CN104196981B - A kind of design method of biradical cone spiral bevel gear form of gear tooth - Google Patents

A kind of design method of biradical cone spiral bevel gear form of gear tooth Download PDF

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CN104196981B
CN104196981B CN201410512635.XA CN201410512635A CN104196981B CN 104196981 B CN104196981 B CN 104196981B CN 201410512635 A CN201410512635 A CN 201410512635A CN 104196981 B CN104196981 B CN 104196981B
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cone
angle
flank
bevel gear
spiral bevel
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CN104196981A (en
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肖望强
潘天龙
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Xiamen Zhenwei Technology Co ltd
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Xiamen University
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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
    • F16H55/17—Toothed wheels
    • 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
    • F16H55/088—Profiling with corrections on tip or foot of the teeth, e.g. addendum relief for better approach contact
    • 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
    • F16H2055/086—Silent gear profiles
    • 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
    • F16H2055/0866—Profiles for improving radial engagement of gears, e.g. chamfers on the tips of the teeth

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  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Gears, Cams (AREA)

Abstract

A kind of design method of biradical cone spiral bevel gear form of gear tooth, is related to gear.Biradical cone spiral bevel gear is provided with 5 conical surfaces, 4 cone angles, 2 base cones；Single gear teeth normal profile is made up of outside circle, root circle, driving side tooth curve, non-drive side tooth curve, teeth directional line；5 conical surfaces are respectively face cone, root cone, pitch cone, back cone and inner cone, and 4 cone angles are respectively face angle, root angle, section angle, dorsal horn.For the gear drive based on single-direction transmission such as vehicle, improve the performance of spiral bevel gear, there is provided and use big profile angle in drive surface, small profile angle is used in non-driving face, both driving direction gear capacity had been increased, topping is turn avoid, spiral bevel gear bearing capacity, fatigue life and output torque can be effectively improved, and reduce the design method of transmission vibration and a kind of biradical cone spiral bevel gear form of gear tooth of noise.

Description

A kind of design method of biradical cone spiral bevel gear form of gear tooth
Technical field
The present invention relates to gear, more particularly to a kind of design method of biradical cone spiral bevel gear form of gear tooth.
Background technology
Spiral bevel gear is compared with straight-tooth and spiral bevel gear, and with registration is big, at contact point, the flank of tooth is relatively bent Rate radius is big, curved face contact region is easily controllable, it is less sensitive to error the advantages of, in intersection axis and the staggeredly transmission of axis In, it is widely used.With the development trend of gear drive middle/high speed heavy-load, conventional helical bevel gear has been difficult to full The requirement of sufficient equipment.Especially in system of vehicle transmission part, the requirement more and more higher to spiral bevel gear output torque.
When profile angle increases, the bending bearing capacity and contact bearing capacity of gear are all significantly increased, but with tooth The increase at shape angle, gear teeth tips gradually come to a point, and when addendum thickness is less than 1.5m (m is module), tooth top is easily in stand under load Shi Fasheng fractures, and causes failure of gear transmission (Li Huamin, the Quality Index Analysis of big tooth form angle involute gear transmission, Ha Er Shore polytechnical university journal, 1987, Z1:86-98).
The content of the invention
The purpose of the present invention is the gear drive based on single-direction transmission for vehicle etc., in order to improve spiral bevel gear The performance of wheel uses small profile angle in non-driving face, had both increased driving direction gear there is provided big profile angle is used in drive surface Bearing capacity, turn avoid topping, can effectively improve spiral bevel gear bearing capacity, fatigue life and output torque, and Reduce the design method of transmission vibration and a kind of biradical cone spiral bevel gear form of gear tooth of noise.
The present invention comprises the following steps：
1) biradical cone spiral bevel gear is provided with 5 conical surfaces, 4 cone angles, 2 base cones；Single gear teeth normal profile is by tooth top Circle, root circle, driving side tooth curve, non-drive side tooth curve, teeth directional line composition；5 conical surfaces are respectively face cone, root Cone, pitch cone, back cone and inner cone, 4 cone angles are respectively face angle, root angle, section angle, dorsal horn；
2) biradical cone spiral bevel gear driving lateral tooth flank Ω1It is δ with basic circle cone anglebdBase cone be tangential on OP1, work as Ω1Along base When cone does pure rolling, the circular arc line such as M in plane using O as the centre of gyration1N1With M2N2Spiral bevel gear wheel drive will be formed in space Side and the non-drive side flank of tooth, because spiral bevel gear both sides profile angle is different, therefore the base cone at two lateral tooth flank beginnings is different；
3) by coordinate transform, the wide spherical involute of the big end tooth of biradical cone spiral bevel gear is transformed into spheric coordinate system, Through deriving, the biradical big end tooth exterior feature equation under spherical coordinate system of cone spiral bevel gear driving lateral tooth flank is under spherical coordinate system
4) driving flank reference circle drift angleWith driving side basic circle cone angle δbdTried to achieve by following formula
δbd=δ '-arctan [(1- αd)tanδ′] (3)
5) the big end tooth exterior feature equation under spherical coordinate system of the biradical cone spiral bevel gear non-drive side flank of tooth is
6) non-driven flank reference circle drift angleWith non-driven flank basic circle cone angle δbcTried to achieve by following formula
δbc=δ '-arctan { [1-arccos (kcos αd)]tanδ′} (6)
The teeth directional line of biradical cone spiral bevel gear is formed by the relative position of wheel blank and cutterhead；
7) selected cutter radius r when according to the helixangleβ of design requirement and processing0, determine facing cutter center With the position relationship in crown axle center, then by coordinate transform, teeth directional line equation is transformed into spheric coordinate system, in spherical coordinate system Under, its teeth directional line equation is
In formula (7),For teeth directional line drift angle, two angles S and j are tried to achieve by following formula
8) when cutterhead goes to small end by big end, j angles one angle Q, Q=j/sin δ ' of correspondence, therefore, outermost point and most Angle corresponding to interior point is respectively Q0=j0/ sin δ ' and Q1=j1/ sin δ ', two jiaos of difference Q1-Q0As from big end to small end The angle that corresponding biradical cone gear form curve is turned in spherical coordinate system, according to Q1-Q0And be changed into the value of rho in formula (1), (4) R-B, you can try to achieve biradical cone spiral bevel gear toe driving side and equation of the non-drive side flank profil under spherical coordinate system；
It is biradical cone spiral bevel gear tip diameter be：
da=mtz+2hadcosδd (10)
Biradical cone spiral bevel gear driving side and non-drive side tip angle are：
δad=δd+θfd (11)
δac=δc+θfc (12)
It is biradical cone spiral bevel gear root diameter be：
df=mtz-hfdcosδd (13)
Biradical cone spiral bevel gear driving side and non-drive side root angle are：
δfd=δd-θfd (14)
δfc=δc-θfc (15)
The flank profil curved surface of biradical cone spiral bevel gear is set up by above-mentioned steps, and sets up spiral bevel gear monodentate entity, is pressed According to subarrays such as number of teeth z progress, then biradical cone spiral bevel gear block mold can be set up, complete biradical cone spiral bevel gear form of gear tooth Design.
Mark in each step for：
Z --- the number of teeth
B --- the facewidth
β --- helical angle
Σ --- crossed axis angle
Rho --- in spherical coordinate system polar diameter, Fig. 2
Theta --- directed line segmentThe positive angle with z-axis
Phi --- go to the angle that OS is turned over counterclockwise from x-axis from the point of view of positive z-axis, S is point P in xOy faces here On projection
mt--- transverse module
D --- reference diameter
R --- outer cone distance
Rm--- mean cone distance
αd--- driving side profile angle
αc--- non-drive side profile angle
K --- tooth form ascent
δ1--- reference cone angle
--- driving flank reference circle drift angle
--- non-driven flank reference circle drift angle
δad--- driving side tip angle
δac--- non-drive side tip angle
δfd--- driving side root angle
δfc--- non-drive side root angle
δbd--- driving side basic circle cone angle
δbc--- non-drive side basic circle cone angle
δ ' --- pitch cone angle
--- teeth directional line drift angle
da--- addendum circle diameter of gear
df--- root diameter of gear
r0--- cutter radius
L1--- distance of the cutter head center to vertex of a cone center
The center of circle drift angle relative to cutter head center of S --- teeth directional line
The center of circle drift angle relative to vertex of a cone center of j --- teeth directional line
βp--- tooth root drift angle
θfd--- driving side dedendum angle
θfc--- non-drive side dedendum angle
had--- driving side height of teeth top
hac--- non-drive side height of teeth top
hfd--- driving side height of teeth root
hfc--- non-drive side height of teeth root
X --- height change coefficient
xt--- coefficient of profile tangential shift dangerous section.
Because the driving side and non-drive side of biradical cone spiral bevel gear have the gears such as different base cones, addendum cone and root vertebra Parameter, the geometrical property and design method with conventional helical bevel gear is entirely different, it is therefore desirable to set up a kind of biradical cone spiral The tooth Shape Design method of bevel gear, to carry out Tool Design, processing and manufacturing, tooth root bending-fatigue strength is calculated and face is tired Labor Strength co-mputation lays the foundation.
Gear drive of the present invention for vehicle etc. based on single-direction transmission, improves the performance of spiral bevel gear, There is provided and use big profile angle in drive surface, use small profile angle in non-driving face, both increased driving direction gear capacity, Topping is turn avoid, spiral bevel gear bearing capacity, fatigue life and output torque can be effectively improved, and reduce transmission and shaken A kind of design method of biradical cone spiral bevel gear form of gear tooth of dynamic and noise.
Brief description of the drawings
Fig. 1 is the biradical cone spiral bevel gear conical surface and cone angle.
Fig. 2 is formed for biradical cone spiral bevel gear driving side, non-drive side spherical involute.
Fig. 3 is biradical cone spiral bevel gear flywheel rotor and wheel blank relative position schematic diagram.
Fig. 4 is the biradical modeling process for boring spiral bevel gear.
Fig. 5 is biradical cone spiral bevel gear pair engagement model.
In figure, each mark for：1 --- biradical cone spiral bevel gear driving side tooth form, 2 --- biradical cone spiral bevel gear Non-drive side tooth form, 3 --- biradical cone spiral bevel gear tooth top, 4 --- biradical cone spiral bevel gear tooth root, 5 --- biradical cone Spiral bevel gear teeth directional line.
Embodiment
Referring to Fig. 1~5, biradical cone spiral bevel gear is provided with 5 conical surfaces, 4 cone angles, 2 base cones；Single gear teeth normal tooth Exterior feature is made up of outside circle, root circle, driving side tooth curve, non-drive side tooth curve, teeth directional line, 5 conical surfaces difference For face cone, root cone, pitch cone, back cone and inner cone, 4 cone angles are respectively face angle, root angle, section angle, dorsal horn；As shown in Figure 1.
Biradical cone spiral bevel gear driving lateral tooth flank Ω1It is δ with basic circle cone anglebdThe 1st base cone (be expressed as base in fig. 2 11) cone is tangential on OP1, work as Ω1When doing pure rolling along base cone 1, the circular arc line such as M in plane using O as the centre of gyration1N1With M2N2Will Spiral bevel gear driving side and the non-drive side flank of tooth are formed in space.Because spiral bevel gear both sides profile angle is different, so two The base cone at lateral tooth flank beginning is different, as shown in Figure 2.The 2nd base cone (being expressed as base cone 21 in fig. 2) is also marked in fig. 2.
By coordinate transform, the wide spherical involute of the big end tooth of biradical cone spiral bevel gear is transformed into spheric coordinate system, passed through Derive, the biradical big end tooth exterior feature equation under spherical coordinate system of cone spiral bevel gear driving lateral tooth flank is under spherical coordinate system
Drive flank reference circle drift angleWith driving side basic circle cone angle δbdIt can be tried to achieve by following formula
δbd=δ '-arctan [(1- αd)tanδ′] (3)
The biradical cone spiral bevel gear non-drive side flank of tooth big end tooth exterior feature equation under spherical coordinate system is
Non-driven flank reference circle drift angleWith non-driven flank basic circle cone angle δbcIt can be tried to achieve by following formula
δbc=δ '-arctan { [1-arccos (kcos αd)]tanδ′} (6)
The teeth directional line of biradical cone spiral bevel gear is formed by the relative position of wheel blank and cutterhead, as shown in Figure 3.
Selected cutter radius r during according to the helixangleβ of design requirement and processing0, determine facing cutter center with The position relationship in crown axle center, then by coordinate transform, spheric coordinate system is transformed into by teeth directional line equation.In spherical coordinate system Under, its teeth directional line equation is：
In formula,For teeth directional line drift angle, two angles S and j can be tried to achieve by following formula
From the cutterhead position shown in Fig. 3, when cutterhead goes to small end by big end, j angles correspondence one angle Q, Q= J/sin δ ', therefore, the angle corresponding to outermost point and innermost point are respectively Q0=j0/ sin δ ' and Q1=j1/sinδ′.Two jiaos it Poor Q1-Q0The angle as turned over from big end to the corresponding biradical cone gear form curve of small end in spherical coordinate system, according to Q1-Q0And The value of rho in formula (1), (4) is changed into R-B, you can try to achieve biradical cone spiral bevel gear toe driving side and non-drive side Equation of the flank profil under spherical coordinate system.
It is biradical cone spiral bevel gear tip diameter be：
da=mtz+2hadcosδd (10)
Biradical cone spiral bevel gear driving side and non-drive side tip angle are：
δad=δd+θfd (11)
δac=δc+θfc (12)
It is biradical cone spiral bevel gear root diameter be：
df=mtz-hfdcosδd (13)
Biradical cone spiral bevel gear driving side and non-drive side root angle are：
δfd=δd-θfd (14)
δfc=δc-θfc (15)
Step can be set up to the flank profil curved surface of biradical cone spiral bevel gear by above-mentioned, and it is real to set up spiral bevel gear monodentate Body, according to subarrays such as number of teeth z progress, then can set up biradical cone spiral bevel gear block mold.
According to the design requirement of biradical cone spiral bevel gear, suitable modulus, normal plane driving side, non-drive side tooth form are selected The basic design parameters such as angle, addendum coefficient, modification coefficient, radial clearance coefficient, the number of teeth, helical angle, rotation direction, then according to changing Calculation relation, calculates each parameter.
A) according to transverse module mt, number of teeth z, facewidth B, helixangleβ, crossed axis angle Σ, driving side profile angle αd, non-drive side Profile angle αc, the parameter such as modification coefficient x can be in the hope of sliding tooth side reference circle drift angleSliding tooth side base coning angle δbd, it is non-drive Dynamic flank reference circle drift angleWith non-driven flank basic circle cone angle δbcEtc. parameter, according to tooth profile equation (1)~(6), it can set up The big end driving side tooth form of biradical cone spiral bevel gear, big end non-drive side tooth form, small end driving side tooth form and small end non-drive side Tooth form.
B) according to above-mentioned parameter, according to equation (10)~(15), the biradical cone big end root circle of spiral bevel gear can be set up Arc, greatly end addendum circle arc, small end tooth root circular arc and small end addendum circle arc.
C) according to above-mentioned parameter, according to equation (7)~(9), biradical cone spiral bevel gear driving side teeth directional line can be set up With non-drive side teeth directional line.
D) entity of first biradical cone spiral bevel gear monodentate is generated.
E) according to subarrays such as number of teeth z progress, then the biradical cone full tooth model of spiral bevel gear can be set up.
The parameter of the biradical cone spiral bevel gear given according to table 1, sets up model process as shown in Figure 4.
The biradical cone spiral bevel gear parameter of table 1
Step can be set up to the flank profil curved surface of biradical cone spiral bevel gear by above-mentioned, and set up biradical cone spiral bevel gear Monodentate entity, according to subarrays such as number of teeth z progress, then can set up biradical cone spiral bevel gear driving wheel, follower engagement model, As shown in Figure 5.

Claims (1)

1. a kind of design method of biradical cone spiral bevel gear form of gear tooth, it is characterised in that comprise the following steps：
1) biradical cone spiral bevel gear is provided with 5 conical surfaces, 4 cone angles, 2 base cones；Single gear teeth normal profile is by outside circle, tooth Root circle, driving flank tooth curve, non-driven flank tooth curve, teeth directional line composition；5 conical surfaces are respectively face cone, root Cone, pitch cone, back cone and inner cone, 4 cone angles are respectively face angle, root angle, section angle, dorsal horn；
2) biradical cone spiral bevel gear sliding tooth lateral tooth flank Ω1It is δ with basic circle cone anglebdBase cone be tangential on OP1, work as Ω1Along base cone When doing pure rolling, the circular arc line M in plane by the centre of gyration of O1N1With M2N2Spiral bevel gear driving flank will be formed in space With the non-driven flank flank of tooth, because spiral bevel gear both sides profile angle is different, therefore the base cone at two lateral tooth flank beginnings is different；
3) by coordinate transform, the wide spherical involute of the big end tooth of biradical cone spiral bevel gear is transformed into spherical coordinate system, through deriving, The wide equation under spherical coordinate system of the big end tooth of biradical cone spiral bevel gear sliding tooth lateral tooth flank is
4) driving flank reference circle drift angleWith sliding tooth side base coning angle δbdTried to achieve by following formula
δbd=δ '-arctan [(1- αd)tanδ′] (3)
5) the big end tooth exterior feature equation under spherical coordinate system of the biradical cone spiral bevel gear non-driven flank flank of tooth is
6) non-driven flank reference circle drift angleWith non-driven flank basic circle cone angle δbcTried to achieve by following formula
δbc=δ '-arctan { [1-arccos (kcos αd)]tanδ′} (6)
The teeth directional line of biradical cone spiral bevel gear is formed by the relative position of wheel blank and cutterhead；
7) selected cutter radius r when according to the helixangleβ of design requirement and processing0, determine facing cutter center and crown The position relationship in axle center, then by coordinate transform, spherical coordinate system is transformed into by teeth directional line equation, under spherical coordinate system, its tooth It is to line equation
In formula (7),For teeth directional line drift angle, two angles S and j are tried to achieve by following formula
<mrow> <mi>S</mi> <mo>=</mo> <mi>&amp;pi;</mi> <mo>-</mo> <mi>arccos</mi> <mfrac> <mrow> <msubsup> <mi>L</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mn>0</mn> <mn>2</mn> </msubsup> <mo>-</mo> <msup> <mi>R</mi> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <msub> <mi>L</mi> <mn>1</mn> </msub> <msub> <mi>r</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>+</mo> <mo>&amp;lsqb;</mo> <mi>arccos</mi> <mfrac> <mrow> <msubsup> <mi>L</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mn>0</mn> <mn>2</mn> </msubsup> <mo>-</mo> <msup> <mi>R</mi> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <msub> <mi>L</mi> <mn>1</mn> </msub> <msub> <mi>r</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>-</mo> <mi>arccos</mi> <mfrac> <mrow> <msubsup> <mi>L</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>r</mi> <mn>0</mn> <mn>2</mn> </msubsup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mi>R</mi> <mo>-</mo> <mi>B</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mrow> <mn>2</mn> <msub> <mi>L</mi> <mn>1</mn> </msub> <msub> <mi>r</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>&amp;rsqb;</mo> <mo>&amp;times;</mo> <mi>t</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <mi>j</mi> <mo>=</mo> <mi>a</mi> <mi>r</mi> <mi>c</mi> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mfrac> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mi>sin</mi> <mi> </mi> <mi>S</mi> </mrow> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>r</mi> <mn>0</mn> </msub> <mi>cos</mi> <mi> </mi> <mi>S</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> 1
8) when cutterhead goes to small end by big end, j angles one angle Q, Q=j/sin δ ' of correspondence, therefore, outermost point and innermost point Corresponding angle is respectively Q0=j0/ sin δ ' and Q1=j1/ sin δ ', two jiaos of difference Q1-Q0As from holding corresponding to small end greatly The angle that is turned in spherical coordinate system of biradical cone gear form curve, according to Q1-Q0And the value of rho in formula (1), (4) is changed into R-B, Try to achieve biradical cone spiral bevel gear toe driving flank and equation of the non-driven flank flank profil under spherical coordinate system；
It is biradical cone spiral bevel gear tip diameter be：
da=mtz+2hadcosδd (10)
Biradical cone spiral bevel gear driving flank and non-driven flank tip angle are：
δad=δd+θfd (11)
δac=δc+θfc (12)
It is biradical cone spiral bevel gear root diameter be：
df=mtz-hfdcosδd (13)
Biradical cone spiral bevel gear driving flank and non-driven flank root angle are：
δfd=δd-θfd (14)
δfc=δc-θfc (15)
The flank profil curved surface of biradical cone spiral bevel gear is set up by above-mentioned steps, and sets up spiral bevel gear monodentate entity, according to tooth The subarrays such as number z progress, then set up biradical cone spiral bevel gear block mold, complete setting for biradical cone spiral bevel gear form of gear tooth Meter；
Mark in each step for：
Z --- the number of teeth
B --- the facewidth
β --- helical angle
Σ --- crossed axis angle
Rho --- spherical coordinate system polar diameter
Theta --- the spherical coordinate system polar diameter angle positive with z-axis
Phi --- go to the angle that OS is turned over counterclockwise from x-axis from the point of view of positive z-axis, S is point P on xOy faces here Projection
mt--- transverse module
D --- reference diameter
R --- outer cone distance
Rm--- mean cone distance
αd--- driving flank profile angle
αc--- non-driven flank profile angle
K --- tooth form ascent
δ1--- reference cone angle
--- driving flank reference circle drift angle
--- non-driven flank reference circle drift angle
δad--- driving flank tip angle
δac--- non-driven flank tip angle
δfd--- sliding tooth lateral root cone angle
δfc--- non-driven flank root angle
δbd--- sliding tooth side base coning angle
δbc--- non-driven flank basic circle cone angle
δ ' --- pitch cone angle
--- teeth directional line drift angle
da--- addendum circle diameter of gear
df--- root diameter of gear
r0--- cutter radius
L1--- distance of the cutter head center to vertex of a cone center
The center of circle drift angle relative to cutter head center of S --- teeth directional line
The center of circle drift angle relative to vertex of a cone center of j --- teeth directional line
βp--- tooth root drift angle
θfd--- driving flank dedendum angle
θfc--- non-driven flank dedendum angle
had--- driving flank height of teeth top
hac--- non-driven flank height of teeth top
hfd--- driving flank height of teeth root
hfc--- non-driven flank height of teeth root
X --- height change coefficient
xt--- coefficient of profile tangential shift dangerous section
δf--- the coning angle of tooth root
δa--- the coning angle of tooth top
δd--- driving flank reference cone angle
δc--- non-driven flank reference cone angle
T --- variable.
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