机械设计：chapter seven belt drives.ppt
92页
Chapter7 Belt Drives Automobile engine (multi wedge belt)汽车发动机（多楔带） Automobile engine (synchronous belt)汽车发动机（同步带） Chapter7 Belt Drives ¡Overview¡Characteristics of Belt Drives¡Potential Failure and Belt Materials ¡Flat Belts¡VBelts ¡Synchronous Belts 7.1 Overview ¡A belt drive consists of a driving and driven pulleys ¡The belt which is mounted on the pulleys with a certain amount of tension and transmits peripheral force by friction ¡Drives may have two or more driven pulleys 7.1.1Characteristics of Belt Drives¡Belt drives are applied mainly to transmit power less than 50kW¡The speeds of belts vary from 5 to 25m/s¡High belt speed willlgenerate high a high centrifugal forcelreduce the friction between the belt and pulleylslipping will take place¡Low belt speed willltransmit centrifugal force is large lbelt number is large¡Special highspeed endless belts permit speeds up to 60m/s 7.1.1Characteristics of Belt Drives¡The speed ratio of belt drives does not exceed 4 to 5lThe small diameter of the pulley can make the drives compactlIf the diameter of the pulley is too small¡make the bend stress of the belt much larger¡reduce the service life¡A speed ratio as higher as 10 can be obtained with Vbelt or a flat drive with an idler pulley(惰轮) 7.1.1 Characteristics of Belt Drives¡Belt drives are well suited to applications in which the center distance between rotating shafts is large. Treadmill Tractor Grinder 7.1.1 Characteristics of Belt Drives¡ With proper design insight, belts are usually lQuietleasily replacedlreduce the transmission of unwanted shock and vibration between shafts ¡because of their flexibility and damping capacity 7.1.1 Characteristics of Belt Drives¡Simplicity of installation¡minimum maintenance requirements¡high reliability¡adaptability to a variety of applications 7.1.1 Characteristics of Belt Drives¡angular velocity ratio between the two rotating shafts may be inexact lBecause of slip打滑 and/or creep滑动 ¡power and torque capacities are limited by lcoefficient of friction linterfacial pressure between belt and pulley 7.1.2 Commercially available belts of different cross sections Belts are available with：•A narrow rectangular cross sectionflat belts•A trapezoidal cross sectionVbelts•Multiple Vbelts•Round cross sectionround belts 7.1.2 Commercially available belts of different cross sections Owing to the wedging effect, the force of friction on Vbelt drives is larger than that of flat belts. ¡ Vbelts have higher pulling capacity, and find more application.¡Vribbed belts have both the advantages of flat belts and Vbelts. ¡Round belts are used to transmit low power. 7.2 V-belts and V-belt pulleys7.2.1 Specification for standard series VbeltslCore¡the main loadcarrying layer¡give great strength in tensionlLayer of rubber above and below ¡tension and compression layers, respectivelylOuter jacket ¡rubberized fabric bonded to other parts of the belt Conventional V-belts Synchronous belt Terms¡Pitch line: when the belt bends vertically relative to its base side, any peripheral line which maintains its length for constant¡Pitch face: the face composed of all the pitch curves¡Pitch width: the width of pitch face Cross section of belt¡Vbelt sizes have been standardized in seven trapezoidal cross sections. They are : Y, Z, A, B, C, D, and E.¡Size “Y” is the smallest¡Size “E” is the largest Cross section dimensions Base length 基准长度¡Vbelts are made as the nojoints endless type.¡Base diameter D: the pulley diameters corresponding to the pitch width of the Vbelts used¡Base length L: under the action of needed tension, the peripheral line length located at the base diameter of pulley Base length series of conventional V-belts Tension cords: primequality cotton; polyamide strips or polyester cords for flat belts and Vribbed (PolyV) belts; polyester, fiberglass, or aramid fibers for toothed timing belts and conventional or high capacity Vbelts. ¡The cords were embedded in a matrix of rubber synthetic rubber compounds, to increase flexibility and friction. ¡Neoprene, to enhance resistance to oil, heat. ¡Belt cover material: cotton or nylon cloth impregnated with synthetic rubber Belt materials Tension cords: ¡primequality cotton¡polyamide strips 聚酰胺带¡polyester 聚酯cords for flat belts and Vribbed (PolyV) belts¡polyester, fiberglass, or aramid芳纶 fibers for toothed timing belts and conventional or high capacity Vbelts Belt materials 7.2.2 V-belt pulleys1. Pulley material¡cast iron such as HT150 and HT200.¡The maximum allowable peripheral velocity for castiron pulley is 25m/s.¡the velocity is higherlthe pulleys are made of cast steel or are welded by steel punched.¡For light loadlthe pulleys are made of alloy aluminum casting or plastics. Pulley structureTypical constructions of Vbelt pulleys: ¡Solid type实心式: pulley base diameter D<=(2.5~3) Ds¡Web type腹板式: D<=300¡Hole plate type孔板式: D<=300¡Spoke type轮辐式: D>300¡Ds is the shaft diameter Solid type Web type Hole plate type Spoke type Cross sectional dimensions of V-belt pulley rim ¡When Vbelts bend on the pulleys, lthe wedge angle will reduce because of the sectional de formation.¡In order to ensure proper contact between the belt and the pulleylthe wedge angles are limited to 320, 340,360, and 380. Construction design of pullets¡Select construction type according to the base diameter of the pulley.¡The pulley groove size is determined on the basis of Vbelt type. Marking exampleType base length standard No. 7.3 Forces and stresses in belts7.3.1 Forces in belts¡Belts are mounted on the pulleys with a certain amount of initial tension F0¡Before drives operate, the force acting on the two sides of belts are equal¡When belts operate, the forces are different owing to the action of the force of friction between the belt and pulley ¡If the sum of the length of an endless belt is constant when drives operate¡The increase amount F1F0 of the pull on the tight side of a belt is equal to the decreases amount F0F2 of the pull on the slack side¡F1=tight side pull¡F2=slack side pullF0F0F0F0F2F1Ffn1Ffn2从动边从动边主动边主动边 ¡According to the moment equilibrium conditionF2F1Ffn1Ffn2从动边从动边主动边主动边F2F1Ffn1O1 ¡The peripheral force acting on the pulleys or useful load of a belt is¡The relationship of the peripheral force F, the belt speed v and transmitted power P is ¡Investigation reveals that the maximum effective pull on the verge of slipping is¡where f is coefficient of friction between a belt and a pulley¡a is the belt angle of contact包角¡e is the base of the natural logarithms Increasing •Initial tension of the belt F0•Angle of contact a•Coefficient of friction f•Can increase the peripheral force of belt drives•Excessive gain of force F0 will reduce the service life of belt When belts operate, stresses in belts consist of the stresses of pull, centrifuge and bendingCentrifugalforceinduced stress Pulling stresses 7.3.2 Stress analysisWhere A= cross section area of the belt Fc=centrifugal force, N q=belt weight, kg/m v=velocity of the belt, m/s ¡When a belt around a pulley, the bending stress yielded owing to curvature of the belt¡y=vertical distance of neutral layer to outermost larger of the belt, mm¡E=modulus of elasticity of the belt, MPa¡d=diameter of pulley (for Vbelt pulley, d is the base diameter), mmBending stress of belt only occurs on the arc section of the belt around pulleyThe bending stress Stress analysis ¡Tight side:¡Slack side:¡Maximum stress:¡Which takes place at the contact place of tight side entering the smaller driving pulley.¡It is necessary to limit minimum diameter of the small pulley 7.4 Creep 打滑and speed rate in belt drives7.4.1 Creep of belt drives¡When a driving pulley is connected by a belt to a driven pulley, the belt tensions on two sides of driver are different.¡The elastic stretch amount of the tight side is more than that of the loose side 7.4.1 Creep of belt drivesIn the process of the belt’s rounding, the driving pulley at point a to leaving the pulley at point b•The belt tension reduces gradually from F1 to F2•The elastic elongation amount of belt decreases correspondently.•The peripheral speed of the belt is not keep up with that of the driving pulley When the belt goes around the driving pulley, •The speed of the belt from v1 drops slowly to v2•Local relative slip occurs between the belt and the pulley For the driven pulley•The elastic stretch amount increases gradually because the belt transits from the loose side to the tight side•The speed of the belt exceeds the peripheral speed of the pulley ¡Relative slip takes place between the belt and the pulley¡Such relative slip is known as belt creep.¡This creep occurs only a part (ab) of the whole arc of contact a, this part being called creep arc.¡The other part that does not creep is called stationary arc. ¡Effective force F¡Angle of slip arc¡Angle of slip arc=angle of contact¡Slipping is generated Difference between slip打滑 and creep滑动¡Slip is caused by overload lBelt will be worn seriously lIt should be avoided¡Creep caused by different tension on the tight side and the loose side lIt is an inevitable physical phenomenon. 7.4.2 Speed rate of belt drives¡Owing to inevitable slip, the peripheral velocity on the driven pulley is less than the velocity v1 on the driving pulley.¡The relative reducing ratio of the peripheral velocity of the drive pulley is named creep factor.¡d1,d2=diameters of the driving and the driven pulleys, respectively¡n1,n2=rotating speeds of the driving and the driven pulleys, respectively ¡The true speed ratio is¡The rotating speed of the driven pulley is¡The creep factor of belt drives is ordinary 1%2%, and it can be neglected in the general calculations. 7.5 V-belt drive designThe main failure of belt drives¡Slip between the belts and the pulleys ¡Fatigue damage of belts due to the action of variable stressDesign criteria in belt drive design¡Prevent the belts from slip when the belts operate¡Make the belts have enough fatigue strength ¡Delamination Fatigue fracture 7.5.1 strength calculation of V-belt drives ¡In order to avoid belt slip in the process of belt running¡It is necessary to limit the peripheral force transmitted by the belt to be not more than the maximum effective pull Fmax ¡Fmax is determined by the equation ¡Transmitted power of belts in the case of ensuring belts against slip is¡In order to ensure enough fatigue life of the belts, it is necessary to make¡Thus, ¡Power transmitted by a single belt is Power transmitted by a single V-belt ¡When speed ratio i is not 1, the diameter of the driven pulley is larger than that of the driving pulley¡Bend stress in the driven pulley is less than that of the driving pulley¡Transmitted capacity is gained¡Transmitted power can be increased¡The power increment is used to consider this influence 7.5.2 design procedure and factor choice for V-belt drives1. Determine the calculating power¡P= nominal power¡KA= factor of the working conditions 2. Selecting the belt type¡The belt type is selected based on the calculating power Pc and the rotational speed n1 of the driving pulley. 3. Determining the base diameters¡The small diameter of the pulley can make the drives compact.¡If the diameter of the pulley is too smalllmake the bend stress of the belt much largerlreduce the service life¡Pulley diameter should be suitable¡Diameter of small pulley should be equal to and more than the minimum base pulley diameter Dmin 4. Checking the belt speedWhen transmitted power is given, with a gain in the belt speed¡useful tension of belt will be decreased ¡number of the belt can be cut downVbelt drives are often set to the highspeed grade in the multiple grade drives ¡With too high belt speeds, lcentrifugal force will be raisedlnormal presses between the belt and the pulley are decreasedlDriving capacity and the service life of the belt are reduced¡The speeds of the belt vary usually from 5 to 25m/s 5. Determining the center distance a between pulleys and the base length Ld of the belt¡The center distance between pulleys may be taken a preliminary selection from the following formula¡After the center distance is determined, we can calculate the belt length Ld0 as ¡Real center distance a, base on selected Ld, can be calculated as 6. Checking the belt angle of contact a¡After the diameters of the pulley and the center distance are fixed¡The belt angle of contact can be calculated as ¡The value of the angle of contact affects directly the working capacity of belt drives¡When the angle of contact reduceslTransmitted capacity is cut downlThe slip between the belt and the pulley is prone to occur on the small pulley¡It is not advisable to use an angle of contact a1<1200 7. Fixing the number of V-belts¡The number of Vbelt Z can be calculated by formula¡Ka= contact angle factor taking into account the influence on transmitted capacity when a is not 1800¡kL=length factor, considering the influence of the belt length on the service life of a belt ¡In order to make each belt loaded equally, it is necessary to ensure the number of the belt is not too big¡We take the number of the belt Z from 3 to 6 and Zmax<=10¡If the number of the belt calculated is more than required, it is necessary to select a new type of the belt and to calculate again 8. Calculating the initial tension¡The initial tension F0 is chosenlthe belt retains its tension for a sufficiently long time without excessive stretchl has a satisfactory service life¡If F0 is too smalllThe force of friction between the belts and the pulley will be reducedlThe slip between the belts and the pulleys is prone to occur easily ¡If the initial tension is much largerlIt will gain pressure between the shafts and the bearingslReduce the service life of the belts¡The initial tension of a single Vbelt is 9.Calculating the force acting on the shafts¡the force acting on the shafts can be calculated as 7.5.4 Tensioning device of V-belt drives¡After a period of operating, plastic stretch and looseness will occur on the belt¡Will reduce its tension¡Hence, Vbelt drive must have a tensioner to maintain its normal operating Regular tensioner¡Slide way type 滑道式张紧装置¡Pendulum type 摆架式张紧装置 Automatic tensioning device自动张紧装置 Tensioner with a tension wheel Assignment 1¡The transmitted power of Vbelt is 5kw. The initial tension is 500N. The diameter of driving pulley is 140mm with the rotation velocity of 1460r/min and the angle of contact is 1400. The friction coefficient between the pulley and belt is 0.5. Calculating the peripheral force and the maximum effective pull. Assignment2 ¡Real power of a Vbelt drive is 7kw, belt velocity is 10m/s, the value of tight side pull is 2 times that of slack side pull, calculate the peripheral force and the tight side pull. Assignment 3¡A Vbelt drive of type A. The velocity of driving pulley is 1480r/min. the velocity of driven pulley is 600r/min, the transmitted power is 1.5kw, belt velocity is 7.75m/s, the center distance is 800, the friction coefficient is 0.5, Calculating the base diameters, the base length, and the initial tension. Assignment requirements¡They would be submitted by November 12,2014¡Two of the best students will have the opportunity of a presentation 。
