CN106112379A - The variable element of a kind of hindley worm pair is combined correction method - Google Patents

Abstract

A variable parameter compound modification method for a straight-profile toroidal worm pair, the steps of which are: establishing a worm machining coordinate system group; determining the relative positional relationship of each coordinate system in the worm machining coordinate system group; determining the process center of the worm during machining distance; determine the process transmission ratio between the worm and the tool seat; determine the height modification amount of the tool seat; install a straight-edge turning tool on the tool seat to complete the modification process of the worm; prepare for hobbing processing of the worm wheel, first prepare A processing hob, the production surface of the hob is consistent with the helical surface of the worm that has been modified, and then the hob and the worm gear are installed on the gear hobbing machine; the worm gear processing coordinate system group is established; the worm gear processing coordinate system group is determined The relative position relationship of each coordinate system in the worm gear; set the transmission ratio of the worm gear and the center distance of the worm gear during the processing of the worm gear; complete the rolling cutting process of the worm gear, and then assemble the processed worm and worm gear, and then obtain the variable parameter composite Modified straight profile toroidal worm pair.

Description

A compound modification method with variable parameters for a straight-profile toroidal worm pair

technical field

The invention belongs to the technical field of modification of a straight-profile toroidal worm pair, in particular to a variable-parameter composite modification method for a straight-profile toroidal worm pair.

Background technique

The application of the straight-profile toroidal worm pair has a long history. During the early application process of the straight-profile toroidal worm pair, technicians made an important discovery, that is, after a period of use of the straight-profile toroidal worm pair, its On the contrary, the meshing performance can be improved. Inspired by this discovery, relevant technical personnel began to study the modification of the straight-profile toroidal worm pair.

In the early days, the modification method of the straight-profile toroidal worm pair was mainly based on the natural modification curve, and the process transmission ratio when processing the toroidal worm was required to be able to change continuously. This modification method has semi-empirical and semi-analytic properties in nature, and can To a certain extent, the running-in time of the worm pair can be shortened, and the ridges that often touch the tooth surface of the worm gear can be removed. However, the modified worm pair obtained by this modification method will have curvature interference on the tooth surface of the worm gear, and the instantaneous contact line will be densely distributed at the meshing end of the worm, which is very unfavorable for heat dissipation and lubrication. At the same time, the use of this modification method has little effect on the range of the contact area of the worm gear tooth surface.

In order to improve the fitting accuracy of the natural shape modification curve, relevant technical personnel have proposed a high-order shape modification method. However, the modified worm pair obtained by this modification method has no obvious advantages in improving the transmission performance of the worm pair.

In order to get rid of the limitation of the modification curve, relevant technical personnel have proposed a constant parameter modification method. However, the modified worm pair obtained by this modification method has not improved the meshing performance.

Recently, relevant technical personnel have proposed a purely rational modification method, which is based on the gear meshing theory, and has completely got rid of the empirical research of straight-profile toroidal worm pair modification, but there are still some problems in this modification method. The disadvantage is that it has little effect on expanding the contact area of the tooth surface of the worm gear, does not help to alleviate the dense distribution of the instantaneous contact line at the meshing end of the worm, and sometimes causes curvature interference on the tooth surface of the worm gear.

Therefore, the existing modification methods have been difficult to further improve the working performance of the straight-profile toroidal worm pair. In order to improve the practical application effect of the straight-profile toroidal worm pair, it is urgent to design a new straight-profile toroidal worm pair modification. method, through this modification method, the working performance of the straight-profile toroidal worm pair can be further improved.

Contents of the invention

Aiming at the problems existing in the prior art, the present invention provides a variable-parameter compound modification method for straight-profile toroidal worm pairs. The modified worm pair obtained by this modification method has no curvature interference on the worm gear tooth surface, and the worm gear teeth The surface contact area has a large range, and the contact area can cover most of the worm gear tooth surface. The effective working length of the worm is longer, and the instantaneous contact line is sparsely and evenly distributed at the meshing end of the worm, which is more conducive to heat dissipation and lubrication.

In order to achieve the above object, the present invention adopts the following technical scheme: a variable parameter compound modification method of a straight-profile toroidal worm pair, comprising the following steps:

Step 1: Establish the worm processing coordinate system group

① Worm moving coordinate system

② Worm static coordinate system

③Tool holder moving coordinate system

④ Tool seat static coordinate system

Step 2: Determine the relative positional relationship of each coordinate system in the worm processing coordinate system group

① Worm moving coordinate system The unit basis vector of Static coordinate system with worm The unit basis vector of overlap;

②Tool holder moving coordinate system The unit basis vector of static coordinate system The unit basis vector of overlap;

③ Rotation center line of worm and static coordinate system of worm The unit basis vector of overlap;

④ Rotation centerline of the tool holder and the static coordinate system of the tool holder The unit basis vector of are coincident, and the tool seat is in the static coordinate system of the tool seat The unit basis vector of Direction has a degree of freedom of linear motion;

⑤ Worm static coordinate system The unit basis vector of static coordinate system The unit basis vector of are perpendicular to each other, and its common perpendicular segment is denoted as and common perpendicular segment Static coordinate system with worm The unit basis vector of The direction is the same, and the process center distance of the worm during processing is recorded as a _d , and

Step 3: Determine the process center distance of the worm during processing

The calculation formula of the process center distance is a _d = a+Δa, where a _d is the process center distance, a is the worm pair center distance, and Δa is the center distance modification amount;

Step 4: Determine the process transmission ratio between the worm and the tool holder

The formula for calculating the process transmission ratio is i _1d = i ₁₂ +Δi, where i _1d is the process transmission ratio, i ₁₂ is the worm pair transmission ratio, and Δi is the transmission ratio modification amount;

Step 5: Determine the height modification amount of the tool seat

Step 6: Install a straight-edge turning tool on the tool holder, and start the turning process of the helical surface of the worm according to the modification parameters set in steps 3 to 5 until the modification of the worm is completed;

Step 7: Prepare for the hobbing of the worm gear. First, prepare a torus hob for processing. The production surface of the hob is consistent with the spiral surface of the modified worm obtained in step 6. Then install the hob and worm gear on the hobbing machine;

Step 8: Establish the worm gear processing coordinate system group

① Worm gear moving coordinate system

② Static coordinate system of worm gear

③The moving coordinate system of the hob follows the moving coordinate system of the worm

④The hob static coordinate system, which follows the worm static coordinate system

Step 9: Determine the relative positional relationship of each coordinate system in the worm gear machining coordinate system group

① Hob moving coordinate system The unit basis vector of static coordinate system with hob The unit basis vector of overlap;

② Worm gear dynamic coordinate system The unit basis vector of Static coordinate system with worm gear The unit basis vector of overlap;

③Rotation center line of the hob and the static coordinate system of the hob The unit basis vector of overlap;

④ Rotation centerline of worm gear and static coordinate system of worm gear The unit basis vector of overlap;

⑤Static coordinate system of hob The unit basis vector of Static coordinate system with worm gear The unit basis vector of are perpendicular to each other, and its common perpendicular segment is denoted as and common perpendicular segment static coordinate system with hob The unit basis vector of The direction is the same, the hob is in the static coordinate system of the hob The unit basis vector of Direction has a degree of freedom of linear motion;

Step 10: Set the process transmission ratio in the process of machining the worm gear by the hob to be the transmission ratio of the worm pair i ₁₂ , and satisfy Equal to the worm auxiliary center distance a;

Step 11: Start the hobbing process of the worm gear until the hobbing process of the worm gear is completed, and then assemble the processed worm and the worm gear, and then obtain a straight-profile toroidal worm pair with variable parameter compound correction.

The center distance modification amount Δa in step 3 is a constant, and its recommended value range is -0.2m _t ~ 1.5m _t , where m _t is the modulus of the end face of the worm gear; when Δa is a positive value, the tool holder needs to be Static coordinate system The unit basis vector of Move the |Δa| length in the positive direction. When Δa takes a negative value, the tool holder needs to move along the static coordinate system of the tool holder. The unit basis vector of Negative movement by |Δa| length.

The transmission ratio modification amount Δi in step 4 is the worm rotation angle function, that is Its expression is

in, Δ _f ＝a(0.0003+0.000034i ₁₂ ), where, Δi is the modification amount of the transmission ratio, i ₁₂ is the transmission ratio of the worm pair, is the rotation angle of the worm, _Δf is the modification amount of the worm’s meshing end, is the working half angle of the worm surrounded by the worm, α is the pressure angle of the worm gear indexing circle, d ₂ is the diameter of the worm wheel indexing circle.

The tool seat height modification amount in step 5 is recorded as Δb, which is the worm rotation angle function, that is Its expression is

in, In the formula, α is the pressure angle of the worm gear indexing circle, is the worm rotation angle, i ₁₂ is the transmission ratio of the worm pair, Δb is the height modification amount of the tool seat, For the working half angle of the worm surrounded by the worm gear, is the nominal angle of the straight line of the blade, b ₀ and b ₁ are constants, the suggested value range of b ₀ is -0.1b ₂ ～0.25b ₂ , and the suggested value range of b ₁ is 0.01b ₂ ～0.1b ₂ , where , b ₂ is the tooth width of the worm gear;

When Δb is a positive value, the tool seat moving coordinate system The origin O _d of is located below the middle plane of the worm pair in the horizontal position; when Δb is negative, the tool seat moving coordinate system The origin O _d of is located above the middle plane of the worm pair in the horizontal position.

Beneficial effects of the present invention:

Compared with the prior art, the modified worm pair obtained by the modification method of the present invention has no curvature interference on the tooth surface of the worm gear, the contact area of the tooth surface of the worm gear is larger, and the contact area can cover most of the worm gear teeth. On the other hand, the effective working length of the worm is longer, and the instantaneous contact line is distributed sparsely and evenly at the worm's engaging end, which is more conducive to heat dissipation and lubrication.

Description of drawings

Fig. 1 is a schematic diagram of the processing coordinate system group of the worm pair (worm + worm gear);

Fig. 2 is the schematic diagram of the processing principle of the worm;

Fig. 3 is a diagram showing the distribution of the worm gear tooth surface contact area and instantaneous contact line in Embodiment 1;

Fig. 4 is a diagram of the distribution of the worm helical surface contact area and the instantaneous contact line in Embodiment 1;

Fig. 5 is a function graph of Δi(k _w ) and Δb(k _w ) in Embodiment 1;

Fig. 6 is a distribution diagram of the worm gear tooth surface contact area and instantaneous contact line in the second embodiment;

Fig. 7 is a diagram of the distribution of the worm helical surface contact area and the instantaneous contact line in the second embodiment;

Fig. 8 is a function graph of Δi(k _w ) and Δb(k _w ) in Example 2;

detailed description

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

Embodiment one

The worm in this embodiment is a right-handed single-head worm.

A variable parameter compound modification method for a straight-profile toroidal worm pair, comprising the following steps:

Step 1: Establish the worm processing coordinate system group

① Worm moving coordinate system

② Worm static coordinate system

③Tool holder moving coordinate system

④ Tool seat static coordinate system

Step 2: As shown in Figure 1, determine the relative positional relationship of each coordinate system in the worm machining coordinate system group

① Worm moving coordinate system The unit basis vector of Static coordinate system with worm The unit basis vector of overlap;

②Tool holder moving coordinate system The unit basis vector of static coordinate system The unit basis vector of overlap;

③ Rotation center line of worm and static coordinate system of worm The unit basis vector of overlap;

④ Rotation centerline of the tool holder and the static coordinate system of the tool holder The unit basis vector of are coincident, and the tool seat is in the static coordinate system of the tool seat The unit basis vector of Direction has a degree of freedom of linear motion;

⑤ Worm static coordinate system The unit basis vector of static coordinate system The unit basis vector of are perpendicular to each other, and its common perpendicular segment is denoted as and common perpendicular segment Static coordinate system with worm The unit basis vector of The direction is the same, and the process center distance of the worm during processing is recorded as a _d , and

Step 3: Determine the process center distance of the worm during processing

The calculation formula of the process center distance is a _d = a+Δa, where a _d is the process center distance, a is the worm pair center distance, and Δa is the center distance modification amount;

The center distance modification value Δa is a constant, and its recommended value range is -0.2m _t ~ 1.5m _t , where m _t is the modulus of the end face of the worm gear; The unit basis vector of Move the |Δa| length in the positive direction. When Δa takes a negative value, the tool holder needs to move along the static coordinate system of the tool holder. The unit basis vector of Negative movement | Δa length;

In this embodiment, the center distance a of the worm pair is 300 mm, and the modulus m _t of the end surface of the worm gear is 10, the suggested value range of Δa is -2 mm to 15 mm, and the actual value of Δa = 5 mm, and a _d = 305 mm; During the actual operation, the tool seat needs to move along the static coordinate system of the tool seat The unit basis vector of Move 5mm in the forward direction, and make the public vertical line segment The length reaches 305mm;

Step 4: Determine the process transmission ratio between the worm and the tool holder

The formula for calculating the process transmission ratio is i _1d = i ₁₂ +Δi, where i _1d is the process transmission ratio, i ₁₂ is the worm pair transmission ratio, and Δi is the transmission ratio modification amount;

Transmission ratio modification amount Δi is the worm rotation angle function, that is Its expression is

in, Δ _f ＝a(0.0003+0.000034i ₁₂ ), where, Δi is the modification amount of the transmission ratio, i ₁₂ is the transmission ratio of the worm pair, is the rotation angle of the worm, _Δf is the modification amount of the worm’s meshing end, is the working half angle of the worm surrounded by the worm, α is the pressure angle of the worm gear indexing circle, d ₂ is the diameter of the worm wheel indexing circle;

In the present embodiment, the transmission ratio i12 _of the worm pair is 50, and the worm surrounds the working half angle of the worm wheel is 16.38°, the pressure angle α of the worm gear index circle is 22.09°, and the diameter d ₂ of the worm wheel index circle is 500mm, it can be obtained that Δ _f =0.6mm, C ₁ =0.0294, C ₂ =0.3029, C ₃ =0.014, and then The expression of transmission ratio modification amount Δi is

Finally, the process transmission ratio i _1d between the worm and the tool holder can be obtained, and its expression is

In the worm machining process, the process transmission ratio i _1d needs to change with the worm rotation angle Changes and real-time dynamic adjustments based on the above formula;

Step 5: Determine the height modification amount of the tool seat

The height modification amount of the tool seat is recorded as Δb, which is the worm rotation angle function, that is Its expression is

in, In the formula, α is the pressure angle of the worm gear indexing circle, is the worm rotation angle, i ₁₂ is the transmission ratio of the worm pair, Δb is the height modification amount of the tool seat, For the working half angle of the worm surrounded by the worm gear, is the nominal angle of the straight line of the blade, b ₀ and b ₁ are constants, the suggested value range of b ₀ is -0.1b ₂ ～0.25b ₂ , and the suggested value range of b ₁ is 0.01b ₂ ～0.1b ₂ , where , b ₂ is the tooth width of the worm gear;

When Δb is a positive value, the tool seat moving coordinate system The origin O _d of is located below the middle plane of the worm pair in the horizontal position; when Δb is negative, the tool seat moving coordinate system The origin O _d of is located above the middle plane of the worm pair in the horizontal position;

In this embodiment, the tooth width b ₂ of the worm gear is 75mm, and the recommended value range of b ₀ is -7.5mm to 18.75mm, and the recommended value range of b ₁ is 0.75mm to 7.5mm, and the actual value of b ₀ =10mm , b ₁ =5mm, the working half angle of the worm surrounded by the worm gear is known is 16.38°, and the pressure angle α of the worm gear indexing circle is 22.09°, the tool seat height modification amount Δb can be finally obtained, and its expression is

In the process of worm machining, the tool seat height modification amount Δb needs to increase with the worm rotation angle Changes and real-time dynamic adjustments based on the above formula;

Step 6: Install a straight-edge turning tool on the tool holder, and follow the modification parameters set in steps 3 to 5, as shown in Figure 2, to start the turning process of the helical surface of the worm until the modification of the worm is completed;

Step 7: Prepare for the hobbing of the worm gear. First, prepare a torus hob for processing. The production surface of the hob is consistent with the spiral surface of the modified worm obtained in step 6. Then install the hob and worm gear on the hobbing machine;

Step 8: Establish the worm gear processing coordinate system group

① Worm gear moving coordinate system

② Static coordinate system of worm gear

③The moving coordinate system of the hob follows the moving coordinate system of the worm

④The hob static coordinate system, which follows the worm static coordinate system

Step 9: Determine the relative positional relationship of each coordinate system in the worm gear machining coordinate system group

① Hob moving coordinate system The unit basis vector of static coordinate system with hob The unit basis vector of overlap;

② Worm gear dynamic coordinate system The unit basis vector of Static coordinate system with worm gear The unit basis vector of overlap;

③Rotation center line of the hob and the static coordinate system of the hob The unit basis vector of overlap;

④ Rotation centerline of worm gear and static coordinate system of worm gear The unit basis vector of overlap;

⑤Static coordinate system of hob The unit basis vector of Static coordinate system with worm gear The unit basis vector of are perpendicular to each other, and its common perpendicular segment is denoted as and common perpendicular segment static coordinate system with hob The unit basis vector of The direction is the same, the hob is in the static coordinate system of the hob The unit basis vector of Direction has a degree of freedom of linear motion;

Step 10: Set the process transmission ratio in the process of machining the worm gear by the hob to be the transmission ratio of the worm pair i ₁₂ , and satisfy Equal to the worm auxiliary center distance a;

In the present embodiment, the transmission ratio i12 _of the worm pair is 50, and the center distance a of the worm pair is 300mm;

Step 11: Start the hobbing process of the worm gear until the hobbing process of the worm gear is completed, at this time It is exactly equal to 300mm, and then the processed worm and worm gear are assembled to obtain a straight-profile toroidal worm pair with variable parameter compound correction.

For the variable parameter compound modified straight-profile toroidal worm pair obtained above, the distribution diagram of the contact area and instantaneous contact line of the worm gear tooth surface is shown in Figure 3, and the distribution diagram of the contact area and instantaneous contact line of the worm helical surface is shown in Figure 3. 4.

In Figure 3, the AB line and the CD line are the reflection lines of the meshing end of the worm on the worm gear tooth surface, and the EF line is the conjugate line of the meshing boundary line of the worm pair on the worm gear tooth surface, and the contact area ABFE is recorded as the first sub-contact area , the contact area CDFE is recorded as the second sub-contact area, and the first and second sub-contact areas are smoothly connected at the conjugate line EF of the meshing boundary, and together constitute the contact area of the worm pair.

The instantaneous contact lines in the first sub-contact area are 1, 2, 3, 4, 5, and the instantaneous contact lines in the second sub-contact area are 1', 2', 3', 4', 5'. During the cycle, the instantaneous contact lines (such as 1 and 1') corresponding to the secondary edge of the worm contact at the same time. Based on this, it can be seen that the variable parameter compound modified straight-profile toroidal worm pair can realize multi-tooth contact during the transmission process. two-wire contact. Furthermore, it can be seen from Figure 3 that the instantaneous contact line is distributed sparsely and evenly in the entire contact area of the worm gear tooth surface, which is more conducive to improving and improving the heat dissipation conditions and lubrication performance of the worm pair.

It can be seen from Fig. 4 that the effective working length of the worm is longer, and in the whole meshing cycle, the variable parameter compound modified straight-profile toroidal worm pair can realize multi-tooth double-line contact in the transmission process. Combining Figure 3 and Figure 4, it shows that the modified worm pair obtained by the modification method of the present invention has good overall meshing characteristics.

In order to further illustrate the working performance of the variable parameter compound modified straight-profile toroidal worm pair obtained above, three meshing points a, b, and c are sequentially taken from the tooth top to the tooth root along each instantaneous contact line of the worm gear contact area, and Calculation of induced principal curvatures at all meshing points and sliding angle θ _vt , the specific numerical results are shown in Table 1.

As can be seen in Table 1, the induced principal curvature throughout the contact zone The positive and negative signs of are unchanged, indicating that there is no curvature interference in the entire contact area; the induced principal curvature at each meshing point The values are relatively close, indicating that the contact stress level between the teeth in the entire contact area is roughly the same, and it is also in line with the principle of equal strength; the values of the sliding angle θ _vt in the entire contact area are relatively large, indicating that the elastic flow between the teeth of the worm gear The conditions of the lubricating oil film are better, so that the worm pair has better lubricating performance. Again, the induced principal curvature in the second sub-contact region The value of is small, while the value of sliding angle θ _vt is large, indicating that the local meshing performance of the second sub-contact area is superior.

In order to further highlight the function curve and At the same time, introduce a coefficient k _w , and draw the function curve of Δi(k _w ) and Δb(k _w ), so as to reflect the change of transmission ratio modification Δi and tool seat height modification Δb along the length of the worm law.

Coefficient k _w and worm rotation angle The functional relation of

In the formula, is the working half angle of the worm surrounded by the worm gear, α is the pressure angle of the worm gear indexing circle, is the worm rotation angle, i ₁₂ is the transmission ratio of the worm pair; when k _w =0, it corresponds to the meshing end of the worm; when k _w =1, it corresponds to the throat of the worm; when k _w =2, it corresponds to the meshing end of the worm out.

Will and Merge and eliminate worm corners The functional relationship between the transmission ratio modification amount Δi and the coefficient k _w can be obtained as

In the formula, Δi is the modification amount of the transmission ratio, i ₁₂ is the transmission ratio of the worm pair, α is the pressure angle of the worm gear indexing circle, is the working half angle of the worm surrounded by the worm gear, Δ _f is the modification amount of the worm meshing end, d ₂ is the diameter of the worm gear pitch circle;

It can be seen from the foregoing that i ₁₂ =50, α=22.09°, Δ _f =0.6mm, d ₂ =500mm, the following functional relationship can be obtained

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 0.12</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.7</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 0.0996</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.2859</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.0024</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.7</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

Will and and Merge and eliminate worm corners The functional relationship between the tool seat height modification amount Δb and the coefficient k _w can be obtained as

Δb(k _w )=Δb=b ₀ +b ₁ (1-k _w )

It can be seen from the above that b ₀ =10mm, b ₁ =5mm, the following functional relationship can be obtained

Δb(k _w )=Δb=15-5k _w

through the function relation And the functional relationship Δb(k _w )=Δb=15-5k _w can be drawn to obtain the function curves of Δi(k _w ) and Δb(k _w ), as shown in FIG. 5 . It can be seen from Fig. 5 that the transmission ratio modification amount Δi is nonlinear and non-monotonic along the length of the worm, and its value is always greater than 0, and it is the largest at the meshing end, while there is a minimum between the throat and the meshing end. value, and its minimum value is close to 0. It can be seen from Fig. 5 that the value of the correction amount Δb of the tool seat height decreases linearly from the biting end to the biting end, and it is the largest at the biting end and the smallest at the biting end.

Embodiment two

The worm in this embodiment is a right-handed five-head worm.

A variable parameter compound modification method for a straight-profile toroidal worm pair, comprising the following steps:

Step 1: Establish the worm processing coordinate system group

① Worm moving coordinate system

② Worm static coordinate system

③Tool holder moving coordinate system

④ Tool seat static coordinate system

Step 2: As shown in Figure 1, determine the relative positional relationship of each coordinate system in the worm machining coordinate system group

① Worm moving coordinate system The unit basis vector of Static coordinate system with worm The unit basis vector of overlap;

②Tool holder moving coordinate system The unit basis vector of static coordinate system The unit basis vector of overlap;

③ Rotation center line of worm and static coordinate system of worm The unit basis vector of overlap;

④ Rotation centerline of the tool holder and the static coordinate system of the tool holder The unit basis vector of are coincident, and the tool seat is in the static coordinate system of the tool seat The unit basis vector of Direction has a degree of freedom of linear motion;

⑤ Worm static coordinate system The unit basis vector of static coordinate system The unit basis vector of are perpendicular to each other, and its common perpendicular segment is denoted as and common perpendicular segment Static coordinate system with worm The unit basis vector of The direction is the same, and the process center distance of the worm during processing is recorded as a _d , and

Step 3: Determine the process center distance of the worm during processing

The calculation formula of the process center distance is a _d = a+Δa, where a _d is the process center distance, a is the worm pair center distance, and Δa is the center distance modification amount;

The center distance modification value Δa is a constant, and its recommended value range is -0.2m _t ~ 1.5m _t , where m _t is the modulus of the end face of the worm gear; The unit basis vector of Move the |Δa| length in the positive direction. When Δa takes a negative value, the tool holder needs to move along the static coordinate system of the tool holder. The unit basis vector of Negative movement | Δa length;

In this embodiment, the center distance a of the worm pair is 300 mm, and the modulus m _t of the end surface of the worm gear is 10. The recommended value range of Δa is -2 mm to 15 mm. The actual value of Δa=10.8 mm, and a _d =310.8 mm; during the actual operation, the tool holder needs to move along the static coordinate system of the tool holder The unit basis vector of Move 10.8mm in the positive direction, and make the public vertical line segment The length reaches 310.8mm;

Step 4: Determine the process transmission ratio between the worm and the tool holder

The formula for calculating the process transmission ratio is i _1d = i ₁₂ +Δi, where i _1d is the process transmission ratio, i ₁₂ is the worm pair transmission ratio, and Δi is the transmission ratio modification amount;

Transmission ratio modification amount Δi is the worm rotation angle function, that is Its expression is

in, Δ _f ＝a(0.0003+0.000034i ₁₂ ), where, Δi is the modification amount of the transmission ratio, i ₁₂ is the transmission ratio of the worm pair, is the rotation angle of the worm, _Δf is the modification amount of the worm’s meshing end, is the working half angle of the worm surrounded by the worm, α is the pressure angle of the worm gear indexing circle, d ₂ is the diameter of the worm wheel indexing circle;

In the present embodiment, the transmission ratio i12 _of the worm pair is 50, and the worm surrounds the working half angle of the worm wheel is 16.38°, the worm gear indexing circle pressure angle α is 22.09°, and the worm wheel indexing circle diameter d ₂ is 500mm, it can be obtained that Δ _f =0.192mm, C ₁ =0.0094, C ₂ =0.3556, C ₃ =0.07, and then The expression of transmission ratio modification amount Δi is

Finally, the process transmission ratio i _1d between the worm and the tool holder can be obtained, and its expression is

In the worm machining process, the process transmission ratio i _1d needs to change with the worm rotation angle Changes and real-time dynamic adjustments based on the above formula;

Step 5: Determine the height modification amount of the tool seat

The height modification amount of the tool seat is recorded as Δb, which is the worm rotation angle function, that is Its expression is

in, In the formula, α is the pressure angle of the worm gear indexing circle, is the worm rotation angle, i ₁₂ is the transmission ratio of the worm pair, Δb is the height modification amount of the tool seat, For the working half angle of the worm surrounded by the worm gear, is the nominal angle of the straight line of the blade, b ₀ and b ₁ are constants, the suggested value range of b ₀ is -0.1b ₂ ～0.25b ₂ , and the suggested value range of b ₁ is 0.01b ₂ ～0.1b ₂ , where , b ₂ is the tooth width of the worm gear;

When Δb is a positive value, the tool seat moving coordinate system The origin O _d of is located below the middle plane of the worm pair in the horizontal position; when Δb is negative, the tool seat moving coordinate system The origin O _d of is located above the middle plane of the worm pair in the horizontal position;

In this embodiment, the tooth width b2 of the worm gear is 75mm, and the suggested value range of b0 is _-7.5mm ～ _18.75mm , the suggested value range of b1 is 0.75mm～7.5mm, and the actual value of _{b0 =} 13mm , b ₁ ＝6mm, it is known that the worm surrounds the working half angle of the worm gear is 16.38°, and the pressure angle α of the worm gear indexing circle is 22.09°, the tool seat height modification amount Δb can be finally obtained, and its expression is

In the process of worm machining, the tool seat height modification amount Δb needs to increase with the worm rotation angle Changes and real-time dynamic adjustments based on the above formula;

Step 6: Install a straight-edge turning tool on the tool holder, and follow the modification parameters set in steps 3 to 5, as shown in Figure 2, to start the turning process of the helical surface of the worm until the modification of the worm is completed;

Step 7: Prepare for the hobbing of the worm gear. First, prepare a torus hob for processing. The production surface of the hob is consistent with the spiral surface of the modified worm obtained in step 6. Then install the hob and worm gear on the hobbing machine;

Step 8: Establish the worm gear processing coordinate system group

① Worm gear moving coordinate system

② Static coordinate system of worm gear

③The moving coordinate system of the hob follows the moving coordinate system of the worm

④The hob static coordinate system, which follows the worm static coordinate system

Step 9: Determine the relative positional relationship of each coordinate system in the worm gear machining coordinate system group

① Hob moving coordinate system The unit basis vector of static coordinate system with hob The unit basis vector of overlap;

② Worm gear dynamic coordinate system The unit basis vector of Static coordinate system with worm gear The unit basis vector of overlap;

③Rotation center line of the hob and the static coordinate system of the hob The unit basis vector of overlap;

④ Rotation centerline of worm gear and static coordinate system of worm gear The unit basis vector of overlap;

⑤Static coordinate system of hob The unit basis vector of Static coordinate system with worm gear The unit basis vector of are perpendicular to each other, and its common perpendicular segment is denoted as and common perpendicular segment static coordinate system with hob The unit basis vector of The direction is the same, the hob is in the static coordinate system of the hob The unit basis vector of Direction has a degree of freedom of linear motion;

Step 10: Set the process transmission ratio in the process of machining the worm gear by the hob to be the transmission ratio of the worm pair i ₁₂ , and satisfy Equal to the worm auxiliary center distance a;

In the present embodiment, the transmission ratio i12 _of the worm pair is 10, and the center distance a of the worm pair is 300mm;

Step 11: Start the hobbing process of the worm gear until the hobbing process of the worm gear is completed, at this time It is exactly equal to 300mm, and then the processed worm and worm gear are assembled to obtain a straight-profile toroidal worm pair with variable parameter compound correction.

For the variable parameter compound modified straight-profile toroidal worm pair obtained above, the distribution diagram of the contact area and instantaneous contact line of the worm gear tooth surface is shown in Fig. 6, and the distribution diagram of the contact area and instantaneous contact line of the worm helical surface is shown in Fig. 7.

In Figure 6, the AB line is the reflection line of the worm meshing end on the worm gear tooth surface, the GH line is the boundary line of the worm gear solid tooth surface, and the EF line is the conjugate line of the meshing boundary line of the worm pair on the worm gear tooth surface. The contact area ABFE It is recorded as the first sub-contact area, and the contact area GHFE is recorded as the second sub-contact area. The first and second sub-contact areas are smoothly connected at the conjugate line EF of the meshing boundary, and together constitute the contact area of the worm pair.

The instantaneous contact lines in the first sub-contact area are 1, 2, 3, 4, 5, and the instantaneous contact lines in the second sub-contact area are 3', 4', 5'. As can be seen in Figure 6, the entire The contact area of the tooth surface of the worm gear is relatively large, which can cover most of the tooth surface of the worm gear. The instantaneous contact line is distributed sparsely and evenly in the entire contact area of the tooth surface of the worm gear, which is more conducive to improving and improving the heat dissipation conditions and lubrication performance of the worm gear pair.

It can be seen from Figure 7 that the effective working length of the worm is longer, although the number of worm heads in this embodiment is large and the transmission ratio of the worm pair is small, causing part of the instantaneous contact line in the second sub-contact area to move to the worm gear teeth out-of-plane, but within the entire meshing period, the variable-parameter compound modified straight-profile toroidal worm pair of this embodiment can still achieve multi-tooth double-line contact during the transmission process. Combining Figure 6 and Figure 7, it shows that the modified worm pair obtained by the modification method of the present invention has good overall meshing characteristics.

In order to further illustrate the working performance of the variable parameter compound modified straight-profile toroidal worm pair obtained above, three meshing points a, b, and c are sequentially taken from the tooth top to the tooth root along each instantaneous contact line of the worm gear contact area, and Calculation of induced principal curvatures at all meshing points and sliding angle θ _vt , the specific numerical results are shown in Table 2.

As can be seen in Table 2, the induced principal curvature over the entire contact zone The positive and negative signs of are unchanged, indicating that there is no curvature interference in the entire contact area; the induced principal curvature at each meshing point The values are relatively close, indicating that the contact stress level between the teeth in the entire contact area is roughly the same, and it is also in line with the principle of equal strength; the values of the sliding angle θ _vt in the entire contact area are relatively large, indicating that the elastic flow between the teeth of the worm gear The conditions of the lubricating oil film are better, so that the worm pair has better lubricating performance. Again, the induced principal curvature in the second sub-contact region The value of is small, while the value of sliding angle θ _vt is large, indicating that the local meshing performance of the second sub-contact area is superior.

In order to further highlight the function curve and At the same time, introduce a coefficient k _w , and draw the function curve of Δi(k _w ) and Δb(k _w ), so as to reflect the change of transmission ratio modification Δi and tool seat height modification Δb along the length of the worm law.

Coefficient k _w and worm rotation angle The functional relation of

In the formula, is the working half angle of the worm surrounded by the worm gear, α is the pressure angle of the worm gear indexing circle, is the worm rotation angle, i ₁₂ is the transmission ratio of the worm pair; when k _w =0, it corresponds to the meshing end of the worm; when k _w =1, it corresponds to the throat of the worm; when k _w =2, it corresponds to the meshing end of the worm out.

Will and Merge and eliminate worm corners The functional relationship between the transmission ratio modification amount Δi and the coefficient k _w can be obtained as

In the formula, Δi is the modification amount of the transmission ratio, i ₁₂ is the transmission ratio of the worm pair, α is the pressure angle of the worm gear indexing circle, is the working half angle of the worm surrounded by the worm gear, Δ _f is the modification amount of the worm meshing end, d ₂ is the diameter of the worm gear pitch circle;

It can be known from the foregoing that i ₁₂ =10, α=22.09°, Δ _f =0.192mm, d ₂ =500mm, the following functional relationship can be obtained

$\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 3.84</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.7</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 192.75</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 142.95</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.384</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.7</span>}{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

Will and and Merge and eliminate worm corners The functional relationship between the tool seat height modification amount Δb and the coefficient k _w can be obtained as

Δb(k _w )=Δb=b ₀ +b ₁ (1-k _w )

It can be seen from the above that b ₀ =13mm, b ₁ =6mm, the following functional relationship can be obtained

Δb(k _w )=Δb=19-6k _w

through the function relation And the functional relationship Δb(k _w )=Δb=19-6k _w can be drawn to obtain the function curves of Δi(k _w ) and Δb(k _w ), as shown in FIG. 8 . It can be seen from Fig. 8 that the transmission ratio modification value Δi changes nonlinearly and non-monotonically along the length of the worm, and its value is always greater than 0, and it is the largest at the biting end, while there is a minimum between the throat and the biting end. value, and its minimum value is close to 0. It can be seen from Fig. 8 that the value of the correction amount Δb of the tool seat height decreases linearly from the biting end to the biting end, and it is the largest at the biting end and the smallest at the biting end.

Embodiment 2 Compared with Embodiment 1, although the number of worm heads in Embodiment 2 is larger and the transmission of the worm pair is relatively small, the modified worm pair obtained by the modification method of the present invention is as good as that in Embodiment 1 and Embodiment 1. Both of them can have the following effects: there is no curvature interference on the tooth surface of the worm gear, the contact area of the tooth surface of the worm gear is large, and the contact area can cover most of the tooth surface of the worm gear, the effective working length of the worm is long, and the instantaneous contact line is between the teeth of the worm gear. The distribution of the inlet ends is sparse and uniform, which is more conducive to heat dissipation and lubrication. It can be seen that the shape modification method of the present invention has universal applicability.

The solutions in the embodiments are not intended to limit the scope of patent protection of the present invention, and all equivalent implementations or changes that do not deviate from the present invention are included in the patent scope of this case.

Table 1

Table 2

Claims (4)

1. A variable parameter composite modification method of a straight profile ring surface worm gear pair is characterized by comprising the following steps:

the method comprises the following steps: establishing a worm machining coordinate system set

① worm moving coordinate system

② Worm static coordinate System

③ tool apron moving coordinate system

④ tool apron static coordinate system

Step two: determining the relative position relation of each coordinate system in the worm processing coordinate system group

① worm moving coordinate systemUnit basal vector ofWith the worm gear in a stationary coordinate systemUnit basal vector ofOverlapping;

② tool apron moving coordinate systemUnit basal vector ofWith the tool holder stationary coordinate systemUnit basal vector ofOverlapping;

③ center line of rotation of worm and static coordinate system of wormUnit basal vector ofOverlapping;

④ center line of rotation of tool apron and tool apron static coordinate systemUnit basal vector ofCoinciding with each other and having the tool holder in the tool holder static coordinate systemUnit basal vector ofThe direction has a linear motion freedom degree;

⑤ Worm static coordinate SystemUnit basal vector ofWith the tool holder stationary coordinate systemUnit basal vector ofPerpendicular to each other, with the common perpendicular line segment thereof being denoted asAnd the public vertical line segmentWith the worm gear in a stationary coordinate systemUnit basal vector ofThe directions are consistent, and the process center distance of the worm in the machining process is marked as a_dAnd is and

step three: determining the process center distance of the worm in the machining process

The calculation formula of the process center distance is a_dA + Δ a, wherein a_dThe method is characterized in that the process center distance is shown, a is the center distance of a worm pair, and delta a is the center distance modification amount;

step four: determining a process transmission ratio between a worm and a tool holder

The calculation formula of the process transmission ratio is i_1d＝i₁₂+ Δ i, where i_1dAs a process transmission ratio, i₁₂The gear ratio of the worm pair is adopted, and delta i is the gear ratio modification amount;

step five: determining the height modification amount of the tool apron

Step six: mounting a linear blade turning tool on the tool apron, and starting the turning process of the spiral surface of the worm according to the shape modification parameters set in the third step to the fifth step until the shape modification processing of the worm is completed;

step seven: preparing a processing ring surface hob, wherein the generating surface of the hob is consistent with the spiral surface of the correction worm obtained in the sixth step, and then installing the hob and the worm wheel on a hobbing machine;

step eight: establishing a worm gear machining coordinate system set

① worm gear moving coordinate system

② static coordinate system of worm gear

③ Hob moving coordinate system, which follows worm moving coordinate system

④ Hob static coordinate system, which follows the worm static coordinate system

Step nine: determining the relative position relationship of each coordinate system in the worm gear processing coordinate system group

① hob moving coordinate systemUnit basal vector ofAnd the static coordinate system of the hobUnit basal vector ofOverlapping;

② worm gear moving coordinate systemUnit basal vector ofStatic coordinate system with worm wheelUnit basal vector ofOverlapping;

③ Hob rotation center line and Hob static coordinate systemUnit basal vector ofOverlapping;

④ center line of rotation of worm gear and worm gear static coordinate systemUnit basal vector ofOverlapping;

⑤ Hob static coordinate systemUnit basal vector ofStatic coordinate system with worm wheelUnit basal vector ofPerpendicular to each other, with the common perpendicular line segment thereof being denoted asAnd the public vertical line segmentAnd the static coordinate system of the hobUnit basal vector ofThe directions are consistent, and the hob is in a hob static coordinate systemUnit basal vector ofThe direction has a linear motion freedom degree;

step ten: setting the technological transmission ratio in the process of processing worm gear by hob as the transmission ratio i of worm pair₁₂After the worm gear is machined by the set hob, the requirement is metEqual to the center distance a of the worm pair;

step eleven: and starting the gear hobbing process of the worm wheel until the gear hobbing process of the worm wheel is finished, and then assembling the processed worm and the worm wheel to obtain the variable-parameter composite correction type straight-profile ring surface worm pair.

2. The variable parameter compound modification method of the straight-profile enveloping worm pair as claimed in claim 1, characterized in that: the center distance modification quantity delta a in the third step is a constant, and the suggested value range is-0.2 m_t～1.5m_tWherein m is_tThe end face modulus of the worm wheel; when Δ a takes a positive value, the tool holder needs to follow the tool holder static coordinate systemUnit basal vector ofThe length of the positive movement is delta a, when delta a takes a negative value, the tool apron needs to be along the static coordinate system of the tool apronUnit basal vector ofMoving in the negative direction by | Δ a | length.

3. The variable parameter compound modification method of the straight-profile enveloping worm pair as claimed in claim 1, characterized in that: the transmission ratio modification quantity delta i in the fourth step is the worm rotation angleA function of, i.e.The expression is

Wherein,Δ_f＝a(0.0003+0.000034i₁₂) Where Δ i is the gear ratio modification amount, i₁₂The transmission ratio of the worm pair is set,angle of rotation of worm, Δ_fThe shape correction quantity of the meshing end of the worm,for the worm to surround the working half angle of the worm wheel, α is the pitch pressure angle of the worm wheel, d₂The pitch circle diameter of the worm wheel.

4. The variable parameter compound modification method of the straight-profile enveloping worm pair as claimed in claim 1, characterized in that: and step five, recording the height modification quantity of the tool apron as delta b which is the rotation angle of the wormA function of, i.e.The expression is

Wherein,wherein α is the reference circle pressure angle of worm wheel,is the angle of rotation of the worm i₁₂Is the transmission ratio of the worm pair, delta b is the height modification amount of the tool apron,the worm surrounds the working half angle of the worm wheel,is the nominal angle of the straight line of the cutting edge, b₀、b₁Are all constants, b₀The suggested value range of (a) is-0.1 b₂～0.25b₂，b₁Is in the range of 0.01b₂～0.1b₂Wherein b is₂The tooth width of the worm wheel is wide;

when delta b is a positive value, the tool apron moves a coordinate systemOrigin O of_dThe worm gear is positioned below the middle plane of the worm gear pair in the horizontal position; when delta b is a negative value, the tool apron moves a coordinate systemOrigin O of_dIs positioned above the middle plane of the worm gear pair in the horizontal position.