CN115264028B - Method for forming enveloping worm drive pair by point contact local conjugate meshing - Google Patents
Method for forming enveloping worm drive pair by point contact local conjugate meshing Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/08—Profiling
- F16H55/0806—Involute profile
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
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- F16H55/02—Toothed members; Worms
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- F16H55/0813—Intersecting-shaft arrangement of the toothed members
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
- F16H55/02—Toothed members; Worms
- F16H55/22—Toothed members; Worms for transmissions with crossing shafts, especially worms, worm-gears
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Abstract
The invention provides a method for forming a point contact local conjugate meshing enveloping worm drive pair, which comprises two forms of enveloping worm drive and enveloping drum worm drive; the worm transmission pair comprises a worm wheel and a worm, the specific configuration adopts a gear tooth surface parameter modification mode, and the modified tooth surface is tangent with a standard gear tooth surface at a modification target position along the tooth height direction; compared with the configuration method of the medium tooth surface in the prior art, the method has wider applicability, solves the difficult problems of profile modification of the involute cylindrical gear tooth profile and modeling of the worm transmission medium tooth surface, can adjust specific parameters according to the use condition, and has better applicability.
Description
Technical Field
The invention relates to the field of machining of mechanical parts, in particular to a method for forming a point contact local conjugate meshing enveloping worm drive pair.
Background
The worm drive is used as a motion and power transmission mechanism with large transmission ratio, high bearing capacity, compact structure, stable transmission and small noise impact, and is widely applied to the national strategic and economic fields of equipment manufacturing, aerospace, mine metallurgy and the like, and is mainly divided into two major categories of motion transmission and power transmission.
According to different application objects and task demands, the worm drive is finely divided again on the basis of motion and power transmission at present, and is divided into three types of precise worm drive, heavy-duty worm drive and precise heavy-duty worm drive on the basis of a complete conjugation principle and a dual forming method. Among them, the precise worm drive mainly focuses on the drive precision, gear backlash, wear compensation, precision life, etc., and the main types are double-lead worm drive, conical worm drive, etc.; the heavy-duty worm drive mainly focuses on bearing capacity, transmission efficiency, service life and the like, and the main types are primary enveloping worm drive, secondary enveloping worm drive, drum worm drive and the like. The two types of worm transmission have the defects of high sensitivity of heavy-load worm transmission errors, incapacity of regulating and controlling backlash, lower bearing capacity of a precise worm transmission pair and the like, and the precision and heavy load are difficult to be combined. With the development of national strategic emerging industries such as natural power generation, intelligent manufacturing, aerospace, weaponry and the like, the transmission system provides high-reliability self-locking, high-precision low-return-difference, high-bearing capacity and other extreme working condition service performance requirements. The precise heavy-load worm drive with precise characteristics and heavy-load characteristics is an important research object for related scientific researchers in the industry at present.
In the prior art, in order to realize point contact transmission with low error sensitivity of worm transmission, local conjugate point contact meshing of novel worm transmission (comprising a novel enveloping worm, a novel enveloping drum worm and the like) is often realized by introducing a medium tooth surface. However, most of the researches on the intermediate tooth surface are plane intermediate tooth surface and small tooth difference intermediate tooth surface, the types are relatively less, the parameters of the intermediate tooth surface are inconvenient to change according to the specific application working condition, and a novel enveloping worm transmission configuration method with wider applicability for the point contact local conjugate meshing is needed to be invented.
Therefore, the invention provides a configuration method of a worm gear and worm drive pair based on the background, so as to solve the problems of profile modification of the involute cylindrical gear and modeling of the tooth surface of a worm drive medium.
Disclosure of Invention
In view of the above, the invention provides a method for forming an enveloping worm drive pair with local conjugate meshing in a point contact way, which has wider applicability, solves the difficult problems of profile modification of involute cylindrical gear tooth profile and modeling of worm drive medium tooth surface, can adjust specific parameters according to the use condition, and has better applicability.
The invention provides a method for forming a point contact local conjugate meshing enveloping worm drive pair,
The worm transmission pair comprises a worm wheel and a worm, and the specific configuration adopts the following method:
The tooth surface of the worm gear is obtained by modifying the tooth surface of a standard involute gear, and the modified tooth surface is tangent with the tooth surface of the standard gear at a modification target position along the tooth height direction; the worm is a standard involute enveloping worm;
Or the worm wheel is a standard involute gear, the tooth surface of the worm is a modified tooth surface, the modified tooth surface of the reference worm wheel is enveloped and formed, and the modified tooth surface of the reference worm wheel is tangent with the tooth surface of the standard gear at a modified target position along the tooth height direction;
Or the tooth surface of the worm gear is obtained by modifying the tooth surface of the standard involute gear, and the modified tooth surface is tangent with the tooth surface of the standard gear at a modification target position along the tooth height direction; the tooth surface of the worm is a modified tooth surface, the modified tooth surface of the worm is formed by enveloping a reference worm gear tooth surface with a set modification amount, and the modified tooth surface of the reference worm gear with the set modification amount is tangent with a standard gear tooth surface at a modification target position along the tooth height direction; the set modification amount of the reference worm wheel is different from the modification amount of the worm wheel tooth surface, but the modification target position is the same.
Furthermore, the tooth surfaces of the worm wheel and the reference worm wheel are involute tooth surfaces, and the tooth profile modification of the involute tooth surfaces is realized through gradual expansion and contraction of involute generating lines.
Further, the method comprises the following steps:
a. Determining a modification quantity function:
Wherein: θ K is the spread angle of any point K on the generation line of the involute;
And the modification function f (θ K) should be continuously derivable, symmetrical with respect to the given target modification point, monotonically increasing on both sides of the given target modification point, and the modification amount having a maximum and a minimum;
b. acquiring a curve equation after involute shape modification:
Wherein: r K is the radial of the K point on the involute; r b is the base radius; alpha K is the pressure angle of the K point on the involute;
c. based on the curve equation in the step b, obtaining a tooth profile modification tooth surface equation:
Left side modified tooth surface equation The method comprises the following steps:
right side modified tooth surface equation The method comprises the following steps:
Wherein: f (τ) is a function of f (θ K) to a function of the involute flank parameter τ, and τ=θ K+αK; The radius of the base circle of the involute surface is modified; τ and θ∈ [ θ 1,θ2 ] are involute tooth surface parameters; delta is the base circle half angle; p is a tooth surface spiral parameter; alpha t is the pressure angle of the end face of the reference circle, and/> Wherein alpha n is the normal pressure angle of the reference circle; beta is the helix angle of the tooth surface; (i 1,j1,k1) are unit vectors of coordinate axes in the coordinate system O 1-x1y1z1, respectively; /(I)Left side modified tooth surface equation/>, respectivelyCoordinate values of (2); /(I)Right side modified tooth surface equation/>, respectivelyIs set in the coordinate value of (a).
Further, the curve equation after involute shape modification in the step b is obtained by substituting the modification quantity function in the step a into a standard involute polar coordinate equation, wherein the standard involute polar coordinate equation is as follows:
Further, it is characterized in that:
The tooth profile modification tooth surface equation in the step c is obtained by substituting a function f (tau) into a standard involute cylindrical gear tooth surface equation, wherein the standard involute cylindrical gear tooth surface equation is as follows:
Left flank equation The method comprises the following steps:
Right flank equation The method comprises the following steps:
Wherein: The radius of the base circle is the standard involute surface; /(I) Left flank equation/>, respectivelyCoordinate values of (2); /(I)Right flank equation/>, respectivelyIs set in the coordinate value of (a).
Further, in the formula (3) and the formula (4), the "±" number is used for expanding and shaping when "+" is taken, and the "-" number is used for contracting and shaping;
when the tooth surfaces of the worm wheel and the worm have a modification, then:
The worm comprises an external-meshing enveloping worm and an internal-meshing enveloping crown worm, the worm wheel comprises an external-tooth worm wheel meshed with the external-meshing enveloping worm and an internal-tooth worm wheel meshed with the internal-meshing enveloping crown worm, and the reference worm wheel comprises an external-tooth reference worm wheel enveloped to form the external-meshing enveloping worm and an internal-tooth reference worm wheel enveloped to form the internal-meshing enveloping crown worm;
When the worm is an external engagement enveloping worm:
The tooth surfaces of the external tooth worm wheel and the external meshing enveloping worm are both shrink modified tooth surfaces, the tooth surface modification of the external meshing enveloping worm is formed by enveloping the modified tooth surface of the external tooth reference worm wheel, and the shrink modification amount of the tooth surface of the external tooth reference worm wheel is smaller than that of the tooth surface of the external tooth worm wheel;
Or the tooth surface of the external tooth worm wheel is a shrinkage modified tooth surface, the tooth surface of the external engagement enveloping worm is an expansion modified tooth surface, and the external tooth enveloping worm wheel is formed by enveloping the external tooth reference worm wheel with the expansion modified tooth surface;
or the tooth surfaces of the external tooth worm wheel and the external meshing enveloping worm are both expansion modification tooth surfaces, the tooth surface modification of the external meshing enveloping worm is formed by enveloping the modified tooth surface of the external tooth reference worm wheel, and the expansion modification amount of the tooth surface of the external tooth reference worm wheel is larger than that of the tooth surface of the external tooth worm wheel;
when the worm is an internal engagement enveloping drum worm:
the tooth surfaces of the internal tooth worm wheel and the internal meshing enveloping crowned worm are both shrink-shaped tooth surfaces, the tooth surface modification of the internal meshing enveloping crowned worm is formed by enveloping the modified tooth surface of the internal tooth reference worm wheel, and the shrink-shaped amount of the tooth surface of the internal tooth reference worm wheel is larger than that of the tooth surface of the internal tooth worm wheel;
Or the tooth surface of the internal tooth worm wheel is an expansion modification tooth surface, the tooth surface of the internal meshing enveloping crowned worm is a contraction modification, and the internal tooth enveloping crowned worm is formed by enveloping an internal tooth reference worm wheel of the contraction modification tooth surface;
Or the tooth surfaces of the internal tooth worm wheel and the internal meshing enveloping crowned worm are both expansion modified tooth surfaces, the tooth surface modification of the internal meshing enveloping crowned worm is formed by enveloping the modified tooth surface of the internal tooth reference worm wheel, and the expansion modification amount of the tooth surface of the internal tooth reference worm wheel is smaller than that of the tooth surface of the internal tooth worm wheel. The invention has the beneficial effects that: the method for forming the enveloping worm transmission pair with the point contact and the partial conjugate engagement adopts a method for modifying the tooth surface of the worm wheel or/and the worm, and the modified tooth surface and the standard tooth surface can be tangent at any position in the tooth height direction according to the specific working condition requirement, so that the conjugation of the worm wheel and the worm pair is the partial conjugation and is the point contact with low error sensitivity in the engagement.
Drawings
The invention is further described below with reference to the accompanying drawings and examples:
FIG. 1 is a schematic diagram of a standard involute forming scheme;
FIG. 2 is a schematic diagram of an involute profile for generating progressive wire extension;
FIG. 3 is a schematic diagram of an involute cylindrical gear;
FIG. 4 is an end schematic of an involute cylindrical gear;
FIG. 5 is a schematic view of a tooth surface after a line taper shrinkage tooth profile modification has occurred;
FIG. 6 is a schematic diagram of a standard involute cylindrical gear tooth surface;
FIG. 7 is a schematic view of a tooth surface after a line taper expansion tooth form modification has occurred;
FIG. 8 is a schematic view of a planar tooth surface after line limit grading elongation tooth profile modification;
FIG. 9 is a relative positional relationship of tooth surfaces before and after tooth form modification;
FIG. 10 is a schematic illustration of a standard involute external mesh external tooth cylindrical gear meshing with a standard envelope toroidal worm;
FIG. 11 is an enlarged view of the worm gear tooth face engagement position at the block of FIG. 10;
FIG. 12 is a relative position of a standard involute gear tooth surface and a tooth surface of a shrink modified external gear (embodying a tangent at the pitch circle);
FIG. 13 is a schematic illustration of the meshing of a shrink modified externally toothed gear with a standard enveloping worm;
FIG. 14 is an enlarged view of the worm gear tooth face engagement position at the box of FIG. 13;
FIG. 15 is a schematic illustration of a standard involute internal tooth spur gear meshing with a standard envelope drum worm;
FIG. 16 is an enlarged view of the worm gear tooth face engagement position at the box of FIG. 15;
FIG. 17 is a relative position of a standard involute gear tooth surface and a tooth surface of an expanding and shaping internally toothed gear (embodying a tangent at the pitch circle);
FIG. 18 is a schematic illustration of the meshing of an expanding and shaping internally toothed gear with a standard crowned worm;
Fig. 19 is an enlarged view of the worm gear tooth face engagement position at the block of fig. 18.
Detailed Description
Items and names marked by reference numerals in the following table:
the invention relates to a method for forming a point contact local conjugate meshing enveloping worm transmission pair, which comprises a worm wheel and a worm, wherein the method is specifically as follows:
the tooth surface of the worm gear is obtained by modifying the tooth surface of a standard involute gear, and the modified tooth surface is tangent with the tooth surface of the standard gear at a modification target position along the tooth height direction; the worm is a standard involute enveloping worm; at the moment, the meshing between the worm wheel and the worm is point contact partial conjugate meshing, so that point contact transmission with low error sensitivity of worm transmission is realized by using a shape correction mode, a transmission pair can take account of the application occasions of heavy load and high-precision transmission, the difficult problems of involute cylindrical gear tooth shape correction and worm transmission medium tooth surface modeling are solved, specific parameters can be adjusted according to the use condition, and the method has better applicability;
of course, the partial conjugate point contact meshing transmission can be realized, the worm wheel is a standard involute gear, the tooth surface of the worm is a modified tooth surface, the modified tooth surface of the reference worm wheel is enveloped and formed, and the modified tooth surface of the reference worm wheel is tangent with the standard gear tooth surface at a modified target position along the tooth height direction; the reference worm wheel herein refers to a worm wheel set for enveloping the worm so that the tooth surface of the worm becomes a modified tooth surface at the time of design, and is not described in detail herein unlike a worm wheel of an actual meshing transmission;
At the same time, the tooth surface of the worm wheel forming the worm transmission pair and the tooth surface of the worm are modified, namely: the tooth surface of the worm gear is obtained by modifying the tooth surface of a standard involute gear, and the modified tooth surface is tangent with the tooth surface of the standard gear at a modification target position along the tooth height direction; the tooth surface of the worm is a modified tooth surface, the modified tooth surface of the worm is formed by enveloping a reference worm gear tooth surface with a set modification amount, and the modified tooth surface of the reference worm gear with the set modification amount is tangent with a standard gear tooth surface at a modification target position along the tooth height direction; the set modification amount of the reference worm wheel is different from that of the worm wheel tooth surface, but the modification target positions are the same; of course, the reference worm wheel and the shape-modifying target position of the worm wheel are consistent, and the corresponding standard involute gears are consistent so as to ensure the partial conjugate point contact engagement of the worm transmission pair, and the description is omitted here;
The modification target position can be any point in the tooth height direction, and the embodiment is selected at the reference circle and is not described herein again;
The modification amounts here differ by:
the two parts shrink and shape-modifying simultaneously, but the sizes of the shrink and shape-modifying are different, so that the tooth surfaces of the two parts form point contact engagement with partial envelope; the two are simultaneously subjected to expansion modification, but the sizes of the expansion modification are different, so that partial enveloping point contact engagement is formed between tooth surfaces of the two; and a shrinkage shaping and an expansion shaping, which also ensure that the tooth surfaces of the two form a partial enveloping point contact engagement; the structure can be different for different worm structures and different meshing modes, and the final purpose is to ensure that the worm gear and the worm can realize point contact meshing of partial envelope;
The tooth surface of the worm of the invention refers to the spiral surface of the worm and is not described in detail herein; meanwhile, the worm gear is an involute cylindrical gear, and of course, the worm gear can be a straight gear or a helical gear, and the description is omitted here.
In this embodiment, tooth surfaces of the worm wheel and the reference worm wheel are involute tooth surfaces, and tooth profile modification of the involute tooth surfaces is realized by gradual expansion and contraction of an involute generating line; compared with the configuration method of the medium tooth surface in the prior art, the method has wider applicability, solves the difficult problems of involute cylindrical gear tooth profile modification and worm transmission medium tooth surface modeling, can adjust specific parameters according to the use condition, and has better applicability.
The following description of fig. 1 to 10 in this embodiment is a modification method of an involute gear, which is used to form a base for modification of a worm gear pair; as shown in the standard involute forming schematic diagram of FIG. 1, when a line occursWhen the base circle 12 is purely rolled, the locus AK of any point K on the generating line is the involute 11 of the base circle, wherein the center of the base circle 12 is an O point, the radius of the base circle is r b, the radial direction of the K point on the involute is r K, the spreading angle of the K point on the involute is theta K, and the pressure angle of the K point on the involute is alpha K.
From the geometric relationship of right triangle, it can be known that the relationship between the pressure angle α K and the base radius r b and the radius r K is:
At the same time, the method comprises the steps of,
Therefore, the involute function inv α K of the spread angle θ K with respect to the pressure angle α K can be obtained from the above relation:
invαK＝θK＝tanαK-αK (10)
The polar equation of the standard involute 11 is then obtained as:
Based on the standard involute forming theory, the length of the generated line is gradually expanded and contracted, so that the linear shape modification of the involute can be realized, and as shown in fig. 2, the specific shape modification method comprises the following steps:
a. Determining a modification quantity function:
Wherein: θ K is the spread angle of any point K on the occurrence line of the involute, i.e., the modifier function is a function about the spread angle θ K, and the modifier function f (θ K) should be continuously conductive, symmetrical with respect to the given target modifier point, monotonically increasing on both sides of the given target modifier point, and the modifier has a maximum and minimum, i.e., the function f (θ K) should satisfy the following conditions: ① Gradual change conductive criteria: the modified line shape still follows the continuous guidance at any point, namely the flexible quantity of the modified line is a function which can be continuously guided in a given interval, and no break points and non-guiding inflection points exist; ② Bilateral symmetry criterion: the occurrence line expansion and contraction amount of the modification is a symmetrical function about a given target modification point, namely the modification amount is a symmetrical continuous derivative function about an expansion angle theta K at any point K on the involute; ③ Monotonically increasing criteria: the more far the two sides are from the target modification point K, the larger the modification amount is, namely the modification amount is a derivative function which monotonically and continuously decreases to zero along with the increase of the expansion angle theta K at any point K on the involute, and then symmetrically monotonically and continuously increases; ④ Limit boundary criteria: the maximum limit of the modification amount should not exceed the tangent value at the target modification point, i.e. the maximum limit modification line is a straight line, while the minimum limit should be defined according to the specific target tooth form, i.e. the lowest limit modification should not modify the tooth root and tooth tip width to zero;
the direction of the simultaneous modification is defined as follows: the line elongation occurs in a positive direction, whereas the line contraction occurs in a negative direction;
b. And according to the defined modification quantity function and a standard involute polar coordinate equation, obtaining:
Therefore, the involute function inv α K of the post-shaping relief angle θ K with respect to the pressure angle α K is:
substituting the modified shape quantity function into a standard involute polar coordinate equation to obtain a curve equation after involute shape modification:
Wherein: r K is the radial of the K point on the involute; r b is the base radius; alpha K is the pressure angle of the K point on the involute;
solving the numerical value of the shaping line according to the formula (2), solving a series of polar coordinate points, and drawing a graph after the shaping according to the solved polar coordinate points;
c. As shown in fig. 2, corresponding shaping lines can be obtained according to the above steps. In FIG. 2, 25 is a base circle, curve Is the standard involute 22 without modification, curve/>Is a negative modification line 21, curve/>, after the line gradual shrinkage modification occursIs the positive modification line 23, straight line/>, after the gradual extension modification of the occurrence lineIs a very large shaping line 24 after the shaping by the gradual elongation of the generating line; point K o is the target modification point at which the corresponding standard involute parameters are as follows: the spreading angle is theta Ko, the pressure angle is alpha Ko, the radial direction is r Ko, and the straight line/>26 Is the corresponding occurrence line 0 state; when the expansion angle is smaller than the expansion angle value corresponding to the target shaping point, the corresponding arbitrary point on the standard involute is K o1, and the corresponding occurrence line 1 is in a straight line/>27; When the expansion angle is larger than the expansion angle value corresponding to the target shaping point, the corresponding arbitrary point on the standard involute is K o2, and the corresponding occurrence line 2 is in a straight line/>28；
As shown in fig. 2, because point K o is the target modification point, the amount of line stretch modification that occurs for the spread angle θ Ko is zero, where the negative modification line 21, standard involute 22, positive modification line 23, and very large modification line 24 coincide, i.e., points K n、Ko、Km and K g are coincident; when the expansion angle is smaller than the expansion angle value corresponding to the target shaping point, the corresponding arbitrary point on the negative shaping line 21 is K n1, and the corresponding line shaping shrinkage isThe corresponding arbitrary point on the positive repair line 23 is K m1, and the corresponding occurrence line repair elongation is/>The corresponding arbitrary point on the maximum shaping line 24 is K g1, and the corresponding occurrence line shaping elongation is/>When the expansion angle is larger than the expansion angle value corresponding to the target shaping point, the corresponding arbitrary point on the negative shaping line 21 is K n2, and the corresponding line shaping shrinkage is/>The corresponding arbitrary point on the positive repair line 23 is K m2, and the corresponding occurrence line repair elongation is/>The corresponding arbitrary point on the maximum shaping line 24 is K g2, and the corresponding occurrence line shaping elongation is/>
The involute is converted to an x 1O1y1 plane in a space rectangular coordinate system O 1-x1y1z1 and spirally moves around a z 1 axis, so that an involute surface 31, namely an involute cylindrical gear tooth surface, is formed, and the involute cylindrical gear tooth surface is shown in fig. 3; wherein the x 1O1y1 plane is a middle section in the tooth width direction, the tooth surface is formed by pure rolling of a plurality of generating lines 33 on the base cylinder 32, the radius of the base cylinder is r b, and the helix angle is beta;
the involute surface in figure 3 is projected onto the x 1O1y1 plane to obtain the involute cylindrical gear end face schematic diagram shown in figure 4, so as to obtain the left tooth surface equation of standard involute cylindrical gear The method comprises the following steps:
The right tooth surface equation of the standard involute cylindrical gear can be obtained by the same method The method comprises the following steps:
Wherein: The radius of the base circle is the standard involute surface; τ and θ∈ [ θ 1,θ2 ] are involute tooth surface parameters; delta is the base circle (tooth thickness) half angle; p is a tooth surface spiral parameter; alpha t is the pressure angle of the end face of the reference circle, and/> Wherein alpha n is the normal pressure angle of the reference circle; beta is the helix angle of the tooth surface; (i 1,j1,k1) are unit vectors of coordinate axes in the coordinate system O 1-x1y1z1, respectively; /(I)Left flank equation/>, respectivelyCoordinate values of (2); /(I)Respectively right tooth surface equationCoordinate values of (2); based on the involute tooth surface equation, MATLAB is utilized to program and solve a generated tooth surface data point set, and the obtained tooth surface data point is imported into UG for three-dimensional modeling, so that a standard involute tooth surface three-dimensional model can be obtained.
Of course, if the helix angles of the left and right flanks are not equal, that is, β L≠βR, the above partial parameters are respectively adjusted to β (the left flank is β L, the right flank is β R)、αt (the left flank is α tL, the right flank is α tR)、αt (the left flank is α tL, the right flank is α tR)), the above partial parameters are respectively adjusted to,(Left flank is/>)Right flank is/>) And p (left flank p L, right flank p R).
The above is a standard involute cylindrical gear tooth surface equation, the standard involute generating line gradual expansion modification theory defined above is introduced, and the standard involute generating line gradual expansion modification theory is converted to the x 1O1y1 plane in the space rectangular coordinate system O 1-x1y1z1 shown in fig. 4, at this time, the modification amount defined above is that the function f (theta K) about the spreading angle theta K is converted into the function f (tau) about the involute tooth surface parameter tau, and tau=theta K+αK; therefore, an involute cylindrical gear tooth profile modification tooth surface equation based on the principle of gradual expansion of the generating line can be obtained; the curve equation and the standard involute cylindrical gear tooth surface equation in the step b are based, and the function f (tau) is substituted into the standard involute cylindrical gear tooth surface equation to obtain the tooth profile modification tooth surface equation:
Left side modified tooth surface equation The method comprises the following steps:
right side modified tooth surface equation The method comprises the following steps:
Wherein: f (τ) is a function of f (θ K) to a function of the involute flank parameter τ, and τ=θ K+αK; The radius of the base circle of the involute surface is modified; similarly, if the helix angles of the left and right flanks are not equal, that is, β L≠βR, the above-mentioned partial parameters are adjusted to β (the left flank is β L, the right flank is β R)、αt (the left flank is α tL, the right flank is α tR),/>, respectively (Left flank is/>)Right flank is/>) And p (left tooth surface is p L, right tooth surface is p R);(i1,j1,k1) are unit vectors of coordinate axes in a coordinate system O 1-x1y1z1 respectively; /(I)Left side modified tooth surface equation/>, respectivelyCoordinate values of (2); /(I)Right side modified tooth surface equation/>, respectivelyIs set in the coordinate value of (a). It should also be noted that "±" in the formula is taken as "+" when the modification is a positive modification, and "-" when the modification is a negative modification.
The invention is further illustrated by the following examples:
firstly, selecting a modification quantity function as a cosine modification function, taking Left side modified flank equation/>The method comprises the following steps: /(I)
Similarly, right side modified tooth surface equationThe method comprises the following steps:
Wherein: w is a tooth surface modification factor, and the parameter factor determines the modification amount. At the same time, it can be seen that the modification quantity function takes tau as the x 1 axis and f (tau) as the y 1 axis On the x 1O1y1 plane is a cosine function symmetrical about τ=tanα t, and f (τ) ∈ [0,w ], the target repair point at this time is on the tooth surface involute dividing circle, so that it can be determined that the function satisfies four major criteria for the involute profile to follow for generating gradual expansion and contraction.
In the embodiment of the invention, the selected tooth number Z 1 is 60, the normal pressure angle alpha n of the reference circle is 20 degrees, the tooth width B is 50mm, the normal modulus m n is 3mm, and the tooth surface modification factor w is 0.2; the standard parameters are brought into the standard involute cylindrical gear tooth surface equation and the modified involute cylindrical gear tooth surface equation, the standard parameters are solved through MATLAB programming, and a tooth surface diagram is drawn through UG, respectively obtaining a tooth surface after the modification of the generating line gradual shrinkage tooth profile, which is shown in the gear 5 in fig. 5, a tooth surface of the standard involute cylindrical gear 6, which is shown in fig. 6, and a tooth surface after the modification of the generating line gradual expansion tooth profile, which is shown in the gear 7 in fig. 7, and a schematic diagram of a planar tooth surface after the modification of the generating line limit gradual elongation tooth profile, which is shown in the gear 8 in fig. 8; the four tooth surfaces are placed under the same coordinate system, and the comparison of the four tooth surfaces with the relative position relationship shown in the gear 9 of fig. 9 can be obtained, namely the tooth surface 91 after the profile modification of the profile of the progressive shrinkage, the tooth surface 92 of the standard involute cylindrical gear, the tooth surface 93 after the profile modification of the profile of the progressive expansion and the plane tooth surface 94 after the profile modification of the profile of the progressive ultimate elongation; in the present example, the four tooth surfaces are tangential at the pitch circle at the same time, and the tangential contact line is the intersection line of the pitch cylinder surface and the tooth surface.
Of course, the shape modifying quantity function is not limited to the cosine function, but may be any other curve function satisfying the four conditions, for example: the objective of the present invention can be achieved under the guidance of the method of the present invention by using a unitary conic function, a sine function, a perfect circular function, an elliptic function, and the like.
Secondly, in the present invention, when the modified tooth surface is applied to the enveloping worm drive (torus envelope and drum envelope), the modified type (elongation and shrinkage) can be selected according to the specific situation and matched with the corresponding worm tooth surface.
The following is the configuration process of the local conjugate point contact worm gear pair:
In the embodiment, the worm is a standard enveloping worm tooth surface, and the worm wheel is a modified tooth surface worm wheel;
In this embodiment, the main parameters of the enveloping worm drive used are as follows: gear number Z 1 =60, worm head number Z 2 =60, helix angle β L＝βR =5°, normal pressure angle m n =3 mm, center distance a=100 mm, and axis intersection angle (angle between Z 1 axis and Z 2 axis) is 90 °; meanwhile, in the invention, an involute tooth surface for enveloping the toroidal worm belongs to an external tooth cylindrical gear tooth surface and is used as a generating tool surface of the enveloping toroidal worm, namely an external tooth reference worm wheel;
To explain the meshing principle of involute enveloping worm drive, a drive pair coordinate system is established as shown in fig. 10; fixed coordinate systems sigma m(Om:xm,ym,zm) and sigma n(On:xn,yn,zn) are respectively fixed at the initial positions of the standard involute tooth surface and the enveloping worm, and the motion coordinate systems sigma 1(O1:x1,y1,z1) and sigma 2(O2:x2,y2,z2) are respectively fixedly connected with the standard involute tooth surface and the enveloping worm. The standard involute flank rotates around the z 1 axis at an angular speed omega 1, while the enveloping torus worm rotates around the z 2 axis at an angular speed omega 2, and at a moment the rotation angles of the standard involute flank and the enveloping torus worm are respectively And/>The shortest distance between the z 1 axis and the z 2 axis, namely the center distance of the enveloping worm gear pair, is a.
In the present example, the enveloping worm tooth surface is in fact a spatial spiral surface conjugated to and created by the standard involute outer tooth surface; based on the gear meshing principle, the standard involute tooth surface and the enveloping toroidal worm tooth surface are tangent all the time in the meshing process; thus, the meshing function of the standard involute flank and the enveloping toroidal worm can be established as follows:
Wherein: Is the relative movement speed between the standard involute tooth surface and the enveloping toroidal worm tooth surface; /(I) Is the unit normal vector of the standard involute flank in the motion coordinate system σ 1(O1:x1,y1,z1).
Thus, the left tooth surface meshing function of the enveloping worm gear can be obtainedThe method comprises the following steps:
Wherein: i 21 is the ratio of the transmission pair, and i 21＝Z1/Z2.
The enveloping worm tooth surface is generated by enveloping a series of standard involute external tooth surfaces, based on the equation and the meshing function of the standard involute tooth surface, the standard involute tooth surface is converted from sigma 1 to sigma 2 through coordinate transformation, and the left tooth surface equation of the enveloping worm can be obtainedThe method comprises the following steps: /(I)
Wherein: is a left tooth surface meshing function of enveloping ring surface worm transmission; (i 2,j2,k2) are unit vectors of coordinate axes in the coordinate system O 2-x2y2z2, respectively; /(I) Left tooth surface equation/>, respectively, of enveloping toroidal wormIs set in the coordinate value of (a).
Likewise, the right tooth surface equation of the enveloping worm can be obtainedThe method comprises the following steps:
Wherein: Is the right tooth surface meshing function of enveloping ring surface worm transmission; (i 2,j2,k2) are unit vectors of coordinate axes in the coordinate system O 2-x2y2z2, respectively; /(I) Right tooth surface equation of enveloping torus worm/>, respectivelyIs set in the coordinate value of (a).
Based on the involute gear equation, programming is carried out by utilizing MATLAB, a tooth surface data point set is solved, the obtained tooth surface data point is imported into UG for three-dimensional modeling, a three-dimensional model of an enveloping torus worm can be obtained, and the model is meshed with a standard involute gear (worm wheel) as shown in figure 10; the meshing contact lines of the standard involute flank with the enveloping torus worm are shown in fig. 11, and include contact line 1101, contact line 1102, contact line 1103, contact line 1104, contact line 1105 and contact line 1106, and it should be noted that the meshing tooth pairs (the number of lines at the junction) are not fixed at the same time, and change as the parameters of the worm drive pair (such as the effective length of the worm, the number of heads, the modulus, the helix angle, etc.) change.
Shrink shaping the worm wheel based on formulas (13) and (14), in this example, taking a shaping factor w=0.2; programming by utilizing MATLAB, solving and generating a tooth surface data point set, and introducing the obtained tooth surface data point into UG for three-dimensional modeling to obtain a shrinkage-shaping involute external tooth cylindrical gear three-dimensional model;
The standard involute gear tooth surface and the shrinkage modified involute external tooth cylindrical gear (worm gear) tooth surface are placed under the same coordinate system, the relative position relationship between the standard involute gear tooth surface and the shrinkage modified involute external tooth cylindrical gear (worm gear) tooth surface can be obtained through analysis, as shown in fig. 12, fig. 12 is a partial enlarged view, the standard involute gear tooth surface and the shrinkage modified involute external tooth cylindrical gear (worm gear) are tangent at a reference circle, and the tangent contact lines of the left tooth surface and the right tooth surface are respectively a left tooth surface contact line 1201 and a right tooth surface contact line 1202;
In design, the involute enveloping worm transmission pair (standard involute gear tooth surface and worm) is combined with the shrinkage shaping involute external tooth cylindrical gear, and the relative position relationship among the standard tooth surface external tooth gear, the shrinkage shaping external tooth gear and the standard enveloping worm is shown in fig. 13; the standard involute gear tooth surface is in conjugate line contact with the involute enveloping worm, the standard involute gear tooth surface is in conjugate line contact with the shrinkage-modification involute external tooth cylindrical gear, and when the standard involute gear tooth surface is removed, the involute enveloping worm and the shrinkage-modification involute external tooth cylindrical gear are in conjugate engagement; as shown in fig. 14 enlarged in part in fig. 13, and in the form of a partial conjugate point contact, the contact points are contact point 1401, contact point 1402, contact point 1403, contact point 1404, contact point 1405, and contact point 1406, respectively.
Therefore, based on the method, a novel point contact partial conjugate meshing enveloping worm drive can be obtained;
Of course, the enveloping worm drive pair belongs to the drive mode of meshing the external cylindrical gear and the enveloping worm, and when the enveloping worm is driven by the inner face of the standard involute gear face, the enveloping drum worm drive can be obtained. The enveloping drum worm drive with the novel point contact local conjugate meshing can be obtained by analogy with reference to the novel point contact local conjugate meshing enveloping ring worm drive model established in the prior art, and the concrete contents are as follows.
To illustrate the meshing principle of the involute surface envelope drum worm drive, a drive pair coordinate system is established as shown in fig. 15. Fixed coordinate systems sigma m(Om:xm,ym,zm) and sigma n(On:xn,yn,zn) are respectively fixed at the initial positions of the standard involute gear surface and the initial positions of the enveloping drum worm, and the motion coordinate systems sigma 1(O1:x1,y1,z1) and sigma 2(O2:x2,y2,z2) are respectively fixedly connected with the standard involute gear surface and the enveloping drum worm. The standard involute flank rotates around the z 1 axis at an angular speed omega 1, while the enveloping drum worm rotates around the z 2 axis at an angular speed omega 2, and at a certain moment the rotation angles of the standard involute flank and the enveloping drum worm are respectivelyAnd/>The shortest distance between the z 1 axis and the z 2 axis, namely the center distance of the enveloping drum worm gear pair is a, and the intersecting angle (the included angle between the z 1 axis and the z 2 axis) is 90 degrees.
In the present invention, the enveloping crowned worm tooth surface is in fact a spatial spiral surface conjugated to and created by the standard involute internal tooth surface. Based on the gear meshing principle, the standard involute tooth surface and the enveloping crowned worm tooth surface are always tangent in the meshing process. Thus, the meshing function of the standard involute flank and the enveloping crown worm can be established as follows:
Wherein: Is the relative movement speed between the standard involute tooth surface and the enveloping crown worm tooth surface; /(I) Is the unit normal vector of the standard involute flank in the motion coordinate system σ 1(O1:x1,y1,z1).
The enveloping crowned worm tooth surface is generated by enveloping a series of standard involute internal tooth surfaces, based on the equation and the meshing function of the standard involute tooth surface, the standard involute tooth surface is converted from sigma 1 to sigma 2 through coordinate transformation, and the left tooth surface equation of the enveloping crowned worm can be obtainedThe method comprises the following steps:
Wherein: A left tooth surface meshing function of the enveloping drum worm drive; (i 2,j2,k2) are unit vectors of coordinate axes in the coordinate system O 2-x2y2z2, respectively; /(I) Left tooth surface equation/>, respectively, of enveloping crowned wormIs set in the coordinate value of (a).
Likewise, the right tooth surface equation of the enveloping crown worm can be obtainedThe method comprises the following steps: /(I)
Wherein: a right tooth surface meshing function of the enveloping drum worm drive; (i 2,j2,k2) are unit vectors of coordinate axes in the coordinate system O 2-x2y2z2, respectively; /(I) Right tooth surface equation of enveloping crowned worm/>, respectivelyIs set in the coordinate value of (a).
Based on the involute tooth surface equation, MATLAB is utilized to program and solve a generated tooth surface data point set, the obtained tooth surface data point is imported into UG for three-dimensional modeling, a three-dimensional model of the enveloping drum worm can be obtained, and the meshing relationship between the enveloping drum worm and the standard involute internal tooth gear is shown in figure 15. The meshing contact lines of standard involute tooth profile and enveloping crown worm are shown in fig. 16, which is a partial enlargement of fig. 15, and include contact line 1601, contact line 1602, contact line 1603, contact line 1604, contact line 1605, and contact line 1606, and it should be noted that the meshing teeth pairs (number of lines at the junction) are not fixed at the same time, and change as the parameters of the worm drive pair (such as effective length of worm, number of heads, modulus, helix angle, etc.) change.
Performing expansion modification on the worm wheel based on formulas (13) and (14), in this embodiment, taking a fixed modification factor w=0.2; and programming by utilizing MATLAB, solving and generating a tooth surface data point set, and introducing the obtained tooth surface data point into UG for three-dimensional modeling to obtain the expansion modification involute external tooth cylindrical gear three-dimensional model.
The relative positional relationship between the standard involute gear tooth surface and the expansion modified involute internal tooth cylindrical gear can be obtained by analyzing the same coordinate system as shown in fig. 17. When the partial enlarged view is observed, the tooth surface of the standard involute gear is tangent to the cylindrical gear with the involute internal teeth in the expansion modification at the pitch circle, and the tangent contact lines of the left tooth surface and the right tooth surface are respectively a left tooth surface contact line 1701 and a right tooth surface contact line 1702, which are similar to the case of the cylindrical gear with the involute external teeth in the contraction modification.
The involute helical worm drive pair (standard involute gear tooth surface + helical worm) is combined with the expansion shaping involute internal tooth cylindrical gear to obtain the relative position relationship of standard tooth surface, expansion shaping internal tooth gear and standard helical worm as shown in figure 18. The standard involute flank is in conjugate line contact with the involute curve drum worm, the standard involute flank is in conjugate line contact with the expanding modified involute internal tooth cylindrical gear, and when the standard involute flank is removed, the involute curve drum worm is in conjugate engagement with the expanding modified involute internal tooth cylindrical gear, as shown in the part of fig. 19 in the enlarged view of fig. 18, and the engagement contact forms are partial conjugate point contacts, and the contact points are a contact point 1901, a contact point 1902, a contact point 1903, a contact point 1904, a contact point 1905 and a contact point 1906 respectively.
In the invention, based on the method, a novel point contact local conjugate meshing enveloping drum worm drive can be obtained.
Through analysis, the novel point contact local conjugate meshing enveloping worm gear transmission and the novel point contact local conjugate meshing enveloping drum worm gear transmission with the configurations are in a form of meshing a worm with a standard tooth surface enveloping and a modified tooth surface gear, and further expansion is performed by analogy, so that the method for forming the local conjugate point contact enveloping worm with more forms can be obtained, namely:
the "±" numbers in the formulas (3) and (4) and the formulas (13) and (14) are expansion modification when "+" is taken, and contraction modification when "-" is taken; when the tooth surfaces of the worm wheel and the worm have a modification, then:
The worm comprises an external-meshing enveloping worm and an internal-meshing enveloping crown worm, the worm wheel comprises an external-tooth worm wheel meshed with the external-meshing enveloping worm and an internal-tooth worm wheel meshed with the internal-meshing enveloping crown worm, and the reference worm wheel comprises an external-tooth reference worm wheel enveloped to form the external-meshing enveloping worm and an internal-tooth reference worm wheel enveloped to form the internal-meshing enveloping crown worm; the mathematical parameter expressions of the tooth surfaces of the external tooth worm gear and the internal tooth worm gear are the same;
When the worm is an external engagement enveloping worm:
The tooth surfaces of the external tooth worm wheel and the external meshing enveloping worm are both shrink modified tooth surfaces, the tooth surface modification of the external meshing enveloping worm is formed by enveloping the modified tooth surface of the external tooth reference worm wheel, and the shrink modification amount of the tooth surface of the external tooth reference worm wheel is smaller than that of the tooth surface of the external tooth worm wheel;
Or the tooth surface of the external tooth worm wheel is a shrinkage modified tooth surface, the tooth surface of the external engagement enveloping worm is an expansion modified tooth surface, and the external tooth enveloping worm wheel is formed by enveloping the external tooth reference worm wheel with the expansion modified tooth surface;
or the tooth surfaces of the external tooth worm wheel and the external meshing enveloping worm are both expansion modification tooth surfaces, the tooth surface modification of the external meshing enveloping worm is formed by enveloping the modified tooth surface of the external tooth reference worm wheel, and the expansion modification amount of the tooth surface of the external tooth reference worm wheel is larger than that of the tooth surface of the external tooth worm wheel;
when the worm is an internal engagement enveloping drum worm:
the tooth surfaces of the internal tooth worm wheel and the internal meshing enveloping crowned worm are both shrink-shaped tooth surfaces, the tooth surface modification of the internal meshing enveloping crowned worm is formed by enveloping the modified tooth surface of the internal tooth reference worm wheel, and the shrink-shaped amount of the tooth surface of the internal tooth reference worm wheel is larger than that of the tooth surface of the internal tooth worm wheel;
Or the tooth surface of the internal tooth worm wheel is an expansion modification tooth surface, the tooth surface of the internal meshing enveloping crowned worm is a contraction modification, and the internal tooth enveloping crowned worm is formed by enveloping an internal tooth reference worm wheel of the contraction modification tooth surface;
Or the tooth surfaces of the internal tooth worm wheel and the internal meshing enveloping crown worm are both expansion modification tooth surfaces, the tooth surface modification of the internal meshing enveloping crown worm is formed by enveloping the modified tooth surface of the internal tooth reference worm wheel, and the expansion modification amount of the tooth surface of the internal tooth reference worm wheel is smaller than that of the tooth surface of the internal tooth worm wheel; in the structure, point contact transmission can be realized; the specific table is shown below:
local conjugate point contact enveloping worm configuration method type table
/>
In the invention, the configuration method of the local conjugate point contact enveloping worm is not only suitable for the conventional case that the axis angle is 90 degrees, but also suitable for the case that the axis angle is not equal to 90 degrees.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the technical solution of the present invention, which is intended to be covered by the scope of the claims of the present invention.
Claims (4)
1. A method for forming a point contact partial conjugate meshing enveloping worm drive pair is characterized by comprising the following steps of: the worm transmission pair comprises a worm wheel and a worm, and the specific configuration adopts the following method:
The tooth surface of the worm gear is obtained by modifying the tooth surface of a standard involute gear, and the modified tooth surface is tangent with the tooth surface of the standard gear at a modification target position along the tooth height direction; the worm is a standard involute enveloping worm;
Or the worm wheel is a standard involute gear, the tooth surface of the worm is a modified tooth surface, the modified tooth surface of the reference worm wheel is enveloped and formed, and the modified tooth surface of the reference worm wheel is tangent with the tooth surface of the standard gear at a modified target position along the tooth height direction;
Or the tooth surface of the worm gear is obtained by modifying the tooth surface of the standard involute gear, and the modified tooth surface is tangent with the tooth surface of the standard gear at a modification target position along the tooth height direction; the tooth surface of the worm is a modified tooth surface, the modified tooth surface of the worm is formed by enveloping a reference worm gear tooth surface with a set modification amount, and the modified tooth surface of the reference worm gear with the set modification amount is tangent with a standard gear tooth surface at a modification target position along the tooth height direction; the set modification amount of the reference worm wheel is different from that of the worm wheel tooth surface, but the modification target positions are the same;
The tooth surfaces of the worm wheel and the reference worm wheel are involute tooth surfaces, and the tooth profile modification of the involute tooth surfaces is realized through gradual expansion and contraction of an involute generating line;
The tooth profile modification method of the involute tooth profile of the worm wheel and the reference worm wheel comprises the following steps:
a. Determining a modification quantity function:
wherein: θ K is the spread angle of any point K on the generation line of the involute;
And the modification function f (θ K) should be continuously derivable, symmetrical with respect to the given target modification point, monotonically increasing on both sides of the given target modification point, and the modification amount having a maximum and a minimum;
b. acquiring a curve equation after involute shape modification:
Wherein: r K is the radial of the K point on the involute; r b is the base radius; alpha K is the pressure angle of the K point on the involute;
c. based on the curve equation in the step b, obtaining a tooth profile modification tooth surface equation:
Left side modified tooth surface equation The method comprises the following steps:
right side modified tooth surface equation The method comprises the following steps:
Wherein: f (τ) is a function of f (θ K) to a function of the involute flank parameter τ, and τ=θ K+αK; The radius of the base circle of the involute surface is modified; τ and θ∈ [ θ 1,θ2 ] are involute tooth surface parameters; delta is the base circle half angle; p is a tooth surface spiral parameter; alpha t is the pressure angle of the end face of the reference circle, and/> Wherein alpha n is the normal pressure angle of the reference circle; beta is the helix angle of the tooth surface; (i 1,j1,k1) are unit vectors of coordinate axes in the coordinate system O 1-x1y1z1, respectively;
Left side modified tooth surface equation/>, respectively Coordinate values of (2); /(I)Right side modified tooth surface equation/>, respectivelyIs set in the coordinate value of (a).
2. The method of forming a point contact partial conjugate meshing enveloping worm drive set according to claim 1, wherein:
the curve equation after involute shape modification in the step b is obtained by substituting the modification quantity function in the step a into a standard involute polar coordinate equation, wherein the standard involute polar coordinate equation is as follows:
3. the method of forming a point contact partial conjugate meshing enveloping worm drive set according to claim 2, wherein:
The tooth profile modification tooth surface equation in the step c is obtained by substituting a function f (tau) into a standard involute cylindrical gear tooth surface equation, wherein the standard involute cylindrical gear tooth surface equation is as follows:
Left flank equation The method comprises the following steps:
Right flank equation The method comprises the following steps:
Wherein: The radius of the base circle is the standard involute surface; /(I) Left flank equation/>, respectivelyCoordinate values of (2); right flank equation/>, respectively Is set in the coordinate value of (a).
4. The method of forming a point contact partial conjugate meshing enveloping worm drive set according to claim 1, wherein: in the formula (3) and the formula (4), the "±" number is used for expanding and shaping when "+" is taken, and the "-" number is used for contracting and shaping;
when the tooth surfaces of the worm wheel and the worm have a modification, then:
The worm comprises an external-meshing enveloping worm and an internal-meshing enveloping crown worm, the worm wheel comprises an external-tooth worm wheel meshed with the external-meshing enveloping worm and an internal-tooth worm wheel meshed with the internal-meshing enveloping crown worm, and the reference worm wheel comprises an external-tooth reference worm wheel enveloped to form the external-meshing enveloping worm and an internal-tooth reference worm wheel enveloped to form the internal-meshing enveloping crown worm;
When the worm is an external engagement enveloping worm:
The tooth surfaces of the external tooth worm wheel and the external meshing enveloping worm are both shrink modified tooth surfaces, the tooth surface modification of the external meshing enveloping worm is formed by enveloping the modified tooth surface of the external tooth reference worm wheel, and the shrink modification amount of the tooth surface of the external tooth reference worm wheel is smaller than that of the tooth surface of the external tooth worm wheel;
Or the tooth surface of the external tooth worm wheel is a shrinkage modified tooth surface, the tooth surface of the external engagement enveloping worm is an expansion modified tooth surface, and the external tooth enveloping worm wheel is formed by enveloping the external tooth reference worm wheel with the expansion modified tooth surface;
or the tooth surfaces of the external tooth worm wheel and the external meshing enveloping worm are both expansion modification tooth surfaces, the tooth surface modification of the external meshing enveloping worm is formed by enveloping the modified tooth surface of the external tooth reference worm wheel, and the expansion modification amount of the tooth surface of the external tooth reference worm wheel is larger than that of the tooth surface of the external tooth worm wheel;
when the worm is an internal engagement enveloping drum worm:
the tooth surfaces of the internal tooth worm wheel and the internal meshing enveloping crowned worm are both shrink-shaped tooth surfaces, the tooth surface modification of the internal meshing enveloping crowned worm is formed by enveloping the modified tooth surface of the internal tooth reference worm wheel, and the shrink-shaped amount of the tooth surface of the internal tooth reference worm wheel is larger than that of the tooth surface of the internal tooth worm wheel;
Or the tooth surface of the internal tooth worm wheel is an expansion modification tooth surface, the tooth surface of the internal meshing enveloping crowned worm is a contraction modification, and the internal tooth enveloping crowned worm is formed by enveloping an internal tooth reference worm wheel of the contraction modification tooth surface;
or the tooth surfaces of the internal tooth worm wheel and the internal meshing enveloping crowned worm are both expansion modified tooth surfaces, the tooth surface modification of the internal meshing enveloping crowned worm is formed by enveloping the modified tooth surface of the internal tooth reference worm wheel, and the expansion modification amount of the tooth surface of the internal tooth reference worm wheel is smaller than that of the tooth surface of the internal tooth worm wheel.
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| 制造的斜齿轮齿向修形曲线的优化分析;崔雪莹;操兵;刘鹏祥;;装备制造技术;20180415(第04期);全文 * |
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