CN106838160B - Non-circular-sinusoidal non-circular-non-circular three-wheel toothed belt transmission design method of Bath main officer of Tibet - Google Patents
Non-circular-sinusoidal non-circular-non-circular three-wheel toothed belt transmission design method of Bath main officer of Tibet Download PDFInfo
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Abstract
The invention discloses non-circular-sinusoidal non-circular-non-circular three-wheel toothed belt transmission design methods of Bath main officer of Tibet.The present invention initially sets up the pitch curve equation of synchronous belt principal and subordinate wheel, and utilizes and cut polar coordinates theoretical calculation principal and subordinate wheel transmission ratio；Then the perimeter for calculating synchronous belt, changes according to synchronous belt perimeter slack and calculates non-circular tensioning synchronous pulley pitch curve by iterative algorithm.Tensioning wheel is the non-circular synchronous pulley of free pitch curve, the problem of non-circular V belt translation of traditional two-wheeled cannot meet non-at the uniform velocity transmission and tensioning in real time simultaneously can be overcome with the synchronous belt sag variable quantity generated in the non-circular driving wheel of real-time compensation Bath main officer of Tibet and sinusoidal non-circular driven wheel transmission process；Circular diameter, length, deformation coefficient and order occur for the non-circular driving wheel pitch curve of Bath main officer of Tibet, four parameters such as the amplitude of sinusoidal non-circular driven wheel pitch curve are controlled variable, by adjusting these parameters, change driving wheel and driven wheel pitch curve shape, meet big center away from it is specific it is non-at the uniform velocity transmission require.
Description
Technical field
The present invention relates to a kind of design methods of non-circular toothed belt transmission, and in particular to self-compensating bar of one kind amount of becoming slack
Non-circular-sinusoidal non-circular-non-circular three-wheel toothed belt transmission design method of this main officer of Tibet.
Background technique
Transmission mechanism changes the forms of motion and speed of input and output component, to meet different operating environmental requirement,
In non-uniform transmission mechanism occupy extremely important status, common are link mechanism, cam mechanism, non-circular gear mechanism etc..Phase
For link mechanism and cam mechanism, non-circular gear mechanism has compact-sized, stable drive, transmitting power larger, easy to be real
The advantages that 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, which is only suitable for center, non-to be at the uniform velocity driven away from smaller, lubrication are convenient
Occasion, therefore be suitable for big center and be driven away from the non-circular flexible element (band/chain) of, the inconvenient and low manufacturing cost occasion of lubrication to meet the tendency of
And it gives birth to.Wherein non-circular chaindriven polygon effect is obvious, therefore when having strict demand to non-at the uniform velocity transmission ratio changing rule
Just it is restricted；Frictional V belt translation common simultaneously cannot be guaranteed accurate transmission ratio rule due to Elastic Sliding.
Current non-round belt (chain) transmission, all only 2 non-circular bands (chain) are taken turns --- and driving wheel and driven wheel are being driven
In the process due to its pitch curve be it is non-circular, the slack of band (chain) is real-time change, therefore cannot guarantee work institute simultaneously
It is required that non-at the uniform velocity transmission ratio changing rule and band (chain) real-time tensioning.In order to compensate for the band (chain) in transmission in practical application
Slack variation, by additional springs with realize tensioning, due in a period of motion its tensile force be variation, 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 will affect in turn in this way, and
And kinetic characteristics are deteriorated；Therefore in practical projects, non-round belt (chain) transmission is rarely applied to accurately load high-speed drive
Occasion.
Summary of the invention
The purpose of the present invention is in view of the above problems, proposing that the self-compensating Bath main officer of Tibet of one kind amount of becoming slack is non-circular-sinusoidal non-
Circle-non-circular three-wheel toothed belt transmission design method provides a whole set of for non-circular synchronous pulley in practical applications and perfect sets
Theoretical basis is counted, realizes non-at the uniform velocity directly accurate transmission of the big center away between.The design method initially sets up synchronous belt principal and subordinate
The pitch curve equation of driving wheel, and synchronous belt pulley transmission ratio is moved using polar coordinates theoretical calculation principal and subordinate is cut；Then synchronous belt is calculated
Perimeter calculates non-circular the every of tensioning synchronous pulley pitch curve by alternative manner according to the variation of synchronous belt perimeter slack and joins
Number.
In order to solve the above technical problems, the technical scheme is that
The specific steps of the present invention are as follows:
Step 1: non-circular driven synchronous according to the transmission rule calculating non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet and sine
Belt wheel pitch curve equation；
The non-circular active synchronization belt wheel of Bath main officer of Tibet is the input link of uniform rotation, cuts polar equation:
In formula, r11、r12The respectively non-circular active synchronization belt wheel pitch curve first segment curve of Bath main officer of Tibet and second segment curve
It is denaturalized polar diameter, b1For the generation circular diameter of the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet, n1For the non-circular active synchronization band of Bath main officer of Tibet
Take turns the order of pitch curve, m11、m12For the change of Bath main officer of Tibet non-circular active synchronization belt wheel pitch curve first segment curve and second segment curve
Shape coefficient,For the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet polar diameter to moving coordinate system x1o1y1Middle x1The corner of axis, l are
The length of the non-circular pitch curve of Bath main officer of Tibet.
In formula, p1Diameter, θ are cut for the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet1For p1To moving coordinate system x1o1y1Middle x1
The corner cut of axis.
Sinusoidal non-circular driven synchronous pulley is the output wheel of synchronous belt, and pitch curve cuts polar equation are as follows:
In formula, r21For the polar diameter of sinusoidal non-circular driven synchronous pulley pitch curve, α is that sinusoidal non-circular driven synchronous pulley section is bent
Line parameter, A are sinusoidal amplitude,γ is positive chord joint parameter of curve, and taking γ=π/6, b is proportionality coefficient, a
It is the center of the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley pitch curve away from β is Bath main officer of Tibet
The relative rotation of non-circular active synchronization belt wheel pitch curve and sinusoidal non-circular driven synchronous pulley pitch curve, β=[0~2 π].p2For
Sinusoidal non-circular driven synchronous pulley pitch curve cuts diameter, θ2For p2To moving coordinate system x2o2y2Middle x2The corner cut of axis,For moving axes
It is x2o2y2Middle x2Axis is to quiet coordinate system xo1The corner of x-axis in y.
Step 2: calculating the transmission of the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley initial position
Than:
Initial position, the moving coordinate system x of the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet1o1y1Middle x1Axis is to quiet coordinate system
xo1The corner of x-axis in yThe moving coordinate system x of sinusoidal non-circular driven synchronous pulley pitch curve2o2y2Middle x2Axis is marked to sitting quietly
It is xo1The corner of x-axis in yAccording to cutting, polar coordinates are theoretical to be obtained:
In formula, p1(θ12) and p2(θ21) it is respectively that the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet and sine are non-circular driven same
Walk belt wheel pitch curve common tangent incision superius C1、C2It is corresponding to cut diameter, p1(θ13) and p3(θ31) it is respectively the non-circular active synchronization of Bath main officer of Tibet
Belt wheel pitch curve and tensioning synchronous pulley pitch curve common tangent incision superius C6、C5It is corresponding to cut diameter, p2(θ23) and p3(θ32) be respectively
Sinusoidal non-circular driven synchronous pulley pitch curve and tensioning synchronous pulley pitch curve common tangent incision superius C3、C4It is corresponding to cut diameter, θ120
Diameter p is cut for the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet1(θ12) with sinusoidal non-circular driven synchronous pulley pitch curve cut diameter p2
(θ21) arrive respective moving coordinate system trunnion axis corner initial value, θ130Diameter p is cut for the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet1
(θ13) with tensioning synchronous pulley pitch curve cut diameter p3(θ31) arrive respective moving coordinate system trunnion axis corner initial value, θ230It is sinusoidal non-
The driven synchronous pulley pitch curve of circle cuts diameter p2(θ23) with tensioning synchronous pulley pitch curve cut diameter p3(θ32) arrive respective moving coordinate system water
The corner initial value of flat axis, θ12、θ13The respectively non-circular active synchronization belt wheel pitch curve incision superius C of Bath main officer of Tibet1、C6Corresponding diameter of cutting is to moving
Coordinate system x1o1y1Middle x1The corner of axis, θ21、θ23Respectively sinusoidal non-circular driven synchronous pulley pitch curve incision superius C2、C3It is corresponding
Diameter is cut to moving coordinate system x2o2y2Middle x2The corner of axis, θ31、θ32Respectively it is tensioned synchronous pulley pitch curve incision superius C4、C5It is corresponding
Diameter is cut to moving coordinate system x3o3y3Middle x3The corner of axis, L1For the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven synchronous belt
Wheel center is away from L2It is sinusoidal non-circular driven synchronous pulley and tensioning synchronous pulley center away from L3For the non-circular active synchronization band of Bath main officer of Tibet
Wheel with tensioning synchronous pulley center away from；
The non-circular active synchronization belt wheel of initial position Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley instantaneous transmission ratio are as follows:
Step 3: calculating the non-circular active synchronization belt wheel of Bath main officer of Tibet, sinusoidal non-circular driven synchronous pulley and tensioning synchronous pulley
Common tangent segment length between every two-wheeled.
Initial time sets circle of the tensioning synchronous pulley pitch curve to give radius, the non-circular active synchronization belt wheel of Bath main officer of Tibet
With the common tangent segment length T between sinusoidal non-circular driven two point of contact of synchronous pulley0, sinusoidal non-circular driven synchronous pulley and tensioning it is same
Walk the common tangent segment length T between two point of contact of belt wheel1And the non-circular active synchronization belt wheel of Bath main officer of Tibet is cut with tensioning synchronous pulley two
Common tangent segment length T between point2It is respectively as follows:
In formula, p1'(θ120)、p1'(θ130) it is respectively p1(θ120)、p1(θ130) first differential, p'2(θ120)、p'2(θ230)
Respectively p2(θ120)、p2(θ230) first differential, p'3(θ130)、p'3(θ230) it is respectively p3(θ130)、p3(θ230) single order it is micro-
Point.
When the non-circular active synchronization belt wheel of Bath main officer of Tibet turns over angleSinusoidal non-circular driven synchronous pulley accordingly turns over angleThe non-circular active synchronization belt wheel pitch curve incision superius C of Bath main officer of Tibet1、C6Corresponding arc length variable quantity is s1、s6, sinusoidal non-circular driven
Synchronous pulley pitch curve incision superius C2、C3Corresponding arc length variable quantity is s2、s3, it is tensioned synchronous pulley pitch curve incision superius C4、C5
Corresponding arc length variable quantity is s4、s5.Then have:
In formula, p1″(θ1) it is p1(θ1) second-order differential, p '2′(θ2) it is p2(θ2) second-order differential, p '3′(θ3) it is p3
(θ3) second-order differential, θ3To be tensioned synchronous belt round cut diameter p3To moving coordinate system x3o3y3Middle x3The corner of axis.
Any time, the public affairs between the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven two point of contact of synchronous pulley are cut
Line segment length T12, common tangent segment length T between sinusoidal non-circular driven synchronous pulley and tensioning two point of contact of synchronous pulley23And
Common tangent segment length T between the non-circular active synchronization belt wheel of Bath main officer of Tibet and tensioning two point of contact of synchronous pulley13It is respectively as follows:
In formula, p1'(θ12)、p1'(θ13) it is respectively p1(θ12)、p1(θ13) first differential, p'2(θ21)、p'2(θ23) respectively
For p2(θ21)、p2(θ23) first differential, p'3(θ32)、p'3(θ31) it is respectively p3(θ32)、p3(θ31) first differential,To open
Tight synchronous pulley pitch curve moving coordinate system x3o3y3Middle x3Axis is to quiet coordinate system xo1The corner of x-axis in y.
Step 4: calculating the transmission of the non-circular active synchronization belt wheel of any time Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley
Than；
The non-circular active synchronization belt wheel uniform rotation of Bath main officer of Tibet, according to formula (2), (4) solve p1, p2, then instantaneous transmission ratio are as follows:
Step 5: calculating any time synchronous belt perimeter；
The non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet and tensioning synchronous pulley pitch curve common tangent incision superius are denoted as C6, appoint
Anticipate moment C1With C6Between arc length be c11, sinusoidal non-circular driven synchronous pulley pitch curve and tensioning synchronous pulley pitch curve common tangent
Incision superius is denoted as C3, any time C2With C3Between arc length be c22, it is tensioned synchronous pulley pitch curve and sinusoidal non-circular driven synchronous belt
Wheel pitch curve common tangent incision superius is denoted as C4, tensioning synchronous pulley pitch curve and the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet are public
Tangent line incision superius is denoted as C5, any time C4With C5Between arc length be c33。
Any time, synchronous belt perimeter are as follows:
C=T12+T13+T23+c11+c22+c33 (14)
Step 6: the free pitch curve of tensioning synchronous pulley calculates；
Iterative algorithm is as follows:
(a) setting tensioning synchronous pulley center of rotation, the radius for being tensioned synchronous pulley are set as variable, are tensioned synchronous pulley
Radius initial value is given, is denoted as r3-0, belt length initial value, which is calculated, according to formula (14) is denoted as C0。
(b) the non-circular active synchronization belt wheel of Bath main officer of Tibet turns over 1 °, is required to calculate sinusoidal non-circular driven synchronous belt according to transmission ratio
Wheel turns over corresponding angle, and the corner for being tensioned synchronous pulley is identical as the non-circular active synchronization belt wheel of Bath main officer of Tibet.Guaranteeing that C is constant
Under the premise of, corresponding tensioning synchronous pulley radius r when turning over 1 ° according to the non-circular active synchronization belt wheel of formula (14) reverse Bath main officer of Tibet3-1,
Correspond to the p at moment3。
(c) it repeats (b) 358 times, obtains when the non-circular active synchronization belt wheel of Bath main officer of Tibet turns over 2 °, 3 ° ..., 359 ° corresponding
Tight synchronous pulley radius is respectively r3-2, r3-3... ..., r3-359。
(d) 360 concentric circles are so far obtained, by the tensioning synchronous pulley radius in (a), (b) and (c), take one every 1 °
The radius of a circle sequentially takes 360 radiuses, to set tensioning synchronous pulley center of rotation as the center of circle, will take 360 radiuses
The outer end point is sequentially connected with, and composition one is closed non-circular.
(e) by obtained in (d) it is non-circular tensioning synchronous pulley each moment to diameter scale up or reduce so that newly
The perimeter of obtained non-circular tensioning synchronous pulley and the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley
Perimeter is equal.
(f) radius value at (e) obtained each moment is substituted into the belt length that formula (14) calculate each moment.
If (g) 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 step (h) is carried out.
(h) 5 ° before and after belt length maximum position corresponds to moment point, reduce non-circular tensioning synchronous pulley respectively to the 1 of diameter value
~5%, 5 ° before and after belt length minimum position corresponds to moment point, increase it is non-circular tensioning synchronous pulley respectively to diameter value 1~
5%, it is then fitted to obtain new non-circular tensioning synchronous pulley with B-spline.
(i) non-circular tensioning synchronous pulley each moment after (h) is scaled up or is reduced to diameter, so that newly obtaining
Non-circular tensioning synchronous pulley perimeter and the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley perimeter
It is equal.
(j) it the non-circular tensioning synchronous pulley after (i) is substituted into formula (14) to diameter is calculated each moment and correspond to synchronous belt
Belt length is walked if each moment corresponds to synchronous belt belt length and the absolute value of the difference of synchronous belt perimeter initial value is respectively less than preset value
Suddenly (k), otherwise (h) is returned to.
(k) establish each moment of non-circular tensioning synchronous pulley to diameter and corresponding cornerRelationship is to be tensioned synchronous pulley
Pitch curve equation.
The invention has the benefit that
1, the present invention is that non-circular-sinusoidal non-circular-non-circular three-wheel toothed belt transmission of the self-compensating Bath main officer of Tibet of the amount of becoming slack exists
A whole set of perfect design theory basis is provided in practical application, can be applied to all Bath main officer of Tibets it is non-circular-sinusoidal it is non-circular-
Non-circular three-wheel synchronous belt drive mechanism, the popularization for promoting non-circular-sinusoidal non-circular-non-circular three-wheel toothed belt transmission of Bath main officer of Tibet make
With.
2, driving wheel pitch curve is Bath main officer of Tibet curve in the present invention, and driven wheel pitch curve is sinusoidal pattern curve, and Bath main officer of Tibet is bent
Four generation circular diameter, length, deformation coefficient and order variables of line, the amplitude of sinusoidal non-circular driven synchronous pulley pitch curve and
α, b and β are controlled variable, can change the shape of driving wheel and driven wheel pitch curve by the adjusting of this tittle, are met more
Specific non-be at the uniform velocity driven.
3, the present invention is easily programmed realization using the exact value for cutting polar coordinates theoretical calculation transmission ratio, and solving precision is high, side
Just quick.
4, the tensioning synchronous pulley in the present invention is the non-circular synchronous pulley of free pitch curve, can be with real-time compensation Bath main officer of Tibet
The belt sag variable quantity generated during non-circular active synchronization belt wheel and sinusoidal non-circular driven synchronous belt pulley transmission, realizes big center
Non- at the uniform velocity directly accurate transmission away between.
Detailed description of the invention
Fig. 1 is transmission schematic diagram of the invention；
Fig. 2 is the transmission of the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley in the embodiment of the present invention
Than with the non-circular active synchronization belt wheel angle relation curve graph of Bath main officer of Tibet；
Synchronous belt belt length change curve when Fig. 3 is the pitch curve using the non-circular tensioning synchronous pulley in the embodiment of the present invention
Figure；
Fig. 4 is the non-circular active synchronization belt wheel pitch curve figure of Bath main officer of Tibet in the embodiment of the present invention；
Fig. 5 is sinusoidal non-circular driven synchronous pulley pitch curve figure in the embodiment of the present invention；
Fig. 6 is the tensioning free pitch curve figure of synchronous pulley in the embodiment of the present invention.
Specific embodiment
With reference to the accompanying drawing and case study on implementation the invention will be further described.
Non-circular-sinusoidal non-circular-non-circular three-wheel toothed belt transmission design method of Bath main officer of Tibet, the specific steps are as follows:
Step 1: such as Fig. 1, the non-circular active synchronization belt wheel pitch curve base circle diameter (BCD) b of Bath main officer of Tibet1=10mm, length l=
40mm, three-wheel center is away from L1=L2=L3=100mm, the order n of the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet1=1, Bath
The deformation coefficient m of main officer of Tibet non-circular active synchronization belt wheel pitch curve first segment curve and second segment curve11=m12=1, three-wheel is isoperimetric
Long closing convex curve, calculates the non-circular active synchronization belt wheel pitch curve polar diameter of Bath main officer of Tibet according to formula (1):
In formula,For the non-circular active synchronization belt wheel pitch curve moving coordinate system x of Bath main officer of Tibet1o1y1Middle x1Axis is to quiet coordinate system xo1y
The corner of middle x-axis.
The non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet cuts polar equation are as follows:
The non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet is as shown in Figure 4.
Step 2: sinusoidal non-circular driven synchronous pulley is output link, output rule determines sinusoidal non-circular driven same
Step belt wheel pitch curve cuts polar equation, gives sinusoidal non-circular driven synchronous pulley pitch curve parameter alpha=π/4, A is sine curve
Amplitude,γ is positive chord joint parameter of curve, takes γ=π/6, and proportionality coefficient b=cos α is then sinusoidal non-circular driven same
Walk belt wheel pitch curve equation are as follows:
r21=50 × [1+0.5773 × cos (0.7071 × β)] (3)
In formula, r21For the polar diameter of sinusoidal non-circular driven synchronous pulley pitch curve, β be the non-circular active synchronization belt wheel of Bath main officer of Tibet with
The relative rotation of sinusoidal non-circular driven synchronous pulley, β=[0~2 π].
In formula, p2Diameter, θ are cut for sinusoidal non-circular driven synchronous pulley pitch curve2To cut diameter p2To moving coordinate system x2o2y2Middle x2
The corner of axis,For sinusoidal non-circular driven synchronous pulley pitch curve moving coordinate system x2o2y2Middle x2Axis is to quiet coordinate system xo1X-axis in y
Corner.Sinusoidal non-circular driven synchronous pulley pitch curve such as Fig. 5.
Step 3: calculating the transmission of the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley initial position
Than:
Initial position, the moving coordinate system x of the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet1o1y1Middle x1Axis is to quiet coordinate system
xo1The corner of x-axis in yThe moving coordinate system x of sinusoidal non-circular driven synchronous pulley pitch curve2o2y2Middle x2Axis is marked to sitting quietly
It is xo1The corner of x-axis in yAccording to cutting, polar coordinates are theoretical to be obtained:
In formula, p1(θ12) and p2(θ21) it is respectively that the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet and sine are non-circular driven same
Walk belt wheel pitch curve common tangent incision superius C1、C2It is corresponding to cut diameter, p1(θ13) and p3(θ31) it is respectively the non-circular active synchronization of Bath main officer of Tibet
Belt wheel pitch curve and tensioning synchronous pulley pitch curve common tangent incision superius C6、C5It is corresponding to cut diameter, p2(θ23) and p3(θ32) be respectively
Sinusoidal non-circular driven synchronous pulley pitch curve and tensioning synchronous pulley pitch curve common tangent incision superius C3、C4It is corresponding to cut diameter, θ120
Diameter p is cut for the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet1(θ12) with sinusoidal non-circular driven synchronous pulley pitch curve cut diameter p2
(θ21) arrive respective moving coordinate system trunnion axis corner initial value, θ130Diameter p is cut for the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet1
(θ13) with tensioning synchronous pulley pitch curve cut diameter p3(θ31) arrive respective moving coordinate system trunnion axis corner initial value, θ230It is sinusoidal non-
The driven synchronous pulley pitch curve of circle cuts diameter p2(θ23) with tensioning synchronous pulley pitch curve cut diameter p3(θ32) arrive respective moving coordinate system water
The corner initial value of flat axis, θ12、θ13The respectively non-circular active synchronization belt wheel pitch curve incision superius C of Bath main officer of Tibet1、C6Corresponding diameter of cutting is to moving
Coordinate system x1o1y1Middle x1The corner of axis, θ21、θ23Respectively sinusoidal non-circular driven synchronous pulley pitch curve incision superius C2、C3It is corresponding
Diameter is cut to moving coordinate system x2o2y2Middle x2The corner of axis, θ31、θ32Respectively it is tensioned synchronous pulley pitch curve incision superius C4、C5It is corresponding
Diameter is cut to moving coordinate system x3o3y3Middle x3The corner of axis, L1For the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven synchronous belt
Wheel center is away from L2It is sinusoidal non-circular driven synchronous pulley and tensioning synchronous pulley center away from L3For the non-circular active synchronization band of Bath main officer of Tibet
Wheel with tensioning synchronous pulley center away from；
It is i according to the instantaneous transmission ratio that formula (6) calculate initial position120=0.6340:
Step 4: calculating the non-circular active synchronization belt wheel of Bath main officer of Tibet, sinusoidal non-circular driven synchronous pulley and tensioning synchronous pulley
Common tangent segment length between every two-wheeled.
Initial time sets circle of the tensioning synchronous pulley pitch curve to give radius, the non-circular active synchronization belt wheel of Bath main officer of Tibet
With the common tangent segment length T between sinusoidal non-circular driven two point of contact of synchronous pulley0, sinusoidal non-circular driven synchronous pulley and tensioning it is same
Walk the common tangent segment length T between two point of contact of belt wheel1And the non-circular active synchronization belt wheel of Bath main officer of Tibet is cut with tensioning synchronous pulley two
Common tangent segment length T between point is respectively as follows:
In formula, p1'(θ120)、p1'(θ130) it is respectively p1(θ120)、p1(θ130) first differential, p'2(θ120)、p'2(θ230)
Respectively p2(θ120)、p2(θ230) first differential, p'3(θ130)、p'3(θ230) it is respectively p3(θ130)、p3(θ230) single order it is micro-
Point.
T is calculated to obtain according to formula (7)0=102.6370mm, T1=105.4651mm, T2=101.5862mm.
When the non-circular active synchronization belt wheel of Bath main officer of Tibet turns over angleSinusoidal non-circular driven synchronous pulley accordingly turns over angleThe non-circular active synchronization belt wheel pitch curve incision superius C of Bath main officer of Tibet1、C6Corresponding arc length variable quantity is s1、s6, sinusoidal non-circular driven
Synchronous pulley pitch curve incision superius C2、C3Corresponding arc length variable quantity is s2、s3, it is tensioned synchronous pulley pitch curve incision superius C4、C5
Corresponding arc length variable quantity is s4、s5.Then have:
In formula, p1″(θ1) it is p1(θ1) second-order differential, p '2′(θ2) it is p2(θ2) second-order differential, p '3′(θ3) it is p3
(θ3) second-order differential, θ3To be tensioned synchronous belt round cut diameter p3To moving coordinate system x3o3y3Middle x3The corner cut of axis.
Any time, the public affairs between the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven two point of contact of synchronous pulley are cut
Line segment length T12, common tangent segment length T between sinusoidal non-circular driven synchronous pulley and tensioning two point of contact of synchronous pulley23And
Common tangent segment length T between the non-circular active synchronization belt wheel of Bath main officer of Tibet and tensioning two point of contact of synchronous pulley13It is respectively as follows:
In formula, p1'(θ12)、p1'(θ13) it is respectively p1(θ12)、p1(θ13) first differential, p'2(θ21)、p'2(θ23) respectively
For p2(θ21)、p2(θ23) first differential, p'3(θ32)、p'3(θ31) it is respectively p3(θ32)、p3(θ31) first differential,For
It is tensioned synchronous pulley pitch curve moving coordinate system x3o3y3Middle x3Axis is to quiet coordinate system xo1The corner of x-axis in y.
Step 5: calculating the transmission of the non-circular active synchronization belt wheel of any time Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley
Than；
The non-circular active synchronization belt wheel of Bath main officer of Tibet be uniform rotation, calculate the non-circular active synchronization belt wheel of Bath main officer of Tibet and sine it is non-
The driven synchronous pulley instantaneous transmission ratio of circle:
According to formula (10), (11), (12), when the calculating non-circular active synchronization belt wheel of Bath main officer of Tibet rotates a circle, instantaneous transmission ratio
It is as shown in Figure 2 with the non-circular active synchronization belt wheel angle relation curve of Bath main officer of Tibet.
Step 6: calculating synchronous belt perimeter；
The non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet and tensioning synchronous pulley pitch curve common tangent incision superius are denoted as C6, appoint
Anticipate moment C1With C6Between arc length be c11, the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley pitch curve are public
Tangent line incision superius is denoted as C2, sinusoidal non-circular driven synchronous pulley pitch curve and tensioning synchronous pulley pitch curve common tangent incision superius are remembered
For C3, any time C2With C3Between arc length be c22, it is tensioned synchronous pulley pitch curve and sinusoidal non-circular driven synchronous pulley pitch curve
Common tangent incision superius is denoted as C4, it is tensioned on synchronous pulley pitch curve and the non-circular active synchronization belt wheel pitch curve common tangent of Bath main officer of Tibet and cuts
Point is denoted as C5, any time C4With C5Between arc length be c33。
Any time, synchronous belt perimeter are as follows:
C=T12+T13+T23+c11+c22+c33 (14)
Initial time is C according to the original perimeter that formula (14) calculate synchronous belt0=682.4570mm；
Each timing synchronization band belt length, each timing synchronization when driving wheel rotates 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 calculates；
Iterative algorithm is as follows:
(a) known to be tensioned synchronous pulley center of rotation, the radius for being tensioned synchronous pulley is set as variable r3, it is tensioned synchronous belt
Wheel radius initial value is denoted as r3-0=30mm, synchronous belt original perimeter C0=682.4570mm.
(b) the non-circular active synchronization belt wheel of Bath main officer of Tibet turns overSuch as Fig. 2, according to the non-circular active synchronization belt wheel of Bath main officer of Tibet with
Sinusoidal non-circular driven synchronous belt pulley transmission calculates sinusoidal non-circular driven synchronous pulley pitch curve and turns over corresponding angle than relationshipThe corner for being tensioned synchronous pulley pitch curve is identical as the non-circular active synchronization belt wheel pitch curve of Bath main officer of TibetUnder the premise of guaranteeing that synchronous belt perimeter C is constant, r is calculated3-1=40.1564mm.
(c) it repeats (b) 358 times, obtains r3-2, r3-3... ..., r3-359。
(d) 360 concentric circles are so far obtained, by the tensioning synchronous pulley radius in (a), (b) and (c), take one every 1 °
The radius of a circle sequentially takes 360 radiuses, to set tensioning synchronous pulley center of rotation as the center of circle, will take 360 radiuses
The outer end point is sequentially connected with, and composition one is closed non-circular.
(e) scaling up each point of non-circular tensioning synchronous pulley obtained in (d) or reduce to diameter, so that new
The week of the perimeter and the non-circular active synchronization belt wheel of Bath main officer of Tibet of the non-circular tensioning synchronous pulley arrived and sinusoidal non-circular driven synchronous pulley
Length is equal.
(f) radius value at (e) obtained each moment is substituted into formula (14) and calculates corresponding belt length of each moment.
If (g) 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 step (h) is carried out.
(h) 5 ° before and after belt length maximum position corresponds to moment point, reduce non-circular tensioning synchronous pulley respectively to diameter value
3%, 5 ° before and after belt length minimum position corresponds to moment point, increase non-circular tensioning synchronous pulley respectively to the 3% of diameter value, then
It is fitted to obtain new non-circular tensioning synchronous pulley with B-spline.
(i) non-circular tensioning synchronous pulley each point after (h) is scaled up or is reduced to diameter, so that newly obtain
The perimeter of non-circular tensioning synchronous pulley and the perimeter of the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley are equal
It is equal.
(j) the non-circular tensioning synchronous pulley that (i) is obtained is substituted into formula (14) to diameter and each moment belt length is calculated, if respectively
The absolute value of the difference of the belt length at a moment and initial belt length is respectively less than preset value, carries out step (k), otherwise returns to (h).
(k) establish each moment of non-circular tensioning synchronous pulley to diameter and corresponding cornerRelationship is to be tensioned synchronous pulley
Pitch curve equation.Three pitch curves taken turns and phase angle, center of rotation all determine, calculate tensioning synchronous pulley and Bath main officer of Tibet is non-circular
Active synchronization belt wheel, the corresponding angle relation of sinusoidal non-circular driven synchronous pulley.
Tensioning synchronous pulley pitch curve such as Fig. 6 after calculating.
Synchronous belt theory belt length variable quantity is 11.86mm in the embodiment, is the 2.23% of synchronous belt total length, because of band
It needs to be tensioned, can satisfy actual operation requirements.
Claims (1)
1. non-circular-sinusoidal non-circular-non-circular three-wheel toothed belt transmission design method of Bath main officer of Tibet, it is characterised in that: this method is specific
It is as follows:
Step 1: calculating the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley according to transmission rule
Pitch curve equation；
The non-circular active synchronization belt wheel of Bath main officer of Tibet is the input link of uniform rotation, cuts polar equation:
In formula, r11、r12The respectively denaturation of Bath main officer of Tibet non-circular active synchronization belt wheel pitch curve first segment curve and second segment curve
Polar diameter, b1For the generation circular diameter of the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet, n1For the non-circular active synchronization belt wheel section of Bath main officer of Tibet
Order of a curve number, m11、m12For the deformation system of Bath main officer of Tibet non-circular active synchronization belt wheel pitch curve first segment curve and second segment curve
Number,For the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet polar diameter to moving coordinate system x1o1y1Middle x1The corner of axis, moving coordinate system
x1o1y1Origin be arranged at the center of rotation of the non-circular active synchronization belt wheel of Bath main officer of Tibet, l be the non-circular pitch curve of Bath main officer of Tibet exhibition
It is long；
In formula, p1Diameter, θ are cut for the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet1For p1To moving coordinate system x1o1y1Middle x1Axis is cut
Angle；
Sinusoidal non-circular driven synchronous pulley is the output wheel of synchronous belt, and pitch curve cuts polar equation are as follows:
In formula, r21For the polar diameter of sinusoidal non-circular driven synchronous pulley pitch curve, α is sinusoidal non-circular driven synchronous pulley pitch curve ginseng
Number, A are sinusoidal amplitude,γ is positive chord joint parameter of curve, and taking γ=π/6, b is proportionality coefficient, and a is bar
The center of the non-circular active synchronization belt wheel pitch curve of this main officer of Tibet and sinusoidal non-circular driven synchronous pulley pitch curve is away from β is that Bath main officer of Tibet is non-circular
The relative rotation of active synchronization belt wheel pitch curve and sinusoidal non-circular driven synchronous pulley pitch curve, β=[0~2 π]；p2For sine
Non-circular driven synchronous pulley pitch curve cuts diameter, θ2For p2To moving coordinate system x2o2y2Middle x2The corner cut of axis,For moving coordinate system
x2o2y2Middle x2Axis is to quiet coordinate system xo1The corner of x-axis in y, moving coordinate system x2o2y2Origin setting in sinusoidal non-circular driven synchronization
At the center of rotation of belt wheel, quiet coordinate system xo1The origin of y is arranged at the center of rotation of the non-circular active synchronization belt wheel of Bath main officer of Tibet；
Step 2: calculating the transmission ratio of the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley initial position:
Initial position, the moving coordinate system x of the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet1o1y1Middle x1Axis is to quiet coordinate system xo1In y
The corner of x-axisThe moving coordinate system x of sinusoidal non-circular driven synchronous pulley pitch curve2o2y2Middle x2Axis is to quiet coordinate system xo1y
The corner of middle x-axisAccording to cutting, polar coordinates are theoretical to be obtained:
In formula, p1(θ12) and p2(θ21) it is respectively the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet and sinusoidal non-circular driven synchronous belt
Take turns pitch curve common tangent incision superius C1、C2It is corresponding to cut diameter, p1(θ13) and p3(θ31) it is respectively the non-circular active synchronization belt wheel of Bath main officer of Tibet
Pitch curve and tensioning synchronous pulley pitch curve common tangent incision superius C6、C5It is corresponding to cut diameter, p2(θ23) and p3(θ32) it is respectively sine
Non-circular driven synchronous pulley pitch curve and tensioning synchronous pulley pitch curve common tangent incision superius C3、C4It is corresponding to cut diameter, θ120For bar
The non-circular active synchronization belt wheel pitch curve of this main officer of Tibet cuts diameter p1(θ12) with sinusoidal non-circular driven synchronous pulley pitch curve cut diameter p2(θ21) arrive
The corner initial value of respective moving coordinate system trunnion axis, θ130Diameter p is cut for the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet1(θ13) and
Tight synchronous pulley pitch curve cuts diameter p3(θ31) arrive respective moving coordinate system trunnion axis corner initial value, θ230It is sinusoidal non-circular driven same
Step belt wheel pitch curve cuts diameter p2(θ23) with tensioning synchronous pulley pitch curve cut diameter p3(θ32) turn to respective moving coordinate system trunnion axis
Angle initial value, θ12、θ13The respectively non-circular active synchronization belt wheel pitch curve incision superius C of Bath main officer of Tibet1、C6Correspondence cuts diameter to moving coordinate system
x1o1y1Middle x1The corner of axis, θ21、θ23Respectively sinusoidal non-circular driven synchronous pulley pitch curve incision superius C2、C3Correspondence is cut diameter and is arrived
Moving coordinate system x2o2y2Middle x2The corner of axis, θ31、θ32Respectively it is tensioned synchronous pulley pitch curve incision superius C4、C5Correspondence is cut diameter and is arrived
Moving coordinate system x3o3y3Middle x3The corner of axis, moving coordinate system x3o3y3Origin be arranged in tensioning synchronous pulley center of rotation at, L1
It is the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley center away from L2For sinusoidal non-circular driven synchronous pulley
With tensioning synchronous pulley center away from L3For the non-circular active synchronization belt wheel of Bath main officer of Tibet and tensioning synchronous pulley center away from；
The non-circular active synchronization belt wheel of initial position Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley instantaneous transmission ratio are as follows:
Step 3: calculating the non-circular active synchronization belt wheel of Bath main officer of Tibet, sinusoidal non-circular driven synchronous pulley and tensioning synchronous pulley every two
Common tangent segment length between wheel；
Initial time, sets the circle that tensioning synchronous pulley pitch curve is given radius, the non-circular active synchronization belt wheel of Bath main officer of Tibet and just
Common tangent segment length T between non-circular driven two point of contact of synchronous pulley of string0, sinusoidal non-circular driven synchronous pulley and tensioning synchronous belt
Take turns the common tangent segment length T between two point of contacts1And the non-circular active synchronization belt wheel of Bath main officer of Tibet and tensioning two point of contact of synchronous pulley it
Between common tangent segment length T2It is respectively as follows:
In formula, p '1(θ120)、p′1(θ130) it is respectively p1(θ120)、p1(θ130) first differential, p'2(θ120)、p'2(θ230) respectively
For p2(θ120)、p2(θ230) first differential, p'3(θ130)、p'3(θ230) it is respectively p3(θ130)、p3(θ230) first differential；
When the non-circular active synchronization belt wheel of Bath main officer of Tibet turns over angleSinusoidal non-circular driven synchronous pulley accordingly turns over angleBar
The non-circular active synchronization belt wheel pitch curve incision superius C of this main officer of Tibet1、C6Corresponding arc length variable quantity is s1、s6, sinusoidal non-circular driven synchronization
Belt wheel pitch curve incision superius C2、C3Corresponding arc length variable quantity is s2、s3, it is tensioned synchronous pulley pitch curve incision superius C4、C5It is corresponding
Arc length variable quantity be s4、s5；Then have:
In formula, p "1(θ1) it is p1(θ1) second-order differential, p "2(θ2) it is p2(θ2) second-order differential, p "3(θ3) it is p3(θ3) two
Rank differential, θ3To be tensioned synchronous belt round cut diameter p3To moving coordinate system x3o3y3Middle x3The corner of axis；
Any time, the common tangent section between the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven two point of contact of synchronous pulley
Length T12, common tangent segment length T between sinusoidal non-circular driven synchronous pulley and tensioning two point of contact of synchronous pulley23And Bath
Common tangent segment length T between the non-circular active synchronization belt wheel of main officer of Tibet and tensioning two point of contact of synchronous pulley13It is respectively as follows:
In formula, p '1(θ12)、p′1(θ13) it is respectively p1(θ12)、p1(θ13) first differential, p'2(θ21)、p'2(θ23) it is respectively p2
(θ21)、p2(θ23) first differential, p'3(θ32)、p'3(θ31) it is respectively p3(θ32)、p3(θ31)
First differential,To be tensioned synchronous pulley pitch curve moving coordinate system x3o3y3Middle x3Axis is to quiet coordinate system xo1X-axis turns in y
Angle；
Step 4: calculating the transmission ratio of the non-circular active synchronization belt wheel of any time Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley；
The non-circular active synchronization belt wheel uniform rotation of Bath main officer of Tibet, according to formula (2), (4) solve p1, p2, then instantaneous transmission ratio are as follows:
Step 5: calculating any time synchronous belt perimeter；
The non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet and tensioning synchronous pulley pitch curve common tangent incision superius are denoted as C6, when any
Carve C1With C6Between arc length be c11, sinusoidal non-circular driven synchronous pulley pitch curve cuts with being tensioned on synchronous pulley pitch curve common tangent
Point is denoted as C3, any time C2With C3Between arc length be c22, it is tensioned synchronous pulley pitch curve and sinusoidal non-circular driven synchronous pulley section
Curve tangent incision superius is denoted as C4, it is tensioned synchronous pulley pitch curve and the non-circular active synchronization belt wheel pitch curve common tangent of Bath main officer of Tibet
Incision superius is denoted as C5, any time C4With C5Between arc length be c33；
Any time, synchronous belt perimeter are as follows:
C=T12+T13+T23+c11+c22+c33 (14)
Step 6: the free pitch curve of tensioning synchronous pulley calculates；
Iterative algorithm is as follows:
(a) setting tensioning synchronous pulley center of rotation, the radius for being tensioned synchronous pulley are set as variable, are tensioned synchronous pulley radius
Initial value is given, is denoted as r3-0, belt length initial value, which is calculated, according to formula (14) is denoted as C0；
(b) the non-circular active synchronization belt wheel of Bath main officer of Tibet turns over 1 °, is required to calculate sinusoidal non-circular driven synchronous belt rotation according to transmission ratio
Corresponding angle is crossed, the corner for being tensioned synchronous pulley is identical as the non-circular active synchronization belt wheel of Bath main officer of Tibet；Guaranteeing the constant premise of C
Under, corresponding tensioning synchronous pulley radius r when turning over 1 ° according to the non-circular active synchronization belt wheel of formula (14) reverse Bath main officer of Tibet3-1Pair, i.e.,
Answer the p at moment3；
(c) it repeats (b) 358 times, obtains the non-circular active synchronization belt wheel of Bath main officer of Tibet and turn over corresponding at 2 °, 3 ° ..., 359 ° be tensioned together
Walking belt wheel radius is respectively r3-2, r3-3... ..., r3-359；
(d) 360 concentric circles are so far obtained, by the tensioning synchronous pulley radius in (a), (b) and (c), a circle is taken every 1 °
Radius, sequentially take 360 radiuses, using set tensioning synchronous pulley center of rotation as the center of circle, the outer end of 360 radiuses will be taken
Point is sequentially connected with, and composition one is closed non-circular；
(e) by obtained in (d) it is non-circular tensioning synchronous pulley each moment to diameter scale up or reduce so that newly obtaining
Non-circular tensioning synchronous pulley perimeter and the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley perimeter
It is equal；
(f) radius value at (e) obtained each moment is substituted into the belt length that formula (14) calculate each moment；
If (g) 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
It carries out step (h)；
(h) 5 ° before and after belt length maximum position corresponds to moment point, reduce it is non-circular tensioning synchronous pulley respectively to diameter value 1~
5%, 5 ° before and after belt length minimum position corresponds to moment point, increase non-circular tensioning synchronous pulley respectively to the 1~5% of diameter value,
Then it is fitted to obtain new non-circular tensioning synchronous pulley with B-spline；
(i) non-circular tensioning synchronous pulley each moment after (h) is scaled up or is reduced to diameter, so that is newly obtained is non-
The perimeter of circle tensioning synchronous pulley and the perimeter of the non-circular active synchronization belt wheel of Bath main officer of Tibet and sinusoidal non-circular driven synchronous pulley are homogeneous
Deng；
(j) it the non-circular tensioning synchronous pulley after (i) is substituted into formula (14) to diameter is calculated each moment and correspond to synchronous belt belt length,
If each moment corresponds to synchronous belt belt length and the absolute value of the difference of synchronous belt perimeter initial value is respectively less than preset value, carry out step (k),
Otherwise (h) is returned to；
(k) establish each moment of non-circular tensioning synchronous pulley to diameter and corresponding cornerRelationship is to be tensioned synchronous pulley section song
Line equation.
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