A finger conical envelope biasing worm pair and method of manufacture

Abstract

The invention relates to a kind of finger conical envelope bias worm pair and its manufacturing method, and the technical scheme is: finger conical grinding wheel is used to grind worm spiral surface, worm blank makes rotary motion around axis, grinding wheel makes translational motion along straight line parallel to worm generatrix, and the moving direction is related to worm blank rotation direction and rotation direction.Rolling cutter is used to roll cut face worm wheel, and the rolling cutter installation distance, the center distance between rolling cutter and face worm blank, shaft intersection angle and transmission ratio are the same as the corresponding quantities of worm pair.The finger conical envelope bias worm pair provided by the invention has wide application range of worm head number and transmission ratio, and the meshing performance of worm pair is excellent.

Description

Technical Field

[0001] This invention relates to the field of offset worm gear transmission technology, and more particularly to a finger-cone envelope offset worm gear pair and its manufacturing method. Background Technology

[0002] Existing types of helical surfaces for tapered worms (with a cone half-angle of 5° or 0°) mainly include: Archimedes helical surfaces formed by turning with a straight-edged lathe tool, circular arc helical surfaces formed by turning with a single circular arc lathe tool, and envelope-type helical surfaces generated by grinding with disc-shaped conical surfaces, toroidal surfaces, or flat grinding wheels. When the worm module is large, using a simple finger-shaped conical grinding wheel to grind the worm helical surface not only simplifies the machining process compared to the traditional disc-shaped conical grinding wheel, but also, compared to trajectory-type worm pairs, facilitates the finishing of the worm helical surface after hardening, further improving the load-bearing capacity of the transmission pair.

[0003] In view of this, based on new principles and using new processing and manufacturing methods, a finger-shaped conical envelope biased worm gear pair was created in this invention. Summary of the Invention

[0004] This invention aims to overcome the shortcomings of existing technologies and provides a novel offset worm gear drive and its manufacturing method. This worm gear drive is called a finger-cone envelope offset worm pair. This type of transmission pair has a high overlap ratio, and the entire length of the worm thread can participate in the meshing operation; the tooth surface of the worm wheel is almost entirely covered by the meshing area; the instantaneous contact lines of the worm pair are evenly distributed, sparse, and without intersections, which is beneficial for heat dissipation and lubrication; the tooth surfaces of the worm pair are not prone to curvature interference, and it is suitable for a wide range of worm threads and transmission ratios; the lubrication angle and induced principal curvature of this transmission are small, the conditions for forming a lubricating oil film between the worm pair teeth are good, and the contact stress level is low. Therefore, the finger-cone envelope offset worm pair has excellent meshing performance.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a finger-shaped conical envelope biased worm gear pair and its manufacturing method, comprising the following steps:

[0006] Step 1: Manufacturing a finger-shaped cone-shaped envelope biased worm gear

[0007] Worm blank and moving coordinate system The unit basis vector of the moving coordinate system σ1 is fixedly connected. Along the axis of the worm blank, from its inner end to its outer end, the coordinate origin O1 is located on the axis of the worm blank and is the midpoint of the worm thread length; the static coordinate system of the worm blank is... With the above They coincide, and are also along the axis of the worm gear blank;

[0008] Finger-shaped conical grinding wheel and coordinate system The coordinate system σ is fixedly connected.d O of the coordinate system d Coinciding with the center of the small end of the grinding wheel, the unit base vector Along the axis of the grinding wheel, from its small end to its large end; unit base vector and Parallel, unit basis vector and The included angle between them is the grinding wheel deflection angle ε. S When S=1, the finger-shaped conical grinding wheel grinds the i-face of the worm, where the i-face is a helical surface facing the inner end of the worm; when S=2, the finger-shaped conical grinding wheel grinds the e-face of the worm, where the e-face is a helical surface facing the outer end of the worm; the initial position, i.e., the tool setting reference point position, is the coordinate origin O. d The distance between O1 and the worm thread is equal to the root circle radius r at the midpoint of the worm thread. Mf During the grinding process of the worm's helical surface by the aforementioned finger-shaped conical grinding wheel, the grinding wheel moves along a straight line parallel to the worm's generatrix. To perform translational motion, in a straight line The angle between the worm blank axis and the worm blank axis is the cone half angle δ1 of the worm.

[0009] When the worm blank is wound Turn the angle At that time, the grinding wheel is relative to the tool setting reference point O. d distance of movement p is the helical parameter of the worm along its generatrix;

[0010] Step 2: Manufacturing the surface worm gear

[0011] The worm gear blank is cut using a hob, the profile of which coincides with the helical surface of the worm obtained in step one. The hob performs a linear translational feed motion along the axis of the worm gear. The static coordinate system of the worm gear blank is... The static coordinate system σ o2 unit basis vector The coordinate system σ coincides with the axis of the worm gear, and its direction is from the tooth tip to the tooth root of the worm gear. o2 unit basis vector Along the direction of the common perpendicular line between the worm axis and the face worm wheel axis; points O′ and O2 are the feet of the perpendicular line on the enveloping worm axis and face worm wheel axis, respectively, a 12 The center distance of the finger-cone envelope offset worm gear pair is z, and the distance from point O′ along the worm gear axis to the origin O1 is z. A +L w / 2,z A and L w These are the worm gear mounting distance and the thread length, respectively.

[0012] During the process of forming a worm gear with a hob, both the hob and the worm gear blank rotate around their respective axes. The process installation distance of the hob and the installation distance of the worm gear are z. A Similarly, the center distance of the process shaft between the hob and the worm gear blank, the angle between the process shafts, and the process transmission ratio are also related to the center distance a of the worm pair. 12 , axis intersection angle Σ 12 and transmission ratio i 12 equal;

[0013] The worm obtained in step one and the worm wheel obtained in step two are connected at a center distance 'a' as specified in the design. 12 , axis intersection angle Σ 12 and worm gear installation distance z A After assembly, a finger-shaped cone envelope biased worm gear pair is formed.

[0014] The range of the worm gear cone half-angle δ1 is -5°≤δ1≤5°; the cone angle δ of the face worm wheel a2 Based on the worm's cone half-angle δ1 and axis intersection angle Σ 12 The value of δ is determined based on the meshing result of the worm gear pair, and its range is generally 75°≤δ. a2 ≤105°.

[0015] The basic parameters of the finger-shaped conical grinding wheel include the radius R of the small end of the grinding wheel. g and the half-aperture cone angle δ of the grinding wheel g The values ​​of both need to be selected based on the meshing performance of the worm gear pair, and it must be ensured that the finger grinding wheel can be placed into the tooth groove.

[0016] The finger-shaped conical grinding wheel deflection angle ε S The value must not only ensure that the worm tooth angle meets the design requirements, but can also be adjusted by adjusting ε. S This is to alleviate the asymmetry in meshing between the two sides of the worm tooth when grinding the i-face and e-face of the worm tooth.

[0017] A finger-shaped conical envelope biased worm gear pair is manufactured using the above-described manufacturing method.

[0018] The beneficial effects of the manufacturing method for the finger-shaped conical envelope biased worm gear pair in this invention are as follows:

[0019] Compared with existing technologies, the finger-cone envelope offset worm gear pair obtained by the manufacturing method of this invention has advantages such as good manufacturing precision, low roughness, and high tooth surface hardness. Furthermore, this type of worm gear has a longer working length and a very wide contact area on the tooth surface of the worm wheel. Curvature interference is less likely to occur on the entire tooth surface of the transmission pair, thus preventing the worm wheel from tangenting. It is suitable for a wide range of worm gear transmission ratios, and the instantaneous contact lines of the transmission pair are evenly distributed, sparse, and without intersections, which is beneficial for improving the heat dissipation and lubrication performance of the transmission pair. This transmission pair has a small induced principal curvature and a small lubrication angle, resulting in low tooth surface contact stress and good lubrication performance. Therefore, the finger-cone envelope offset worm gear pair has excellent meshing performance. Attached Figure Description

[0020] Figure 1 Finger-shaped conical grinding wheel used for grinding worm gear blanks;

[0021] Figure 2 This is a schematic diagram showing the relative position and relative motion between the grinding wheel and the worm gear blank during the grinding process;

[0022] Figure 3 This is a schematic diagram showing the relative position and relative motion between the hob and the worm gear blank during the forming process;

[0023] Figure 4 This is a projection of the contact area on the i-th surface of the worm gear in the worm gear axial section in Example 1;

[0024] Figure 5 This is a projection view of the convex contact area of ​​the worm gear in the cross-section of the worm gear shaft in Embodiment 1;

[0025] Figure 6 This is a projection of the contact area on the e-face of the worm gear in the worm gear axial section in Example 1;

[0026] Figure 7 This is a projection view of the concave contact area of ​​the worm gear in the cross-section of the worm gear shaft in Example 1;

[0027] Figure 8 This is a projection of the worm gear i-face contact area within the worm gear axial section in Example 2;

[0028] Figure 9 This is a projection view of the convex contact area of ​​the worm gear in the cross-section of the worm gear shaft in Example 2;

[0029] Figure 10 This is a projection of the contact area on the e-face of the worm gear in the worm gear axial section in Example 2;

[0030] Figure 11 This is a projection view of the concave contact area of ​​the worm gear in the cross-section of the worm gear shaft in Example 2;

[0031] Figure 12This is a projection of the worm gear i-face contact area within the worm gear axial section in Example 3;

[0032] Figure 13 This is a projection view of the convex contact area of ​​the worm gear in the cross-section of the worm gear shaft in Example 3;

[0033] Figure 14 This is a projection of the contact area on the e-face of the worm gear in the worm gear axial section in Example 3;

[0034] Figure 15 This is a projection view of the concave contact area of ​​the worm gear in the cross-section of the worm gear shaft in Example 3;

[0035] Figure 16 This is a schematic diagram illustrating the effect of a finger-shaped conical grinding wheel grinding a worm gear. Detailed Implementation

[0036] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. The embodiments of the present invention include, but are not limited to, the following embodiments.

[0037] Example 1

[0038] In this embodiment, the worm is right-handed, the number of threads Z1 = 1, and the module m of the worm along the generatrix of the cone is... δ =10mm, axial angle Σ 12 =90°, the manufacturing method of this embodiment adopts the following steps:

[0039] Step 1: Manufacturing a finger-shaped cone-shaped envelope biased worm gear

[0040] like Figure 2 As shown, the worm blank and the moving coordinate system The unit basis vector of the fixed-coupled, moving coordinate system σ1 Along the axis of the worm blank, from its inner end to its outer end, the origin O1 is located on the axis of the worm blank and is the midpoint of the worm thread length; the static coordinate system of the worm blank is... With the above They coincide, and are also along the axis of the worm gear blank;

[0041] like Figure 3 As shown, the finger-shaped conical grinding wheel and the coordinate system Fixed connection, origin O d Coinciding with the center of the small end of the grinding wheel, the unit base vector Along the axis of the grinding wheel, from its small end to its large end; unit base vector and Parallel, unit basis vector and The included angle between them is the grinding wheel deflection angle ε. SWhen S=1, the finger-shaped conical grinding wheel grinds the i-face of the worm, which is the helical surface facing the inner end of the worm; when S=2, the finger-shaped conical grinding wheel grinds the e-face of the worm, which is the helical surface facing the outer end of the worm; the initial position, i.e., the tool setting reference point position, is the coordinate origin O. d The distance between O1 and the worm thread is equal to the root circle radius r at the midpoint of the worm thread. Mf , where r Mf =37.5mm; During the grinding of the helical surface of the worm gear with a finger-shaped conical grinding wheel, the grinding wheel moves along a straight line parallel to the generatrix of the worm gear. To perform translational motion, in a straight line The angle between the worm blank axis and the worm blank axis is the cone half angle δ1 of the worm, where δ1 = 5°;

[0042] In this embodiment, the grinding wheel radius R is used for grinding the worm gear. g =2mm. To ensure sufficient worm tooth tip thickness and that the entire worm tooth surface is located on one side of the usable area of ​​the meshing boundary, the half-cone angle of the grinding wheel is taken as δ when grinding the i-face of the worm. g1 =15°, the grinding wheel deflection angle is taken as ε1=5°, and when grinding the e-face of the worm, the half-point cone angle of the grinding wheel is taken as δ. g2 =15°, the grinding wheel deflection angle is taken as ε2 = 15°;

[0043] When the worm blank is wound Turn the angle At that time, the grinding wheel is relative to the tool setting reference point O. d distance of movement p is the helical parameter of the worm along its generatrix.

[0044] Step 2: Manufacturing the surface worm gear

[0045] The worm gear blank is cut with a hob, the profile of which coincides with the helical surface of the worm obtained in step one. The hob makes a linear translational feed motion along the axis of the worm gear. The static coordinate system of the worm gear blank is... static coordinate system σ o2 unit basis vector Coinciding with the axis of the worm gear, its direction is from the tooth tip to the tooth root, in coordinate system σ o2 unit basis vector Along the direction of the common perpendicular line between the worm axis and the face worm wheel axis; points O′ and O2 are the feet of the perpendicular line on the enveloping worm axis and face worm wheel axis, respectively, a 12 Let a be the center distance of the finger-cone envelope biased worm gear pair. 12 =250mm, the distance from point O′ along the worm shaft axis to the origin O1 is z A +L w / 2,z A and L wThese are the worm gear mounting distance and thread length, respectively, where z A =k A a 12 =150mm, where the worm gear installation distance coefficient k is... A =0.6, L w =0.73×a 12 =182.5mm;

[0046] During the process of forming a worm gear with a hob, both the hob and the worm gear blank rotate around their respective axes. The process installation distance of the hob and the installation distance of the worm gear are z. A Similarly, the center distance of the process shaft between the hob and the worm gear blank, the angle between the process shafts, and the process transmission ratio are also related to the center distance a of the worm pair. 12 , axis intersection angle Σ 12 and transmission ratio i 12 Equal, here Σ 12 =90°, i 12 =52.

[0047] like Figure 4 As shown, in this embodiment, to avoid excessive redundancy on the worm gear tooth surface outside the contact area, and to fully utilize the worm gear tooth surface, the worm gear cone angle is set to δ. a2 =83°; the face width coefficient of the worm gear can be taken as k. g =0.47;

[0048] The worm obtained in step one and the worm wheel obtained in step two are connected at a center distance 'a' as specified in the design. 12 , axis intersection angle Σ 12 and worm gear installation distance z A After assembly, a finger-shaped cone envelope biased worm gear pair is formed.

[0049] The aforementioned finger-conical envelope offset worm pair, where the worm's i-face meshes with the convex surface of the worm wheel, has the tooth surface contact area and instantaneous contact line distributed as follows: Figure 4 and Figure 5 As shown; the worm gear e-face meshes with the concave surface of the worm wheel, and the tooth surface contact area and instantaneous contact line are distributed as follows. Figure 6 and Figure 7 As shown.

[0050] exist Figure 4 In the diagram, the projection of the worm's i-face contact area onto its axial section is region MABC, where MA is the reflection line of the small end of the worm wheel on the worm, AB is the reflection line of the worm wheel tooth tip on the worm, BC is the reflection line of the large end of the worm wheel on the worm, and CM is the worm tooth tip. Figure 6 In the diagram, the projection of the worm's contact area on its axial section is region ABCDE, where AB is the reflection line of the worm gear tooth tip on the worm, BC is the reflection line of the large end of the worm gear on the worm, CD is the worm tooth tip, and EA is the small end of the worm.

[0051] Combination Figure 4 and Figure 6 It can be seen that the working length of the worm gear's i-face is relatively long, almost equal to the total length of its thread. Figure 5 In the diagram, the contact area of ​​the convex surface of the worm gear is region MABC, where MA is the small end of the worm gear, AB is the tooth tip of the worm gear, BC is the large end of the worm gear, and CD is the reflection line of the worm tooth tip on the worm gear. Figure 7 In the diagram, the contact area of ​​the concave surface of the worm gear is region ABCD, where AB is the tooth tip of the worm gear, BC is the large end of the worm gear, CD is the reflection line of the worm tooth tip on the worm gear, and DA is the reflection line of the small end of the worm on the worm gear.

[0052] Combination Figure 5 and Figure 7 It can be seen that the contact areas of the convex and concave surfaces of the worm gear corresponding to the i-face and e-face of the worm are relatively wide, almost covering the entire tooth surface of the worm gear. Moreover, the instantaneous contact lines are evenly distributed without intersection within the contact area of ​​the entire tooth surface of the worm gear, which is beneficial to the heat dissipation and lubrication of the worm pair.

[0053] Figure 4 —7 indicates that the distribution of the contact area and instantaneous contact line on both sides of one tooth of the transmission pair is not significantly different. This reflects, from the perspective of global meshing characteristics, that the meshing asymmetry of the finger-cone envelope biased worm gear pair in this embodiment is not significant.

[0054] To further illustrate the meshing performance of the finger-cone envelope offset worm gear pair obtained above, three meshing points (a, b, and c) are sequentially selected along the direction from the tooth tip to the tooth root on each instantaneous contact line of the face worm gear tooth surface, and the induced principal curvature at these meshing points is calculated. and lubrication angle Ω L Some of the numerical results are listed in Table 1:

[0055] Table 1

[0056]

[0057]

[0058] Table 1 shows that the induced principal curvature in the entire contact area of ​​the worm gear pair is... The signs are the same, both being positive, indicating that there is no root cut in the worm gear throughout the entire contact area; within the entire contact area, the induced principal curvature... The values ​​are all relatively small, indicating that the contact stress at these meshing points is not high, and that at each meshing point... The values ​​are also quite close, indicating that the contact stress is roughly equal between the teeth throughout the entire contact area, which conforms to the principle of equal strength; the lubrication angle Ω throughout the entire contact area LThe values ​​are all relatively small, indicating that the worm gear pair has excellent lubrication performance.

[0059] Furthermore, the values ​​in Table 1 show the induced principal curvature on both sides of one tooth of the transmission pair. and lubrication angle Ω L The numerical differences are not significant. From these two meshing parameters, it can be seen that the local meshing characteristics of the finger-cone envelope biased worm pair in this embodiment are that the meshing asymmetry of the worm pair in this embodiment is not significant.

[0060] Example 2

[0061] A finger-conical envelope biased worm gear pair and its manufacturing method are disclosed, comprising a finger-conical envelope biased worm gear and a matching faceted worm wheel. The worm gear pair processing method in this embodiment is the same as that in Embodiment 1, but the cone half-angle of the worm gear and the faceted cone angle of the worm wheel are different.

[0062] In this embodiment, the module, center distance, and axial angle of the worm along the generatrix of the cone are the same as in Embodiment 1, i.e., m δ =10mm, a 12 =250mm, Σ 12 =90°; worm length L w =0.73a 12 =182.5mm, worm cone half angle δ1=0°, worm thread root circle radius r at the midpoint of the thread. Mf = 37.5mm; Select grinding wheel radius R g =2mm. To ensure sufficient worm tooth tip thickness and that the entire worm tooth surface is located on one side of the usable area of ​​the meshing boundary, the grinding wheel half-cone angle is δ when grinding the i-face of the worm. g1 =15°, the grinding wheel deflection angle is taken as ε1 = 5°; when grinding the e-face of the worm, the half-point cone angle of the grinding wheel is taken as δ g2 =15°, the grinding wheel deflection angle is taken as ε2 = 15°;

[0063] Helical parameters of the worm along its generatrix Due to the worm gear countershaft angle Σ in this embodiment 12 =90°, worm gear installation distance coefficient k A Same as in Example 1, i.e., k A =0.6, therefore the worm gear pair installation distance is: z A =k A a 12 =150mm

[0064] like Figure 8 As shown, in this embodiment, in order to ensure that the entire length of the worm thread can be utilized and that the contact areas of the convex and concave tooth surfaces of the worm gear are approximately equal, and to avoid excessive redundancy on the worm gear tooth surface outside the contact area, the face width coefficient of the worm gear can be taken as k. g =0.47; at the axis intersection angle Σ12 When the angle is 90°, in order to make full use of the tooth height of the worm gear, the cone angle of the worm gear face can be taken as δ. a2 =90°;

[0065] The remaining steps are the same as in Example 1. This results in a finger-shaped conical envelope biased worm and a faceted worm wheel, with their centers spaced a distance 'a' as specified in the design. 12 , axis intersection angle Σ 12 and worm gear installation distance z A After assembly, a finger-shaped cone envelope biased worm gear pair is formed.

[0066] In this embodiment, the tooth surface contact area and instantaneous contact line between the convex surface of the i-side and the concave surface of the e-side and the convex surface of the worm gear are distributed as follows: Figure 8 —As shown in Example 11; unlike Example 1, in Figure 6 In this embodiment, the projection of the worm's contact area on its axial section is region ABCD, where AB is the reflection line of the worm wheel tooth tip on the worm, BC is the reflection line of the large end of the worm wheel on the worm, CD is the worm tooth tip, and DA is the small end of the worm. The induced principal curvature of the meshing point within the contact area in this embodiment is... and lubrication angle Ω L The values ​​are listed in Table 2:

[0067] Table 2

[0068]

[0069] Combination Figure 8 and Figure 10 It can be seen that the working length of the worm gear's i-face is relatively long, almost equal to the total length of its thread. Combined with... Figure 9 and Figure 11 It can be seen that the contact areas of the convex and concave surfaces of the worm gear corresponding to the i-face and e-face of the worm are relatively wide, almost covering the entire tooth surface of the worm gear. Moreover, the instantaneous contact lines are evenly distributed without intersection within the contact area of ​​the entire tooth surface of the worm gear, which is beneficial to the heat dissipation and lubrication of the worm pair.

[0070] Figure 8 —11 indicates that the distribution of the contact area and instantaneous contact line on both sides of one tooth of the transmission pair is not significantly different. This reflects, from the perspective of global meshing characteristics, that the meshing asymmetry of the finger-cone envelope biased worm gear pair in this embodiment is not significant.

[0071] As can be seen from Table 2, in this embodiment, the worm gear does not exhibit undercutting on the worm wheel within the entire contact area; the contact stress at these meshing points is low throughout the entire contact area, and the inter-tooth contact stress level is approximately the same, conforming to the principle of equal strength; the conditions for forming an elastohydrodynamic lubricating oil film between the worm gear teeth are favorable, resulting in superior lubrication performance of the transmission pair. Furthermore, the meshing asymmetry of the finger-cone envelope offset worm gear pair in this embodiment is not significant.

[0072] Example 3

[0073] A finger-cone envelope biased worm gear pair and its manufacturing method are disclosed, comprising a finger-cone envelope biased worm gear and a matching face worm wheel. The worm gear pair processing method in this embodiment is the same as in Embodiments 1 and 2, but the worm's cone half-angle, the worm wheel's face cone angle, and the grinding wheel parameters are different. To improve the meshing between the worm's e-face and the worm wheel's concave surface, the process transmission ratio i in this embodiment is adjusted. 12 Increase, i 12 =54.

[0074] In this embodiment, the module, center distance, and axial angle of the worm along the generatrix of the cone are the same as in Embodiments 1 and 2, i.e., m δ =10mm, a 12 =250mm, Σ 12 =90°; worm length L w =0.73a 12 =182.5mm, worm cone half angle δ1=-5°, worm root circle radius r at the midpoint of the worm thread Mf = 37.45mm; Select grinding wheel radius R g =2mm, the same as in Examples 1 and 2, when grinding the i-face of the worm, the semi-cone angle of the grinding wheel is δ. g1 =15°, the grinding wheel deflection angle is taken as ε1 = 5°; when grinding the e-face of the worm, the half-point cone angle of the grinding wheel is taken as δ g2 =15°, the grinding wheel deflection angle is taken as ε2 = 15°;

[0075] Helical parameters of the worm along the generatrix of the worm cone Due to the worm gear countershaft angle Σ in this embodiment 12 =90°, compared to the worm gear installation distance coefficient k in Examples 1 and 2 A Different, k A =0.65, therefore the worm gear pair installation distance z A =k A a 12 =162.5mm;

[0076] like Figure 12 As shown, in this embodiment, in order to ensure that the entire length of the worm thread can be utilized and that the contact areas of the convex and concave tooth surfaces of the worm gear are approximately equal, and to avoid excessive redundancy on the worm gear tooth surface outside the contact area, the face width coefficient of the worm gear can be taken as k. g =0.47; at the axis intersection angle Σ 12 When the angle is 90°, the cone angle of the worm gear face is taken as δ. a2 =97.8°;

[0077] The remaining steps are the same as in Examples 1 and 2. This results in a finger-shaped conical envelope biased worm and a faceted worm wheel, with their centers spaced a distance 'a' as specified in the design. 12 , axis intersection angle Σ 12 and worm gear installation distance z A After assembly, a finger-shaped cone envelope biased worm gear pair is formed.

[0078] In this embodiment, the tooth surface contact area and instantaneous contact line between the convex surface of the i-side and the concave surface of the e-side and the convex surface of the worm gear are distributed as follows: Figure 12 —15; and the induced principal curvature of the meshing point in the contact area. and lubrication angle Ω L The values ​​are listed in Table 3. The above charts illustrate that the meshing performance of this embodiment is the same as that obtained in Embodiments 1 and 2.

[0079] Table 3

[0080]

[0081] The above three embodiments illustrate that the finger-cone envelope offset worm gear transmission proposed in this invention is suitable for applications where the cone half-angle is equal to 5°, 0°, or -5°. Although the cone half-angle of the worm and the cone angle of the worm wheel differ in these three embodiments, the finger-cone envelope offset worm gear pair obtained using the manufacturing method of this invention all possess the following effects: the working length of the worm is almost close to the full length of the worm thread, and the contact area on the worm wheel tooth surface is wide; curvature interference is not easily generated on the tooth surfaces of the transmission pair, and the curvature interference characteristics are almost unaffected by the cone half-angle of the worm and the cone angle of the worm wheel; the instantaneous contact lines of the transmission pair are evenly distributed, sparse, and without intersections, which is beneficial for improving and enhancing the heat dissipation conditions and lubrication performance of the transmission pair; the induced principal curvature is small and the lubrication angle is small, resulting in low tooth surface contact stress and good lubrication performance; the induced principal curvature of the transmission pair is small. and lubrication angle Ω L The numerical values, as well as the distribution of the contact area and instantaneous contact line on both sides of one tooth, are not significantly different, and the meshing asymmetry is not significant. Therefore, the finger-cone envelope offset worm gear pair proposed in this invention has a wide applicable transmission ratio range and good meshing performance.

[0082] All matters not covered in this invention are common knowledge.

[0083] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for manufacturing a finger-shaped conical envelope biased worm gear pair, characterized in that, It includes the following two steps: Step 1: Manufacturing a finger-shaped cone-shaped envelope biased worm gear Worm blank and moving coordinate system The unit basis vector of the fixed-connected, moving coordinate system σ1 Along the axis of the worm blank, from its inner end to its outer end, the origin O1 is located on the axis of the worm blank and is the midpoint of the worm thread length; the static coordinate system of the worm blank is... With the above They coincide, and are also along the axis of the worm gear blank; Finger-shaped conical grinding wheel and coordinate system Fixed connection, origin O d Coinciding with the center of the small end of the grinding wheel, the unit base vector Along the axis of the grinding wheel, from its small end to its large end; unit base vector and Parallel, unit basis vector and The included angle between them is the grinding wheel deflection angle ε. S When S=1, the finger-shaped conical grinding wheel grinds the i-face of the worm, which is the helical surface facing the inner end of the worm; when S=2, the finger-shaped conical grinding wheel grinds the e-face of the worm, which is the helical surface facing the outer end of the worm; the initial position, i.e., the tool setting reference point position, is the coordinate origin O. d The distance between O1 and the worm thread is equal to the root circle radius r at the midpoint of the worm thread. Mf During the grinding of the helical surface of a worm gear with a finger-shaped conical grinding wheel, the grinding wheel moves along a straight line parallel to the generatrix of the worm gear. To perform translational motion, in a straight line The angle between the worm blank axis and the worm blank axis is the cone half angle δ1 of the worm. When the worm blank is wound Turn the angle At that time, the grinding wheel is relative to the tool setting reference point O. d distance of movement p is the helical parameter of the worm along its generatrix; Step 2: Manufacturing the surface worm gear The worm gear blank is cut with a hob, the profile of which coincides with the helical surface of the worm obtained in step one. The hob makes a linear translational feed motion along the axis of the worm gear. The static coordinate system of the worm gear blank is... Unit basis vector Coinciding with the axis of the worm gear, its direction is from the tooth tip to the tooth root, and the unit base vector is... Along the direction of the common perpendicular line between the worm axis and the face worm wheel axis; points O′ and O2 are the feet of the perpendicular line on the enveloping worm axis and face worm wheel axis, respectively, a 12 Let z be the center distance of the finger-cone envelope offset worm pair, and let z be the distance from point O′ along the worm axis to the origin O1. A +L w / 2,z A and L w These are the worm gear mounting distance and thread length, respectively. During the process of forming a worm gear with a hob, both the hob and the worm gear blank rotate around their respective axes. The process installation distance of the hob and the installation distance of the worm gear are z. A Similarly, the center distance of the process shaft between the hob and the worm gear blank, the angle between the process shafts, and the process transmission ratio are also related to the center distance a of the worm pair. 12 , axis intersection angle Σ 12 and transmission ratio i 12 equal; The worm obtained in step one and the worm wheel obtained in step two are connected at a center distance 'a' as specified in the design. 12 , axis intersection angle Σ 12 and worm gear installation distance z A After assembly, a finger-shaped cone envelope biased worm gear pair is formed.

2. The manufacturing method of a finger-shaped conical envelope biased worm gear pair according to claim 1, characterized in that: The range of the worm gear cone half-angle δ1 mentioned in step one is -5°≤δ1≤5°; the cone angle δ of the face worm wheel a2 Based on the worm's cone half-angle δ1 and axis intersection angle Σ 12 The value of δ is determined based on the meshing result of the worm gear pair, and its range is usually 75°≤δ. a2 ≤105°.

3. The manufacturing method of a finger-cone envelope biased worm gear pair according to claim 1, characterized in that: The finger-shaped conical grinding wheel mentioned in step one has the following basic parameters: the radius R of the small end of the grinding wheel. g and the half-aperture cone angle δ of the grinding wheel g The values ​​of both need to be selected based on the meshing performance of the worm gear pair, and it must be ensured that the finger grinding wheel can be placed into the tooth groove.

4. The manufacturing method of a finger-cone envelope biased worm gear pair according to claim 1, characterized in that: The finger-shaped conical grinding wheel deflection angle ε mentioned in step one S The value must not only ensure that the worm tooth angle meets the design requirements, but can also be adjusted by adjusting ε. S This is to alleviate the asymmetry in meshing between the two sides of the worm tooth when grinding the i-face and e-face of the worm tooth.

5. A finger-shaped conical envelope biased worm gear pair, characterized in that: The worm gear pair is manufactured using the manufacturing method described in any one of claims 1-4.

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