CN106917851B - Bath main officer of Tibet is non-circular-non-circular-non-circular three-wheel toothed belt transmission design method of Bath main officer of Tibet - Google Patents
Bath main officer of Tibet is non-circular-non-circular-non-circular three-wheel toothed belt transmission design method of Bath main officer of Tibet Download PDFInfo
- Publication number
- CN106917851B CN106917851B CN201710191398.5A CN201710191398A CN106917851B CN 106917851 B CN106917851 B CN 106917851B CN 201710191398 A CN201710191398 A CN 201710191398A CN 106917851 B CN106917851 B CN 106917851B
- Authority
- CN
- China
- Prior art keywords
- circular
- tibet
- synchronous pulley
- bath main
- main officer
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
- 230000005540 biological transmission Effects 0.000 title claims abstract description 48
- 238000000034 method Methods 0.000 title claims abstract description 13
- 230000001360 synchronised effect Effects 0.000 claims abstract description 258
- 238000004925 denaturation Methods 0.000 claims abstract description 6
- 230000036425 denaturation Effects 0.000 claims abstract description 6
- 238000005520 cutting process Methods 0.000 claims description 3
- 238000013341 scale-up Methods 0.000 claims description 2
- 238000004364 calculation method Methods 0.000 abstract description 3
- 230000007246 mechanism Effects 0.000 description 9
- 230000008859 change Effects 0.000 description 3
- 230000008901 benefit Effects 0.000 description 2
- 238000005461 lubrication Methods 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 241000208340 Araliaceae Species 0.000 description 1
- 235000005035 Panax pseudoginseng ssp. pseudoginseng Nutrition 0.000 description 1
- 235000003140 Panax quinquefolius Nutrition 0.000 description 1
- 230000003466 anti-cipated effect Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000007613 environmental effect Effects 0.000 description 1
- 235000008434 ginseng Nutrition 0.000 description 1
- 238000003754 machining Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 238000009987 spinning Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 230000007306 turnover Effects 0.000 description 1
Classifications
-
- 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
-
- 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
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computational Mathematics (AREA)
- Mechanical Engineering (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Devices For Conveying Motion By Means Of Endless Flexible Members (AREA)
Abstract
The invention discloses Bath main officer of Tibet it is non-circular-non-circular-non-circular three-wheel toothed belt transmission design method 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 obtains the parameters of non-circular tensioning synchronous pulley pitch curve by iterative algorithm according to the variation of synchronous belt perimeter slack.Tensioning wheel in the present invention is the non-circular synchronous pulley of free pitch curve, can overcome 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 with belt sag variable quantity synchronous in real-time compensation transmission process；Generation circular diameter, length, denaturation coefficient and the order of the non-circular pitch curve of Bath main officer of Tibet are controlled variable, and by the shape of four non-circular pitch curves of parameter regulation Bath main officer of Tibet, the transmission ratio of wider range may be implemented, and meet more specific non-at the uniform velocity transmissions and 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
This main officer of Tibet is non-circular-non-circular-non-circular three-wheel toothed belt transmission design method of Bath 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, propose the self-compensating Bath main officer of Tibet of one kind amount of becoming slack it is non-circular-Bath main officer of Tibet
It is perfect to provide a whole set of for non-circular synchronous pulley in practical applications for non-circular-non-circular three-wheel toothed belt transmission design method
Non- at the uniform velocity directly accurate transmission of the big center away between is realized on design theory basis.The design method initially sets up synchronous belt master
The pitch curve equation of driven 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, every ginseng of non-circular tensioning synchronous pulley pitch curve is calculated by alternative manner according to the variation of synchronous belt perimeter slack
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: determining the non-circular active synchronization belt wheel of Bath main officer of Tibet and the non-circular driven synchronous pulley of Bath main officer of Tibet 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, n11For the order of the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet, l1For the non-circular active synchronization band of Bath main officer of Tibet
Take turns the length of pitch curve, r11、r12The respectively non-circular active synchronization belt wheel pitch curve first segment curve of Bath main officer of Tibet 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,For the non-circular active synchronization band of Bath main officer of Tibet
Take turns pitch curve moving coordinate system x1o1y1Middle x1Axis is to quiet coordinate system xo1The corner of x-axis, m in y11、m12The respectively non-circular master of Bath main officer of Tibet
The denaturation coefficient of first segment curve and second segment curve on dynamic synchronous pulley pitch curve.
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, and
The non-circular driven synchronous pulley of Bath main officer of Tibet is output link, and pitch curve cuts polar equation:
In formula, n21For the non-circular driven synchronous pulley pitch curve order of Bath main officer of Tibet, l2For the non-circular driven synchronous pulley of Bath main officer of Tibet
The length of pitch curve, r21, r22First segment curve and second segment curve respectively on the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet
Polar diameter, b2For the generation circular diameter of the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet,For the non-circular driven synchronous belt of Bath main officer of Tibet
Take turns pitch curve moving coordinate system x2o2y2Middle x2Axis is to quiet coordinate system xo1The corner of x-axis, m in y21、m22Respectively Bath main officer of Tibet it is non-circular from
The denaturation coefficient of first segment curve and second segment curve on dynamic synchronous pulley pitch curve.
In formula, p2Diameter, θ are cut for the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet2For p2To moving coordinate system x2o2y2Middle x2
The corner cut of axis.
Step 2: calculating the biography of the non-circular active synchronization belt wheel of Bath main officer of Tibet and the non-circular driven synchronous pulley initial position of Bath main officer of Tibet
Dynamic ratio:
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 the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet2o2y2Middle x2Axis is to sitting quietly
Mark system 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 Bath main officer of Tibet are non-circular driven
Synchronous pulley pitch curve common tangent incision superius C1、C2Cut diameter value, p1(θ13) and p3(θ31) it is respectively the non-circular active synchronization of Bath main officer of Tibet
Belt wheel pitch curve and non-circular tensioning synchronous pulley pitch curve common tangent incision superius C6、C5Cut diameter value, p2(θ23) and p3(θ32) respectively
For the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet and non-circular tensioning synchronous pulley pitch curve common tangent incision superius C3、C4Cut diameter
Value, θ120Diameter p is cut for the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet1(θ12) and the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet
Cut diameter p2(θ21) arrive respective moving coordinate system trunnion axis corner initial value, θ130It is cut for the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet
Diameter p1(θ13) with non-circular tensioning synchronous pulley pitch curve cut diameter p3(θ31) arrive respective moving coordinate system trunnion axis corner initial value, θ230
Diameter p is cut for the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet2(θ23) with non-circular tensioning synchronous pulley pitch curve cut diameter p3(θ32) arrive
The corner initial value of respective moving coordinate system trunnion axis, 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 cut of axis, θ21、θ23The respectively non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet
Incision superius C2、C3Correspondence cuts diameter to moving coordinate system x2o2y2Middle x2The corner cut of axis, θ31、θ32Respectively non-circular tensioning synchronous pulley section
Curve incision superius C4、C5Correspondence cuts diameter to moving coordinate system x3o3y3Middle x3The corner cut of axis, L1For the non-circular active synchronization belt wheel of Bath main officer of Tibet
With the non-circular driven synchronous pulley center of Bath main officer of Tibet away from L2For in the non-circular driven synchronous pulley of Bath main officer of Tibet and non-circular tensioning synchronous pulley
The heart is away from L3For the non-circular active synchronization belt wheel of Bath main officer of Tibet and non-circular tensioning synchronous pulley center away from；
The non-circular active synchronization belt wheel of initial position Bath main officer of Tibet and the non-circular driven synchronous pulley instantaneous transmission ratio of Bath main officer of Tibet are as follows:
Step 3: it is same to calculate the non-circular active synchronization belt wheel of Bath main officer of Tibet, the non-circular driven synchronous pulley of Bath main officer of Tibet and non-circular tensioning
Walk the common tangent segment length between the every two-wheeled of belt wheel.
Initial time sets circle of the non-circular tensioning synchronous pulley pitch curve to give radius, the non-circular active synchronization of Bath main officer of Tibet
Common tangent segment length T between belt wheel and non-circular driven two point of contact of synchronous pulley of Bath main officer of Tibet0, the non-circular driven synchronous pulley of Bath main officer of Tibet
With the common tangent segment length T between non-circular tensioning two point of contact of synchronous pulley1, the non-circular active synchronization belt wheel of Bath main officer of Tibet and non-circular tensioning
Common tangent segment length T between two point of contact of synchronous pulley2It 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 the non-circular active synchronization belt wheel of Bath main officer of Tibet turns over angleThe non-circular driven synchronous pulley of Bath main officer of Tibet 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, Bath main officer of Tibet it is non-circular from
Dynamic synchronous pulley pitch curve incision superius C2、C3Corresponding arc length variable quantity is s2、s3, cut on non-circular tensioning synchronous pulley pitch curve
Point C4、C5Corresponding arc length variable quantity is s4、s5.Then have:
In formula, p1"(θ1) it is p1(θ1) second-order differential, p2"(θ2) it is p2(θ2) second-order differential, p3"(θ3) it is p3(θ3)
Second-order differential, θ3For non-circular tensioning 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 non-circular driven two point of contact of synchronous pulley of Bath main officer of Tibet
Tangent line segment length T12, the non-circular driven synchronous pulley of Bath main officer of Tibet and it is non-circular tensioning two point of contact of synchronous pulley between common tangent segment length
T23With the common tangent segment length T between the non-circular active synchronization belt wheel of Bath main officer of Tibet, 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 the biography of the non-circular active synchronization belt wheel of any time Bath main officer of Tibet and the non-circular driven synchronous pulley of Bath main officer of Tibet
Dynamic ratio；
The non-circular active synchronization belt wheel uniform rotation of Bath main officer of Tibet, according to formula (2), (5) 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 is denoted as with non-circular tensioning synchronous pulley pitch curve common tangent incision superius
C6, any time C1With C6Between arc length be c11, the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet and non-circular tensioning synchronous pulley section
Curve tangent incision superius is denoted as C3, any time C2With C3Between arc length be c22, non-circular tensioning synchronous pulley pitch curve and Bath
The non-circular driven synchronous pulley pitch curve common tangent incision superius of main officer of Tibet is denoted as C4, non-circular tensioning synchronous pulley pitch curve and Bath main officer of Tibet are non-circular
Active synchronization belt wheel pitch curve common tangent 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 (16)
Step 6: 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 (16) 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 the non-circular driven synchronization of Bath main officer of Tibet according to transmission ratio
Belt wheel turns over corresponding angle, and the corner of non-circular tensioning synchronous pulley is identical as the non-circular active synchronization belt wheel of Bath main officer of Tibet.Guaranteeing C
Under the premise of constant, corresponding non-circular tensioning synchronous belt when turning over 1 ° according to the non-circular active synchronization belt wheel of formula (16) reverse Bath main officer of Tibet
Take turns radius r3-1, that is, correspond to the p at moment3。
(c) repeat (b) 358 times, obtain the non-circular active synchronization belt wheel of Bath main officer of Tibet turn over it is corresponding non-at 2 °, 3 ° ..., 359 °
Circle tensioning 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 so that newly
The perimeter and the non-circular active synchronization belt wheel of Bath main officer of Tibet and the non-circular driven synchronous pulley of Bath main officer of Tibet of obtained non-circular tensioning synchronous pulley
Perimeter be equal.
(f) radius value at (e) obtained each moment is substituted into the belt length that formula (16) 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 the non-circular driven synchronous pulley of Bath main officer of Tibet week
Length is equal.
(j) it the non-circular tensioning synchronous pulley after (i) is substituted into formula (16) 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.
The invention has the benefit that
1, the present invention be the self-compensating Bath main officer of Tibet of the amount of becoming slack it is non-circular-non-circular-non-circular three-wheel toothed belt transmission of Bath main officer of Tibet
Provide a whole set of perfect design theory basis in practical applications, can be applied to all Bath main officer of Tibets it is non-circular-Bath main officer of Tibet is non-
Circle-non-circular three-wheel synchronous belt drive mechanism, promote Bath main officer of Tibet it is non-circular-non-circular-non-circular three-wheel toothed belt transmission of Bath main officer of Tibet
It promotes the use of.
2, driving wheel and driven wheel pitch curve are Bath main officer of Tibet curve in the present invention, the generation circular diameter of Bath main officer of Tibet curve,
Length, denaturation coefficient and order are controlled variable, by the shape of four non-circular pitch curves of parameter regulation Bath main officer of Tibet, so as to obtain
To the transmission ratio of wider range, meets more specific non-at the uniform velocity transmissions and require.
3, 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 bar
The synchronous belt sag variable quantity of the non-circular active synchronization belt wheel of this main officer of Tibet and generation during the non-circular driven synchronous belt pulley transmission of Bath main officer of Tibet,
Realize non-at the uniform velocity directly accurate transmission of the big center away between.
4, 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.
Detailed description of the invention
Fig. 1 is transmission principle figure of the invention；
Fig. 2 is the non-circular active synchronization belt wheel of Bath main officer of Tibet and the non-circular driven synchronous belt pulley transmission of Bath main officer of Tibet 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 pitch curve figure of the non-circular active synchronization belt wheel of Bath main officer of Tibet in the embodiment of the present invention；
Fig. 5 is the pitch curve figure of the non-circular driven synchronous pulley of Bath main officer of Tibet in the embodiment of the present invention；
Fig. 6 is the pitch curve figure of non-circular tensioning 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.
Bath main officer of Tibet is non-circular-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, center in three wheels between every two wheel is given away from being 100mm, the non-circular active of Bath main officer of Tibet
Synchronous pulley pitch curve parameter are as follows: circular diameter b occurs1=10mm, length l1=40mm, order n11=1, it is denaturalized Coefficient m11=1,
m12=1, three wheels are closing convex curve, calculate the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet according to the above parameter, such as scheme
4。
?By numerical solution in section, r is obtained11、r12Numerical solution.
u1For the angle of tangent line and polar diameter on the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet；
CornerCorner cut θ1, angle u1Between exist
So that it is determined that the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet cuts polar equation are as follows:
Step 2: circular diameter b occurs for the given non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet2=5mm is closed according to transmission
The order of system, the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet and the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet is equal, is
1, it is equal with the non-circular driven synchronous pulley pitch curve perimeter of Bath main officer of Tibet according to the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet, it acquires
The non-circular driven synchronous pulley pitch curve length l of Bath main officer of Tibet2=40mm is denaturalized Coefficient m21=1, m22=1, it is calculated according to the above parameter
The polar diameter of the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet.
?By numerical solution in section, r is obtained21、r22Numerical solution.
u2For the angle of tangent line and polar diameter on the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet；
CornerCorner cut θ2, angle u2Between there are following relationships:
Determine the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet cuts polar equation are as follows:
Pitch curve such as Fig. 5 of the non-circular driven synchronous pulley of Bath main officer of Tibet.
Step 3: calculating the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet and the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet
The transmission ratio of 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
xo1The corner of x-axis in yThe moving coordinate system x of the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet2o2y2Middle x2Axis is to sitting quietly
Mark system xo1The corner of x-axis in yThe non-circular active synchronization belt wheel of Bath main officer of Tibet and the non-circular driven synchronous pulley center of Bath main officer of Tibet
Square L1=100mm, then have:
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 Bath main officer of Tibet are non-circular driven
Synchronous pulley pitch curve common tangent incision superius C1、C2Cut diameter value, p1(θ13) and p3(θ31) it is respectively the non-circular active synchronization of Bath main officer of Tibet
Belt wheel pitch curve and non-circular tensioning synchronous pulley pitch curve common tangent incision superius C6、C5Cut diameter value, p2(θ23) and p3(θ32) respectively
For the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet and non-circular tensioning synchronous pulley pitch curve common tangent incision superius C3、C4Cut diameter
Value, θ120Diameter p is cut for the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet1(θ12) and the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet
Cut diameter p2(θ21) arrive respective moving coordinate system trunnion axis corner initial value, θ130It is cut for the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet
Diameter p1(θ13) with non-circular tensioning synchronous pulley pitch curve cut diameter p3(θ31) arrive respective moving coordinate system trunnion axis corner initial value, θ230
Diameter p is cut for the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet2(θ23) with non-circular tensioning synchronous pulley pitch curve cut diameter p3(θ32) arrive
The corner initial value of respective moving coordinate system trunnion axis, 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 cut of axis, θ21、θ23The respectively non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet
Incision superius C2、C3Correspondence cuts diameter to moving coordinate system x2o2y2Middle x2The corner cut of axis, θ31、θ32Respectively non-circular tensioning synchronous pulley section
Curve incision superius C4、C5Correspondence cuts diameter to moving coordinate system x3o3y3Middle x3The corner cut of axis, L1For the non-circular active synchronization belt wheel of Bath main officer of Tibet
With the non-circular driven synchronous pulley center of Bath main officer of Tibet away from L2For in the non-circular driven synchronous pulley of Bath main officer of Tibet and non-circular tensioning synchronous pulley
The heart is away from L3For the non-circular active synchronization belt wheel of Bath main officer of Tibet and non-circular tensioning synchronous pulley center away from；
It is i according to the instantaneous transmission ratio that formula (10) calculate initial position120=1.1121；
Step 4: it is same to calculate the non-circular active synchronization belt wheel of Bath main officer of Tibet, the non-circular driven synchronous pulley of Bath main officer of Tibet and non-circular tensioning
Walk the common tangent segment length between the every two-wheeled of belt wheel.
Initial position sets circle of the non-circular tensioning synchronous pulley pitch curve to give radius, the non-circular active synchronization of Bath main officer of Tibet
Common tangent segment length T between belt wheel and non-circular driven two point of contact of synchronous pulley of Bath main officer of Tibet0, the non-circular driven synchronous pulley of Bath main officer of Tibet
With the common tangent segment length T between non-circular tensioning two point of contact of synchronous pulley1, the non-circular active synchronization belt wheel of Bath main officer of Tibet and non-circular tensioning
Common tangent segment length T between two point of contact of synchronous pulley2It is respectively as follows:
T is calculated to obtain according to formula (11)0=106.3370mm, T1=109.6547mm, T2=105.2783mm.
When the non-circular active synchronization belt wheel of Bath main officer of Tibet turns over angleThe non-circular driven synchronous pulley of Bath main officer of Tibet 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, Bath main officer of Tibet it is non-circular from
Dynamic synchronous pulley pitch curve incision superius C2、C3Corresponding arc length variable quantity is s2、s3, cut on non-circular tensioning synchronous pulley pitch curve
Point C4、C5Corresponding arc length variable quantity is s4、s5.Then have:
In formula, p1"(θ1) it is p1(θ1) second-order differential, p2"(θ2) it is p2(θ2) second-order differential, p3"(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.
Set circle of the non-circular tensioning synchronous pulley to give radius, the non-circular active synchronization belt wheel uniform rotation of Bath main officer of Tibet；Appoint
The common tangent segment length anticipated between the non-circular active synchronization belt wheel of moment Bath main officer of Tibet and non-circular driven two point of contact of synchronous pulley of Bath main officer of Tibet
T12, the non-circular driven synchronous pulley of Bath main officer of Tibet and it is non-circular tensioning two point of contact of synchronous pulley between common tangent segment length T23, Bath main officer of Tibet
Common tangent segment length T between non-circular 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 5: calculating the biography of the non-circular active synchronization belt wheel of any time Bath main officer of Tibet and the non-circular driven synchronous pulley of Bath main officer of Tibet
Dynamic ratio；
The non-circular active synchronization belt wheel uniform rotation of Bath main officer of Tibet, and then according to formula (4), (8) solve p1, p2, then Bath is calculated to obtain
The non-circular active synchronization belt wheel of main officer of Tibet and the non-circular driven synchronous pulley instantaneous transmission ratio of Bath main officer of Tibet:
According to formula (14), (15), (16), when calculating circle driving wheel rotates a circle, the non-circular active synchronization belt wheel of Bath main officer of Tibet turns
Angle and the non-circular driven synchronous belt pulley transmission of Bath main officer of Tibet are more as shown in Figure 2 than curve.
Step 6: calculating synchronous belt perimeter；
The non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet is denoted as with non-circular tensioning synchronous pulley pitch curve common tangent incision superius
C6, any time C1With C6Between arc length be c11, the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet and non-circular tensioning synchronous pulley section
Curve point of contact is denoted as C3, any time C2With C3Between arc length be c22, non-circular tensioning synchronous pulley pitch curve and Bath main officer of Tibet it is non-circular from
Dynamic synchronous pulley pitch curve common tangent incision superius is denoted as C4, non-circular tensioning synchronous pulley pitch curve and the non-circular active synchronization of Bath main officer of Tibet
Belt wheel pitch curve common tangent 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 (18)
It carves at the beginning, is C according to the original perimeter that formula (18) calculate synchronous belt0=656.67mm；
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 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 r3, non-
Circle tensioning synchronous pulley radius initial value is denoted as r3-0=30mm, synchronous belt original perimeter are denoted as C0=656.67mm.
(b) the non-circular active synchronization belt wheel of Bath main officer of Tibet turns overAccording to the non-circular active synchronization belt wheel of Bath main officer of Tibet and Bath main officer of Tibet
Non-circular driven synchronous belt pulley transmission calculates the non-circular driven synchronous pulley of Bath main officer of Tibet and turns over corresponding angle than relationshipThe corner of non-circular tensioning synchronous pulley is identical as the non-circular active synchronization belt wheel of Bath main officer of TibetUnder the premise of guaranteeing that synchronous belt perimeter is constant, r is calculated3-1=30.1562mm.
(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) scaling up each point of non-circular tensioning synchronous pulley obtained in (d) or reduce to diameter, so that new
The perimeter of the non-circular tensioning synchronous pulley arrived and the non-circular active synchronization belt wheel of Bath main officer of Tibet and the non-circular driven synchronous pulley of Bath main officer of Tibet
Perimeter is equal.
(f) radius value at (e) obtained each moment is substituted into the belt length that formula (18) 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 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 the non-circular driven synchronous pulley of Bath main officer of Tibet
It is equal.
(j) each point is calculated to diameter substitution formula (18) in the non-circular tensioning synchronous pulley after (i) and corresponds to synchronous belt band
It is long, 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, carry out step
(k), otherwise (h) is returned to.
(k) three pitch curves taken turns and phase angle, center of rotation all determine, establish each moment of non-circular tensioning synchronous pulley
With corresponding angle relation be non-circular tensioning synchronous pulley pitch curve equation to diameter.Non-circular tensioning synchronous pulley after calculating is certainly
By pitch curve such as Fig. 6.
Synchronous belt theory belt length variable quantity is 12.06mm in the embodiment, is the 1.8% of synchronous belt total length, because of band
It needs to be tensioned, can satisfy actual operation requirements.
Claims (1)
1. Bath main officer of Tibet is non-circular-non-circular-non-circular three-wheel toothed belt transmission design method of Bath main officer of Tibet, it is characterised in that: this method tool
Body is as follows:
Step 1: determining that the non-circular active synchronization belt wheel of Bath main officer of Tibet and the non-circular driven synchronous pulley section of Bath main officer of Tibet are bent according to transmission rule
Line 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, n11For the order of the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet, l1For the non-circular active synchronization belt wheel section of Bath main officer of Tibet
The length of curve, r11、r12The respectively pole of Bath main officer of Tibet non-circular active synchronization belt wheel pitch curve first segment curve and second segment curve
Diameter, b1For the generation circular diameter of the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet,For the non-circular active synchronization belt wheel section of Bath main officer of Tibet
Curve moving coordinate system x1o1y1Middle x1Axis is to quiet coordinate system xo1The corner of x-axis in y, moving coordinate system x1o1y1Origin be arranged in Bath
At the center of rotation of the non-circular active synchronization belt wheel of main officer of Tibet, m11、m12Respectively first on the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet
The denaturation coefficient of section curve and second segment curve；
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, and
The non-circular driven synchronous pulley of Bath main officer of Tibet is output link, and pitch curve cuts polar equation:
In formula, n21For the non-circular driven synchronous pulley pitch curve order of Bath main officer of Tibet, l2It is bent for the non-circular driven synchronous pulley section of Bath main officer of Tibet
The length of line, r21, r22The pole of first segment curve and second segment curve respectively on the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet
Diameter, b2For the generation circular diameter of the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet,For the non-circular driven synchronous pulley section of Bath main officer of Tibet
Curve moving coordinate system x2o2y2Middle x2Axis is to quiet coordinate system xo1The corner of x-axis in y, moving coordinate system x2o2y2Origin be arranged in Bath
At the center of rotation of the non-circular driven synchronous pulley of main officer of Tibet, quiet coordinate system xo1The origin of y is arranged in the non-circular active synchronization belt wheel of Bath main officer of Tibet
Center of rotation at, m21、m22First segment curve and second segment curve respectively on the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet
Denaturation coefficient；
In formula, p2Diameter, θ are cut for the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet2For p2To moving coordinate system x2o2y2Middle x2Axis is cut
Angle；
Step 2: calculating the transmission of the non-circular active synchronization belt wheel of Bath main officer of Tibet and the non-circular driven synchronous pulley initial position of Bath main officer of Tibet
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 xo1In y
The corner of x-axisThe moving coordinate system x of the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet2o2y2Middle x2Axis is to quiet coordinate system
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 is non-circular driven synchronous with Bath main officer of Tibet
Belt wheel pitch curve common tangent incision superius C1、C2Cut diameter value, p1(θ13) and p3(θ31) it is respectively the non-circular active synchronization belt wheel of Bath main officer of Tibet
Pitch curve and non-circular tensioning synchronous pulley pitch curve common tangent incision superius C6、C5Cut diameter value, p2(θ23) and p3(θ32) it is respectively bar
The non-circular driven synchronous pulley pitch curve of this main officer of Tibet and non-circular tensioning synchronous pulley pitch curve common tangent incision superius C3、C4Cut diameter value,
θ120Diameter p is cut for the non-circular active synchronization belt wheel pitch curve of Bath main officer of Tibet1(θ12) with the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet 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 non-circular tensioning synchronous pulley pitch curve cut diameter p3(θ31) arrive respective moving coordinate system trunnion axis corner initial value, θ230For bar
The non-circular driven synchronous pulley pitch curve of this main officer of Tibet cuts diameter p2(θ23) with non-circular tensioning synchronous pulley pitch curve cut diameter p3(θ32) to respectively
The corner initial value of moving coordinate system trunnion axis, θ12、θ13The respectively non-circular active synchronization belt wheel pitch curve incision superius C of Bath main officer of Tibet1、C6It is right
Diameter should be cut to moving coordinate system x1o1y1Middle x1The corner cut of axis, θ21、θ23Respectively cut on the non-circular driven synchronous pulley pitch curve of Bath main officer of Tibet
Point C2、C3Correspondence cuts diameter to moving coordinate system x2o2y2Middle x2The corner cut of axis, θ31、θ32Respectively non-circular tensioning synchronous pulley pitch curve
Incision superius C4、C5Correspondence cuts diameter to moving coordinate system x3o3y3Middle x3The corner cut of axis, moving coordinate system x3o3y3Origin be arranged at non-circular
At the center of rotation of tight synchronous pulley, L1For the non-circular active synchronization belt wheel of Bath main officer of Tibet and the non-circular driven synchronous pulley center of Bath main officer of Tibet
Away from L2It is the non-circular driven synchronous pulley of Bath main officer of Tibet and non-circular tensioning synchronous pulley center away from L3For the non-circular active synchronization band of Bath main officer of Tibet
Wheel with non-circular tensioning synchronous pulley center away from；
The non-circular active synchronization belt wheel of initial position Bath main officer of Tibet and the non-circular driven synchronous pulley instantaneous transmission ratio of Bath main officer of Tibet are as follows:
Step 3: calculating the non-circular active synchronization belt wheel of Bath main officer of Tibet, the non-circular driven synchronous pulley of Bath main officer of Tibet and non-circular tensioning synchronous belt
Take turns the common tangent segment length between every two-wheeled；
Initial time sets circle of the non-circular 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 non-circular driven two point of contact of synchronous pulley of Bath main officer of Tibet0, the non-circular driven synchronous pulley of Bath main officer of Tibet with it is non-
Common tangent segment length T between circle tensioning two point of contact of synchronous pulley1, the non-circular active synchronization belt wheel of Bath main officer of Tibet it is synchronous with non-circular tensioning
Common tangent segment length T between two point of contact of belt wheel2It 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 angleThe non-circular driven synchronous pulley of Bath main officer of Tibet accordingly turns over angle
The 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, Bath main officer of Tibet is non-circular driven
Synchronous pulley pitch curve incision superius C2、C3Corresponding arc length variable quantity is s2、s3, non-circular 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) two
Rank differential, θ3For non-circular tensioning synchronous belt round cut diameter p3To moving coordinate system x3o3y3Middle x3The corner of axis；
Common tangent between the non-circular active synchronization belt wheel of any time Bath main officer of Tibet and non-circular driven two point of contact of synchronous pulley of Bath main officer of Tibet
Segment length T12, the non-circular driven synchronous pulley of Bath main officer of Tibet and it is non-circular tensioning two point of contact of synchronous pulley between common tangent segment length T23、
Common tangent segment length T between the non-circular active synchronization belt wheel of Bath main officer of Tibet 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 the transmission of the non-circular active synchronization belt wheel of any time Bath main officer of Tibet and the non-circular driven synchronous pulley of Bath main officer of Tibet
Than；
The non-circular active synchronization belt wheel uniform rotation of Bath main officer of Tibet, according to formula (2), (5) 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 non-circular 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 driven synchronous pulley pitch curve of Bath main officer of Tibet and non-circular tensioning synchronous pulley pitch curve
Common tangent incision superius is denoted as C3, any time C2With C3Between arc length be c22, non-circular tensioning synchronous pulley pitch curve and Bath main officer of Tibet are non-
The driven synchronous pulley pitch curve common tangent incision superius of circle is denoted as C4, non-circular tensioning synchronous pulley pitch curve and the non-circular active of Bath main officer of Tibet
Synchronous pulley pitch curve common tangent 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 (16)
Step 6: 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 (16) 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 the non-circular driven synchronous pulley of Bath main officer of Tibet according to transmission ratio
Corresponding angle is turned over, the corner of non-circular tensioning 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 non-circular tensioning synchronous pulley half when turning over 1 ° according to the non-circular active synchronization belt wheel of formula (16) reverse Bath main officer of Tibet
Diameter r3-1, that is, correspond to 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 at 2 °, 3 ° ..., 359 ° corresponding non-circular
Tight 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), 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 obtaining
Non-circular tensioning synchronous pulley perimeter and the non-circular active synchronization belt wheel of Bath main officer of Tibet and the non-circular driven synchronous pulley of Bath main officer of Tibet week
Length is equal；
(f) radius value at (e) obtained each moment is substituted into the belt length that formula (16) 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 the non-circular driven synchronous pulley of Bath main officer of Tibet are equal
It is equal；
(j) it the non-circular tensioning synchronous pulley after (i) is substituted into formula (16) 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 non-circular tensioning synchronous pulley
Pitch curve equation.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710191398.5A CN106917851B (en) | 2017-03-28 | 2017-03-28 | Bath main officer of Tibet is non-circular-non-circular-non-circular three-wheel toothed belt transmission design method of Bath main officer of Tibet |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710191398.5A CN106917851B (en) | 2017-03-28 | 2017-03-28 | Bath main officer of Tibet is non-circular-non-circular-non-circular three-wheel toothed belt transmission design method of Bath main officer of Tibet |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106917851A CN106917851A (en) | 2017-07-04 |
| CN106917851B true CN106917851B (en) | 2019-02-26 |
Family
ID=59462037
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710191398.5A Expired - Fee Related CN106917851B (en) | 2017-03-28 | 2017-03-28 | Bath main officer of Tibet is non-circular-non-circular-non-circular three-wheel toothed belt transmission design method of Bath main officer of Tibet |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106917851B (en) |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE4241231A1 (en) * | 1992-12-08 | 1994-06-09 | Wilfried Rahe | Contact belt gear box with periodically changing translation - has two or more discs with fixed rotary axes looped by contact belt of constant length in each position of discs. |
| CN1758852A (en) * | 2003-04-23 | 2006-04-12 | 波利-克利普系统两合公司 | Elliptical synchronous belt drive |
| CN101379320A (en) * | 2006-02-01 | 2009-03-04 | 谢夫勒两合公司 | Chain drive and use of a chain in a chain drive |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE102004045751A1 (en) * | 2004-09-21 | 2006-04-27 | Ina-Schaeffler Kg | Method for designing a control gear having at least one non-circular disk |
-
2017
- 2017-03-28 CN CN201710191398.5A patent/CN106917851B/en not_active Expired - Fee Related
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE4241231A1 (en) * | 1992-12-08 | 1994-06-09 | Wilfried Rahe | Contact belt gear box with periodically changing translation - has two or more discs with fixed rotary axes looped by contact belt of constant length in each position of discs. |
| CN1758852A (en) * | 2003-04-23 | 2006-04-12 | 波利-克利普系统两合公司 | Elliptical synchronous belt drive |
| CN101379320A (en) * | 2006-02-01 | 2009-03-04 | 谢夫勒两合公司 | Chain drive and use of a chain in a chain drive |
Non-Patent Citations (2)
| Title |
|---|
| Non-circular belt transmission design of mechanical press;Enlai Zheng等;《Mechanism and Machine Theory》;20120821;第57卷(第11期);第126-138页 |
| 非圆齿形带轮(链轮)节曲线为凸形的条件;李宇鹏等;《机械设计》;19990331;第36-38页 |
Also Published As
| Publication number | Publication date |
|---|---|
| CN106917851A (en) | 2017-07-04 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110879910B (en) | Closed non-circular gear pair with transmission ratio of Fourier series | |
| CN105042002A (en) | Variable-transmission-ratio line gear mechanism | |
| CN108331900B (en) | Non-circular gear pair design method based on curvature change | |
| CN111322374B (en) | Elastic variable transmission ratio line gear mechanism | |
| CN106917851B (en) | Bath main officer of Tibet is non-circular-non-circular-non-circular three-wheel toothed belt transmission design method of Bath main officer of Tibet | |
| CN106838160B (en) | Non-circular-sinusoidal non-circular-non-circular three-wheel toothed belt transmission design method of Bath main officer of Tibet | |
| CN106838159B (en) | Non-circular-non-circular three-wheel toothed belt transmission design method of circle-Fourier | |
| WO2014144242A3 (en) | Continuously variable transmission having a periodic displacement waveform with a constant velocity portion | |
| CN204985583U (en) | Variable ratio line gear | |
| CN106907436B (en) | The non-circular three-wheel toothed belt transmission design method of circle-off-centre operation- | |
| CN106907435B (en) | Free non-circular-non-circular three-wheel toothed belt transmission design method of circle- | |
| CN202659811U (en) | Non-circular gear pair with Fourier function pitch curve | |
| CN106949204B (en) | The design method of the non-circular toothed belt transmission of the self-compensating pleiotaxy of the amount of becoming slack | |
| CN107061643B (en) | Oval-sinusoidal non-circular-non-circular three-wheel toothed belt transmission design method | |
| CN106870661B (en) | Oval-not rounded three-wheel toothed belt transmission design method of circle- | |
| CN106838158B (en) | Not rounded-not rounded three-wheel toothed belt transmission design method of off-centre operation-Fourier | |
| CN110657216B (en) | Mechanism for realizing cosine acceleration motion law and reverse solving method | |
| CN102705448A (en) | Non-circular gear pair with Fourier function pitch curves | |
| CN208595203U (en) | Speed reducer | |
| US11339859B2 (en) | Infinitely variable transmission with uniform input-to-output ratio that is non-dependant on friction | |
| CN103939576B (en) | High-order multistage modified elliptical gear | |
| CN104791426A (en) | Harmonic gear transmission mechanism | |
| CN203868283U (en) | High-order multi-segment modified elliptic gear | |
| CN201032823Y (en) | Tea machine transmission device with varied transmission ratio | |
| RU2617245C2 (en) | Rack and impulse variator with single-shaft eliminator |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20190226 |