CN101334090A - Worm gear device and manufacturing method thereof - Google Patents

Abstract

The worm gear of the present invention is provided by finding the tolerance of the axial maximum meshing position of the worm shaft with respect to the worm wheel which is higher than that of the conventional worm gear.

Description

Worm gear device and manufacturing method thereof

technical field

The present invention generally relates to a worm gear including an intermeshing worm shaft and a worm wheel and a method of manufacturing the same, and more particularly to a Niemann type worm gear and a method of manufacturing the same. The Niemann-type worm gear device includes a Niemann-type worm shaft and a Niemann-type worm gear.

Background technique

Various worm gear devices have been proposed so far, and they are used especially in the field of motor vehicles. Worm gears are sometimes referred to simply as "worm gears".

One of the worm gears is disclosed in Japanese Published Utility Model Application (Jikkaihei) 4-562,50. The worm gearing shown in the publication is of the Niemann type comprising a Niemann type worm shaft and a Niemann type worm wheel which are operatively engaged or meshed in use. This type of worm shaft and worm gear has arcuate continuous ribs (or helical ridges) and arcuate teeth, respectively. Due to this Niemann-type characteristic, the continuous ribs and teeth of the worm gear have a larger tooth width, and therefore, the continuous ribs and teeth of the Niemann-type worm gear can have increased mechanical strength.

Contents of the invention

However, such Niemann-type worm shafts and worm gears are complex in structure and shape, and therefore, the manufacture of such worm shafts and worm gears requires a very advanced thread cutting technology, thereby resulting in high-cost products of the worm gear device.

It is therefore an object of the present invention to provide a Niemann-type worm gear which has satisfactory mechanical strength and which can be manufactured without requiring very advanced thread cutting techniques.

Another object of the present invention is to provide a method of manufacturing such a worm gear.

According to a first object of the present invention there is provided a worm gear arrangement comprising a worm wheel having teeth equidistantly spaced around it, each tooth of the worm wheel having a circular convex outer surface on each side, Each groove bounded by two adjacent teeth of the worm wheel has a curved base with a first radius of curvature; and a worm shaft with a helical tooth ridge with a circular recess on each side Into the outer surface, the helical ridge meshes with the teeth of the worm wheel and has a second radius of curvature smaller than the first radius of curvature, wherein the engagement between each tooth of the worm wheel and the helical ridge of the worm shaft is described in the characteristic diagram The first characteristic line represents the characteristic graph showing the relationship between the allowable error of the maximum meshing position of the worm shaft in the axial direction relative to the worm wheel and the radius ratio between the first radius of curvature and the second radius of curvature, wherein the reference worm wheel The meshing between each tooth and the helical tooth ridge of the reference worm shaft, each tooth of the reference worm having a flat outer surface on each side, and the helical tooth ridge of the reference worm shaft is represented by the second characteristic line in said characteristic diagram has a flat outer surface on each side; wherein the first characteristic line and the second characteristic line in the characteristic diagram intersect at a given point; and wherein the meshing between each tooth of the worm wheel and the helical tooth ridge of the worm shaft is consistent with the first A portion of a characteristic line coincides, the portion being drawn when the ratio of the radii is equal to or greater than a predetermined value representing or corresponding to a fixed point where the first and second characteristic lines intersect.

According to a second aspect of the present invention there is provided a method of manufacturing a worm wheel for engagement with a worm shaft having helical ridges with circular concave outer surfaces on each side, the The method comprises: preparing a circular plate blank; and cutting a cylindrical peripheral portion of the circular plate blank to form equally spaced teeth thereabout, each tooth having a circular convex outer surface on each side, The circular convex outer surface is shaped to closely engage the circular concave outer surface of the helical tooth ridge of the worm shaft when a proper fit is formed between the worm shaft and the worm wheel, wherein the The radius of curvature of the curved bottom of each groove is greater than the radius of curvature of the helical tooth ridge of the worm shaft.

According to a third aspect of the present invention there is provided a method of manufacturing a worm shaft having a helical ridge having a circular convex outer surface on each side, the method comprising: preparing a cylinder of the worm shaft blank; cutting the outer surface of the cylindrical blank to form helical tooth ridges adjacent thereto, thereby producing a semi-finished worm shaft; and subjecting the semi-finished worm shaft to surface finishing without heat treatment.

Description of drawings

Other objects and advantages of the present invention will become apparent from the following description when considered in conjunction with the accompanying drawings, in which:

Fig. 1 is a perspective view of an electric steering device for a motor vehicle, on which the worm gear device of the present invention is actually applied;

Fig. 2 is a sectional view cut along line II-II in Fig. 1;

Fig. 3 is a sectional view cut along line III-III in Fig. 1;

Fig. 4 is the perspective view of the worm shaft of the worm gear device of the present invention installed on the electric power steering device shown in Fig. 1;

Figure 5 is an enlarged cross-sectional view of a part of the worm shaft helical tooth ridge (or continuous rib) taken along the line V-V in Figure 4;

Figure 6 is a view similar to Figure 5 but showing an enlarged cross-sectional view of a conventional worm shaft helical ridge;

FIG. 7 is a plan view, partially broken away, of a worm wheel of a worm gear assembly of the present invention which will engage the worm shaft of FIG. 4;

Fig. 8 is a sectional view taken along line VIII-VIII in Fig. 7;

Fig. 9 is an enlarged sectional view cut along line IX-IX in Fig. 8;

Fig. 10 is a graph simply showing the mechanical strength (i.e., yield strength) of the worm wheel of the device of the present invention and the worm wheel of a conventional worm gear device;

Fig. 11 is an enlarged cross-sectional view showing a state in which the worm shaft and the worm wheel of the worm gear device of the present invention are operatively engaged;

Figure 12 is an enlarged cross-sectional view showing details of engagement between the worm shaft and the worm wheel of the worm gear device of the present invention;

13A-13D are schematic diagrams showing the production process of the worm shaft of the worm gear device of the present invention and the production process of the traditional worm shaft;

Figure 14 is a schematic diagrammatic perspective view of the worm gear assembly of the present invention showing the intermeshing worm shaft and worm wheel;

Fig. 15 is a graph showing the relationship between the meshing angle and the transmission torque loss in the case of the worm gear device of the present invention;

Figure 16 is a graph similar to Figure 15 but showing the relationship in the case of a conventional worm gear arrangement;

Fig. 17 is a graph showing the relationship between the radius ratio between the radius of curvature "R" of the worm wheel and the radius of curvature "r" of the worm shaft and the maximum allowable meshing angle therebetween;

Fig. 18 is a graph showing the relationship between the meshing position and the transmission torque loss in the case of the worm gear device of the present invention;

Figure 19 is a graph similar to Figure 18, but showing the relationship for a conventional worm gear arrangement; and

Fig. 20 is a graph showing the relationship between the radius ratio between the radius of curvature "R" of the worm wheel and the radius of curvature "r" of the worm shaft and the allowable error of the maximum meshing position.

Detailed ways

Hereinafter, the present invention will be described in detail with the aid of the accompanying drawings.

For ease of understanding, various directional terms such as right, left, up, down, rightward, etc. are used in the following description. However, such terms should only be understood from the drawings showing the corresponding parts or parts. In the specification, substantially the same parts or parts are denoted by the same reference numerals.

Referring to Figures 1-3, there is shown an electric steering device for a motor vehicle, on which the worm gear device of the present invention is actually mounted.

In order to clarify the features of the worm gear device of the present invention, an electric power steering device will be briefly described with the help of FIGS. 1-3.

As shown, especially in FIGS. 2 and 3 , the electric power steering device includes a motor housing 6 , a worm gear housing 7 , a torque sensor 9 and a motor 20 .

As shown in FIG. 2 , the torque sensor housing 5 accommodating the torque sensor 9 therein supports the input shaft 1 via a bearing 15 therein. Although not shown in the drawings, the input shaft 1 is connected to a steering wheel (not shown) to be driven therefrom, more specifically, by a driver who controls the steering wheel. The worm gear housing 7 , which is connected to the torque sensor housing 5 , supports the pinion shaft 2 in its interior via bearings 72 .

The pinion shaft 2 is coaxially connected to the input shaft 1 via a so-called loose splined connection 12 and torsion bar 3 . It should be noted that due to the loose splined connection 12 , the pinion shaft 2 and the input shaft 1 are allowed to rotate slightly relative to each other about a common axis against the force generated by the torsion bar 3 .

As shown in FIG. 3 , the motor housing 6 connected to the worm gear case housing 7 receives a brushless motor 20 inside. As shown in the figure, a worm shaft 200 as an output shaft of the motor 20 extends across the common axis of the input shaft 1 and the pinion shaft 2 .

Referring again to FIG. 2 , the pinion shaft 2 coaxially connected to the input shaft 1 by a torsion bar 3 has a worm wheel 100 closely fitted thereto. As shown, the worm gear 100 is housed in the stepped bottom of the worm gear case housing 7 .

As shown in FIGS. 2 and 3 , the worm shaft 200 is formed with helical tooth ridges 200 a (or continuous ribs) that operatively engage or mesh with equally spaced teeth 100 a of the worm wheel 100 .

As can be understood from FIG. 2 , when a driver applies a certain rotational force through the steering wheel, the input shaft 1 is forced to rotate about a common axis relative to the pinion shaft 2 while twisting the torsion bar 3 . Therefore, the torque sensor 9 senses the torque actually applied to the input shaft 1 and sends out a corresponding torque signal.

As shown in FIG. 2 , the worm wheel 100 is concentrically and closely connected to the pinion shaft 2 and is in operative engagement with a worm shaft 200 which extends perpendicular to the axis of the pinion shaft 2 .

As shown in FIG. 3 , a control circuit assembly 4 with a microcomputer is installed inside the motor housing 6 . The control circuit assembly 4 is configured to control the operation of the motor 20 by processing numerous information signals provided thereto, such as signals indicating the operating status of the relevant motor vehicle, torque signals from the torque sensor 9 and the like.

As shown in FIG. 2 , the rotational speed sensor 8 is installed near the worm shaft 200 to detect the rotational speed of the worm shaft 200 , that is, the rotational speed of the motor 20 . The rotational speed sensor 8 is of a magnetic type, and counts the number of occurrences of a given position of the helical tooth ridge 200a of the worm shaft within a given time, thereby detecting the rotational speed.

Referring to Figure 4, a worm shaft 200 having a helical tooth ridge 200a is shown. The worm shaft 200 is made of metal.

It should be noted that in the present invention, the helical tooth ridge 200a of the worm shaft 200 is a Niemann type.

That is, as shown in FIG. 5, wherein FIG. 5 is an enlarged cross-sectional view of a part of the spiral tooth ridge 200a taken along the line V-V in FIG. 4, the spiral tooth ridge 200a has a circular concave outer surface on each side, the The outer surface is bounded by a circle with radius "C". It should be noted that, as shown in FIG. 6, in the ordinary type worm shaft 200', its helical tooth ridge 200'b has a flat outer surface on each side.

Therefore, as can be understood from FIGS. 5 and 6, under the same pitch, the dedendum width "Sf" of the Niemann type helical ridge 200a is larger than the dedendum width "Sf'" of the ordinary helical ridge 200'b. , the Niemann-type helical ridge 200a has a tooth tip width "Sa" smaller than that of the general helical ridge 200'b.

As will be described in detail below, the surface finish of the worm shaft 200 is achieved by texturing. With this surface finishing, the outer surface of the helical tooth ridge 200a becomes smooth, thus protecting the outer surface of the tooth 100a of the worm wheel 100 engaged with the worm shaft 200 from scratches.

Referring to FIG. 7 , a partially cut-away plan view of the worm gear 100 is shown.

The worm gear 100 comprises a toothed annular metal core 110 having a central hole (not numbered) into which the pinion shaft 2 (see FIG. 2 ) is inserted, and a toothed annular plastic cover 120 . The cover 120 is concentrically and tightly fitted to the toothed annular core 110 as shown. Preferably, the plastic used for the cover 120 is Nylon (trade name) without reinforcing fibers such as glass fibers. The toothed annular metal core 110 may be made by cutting teeth from a circular metal plate or by using a sintering method.

The structure of the worm gear 100 can be better understood from FIGS. 8 and 9 . 8 is a cross-sectional view taken along line VIII-VIII in FIG. 7, and FIG. 9 is an enlarged cross-sectional view taken along line IX-IX in FIG.

As shown in FIG. 9, each tooth of the toothed annular plastic cover 120 of the worm wheel 100 has a circular convex outer surface 101 on each side, which can be matched with the above-mentioned circular concave surface 101 of the Niemann-type helical tooth ridge 200a of the worm shaft 200. Into the outer surface tight fit (see Figure 12). That is, the worm wheel 100 and the worm shaft 200 constitute a so-called Niemann type worm gear device.

As mentioned above, the toothed ring-shaped cover 120 is made of nylon (trade name) without reinforcing fibers, therefore, when engaged with the worm shaft 200, the toothed ring-shaped plastic cover 120 is subjected to elastic deformation and thermal deformation, which eliminates or at least Undesirable backlash of the worm gear arrangement is reduced. In addition, since the toothed annular plastic cover 120 does not contain reinforcing fibers, the outer surface of the helical tooth ridge 200a of the worm shaft 200 is protected from scratches.

In addition, as shown in FIG. 9 , since the circular convex outer surface 101 is provided, each tooth of the toothed annular plastic cover 120 of the worm wheel 100 can have a thicker thickness, resulting in increased mechanical strength of the worm wheel 100 . Therefore, it should be noted that each tooth of the toothed annular plastic cover 120 may have a satisfactory mechanical strength even though it does not contain reinforcing fibers.

This can be seen clearly from the graph of Figure 10, which shows the mechanical strength (ie yield strength) of the worm gear 100 and a conventional worm gear.

As shown in FIG. 9 , each tooth 111 of the toothed annular metal core 110 protrudes into the middle portion of the corresponding tooth of the toothed annular plastic cover 120 . With this structure, any heat generated in the teeth 100 a of the toothed annular plastic cover 120 is efficiently radiated through the toothed annular metal core 110 which has excellent thermal conductivity compared with the plastic cover 120 .

Hereinafter, the meshing between the worm wheel 100 and the worm shaft 200 will be discussed with reference to FIGS. 11 and 12 in order to make the advantages of the Niemann-type worm gear device of the present invention comprising the worm wheel 100 and the worm shaft 200 clearer.

11 is an enlarged sectional view showing the operatively engaged state of the worm shaft 200 and the worm wheel 100 of the worm gear device of the present invention, and FIG. 12 is an enlarged sectional view showing details of the meshing between the worm shaft 200 and the worm wheel 100 .

As can be seen from these drawings, especially from FIG. 12, when the worm wheel 100 and the worm shaft 200 are properly meshed or assembled, the circular convex outer surface 101 of each tooth of the worm wheel 100 engages with the helix of the worm shaft 200. The circular concave outer surfaces of the tooth ridges 200a are in close and deep contact. That is, the contact area defined between each tooth of the worm wheel 100 and the helical tooth ridge 200a of the worm shaft 200 is significantly larger than the contact area defined between corresponding parts of a conventional worm gear device. Consequently, the resulting bearing stresses are considerably lower in the case of the worm gear according to the invention compared to conventional worm gears. Therefore, in the case of the present invention, it is not necessary to use reinforcing fibers to reinforce the toothed annular plastic cover 120 .

In FIG. 11, the radius of curvature of each curved groove 102 defined between two adjacent teeth 100a of the worm wheel 100 is indicated by "R", and the radius of curvature of the helical tooth ridge 200a of the worm shaft 200 is indicated by "r". The meshing area between each tooth of the worm wheel 100 and the helical tooth ridge 200a of the worm shaft 200 is indicated by "D". As shown, when properly mated between the worm wheel 100 and the worm shaft 200, the engagement area "D" has a radius of curvature "r".

It should be noted in the present invention that there is the following relationship between "R" and "r":

R＞r…………(1)

Due to the large radius of curvature "R" of each curved groove 102 of the worm wheel 100, it is not necessary to use very advanced thread cutting techniques to manufacture the worm wheel 100, and thus, the worm wheel 100 can be manufactured at a lower cost.

As mentioned above, the thickness of the crest 211 of the helical tooth ridge 200a of the worm shaft 200 is small (see FIG. 5 ). Therefore, as can be understood from FIG. 12 , even if a significant force is applied to the worm shaft 200 in a direction oblique to the worm wheel 100 , a tooth crest 211 of the helical tooth ridge 200 a of the worm shaft 200 and each tooth of the worm wheel 100 generate a force. The frictional force between the circular convex outer surfaces 101 of the worm shaft 200 is also very small, therefore, the torque transmission from the worm shaft 200 to the worm wheel 100 is basically not affected.

Referring to Figures 13A-13D, a method of manufacturing a worm shaft 200 and a conventional worm shaft 200' is shown.

First, a method of manufacturing the worm shaft 200 of the present invention will be described with reference to the drawings.

As shown in FIG. 13A, a semi-finished cylindrical metal member 2000 having a cylindrical main portion 2000a and a splined end 2000b is prepared. Subsequently, as shown in FIG. 13B , cutting work is performed on the main portion 2000a to provide a helical tooth ridge 2000c nearby. For this cutting method, two cutting tools C1 and C2 are used. That is, as shown in the figure, in order to manufacture the helical tooth ridge 2000c, the semi-finished cylindrical member 2000 is rotated at a certain speed around its axis, and then the cutting tools C1 and C2 with the tips pressed against the cylindrical main part 2000a are moved along the cylindrical member 2000. axis moves. Using this method, a so-called semi-finished worm shaft 2000A is manufactured.

Subsequently, as shown in FIG. 13C, the semi-finished worm shaft 2000A thus formed with the helical tooth ridge 2000c is subjected to component rolling finishing processing. For this method, two polishing rolls R1 and R2 are used. That is, a so-called roller polishing method is used. Using this trimming method, a finished worm shaft 200 is provided, as shown.

It should be noted in the present invention that the semi-finished worm shaft 2000A is immediately subjected to component rolling finishing without heat treatment.

As shown in FIGS. 13B and 13D , in the case of manufacturing a conventional worm shaft 200 ′, a semi-finished worm shaft 2000A is subjected to heat treatment, followed by polishing processing.

As mentioned above, in the worm gear device according to the present invention, the bearing stress generated between the worm wheel 100 and the worm shaft 200 is extremely small, and thus the load applied to the worm shaft 200 is extremely small. Therefore, it is not necessary to perform the above heat treatment on the worm shaft 200, more specifically, the semi-finished worm shaft 2000A. Since such heat treatment is unnecessary, the polishing process necessary when using such heat treatment is no longer necessary in the present invention.

Hereinafter, the worm gear of the present invention will be discussed in terms of its unique configuration.

Fig. 14 schematically shows a perspective view of the worm gear device of the present invention.

It should be noted that the angle (or engagement angle) of the axis "A" of the worm shaft 200 with respect to the radial direction "B" of the worm wheel 100 is represented by "θ". Therefore, when the radial direction "B" of the worm wheel 100 coincides with the axial direction "A" of the worm shaft 200, the angle "θ" shows 0 (zero) degrees.

It should also be noted that the position of the worm shaft 200 in the axial direction "A" relative to the worm wheel 100 (hereinafter will be referred to as the meshing position) is represented by "y". Therefore, when each tooth 100a of the worm wheel 100 is properly or completely engaged with the helical tooth ridge 200a of the worm shaft 200, the mesh position "y" shows 0 (zero).

For ease of description, hereinafter, the radius of curvature "R" of each curved groove 102 (see FIG. 11 ) defined between two adjacent teeth of the worm wheel 100 will be referred to as the radius of curvature "of the teeth of the worm wheel 100". R", the curvature radius "r" of the helical tooth ridge 200a of the worm shaft 200 will be referred to as the curvature radius "r" of the helical tooth ridge of the worm shaft 200 .

15 and 16 are graphs showing the loss of transmission torque in relation to the meshing angle "θ" in the case of the worm gear of the present invention and in the case of the conventional worm gear, respectively. In each graph, two types of data are shown, one for when the radius of curvature "R" of the worm gear tooth is large and the other for when the radius of curvature "R" is small.

As can be seen from the graphs of FIGS. 15 and 16, in the worm gear device of the present invention, the range in which the transmission torque loss is small is larger than that of the conventional worm gear device. That is, in the case of the present invention, the transmission loss shows only a small loss even if the meshing error is somewhat large. The reasons are as follows. That is, as mentioned above, the spiral tooth ridge 200a (see FIG. 5 ) of the worm shaft 200 has a circular concave outer surface on each side, and therefore, the width "Sa" of the tooth crest 211 of the spiral tooth ridge 200a very small. Therefore, as shown in FIG. 12 , when meshing with the teeth of the worm wheel 100 , the crests 211 of the helical tooth ridges 200 a smoothly and deeply contact the circular convex outer surface 101 of each tooth of the worm wheel 100 .

17 is a graph showing the maximum permissible meshing angle "θmax" of the worm gear of the present invention and the conventional worm gear in relation to the radius ratio between the curvature radius "R" of the worm gear tooth and the curvature radius "r" of the worm shaft helical ridge .

As shown in the graph, the maximum allowable engagement angle "θmax" of the worm gear of the present invention is higher than that of the conventional worm gear.

18 and 19 are graphs showing the loss of transmission torque in relation to the meshing position "y" in the case of the worm gear of the present invention and in the case of a conventional worm gear, respectively. In each graph, two types of data are shown, one for when the radius of curvature "R" of the worm gear tooth is large and the other for when the radius of curvature "R" is small.

As shown in the graphs in FIGS. 18 and 19 , the worm gear of the present invention shows no advantage in transmission torque loss as compared to the conventional worm gear with respect to the meshing position (y). That is, as shown in the graph, when the radius of curvature "R" of the teeth of the worm gear is large, the range in which the loss of transmitted torque is small is large in the case of the worm gear device of the present invention. However, when the radius of curvature "R" of the teeth of the worm gear is small, the range in which the loss of the transmitted torque is small is small in the case of the worm gear device of the present invention.

Fig. 20 is a diagram showing the allowable error of the maximum meshing position "ymax" of the worm gear device of the present invention and the conventional worm gear device in relation to the radius ratio between the curvature radius "R" of the worm gear tooth and the curvature radius "r" of the worm shaft helical ridge chart.

As shown in the graph, in the case of the allowable error of the maximum meshing position "ymax", the respective characteristic lines of the worm gear of the present invention and the conventional worm gear at the point "α" represented by the value of the radius ratio R/r(α) "Intersect at. As shown in the graph, the worm gear according to the present invention should take a radius ratio R/r equal to or greater than a value of R/r(α) in consideration of a higher allowable error of the maximum meshing position "ymax". In one example of the present invention, the radius ratio (R/r) is 5/3. As shown in the graph, if the radius ratio is 5/3, the worm gear of the present invention obtains a higher allowable error than the maximum meshing position (ymax) of the conventional worm gear. Preferably, the radius ratio (R/r) is in the range of 5/3 to 2.

The following modifications can be applied to the worm shaft 200, if desired. That is, the worm shaft 200 may be formed with two helical tooth ridges extending parallel therearound.

The entire contents of Japanese Patent Application No. 2005-374089 filed on December 27, 2006 are hereby incorporated by reference.

Although the invention has been described above with respect to the embodiments of the invention, the invention is not limited to the embodiments described above. According to the above description, those skilled in the art can make various improvements and modifications to this embodiment.

Claims (20)

1. A worm gear device, comprising: A worm wheel (100) having teeth equally spaced around it, each tooth of the worm wheel having a circular convex outer surface on each side, each slot (102) bounded by two adjacent teeth of the worm wheel ) has a curved base with a first radius of curvature (R); and a worm shaft (200) having a helical ridge (200a) with a circular concave outer surface on each side, the helical ridge engaging the teeth of the worm wheel (100) and having a second radius of curvature (r) smaller than the first radius of curvature (R), Wherein, the meshing between each tooth of the worm wheel (100) and the helical tooth ridge of the worm shaft is represented by the first characteristic line depicted in the characteristic diagram showing the axial relative to the worm shaft (200) The relationship between the allowable error of the maximum meshing position of (100) and the radius ratio (R/r) between the first radius of curvature (R) and the second radius of curvature (r), Wherein, the meshing between each tooth of the reference worm wheel and the helical tooth ridge of the reference worm shaft is represented by the second characteristic line in said characteristic diagram, each tooth of the reference worm wheel has a flat outer surface on each side, the reference worm The helical ridge of the shaft has a flat outer surface on each side; wherein the first characteristic line and the second characteristic line in the characteristic diagram intersect at a given point; and Wherein, the engagement between each tooth of the worm wheel (100) and the helical tooth ridge of the worm shaft (200) coincides with a portion of the first characteristic line drawn when the radius ratio is equal to or greater than a predetermined value, said predetermined The value represents or corresponds to the intersection of the first and second characteristic lines to a fixed point. 2. Worm gear arrangement according to claim 1, characterized in that the predetermined value of the radius ratio (R/r) is about 5/3. 3. The worm gear unit according to claim 2, characterized in that the predetermined value of the radius ratio (R/r) is in the range of 5/3 to 2. 4. A worm gear arrangement according to claim 1, characterized in that the equally spaced teeth of the worm wheel (100) are integrally formed on the annular plastic cover (120). 5. A worm gear arrangement according to claim 4, characterized in that said annular plastic cover (120) has no reinforcing fibers contained inside it. 6. The worm gear device according to claim 4, characterized in that the annular plastic cover (120) is concentrically and closely fitted to the annular metal core (110) to constitute the worm wheel (100). 7. Worm gear arrangement according to claim 6, characterized in that said annular metal core (110) is formed around it with equidistantly spaced teeth (111), each tooth (111) protruding into an annular plastic cover (120) the middle of a corresponding one of the teeth. 8. The worm gear device according to claim 1, characterized in that, the worm wheel (100) is connected to the steering mechanism of the motor vehicle, and the worm shaft (200) is connected to the electric motor, so that the driving torque of the electric motor passes through each other The engaged worm shaft (200) and worm wheel (100) are transmitted to the steering mechanism. 9. A method of manufacturing a worm wheel for engagement with a worm shaft having a helical ridge (200a) with a circular concave outer surface on each side, the method comprising: preparing the circular plate blank; and A cylindrical peripheral portion of a circular plate blank is cut to form equidistantly spaced teeth (100a) therearound, each said tooth (100a) having a circular convex outer surface (101 ) on each side, when the snail When a proper fit is formed between the shaft (200) and the worm wheel (100), said circular convex outer surface (101) is shaped to closely engage the circular concave outer surface of the helical ridge (200a) of the worm shaft, Wherein, the curvature radius (R) of the curved bottom of each slot (102) defined by two adjacent teeth of the worm wheel (100) is greater than the curvature radius (r) of the helical tooth ridge (200a) of the worm shaft (200). 10. The method of claim 9, wherein: The meshing between each tooth of the worm wheel (100) and the helical tooth ridge of the worm shaft is represented by the first characteristic line depicted in the characteristic diagram showing the axial relative relation of the worm shaft (200) to the worm wheel (100 The relationship between the allowable error of the maximum meshing position of ) and the radius ratio (R/r) between the first radius of curvature (R) and the second radius of curvature (r), The meshing between each tooth of the reference worm wheel, each tooth of the reference worm wheel having a flat outer surface on each side, and the helical tooth ridge of the reference worm shaft is represented by the second characteristic line in said characteristic diagram, and the reference worm shaft's The helical ridge has a flat outer surface on each side; the first characteristic line and the second characteristic line in the characteristic diagram intersect at a given point; and The engagement between each tooth of the worm wheel (100) and the helical tooth ridge of the worm shaft (200) coincides with a portion of the first characteristic line drawn when the radius ratio is equal to or greater than a predetermined value representing Or to a fixed point corresponding to the intersection of the first and second characteristic lines. 11. The method of claim 10, wherein the predetermined value of the radius ratio (R/r) is about 5/3. 12. The method according to claim 11, characterized in that the predetermined value of the radius ratio (R/r) is in the range of 5/3 to 2. 13. The method according to claim 9, characterized in that the worm wheel comprises an annular metal core (110) and an annular plastic cover (120) which is concentric and tightly fitted to the outer peripheral portion of the annular metal core, The annular plastic cover has around it teeth that engage with the helical tooth ridges (200a) of the worm shaft (200), and the annular metal core (110) is made by a cutting method. 14. The method according to claim 9, characterized in that the worm wheel comprises an annular metal core (110) and an annular plastic cover (120) which is concentric and tightly fitted to the outer peripheral portion of the annular metal core, The annular plastic cover has around it teeth that engage with the helical tooth ridges (200a) of the worm shaft (200), and the annular metal core (110) is made by sintering. 15. A method of manufacturing a worm shaft having a helical ridge (200a) with a rounded convex outer surface on each side, the method comprising: preparation of a cylindrical blank of the snail shaft; cutting the outer surface of the cylindrical blank to form a helical tooth ridge (200a) therearound, thereby making a semi-finished worm shaft; and Surface finishing of semi-finished worm shafts without heat treatment. 16. The method of claim 15, wherein said surface finishing is accomplished by texturing. 17. A method according to claim 16, characterized in that said deforming is performed such that the dimensional variation in the face width of the helical ridge (200a) decreases as said portion approaches the crest of the helical ridge. 18. The method of claim 16, wherein the deforming is performed such that the deforming rate decreases as the portion approaches the crest of the helical crest. 19. The method of claim 16, wherein the tolerance of the face width of the helical ridges varies as the portion approaches the helical ridges compared to the helical ridges of a surface-finished worm shaft The tooth tip is reduced. 20. The method of claim 16, wherein the worm shaft is formed with two helical ridges extending parallel thereabout, and wherein the two helical ridges are formed using two roll moldings.

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