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, p1(θ12) and p2(θ21) 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, p1(θ13) and p3(θ31) 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, p2(θ23) and p3(θ32) 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 p1(θ12) cut footpath p with oval driven synchronous pulley pitch curve2(θ21) to respective moving coordinate system trunnion axis corner at the beginning of
Value, θ130For round active synchronization belt wheel pitch curve cuts footpath p1(θ13) cut footpath p with tensioning synchronous pulley pitch curve3(θ31) to each
The corner initial value of moving coordinate system trunnion axis, θ230For oval driven synchronous pulley pitch curve cuts footpath p2(θ23) and tensioning synchronous pulley
Pitch curve cuts footpath p3(θ32) 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 '1(θ120)、p′1(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 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 "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)
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 '1(θ12)、p′1(θ13) it is respectively p1(θ12)、p1(θ13) first differential, p'2(θ21)、p'2(θ23) respectively
It is 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 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, p1(θ12) and p2(θ21) 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, p1(θ13) and p3(θ31) 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, p2(θ23) and p3(θ32) 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 p1(θ12) cut footpath p with oval driven synchronous pulley pitch curve2(θ21) to respective moving coordinate system trunnion axis corner at the beginning of
Value, θ130For round active synchronization belt wheel pitch curve cuts footpath p1(θ13) cut footpath p with tensioning synchronous pulley pitch curve3(θ31) to each
The corner initial value of moving coordinate system trunnion axis, θ230For oval driven synchronous pulley pitch curve cuts footpath p2(θ23) and tensioning synchronous pulley
Pitch curve cuts footpath p3(θ32) 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 "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)
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 '1(θ12)、p′1(θ13) it is respectively p1(θ12)、p1(θ13) first differential, p'2(θ21)、p'2(θ23) respectively
It is 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 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.