of the worm pair is ensured. Furthermore, the embodiment of the invention is different from the traditional manufacturing technology of the planar double-enveloping ring surface worm gear pair in that the purpose of improving the performance of the multi-head (middle and small transmission ratio) planar enveloping ring surface worm gear pair can be realized by applying the advanced computer optimization simulation technology and adopting a novel processing method of a worm gear with curvature tooth shape and zero tooth difference.
The method for manufacturing the worm pair can be used for manufacturing the worm with the plane enveloping ring surface of the curvature tooth shape.
According to an embodiment of the present invention, the method for machining the worm may be a center distance displacement method, a transmission ratio displacement method, a variable center distance method, a variable transmission ratio method or a composite method according to the geometric parameters and the process parameters of the optimized worm gear pair. The method for machining the worm is suitable for various machining devices, a user can select the method according to specific conditions, and the result of optimal design can be guaranteed. The center distance displacement method and the transmission ratio displacement method are simple and can be implemented on a common ring surface worm processing machine tool. The center distance displacement method is adopted in the embodiment.
According to one embodiment of the invention, the worm wheel is machined according to the calculated geometric parameters and process parameters by adopting a hob with the shape consistent with the shape of the worm tooth surface, and the number of the process worm wheel is the same as the actual number of the worm wheel teeth (zero-tooth-difference process worm wheel) so as to ensure the conjugate relation between the worm wheel tooth surface and the worm tooth surface. Specifically, the worm wheel of the present embodiment can be processed by a dual method. Firstly, a normal-inserted hob is manufactured, and in order to ensure the conjugate relation between a worm wheel and a worm, the main processing parameters of the hob are consistent with those of a processed worm. The number of teeth of the process worm wheel is the same as the actual number of teeth of the worm wheel (zero-tooth-difference process worm wheel).
In this embodiment, the plane enveloping worm gear pair (as shown in fig. 1) processed according to the above steps has the following characteristics:
(1) the worm tooth surface is identical to the ideal tooth surface shape without running-in and is well meshed with the worm wheel tooth surface.
(2) The worm flanks do not undercut and the tooth tips become sharp.
(3) On the worm gear tooth surface, the first contact line of the worm inlet is at the inlet edge of the worm gear tooth surface; the last contact line of the outlet is arranged in the middle of the tooth surface of the worm wheel. The maximum working length of the worm is ensured, namely the maximum number of meshing teeth.
(4) The worm pair has good induction method curvature.
(5) The tooth profile of the worm tooth flanks in the direction of relative movement (tooth length direction or helical direction) meets the following condition:
de＝λdρ(λ≥0)
in the above formula:
de-the differential, or rate of change, of the amount of thinning of the tooth flanks of the worm.
dp-the differential, or rate of change, of the radius of curvature of the tooth surface of the worm.
Coefficient of lambda-
Specific examples will be given below of the method of manufacturing the worm gear pair described above.
Step A: the method comprises the following steps of optimally designing and simulating a planar double-enveloping ring surface worm gear pair, wherein the method comprises the following specific steps:
a1: setting the center distance a as 910mm and the number z of worm heads14, number of worm teeth z274. Selecting the worm type as a curvature tooth form;
a2: and D, importing the data in the step A into an objective function formula for parameter calculation. The optimization objectives can be set as follows:
(1) the meshing length of the worm tooth surface is more than 95%.
(2) The meshing area of the worm gear tooth surface is more than 90 percent.
(3) The thickness of the tooth top of the worm edge is more than 0.4 times of the modulus.
(4) The worm flanks have no undercuts.
(5) The worm has a curved profile.
In the calculation process, iteration and approximation of a complex shape method are adopted to obtain the geometric parameters and the technological parameters of the enveloping worm pair, and the obtained main basic parameters specifically comprise:
worm calculating circle diameter d1；
Number of teeth of worm gear: z';
diameter of main base circle: db；
Modification parameters are as follows: δ;
width of worm wheel: b;
tip arc offset of wormHeart volume: e.g. of the type1。
The remaining parameters are determined by the basic parameters and can be calculated from the parameters.
A3: and (3) viewing the three-dimensional graph of the worm on a computer screen, and further viewing a contact line graph, an undercut graph and a tooth profile graph of the worm to confirm that the worm meets the optimization design target, such as confirming that the worm does not have undercut and the tooth top is pointed.
And B: and machining and manufacturing the worm gear pair according to the calculated geometric parameters and technological parameters.
The geometric parameters and the process parameters optimized by the computer are matched, and the parameters in the geometric parameters and the process parameters cannot be modified randomly.
The machined worm gear pair of the example fully achieves the indexes of the optimization target.
According to the worm pair manufacturing method provided by the invention, the parameters of the enveloping worm pair and the technological parameters are obtained through iteration and approximation by utilizing the target function calculation; the geometric parameters and the process parameters of the curvature tooth profile and multi-head large-center-distance plane secondary enveloping worm gear pair device are optimally designed, so that the problems of design and calculation of the geometric parameters and the process parameters of the curvature tooth profile and multi-head large-center-distance plane secondary enveloping worm gear pair device are solved; the reliability of the parameters is ensured. More advanced and reasonable than parameters obtained by experience or experiment.
It should be appreciated by those of skill in the art that while the present invention has been described in terms of several embodiments, not every embodiment includes only a single embodiment. The description is given for clearness of understanding only, and it is to be understood that all matters in the embodiments are to be interpreted as including technical equivalents which are related to the embodiments and which are combined with each other to illustrate the scope of the present invention.
The above description is only an exemplary embodiment of the present invention, and is not intended to limit the scope of the present invention. Any equivalent alterations, modifications and combinations can be made by those skilled in the art without departing from the spirit and principles of the invention.
Claims (5)
1. A method of manufacturing a worm gear set comprising the steps of:
A. the optimized design and simulation of the planar double-enveloping ring surface worm gear pair comprise the following steps:
a1, inputting basic parameters of worm pair, center distance a and number z of worm heads1Number of teeth of worm gear z2；
A2, importing the data of the previous step into an objective function formula for parameter calculation, and obtaining the geometric parameters and the technological parameters of the enveloping worm pair by adopting iteration and approximation of a complex shape method in the objective function calculation process, wherein the geometric parameters and the technological parameters are set in a matching way,
the objective function formula is:
wherein f (x) is an objective function,
ai is a weighting coefficient, epsilon is a convergence coefficient, and k is an optimization parameter;
a3, generating a three-dimensional solid figure of the worm, and confirming that the worm does not have undercut and tooth top sharpening through the three-dimensional solid figure of the worm;
B. and respectively machining and manufacturing the worm and the worm wheel of the worm pair according to the geometrical parameters and the technological parameters.
2. The method for manufacturing a worm gear according to claim 1, wherein in the step B, the machining method for manufacturing the worm gear according to the calculated geometric parameter and the process parameter includes a center distance displacement method, a transmission ratio displacement method, a center distance variation method, a transmission ratio variation method, or a composite method.
3. Method for producing a worm gear according to claim 2, characterized in that the profile of the flanks of the worm in the direction of relative movement meets the following condition:
de＝λdρ λ≥0
in the above formula:
de-the differential, or rate of change, of the amount of thinning of the tooth flanks of the worm;
dp is the differential, or rate of change, of the radius of curvature of the worm tooth surface method;
λ -coefficient.
4. The method of manufacturing a worm screw pair according to claim 1, wherein the worm screw is a flat enveloping toroid worm screw with a curvature profile.
5. The method of manufacturing a worm gear set according to claim 1, wherein in the step B, the worm wheel is manufactured by using a hob having a tooth surface shape corresponding to the tooth surface shape of the worm, and the number of teeth of the worm wheel is the same as the actual number of teeth of the worm wheel.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104308279A (en) * | 2014-08-27 | 2015-01-28 | 薛明 | Method for processing hindley worm based on mathematical modeling macroprogram and product of hindley worm |
| CN104675926A (en) * | 2013-12-02 | 2015-06-03 | 洛阳世必爱特种轴承有限公司 | globoid worm gear transmission pair |
| CN112191946A (en) * | 2020-09-28 | 2021-01-08 | 河北涞博传动机械制造有限公司 | Method for generating point contact ring surface worm gear pair by double generating surfaces |
-
2011
- 2011-12-13 CN CN2011104143458A patent/CN102513614A/en active Pending
Non-Patent Citations (1)
| Title |
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| 文庆明 等: "平面二次包络环面蜗杆传动的优化设计", 《现代机械》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104675926A (en) * | 2013-12-02 | 2015-06-03 | 洛阳世必爱特种轴承有限公司 | globoid worm gear transmission pair |
| CN104308279A (en) * | 2014-08-27 | 2015-01-28 | 薛明 | Method for processing hindley worm based on mathematical modeling macroprogram and product of hindley worm |
| CN112191946A (en) * | 2020-09-28 | 2021-01-08 | 河北涞博传动机械制造有限公司 | Method for generating point contact ring surface worm gear pair by double generating surfaces |
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Application publication date: 20120627 |