CN110434409A - One kind parallels to the axis gear hob and its design method - Google Patents
One kind parallels to the axis gear hob and its design method Download PDFInfo
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- CN110434409A CN110434409A CN201910684788.5A CN201910684788A CN110434409A CN 110434409 A CN110434409 A CN 110434409A CN 201910684788 A CN201910684788 A CN 201910684788A CN 110434409 A CN110434409 A CN 110434409A
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- 238000012545 processing Methods 0.000 claims abstract description 16
- 238000003801 milling Methods 0.000 claims description 7
- 238000005096 rolling process Methods 0.000 claims description 7
- 238000005520 cutting process Methods 0.000 claims description 6
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F21/00—Tools specially adapted for use in machines for manufacturing gear teeth
- B23F21/12—Milling tools
- B23F21/16—Hobs
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Abstract
It parallels to the axis gear hob and hobboing cutter design method the invention discloses one kind, the gear hob that parallels to the axis includes double wedge and concave tooth two types, its barrel shaped tooth gear hob that parallels to the axis parallels to the axis the gear hobbing process of gear for concave tooth, and the concave tooth gear hob that parallels to the axis parallels to the axis the gear hobbing process of gear for double wedge.The gear hob design method that parallels to the axis is: the contrate tooth profile using one section of simple curve between double wedge line gear imagination rack gear contrate tooth profile curve and concave tooth line gear imagination rack gear contrate tooth profile curve as hobboing cutter basic rack, it takes the normal direction of basic rack contrate tooth profile curve to project as basic rack tooth profile, and the design to hobboing cutter is completed according to basic rack tooth profile.A kind of gear hobbing cutter and its design method dedicated for processing the gear that parallels to the axis proposed by the present invention, the hobboing cutter that can be greatly simplified the gear hob design process that parallels to the axis, and design is convenient for manufacture.To parallel to the axis, gear mass production provides basis.
Description
Technical field
It parallels to the axis gear hob and its design side the present invention relates to gear cutting tool technical field more particularly to one kind
Method.
Background technique
The gear that parallels to the axis is a kind of new gear based on spatial conjugation curve mesh theory, effect few with the number of teeth
Rate is high, slides, the advantages that contact point composite curve radius is small without opposite.It can be used for field of food, package packing machine, robot
Equal fields.Currently, the processing for the gear that parallels to the axis mainly uses the forming tools such as finger cutter, disc milling cutter to add
Work.But the error of division can be generated using forming tool, and processing efficiency is relatively low.
Common gear manufacturing technology has mill teeth, gear hobbing, gear-shaping, shaving, gear shaping, roll flute etc..Wherein gear hobbing process technique
It is most widely used.Its high production efficiency, machining accuracy are high, adaptability is good, for the gear with identical modulus and pressure angle
Hobboing cutter is processed using same.But due to tooth form difference, current existing gear hob can not be to the gear that parallels to the axis
It is processed.It is parallel axes to improve line gear production efficiency therefore, it is necessary to be designed to the gear hob that parallels to the axis
Line gear mass production provides basis.
Summary of the invention
In order to solve the problems, such as it is existing parallel to the axis that Gear Processing means are single, production efficiency is low, the present invention provides one
Special-purpose hob cutter and hobboing cutter design method of the kind for the gear teeth processing that parallels to the axis.Improve line gear processing efficiency and processing
Precision, to parallel to the axis, gear mass production provides basis.
The purpose of the present invention is realized at least through one of following technical solution.
One kind parallels to the axis gear hob, the basic spiral being spirally distributed including base cylinder and on base cylinder
Surface；Hobboing cutter cutter tooth and chip pocket, the corresponding chip pocket of row's hobboing cutter cutter tooth are intervally distributed in basic helical surface；It is each
A hobboing cutter cutter tooth includes a rake face, a top sword flank, a side edge flank, a cutting edge and a top
Sword；
The basic helicoid is revolved by paralleling to the axis gear hob axial tooth profile profile or contrate tooth profile profile along helix
Turn to obtain.
The gear hob that parallels to the axis includes double wedge hobboing cutter and concave tooth hobboing cutter two types, and barrel shaped tooth hobboing cutter is for recessed
Tooth parallels to the axis the gear hobbing process of gear, and concave tooth hobboing cutter parallels to the axis the gear hobbing process of gear for double wedge.
The gear hob that parallels to the axis, the contrate tooth profile of double wedge hobboing cutter is two sections of symmetrical convex curves, described
The contrate tooth profile of concave tooth hobboing cutter is two sections of symmetrical concave curves.The gear hob contrate tooth profile curve that parallels to the axis unifies table
It is shown as:
(sin(α0)+sin(t))
In formula, t is parameter, xd1For the abscissa for the gear hob contrate tooth profile curve that parallels to the axis, yd1To parallel to the axis
The ordinate of gear hob contrate tooth profile curve, r are the arc radius of basic rack tooth profile, β1For the gear hob spiral that parallels to the axis
Angle, α0For the nominal pressure angle of basic rack, rjFor the gear hob pitch radius that parallels to the axis, basic rack tooth profile is the tooth that parallels to the axis
Take turns the normal tooth profile curve of hobboing cutter basic rack；Work as α0> 0, t ∈ (0, pi), the gear hob contrate tooth profile curve that parallels to the axis are
Concave curve；Work as α0< 0, t ∈ (pi, 2*pi), the gear hob contrate tooth profile curve that parallels to the axis are convex curve.
The gear hob that parallels to the axis, compares the involute gear hob of identical modulus, and parallel to the axis gear hob tooth
The high 1/3-1/4 of a height of involute gear hob tooth.Since the gear that parallels to the axis is point contact gear, increasing tooth height not will increase
The registration of line gear can weaken the teeth bending strength of line gear instead；Therefore the gear teeth height that parallels to the axis is only involute
The high 1/3-1/4 of gear hob tooth, hob teeth height are also only the high 1/3-1/4 of involute gear hob tooth.
The gear hob that parallels to the axis, the gears that parallel to the axis identical for modulus, that the number of teeth is different are able to use one
The gear hob that parallels to the axis is processed.The line gear that the gear hob that parallels to the axis processes is pure rolling gear.Line gear
On contact line indicate are as follows:
Since line gear is point contact gear, collection of the contact point on the flank of tooth is combined into a helix, which is
The contact line of line gear.In formula, x is the abscissa of contact line, and y is the ordinate of contact line, and z is the ordinate of contact line, and m is
Helix radius where contact point, n are helix screw pitch parameter, and t is parameter, and ts is contact point start angle, and te is contact
Line angle at the end.
The basic rack normal tooth profile curve of two sides two of the gear hob that parallels to the axis is symmetrical.When paralleling to the axis
When the corresponding basic rack normal tooth profile curve of gear hob is circular arc, the basic rack normal tooth profile curve is expressed as:
xf2=e+r*cos (t)；
yf2=r*sin (t)-r*sin (α0)；
In formula, t is parameter, xf2For the abscissa for the gear hob basic rack normal tooth profile curve that parallels to the axis, yf2For
Parallel to the axis the ordinate of gear hob basic rack normal tooth profile curve, and e is offset distance；R is the circular arc half of basic rack tooth profile
Diameter, the normal tooth profile curve of basic rack are basic rack tooth profile, α0For the nominal pressure angle of basic rack tooth profile.
It is corresponding that the contrate tooth profile curve of the gear hob basic rack that parallels to the axis is located at the concave tooth gear that parallels to the axis
Imaginary rack gear contrate tooth profile curve and double wedge parallel to the axis between the corresponding imaginary rack gear contrate tooth profile curve of gear；For difference
The gear that parallels to the axis of the number of teeth, which can be used, same to be processed milling cutter.The line gear that the gear hob that parallels to the axis is processed can
It is interchangeable with the same gear that parallels to the axis that line gear milling cutter is processed.
The gear hob design method that parallels to the axis comprises the steps of:
S1: solution parallels to the axis gear face tooth form: the gear that parallels to the axis include double wedge parallel to the axis gear and concave tooth it is flat
Two kinds of row axis gear.According to spiral surface properties, its general contrate tooth profile, the general contrate tooth profile equation of the gear that parallels to the axis are solved
Are as follows:
In formula, t2For parameter, xd3For the gear face tooth form abscissa that parallels to the axis, yd3For the gear face tooth that parallels to the axis
Shape ordinate.M is helix radius where contact point, and n is helix screw pitch parameter, t0For the start angle of helix, r1For base
The normal tooth profile curve arc radius of this rack gear, q is deflection angle, whenThe end-tooth of this equation expression double wedge line gear
Shape；WhenThe contrate tooth profile of this equation expression concave tooth line gear；
S2: it solves characteristic parameter of the line gear rack gear contrate tooth profile at contact point: solving line gear rack gear contrate tooth profile
Radius of curvature and normal vector at contact point.These parameters have determined that the family of curves that can satisfy interchangeability requirement should expire
The primary condition of foot.For paralleling to the axis, radius of curvature of the gear face tooth curve in contact point is indicated are as follows:
In formula ρ be parallel to the axis gear face tooth curve contact point radius of curvature；x′d3、y′d3、xd3"、yd3" point
It Wei not xd3And yd3First derivative and second dervative；
Radius of curvature and normal vector of the line gear rack gear contrate tooth profile at contact point can be acquired by substituting into following formula:
α is line gear rack gear contrate tooth profile in contact normal direction and x-axis angle, α in formula0For the name of basic rack tooth profile
Pressure angle,ρ ' is radius of curvature of the line gear rack gear contrate tooth profile at contact point,For line gear rack gear
Normal vector of the contrate tooth profile at contact point, β2For the gear helical angle that parallels to the axis.
S3: its corresponding imaginary rack gear contrate tooth profile curve is solved according to line gear contrate tooth profile curve: according to above-mentioned
The gear face tooth curve that parallels to the axis substitutes into following formula and solves its corresponding imaginary rack gear contrate tooth profile curve:
xd4=x (t2)*cos(s)-y(t2)*sin(s)+m*s；
yd4=x (t2)*sin(s)+y(t2)*cos(s)-m；
In formula, τ is that the gear face tooth curve that parallels to the axis locates the angle of tangent line and x-axis on one point, and s is simplified expression
The variable of introduction, xd4For the corresponding imaginary rack gear contrate tooth profile curvilinear abscissa of line gear contrate tooth profile, yd4For line gear end face
The corresponding imaginary rack gear contrate tooth profile curve ordinate of tooth form.
S4: basic rack contrate tooth profile curve is solved according to imaginary rack gear contrate tooth profile curve: flat according to the double wedge acquired
The corresponding imaginary rack gear contrate tooth profile of row axis gear face tooth form and concave tooth parallel to the axis the corresponding imaginary rack gear end of gear
Face tooth form selects a contrate tooth profile curve of the curve as the gear hob basic rack that parallels to the axis being located between the two.
Since normal gear shape of a hob is is convenient for manufacture when circular arc, the present invention is by taking basic rack normal tooth profile is circular arc as an example.Work as parallel axes
The normal tooth profile curve of line gear hobboing cutter basic rack is circular arc, the contrate tooth profile curve for the gear hob basic rack that parallels to the axis
It is an ellipse, may be expressed as:
yd2=r*sin (t)-r*sin (α0)；
X in formulad2For the contrate tooth profile curvilinear abscissa for the gear hob basic rack that parallels to the axis, yd2For the tooth that parallels to the axis
Take turns the contrate tooth profile curve ordinate of hobboing cutter basic rack, β2For the gear helical angle that parallels to the axis.
Curve and the double wedge and concave tooth for being selected as the contrate tooth profile curve for the gear hob basic rack that parallels to the axis are flat
Row axis gear face tooth form contact point should normal direction having the same, and its radius of curvature should be greater than double wedge parallel axes
Line gear contrate tooth profile contact point radius of curvature, less than concave tooth parallel to the axis gear face tooth form contact point curvature half
Diameter；
Since line gear pitch radius is bigger, a pair of intermeshing parallel axes concave tooth line gear and double wedge line gear are corresponding
Rack gear contrate tooth profile it is more and more separated.So the hobboing cutter of design can be greater than selected a pair of of concave tooth and double wedge line with pair radius
The gear that parallels to the axis of gear is processed.
S5: hobboing cutter is solved according to obtained basic rack contrate tooth profile curve is solved: with the basic rack end face solved
Tooth curve projects to obtain the normal tooth profile curve of basic rack.It is basic that hobboing cutter is solved according to the normal tooth profile curve of basic rack
Worm tooth-surface equation is zero to hobboing cutter basic worm x-axis or y-axis value, can solve hobboing cutter axial tooth profile.According to hobboing cutter axial direction
The tooth form that tooth form solves other sections can design universal method according to hobboing cutter and solve, and details are not described herein.As above-mentioned it is found that basic
The normal tooth profile curve of rack gear are as follows:
xf2=e+r*cos (t)；
yf2=r*sin (t)-r*sin (α0)；
X in formulaf2For the abscissa of basic rack normal tooth profile curve, yf2For the vertical seat of basic rack normal tooth profile curve
Mark.R is the arc radius of basic rack tooth profile, α0For the nominal pressure angle of basic rack tooth profile.
Compared with the prior art, the beneficial effects of the present invention are embodied in:
1, compared with existing line gear processing technology, dividing movement is not present in the present invention during processing line gear, because
And machining accuracy is higher.And process is continuous cutting, processing efficiency is higher.
2, use one can process line gear hobboing cutter to the line gear of same modulus, reduce number of cutters, just
In management, production cost is advantageously reduced.
3, gear hobbing process manufacturing process is fairly simple, is only needed to change when processing different gears as corresponding module hob
Processing can be completed.
4, line gear can be processed using traditional gear-hobbing machine in the case where not changing traditional hobbing machine structure, without in addition
Increase entreprise cost, is conducive to the popularization and development of line gear.
Detailed description of the invention
Fig. 1 is hob-cutter structure schematic diagram of the present invention.
Fig. 2 is the normal tooth profile curve of double wedge line gear hobboing cutter basic rack of the present invention.
Fig. 3 is the normal tooth profile curve of concave tooth line gear hobboing cutter basic rack of the present invention.
Fig. 4 is convex arc line gear hobboing cutter basic worm and basic rack meshing state schematic diagram.
Fig. 5 is concave arc line gear hobboing cutter basic worm and basic rack meshing state schematic diagram.
Fig. 6 is convex arc line gear and the corresponding imaginary rack gear contrate tooth profile curve of concave arc line gear and the gear rolling that parallels to the axis
The corresponding basic rack contrate tooth profile comparison of knife.
Fig. 7 is that parallel to the axis gear and double wedge of different pitch radius concave tooth parallels to the axis the end-tooth of the corresponding rack gear of gear
Shape curve.
Fig. 8 is line gear parallel axes hobboing cutter design flow diagram.
In figure:
Base cylinder 1, basic helical surface 2, hobboing cutter cutter tooth 3, chip pocket 4, rake face 5 push up sword flank 6, knife after side edge
Face 7, cutting edge 8 push up sword 9, hobboing cutter axial tooth profile profile 10, the corresponding imaginary rack gear end face of mill teeth convex arc line gear contrate tooth profile
Tooth form 11, basic rack contrate tooth profile 12, the corresponding imaginary rack gear contrate tooth profile 13 of mill teeth concave arc line gear contrate tooth profile are big to save
Radius of circle double wedge parallels to the axis gear 14, and small pitch radius double wedge parallels to the axis gear 15, and big pitch radius concave tooth parallels to the axis
Gear 16, small pitch radius double wedge parallel to the axis gear 17.
Specific embodiment
In order to more clearly illustrate the technical solution in the embodiment of the present invention, below in conjunction in the embodiment of the present invention
Attached drawing, the technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is only
A part of the embodiments of the present invention, it is obtained by those of ordinary skill in the art without making creative efforts all
The scope of the present invention all should belong in other embodiments.
Embodiment:
As shown in Figure 1, the present embodiment is a kind of line gear hobboing cutter, including base cylinder 1 and on base cylinder 1 in the shape of a spiral
The basic helical surface 2 being dispersed with；Hobboing cutter cutter tooth 3 and chip pocket 4, row's hobboing cutter knife are intervally distributed in basic helical surface 2
Tooth corresponds to a chip pocket；Each hobboing cutter cutter tooth 3 includes knife after 5, top 6, side edges of sword flank of a rake face
7, the top swords 9 in face and a cutting edge 8.The basic helicoid 2 is it is believed that by the gear hob axial tooth profile that parallels to the axis
Profile 10 or contrate tooth profile profile rotate to obtain along helix.
The gear hob that parallels to the axis includes double wedge hobboing cutter and concave tooth hobboing cutter two types, and barrel shaped tooth hobboing cutter is flat for concave tooth
The gear hobbing process of row axis gear, concave tooth hobboing cutter parallel to the axis the gear hobbing process of gear for double wedge.
The contrate tooth profile of the double wedge hobboing cutter is two sections of symmetrical convex curves, the contrate tooth profile of the concave tooth hobboing cutter
For two sections of symmetrical concave curves；Parallel to the axis gear hob contrate tooth profile curve unified representation are as follows:
(sin(α0)+sin(t))
In formula, t is parameter, xd1For the abscissa for the gear hob contrate tooth profile curve that parallels to the axis, yd1To parallel to the axis
The ordinate of gear hob contrate tooth profile curve, r are the arc radius of basic rack tooth profile, and basic rack tooth profile is the gear hob that parallels to the axis
The normal tooth profile curve of basic rack, β1For the gear hob helical angle that parallels to the axis, α0For the nominal pressure angle of basic rack tooth profile, rj
For the gear hob pitch radius that parallels to the axis；Work as α0> 0, t ∈ (0, pi), the gear hob contrate tooth profile curve that parallels to the axis are recessed
Type curve；Work as α0< 0, t ∈ (pi, 2*pi), the gear hob contrate tooth profile curve that parallels to the axis are convex curve.
In order to obtain good teeth bending strength, the gear hob tooth height that parallels to the axis is that involute gear hob tooth is high
1/3-1/4.As shown in Figures 2 and 3, the normal tooth profile curve of gear hob two sides two that parallels to the axis is symmetrical, basic rack
Normal tooth profile curve is circular arc.The gear hob basic rack normal tooth profile curve that parallels to the axis is expressed as:
xf2=e+r*cos (t)；
yf2=r*sin (t)-r*sin (α0)；
In formula, t is parameter, xf2For the abscissa for the gear hob basic rack normal tooth profile curve that parallels to the axis, yf2For
Parallel to the axis the ordinate of gear hob basic rack normal tooth profile curve, and e is offset distance；R is the circular arc half of basic rack tooth profile
Diameter, the normal tooth profile curve of basic rack are basic rack tooth profile, α0For the nominal pressure angle of basic rack tooth profile.
As shown in Figure 4 and Figure 5, in the present embodiment, the gear hob that parallels to the axis is engaged with basic rack conjugation.It parallels to the axis
Gear hob includes double wedge hobboing cutter and concave tooth hobboing cutter two types, and barrel shaped tooth hobboing cutter parallels to the axis the gear hobbing of gear for concave tooth
Processing, concave tooth hobboing cutter parallel to the axis the gear hobbing process of gear for double wedge.
The gear hob basic rack contrate tooth profile curve that parallels to the axis is expressed as:
yd2=r*sin (t)-r*sin (α0)；
In formula, xd2For the contrate tooth profile curvilinear abscissa for the gear hob basic rack that parallels to the axis, yd2For the tooth that parallels to the axis
Take turns the contrate tooth profile curve ordinate of hobboing cutter basic rack.
The gears that parallel to the axis identical for modulus, that the number of teeth is different are able to use the gear hob that parallels to the axis and add
Work；The line gear that the gear hob that parallels to the axis processes is pure rolling gear；Since line gear is point contact gear,
Collection of the contact point on the flank of tooth is combined into a helix, which is the contact line of line gear；Contact line table on line gear
It is shown as:
In formula, x is the abscissa of contact line, and y is the ordinate of contact line, and z is the ordinate of contact line, and m is contact point
Place helix radius, n are helix screw pitch parameter, and t is parameter, and ts is contact point start angle, and te terminates for contact line
Angle.
As shown in fig. 6, basic rack contrate tooth profile curve 12 be located at it is corresponding with the concave arc gear face tooth form that parallels to the axis
Imaginary rack gear contrate tooth profile curve 13 and convex arc parallel to the axis the corresponding imaginary rack gear contrate tooth profile curve 11 of gear face tooth form
Between.Therefore, it is flat that the gear face tooth form that parallels to the axis cut also is located at parallel to the axis gear face tooth form and convex arc of concave arc
Between row axis gear face tooth form.So the line gear contrate tooth profile that the gear hob gear hobbing process that parallels to the axis obtains is milling
The approximation for gear face tooth form that tooth was processed parallel to the axis has interchangeability between the two.
As shown in fig. 7, big pitch radius double wedge parallels to the axis, gear imagination rack gear contrate tooth profile 14 is located at small pitch radius
Double wedge parallels to the axis on the inside of gear imagination rack gear contrate tooth profile 15.Big pitch radius concave tooth parallels to the axis gear imagination rack gear end face
Tooth form 16 is located at small pitch radius concave tooth and parallels to the axis the outside of gear imagination rack gear contrate tooth profile 17.Line gear pitch radius is got over
Greatly, a pair of intermeshing parallel axes concave tooth line gear and the corresponding rack gear contrate tooth profile of double wedge line gear are more and more separated.Institute
The flat of selected a pair of of concave tooth and double wedge line gear pitch radius can be greater than with pair radius with the gear hob that parallels to the axis of, design
Row axis gear is processed, and the gear that parallels to the axis that can be obtained with Gear Milling is interchangeable.
As shown in figure 8, as follows to hobboing cutter design procedure in the present embodiment:
S1: the gear face tooth form that parallels to the axis is solved；The gear that parallels to the axis includes that parallel to the axis gear and concave tooth of double wedge is flat
Two kinds of row axis gear.According to spiral surface properties, its general contrate tooth profile equation is solved using method of section.In the present embodiment, with
A pair of of m1=60, r1=6,And m2=60, r1=20,N=180, line gear for, end-tooth
Shape indicates are as follows:
In formula,Respectively double wedge and concave tooth parallels to the axis gear face tooth form abscissa,Respectively
Double wedge and concave tooth parallel to the axis gear face tooth form ordinate；
S2: characteristic parameter of the line gear rack gear contrate tooth profile at contact point is solved；Solve line gear rack gear contrate tooth profile
Radius of curvature and normal vector at contact point.These parameters have determined that the family of curves that can satisfy interchangeability requirement should expire
The primary condition of foot.To paralleling to the axis in this present embodiment, radius of curvature of the gear face tooth curve in contact point is 5.87
With -20.46, negative sign indicates that tooth form is recessed.The present embodiment middle line rack-and-pinion contrate tooth profile is acquired according to formula above contacting
Radius of curvature and normal vector at point are as follows:
ρ′t=-7.23, ρ 'a=12.36
In formula, ρ 't、ρ’aFor the radius of curvature of double wedge and the corresponding rack gear contrate tooth profile of concave tooth line gear at contact point,For normal vector of the line gear rack gear contrate tooth profile at contact point.
S3: its corresponding imaginary rack gear contrate tooth profile curve is solved according to line gear contrate tooth profile curve；According to above-mentioned
The gear face tooth curve that parallels to the axis substitutes into following formula and solves its corresponding imaginary rack gear contrate tooth profile curve, solves imaginary tooth
Contrate tooth profile curve, and map, as shown in curve 11 in Fig. 6 and curve 13.
xd4=x (t2)*cos(s)-y(t2)*sin(s)+m*s；
yd4=x (t2)*sin(s)+y(t2)*cos(s)-m；
In formula, τ is that the gear face tooth curve that parallels to the axis locates the angle of tangent line and x-axis on one point, and s is simplified expression
The variable of introduction, xd4For the corresponding imaginary rack gear contrate tooth profile curvilinear abscissa of line gear contrate tooth profile, yd4For line gear end face
The corresponding imaginary rack gear contrate tooth profile curve ordinate of tooth form.
S4: basic rack contrate tooth profile curve is solved according to imaginary rack gear contrate tooth profile curve；It is flat according to the double wedge acquired
The corresponding imaginary rack gear contrate tooth profile of row axis gear face tooth form and concave tooth parallel to the axis the corresponding imaginary rack gear end of gear
Face tooth form selects a contrate tooth profile curve of the curve as the gear hob basic rack that parallels to the axis being located between the two.
Since hobboing cutter basic rack normal tooth profile is is convenient for manufacture when circular arc, the present embodiment is using basic rack normal tooth profile as circular arc
Example.Select arc radius for 10；When the normal tooth profile curve for the gear hob basic rack that parallels to the axis is circular arc, parallel to the axis tooth
The contrate tooth profile curve for taking turns hobboing cutter basic rack is an ellipse, be may be expressed as:
yd2=10*sin (t) -5；
In formula, xd2For the contrate tooth profile curvilinear abscissa for the gear hob basic rack that parallels to the axis, yd2For the tooth that parallels to the axis
Take turns the contrate tooth profile curve ordinate of hobboing cutter basic rack.
S5: hobboing cutter is solved according to the obtained gear hob basic rack contrate tooth profile curve that parallels to the axis is solved；To solve
The gear hob basic rack contrate tooth profile that parallels to the axis out projects to obtain the normal tooth for the gear hob basic rack that parallels to the axis
Shape curve.The normal tooth profile curve of basic rack are as follows:
yf2=10*sin (t) -5；
In formula, xf2For the abscissa for the gear hob basic rack normal tooth profile curve that parallels to the axis, yf2For the tooth that parallels to the axis
Take turns the ordinate of hobboing cutter basic rack normal tooth profile curve.
Hobboing cutter contrate tooth profile curve is solved, taking hobboing cutter helical angle is β1, hobboing cutter pitch radius is rjFor 60mm, then hobboing cutter spiral shell
Away from forIts contrate tooth profile curve is expressed as:
In formulaThe respectively contrate tooth profile abscissa of double wedge line gear hobboing cutter corresponding with concave tooth line gear,The respectively contrate tooth profile ordinate of double wedge line gear hobboing cutter corresponding with concave tooth line gear.
Known hobboing cutter contrate tooth profile, then hobboing cutter basic worm tooth surface equation indicates are as follows:
X=xd1*cos(t)-yd1*sin(t)
Y=xd1*sin(t)+yd1*cos(t)
In formula, X, Y, Z are the coordinate value of hobboing cutter basic worm equation, xd1、yd1For concave arc and convex arc hobboing cutter contrate tooth profile
Transverse and longitudinal coordinate, sign is related with the rotation direction of hobboing cutter, takes timing, and hobboing cutter is dextrorotation, and hobboing cutter is left-handed when taking negative
Y=0 is enabled, the axial tooth profile of hobboing cutter is obtained.After acquiring hobboing cutter axial tooth profile, the tooth form in remaining section is according to method of section
It is calculated, completes the design to hobboing cutter, details are not described herein.
The present invention is directed to the design feature of line gear, proposes one kind and parallels to the axis gear hob and the gear that parallels to the axis
Hobboing cutter design method enormously simplifies the gear hob design process that parallels to the axis.The Gear Processing precision that parallels to the axis is improved, is mentioned
The high Gear Processing efficiency that parallels to the axis.Production basis has been established for the gear mass production that parallels to the axis.Be conducive to line gear
Further genralrlization and application.
Claims (7)
- The gear hob 1. one kind parallels to the axis, including double wedge hobboing cutter and concave tooth hobboing cutter two types, barrel shaped tooth hobboing cutter is for recessed Tooth parallels to the axis the gear hobbing process of gear, and concave tooth hobboing cutter parallels to the axis the gear hobbing process of gear for double wedge, which is characterized in that flat Row axis gear hob includes base cylinder and the basic helical surface being spirally distributed on base cylinder；Basic spiral table Hobboing cutter cutter tooth and chip pocket are intervally distributed on face, row's hobboing cutter cutter tooth corresponds to a chip pocket before cutter tooth；Each hobboing cutter Cutter tooth includes a rake face, a top sword flank, a side edge flank, a cutting edge and a top sword；The basic helicoid is rotated by paralleling to the axis gear hob axial tooth profile profile or contrate tooth profile profile along helix It arrives.
- 2. the gear hob according to claim 1 that parallels to the axis, which is characterized in that the contrate tooth profile of the double wedge hobboing cutter is Two sections of symmetrical convex curves, the contrate tooth profile of the concave tooth hobboing cutter are two sections of symmetrical concave curves；Parallel axes Line gear hobboing cutter contrate tooth profile curve unified representation are as follows:(sin(α0)+sin(t))In formula, t is parameter, xd1For the abscissa for the gear hob contrate tooth profile curve that parallels to the axis, yd1For the gear that parallels to the axis The ordinate of hobboing cutter contrate tooth profile curve, r are the arc radius of basic rack tooth profile, and basic rack tooth profile is basic for the gear hob that parallels to the axis The normal tooth profile curve of rack gear, β1For the gear hob helical angle that parallels to the axis, α0For the nominal pressure angle of basic rack tooth profile, rjIt is flat Row axis gear hob pitch radius；Work as α0> 0, t ∈ (0, pi), the gear hob contrate tooth profile curve that parallels to the axis are that concave is bent Line；Work as α0< 0, t ∈ (pi, 2*pi), the gear hob contrate tooth profile curve that parallels to the axis are convex curve.
- 3. the gear hob according to claim 1 that parallels to the axis, it is characterised in that: compare the involute gear of identical modulus Hobboing cutter, the high 1/3-1/4 of a height of involute gear hob tooth of the gear hob tooth that parallels to the axis.
- 4. the gear hob according to claim 1 that parallels to the axis, which is characterized in that identical for modulus, the number of teeth is different The gear that parallels to the axis is able to use the gear hob that parallels to the axis and is processed；The gear hob that parallels to the axis processes Line gear be pure rolling gear；Since line gear is point contact gear, collection of the contact point on the flank of tooth is combined into a spiral Line, the helix are the contact line of line gear；Contact line on line gear indicates are as follows:In formula, x is the abscissa of contact line, and y is the ordinate of contact line, and z is the ordinate of contact line, and m is contact point place Helix radius, n are helix screw pitch parameter, and t is parameter, and ts is contact point start angle, and te is contact line angle at the end.
- 5. the gear hob according to claim 2 that parallels to the axis, which is characterized in that the two sides two for the gear hob that parallels to the axis The normal tooth profile curve of basic rack is symmetrical；When the corresponding basic rack normal tooth profile curve of the gear hob that parallels to the axis When for circular arc, the gear hob basic rack normal tooth profile curve that parallels to the axis is expressed as:xf2=e+r*cos (t)；yf2=r*sin (t)-r*sin (α0)；In formula, xf2For the abscissa for the gear hob basic rack normal tooth profile curve that parallels to the axis, yf2For the gear rolling that parallels to the axis The ordinate of knife basic rack normal tooth profile curve, e is offset distance；R is the arc radius of basic rack tooth profile, α0For basic rack tooth profile Nominal pressure angle.
- 6. the gear hob according to claim 1 that parallels to the axis, it is characterised in that: parallel to the axis gear hob basic rack Contrate tooth profile curve be located at that concave tooth parallels to the axis the corresponding imaginary rack gear contrate tooth profile curve of gear and double wedge parallels to the axis tooth It takes turns between corresponding imaginary rack gear contrate tooth profile curve；The gear that parallels to the axis of the different numbers of teeth can be used same milling cutter Processing；What the gear hob that parallels to the axis was processed parallel to the axis gear can with it is same line gear milling cutter processed it is flat Row axis gear is interchangeable.
- 7. a kind of design method for the gear hob that parallels to the axis described in claim 1 comprising the steps of:S1: solution parallels to the axis gear face tooth form: the gear that parallels to the axis includes that double wedge parallels to the axis gear and concave tooth parallel axes Two kinds of line gear；According to spiral surface properties, its general contrate tooth profile, the general contrate tooth profile equation of the gear that parallels to the axis are solved are as follows:In formula, t2For parameter, xd3For the gear face tooth curve abscissa that parallels to the axis, yd3For the gear face tooth that parallels to the axis Shape curve ordinate, r1For the normal tooth profile curve arc radius of basic rack, t0For the start angle of helix, q is deflection Angle, whenThe contrate tooth profile of this equation expression double wedge line gear；WhenThe end of this equation expression concave tooth line gear Face tooth form；S2: it solves characteristic parameter of the line gear rack gear contrate tooth profile at contact point: solving line gear rack gear contrate tooth profile and connecing Radius of curvature and normal vector at contact；These parameters have determined what the family of curves that can satisfy interchangeability requirement should meet Primary condition；For paralleling to the axis, radius of curvature of the gear face tooth curve in contact point is indicated are as follows:In formula, ρ is radius of curvature of the gear face tooth curve in contact point that parallel to the axis, x 'd3、y′d3、xd3″、yd3" it is respectively xd3And yd3First derivative and second dervative；Radius of curvature and normal vector of the line gear rack gear contrate tooth profile at contact point can be acquired by substituting into following formula:In formula, α is line gear rack gear contrate tooth profile in contact normal direction and x-axis angle, α0For the nominal pressure of basic rack tooth profile Angle,ρ ' is radius of curvature of the line gear rack gear contrate tooth profile at contact point,For line gear rack gear end face Normal vector of the tooth form at contact point, β2For the gear helical angle that parallels to the axis；S3: its corresponding imaginary rack gear contrate tooth profile curve is solved according to line gear contrate tooth profile curve: according to above-mentioned parallel Axis gear face tooth curve substitutes into following formula and solves its corresponding imaginary rack gear contrate tooth profile curve:xd4=x (t2)*cos(s)-y(t2)*sin(s)+m*s；yd4=x (t2)*sin(s)+y(t2)*cos(s)-m；In formula, τ is that the gear face tooth curve that parallels to the axis locates the angle of tangent line and x-axis on one point, and s is to simplify expression to introduce Variable, xd4For the corresponding imaginary rack gear contrate tooth profile curvilinear abscissa of line gear contrate tooth profile, yd4For line gear contrate tooth profile Corresponding imagination rack gear contrate tooth profile curve ordinate；S4: basic rack contrate tooth profile curve is solved according to imaginary rack gear contrate tooth profile curve: according to the double wedge parallel axes acquired The corresponding imaginary rack gear contrate tooth profile of line gear contrate tooth profile and concave tooth parallel to the axis the corresponding imaginary tooth of gear face tooth form Contrate tooth profile selects the curve being located between the two as the contrate tooth profile song for the gear hob basic rack that parallels to the axis Line；When the normal tooth profile curve for the gear hob basic rack that parallels to the axis is circular arc, parallel to the axis gear hob basic rack Contrate tooth profile curve be an ellipse, may be expressed as:yd2=r*sin (t)-r*sin (α0)；In formula, xd2For the contrate tooth profile curvilinear abscissa for the gear hob basic rack that parallels to the axis, yd2For the gear rolling that parallels to the axis The contrate tooth profile curve ordinate of knife basic rack, β2For the gear helical angle that parallels to the axis；It is selected as the curve and double wedge and concave tooth parallel axes of the contrate tooth profile curve for the gear hob basic rack that parallels to the axis Line gear contrate tooth profile curve contact point should normal direction having the same, and its radius of curvature should be greater than double wedge parallel axes Line gear contrate tooth profile contact point radius of curvature, less than concave tooth parallel to the axis gear face tooth form contact point curvature half Diameter；S5: the gear hob that parallels to the axis is solved according to obtained basic rack contrate tooth profile is solved: with the basic rack solved Contrate tooth profile projects to obtain the normal tooth profile curve of basic rack；It is paralleled to the axis according to the solution of the normal tooth profile curve of basic rack Gear hob basic worm tooth surface equation can be solved to gear hob basic worm x-axis is paralleled to the axis or y-axis value is zero Parallel to the axis gear hob axial tooth profile；Universal method can be designed according to hobboing cutter after solution obtains hobboing cutter axial tooth profile to complete Design to hobboing cutter, details are not described herein；As it is above-mentioned it is found that the gear hob basic rack that parallels to the axis normal tooth profile curve Are as follows:xf2=e+r*cos (t)；yf2=r*sin (t)-r*sin (α0)；In formula, xf2For the abscissa for the gear hob basic rack normal tooth profile curve that parallels to the axis, yf2For the gear rolling that parallels to the axis The ordinate of knife basic rack normal tooth profile curve, r are the arc radius of basic rack tooth profile, α0For the nominal pressure of basic rack tooth profile Angle.
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| CN112935415B (en) * | 2021-03-18 | 2022-05-24 | 重庆大学 | Hobbing and hobbing method for variable-tooth-thickness involute helical gear and hobbing cutter design method |
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