CN106907435B - Free non-circular-non-circular three-wheel toothed belt transmission design method of circle- - Google Patents
Free non-circular-non-circular three-wheel toothed belt transmission design method of circle- Download PDFInfo
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- CN106907435B CN106907435B CN201710191357.6A CN201710191357A CN106907435B CN 106907435 B CN106907435 B CN 106907435B CN 201710191357 A CN201710191357 A CN 201710191357A CN 106907435 B CN106907435 B CN 106907435B
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H7/00—Gearings for conveying rotary motion by endless flexible members
- F16H7/02—Gearings for conveying rotary motion by endless flexible members with belts; with V-belts
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
Abstract
The invention discloses non-circular-non-circular three-wheel toothed belt transmission design methods of circle-freedom.The invention firstly uses polar coordinates theoretical calculation is cut, according to given principal and subordinate wheel transmission ratio, the pitch curve equation of synchronous belt principal and subordinate wheel is established；Then the perimeter for calculating synchronous belt, changes according to synchronous belt perimeter slack and obtains non-circular tensioning synchronous pulley pitch curve by iterative algorithm.Tensioning wheel of the invention is the non-circular synchronous pulley of free pitch curve, the belt sag variable quantity that can be generated during non-circular driven synchronous belt pulley transmission with the round active synchronization belt wheel of real-time compensation and freely overcomes the problems, such as that the non-circular V belt translation of traditional two-wheeled cannot meet non-at the uniform velocity transmission and real-time tensioning simultaneously.Driven wheel pitch curve of the present invention is free non-circular pitch curve, and not by the constraint of specific curves form, flexible design can satisfy the more free center greatly of transmission ratio variation and at the uniform velocity be driven away from non-.
Description
Technical field
The present invention relates to a kind of design methods of non-circular toothed belt transmission, and in particular to one kind amount of becoming slack is self-compensating
Free non-circular-non-circular three-wheel toothed belt transmission design method of circle-.
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 circle-freedom of one kind amount of becoming slack is non-circular-non-circular
Three-wheel toothed belt transmission design method provides a whole set of perfect design theory base for non-circular synchronous pulley in practical applications
Plinth realizes non-at the uniform velocity directly accurate transmission of the big center away between.The design method is first with cutting polar coordinates theoretical calculation, root
According to given principal and subordinate wheel transmission ratio, the pitch curve equation of synchronous belt principal and subordinate wheel is established；Then the perimeter for calculating synchronous belt, according to
The variation of synchronous belt perimeter slack calculates the parameters of non-circular tensioning synchronous pulley pitch curve by alternative manner.
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: round active synchronization belt wheel is the input link of uniform rotation, polar equation is cut are as follows:
p1=r (1)
S=2 π × r (2)
In formula, p1For the diameter of cutting of round active synchronization belt wheel pitch curve, r is the half of round active synchronization belt wheel pitch curve
Diameter, s are the perimeter of round active synchronization belt wheel pitch curve.
Step 2: calculating freely non-circular driven synchronous pulley pitch curve equation；
Determine round active synchronization belt wheel pitch curve and freely non-circular driven synchronous pulley pitch curve angle relation:
In formula,For the moving coordinate system x of round active synchronization belt wheel pitch curve1o1y1Middle x1Axis is to quiet coordinate system xo1X in y
The corner of axis,For the moving coordinate system x of freely non-circular driven synchronous pulley pitch curve2o2y2Middle x2Axis is to quiet coordinate system xo1X in y
The corner of axis, i12For given round active synchronization belt wheel and free non-circular driven synchronous belt pulley transmission ratio；
There are following relationships with corner for round active synchronization belt wheel and the freely corner cut of non-circular driven synchronous pulley
In formula, θ1For p1To moving coordinate system x1o1y1Middle x1The corner of axis, θ2For freely non-circular driven synchronous pulley pitch curve
Cut diameter p2To moving coordinate system x2o2y2Middle x2The corner of axis；
In formula, L1For round active synchronization belt wheel and freely non-circular driven synchronous pulley center away from.
p2=i12×p1 (6)
Step 3: calculating, round active synchronization belt wheel, freely non-circular driven synchronous pulley and non-circular tensioning synchronous pulley are every
Common tangent segment length between two-wheeled.
Initial time, the moving coordinate system x of round active synchronization belt wheel pitch curve1o1y1Middle x1Axis is to quiet coordinate system xo1X in y
The corner of axisThe freely moving coordinate system x of 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 round active synchronization belt wheel pitch curve and free non-circular driven synchronous pulley
Pitch curve common tangent incision superius C1、C2It is corresponding to cut diameter, p1(θ13) and p3(θ31) be respectively round active synchronization belt wheel pitch curve with
Non-circular tensioning synchronous pulley pitch curve common tangent incision superius C6、C5It is corresponding to cut diameter, p2(θ23) and p3(θ32) it is respectively freely non-circular
Driven synchronous pulley pitch curve and non-circular tensioning synchronous pulley pitch curve common tangent incision superius C3、C4It is corresponding to cut diameter, θ120For circle
Type active synchronization belt wheel pitch curve cuts diameter p1(θ12) and freely non-circular driven synchronous pulley pitch curve cuts diameter p2(θ21) to each automatic
The corner initial value of coordinate system trunnion axis, θ130Diameter p is cut for round active synchronization belt wheel pitch curve1(θ13) and non-circular tensioning synchronous belt
Wheel pitch curve cuts diameter p3(θ31) arrive respective moving coordinate system trunnion axis corner initial value, θ230For freely non-circular driven synchronous pulley section
Curve cuts diameter p2(θ23) with non-circular tensioning synchronous pulley pitch curve cut diameter p3(θ32) to respective moving coordinate system trunnion axis corner at the beginning of
Value, θ12、θ13Respectively round active synchronization belt wheel pitch curve incision superius C1、C6Correspondence cuts diameter to moving coordinate system x1o1y1Middle x1Axis
Corner, θ21、θ23Respectively freely non-circular driven synchronous pulley pitch curve incision superius C2、C3Correspondence cuts diameter to moving coordinate system
x2o2y2Middle x2The corner of axis, θ31、θ32Respectively non-circular tensioning synchronous pulley pitch curve incision superius C4、C5Corresponding diameter of cutting is sat to dynamic
Mark system x3o3y3Middle x3The corner of axis, L1It is round active synchronization belt wheel and free non-circular driven synchronous pulley center away from L2For certainly
By non-circular driven synchronous pulley and non-circular tensioning synchronous pulley center away from L3It is synchronous with non-circular tensioning for round active synchronization belt wheel
Center distance of belt wheel；
Initial time, sets the circle that non-circular tensioning synchronous pulley pitch curve is given radius, round active synchronization belt wheel and
The freely common tangent segment length T between non-circular driven two point of contact of synchronous pulley0, freely non-circular driven synchronous pulley and non-circular tensioning
Common tangent segment length T between two point of contact of synchronous pulley1And round active synchronization belt wheel is cut with non-circular tensioning synchronous pulley two
Common tangent segment length T between point2It 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 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 angleFreely non-circular driven synchronous pulley accordingly turns over angleIt is round
Active synchronization belt wheel pitch curve incision superius C1、C6Corresponding arc length variable quantity is s1、s6, freely non-circular driven synchronous pulley section is bent
Line incision superius C2、C3Corresponding arc length variable quantity is s2、s3, non-circular tensioning synchronous pulley pitch curve incision superius C4、C5Corresponding arc
Long 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, θ3For non-circular tensioning synchronous belt round cut diameter p3To moving coordinate system x3o3y3Middle x3The corner of axis.
Any time, the common tangent segment length between round active synchronization belt wheel and freely non-circular driven two point of contact of synchronous pulley
Spend T12, the free common tangent segment length T between non-circular driven synchronous pulley and non-circular tensioning two point of contact of synchronous pulley23And circle
Common tangent segment length T between type active synchronization belt wheel and non-circular 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) respectively
For p2(θ21)、p2(θ23) first differential, p'3(θ32)、p'3(θ31) it is respectively p3(θ32)、p3(θ31) first differential,It is non-
Circle tensioning synchronous pulley pitch curve moving coordinate system x3o3y3Middle x3Axis is to quiet coordinate system xo1The corner of x-axis in y.
Step 4: calculating any time synchronous belt perimeter；
Round active synchronization belt wheel pitch curve and non-circular tensioning synchronous pulley pitch curve common tangent incision superius are denoted as C6, arbitrarily
Moment C1With C6Between arc length be c11, cut on round active synchronization belt wheel and freely non-circular driven synchronous pulley pitch curve common tangent
Point is denoted as C2, freely non-circular driven synchronous pulley pitch curve and non-circular tensioning synchronous pulley pitch curve common tangent incision superius are denoted as C3,
Any time C2With C3Between arc length be c22, non-circular tensioning synchronous pulley pitch curve and freely non-circular driven synchronous pulley pitch curve
Common tangent incision superius is denoted as C4, non-circular tensioning synchronous pulley pitch curve and round active synchronization belt wheel pitch curve common tangent incision superius
It 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 (12)
Step 5: the non-circular free pitch curve of tensioning synchronous pulley calculates；
Iterative algorithm is as follows:
(a) non-circular tensioning synchronous pulley center of rotation is set, the radius of non-circular tensioning synchronous pulley is set as variable, non-circular
It is given to be tensioned synchronous pulley radius initial value, is denoted as r3-0, belt length initial value, which is calculated, according to formula (12) is denoted as C0。
(b) round active synchronization belt wheel turns over 1 °, requires to calculate freely non-circular driven synchronous pulley according to transmission ratio and turns over
The corner of corresponding angle, non-circular tensioning synchronous pulley is identical as round active synchronization belt wheel.Under the premise of guaranteeing that C is constant,
Corresponding non-circular tensioning synchronous pulley radius r when turning over 1 ° according to the round active synchronization belt wheel of formula (12) reverse3-1, i.e., to it is corresponding when
The p at quarter3。
(c) it repeats (b) 358 times, obtains round active synchronization belt wheel and turn over corresponding non-circular tensioning at 2 °, 3 ° ..., 359 °
Synchronous pulley radius is respectively r3-2, r3-3... ..., r3-359。
(d) 360 concentric circles are so far obtained, by the non-circular tensioning synchronous pulley radius in (a), (b) and (c), every 1 °
A round radius is taken, 360 radiuses are sequentially taken, to set non-circular tensioning synchronous pulley center of rotation as the center of circle, 360 will be taken
The outer end point of a radius 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, make
Obtain the perimeter and round active synchronization belt wheel and free non-circular driven synchronous pulley of the non-circular tensioning synchronous pulley newly obtained
Perimeter be equal.
(f) radius value at (e) obtained each moment is substituted into the belt length that formula (12) 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 diameter
The 1~5% of value increases non-circular tensioning synchronous pulley respectively to diameter 5 ° before and after belt length minimum position corresponds to moment point
The 1~5% of value, is then fitted to obtain new non-circular tensioning synchronous pulley with B-spline.
(i) by after (h) 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 round active synchronization belt wheel and the freely week of non-circular driven synchronous pulley
Length is equal.
(j) the non-circular tensioning synchronous pulley after (i) is substituted into formula (12) to diameter and each moment correspondence is calculated together
Step band 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, into
Row step (k) otherwise returns to (h).
(k) establish each moment of non-circular tensioning synchronous pulley to diameter and corresponding cornerRelationship is non-circular tensioning
Synchronous pulley pitch curve equation.
The invention has the benefit that
1, the present invention is non-circular-non-circular three-wheel toothed belt transmission of the self-compensating circle-freedom of the amount of becoming slack in practical application
In provide a whole set of perfect design theory basis, can be applied to non-circular-non-circular three-wheel synchronous belt biography of all circle-freedom
Motivation structure promotes the popularization and use of free non-circular-non-circular three-wheel toothed belt transmission of circle-.
2, driving wheel pitch curve is circle in the present invention, and gear ratio calculation is simple, and driven wheel pitch curve is that freely non-round knot is bent
Line, not by the constraint of specific curves form, flexible design can satisfy the more free center greatly of transmission ratio variation and at the uniform velocity pass away from non-
It is dynamic.
3, the present invention is easily programmed realization, solving precision is high, convenient and efficient using polar coordinates theory is cut.
4, the non-circular tensioning synchronous pulley in the present invention is the non-circular synchronous pulley of free pitch curve, can be with real-time compensation circle
The belt sag variable quantity generated during type active synchronization belt wheel and freely non-circular driven synchronous belt pulley transmission.
Detailed description of the invention
Fig. 1 is transmission schematic diagram of the invention；
Fig. 2 is the transmission ratio and circle of round active synchronization belt wheel and free non-circular driven synchronous pulley in the embodiment of the present invention
Type active synchronization belt wheel angle relation curve graph；
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 free non-circular driven synchronous pulley pitch curve figure in the embodiment of the present invention；
Fig. 5 is the non-circular free pitch curve figure of tensioning synchronous pulley in the embodiment of the present invention.
Specific embodiment
Below in conjunction with the accompanying drawings and embodiment the invention will be further described.
Free non-circular-non-circular three-wheel toothed belt transmission design method of circle-, the specific steps are as follows:
Step 1: giving round active synchronization belt wheel pitch curve radius r=30mm, three-wheel center is away from L1=L2=L3=
100mm, three-wheel are that perimeters is waited to close convex curve, and the perimeter s=of round active synchronization belt wheel pitch curve is calculated according to following formula
188.4956mm:
S=2 π × r (1)
Round active synchronization belt wheel pitch curve cuts diameter p1=r.
Step 2: calculating freely non-circular driven synchronous pulley pitch curve equation；
Determine round active synchronization belt wheel and freely non-circular driven synchronous pulley angle relation:
In formula,For the moving coordinate system x of round active synchronization belt wheel pitch curve1o1y1Middle x1Axis is to quiet coordinate system xo1X in y
The corner of axis,For the moving coordinate system x of freely non-circular driven synchronous pulley pitch curve2o2y2Middle x1Axis is to quiet coordinate system xo1X in y
The corner of axis, such as Fig. 2,It is non-circular driven for given round active synchronization belt wheel and freedom
Synchronous belt pulley transmission ratio；
As shown in Figure 1, round active synchronization belt wheel and free non-circular driven synchronous pulley corner cut and corner exist with ShiShimonoseki
System
In formula, θ1For the corner cut of round active synchronization belt wheel pitch curve, θ2It is cut for freely non-circular driven synchronous pulley pitch curve
Angle；
p2=i12×p1 (5)
In formula, p2Diameter, L are cut for freely non-circular driven synchronous pulley pitch curve1It is non-for round active synchronization belt wheel and freedom
The center of the driven synchronous pulley of circle away from；Freely non-circular driven synchronous pulley pitch curve such as Fig. 4.
Step 3: calculating, round active synchronization belt wheel, freely non-circular driven synchronous pulley and non-circular tensioning synchronous pulley are every
Common tangent segment length between two-wheeled.
Initial time, the moving coordinate system x of round active synchronization belt wheel pitch curve1o1y1Middle x1Axis is to quiet coordinate system xo1X in y
The corner of axisThe freely moving coordinate system x of 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 round active synchronization belt wheel pitch curve and free non-circular driven synchronous pulley
Pitch curve common tangent incision superius C1、C2It is corresponding to cut diameter, p1(θ13) and p3(θ31) be respectively round active synchronization belt wheel pitch curve with
Non-circular tensioning synchronous pulley pitch curve common tangent incision superius C6、C5It is corresponding to cut diameter, p2(θ23) and p3(θ32) it is respectively freely non-circular
Driven synchronous pulley pitch curve and non-circular tensioning synchronous pulley pitch curve common tangent incision superius C3、C4It is corresponding to cut diameter, θ120For circle
Type active synchronization belt wheel pitch curve cuts diameter p1(θ12) and freely non-circular driven synchronous pulley pitch curve cuts diameter p2(θ21) to each automatic
The corner initial value of coordinate system trunnion axis, θ130Diameter p is cut for round active synchronization belt wheel pitch curve1(θ13) and non-circular tensioning synchronous belt
Wheel pitch curve cuts diameter p3(θ31) arrive respective moving coordinate system trunnion axis corner initial value, θ230For freely non-circular driven synchronous pulley section
Curve cuts diameter p2(θ23) with non-circular tensioning synchronous pulley pitch curve cut diameter p3(θ32) to respective moving coordinate system trunnion axis corner at the beginning of
Value, θ12、θ13Respectively round active synchronization belt wheel pitch curve incision superius C1、C6Correspondence cuts diameter to moving coordinate system x1o1y1Middle x1Axis
Corner, θ21、θ23Respectively freely non-circular driven synchronous pulley pitch curve incision superius C2、C3Correspondence cuts diameter to moving coordinate system
x2o2y2Middle x2The corner of axis, θ31、θ32Respectively non-circular tensioning synchronous pulley pitch curve incision superius C4、C5Corresponding diameter of cutting is sat to dynamic
Mark system x3o3y3Middle x3The corner of axis, L1It is round active synchronization belt wheel and free non-circular driven synchronous pulley center away from L2For certainly
By non-circular driven synchronous pulley and non-circular tensioning synchronous pulley center away from L3It is synchronous with non-circular tensioning for round active synchronization belt wheel
Center distance of belt wheel；
Initial time, sets the circle that non-circular tensioning synchronous pulley pitch curve is given radius, round active synchronization belt wheel and
The freely common tangent segment length T between non-circular driven two point of contact of synchronous pulley0, freely non-circular driven synchronous pulley and non-circular tensioning
Common tangent segment length T between two point of contact of synchronous pulley1, round active synchronization belt wheel and non-circular two point of contact of tensioning 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 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.
Calculate to obtain T0=102.3570mm, T1=100.8972mm, T2=103.7259mm.
When round active synchronization belt wheel turns over angleFreely non-circular driven synchronous pulley accordingly turns over angleIt is round
Active synchronization belt wheel pitch curve incision superius C1、C6Corresponding arc length variable quantity is s1、s6, freely non-circular driven synchronous pulley section is bent
Line incision superius C2、C3Corresponding arc length variable quantity is s2、s3, non-circular tensioning synchronous pulley pitch curve incision superius C4、C5Corresponding arc
Long 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, θ3For non-circular tensioning synchronous belt round cut diameter p3To moving coordinate system x3o3y3Middle x3The corner of axis.
Any time, the common tangent segment length between round active synchronization belt wheel and freely non-circular driven two point of contact of synchronous pulley
Spend T12, the free common tangent segment length T between non-circular driven synchronous pulley and non-circular tensioning two point of contact of synchronous pulley23, round master
Common tangent segment length T between dynamic synchronous pulley and non-circular 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) respectively
For p2(θ21)、p2(θ23) first differential, p'3(θ32)、p'3(θ31) it is respectively p3(θ32)、p3(θ31) first differential,It is non-
Circle tensioning synchronous pulley pitch curve moving coordinate system x3o3y3Middle x3Axis is to quiet coordinate system xo1The corner of x-axis in y.
Step 4: calculating synchronous belt perimeter；
Round active synchronization belt wheel pitch curve and non-circular tensioning synchronous pulley pitch curve common tangent incision superius are denoted as C6, arbitrarily
Moment C1With C6Between arc length be c11, cut on round active synchronization belt wheel and freely non-circular driven synchronous pulley pitch curve common tangent
Point is denoted as C2, freely non-circular driven synchronous pulley pitch curve and non-circular tensioning synchronous pulley pitch curve common tangent incision superius are denoted as C3,
Any time C2With C3Between arc length be c22, non-circular tensioning synchronous pulley pitch curve and freely non-circular driven synchronous pulley pitch curve
Common tangent incision superius is denoted as C4, non-circular tensioning synchronous pulley pitch curve and round active synchronization belt wheel pitch curve common tangent incision superius
It 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 (11)
Initial time calculates synchronous belt original perimeter C according to formula (10)0=611.8580mm；
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 5: the non-circular free pitch curve of tensioning synchronous pulley calculates；
Iterative algorithm is as follows:
(a) radius of non-circular tensioning synchronous pulley center of rotation known to, non-circular tensioning synchronous pulley is set as variable r3, non-
Circle tensioning synchronous pulley radius initial value is denoted as r3-0=30mm, synchronous belt original perimeter are denoted as C0=611.8580mm.
(b) round active synchronization belt wheel turns over 1 °, requires to calculate freely non-circular driven synchronous pulley according to transmission ratio and turns over
The corner of corresponding angle, non-circular tensioning synchronous pulley is identical as freely non-round active synchronization belt wheel.Before guaranteeing that C is constant
It puts, corresponding non-circular tensioning synchronous pulley radius r when turning over 1 ° according to the round active synchronization belt wheel of formula (11) reverse3-1=
24.9687mm。
(c) it repeats (b) 358 times, obtains r3-2, r3-3... ..., r3-359。
(d) 360 concentric circles are so far obtained, by the non-circular tensioning synchronous pulley radius in (a), (b) and (c), every 1 °
A round radius is taken, 360 radiuses are sequentially taken, to set non-circular tensioning synchronous pulley center of rotation as the center of circle, 360 will be taken
The outer end point of a radius is sequentially connected with, and composition one is closed non-circular.
(e) by obtained in (d) it is non-circular tensioning synchronous pulley each point to diameter scale up or reduce so that
The perimeter of the non-circular tensioning synchronous pulley newly obtained and round active synchronization belt wheel and freely non-circular driven synchronous pulley
Perimeter is equal.
(f) radius value at (e) obtained each moment is substituted into the belt length that formula (11) 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 diameter
The 3% of value increases non-circular tensioning synchronous pulley respectively to diameter value 5 ° before and after belt length minimum position corresponds to moment point
3%, it is then fitted to obtain new non-circular tensioning synchronous pulley with B-spline.
(i) scaling up the non-circular tensioning synchronous pulley each point after (h) or reduce to diameter, so that new
The perimeter of the non-circular tensioning synchronous pulley arrived and round active synchronization belt wheel and the freely perimeter of non-circular driven synchronous pulley
It is equal.
(j) the non-circular tensioning synchronous pulley after (i) is substituted into formula (11) to diameter and the corresponding synchronization of each point is calculated
Band belt length is walked if each point 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 non-circular tensioning
Synchronous pulley pitch curve equation.Three pitch curves taken turns and phase angle, center of rotation all determine, calculate non-circular tensioning synchronous pulley
Angle relation corresponding with freely non-circular driven synchronous pulley with round active synchronization belt wheel.
Non-circular tensioning synchronous pulley pitch curve such as Fig. 5 after calculating.
Synchronous belt theory belt length variable quantity is 17.3mm in the embodiment, is the 2.83% of synchronous belt total length, because of band
It needs to be tensioned, can satisfy actual operation requirements.
Claims (1)
1. free non-circular-non-circular three-wheel toothed belt transmission design method of circle-, it is characterised in that: this method is specific as follows:
Step 1: round active synchronization belt wheel is the input link of uniform rotation, polar equation is cut are as follows:
p1=r (1)
S=2 π × r (2)
In formula, p1For the diameter of cutting of round active synchronization belt wheel pitch curve, r is the radius of round active synchronization belt wheel pitch curve, and s is
The perimeter of round active synchronization belt wheel pitch curve；
Step 2: calculating freely non-circular driven synchronous pulley pitch curve equation；
Determine round active synchronization belt wheel pitch curve and freely non-circular driven synchronous pulley pitch curve angle relation:
In formula,For the moving coordinate system x of round active synchronization belt wheel pitch curve1o1y1Middle x1Axis is to quiet coordinate system xo1X-axis in y
Corner,For the moving coordinate system x of freely non-circular driven synchronous pulley pitch curve2o2y2Middle x2Axis is to quiet coordinate system xo1X-axis in y
Corner, i12For given round active synchronization belt wheel and free non-circular driven synchronous belt pulley transmission ratio；
There are following relationships with corner for round active synchronization belt wheel and the freely corner cut of non-circular driven synchronous pulley
In formula, θ1For p1To moving coordinate system x1o1y1Middle x1The corner of axis, θ2Diameter p is cut for freely non-circular driven synchronous pulley pitch curve2
To moving coordinate system x2o2y2Middle x2The corner of axis；
In formula, L1For round active synchronization belt wheel and freely non-circular driven synchronous pulley center away from；
p2=i12×p1 (6)
Step 3: calculating round active synchronization belt wheel, freely non-circular driven synchronous pulley and the every two-wheeled of non-circular tensioning synchronous pulley
Between common tangent segment length；
Initial time, the moving coordinate system x of round active synchronization belt wheel pitch curve1o1y1Middle x1Axis is to quiet coordinate system xo1X-axis in y
CornerThe freely moving coordinate system x of non-circular driven synchronous pulley pitch curve2o2y2Middle x2Axis 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) it is respectively that round active synchronization belt wheel pitch curve and free non-circular driven synchronous pulley section are bent
Line common tangent incision superius C1、C2It is corresponding to cut diameter, p1(θ13) and p3(θ31) be respectively round active synchronization belt wheel pitch curve with it is non-circular
It is tensioned synchronous pulley pitch curve common tangent incision superius C6、C5It is corresponding to cut diameter, p2(θ23) and p3(θ32) it is respectively freely non-circular driven
Synchronous pulley pitch curve and non-circular tensioning synchronous pulley pitch curve common tangent incision superius C3、C4It is corresponding to cut diameter, θ120For round master
Dynamic synchronous pulley pitch curve cuts diameter p1(θ12) and freely non-circular driven synchronous pulley pitch curve cuts diameter p2(θ21) arrive respective moving axes
It is the corner initial value of trunnion axis, θ130Diameter p is cut for round active synchronization belt wheel pitch curve1(θ13) and non-circular tensioning synchronous pulley section
Curve cuts diameter p3(θ31) arrive respective moving coordinate system trunnion axis corner initial value, θ230For freely non-circular driven synchronous pulley pitch curve
Cut diameter p2(θ23) with non-circular tensioning synchronous pulley pitch curve cut diameter p3(θ32) arrive respective moving coordinate system trunnion axis corner initial value,
θ12、θ13Respectively round active synchronization belt wheel pitch curve incision superius C1、C6Correspondence cuts diameter to moving coordinate system x1o1y1Middle x1Axis turns
Angle, θ21、θ23Respectively freely non-circular driven synchronous pulley pitch curve incision superius C2、C3Correspondence cuts diameter to moving coordinate system x2o2y2In
x2The corner of axis, θ31、θ32Respectively non-circular tensioning synchronous pulley pitch curve incision superius C4、C5Correspondence cuts diameter to moving coordinate system
x3o3y3Middle x3The corner of axis, L1It is round active synchronization belt wheel and free non-circular driven synchronous pulley center away from L2It is freely non-
The driven synchronous pulley of circle and non-circular tensioning synchronous pulley center are away from L3For round active synchronization belt wheel and non-circular tensioning synchronous pulley
Center away from；
Initial time sets circle of the non-circular tensioning synchronous pulley pitch curve to give radius, round active synchronization belt wheel and freedom
Common tangent segment length T between non-circular two point of contact of driven synchronous pulley0, freely non-circular driven synchronous pulley it is synchronous with non-circular tensioning
Common tangent segment length T between two point of contact of belt wheel1And round active synchronization belt wheel and non-circular two point of contact of tensioning 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 round active synchronization belt wheel turns over angleFreely non-circular driven synchronous pulley accordingly turns over angleRound active
Synchronous pulley pitch curve incision superius C1、C6Corresponding arc length variable quantity is s1、s6, freely on non-circular driven synchronous pulley pitch curve
Point of contact C2、C3Corresponding arc length variable quantity is s2、s3, non-circular tensioning synchronous pulley pitch curve incision superius C4、C5Corresponding arc length becomes
Change amount 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) two
Rank differential, θ3For non-circular tensioning synchronous belt round cut diameter p3To moving coordinate system x3o3y3Middle x3The corner of axis；
Any time, the common tangent segment length between round active synchronization belt wheel and freely non-circular driven two point of contact of synchronous pulley
T12, the free common tangent segment length T between non-circular driven synchronous pulley and non-circular tensioning two point of contact of synchronous pulley23And it is round
Common tangent segment length T between active synchronization belt wheel and non-circular 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,It is non-circular
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 4: calculating any time synchronous belt perimeter；
Round active synchronization belt wheel pitch curve and non-circular tensioning synchronous pulley pitch curve common tangent incision superius are denoted as C6, any time
C1With C6Between arc length be c11, round active synchronization belt wheel and freely non-circular driven synchronous pulley pitch curve common tangent incision superius note
For C2, freely non-circular driven synchronous pulley pitch curve and non-circular tensioning synchronous pulley pitch curve common tangent incision superius are denoted as C3, arbitrarily
Moment C2With C3Between arc length be c22, non-circular tensioning synchronous pulley pitch curve cuts with freely non-circular driven synchronous pulley pitch curve public affairs
Line incision superius is denoted as C4, non-circular tensioning synchronous pulley pitch curve is denoted as with round active synchronization belt wheel pitch curve common tangent incision superius
C5, any time C4With C5Between arc length be c33；
Any time, synchronous belt perimeter are as follows:
C=T12+T13+T23+c11+c22+c33 (12)
Step 5: the non-circular free pitch curve of tensioning synchronous pulley calculates；
Iterative algorithm is as follows:
(a) non-circular tensioning synchronous pulley center of rotation is set, the radius of non-circular tensioning synchronous pulley is set as variable, non-circular tensioning
Synchronous pulley radius initial value is given, is denoted as r3-0, belt length initial value, which is calculated, according to formula (12) is denoted as C0；
(b) round active synchronization belt wheel turns over 1 °, requires to calculate freely non-circular driven synchronous pulley according to transmission ratio and turns over accordingly
Angle, it is non-circular tensioning synchronous pulley corner it is identical as round active synchronization belt wheel；Under the premise of guaranteeing that C is constant, according to
The round active synchronization belt wheel of formula (12) reverse turns over corresponding non-circular tensioning synchronous pulley radius r at 1 °3-1, that is, correspond to the moment
p3；
(c) it repeats (b) 358 times, obtains round active synchronization belt wheel and turn over corresponding non-circular tensioning synchronization at 2 °, 3 ° ..., 359 °
Belt wheel radius is respectively r3-2, r3-3... ..., r3-359；
(d) 360 concentric circles are so far obtained, by the non-circular tensioning synchronous pulley radius in (a), (b) and (c), take one every 1 °
The radius of a circle sequentially takes 360 radiuses, to set non-circular tensioning synchronous pulley center of rotation as the center of circle, will take 360 half
The outer end point of diameter 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 round active synchronization belt wheel and the freely week of non-circular driven synchronous pulley
Length is equal；
(f) radius value at (e) obtained each moment is substituted into the belt length that formula (12) 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 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 non-circular tensioning synchronous pulley respectively to the 1 of diameter value
~5%, it is then fitted to obtain new non-circular tensioning synchronous pulley with B-spline；
(i) by after (h) 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 round active synchronization belt wheel and the non-circular driven synchronous pulley of freedom perimeter it is equal
It is equal；
(j) it the non-circular tensioning synchronous pulley after (i) is substituted into formula (12) 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 that non-circular tensioning synchronizes
Belt wheel pitch curve equation.
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| DE4241231C2 (en) * | 1992-12-08 | 1994-11-17 | Wilfried Rahe | Belt transmission with periodically variable transmission |
| AU2002333137C1 (en) * | 2001-11-27 | 2009-05-14 | Litens Automotive | Synchronous drive apparatus with non-circular drive elements |
| DE102004027064A1 (en) * | 2004-06-03 | 2005-12-29 | Ina-Schaeffler Kg | Traction mechanism for internal combustion engine, has belt pulley of nonround configuration of driven wheel, and traction device is designed as endless belt and partially surrounds driven wheel |
| CA2583564A1 (en) * | 2004-10-22 | 2006-04-27 | Litens Automotive Partnership | Sprocket with 1.5 order, and multiples thereof, vibration canceling profile and synchronous drive employing such a sprocket |
| DE102005055716A1 (en) * | 2005-11-23 | 2007-06-21 | Schaeffler Kg | belt drive |
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