CN104154210A - Logarithmic spiral gear - Google Patents

Logarithmic spiral gear Download PDF

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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
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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
Application number
CN201410171935.6A
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Chinese (zh)
Inventor
岑昊
武文昌
Original Assignee
岑昊
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by 岑昊 filed Critical 岑昊
Priority to CN201410171935.6A priority Critical patent/CN104154210A/en
Publication of CN104154210A publication Critical patent/CN104154210A/en
Pending legal-status Critical Current

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Classifications

    • 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
    • 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
    • F16H55/17Toothed 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 non-instantaneous 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

Logarithmic spiral gear
(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 non-instantaneous 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 2be respectively the root footpath of two gears that are meshed, h is the common tooth depth of two gears, n 1,n 2be respectively the number of teeth of two gears, r / 1, r / 2be 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 straight-tooth 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, non-instantaneous 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 2be respectively the root footpath of two gears that are meshed, h is the common tooth depth of two gears, n 1,n 2be respectively the number of teeth of two gears, r / 1, r / 2be 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 straight-tooth 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 gear-profile 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, gear-profile 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 1with G 2the 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 1with G 2the number of teeth be respectively n 1and n 2, common tooth depth is h, common form factor is k:
; (r 1,r 2be respectively the root footpath of two gears that are meshed, h is the common tooth depth of two gears, n 1,n 2be respectively the number of teeth of two gears, r / 1, r / 2be 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 1for driving wheel, G 2for follower, initial position is G 1tooth root and G 2crown contact, G 1maintenance angular velocity is ω 1the counterclockwise uniform rotation of (definite value).Be located at t G constantly 1turn over φ 1(t), G 2turn over φ 2(t), G 2angular velocity be ω 2(t); Point of contact P(t) with two gears gyration center 0 separately 1, O 2distance be respectively ρ 1and ρ (t) 2(t) arc length of, passing by flank profil separately at two gears is respectively s 1and 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 1every radian that just in time turns over a whole angle between teeth, G 2just just in time turn over the radian of a whole angle between teeth.And then ρ 1and ρ (t) 2(t) be ω, i.e. G with T=2 π/n 1the 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 2also take T as the cycle, and, .
So, for any t ∈ [0, T/2], φ 1, φ 2meet 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 gear-profiles equates all the time, thus transmission is without slippage.
According to above for G 2the discussion of angular velocity and Changing Pattern thereof, be not difficult to draw:
G 2the mean angular velocity of rotation is: ,
G 2the highest angular velocity of rotation is: ,
G 2the minimum angular velocity of rotation is: ,
G 2what rotate with the ratio of lowest speed is the most at a high speed: ,
G 2pulsation 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 2be respectively the root footpath of two gears that are meshed, h is the common tooth depth of two gears, n 1,n 2be respectively the number of teeth of two gears, r / 1, r / 2be 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 straight-tooth gear, can be also cylindrical screw gear or bevel gear.
CN201410171935.6A 2014-04-28 2014-04-28 Logarithmic spiral gear Pending CN104154210A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201410171935.6A CN104154210A (en) 2014-04-28 2014-04-28 Logarithmic spiral gear

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201410171935.6A CN104154210A (en) 2014-04-28 2014-04-28 Logarithmic spiral gear

Publications (1)

Publication Number Publication Date
CN104154210A true CN104154210A (en) 2014-11-19

Family

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Family Applications (1)

Application Number Title Priority Date Filing Date
CN201410171935.6A Pending CN104154210A (en) 2014-04-28 2014-04-28 Logarithmic spiral gear

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CN (1) CN104154210A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106402327A (en) * 2016-12-09 2017-02-15 东华大学 Robot joint precision transmission gear structure

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4867002A (en) * 1986-09-09 1989-09-19 Jacques Bouchet Toothing and gears made therewith
JP3669273B2 (en) * 2001-02-01 2005-07-06 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) * 2008-06-06 2008-10-22 东华大学 All-tooth profile engaged dedicated gear
CN101627228A (en) * 2007-03-06 2010-01-13 维特恩斯坦股份公司 Coaxial gear set
CN203979325U (en) * 2014-04-28 2014-12-03 岑昊 Logarithmic spiral gear

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4867002A (en) * 1986-09-09 1989-09-19 Jacques Bouchet Toothing and gears made therewith
JP3669273B2 (en) * 2001-02-01 2005-07-06 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) * 2007-03-06 2010-01-13 维特恩斯坦股份公司 Coaxial gear set
CN101290009A (en) * 2008-06-06 2008-10-22 东华大学 All-tooth profile engaged dedicated gear
CN203979325U (en) * 2014-04-28 2014-12-03 岑昊 Logarithmic spiral gear

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
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)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106402327A (en) * 2016-12-09 2017-02-15 东华大学 Robot joint precision transmission gear structure

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Application publication date: 20141119