CN106870661A - Circle-ellipse-not rounded three-wheel toothed belt transmission method for designing - Google Patents

Circle-ellipse-not rounded three-wheel toothed belt transmission method for designing Download PDF

Info

Publication number
CN106870661A
CN106870661A CN201710191389.6A CN201710191389A CN106870661A CN 106870661 A CN106870661 A CN 106870661A CN 201710191389 A CN201710191389 A CN 201710191389A CN 106870661 A CN106870661 A CN 106870661A
Authority
CN
China
Prior art keywords
synchronous pulley
theta
pitch curve
belt wheel
active synchronization
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.)
Granted
Application number
CN201710191389.6A
Other languages
Chinese (zh)
Other versions
CN106870661B (en
Inventor
陈建能
蔡双雷
肖达度
王恒丰
冯开阳
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Ningbo Fulong Synchronous Belt Co Ltd
Original Assignee
Zhejiang University of Technology ZJUT
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 Zhejiang University of Technology ZJUT filed Critical Zhejiang University of Technology ZJUT
Priority to CN201710191389.6A priority Critical patent/CN106870661B/en
Publication of CN106870661A publication Critical patent/CN106870661A/en
Application granted granted Critical
Publication of CN106870661B publication Critical patent/CN106870661B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

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
    • F16H7/00Gearings for conveying rotary motion by endless flexible members
    • F16H7/02Gearings for conveying rotary motion by endless flexible members with belts; with V-belts
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/10Geometric CAD
    • G06F30/17Mechanical parametric or variational design

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Mathematical Analysis (AREA)
  • Computational Mathematics (AREA)
  • Mechanical Engineering (AREA)
  • Devices For Conveying Motion By Means Of Endless Flexible Members (AREA)

Abstract

The invention discloses circle-ellipse-not rounded three-wheel toothed belt transmission method for designing.The present invention initially sets up the pitch curve equation of Timing Belt principal and subordinate wheel, and polar coordinates theoretical calculation principal and subordinate wheel gearratio is cut in utilization;Then the girth of Timing Belt is calculated, not rounded is calculated by iterative algorithm according to the change of Timing Belt girth slack and is tensioned the free pitch curve of synchronous pulley, tensioning wheel is the not rounded synchronous pulley of free pitch curve, can be with the synchronous belt sag variable quantity of generation in real-Time Compensation transmission process, overcoming traditional two-wheeled not rounded V belt translation can not be while meets non-at the uniform velocity transmission and the in real time problem of tensioning;The radius of circle active synchronization belt wheel pitch curve and the major axis of oval driven synchronous pulley pitch curve, eccentricity are controlled variable, change the shape of circle driving wheel pitch curve and oval driven pulley pitch curve by the regulation of three amounts, the specific non-at the uniform velocity transmission for meeting big centre-to-centre spacing is required.

Description

Circle-ellipse-not rounded three-wheel toothed belt transmission method for designing
Technical field
The present invention relates to a kind of method for designing of not rounded toothed belt transmission, and in particular to one kind amount of becoming slack is self-compensating Circle-ellipse-not rounded three-wheel toothed belt transmission method for designing.
Background technology
Transmission mechanism changes the forms of motion and speed of input and output component, to meet different operating environmental requirement, its In non-uniform transmission mechanism occupy extremely important status, common are linkage, cam mechanism, non-circular gear mechanism etc..Phase For linkage and cam mechanism, non-circular gear mechanism has compact conformation, stable drive, power is larger for transmission, easy reality The advantages of existing dynamic balancing, therefore it has been successfully applied to machining tool, automation, transport, instrument and meter, pump class, flowmeter, spinning On loom tool and agricultural machinery.But non-circular gear drive is only suitable for, and centre-to-centre spacing is smaller, lubrication is convenient non-is at the uniform velocity driven Occasion, is thus suitable for big centre-to-centre spacing, the not rounded flexible element (band/chain) of the inconvenient and low manufacturing cost occasion of lubrication and is driven and meets the tendency of And give birth to.Wherein the chaindriven polygon effect of not rounded is obvious, therefore when having strict demand to non-at the uniform velocity gearratio Changing Pattern Just it is restricted;Simultaneously common frictional V belt translation is due to Elastic Sliding it cannot be guaranteed that accurate gearratio rule.
Current non-round belt (chain) transmission, all only 2 band of not rounded (chain) wheels --- driving wheel and driven pulley, in transmission During due to its pitch curve be not rounded, the slack of band (chain) is real-time change, therefore cannot simultaneously ensure work institute It is required that non-at the uniform velocity gearratio Changing Pattern and band (chain) real-time tensioning.In order to compensate the band (chain) in transmission in practical application Slack change, by additional springs with realize tensioning, due in a period of motion its tensile force be change, and As the amplitude of variation of the aggravation tensile force of non-at the uniform velocity characteristic is bigger, the non-precision being at the uniform velocity driven can be so influenceed in turn, and And dynamics is deteriorated;Therefore in Practical Project, non-round belt (chain) transmission is rarely applied to accurately load high-speed drive Occasion.
The content of the invention
The purpose of the present invention is directed to problem above, proposes the self-compensating circle-ellipse-not rounded three-wheel of one kind amount of becoming slack Toothed belt transmission method for designing, is that not rounded synchronous pulley provides a whole set of perfect design theory basis in actual applications, Realize the non-at the uniform velocity directly accurate transmission between big centre-to-centre spacing.The method for designing initially sets up the pitch curve of Timing Belt principal and subordinate wheel Equation, and move synchronous belt pulley transmission ratio using polar coordinates theoretical calculation principal and subordinate is cut;Then the girth of Timing Belt is calculated, according to synchronization The parameters that not rounded is tensioned the free pitch curve of synchronous pulley are calculated by alternative manner with the change of girth slack.
In order to solve the above technical problems, the technical scheme is that:
It is of the invention to comprise the following steps that:
Step one, according to transmission rule determine round active synchronization belt wheel pitch curve with oval driven synchronous pulley pitch curve Equation;
Round active synchronization belt wheel is the input link of uniform rotation,It is the dynamic seat of round active synchronization belt wheel pitch curve Mark system x1o1y1Middle x1Axle is to quiet coordinate system xo1The corner of x-axis, θ in y1It is p1To moving coordinate system x1o1y1Middle x1The corner cut of axle, it is round Active synchronization belt wheel cuts polar equation:
p1=r1 (1)
S=2 π × r1 (2)
In formula, p1Footpath, r are cut for round active synchronization belt wheel pitch curve1It is the half of round active synchronization belt wheel pitch curve Footpath, s is the girth of round active synchronization belt wheel pitch curve.
Oval driven synchronous pulley is output link, cuts polar equation:
p2=a × (1-e2)-a×e2×cos(θ2) (3)
In formula, p2Footpath, θ are cut for oval driven synchronous pulley pitch curve2It is p2To moving coordinate system x2o2y2Middle x2Axle is cut Angle, e2It is the eccentricity of oval driven synchronous pulley pitch curve, a is the major axis of oval driven synchronous pulley pitch curve.
In formula, b is the short axle of oval driven synchronous pulley pitch curve, and c is the focal length of oval driven synchronous pulley pitch curve.
C=a × e2 (6)
Step 2, round active synchronization belt wheel is calculated with the gearratio of oval driven synchronous pulley initial position;
Initial position, the moving coordinate system x of round active synchronization belt wheel pitch curve1o1y1Middle x1Axle is to quiet coordinate system xo1X in y The corner of axleThe moving coordinate system x of oval driven synchronous pulley pitch curve2o2y2Middle x2Axle is to quiet coordinate system xo1X-axis in y CornerAccording to cutting, polar coordinates are theoretical to be obtained:
In formula, p112) and p221) round active synchronization belt wheel pitch curve is respectively with oval driven synchronous pulley section song Line common tangent incision superius C1、C2It is corresponding to cut footpath, p113) and p331) round active synchronization belt wheel pitch curve is respectively with tensioning Synchronous pulley pitch curve common tangent incision superius C6、C5It is corresponding to cut footpath, p223) and p332) it is respectively oval driven synchronous pulley Pitch curve and tensioning synchronous pulley pitch curve common tangent incision superius C3、C4It is corresponding to cut footpath, θ120It is round active synchronization belt wheel section Curve cuts footpath p112) cut footpath p with oval driven synchronous pulley pitch curve221) to respective moving coordinate system trunnion axis corner at the beginning of Value, θ130For round active synchronization belt wheel pitch curve cuts footpath p113) cut footpath p with tensioning synchronous pulley pitch curve331) to each The corner initial value of moving coordinate system trunnion axis, θ230For oval driven synchronous pulley pitch curve cuts footpath p223) and tensioning synchronous pulley Pitch curve cuts footpath p332) to respective moving coordinate system trunnion axis corner initial value, θ12、θ13Respectively round active synchronization belt wheel section Curve incision superius C1、C6Correspondence cuts footpath to moving coordinate system x1o1y1Middle x1The corner cut of axle, θ21、θ23Respectively oval driven Timing Belt Wheel pitch curve incision superius C2、C3Correspondence cuts footpath to moving coordinate system x2o2y2Middle x2The corner cut of axle, θ31、θ32Respectively it is tensioned Timing Belt Wheel pitch curve incision superius C4、C5Correspondence cuts footpath to moving coordinate system x3o3y3Middle x3The corner cut of axle, L1For round active synchronization belt wheel with Oval driven synchronous pulley centre-to-centre spacing, L2It is oval driven synchronous pulley and tensioning synchronous pulley centre-to-centre spacing, L3For round active is same Step belt wheel and tensioning synchronous pulley centre-to-centre spacing;
The round active synchronization belt wheel of initial position is with oval driven synchronous belt pulley transmission ratio:
Between step 3, the round active synchronization belt wheel of calculating, oval driven synchronous pulley and tensioning synchronous pulley are per two-wheeled Common tangent segment length.
Initial time, sets tensioning synchronous pulley pitch curve to give the circle of radius, round active synchronization belt wheel and ellipse Common tangent segment length T between the point of contact of driven synchronous pulley two0, oval driven synchronous pulley and tensioning synchronous pulley two point of contact it Between common tangent segment length T1, common tangent segment length T between round active synchronization belt wheel and tensioning synchronous pulley two point of contact2Point It is not:
In formula, p '1120)、p′1130) it is respectively p1120)、p1130) first differential, p'2120)、p'2230) Respectively p2120)、p2230) first differential, p'3130)、p'3230) it is respectively p3130)、p3230) single order it is micro- Point.
When round active synchronization belt wheel turns over angleOval driven synchronous pulley accordingly turns over angleRound active Synchronous pulley pitch curve incision superius C1、C6Corresponding arc length variable quantity is s1、s6, oval driven synchronous pulley pitch curve incision superius C2、C3Corresponding arc length variable quantity is s2、s3, tensioning synchronous pulley pitch curve incision superius C4、C5Corresponding arc length variable quantity is s4、 s5.Then have:
In formula, p "11) it is p11) second-order differential, p "22) it is p22) second-order differential, p "33) it is p33) Second-order differential, θ3It is tensioning Timing Belt round cut footpath p3To moving coordinate system x3o3y3Middle x3The corner cut of axle.
Any time, the common tangent segment length between round active synchronization belt wheel and the oval point of contact of driven synchronous pulley two T12, common tangent segment length T between oval driven synchronous pulley and tensioning synchronous pulley two point of contact23, round active synchronization belt wheel With the common tangent segment length T between tensioning synchronous pulley two point of contact13Respectively:
In formula, p '112)、p′113) it is respectively p112)、p113) first differential, p'221)、p'223) respectively It is p221)、p223) first differential, p'332)、p'331) it is respectively p332)、p331) first differential,To open Tight synchronous pulley pitch curve moving coordinate system x3o3y3Middle x3Axle is to quiet coordinate system xo1The corner of x-axis in y.
Step 4, the gearratio for calculating any time round active synchronization belt wheel and oval driven synchronous pulley;
Round active synchronization belt wheel uniform rotation, according to formula (1), (3) solve p1, p2, then instantaneous transmission ratio be:
Step 5, calculating any time Timing Belt girth;
Round active synchronization belt wheel pitch curve is designated as C with tensioning synchronous pulley pitch curve common tangent incision superius6, any time C1With C6Between arc length be c11, oval driven synchronous pulley pitch curve with tensioning synchronous pulley pitch curve common tangent incision superius be designated as C3, any time C2With C3Between arc length be c22, it is tensioned synchronous pulley pitch curve and is designated as with driven pulley pitch curve common tangent incision superius C4, it is tensioned synchronous pulley pitch curve and is designated as C with round active synchronization belt wheel pitch curve common tangent incision superius5, any time C4With C5 Between arc length be c33
Any time, Timing Belt Zhou Changwei:
C=T12+T13+T23+c11+c22+c33 (16)
Step 6, the free pitch curve of tensioning synchronous pulley are calculated;
Iterative algorithm is as follows:
A () setting tensioning synchronous pulley center of rotation, the radius for being tensioned synchronous pulley is set to variable, is tensioned synchronous pulley Radius initial value gives, and is designated as r3-0, belt length initial value is calculated according to formula (16) and is designated as C0
B () round active synchronization belt wheel turns over 1 °, calculating oval driven synchronous pulley according to gearratio requirement turns over accordingly Angle, be tensioned synchronous pulley corner it is identical with round active synchronization belt wheel.On the premise of ensureing that C is constant, according to formula (16) the round active synchronization belt wheel of reverse turns over corresponding tensioning synchronous pulley radius r at 1 °3-1, that is, correspond to the p at moment3
C () repeats (b) 358 times, obtain round active synchronization belt wheel and turn over 2 °, and 3 ° ..., corresponding tensioning is synchronous at 359 ° Belt wheel radius is respectively r3-2, r3-3... ..., r3-359
D () so far obtains 360 concentric circles, by the tensioning synchronous pulley radius in (a), (b) and (c), one is taken every 1 ° The radius of individual circle, sequentially takes 360 radiuses, is the center of circle to set tensioning synchronous pulley center of rotation, will take 360 radiuses The outer end point is sequentially connected with, and constitutes a not rounded for closing.
E not rounded that () will obtain in (d) is tensioned being scaled up to footpath or diminution for each moment of synchronous pulley so that new The girth of the not rounded tensioning synchronous pulley for obtaining is equal with the girth of round active synchronization belt wheel and oval driven synchronous pulley.
The radius value at f each moment that () is tried to achieve (e) substitutes into the belt length that formula (16) calculates each moment.
If g the absolute value of the difference of the belt length at () each moment and initial belt length is respectively less than preset value, step (k) is carried out, Otherwise carry out step (h).
H () reduces not rounded tensioning synchronous pulley is each worth to footpath 15 ° before and after belt length maximum position correspondence moment point ~5%, belt length minimum position correspondence moment point before and after 5 °, increase not rounded tensioning synchronous pulley each to footpath value 1~ 5%, then it is fitted with B-spline and obtains new not rounded tensioning synchronous pulley.
I () will be scaled to footpath through the not rounded tensioning synchronous pulley each moment after (h) or reduce so that newly obtain Not rounded tensioning synchronous pulley girth it is equal with the girth of round active synchronization belt wheel and oval driven synchronous pulley.
J () will substitute into formula (16) and be calculated each moment correspondence Timing Belt through the not rounded tensioning synchronous pulley after (i) to footpath Belt length, if the absolute value of the difference of correspondence Timing Belt belt length of each moment and Timing Belt girth initial value is respectively less than preset value, is walked Suddenly (k), otherwise (h) is returned to.
(k) set up not rounded tensioning synchronous pulley each moment to footpath and corresponding cornerRelation is tensioning synchronous pulley Pitch curve equation.
The device have the advantages that:
1st, it is of the invention for the self-compensating circle-ellipse of the amount of becoming slack-not rounded three-wheel toothed belt transmission is carried in actual applications A whole set of perfect design theory basis is supplied, all circle-ellipses-not rounded three-wheel synchronous belt drive mechanism can be applied to, Promote promoting the use of for circle-ellipse-not rounded three-wheel toothed belt transmission.
2nd, driving wheel pitch curve is circle in the present invention, and driven pulley pitch curve is ellipse, and gearratio design is simple, round active The radius of synchronous pulley pitch curve, the major axis of oval driven synchronous pulley pitch curve, eccentricity are controlled variable, by three amounts Regulation change the shape of round active synchronization belt wheel pitch curve and oval driven synchronous pulley pitch curve, meet it is specific it is non-at the uniform velocity It is required that transmission.
3rd, the present invention is using the exact value for cutting polar coordinates theoretical calculation gearratio, it is easy to which programming realization, solving precision is high, side Just it is quick.
4th, the not rounded tensioning synchronous pulley in the present invention is the not rounded synchronous pulley of free pitch curve, can be justified with real-Time Compensation The belt sag variable quantity produced during type active synchronization belt wheel and the driven synchronous belt pulley transmission of free not rounded, realizes big centre-to-centre spacing Between non-at the uniform velocity directly accurate transmission.
Brief description of the drawings
Fig. 1 is transmission schematic diagram of the invention;
Fig. 2 is the gearratio and round active synchronization of round active synchronization belt wheel and oval driven synchronous pulley in the present invention Belt wheel angle relation curve map;
Fig. 3 is Timing Belt belt length change curve when being tensioned the pitch curve of synchronous pulley using the not rounded in the present invention;
Fig. 4 is oval driven synchronous pulley pitch curve figure in the present invention;
Fig. 5 is the tensioning free pitch curve fitted figure of synchronous pulley in the present invention.
Specific embodiment
Below in conjunction with the accompanying drawings and case study on implementation the invention will be further described.
Circle-ellipse-not rounded three-wheel toothed belt transmission method for designing, comprises the following steps that:
Step one, such as Fig. 1, give round active synchronization belt wheel pitch curve radius r1=30mm, round active synchronization belt wheel Pitch curve cuts footpath p1=r1, tensioning synchronous pulley is the not rounded belt wheel according to the change fitting of Timing Belt girth slack;Three-wheel center Away from L1=L2=L3=100mm, three-wheel calculates round active synchronization belt wheel section to wait girth closing convex curve according to formula below The girth s=188.4956mm of curve:
S=2 π × r1 (1)
Step 2, the eccentricity e for giving oval driven synchronous pulley pitch curve2=0.8, according to round active synchronization belt wheel The pitch curve principle equal with oval driven synchronous pulley pitch curve girth, calculates oval driven synchronous pulley pitch curve long respectively Axle a=35.1022mm, short axle b=21.0613mm.
It is determined that the polar equation of cutting of oval driven synchronous pulley pitch curve is:
p2=7.0204-28.0818 × cos (θ2) (4)
In formula, θ2For oval driven synchronous pulley pitch curve cuts footpath p2To moving coordinate system x2o2y2Middle x2The corner cut of axle.
Oval driven synchronous pulley pitch curve is as shown in Figure 4.
Step 3, round active synchronization belt wheel is calculated with the gearratio of oval driven synchronous pulley initial position:
Initial position, the moving coordinate system x of round active synchronization belt wheel pitch curve1o1y1Middle x1Axle is to quiet coordinate system xo1X in y The corner of axleThe moving coordinate system x of oval driven synchronous pulley pitch curve2o2y2Middle x2Axle is to quiet coordinate system xo1X-axis in y CornerAccording to cutting, polar coordinates are theoretical to be obtained:
In formula, p112) and p221) round active synchronization belt wheel pitch curve is respectively with oval driven synchronous pulley section song Line common tangent incision superius C1、C2It is corresponding to cut footpath, p113) and p331) round active synchronization belt wheel pitch curve is respectively with tensioning Synchronous pulley pitch curve common tangent incision superius C6、C5It is corresponding to cut footpath, p223) and p332) it is respectively oval driven synchronous pulley Pitch curve and tensioning synchronous pulley pitch curve common tangent incision superius C3、C4It is corresponding to cut footpath, θ120It is round active synchronization belt wheel section Curve cuts footpath p112) cut footpath p with oval driven synchronous pulley pitch curve221) to respective moving coordinate system trunnion axis corner at the beginning of Value, θ130For round active synchronization belt wheel pitch curve cuts footpath p113) cut footpath p with tensioning synchronous pulley pitch curve331) to each The corner initial value of moving coordinate system trunnion axis, θ230For oval driven synchronous pulley pitch curve cuts footpath p223) and tensioning synchronous pulley Pitch curve cuts footpath p332) to respective moving coordinate system trunnion axis corner initial value, θ12、θ13Respectively round active synchronization belt wheel section Curve incision superius C1、C6Correspondence cuts footpath to moving coordinate system x1o1y1Middle x1The corner cut of axle, θ21、θ23Respectively oval driven Timing Belt Wheel pitch curve incision superius C2、C3Correspondence cuts footpath to moving coordinate system x2o2y2Middle x2The corner cut of axle, θ31、θ32Respectively it is tensioned Timing Belt Wheel pitch curve incision superius C4、C5Correspondence cuts footpath to moving coordinate system x3o3y3Middle x3The corner cut of axle, L1For round active synchronization belt wheel with Oval driven synchronous pulley centre-to-centre spacing, L2It is oval driven synchronous pulley and tensioning synchronous pulley centre-to-centre spacing, L3For round active is same Step belt wheel and tensioning synchronous pulley centre-to-centre spacing;
The gearratio for calculating initial position according to formula (6) is i120=1.1667:
Between step 4, the round active synchronization belt wheel of calculating, oval driven synchronous pulley and tensioning synchronous pulley are per two-wheeled Common tangent segment length.
Initial time, sets tensioning synchronous pulley pitch curve to give the circle of radius, round active synchronization belt wheel and ellipse Common tangent segment length T between the point of contact of driven synchronous pulley two0, oval driven synchronous pulley and tensioning synchronous pulley two point of contact it Between common tangent segment length T1, common tangent segment length T between round active synchronization belt wheel and tensioning synchronous pulley two point of contact2Point It is not:
T is calculated according to formula (7)0=103.3370mm, T1=100.7259mm, T2=102.9287mm.
When round active synchronization belt wheel turns over angleOval driven synchronous pulley accordingly turns over angleRound active Synchronous pulley pitch curve incision superius C1、C6Corresponding arc length variable quantity is s1、s6, oval driven synchronous pulley pitch curve incision superius C2、C3Corresponding arc length variable quantity is s2、s3, tensioning synchronous pulley pitch curve incision superius C4、C5Corresponding arc length variable quantity is s4、 s5.Then have:
In formula, p "11) it is p11) second-order differential, p "22) it is p22) second-order differential, p "33) it is p33) Second-order differential, θ3It is tensioning Timing Belt round cut footpath p3To moving coordinate system x3o3y3Middle x3The corner of axle.
Any time, the common tangent segment length between round active synchronization belt wheel and the oval point of contact of driven synchronous pulley two T12, common tangent segment length T between oval driven synchronous pulley and tensioning synchronous pulley two point of contact23, round active synchronization belt wheel With the common tangent segment length T between tensioning synchronous pulley two point of contact13Respectively:
In formula, p '112)、p′113) it is respectively p112)、p113) first differential, p'221)、p'223) respectively It is p221)、p223) first differential, p'332)、p'331) it is respectively p332)、p331) first differential,To open Tight synchronous pulley pitch curve moving coordinate system x3o3y3Middle x3Axle is to quiet coordinate system xo1The corner of x-axis in y.
Step 5, the gearratio for calculating any time round active synchronization belt wheel and oval driven synchronous pulley;
Round active synchronization belt wheel uniform rotation, p1=r1, p is solved according to formula (4)2, then round active synchronization band is calculated Wheel and oval driven synchronous pulley instantaneous transmission ratio:
According to formula (10), (11), (12), when the round active synchronization belt wheel of calculating rotates a circle, round active synchronization belt wheel With the gearratio change such as Fig. 2 of oval driven synchronous pulley.
Step 6, calculating Timing Belt girth;
Round active synchronization belt wheel pitch curve is designated as C with tensioning synchronous pulley pitch curve common tangent incision superius6, any time C1With C6Between arc length be c11, round active synchronization belt wheel is designated as C with oval driven synchronous pulley pitch curve common tangent incision superius2, Oval driven synchronous pulley pitch curve is designated as C with tensioning synchronous pulley pitch curve common tangent incision superius3, any time C2With C3Between Arc length be c22, it is tensioned synchronous pulley pitch curve and is designated as C with oval driven synchronous pulley pitch curve common tangent incision superius4, tensioning Synchronous pulley pitch curve is designated as C with round active synchronization belt wheel pitch curve common tangent incision superius5, any time C4With C5Between arc A length of c33
Any time, Timing Belt Zhou Changwei:
C=T12+T13+T23+c11+c22+c33 (14)
Initial time, Timing Belt original perimeter C is calculated according to formula (14)0=515mm;
Each timing synchronization band belt length, each timing synchronization when driving wheel is rotated one week are sequentially calculated according to above method Band belt length change curve such as Fig. 3.
Step 7, the free pitch curve of tensioning synchronous pulley are calculated.
Iterative algorithm is as follows:
A () known tensioning synchronous pulley center of rotation, the radius for being tensioned synchronous pulley is set to variable r3, it is tensioned Timing Belt Wheel radius initial value is designated as r3-0=30mm, Timing Belt belt length initial value is designated as C0=515mm.
B () round active synchronization belt wheel turns over 1 °, calculating oval driven synchronous pulley according to gearratio requirement turns over accordingly Angle, be tensioned synchronous pulley corner it is identical with round active synchronization belt wheel.On the premise of ensureing that C is constant, according to formula (14) when the round active synchronization belt wheel of reverse turns over 1 °, corresponding tensioning synchronous pulley radius r3-1=30.0562mm.
C () repeats (b) 358 times, obtains r3-2, r3-3... ..., r3-359
D () so far obtains 360 concentric circles, by the tensioning synchronous pulley radius in (a), (b) and (c), one is taken every 1 ° The radius of individual circle, sequentially takes 360 radiuses, is the center of circle to set tensioning synchronous pulley center of rotation, will take 360 radiuses The outer end point is sequentially connected with, and constitutes a not rounded for closing.
E not rounded that () will obtain in (d) is tensioned being scaled up to footpath or diminution for each point of synchronous pulley so that new The girth of the not rounded tensioning synchronous pulley for arriving is equal with the girth of round active synchronization belt wheel and oval driven synchronous pulley.
The radius value at f each moment that () is tried to achieve (e) substitutes into the belt length that formula (14) calculates each moment.
If g the absolute value of the difference of the belt length at () each moment and initial belt length is respectively less than preset value, step (k) is carried out, Otherwise carry out step (h).
H () reduces what not rounded tensioning synchronous pulley was each worth to footpath 5 ° before and after belt length maximum position correspondence moment point 3%, 5 ° before and after belt length minimum position correspondence moment point, increase not rounded tensioning synchronous pulley is each worth to footpath 3%, then It is fitted with B-spline and obtains new not rounded tensioning synchronous pulley.
I () will be tensioned being scaled up to footpath or diminution for synchronous pulley each point through the not rounded after (h) so that newly obtain The girth of not rounded tensioning synchronous pulley is equal with the girth of round active synchronization belt wheel and oval driven synchronous pulley.
J () will substitute into formula (14) and be calculated each point correspondence Timing Belt band through the not rounded tensioning synchronous pulley after (i) to footpath It is long, if the absolute value of the difference of each point correspondence Timing Belt belt length and Timing Belt girth initial value is respectively less than preset value, carry out step K (), otherwise returns to (h).
(k) set up not rounded tensioning synchronous pulley each moment to footpath and corresponding cornerRelation is tensioning synchronous pulley Pitch curve equation.Three pitch curves taken turns and phase angle, center of rotation all determine, calculate tensioning synchronous pulley and round active is same Step belt wheel angle relation corresponding with oval driven synchronous pulley.
The free pitch curve of tensioning synchronous pulley such as Fig. 5 after calculating.
Timing Belt theory belt length variable quantity is 12mm in the embodiment, is the 2.3% of Timing Belt total length, because band needs Tensioning, can meet actual operation requirements.

Claims (1)

1. circle-ellipse-not rounded three-wheel toothed belt transmission method for designing, it is characterised in that:The method is specific as follows:
Step one, according to transmission rule determine round active synchronization belt wheel pitch curve with oval driven synchronous pulley pitch curve side Journey;
Round active synchronization belt wheel is the input link of uniform rotation,It is the moving coordinate system of round active synchronization belt wheel pitch curve x1o1y1Middle x1Axle is to quiet coordinate system xo1The corner of x-axis, θ in y1It is p1To moving coordinate system x1o1y1Middle x1The corner cut of axle, round active Synchronous pulley cuts polar equation:
p1=r1 (1)
S=2 π × r1 (2)
In formula, p1Footpath, r are cut for round active synchronization belt wheel pitch curve1It is the radius of round active synchronization belt wheel pitch curve, s is The girth of round active synchronization belt wheel pitch curve;
Oval driven synchronous pulley is output link, cuts polar equation:
p2=a × (1-e2)-a×e2×cos(θ2) (3)
In formula, p2Footpath, θ are cut for oval driven synchronous pulley pitch curve2It is p2To moving coordinate system x2o2y2Middle x2The corner cut of axle, e2 It is the eccentricity of oval driven synchronous pulley pitch curve, a is the major axis of oval driven synchronous pulley pitch curve;
a = s [ ( 2 π - 4 ) × 1 - e 2 2 + 4 ] - - - ( 4 )
b = a 2 - c 2 - - - ( 5 )
In formula, b is the short axle of oval driven synchronous pulley pitch curve, and c is the focal length of oval driven synchronous pulley pitch curve;
C=a × e2 (6)
Step 2, round active synchronization belt wheel is calculated with the gearratio of oval driven synchronous pulley initial position;
Initial position, the moving coordinate system x of round active synchronization belt wheel pitch curve1o1y1Middle x1Axle is to quiet coordinate system xo1X-axis in y CornerThe moving coordinate system x of oval driven synchronous pulley pitch curve2o2y2Middle x2Axle is to quiet coordinate system xo1X-axis turns in y AngleAccording to cutting, polar coordinates are theoretical to be obtained:
θ 12 = θ 21 = θ 120 θ 13 = θ 31 = θ 130 θ 23 = θ 32 = θ 230 p 2 ( θ 21 ) - p 1 ( θ 12 ) = - L 1 × c o s ( θ 120 ) p 3 ( θ 31 ) - p 1 ( θ 13 ) = - L 3 × c o s ( θ 130 ) p 3 ( θ 32 ) - p 2 ( θ 23 ) = - L 2 × c o s ( θ 230 ) - - - ( 7 )
In formula, p112) and p221) round active synchronization belt wheel pitch curve is respectively with oval driven synchronous pulley pitch curve public affairs Tangent line incision superius C1、C2It is corresponding to cut footpath, p113) and p331) to be respectively round active synchronization belt wheel pitch curve synchronous with tensioning Belt wheel pitch curve common tangent incision superius C6、C5It is corresponding to cut footpath, p223) and p332) it is respectively oval driven synchronous pulley section song Line and tensioning synchronous pulley pitch curve common tangent incision superius C3、C4It is corresponding to cut footpath, θ120It is round active synchronization belt wheel pitch curve Cut footpath p112) cut footpath p with oval driven synchronous pulley pitch curve221) to the corner cut initial value of respective moving coordinate system trunnion axis, θ130For round active synchronization belt wheel pitch curve cuts footpath p113) cut footpath p with tensioning synchronous pulley pitch curve331) arrive each automatic seat The corner cut initial value of mark system trunnion axis, θ230For oval driven synchronous pulley pitch curve cuts footpath p223) bent with tensioning synchronous pulley section Line cuts footpath p332) to respective moving coordinate system trunnion axis corner cut initial value, θ12、θ13Respectively round active synchronization belt wheel pitch curve Incision superius C1、C6Correspondence cuts footpath to moving coordinate system x1o1y1Middle x1The corner cut of axle, θ21、θ23Respectively oval driven synchronous pulley section Curve incision superius C2、C3Correspondence cuts footpath to moving coordinate system x2o2y2Middle x2The corner cut of axle, θ31、θ32Respectively it is tensioned synchronous pulley section Curve incision superius C4、C5Correspondence cuts footpath to moving coordinate system x3o3y3Middle x3The corner cut of axle, L1It is round active synchronization belt wheel and ellipse Driven synchronous pulley centre-to-centre spacing, L2It is oval driven synchronous pulley and tensioning synchronous pulley centre-to-centre spacing, L3It is round active synchronization band Wheel and tensioning synchronous pulley centre-to-centre spacing;
The round active synchronization belt wheel of initial position is with oval driven synchronous belt pulley transmission ratio:
i 120 = p 2 ( θ 120 ) p 1 ( θ 120 ) - - - ( 8 )
Step 3, the public affairs for calculating round active synchronization belt wheel, oval driven synchronous pulley and being tensioned between the every two-wheeled of synchronous pulley Tangent line segment length;
Initial time, sets tensioning synchronous pulley pitch curve driven with ellipse to give the circle of radius, round active synchronization belt wheel Common tangent segment length T between the point of contact of synchronous pulley two0, between oval driven synchronous pulley and tensioning synchronous pulley two point of contact Common tangent segment length T1, common tangent segment length T between round active synchronization belt wheel and tensioning synchronous pulley two point of contact2Respectively:
In formula, p '1120)、p′1130) it is respectively p1120)、p1130) first differential, p '2120)、p′2230) respectively It is p2120)、p2230) first differential, p '3130)、p′3230) it is respectively p3130)、p3230) first differential;
When round active synchronization belt wheel turns over angleOval driven synchronous pulley accordingly turns over angleRound active synchronization Belt wheel pitch curve incision superius C1、C6Corresponding arc length variable quantity is s1、s6, oval driven synchronous pulley pitch curve incision superius C2、C3 Corresponding arc length variable quantity is s2、s3, tensioning synchronous pulley pitch curve incision superius C4、C5Corresponding arc length variable quantity is s4、s5;Then Have:
s 1 = ∫ θ 120 θ 12 ( p 1 ( θ 1 ) + p 1 ′ ′ ( θ 1 ) ) dθ 1 s 2 = ∫ θ 120 θ 21 ( p 2 ( θ 2 ) + p 2 ′ ′ ( θ 2 ) ) dθ 2 s 3 = ∫ θ 230 θ 21 ( p 2 ( θ 2 ) + p 2 ′ ′ ( θ 2 ) ) dθ 2 s 4 = ∫ θ 230 θ 32 ( p 3 ( θ 3 ) + p 3 ′ ′ ( θ 3 ) ) dθ 3 s 5 = ∫ θ 130 θ 31 ( p 3 ( θ 3 ) + p 3 ′ ′ ( θ 3 ) ) dθ 3 s 6 = ∫ θ 130 θ 13 ( p 1 ( θ 1 ) + p 1 ′ ′ ( θ 1 ) ) dθ 1 - - - ( 10 )
In formula, p "11) it is p11) second-order differential, p "22) it is p22) second-order differential, p "33) it is p33) two Rank differential, θ3It is tensioning Timing Belt round cut footpath p3To moving coordinate system x3o3y3Middle x3The corner cut of axle;
Any time, the common tangent segment length T between round active synchronization belt wheel and the oval point of contact of driven synchronous pulley two12, it is ellipse Common tangent segment length T between the driven synchronous pulley of circle and tensioning synchronous pulley two point of contact23, round active synchronization belt wheel with tensioning Common tangent segment length T between the point of contact of synchronous pulley two13Respectively:
In formula, p '112)、p′113) it is respectively p112)、p113) first differential, p '221)、p′223) it is respectively p221)、p223) first differential, p '332)、p′331) it is respectively p332)、p331) first differential,It is tensioning Synchronous pulley pitch curve moving coordinate system x3o3y3Middle x3Axle is to quiet coordinate system xo1The corner of x-axis in y;
Step 4, the gearratio for calculating any time round active synchronization belt wheel and oval driven synchronous pulley;
Round active synchronization belt wheel uniform rotation, according to formula (1), (3) solve p1, p2, then instantaneous transmission ratio be:
i 12 = p 2 p 1 - - - ( 14 )
Step 5, calculating any time Timing Belt girth;
Round active synchronization belt wheel pitch curve is designated as C with tensioning synchronous pulley pitch curve common tangent incision superius6, any time C1With C6Between arc length be c11, oval driven synchronous pulley pitch curve and tensioning synchronous pulley pitch curve common tangent incision superius are designated as C3, Any time C2With C3Between arc length be c22, tensioning synchronous pulley pitch curve and driven pulley pitch curve common tangent incision superius are designated as C4, Tensioning synchronous pulley pitch curve is designated as C with round active synchronization belt wheel pitch curve common tangent incision superius5, any time C4With C5Between Arc length be c33
c 11 = ∫ θ 12 θ 13 [ p 1 ( θ 1 ) + p 1 ′ ′ ( θ 1 ) ] dθ 1 c 22 = ∫ θ 23 θ 21 [ p 2 ( θ 2 ) + p 2 ′ ′ ( θ 2 ) ] dθ 2 c 33 = ∫ θ 31 θ 32 [ p 3 ( θ 3 ) + p 3 ′ ′ ( θ 3 ) ] dθ 3 - - - ( 15 )
Any time, Timing Belt Zhou Changwei:
C=T12+T13+T23+c11+c22+c33 (16)
Step 6, the free pitch curve of tensioning synchronous pulley are calculated;
Iterative algorithm is as follows:
A () setting tensioning synchronous pulley center of rotation, the radius for being tensioned synchronous pulley is set to variable, is tensioned synchronous pulley radius Initial value gives, and is designated as r3-0, belt length initial value is calculated according to formula (16) and is designated as C0
B () round active synchronization belt wheel turns over 1 °, calculating oval driven synchronous pulley according to gearratio requirement turns over corresponding angle Degree, the corner for being tensioned synchronous pulley is identical with round active synchronization belt wheel;It is anti-according to formula (16) on the premise of ensureing that C is constant Round active synchronization belt wheel is asked to turn over corresponding tensioning synchronous pulley radius r at 1 °3-1, that is, correspond to the p at moment3
C () repeats (b) 358 times, obtains round active synchronization belt wheel and turn over 2 °, 3 ° ..., corresponding tensioning synchronous pulley at 359 ° Radius is respectively r3-2, r3-3... ..., r3-359
D () so far obtains 360 concentric circles, by the tensioning synchronous pulley radius in (a), (b) and (c), a circle is taken every 1 ° Radius, sequentially take 360 radiuses, with set tensioning synchronous pulley center of rotation be the center of circle, 360 outer ends of radius will be taken Point is sequentially connected with, and constitutes a not rounded for closing;
E not rounded that () will obtain in (d) is tensioned being scaled up to footpath or diminution for each moment of synchronous pulley so that newly obtain Not rounded tensioning synchronous pulley girth it is equal with the girth of round active synchronization belt wheel and oval driven synchronous pulley;
The radius value at f each moment that () is tried to achieve (e) substitutes into the belt length that formula (16) calculates each moment;
If g the absolute value of the difference of the belt length at () each moment and initial belt length is respectively less than preset value, step (k) is carried out, otherwise Carry out step (h);
(h) belt length maximum position correspondence moment point before and after 5 °, reduce not rounded tensioning synchronous pulley each to footpath value 1~ 5%, 5 ° before and after belt length minimum position correspondence moment point, increase not rounded tensioning synchronous pulley is each worth to footpath 1~5%, Then it is fitted with B-spline and obtains new not rounded tensioning synchronous pulley;
I () will be scaled to footpath through the not rounded tensioning synchronous pulley each moment after (h) or reduce so that what is newly obtained is non- The girth of circle tensioning synchronous pulley is equal with the girth of round active synchronization belt wheel and oval driven synchronous pulley;
J () will substitute into formula (16) and be calculated each moment correspondence Timing Belt belt length through the not rounded tensioning synchronous pulley after (i) to footpath, If the absolute value of the difference of each moment correspondence Timing Belt belt length and Timing Belt girth initial value is respectively less than preset value, step (k) is carried out, Otherwise return to (h);
(k) set up not rounded tensioning synchronous pulley each moment to footpath and corresponding cornerIt is bent that relation is tensioning synchronous pulley section Line equation.
CN201710191389.6A 2017-03-28 2017-03-28 Oval-not rounded three-wheel toothed belt transmission design method of circle- Active CN106870661B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710191389.6A CN106870661B (en) 2017-03-28 2017-03-28 Oval-not rounded three-wheel toothed belt transmission design method of circle-

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710191389.6A CN106870661B (en) 2017-03-28 2017-03-28 Oval-not rounded three-wheel toothed belt transmission design method of circle-

Publications (2)

Publication Number Publication Date
CN106870661A true CN106870661A (en) 2017-06-20
CN106870661B CN106870661B (en) 2018-11-02

Family

ID=59159458

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710191389.6A Active CN106870661B (en) 2017-03-28 2017-03-28 Oval-not rounded three-wheel toothed belt transmission design method of circle-

Country Status (1)

Country Link
CN (1) CN106870661B (en)

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4865577A (en) * 1988-09-08 1989-09-12 Trustees Of Columbia University In The City Of New York Noncircular drive
CN202659811U (en) * 2012-06-04 2013-01-09 浙江理工大学 Non-circular gear pair with Fourier function pitch curve
CN104455211A (en) * 2014-10-09 2015-03-25 浙江理工大学 Design method of high-order modified Fourier non-circular gear pair
CN104455313A (en) * 2014-10-09 2015-03-25 浙江理工大学 Design method of high-order modified eccentric circular gear and non-circular gear pair conjugated with high-order modified circular gear
CN104462638A (en) * 2014-10-09 2015-03-25 浙江理工大学 Design method of high-order modified Pascal spiral curve non-circular gear pair

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4865577A (en) * 1988-09-08 1989-09-12 Trustees Of Columbia University In The City Of New York Noncircular drive
CN202659811U (en) * 2012-06-04 2013-01-09 浙江理工大学 Non-circular gear pair with Fourier function pitch curve
CN104455211A (en) * 2014-10-09 2015-03-25 浙江理工大学 Design method of high-order modified Fourier non-circular gear pair
CN104455313A (en) * 2014-10-09 2015-03-25 浙江理工大学 Design method of high-order modified eccentric circular gear and non-circular gear pair conjugated with high-order modified circular gear
CN104462638A (en) * 2014-10-09 2015-03-25 浙江理工大学 Design method of high-order modified Pascal spiral curve non-circular gear pair

Also Published As

Publication number Publication date
CN106870661B (en) 2018-11-02

Similar Documents

Publication Publication Date Title
CN105042002A (en) Variable-transmission-ratio line gear mechanism
CN108331900B (en) Non-circular gear pair design method based on curvature change
CN111322374B (en) Elastic variable transmission ratio line gear mechanism
US20190003564A1 (en) Continuously variable transmission with uniform input-to-output ratio that is non- dependent on friction
CN110848332B (en) Intersecting-axis non-circular-face gear transmission mechanism
CN106838159A (en) Circle-Fourier's not rounded-not rounded three-wheel toothed belt transmission method for designing
CN106870661A (en) Circle-ellipse-not rounded three-wheel toothed belt transmission method for designing
CN106838160A (en) Bath main officer of Tibet not rounded-sine not rounded-not rounded three-wheel toothed belt transmission method for designing
CN204985583U (en) Variable ratio line gear
CN202659811U (en) Non-circular gear pair with Fourier function pitch curve
CN106907436A (en) Circle-off-centre operation-not rounded three-wheel toothed belt transmission method for designing
CN105202143B (en) Power transmission apparatus for vehicle
CN106907435A (en) Circle-free not rounded-not rounded three-wheel toothed belt transmission method for designing
CN106917851A (en) Bath main officer of Tibet not rounded-Bath main officer of Tibet not rounded-not rounded three-wheel toothed belt transmission method for designing
CN106838158A (en) Off-centre operation-Fourier's not rounded-not rounded three-wheel toothed belt transmission method for designing
CN107061643A (en) Oval-sinusoidal not rounded-not rounded three-wheel toothed belt transmission design method
US3859862A (en) Cyclicly repetitive motion generating system
US11339859B2 (en) Infinitely variable transmission with uniform input-to-output ratio that is non-dependant on friction
CN106949204B (en) The design method of the non-circular toothed belt transmission of the self-compensating pleiotaxy of the amount of becoming slack
CN110657216B (en) Mechanism for realizing cosine acceleration motion law and reverse solving method
CN102705448A (en) Non-circular gear pair with Fourier function pitch curves
US20180209523A1 (en) Continuously variable transmission with uniform input-to-output ratio that is non- dependent on friction
CN101821484A (en) Non-synchronous belt driven camshaft phase shift device
Medvecká-Beňová Designing pitch curves of non-circular gears
CN101311393A (en) Transmission mechanism of combing machine detaching roller

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant
TR01 Transfer of patent right
TR01 Transfer of patent right

Effective date of registration: 20200610

Address after: Room 415, building 19-4, e-commerce Industrial Park, Wuhe County, Bengbu City, Anhui Province

Patentee after: Anhui huajingdao e-commerce Co.,Ltd.

Address before: Hangzhou City, Zhejiang province 310018 Xiasha Higher Education Park No. 2 Street No. 928

Patentee before: ZHEJIANG SCI-TECH University

TR01 Transfer of patent right
TR01 Transfer of patent right

Effective date of registration: 20221209

Address after: Longtouchang village, Longshan Town, Cixi City, Ningbo City, Zhejiang Province

Patentee after: NINGBO FULONG SYNCHRONOUS BELT Co.,Ltd.

Address before: 233300 room 415, building 19-4, Bengbu Electric Power Industrial Park, Wuhe County, Anhui

Patentee before: Anhui huajingdao e-commerce Co.,Ltd.