CN104154210A  Logarithmic spiral gear  Google Patents
Logarithmic spiral gear Download PDFInfo
 Publication number
 CN104154210A CN104154210A CN201410171935.6A CN201410171935A CN104154210A CN 104154210 A CN104154210 A CN 104154210A CN 201410171935 A CN201410171935 A CN 201410171935A CN 104154210 A CN104154210 A CN 104154210A
 Authority
 CN
 China
 Prior art keywords
 gear
 gears
 logarithmic spiral
 tooth
 meshed
 Prior art date
 Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
 Pending
Links
 230000005540 biological transmission Effects 0.000 abstract description 8
 210000004746 Tooth Root Anatomy 0.000 description 2
 230000002596 correlated Effects 0.000 description 1
 238000010586 diagram Methods 0.000 description 1
 230000000694 effects Effects 0.000 description 1
 238000000034 method Methods 0.000 description 1
Classifications

 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

 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
Abstract
The invention relates to a gear driving device, in particular to a logarithmic spiral gear. The logarithmic spiral gear is characterized in that a logarithmic spiral serves as a bus of the tooth surface of the gear, the normal section of the gear is the logarithmic spiral, the following equation is met, wherein ri and r2 are respectively the root diameters of two meshed gears, h is the common tooth height of the two gears, n1 and n2 are respectively the number of teeth of the two gears, r'1 and r'2 are respectively the crest diameters of the two gears, a is the center distance of two meshed gears, and k is the common tooth form factor of the two gears. The logarithmic spiral gear has the advantages that the logarithmic spiral gear which is in pulsating motion and in angle transmission such as noninstantaneous transmission at a uniform velocity ratio is provided, and the tooth surface is free of relative slip when the gear is in meshed transmission.
Description
(1) technical field
The present invention relates to a kind of gear drive, particularly a kind of logarithmic spiral gear.
(2) background technique
At present, in gear drive, involute gear, camber line gear in engagement driving, be all etc. velocity ratio, etc. instantaneous corner rotate, exist the flank of tooth to have the problem of relative slippage.
(3) summary of the invention
The present invention is in order to make up the deficiencies in the prior art, provide a kind of flank of tooth without slippage relatively, at the uniform velocity than, make the logarithmic spiral gear of the pulsating motion of noninstantaneous transmission equal angle transmission.
The present invention is achieved through the following technical solutions:
A logarithmic spiral gear, is characterized in that: the flank of tooth of gear be take logarithmic spiral as bus, and its normal cross section is logarithmic spiral, meets:
;
(r
_{1,}r
_{2}be respectively the root footpath of two gears that are meshed, h is the common tooth depth of two gears, n
_{1,}n
_{2}be respectively the number of teeth of two gears, r
^{/} _{1}, r
^{/} _{2}be respectively the footpath, top of two gears, a is the centre distance of two gears that are meshed, and k is the common form factor of two gears).
Described gear can be logarithmic spiral cylindric straighttooth gear, can be also cylindrical screw gear or bevel gear.
The invention has the beneficial effects as follows: provide a kind of at the uniform velocity than the logarithmic spiral gear of the pulsating motion of, noninstantaneous transmission equal angle transmission, gear in engagement driving the flank of tooth without relative slippage.
(4) accompanying drawing explanation
Below in conjunction with accompanying drawing, the present invention is further illustrated.
Accompanying drawing 1 is logarithmic spiral gear structure schematic diagram of the present invention;
Accompanying drawing 2 is logarithmic spiral gear mesh schematic representation of the present invention.
(5) embodiment
Accompanying drawing is a kind of specific embodiment of the present invention.The flank of tooth of this embodiment's gear be take logarithmic spiral as bus, and its normal cross section is logarithmic spiral, meets:
;
(r
_{1,}r
_{2}be respectively the root footpath of two gears that are meshed, h is the common tooth depth of two gears, n
_{1,}n
_{2}be respectively the number of teeth of two gears, r
^{/} _{1}, r
^{/} _{2}be respectively the footpath, top of two gears, a is the centre distance of two gears that are meshed, and k is the common form factor of two gears).Gear can be logarithmic spiral cylindric straighttooth gear, can be also cylindrical screw gear or bevel gear.
Adopt logarithmic spiral gear of the present invention, the correlated measure of gear comprises: number of teeth n, and form factor k, root footpath (distance at tooth root and center) r, top footpath (distance at crown and center) r ', tooth depth h (=r 'r).
The polar equation of gearprofile curve (take gyration center as initial point) as:
.
And then there is r '=re
^{k π/n}, and flank profil and ray θ=2l π/n intersection point place be tooth root, place is crown with θ=(2l+1 π)/n intersection point.
Therefore, gearprofile equation ρ=ρ (θ) meets:
.
So the tangent line of any point is α=arccotk with angle (being also equal to laterally and the angle of normal, the i.e. pressure angle of gear) radially on line.
Like this, gear G
_{1}with G
_{2}the condition that can mesh is:
1. r
_{1}+ r '
_{2}=r '
_{1}+ r
_{2}=d (d is the distance that connects with the heart of two gears);
2. contact smoothly, two gears are identical at the tangent line at point of contact place.That is:
.
Number of teeth n, form factor k and tooth depth h are the three elements of logarithmic spiral gear.
When meeting the gear G of meshing condition
_{1}with G
_{2}the number of teeth be respectively n
_{1}and n
_{2}, common tooth depth is h, common form factor is k:
;
(r
_{1,}r
_{2}be respectively the root footpath of two gears that are meshed, h is the common tooth depth of two gears, n
_{1,}n
_{2}be respectively the number of teeth of two gears, r
^{/} _{1}, r
^{/} _{2}be respectively the footpath, top of two gears, a is the centre distance of two gears that are meshed, and k is the common form factor of two gears).
Might as well establish G
_{1}for driving wheel, G
_{2}for follower, initial position is G
_{1}tooth root and G
_{2}crown contact, G
_{1}maintenance angular velocity is ω
_{1}the counterclockwise uniform rotation of (definite value).Be located at t G constantly
_{1}turn over φ
_{1}(t), G
_{2}turn over φ
_{2}(t), G
_{2}angular velocity be ω
_{2}(t); Point of contact P(t) with two gears gyration center 0 separately
_{1}, O
_{2}distance be respectively ρ
_{1}and ρ (t)
_{2}(t) arc length of, passing by flank profil separately at two gears is respectively s
_{1}and s (t)
_{2}(t). obviously to any t>0, meet:
。
Because point of contact is on line of centers, so instantaneous, be point of contact P, two gears instantaneous Center separately i.e. flank profil .G separately
_{1}every radian that just in time turns over a whole angle between teeth, G
_{2}just just in time turn over the radian of a whole angle between teeth.And then ρ
_{1}and ρ (t)
_{2}(t) be ω, i.e. G with T=2 π/n
_{1}the radian time used that turns over a whole angle between teeth is the cycle, and for any t ∈ [0, T/2],
,
So
, t ∈ [0, T/2].
Be not difficult to draw ω
_{2}also take T as the cycle, and,
.
So, for any t ∈ [0, T/2], φ
_{1}, φ
_{2}meet following character:
，
；
To any t ∈ [0, T], meet:
.
So for any t ∈ [0, T/2], have:
，
。
And then
，
。
Again by
, know
thereby,
.Quadrature for t simultaneously in equal sign two ends,
, and
.
Obviously, for arbitrarily
; For arbitrarily
.Therefore for arbitrarily
, total arc length that point of contact is passed by two gearprofiles equates all the time, thus transmission is without slippage.
According to above for G
_{2}the discussion of angular velocity and Changing Pattern thereof, be not difficult to draw:
G
_{2}the mean angular velocity of rotation is:
,
G
_{2}the highest angular velocity of rotation is:
,
G
_{2}the minimum angular velocity of rotation is:
,
G
_{2}what rotate with the ratio of lowest speed is the most at a high speed:
,
G
_{2}pulsation rate be:
.
Claims (2)
1. a logarithmic spiral gear, is characterized in that: the flank of tooth of gear be take logarithmic spiral as bus, and its normal cross section is logarithmic spiral, meets:
;
(r
_{1,}r
_{2}be respectively the root footpath of two gears that are meshed, h is the common tooth depth of two gears, n
_{1,}n
_{2}be respectively the number of teeth of two gears, r
^{/} _{1}, r
^{/} _{2}be respectively the footpath, top of two gears, a is the centre distance of two gears that are meshed, and k is the common form factor of two gears).
2. logarithmic spiral gear according to claim 1, is characterized in that: described gear can be logarithmic spiral cylindric straighttooth gear, can be also cylindrical screw gear or bevel gear.
Priority Applications (1)
Application Number  Priority Date  Filing Date  Title 

CN201410171935.6A CN104154210A (en)  20140428  20140428  Logarithmic spiral gear 
Applications Claiming Priority (1)
Application Number  Priority Date  Filing Date  Title 

CN201410171935.6A CN104154210A (en)  20140428  20140428  Logarithmic spiral gear 
Publications (1)
Publication Number  Publication Date 

CN104154210A true CN104154210A (en)  20141119 
Family
ID=51879789
Family Applications (1)
Application Number  Title  Priority Date  Filing Date 

CN201410171935.6A Pending CN104154210A (en)  20140428  20140428  Logarithmic spiral gear 
Country Status (1)
Country  Link 

CN (1)  CN104154210A (en) 
Cited By (1)
Publication number  Priority date  Publication date  Assignee  Title 

CN106402327A (en) *  20161209  20170215  东华大学  Robot joint precision transmission gear structure 
Citations (5)
Publication number  Priority date  Publication date  Assignee  Title 

US4867002A (en) *  19860909  19890919  Jacques Bouchet  Toothing and gears made therewith 
JP3669273B2 (en) *  20010201  20050706  セイコーエプソン株式会社  GEAR, POWER TRANSMISSION DEVICE INCLUDING THIS GEAR, DEVICE HAVING THIS POWER TRANSMISSION DEVICE, AND GEAR MANUFACTURING METHOD 
CN101290009A (en) *  20080606  20081022  东华大学  Alltooth profile engaged dedicated gear 
CN101627228A (en) *  20070306  20100113  维特恩斯坦股份公司  Coaxial gear set 
CN203979325U (en) *  20140428  20141203  岑昊  Logarithmic spiral gear 

2014
 20140428 CN CN201410171935.6A patent/CN104154210A/en active Pending
Patent Citations (5)
Publication number  Priority date  Publication date  Assignee  Title 

US4867002A (en) *  19860909  19890919  Jacques Bouchet  Toothing and gears made therewith 
JP3669273B2 (en) *  20010201  20050706  セイコーエプソン株式会社  GEAR, POWER TRANSMISSION DEVICE INCLUDING THIS GEAR, DEVICE HAVING THIS POWER TRANSMISSION DEVICE, AND GEAR MANUFACTURING METHOD 
CN101627228A (en) *  20070306  20100113  维特恩斯坦股份公司  Coaxial gear set 
CN101290009A (en) *  20080606  20081022  东华大学  Alltooth profile engaged dedicated gear 
CN203979325U (en) *  20140428  20141203  岑昊  Logarithmic spiral gear 
NonPatent Citations (1)
Title 

尚珂: ""对数螺旋锥齿轮的三维建模与几何参数设计"", 《中国优秀硕士学位论文全文数据库工程科技II辑》 * 
Cited By (1)
Publication number  Priority date  Publication date  Assignee  Title 

CN106402327A (en) *  20161209  20170215  东华大学  Robot joint precision transmission gear structure 
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PB01  Publication  
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Application publication date: 20141119 