CN105114542A - Planetary gear transmission device based on conjugate curve herringbone gear - Google Patents

Planetary gear transmission device based on conjugate curve herringbone gear Download PDF

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CN105114542A
CN105114542A CN201510550894.6A CN201510550894A CN105114542A CN 105114542 A CN105114542 A CN 105114542A CN 201510550894 A CN201510550894 A CN 201510550894A CN 105114542 A CN105114542 A CN 105114542A
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theta
rho
curve
gear
sin
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CN105114542B (en
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陈兵奎
梁栋
张录合
彭帅
覃思玲
安来强
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Chongqing University
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Chongqing University
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16HGEARING
    • F16H1/00Toothed gearings for conveying rotary motion
    • F16H1/28Toothed gearings for conveying rotary motion with gears having orbital motion
    • F16H1/32Toothed gearings for conveying rotary motion with gears having orbital motion in which the central axis of the gearing lies inside the periphery of an orbital gear
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16HGEARING
    • F16H55/00Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02Toothed members; Worms
    • F16H55/08Profiling
    • F16H55/0826Novikov-Wildhaber profile
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16HGEARING
    • F16H1/00Toothed gearings for conveying rotary motion
    • F16H1/28Toothed gearings for conveying rotary motion with gears having orbital motion
    • F16H1/32Toothed gearings for conveying rotary motion with gears having orbital motion in which the central axis of the gearing lies inside the periphery of an orbital gear
    • F16H2001/327Toothed gearings for conveying rotary motion with gears having orbital motion in which the central axis of the gearing lies inside the periphery of an orbital gear with orbital gear sets comprising an internally toothed ring gear

Abstract

The invention relates to a planetary gear transmission device based on a conjugate curve herringbone gear, and belongs to the technical field of gear transmission. The planetary gear transmission device comprises a sun gear, a planet gear, a planet carrier and an inner gear ring. The sun gear and the planet gear are driven by the conjugate curve herringbone gear to form a sun gear and planet gear engagement pair, and contact curves formed by tooth surface engagement points are conjugate curves. The planet gear and the inner gear ring are driven by the conjugate curve herringbone gear to form a planet gear and inner gear ring engagement pair, and contact curves formed by tooth surface engagement points are conjugate curves. According to the planetary gear transmission device based on the conjugate curve herringbone gear, few-tooth large-modulus optimization design can be carried out, the whole machine weight is effectively reduced, and the requirement for low weight is met; the bearing capacity is high, no axial force influence exists in the gear surface engagement process, relative gear surface sliding is reduced through point contact engagement, the transmission efficiency is effectively improved, and the whole machine service life is effectively prolonged.

Description

A kind of planetary type gear transmission unit based on conjugate curve herringbone gear
Technical field
The invention belongs to gear transmission technology field, relate to a kind of planetary type gear transmission unit based on conjugate curve herringbone gear.
Background technique
Involute planet gear transmission is a kind of gear-driven form having at least a gear to circle around the geometrical axis that position is fixed, and this transmission uses internal messing and the several planet wheel of many employings transmitted load simultaneously usually, to make power dividing.Involute planet gear transmission has the following advantages: gear range is large, compact structure, volume and quality are little, efficiency is higher, noise is low and smooth running etc., be therefore widely used in lifting, metallurgy, engineering machinery, transport, aviation, lathe, technical machinery and national defense industry etc. as slowing down, speed change or increasing speed gearing transmission mechanism.
At present, double helical tooth planetary transmission system is as a kind of transmission part be mainly used in high speed, heavy loading mechanism, and have the advantage of reliable transmission, smooth running, the quality of its structure directly has influence on the performance of equipment.Usually, the main flank profil form of herringbone gear is involute profile, although be widely used, but still there is following problem: involute profile is all having slip except node, also there is larger slip, affect transmission efficiency and working life during few number of teeth at tooth top and tooth root; The flexural strength of involute gear tooth allows overload 1.5 ~ 2 times usually, can not meet the overload requirement of 5 times even higher; Profile contact form is convex-convex contact, and contact strength is limited.
Summary of the invention
In view of this, the object of the present invention is to provide a kind of planetary type gear transmission unit based on conjugate curve herringbone gear, this device effectively reduces complete machine weight, realizes lightweight requirements, and improves transmission efficiency and machine life.
For achieving the above object, the invention provides following technological scheme:
Based on a planetary type gear transmission unit for conjugate curve herringbone gear, comprise sun gear, planet wheel, planet carrier and ring gear; Described sun gear and planet wheel adopt the transmission of conjugate curve herringbone gear, composition sun gear and planet wheel engagement pair, the inter_curve conjugate curve each other that tooth face meshing point is formed; Described planet wheel and ring gear adopt the transmission of conjugate curve herringbone gear, the planet wheel of composition and ring gear engagement pair, the inter_curve conjugate curve each other that tooth face meshing point is formed.
Further, described planet wheel has three.
Further, described conjugate curve herringbone gear comprises left-handed conjugate curve helical gear and dextrorotation conjugate curve helical gear.
Further, the left-hand teeth of described sun gear, planet wheel and ring gear and the right-hand teeth flank of tooth can be selected space arbitrary curve to build and form, and flank profil curved surface is single-contact or two point contact.
Further, left-hand helical gear and the dextrorotation helical gear of described sun gear, planet wheel and ring gear are centrosymmetric, seamless connection or there is tool withdrawal groove.
Further, described sun gear adopts convex side circular arc profile form, and face curve is circular helix;
Sun gear left-hand teeth face curvilinear equation is:
x 1 l = ρ c o s θ 1 y 1 l = ρsinθ 1 z 1 l = pθ 1
Wherein, ρ is that cylindrical screw Curves is at cylndrical surface radius; θ 1for cylindrical screw parameter of curve, p is helix parameter;
The sun gear left-hand teeth flank of tooth is tried to achieve based on equidistant envelope method, and its Equidistant curve equation is:
x 1 l h = ρ c o s θ 1 + ρ 1 · n x 1 l y 1 l h = ρsinθ 1 + ρ 1 · n y 1 l z 1 l h = pθ 1 + ρ 1 · n z 1 l
Wherein, ρ 1it is the equidistant distance along the Normal direction of specifying; n x1l, n y1land n z1lrepresent the component of the equidistance motion normal of specifying at each change in coordinate axis direction respectively;
Curve centered by equidistant curve, the sphere centre of sphere moves continuously along this curve, forms a tubulose envelope surface, and sun gear left-hand teeth convex side equation is:
In formula
r θ 1 = { - ρsinθ 1 + ρ 1 n x 1 l ( θ 1 ) , ρcosθ 1 + ρ 1 n y 1 l ( θ 1 ) , p + ρ 1 n z 1 l ( θ 1 ) }
Wherein and α 1represent sphere parameters respectively, and meet
Sun gear right-hand teeth face curvilinear equation is:
x 1 r = ρ c o s θ 1 y 1 r = ρsinθ 1 z 1 r = - pθ 1
Wherein, ρ is that cylindrical screw Curves is at cylndrical surface radius; θ 1for cylindrical screw parameter of curve, p is helix parameter;
The sun gear right-hand teeth flank of tooth is tried to achieve based on equidistant envelope method, and its Equidistant curve equation is:
x 1 r h = ρ c o s θ 1 + ρ 1 · n x 1 r y 1 r h = ρsinθ 1 + ρ 1 · n y 1 r z 1 r h = - pθ 1 + ρ 1 · n z 1 r
Wherein, ρ 1it is the equidistant distance along the Normal direction of specifying; n x1l, n y1land n z1lrepresent the component of the equidistance motion normal of specifying at each change in coordinate axis direction respectively;
Curve centered by equidistant curve, the sphere centre of sphere moves continuously along this curve, and form a tubulose envelope surface, right-hand teeth convex side equation is:
r θ 1 = { - ρsinθ 1 + ρ 1 n x 1 l ( θ 1 ) , ρcosθ 1 + ρ 1 n y 1 l ( θ 1 ) , p + ρ 1 n z 1 l ( θ 1 ) }
Wherein and α 1represent sphere parameters respectively, and meet
Further, described planet wheel adopts recessed flank of tooth parabolic tooth-shape form, and face curve is circular helix,
Planet wheel left-hand teeth normal direction parabolic tooth-shape curvilinear equation is
x 2 l = θ 2 y 2 l = θ 2 2 2 q z 2 l = 0
Wherein, θ 2represent independent variable parameter; Q is parabola parameter;
The left-handed mark of mouth tooth surface equation of planet wheel is:
x Σ 2 l = ( θ 2 cos α - θ 2 2 2 q sin α + L sin α ) cosφ 1 - ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) cosβsinφ 1 + r 1 cosφ 1 y Σ 2 l = ( θ 2 cos α - θ 2 2 2 q sin α + L sin α ) sinφ 1 + ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) cosβcosφ 1 + r 1 sinφ 1 z Σ 2 l = r 1 φ 1 cot β - ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) sin β
Wherein α is the angle of parabola summit and substantially horizontal coordinate axes; β is the helix angle of gear; r is tooth curve radius, and δ is the angle on parabolic tooth-shape between contact points and summit;
Planet wheel right-hand teeth normal direction parabolic tooth-shape curvilinear equation is:
x 2 l r = θ 2 y 2 l r = θ 2 2 2 q z 2 l r = 0
Wherein θ 2represent independent variable parameter; Q is parabola parameter;
Planet wheel dextrorotation mark of mouth tooth surface equation is:
x Σ 2 r = ( θ 2 cos α - θ 2 2 2 q sin α + L sin α ) cosφ 1 - ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) cosβsinφ 1 + r 1 cosφ 1 y Σ 2 r = ( θ 2 cos α - θ 2 2 2 q sin α + L sin α ) sinφ 1 + ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) cosβcosφ 1 + r 1 sinφ 1 z Σ 2 r = - r 1 φ 1 cot β + ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) sin β
Wherein α is the angle of parabola summit and substantially horizontal coordinate axes; β is the helix angle of gear; r is tooth curve radius, and δ is the angle on parabolic tooth-shape between contact points and summit.
Further, described ring gear adopts convex side circular arc profile form, and form engagement pair with the recessed flank of tooth of planet wheel, face curve is circular helix;
Ring gear left-hand teeth face curvilinear equation is:
x 3 l = ρ c o s θ 3 y 3 l = ρsinθ 3 z 3 l = pθ 3
Wherein, ρ is that cylindrical screw Curves is at cylndrical surface radius; θ 3be cylindrical screw parameter of curve, p is helix parameter;
The ring gear left-hand teeth flank of tooth is tried to achieve based on equidistant envelope method, and its Equidistant curve equation is:
x 3 l h = ρ c o s θ 3 + ρ 1 · n x 3 l y 3 l h = ρsinθ 3 + ρ 1 · n y 3 l z 3 l h = pθ 3 + ρ 1 · n z 3 l
Wherein, ρ 1for the equidistant distance along the Normal direction of specifying; n x3l, n y3land n z3lrepresent the component of the equidistance motion normal of specifying at each change in coordinate axis direction respectively;
Curve centered by equidistant curve, the sphere centre of sphere moves continuously along this curve, forms a tubulose envelope surface, and ring gear left-hand teeth convex side equation is:
In formula
r θ 3 = { - ρsinθ 3 + ρ 1 n x 3 l ( θ 3 ) , ρcosθ 3 + ρ 1 n y 3 l ( θ 3 ) , p + ρ 1 n z 3 l ( θ 3 ) }
Wherein and α 3represent sphere parameters respectively, and meet
Ring gear right-hand teeth face curvilinear equation is
x 3 r = ρ c o s θ 3 y 3 r = ρsinθ 3 z 3 r = - pθ 3
Wherein, ρ is that cylindrical screw Curves is at cylndrical surface radius; θ 3for cylindrical screw parameter of curve, p is helix parameter;
The right-hand teeth flank of tooth is tried to achieve based on equidistant envelope method, and its Equidistant curve equation is:
x 3 r h = ρ c o s θ 3 + ρ 1 · n x 3 r y 3 r h = ρsinθ 3 + ρ 1 · n y 3 r z 3 r h = - pθ 3 + ρ 1 · n z 3 r
In formula, ρ 1for the equidistant distance along the Normal direction of specifying; n x3r, n y3rand n z3rrepresent the component of the equidistance motion normal of specifying at each change in coordinate axis direction respectively;
Curve centered by equidistant curve, the sphere centre of sphere moves continuously along this curve, form a tubulose envelope surface, thus right-hand teeth convex side equation is:
In formula
r θ 3 = { - ρsinθ 3 + ρ 1 n x 3 r ( θ 3 ) , ρcosθ 3 + ρ 1 n y 3 r ( θ 3 ) , p + ρ 1 n z 3 r ( θ 3 ) }
Wherein and α 3represent sphere parameters respectively, and meet
Beneficial effect of the present invention is: a kind of planetary type gear transmission unit based on conjugate curve herringbone gear provided by the invention, compared with existing involute planet gear transmission, Planetary Gear Transmission can carry out few number of teeth, large modulus optimal design, effective reduction complete machine weight, realizes lightweight requirements; There is higher bearing capacity; Flank engagement process affects without axial force, and point cantact engagement reduces flank of tooth relative sliding, effectively improves transmission efficiency and machine life.
Accompanying drawing explanation
In order to make the object, technical solutions and advantages of the present invention clearly, below in conjunction with accompanying drawing, the present invention is described in further detail, wherein:
Fig. 1 is the structural representation of planetary type gear transmission unit of the present invention;
Fig. 2 is sun gear conjugate curve herringbone gear entity structure schematic diagram in the present embodiment;
Fig. 3 is sun gear conjugate curve herringbone gear normal tooth profile schematic diagram in the present embodiment;
Fig. 4 is planet wheel conjugate curve herringbone gear entity structure schematic diagram in the present embodiment;
Fig. 5 is planet wheel conjugate curve herringbone gear normal tooth profile schematic diagram in the present embodiment;
Fig. 6 is planet wheel conjugate curve herringbone gear flank of tooth formingspace system of coordinates schematic diagram in the present embodiment;
Fig. 7 is ring gear conjugate curve herringbone gear entity structure schematic diagram in the present embodiment;
Wherein, 1 is sun gear, and 2 is planet wheel, and 3 is planet carrier, and 4 is ring gear.
Embodiment
Below in conjunction with accompanying drawing, the preferred embodiments of the present invention are described in detail.
A kind of planetary type gear transmission unit based on conjugate curve herringbone gear provided by the invention comprises sun gear 1, planet wheel 2, planet carrier 3 and ring gear 4, and sun gear, planet wheel and ring gear adopt the transmission of conjugate curve herringbone gear; Left-hand teeth and the right-hand teeth flank of tooth can be selected space arbitrary curve to build and form, and flank profil curved surface can realize single-contact or two point contact based on design requirement; Left-hand helical gear and dextrorotation helical gear are centrosymmetric, and both can seamlessly connect, and also can there is tool withdrawal groove.The sun gear be made up of conjugate curve herringbone gear and planet wheel engagement pair, meet the inter_curve conjugate curve each other that tooth face meshing point is formed; The planet wheel be made up of conjugate curve herringbone gear and ring gear engagement pair, meet the inter_curve conjugate curve each other that tooth face meshing point is formed.As shown in Figure 1, its transmission principle is that motor driven belts moves conjugate curve herringbone gear--sun gear 1 turns round, along with Movement transmit makes conjugate curve herringbone gear--planet wheel 2 rotates, due to conjugate curve herringbone gear--ring gear 4 maintains static, just planet carrier 3 is driven to make output movement, planet wheel not only does rotation but also revolve round the sun on planet carrier, with this same structure composition secondary, three grades or Multi-stage transmission.
Come that the present invention is further described in conjunction with specific embodiments, the present embodiment adopt double wedge flank profil to cut shape is circular arc, to cut shape be parabolical two point contact form to recessed tooth flank profil.Fig. 2 is the sun gear conjugate curve herringbone gear entity structure schematic diagram of the present embodiment, and Fig. 3 is the sun gear conjugate curve herringbone gear normal tooth profile schematic diagram of the present embodiment.Assuming that sun gear adopts convex side circular arc profile form, face curve is circular helix.
(1) left-hand teeth face curvilinear equation is
x 1 l = ρ c o s θ 1 y 1 l = ρsinθ 1 z 1 l = pθ 1
In formula, ρ is that cylindrical screw Curves is at cylndrical surface radius; θ 1be cylindrical screw parameter of curve, p is helix parameter.
The left-hand teeth flank of tooth is tried to achieve based on equidistant envelope method, and by above-mentioned inter_curve along the Normal direction equidistance motion of specifying, obtaining its Equidistant curve equation is
x 1 l h = ρ c o s θ 1 + ρ 1 · n x 1 l y 1 l h = ρsinθ 1 + ρ 1 · n y 1 l z 1 l h = pθ 1 + ρ 1 · n z 1 l
In formula, ρ 1it is the equidistant distance along the Normal direction of specifying; n x1l, n y1land n z1lrepresent the component of the equidistance motion normal of specifying at each change in coordinate axis direction respectively.
Curve centered by obtained equidistant curve, the sphere centre of sphere moves continuously along this curve, form a tubulose envelope surface, thus left-hand teeth convex side equation is
In formula
r θ 1 = { - ρsinθ 1 + ρ 1 n x 1 l ( θ 1 ) , ρcosθ 1 + ρ 1 n y 1 l ( θ 1 ) , p + ρ 1 n z 1 l ( θ 1 ) }
Wherein and α 1represent sphere parameters respectively, and meet
(2) right-hand teeth face curvilinear equation is
x 1 r = ρ c o s θ 1 y 1 r = ρsinθ 1 z 1 r = - pθ 1
In formula, ρ is that cylindrical screw Curves is at cylndrical surface radius; θ 1be cylindrical screw parameter of curve, p is helix parameter.
The right-hand teeth flank of tooth also can be tried to achieve based on equidistant envelope method, and by above-mentioned inter_curve along the Normal direction equidistance motion of specifying, obtaining its Equidistant curve equation is
x 1 r h = ρ c o s θ 1 + ρ 1 · n x 1 r y 1 r h = ρsinθ 1 + ρ 1 · n y 1 r z 1 r h = - pθ 1 + ρ 1 · n z 1 r
In formula, ρ 1it is the equidistant distance along the Normal direction of specifying; n x1r, n y1rand n z1rrepresent the component of the equidistance motion normal of specifying at each change in coordinate axis direction respectively.
Curve centered by obtained equidistant curve, the sphere centre of sphere moves continuously along this curve, form a tubulose envelope surface, thus right-hand teeth convex side equation is
In formula
r θ 1 = { - ρsinθ 1 + ρ 1 n x 1 r ( θ 1 ) , ρcosθ 1 + ρ 1 n y 1 r ( θ 1 ) , - p + ρ 1 n z 1 r ( θ 1 ) }
Wherein and α 1represent sphere parameters respectively, and meet
When mesh tooth face has two pairs of conjugate curve to participate in engagement simultaneously, namely mesh tooth face has two point of contact, assuming that planet wheel adopts recessed flank of tooth parabolic tooth-shape form, face curve is still circular helix.Fig. 4 is the planet wheel conjugate curve herringbone gear entity structure schematic diagram of the present embodiment; Fig. 5 is the planet wheel conjugate curve herringbone gear normal tooth profile schematic diagram of the present embodiment.
(1) left-hand teeth normal direction parabolic tooth-shape curvilinear equation is
x 2 l = θ 2 y 2 l = θ 2 2 2 q z 2 l = 0
θ in formula 2represent independent variable parameter; Q is parabola parameter.
Fig. 6 is the planet wheel conjugate curve herringbone gear flank of tooth formingspace system of coordinates schematic diagram of the present embodiment.System of coordinates S is had in figure n(O n-x ny nz n), S s(O s-x sy sz s) and S 1(O 1-x 1y 1z 1).Coordinate axes z ndirection be the tangent direction of helix on pitch cylinder, x no ny nplane is the normal plane of gear, x so sy splane is the end face of gear, y saxle by Gear axis and in the height direction with y naxle difference pitch circle radius r 1, x no ny nwith x so sy sthe angle of two planes is the helixangleβ of gear, system of coordinates S sat system of coordinates S 1in spin motion rotate φ 1angle, moves forward r simultaneously 1φ 1cot β.
Adopt kinematic method, by this normal tooth profile along the curvilinear motion of face cylindrical screw, thus form the gear teeth flank of tooth, left-handed mark of mouth tooth surface equation can be expressed as
x Σ 2 l = ( θ 2 cos α - θ 2 2 2 q sin α + L sin α ) cosφ 1 - ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) cosβsinφ 1 + r 1 cosφ 1 y Σ 2 l = ( θ 2 cos α - θ 2 2 2 q sin α + L sin α ) sinφ 1 + ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) cosβcosφ 1 + r 1 sinφ 1 z Σ 2 l = r 1 φ 1 cot β - ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) sin β
In formula, α is the angle of parabola summit and substantially horizontal coordinate axes; wherein r is tooth curve radius, and δ is the angle on parabolic tooth-shape between contact points and summit.
(2) right-hand teeth normal direction parabolic tooth-shape curvilinear equation is
x 2 l r = θ 2 y 2 l r = θ 2 2 2 q z 2 l r = 0
θ in formula 2represent independent variable parameter; Q is parabola parameter.
With reference to left-hand teeth flank of tooth mould-forming method, by this normal tooth profile along the curvilinear motion of face cylindrical screw, thus form the gear teeth flank of tooth.That this face cylindrical screw curve and left-hand teeth flank of tooth cylindrical screw curve symmetrically curve, so dextrorotation mark of mouth tooth surface equation can be expressed as with should be noted that
x Σ 2 r = ( θ 2 cos α - θ 2 2 2 q sin α + L sin α ) cosφ 1 - ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) cosβsinφ 1 + r 1 cosφ 1 y Σ 2 r = ( θ 2 cos α - θ 2 2 2 q sin α + L sin α ) sinφ 1 + ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) cosβcosφ 1 + r 1 sinφ 1 z Σ 2 r = - r 1 φ 1 cot β + ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) sin β
In formula each parameter item represent implication with describe in left-hand teeth identical.
Fig. 7 is the ring gear conjugate curve herringbone gear entity structure schematic diagram of the present embodiment.Ring gear adopts convex side circular arc profile form, and form engagement pair with the recessed flank of tooth of planet wheel, face curve is still circular helix.Tooth surface equation method for solving is identical with sun gear.
(1) left-hand teeth face curvilinear equation is
x 3 l = ρ c o s θ 3 y 3 l = ρsinθ 3 z 3 l = pθ 3
In formula, ρ is that cylindrical screw Curves is at cylndrical surface radius; θ 3be cylindrical screw parameter of curve, p is helix parameter.
The left-hand teeth flank of tooth is tried to achieve based on equidistant envelope method, and by above-mentioned inter_curve along the Normal direction equidistance motion of specifying, obtaining its Equidistant curve equation is
x 3 l h = ρ c o s θ 3 + ρ 1 · n x 3 l y 3 l h = ρsinθ 3 + ρ 1 · n y 3 l z 3 l h = pθ 3 + ρ 1 · n z 3 l
In formula, ρ 1it is the equidistant distance along the Normal direction of specifying; n x3l, n y3land n z3lrepresent the component of the equidistance motion normal of specifying at each change in coordinate axis direction respectively.
Curve centered by obtained equidistant curve, the sphere centre of sphere moves continuously along this curve, form a tubulose envelope surface, thus left-hand teeth convex side equation is
In formula
r θ 3 = { - ρsinθ 3 + ρ 1 n x 3 l ( θ 3 ) , ρcosθ 3 + ρ 1 n y 3 l ( θ 3 ) , p + ρ 1 n z 3 l ( θ 3 ) }
Wherein and α 3represent sphere parameters respectively, and meet
(2) right-hand teeth face curvilinear equation is
x 3 r = ρ c o s θ 3 y 3 r = ρsinθ 3 z 3 r = - pθ 3
In formula, ρ is that cylindrical screw Curves is at cylndrical surface radius; θ 3be cylindrical screw parameter of curve, p is helix parameter.
The right-hand teeth flank of tooth is tried to achieve based on equidistant envelope method, and by above-mentioned inter_curve along the Normal direction equidistance motion of specifying, obtaining its Equidistant curve equation is
x 3 r h = ρ c o s θ 3 + ρ 1 · n x 3 r y 3 r h = ρsinθ 3 + ρ 1 · n y 3 r z 3 r h = - pθ 3 + ρ 1 · n z 3 r
In formula, ρ 1it is the equidistant distance along the Normal direction of specifying; n x3r, n y3rand n z3rrepresent the component of the equidistance motion normal of specifying at each change in coordinate axis direction respectively.
Curve centered by obtained equidistant curve, the sphere centre of sphere moves continuously along this curve, form a tubulose envelope surface, thus right-hand teeth convex side equation is
In formula
r θ 3 = { - ρsinθ 3 + ρ 1 n x 3 r ( θ 3 ) , ρcosθ 3 + ρ 1 n y 3 r ( θ 3 ) , p + ρ 1 n z 3 r ( θ 3 ) }
Wherein and α 3represent sphere parameters respectively, and meet
What finally illustrate is, above preferred embodiment is only in order to illustrate technological scheme of the present invention and unrestricted, although by above preferred embodiment to invention has been detailed description, but those skilled in the art are to be understood that, various change can be made to it in the form and details, and not depart from claims of the present invention limited range.

Claims (8)

1. based on a planetary type gear transmission unit for conjugate curve herringbone gear, it is characterized in that: comprise sun gear, planet wheel, planet carrier and ring gear; Described sun gear and planet wheel adopt the transmission of conjugate curve herringbone gear, composition sun gear and planet wheel engagement pair, the inter_curve conjugate curve each other that tooth face meshing point is formed; Described planet wheel and ring gear adopt the transmission of conjugate curve herringbone gear, the planet wheel of composition and ring gear engagement pair, the inter_curve conjugate curve each other that tooth face meshing point is formed.
2. a kind of planetary type gear transmission unit based on conjugate curve herringbone gear according to claim 1, is characterized in that: described planet wheel has three.
3. a kind of planetary type gear transmission unit based on conjugate curve herringbone gear according to claim 1, is characterized in that: described conjugate curve herringbone gear comprises left-handed conjugate curve helical gear and dextrorotation conjugate curve helical gear.
4. a kind of planetary type gear transmission unit based on conjugate curve herringbone gear according to claim 1, it is characterized in that: the left-hand teeth of described sun gear, planet wheel and ring gear and the right-hand teeth flank of tooth can be selected space arbitrary curve to build and form, and flank profil curved surface is single-contact or two point contact.
5. a kind of planetary type gear transmission unit based on conjugate curve herringbone gear according to claim 1, it is characterized in that: left-hand helical gear and the dextrorotation helical gear of described sun gear, planet wheel and ring gear are centrosymmetric, seamless connection or there is tool withdrawal groove.
6. a kind of planetary type gear transmission unit based on conjugate curve herringbone gear according to claim 1, is characterized in that: described sun gear adopts convex side circular arc profile form, and face curve is circular helix; Sun gear left-hand teeth face curvilinear equation is:
x 1 l = ρ c o s θ 1 y 1 l = ρsinθ 1 z 1 l = pθ 1
Wherein, ρ is that cylindrical screw Curves is at cylndrical surface radius; θ 1for cylindrical screw parameter of curve, p is helix parameter;
The sun gear left-hand teeth flank of tooth is tried to achieve based on equidistant envelope method, and its Equidistant curve equation is:
x 1 l h = ρ c o s θ 1 + ρ 1 · n x 1 l y 1 l h = ρsinθ 1 + ρ 1 · n y 1 l z 1 l h = pθ 1 + ρ 1 · n z 1 l
Wherein, ρ 1it is the equidistant distance along the Normal direction of specifying; n x1l, n y1land n z1lrepresent the component of the equidistance motion normal of specifying at each change in coordinate axis direction respectively;
Curve centered by equidistant curve, the sphere centre of sphere moves continuously along this curve, forms a tubulose envelope surface, and sun gear left-hand teeth convex side equation is:
In formula
r θ 1 = { - ρsinθ 1 + ρ 1 n x 1 l ( θ 1 ) , ρcosθ 1 + ρ 1 n y 1 l ( θ 1 ) , p + ρ 1 n z 1 l ( θ 1 ) }
Wherein and α 1represent sphere parameters respectively, and meet
Sun gear right-hand teeth face curvilinear equation is:
x 1 r = ρ c o s θ 1 y 1 r = ρsinθ 1 z 1 r = - pθ 1
Wherein, ρ is that cylindrical screw Curves is at cylndrical surface radius; θ 1for cylindrical screw parameter of curve, p is helix parameter;
The sun gear right-hand teeth flank of tooth is tried to achieve based on equidistant envelope method, and its Equidistant curve equation is:
x 1 r h = ρ c o s θ 1 + ρ 1 · n x 1 r y 1 r h = ρsinθ 1 + ρ 1 · n y 1 r z 1 r h = - pθ 1 + ρ 1 · n z 1 r
Wherein, ρ 1it is the equidistant distance along the Normal direction of specifying; n x1l, n y1land n z1lrepresent the component of the equidistance motion normal of specifying at each change in coordinate axis direction respectively;
Curve centered by equidistant curve, the sphere centre of sphere moves continuously along this curve, and form a tubulose envelope surface, right-hand teeth convex side equation is:
r θ 1 = { - ρsinθ 1 + ρ 1 n x 1 l ( θ 1 ) , ρcosθ 1 + ρ 1 n y 1 l ( θ 1 ) , p + ρ 1 n z 1 l ( θ 1 ) }
Wherein and α 1represent sphere parameters respectively, and meet
7. a kind of planetary type gear transmission unit based on conjugate curve herringbone gear according to claim 1, is characterized in that:
Described planet wheel adopts recessed flank of tooth parabolic tooth-shape form, and face curve is circular helix,
Planet wheel left-hand teeth normal direction parabolic tooth-shape curvilinear equation is
x 2 l = θ 2 y 2 l = θ 2 2 2 q z 2 l = 0
Wherein, θ 2represent independent variable parameter; Q is parabola parameter;
The left-handed mark of mouth tooth surface equation of planet wheel is:
x Σ 2 l = ( θ 2 cos α - θ 2 2 2 q sin α + L sin α ) cosφ 1 - ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) cosβsinφ 1 + r 1 cosφ 1 y Σ 2 l = ( θ 2 cos α - θ 2 2 2 q sin α + L sin α ) cosφ 1 + ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) cosβcosφ 1 + r 1 sinφ 1 z Σ 2 l = r 1 φ 1 cot β - ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) sin β
Wherein α is the angle of parabola summit and substantially horizontal coordinate axes; β is the helix angle of gear; r is tooth curve radius, and δ is the angle on parabolic tooth-shape between contact points and summit;
Planet wheel right-hand teeth normal direction parabolic tooth-shape curvilinear equation is:
x 2 l r = θ 2 y 2 l r = θ 2 2 2 q z 2 l r = 0
Wherein θ 2represent independent variable parameter; Q is parabola parameter;
Planet wheel dextrorotation mark of mouth tooth surface equation is:
x Σ 2 r = ( θ 2 cos α - θ 2 2 2 q sin α + L sin α ) cosφ 1 - ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) cosβsinφ 1 + r 1 cosφ 1 y Σ 2 r = ( θ 2 cos α - θ 2 2 2 q sin α + L sin α ) sinφ 1 + ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) cosβcosφ 1 + r 1 sinφ 1 z Σ 2 r = - r 1 φ 1 cot β + ( θ 2 sin α + θ 2 2 2 q cos α - L cos α ) sin β
Wherein α is the angle of parabola summit and substantially horizontal coordinate axes; β is the helix angle of gear; r is tooth curve radius, and δ is the angle on parabolic tooth-shape between contact points and summit.
8. a kind of planetary type gear transmission unit based on conjugate curve herringbone gear according to claim 1, is characterized in that:
Described ring gear adopts convex side circular arc profile form, and form engagement pair with the recessed flank of tooth of planet wheel, face curve is circular helix;
Ring gear left-hand teeth face curvilinear equation is:
x 3 l = ρ c o s θ 3 y 3 l = ρsinθ 3 z 3 l = pθ 3
Wherein, ρ is that cylindrical screw Curves is at cylndrical surface radius; θ 3be cylindrical screw parameter of curve, p is helix parameter;
The ring gear left-hand teeth flank of tooth is tried to achieve based on equidistant envelope method, and its Equidistant curve equation is:
x 3 l h = ρ c o s θ 3 + ρ 1 · n x 3 l y 3 l h = ρsinθ 3 + ρ 1 · n y 3 l z 3 l h = pθ 3 + ρ 1 · n z 3 l
Wherein, ρ 1for the equidistant distance along the Normal direction of specifying; n x3l, n y3land n z3lrepresent the component of the equidistance motion normal of specifying at each change in coordinate axis direction respectively;
Curve centered by equidistant curve, the sphere centre of sphere moves continuously along this curve, forms a tubulose envelope surface, and ring gear left-hand teeth convex side equation is:
In formula
r θ 3 = { - ρsinθ 3 + ρ 1 n x 3 l ( θ 3 ) , ρcosθ 3 + ρ 1 n y 3 l ( θ 3 ) , p + ρ 1 n z 3 l ( θ 3 ) }
Wherein and α 3represent sphere parameters respectively, and meet
Ring gear right-hand teeth face curvilinear equation is
x 3 r = ρ c o s θ 3 y 3 r = ρsinθ 3 z 3 r = - pθ 3
Wherein, ρ is that cylindrical screw Curves is at cylndrical surface radius; θ 3for cylindrical screw parameter of curve, p is helix parameter;
The right-hand teeth flank of tooth is tried to achieve based on equidistant envelope method, and its Equidistant curve equation is:
x 3 r h = ρ c o s θ 3 + ρ 1 · n x 3 r y 3 r h = ρsinθ 3 + ρ 1 · n y 3 r z 3 r h = - pθ 3 + ρ 1 · n z 3 r
In formula, ρ 1for the equidistant distance along the Normal direction of specifying; n x3r, n y3rand n z3rrepresent the component of the equidistance motion normal of specifying at each change in coordinate axis direction respectively;
Curve centered by equidistant curve, the sphere centre of sphere moves continuously along this curve, form a tubulose envelope surface, thus right-hand teeth convex side equation is:
In formula
r θ 3 = { - ρsinθ 3 + ρ 1 n x 3 r ( θ 3 ) , ρcosθ 3 + ρ 1 n y 3 r ( θ 3 ) , p + ρ 1 n z 3 r ( θ 3 ) }
Wherein and α 3represent sphere parameters respectively, and meet
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CN107061637A (en) * 2017-03-10 2017-08-18 安徽理工大学 A kind of planetary transmission system of the double uniform flow dividing structure in parallel of planetary gear
CN107327559A (en) * 2017-09-01 2017-11-07 西南大学 A kind of helical gear of circular arc parabola Multi-contact
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