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

Abstract

The variable element of a kind of hindley worm pair is combined correction method, and step is: set up worm screw Cutter coordinate system group；Determine the relative position relation of worm screw Cutter coordinate system group each coordinate system interior；Determine worm screw technique centre-to-centre spacing in the course of processing；Determine the technique gear ratio between worm screw and tool rest；Determine the height profiling quantity of tool rest；Tool rest is installed straight line sword lathe tool, completes the correction of the flank shape processing of worm screw；Being ready for the Rolling-cut shear of worm gear, first prepare a processing hobboing cutter, the generating surface of hobboing cutter is consistent with the helicoid of the worm screw completing correction of the flank shape processing, then hobboing cutter and worm gear is installed on gear-hobbing machine；Set up spiral case making coordinate system group；Determine the relative position relation of spiral case making coordinate system group each coordinate system interior；Set worm gear worm gear pair transmission when worm gear pair centre-to-centre spacing in the course of processing；Complete the Rolling-cut shear of worm gear, then the worm and worm wheel processed are assembled, and then obtaining variable element, to be combined correction type hindley worm secondary.

Description

Variable parameter composite modification method for straight profile ring surface worm gear pair

Technical Field

The invention belongs to the technical field of straight-profile torus worm pair shape modification, and particularly relates to a variable parameter composite shape modification method of a straight-profile torus worm pair.

Background

The application of the straight-profile enveloping worm pair has a long history, and in the early application process of the straight-profile enveloping worm pair, technicians have an important finding that the meshing performance of the straight-profile enveloping worm pair can be improved after the straight-profile enveloping worm pair is used for a period of time.

In the early stage, the shape modification method of the straight-profile torus worm pair is mainly based on a natural shape modification curve, and requires that the process transmission ratio during processing the torus worm can be continuously changed. However, the modified worm gear pair obtained by the modification method has curvature interference on the worm gear tooth surface, and the instantaneous contact lines are densely distributed at the meshing end of the worm, so that the modified worm gear pair is quite unfavorable for heat dissipation and lubrication. Meanwhile, the modification method has little influence on the range of the contact area of the tooth surface of the worm wheel.

In order to improve the fitting accuracy of the natural shape modification curve, related technicians provide a high-order shape modification method. However, the modified worm gear obtained by the modification method has no obvious advantage in the aspect of improving the transmission performance of the worm gear.

In order to get rid of the limitation of the modification curve, the related technical personnel also propose a constant parameter modification method. However, the modified worm gear obtained by the modification method is not improved in the meshing performance.

In recent years, related technicians provide a pure-principle shape modifying method, the shape modifying method is based on a gear meshing theory, experience of shape modifying research of a straight-profile torus worm pair is thoroughly eliminated, but the shape modifying method still has some defects, namely, the shape modifying method has little effect on expanding the range of a contact area of a tooth surface of a worm wheel, is not helpful to relieve the dense distribution condition of instantaneous contact lines at the meshing end of the worm, and sometimes causes curvature interference of the tooth surface of the worm wheel.

Therefore, the working performance of the straight-profile enveloping worm pair is difficult to further improve by the existing shape modifying method, and in order to improve the practical application effect of the straight-profile enveloping worm pair, a brand-new shape modifying method for the straight-profile enveloping worm pair needs to be designed urgently, so that the working performance of the straight-profile enveloping worm pair can be further improved by the shape modifying method.

Disclosure of Invention

Aiming at the problems in the prior art, the invention provides a variable parameter composite shape modification method of a straight-profile torus worm pair, and the modified worm pair obtained by adopting the shape modification method has the advantages that the worm gear tooth surface has no curvature interference, the range of the contact area of the worm gear tooth surface is larger, the contact area can cover most of the worm gear tooth surface, the effective working length of the worm is longer, the instantaneous contact lines are sparsely and uniformly distributed at the meshing end of the worm, and the heat dissipation and the lubrication are better facilitated.

In order to achieve the purpose, the invention adopts the following technical scheme: a variable parameter composite modification method for a straight profile ring surface worm gear pair comprises 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.

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.

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.

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.

The invention has the beneficial effects that:

compared with the prior art, the modified worm gear pair obtained by the modification method has the advantages that the worm gear tooth surface does not have curvature interference, the range of the worm gear tooth surface contact area is large, the contact area can cover most of the worm gear tooth surface, the effective working length of the worm is long, instantaneous contact lines are distributed sparsely and uniformly at the worm meshing end, and heat dissipation and lubrication are facilitated.

Drawings

FIG. 1 is a schematic view of a set of machining coordinates of a worm pair (worm + worm wheel);

FIG. 2 is a schematic view of the machining principle of the worm;

FIG. 3 is a diagram illustrating the profile of the tooth flank contact area and the instantaneous contact line of the worm gear according to one embodiment;

FIG. 4 is a diagram illustrating the contact area and the instantaneous contact line distribution of the spiral surface of the worm in the first embodiment;

FIG. 5 shows Δ i (k) in the first embodiment_w) And Δ b (k)_w) Graph of the function of (a);

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

FIG. 7 is a diagram showing the distribution of the contact area and the instantaneous contact line of the helicoid of the worm in the second embodiment;

FIG. 8 shows Δ i (k) in the second embodiment_w) And Δ b (k)_w) Graph of the function of (a);

Detailed Description

The invention is described in further detail below with reference to the figures and the specific embodiments.

Example one

The worm in the embodiment is a right-handed single-headed worm.

A variable parameter composite modification method for a straight profile ring surface worm gear pair comprises 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: according to the figure 1, the relative position relation of each coordinate system in the worm processing coordinate system set is determined

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;

the center distance modification quantity delta a 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 ofNegative shift by | Δ a length;

in the embodiment, the center distance a of the worm pair is 300mm, and the modulus m of the end face of the worm wheel_tA suggested range for Δ a to be obtained is-2 mm to 15mm, and Δ a is actually 5mm, and a is obtained_d305 mm; in practical operation, the tool apron needs to be along the tool apron static coordinate systemUnit basal vector ofForward moving by 5mm and making the male vertical line segmentUp to 305mm in length;

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;

the modification quantity delta i of the transmission ratio is the rotation angle of the wormA 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 diameter of the pitch circle of the worm wheel;

in the embodiment, the transmission ratio i of the worm gear pair₁₂50, the worm surrounds the working half angle of the worm wheel16.38 degrees, a worm gear pitch pressure angle α of 22.09 degrees, and a worm gear pitch diameter d₂At 500mm, a.DELTA.is obtained_f＝0.6mm，C₁＝0.0294，C₂＝0.3029，C₃0.014, and the expression of the available gear ratio modification amount Δ i is

Finally, the process transmission ratio i between the worm and the tool apron can be obtained_1dWhich is represented by the formula

In the process of worm machining, the process transmission ratio i_1dNeed to follow the turning angle of the wormAnd real-time dynamic adjustment is performed based on the formula;

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

The height modification amount of the tool apron is recorded as delta b which is the worm rotation angleA 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_dThe worm gear is positioned above the middle plane of the worm pair in the horizontal position;

in this embodiment, the width b of the worm wheel teeth₂75mm, can give b₀The suggested value range of (a) is-7.5 mm-18.75 mm, b₁The suggested value range of (b) is 0.75-7.5 mm₀＝10mm，b₁Known worms enclose the working half-angle of the worm wheel by 5mm16.38 deg., worm gear pitch pressure angle α of 22.09 deg., and the resulting seat height modification Δ b expressed as seat height correction Δ b

In the process of machining the worm, the height modification quantity delta b of the tool apron needs to rotate along with the rotation angle of the wormAnd real-time dynamic adjustment is performed based on the formula;

step six: installing a linear blade turning tool on the tool apron, 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 as shown in figure 2 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;

in the embodiment, the transmission ratio i of the worm gear pair₁₂The center distance a of the worm pair is 300mm, and the worm pair is a worm gear;

step eleven: starting the gear hobbing process of the worm gear until the gear hobbing process of the worm gear is finished, and at the momentAnd (3) precisely equal to 300mm, assembling the processed worm and the worm wheel to obtain the variable-parameter composite modified straight-profile torus worm pair.

For the variable parameter composite modified straight-profile torus worm pair obtained above, the distribution diagram of the worm gear tooth surface contact area and the instantaneous contact line is shown in fig. 3, and the distribution diagram of the worm helicoid contact area and the instantaneous contact line is shown in fig. 4.

In fig. 3, line AB and line CD are reflection lines of the worm meshing end on the worm gear tooth surface, line EF is a conjugate line of the meshing boundary line of the worm gear pair on the worm gear tooth surface, the contact area ABFE is denoted as a first sub-contact area, the contact area CDFE is denoted as a second sub-contact area, and the first and second sub-contact areas are smoothly connected at the conjugate line EF of the meshing boundary line to jointly form the contact area of the worm gear pair.

The instantaneous contact lines in the first sub-contact areas are 1, 2, 3, 4 and 5, the instantaneous contact lines in the second sub-contact areas are 1', 2', 3', 4' and 5', and the worm pairs are contacted along the corresponding instantaneous contact lines (such as 1 and 1') at the same moment in one meshing period. Furthermore, as can be seen from fig. 3, the instantaneous contact lines are distributed sparsely and uniformly in the entire worm gear tooth surface contact area, which is more beneficial to improving and enhancing the heat dissipation condition and the lubricating performance of the worm gear pair.

As can be seen from fig. 4, the effective working length of the worm is long, and in the whole meshing period, the variable-parameter composite modified straight-profile torus worm pair can realize multi-tooth double-line contact in the transmission process. The modified worm gear pair obtained by the modification method of the invention has good overall meshing characteristics by combining fig. 3 and fig. 4.

To further illustrate the working performance of the obtained variable parameter composite modified straight-profile torus worm pair, three meshing points a, b and c are sequentially taken from the tooth crest to the tooth root along each instantaneous contact line of the worm wheel contact zone, and the induced principal curvature of all the meshing points is calculatedAnd sliding angle theta_vtThe results are shown in Table 1.

As can be seen in Table 1, the induced principal curvature is within the entire contact areaIs unchanged, indicating that there is no curvature interference throughout the contact region; induced principal curvature at each engagement pointAll numerical values ofThe contact stress levels are approximately equivalent in the whole contact zone, and the equal strength principle is relatively met; sliding angle theta in the whole contact area_vtThe numerical values are all larger, which indicates that the condition of forming a spring flow lubricating oil film between the worm pair teeth is better, so that the worm pair has better lubricating performance. Furthermore, the induced principal curvature in the second sub-contact regionIs smaller, and the slip angle theta_vtThe larger value of (A) indicates that the partial engagement performance of the second sub-contact region is superior.

To further highlight the function curveAndwhile introducing a coefficient k_wAnd plotting Δ i (k)_w) And Δ b (k)_w) So as to reflect the change rule of the transmission ratio modification quantity delta i and the tool apron height modification quantity delta b along the length of the worm.

Coefficient k_wAngle of rotation with wormHas a functional relation of

In the formula,the worm surrounds the working half angle of the worm wheel, α is the pitch circle pressure angle of the worm wheel,is the angle of rotation of the worm i₁₂The transmission ratio of the worm pair is adopted;when k is_wWhen equal to 0, corresponding to the engaged end of the worm, when k is_wWhen 1, it corresponds to the throat of the worm, when k is_wWhen the length is 2, the meshing end of the worm is corresponded.

Will be provided withAndmerging and eliminating worm angleThe transmission ratio modification quantity delta i and the coefficient k can be obtained_wHas a functional relation of

Wherein, Delta i is the transmission ratio modification amount i₁₂For the worm gear pair transmission ratio, α is the worm wheel reference circle pressure angle,for the worm to enclose the working half-angle, Δ, of the worm wheel_fModification of the worm-engaging end, d₂The diameter of the pitch circle of the worm wheel;

from the foregoing, i₁₂＝50，α＝22.09°，Δ_f＝0.6mm，d₂The following functional relation can be obtained at 500mm

$\mathrm{\Δ}i\left(k_w\right)=\mathrm{\Δ}i=\frac{0.12{(1-0.7k_w)}^2}{0.0996+0.2859k_w-0.0024{(1-0.7k_w)}^2}$

Will be provided withAndandmerging and eliminating worm angleThe height modification quantity delta b and the coefficient k of the tool apron can be obtained_wHas a functional relation of

Δb(k_w)＝Δb＝b₀+b₁(1-k_w)

As can be seen from the foregoing, b₀＝10mm，b₁The following functional relation can be obtained when the thickness is 5mm

Δb(k_w)＝Δb＝15-5k_w

Through a functional relationAnd the functional relation Δ b (k)_w)＝Δb＝15-5k_wCan be plotted to yield Δ i (k)_w) And Δ b (k)_w) Fig. 5 shows a function curve of (a). It can be seen in fig. 5 that the ratio modification Δ i varies non-linearly and non-monotonically along the length of the worm, with a value constantly greater than 0 and being greatest at the tip of engagement and a minimum value between the throat and tip of engagement, with the minimum value being close to 0. It can be seen in fig. 5 that the value of the tool holder height modification Δ b decreases linearly from the tip-in end to the tip-out end, and is greatest at the tip-in end and smallest at the tip-out end.

Example two

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

A variable parameter composite modification method for a straight profile ring surface worm gear pair comprises 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: according to the figure 1, the relative position relation of each coordinate system in the worm processing coordinate system set is determined

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;

the center distance modification quantity delta a 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 ofNegative shift by | Δ a length;

in the embodiment, the center distance a of the worm pair is 300mm, and the modulus m of the end face of the worm wheel_tA suggested range for obtaining Δ a is-2 mm to 15mm, and a suggested range for obtaining Δ a is 10.8mm, and a is obtained_d310.8 mm; in practical operation, the tool apron needs to be along the tool apron static coordinate systemUnit basal vector ofForward movement of 10.8mm and making a common vertical line segmentThe length of (A) reaches 310.8 mm;

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;

the modification quantity delta i of the transmission ratio is the rotation angle of the wormA 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 diameter of the pitch circle of the worm wheel;

in the embodiment, the transmission ratio i of the worm gear pair₁₂50, the worm surrounds the working half angle of the worm wheel16.38 degrees, a worm gear pitch pressure angle α of 22.09 degrees, and a worm gear pitch diameter d₂At 500mm, a.DELTA.is obtained_f＝0.192mm，C₁＝0.0094，C₂＝0.3556，C₃Not more than 0.07, and further mayObtaining the expression of the gear ratio modification quantity delta i as

Finally, the process transmission ratio i between the worm and the tool apron can be obtained_1dWhich is represented by the formula

In the process of worm machining, the process transmission ratio i_1dNeed to follow the turning angle of the wormAnd real-time dynamic adjustment is performed based on the formula;

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

The height modification amount of the tool apron is recorded as delta b which is the worm rotation angleA 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_dThe worm gear is positioned above the middle plane of the worm pair in the horizontal position;

in this embodiment, the width b of the worm wheel teeth₂75mm, can give b₀The suggested value range of (a) is-7.5 mm-18.75 mm, b₁The suggested value range of (b) is 0.75-7.5 mm₀＝13mm，b₁Known worms enclose the working half-angle of the worm wheel at 6mm16.38 deg., worm gear pitch pressure angle α of 22.09 deg., and the resulting seat height modification Δ b expressed as seat height correction Δ b

In the process of machining the worm, the height modification quantity delta b of the tool apron needs to rotate along with the rotation angle of the wormAnd real-time dynamic adjustment is performed based on the formula;

step six: installing a linear blade turning tool on the tool apron, 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 as shown in figure 2 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;

in the embodiment, the transmission ratio i of the worm gear pair₁₂10, the center distance a of the worm pair is 300 mm;

step eleven: starting the gear hobbing process of the worm gear until the gear hobbing process of the worm gear is finished, and at the momentAnd (3) precisely equal to 300mm, assembling the processed worm and the worm wheel to obtain the variable-parameter composite modified straight-profile torus worm pair.

For the variable parameter composite modified straight-profile torus worm pair obtained above, the distribution diagram of the worm gear tooth surface contact area and the instantaneous contact line is shown in fig. 6, and the distribution diagram of the worm helicoid contact area and the instantaneous contact line is shown in fig. 7.

In fig. 6, line AB is a reflection line of the worm meshing end on the worm gear tooth surface, line GH is a boundary line of the worm gear solid tooth surface, line EF is a conjugate line of the meshing boundary line of the worm gear pair on the worm gear tooth surface, contact area ABFE is a first sub contact area, contact area GHFE is a second sub contact area, and the first and second sub contact areas are smoothly connected at the conjugate line EF of the meshing boundary line to jointly form the contact area of the worm gear pair.

The instantaneous contact lines in the first sub-contact areas are 1, 2, 3, 4 and 5, the instantaneous contact lines in the second sub-contact areas are 3', 4' and 5', and as can be seen in fig. 6, the whole worm gear tooth surface contact area is large and can cover most of the worm gear tooth surfaces, and the instantaneous contact lines are distributed sparsely and uniformly in the whole worm gear tooth surface contact area, so that the improvement of the heat dissipation condition and the lubrication performance of the worm pair is facilitated.

As can be seen from fig. 7, the effective working length of the worm is long, and although the number of the worm heads in the present embodiment is large and the transmission ratio of the worm pair is small, so that part of the instantaneous contact line in the second sub-contact region moves out of the gear surface of the worm, the variable parameter complex modified straight-profile toroidal worm pair of the present embodiment can still realize multi-tooth double-line contact in the transmission process in the whole meshing period. The modified worm gear pair obtained by the modification method of the invention has good overall meshing characteristics by combining fig. 6 and 7.

To further illustrate the working performance of the obtained variable parameter composite modified straight-profile torus worm pair, three meshing points a, b and c are sequentially taken from the tooth crest to the tooth root along each instantaneous contact line of the worm wheel contact zone, and the induced principal curvature of all the meshing points is calculatedAnd sliding angle theta_vtThe results are shown in Table 2.

As can be seen in Table 2, the induced principal curvature is within the entire contact areaIs unchanged, indicating that there is no curvature interference throughout the contact region; induced principal curvature at each engagement pointThe numerical values of the contact stress values are relatively close, which shows that the contact stress levels of the teeth in the whole contact zone are approximately equivalent, and the equal strength principle is relatively met; sliding angle theta in the whole contact area_vtThe numerical values are all larger, which indicates that the condition of forming a spring flow lubricating oil film between the worm pair teeth is better, so that the worm pair has better lubricating performance. Furthermore, the induced principal curvature in the second sub-contact regionIs smaller, and the slip angle theta_vtThe larger value of (A) indicates that the partial engagement performance of the second sub-contact region is superior.

To further highlight the function curveAndwhile introducing a coefficient k_wAnd plotting Δ i (k)_w) And Δ b (k)_w) So as to reflect the transmission ratio modification quantity delta i and the height of the tool apronAnd the change rule of the modification amount delta b along the length of the worm.

Coefficient k_wAngle of rotation with wormHas a functional relation of

In the formula,the worm surrounds the working half angle of the worm wheel, α is the pitch circle pressure angle of the worm wheel,is the angle of rotation of the worm i₁₂The transmission ratio of the worm pair is adopted; when k is_wWhen equal to 0, corresponding to the engaged end of the worm, when k is_wWhen 1, it corresponds to the throat of the worm, when k is_wWhen the length is 2, the meshing end of the worm is corresponded.

Will be provided withAndmerging and eliminating worm angleThe transmission ratio modification quantity delta i and the coefficient k can be obtained_wHas a functional relation of

Wherein, Delta i is the transmission ratio modification amount i₁₂For the worm gear pair transmission ratio, α is the worm wheel reference circle pressure angle,for the worm to enclose the working half-angle, Δ, of the worm wheel_fModification of the worm-engaging end, d₂The diameter of the pitch circle of the worm wheel;

from the foregoing, i₁₂＝10，α＝22.09°，Δ_f＝0.192mm，d₂The following functional relation can be obtained at 500mm

$\mathrm{\Δ}i\left(k_w\right)=\mathrm{\Δ}i=\frac{3.84{(1-0.7k_w)}^2}{192.75+142.95(1-k_w)-0.384{(1-0.7k_w)}^2}$

Will be provided withAndandmerging and eliminating worm angleThe height modification quantity delta b and the coefficient k of the tool apron can be obtained_wHas a functional relation of

Δb(k_w)＝Δb＝b₀+b₁(1-k_w)

As can be seen from the foregoing, b₀＝13mm，b₁The following functional relation can be obtained when the thickness is 6mm

Δb(k_w)＝Δb＝19-6k_w

Through a functional relationAnd the functional relation Δ b (k)_w)＝Δb＝19-6k_wCan be plotted to yield Δ i (k)_w) And Δ b (k)_w) Fig. 8 shows a function curve of (a). It can be seen in fig. 8 that the ratio modification Δ i varies non-linearly and non-monotonically along the length of the worm, with a value constantly greater than 0 and being greatest at the tip of engagement and a minimum between the throat and tip of engagement, with the minimum value being close to 0. It can be seen in fig. 8 that the value of the tool holder height modification Δ b decreases linearly from the tip-in end to the tip-out end, and is largest at the tip-in end and smallest at the tip-out end.

In the second embodiment, although the number of the worm heads is larger and the worm gear transmission is smaller in the second embodiment compared to the first embodiment, the modified worm gear obtained by the modification method of the present invention has the following effects in both the first embodiment and the second embodiment: the worm gear tooth surface has no curvature interference, the range of the worm gear tooth surface contact area is large, the contact area can cover most of the worm gear tooth surface, the effective working length of the worm is long, instantaneous contact lines are distributed sparsely and uniformly at the worm meshing end, and heat dissipation and lubrication are facilitated.

The embodiments are not intended to limit the scope of the present invention, and all equivalent implementations or modifications without departing from the scope of the present invention are intended to be included in the scope of the present invention.

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.