1、1.Forces Acting on a Machine(1)Working resistance Working resistance refers to the types of machines.(2)Driving force The different prime motors have different operating peculiarities.The relationship between the driving force and its speed is often represented by the peculiar curve of a machine.Fig
2、.12-1a shows a peculiar curve of an internal combustion engine,and Fig.12-1b shows a peculiar curve of an AC electromotor.12.1 Operating Analysis of MachineryFig.12-1Mechanical behavior curve of prime machines(原动机的机械特性曲线图)2.Operating Process of Machines(1)Start up period The running speed of a machi
3、ne is from zero to work running speed in this period,and the work done by the driving force is greater than the work done by the resistance.(2)Steady running period In the steady running period,the work done by the driving force is equal to the work done by the resistance in a period.The increment o
4、f the kinetic energy is zero.(3)Stopping period In the stopping period,the driving force will cease to work,thus Wd=0.The motion continues for a certain time owing to the inertia kinetic energy of the machine.Fig.12-2Crank punch(曲柄压力机)Fig.12-3Operating process of machinery(机械的运转过程)12.2 Equivalent Ki
5、netic Model of Mechanism Systems1.The Method of Researching Running Process of Machines Fig.12-4Force analysis of a crank punch(曲柄压力机的受力分析)In order to find the actual motion of a mechanism shown in Fig.12-4,we must solve the driving torque acting on the link 1 and the angular velocity.The dynamic fo
6、rce analysis of the slider crank mechanism has a large number of unknowns to solve.We often select the rotating link or reciprocating link as an equivalent link.Fig.12-5 shows those equivalent links.Fig.12-5Equivalent links(等效构件)(1)Rotating equivalent link When the equivalent link is rotating about
7、an axis with a constant angular velocity,the kinetic energy is as follows：2.The Parameter of The Equivalent Link If the equivalent link performs a rotating motion,the instant power is as follows:The instant power generated by the equivalent link is equal to the ones generated by the whole machine,so
8、 we have：(2)Reciprocating equivalent link All the driving forces or moments acting on the machine are replaced by one force or moment applied to the equivalent link,this is called the equivalent driving force or driving moment.All the resistances acting on the machine are replaced by one force or mo
9、ment applied to the equivalent link,this is called the equivalent resistant force or resistant moment.Obviously,we can write them as follows：Example 12-1 Fig.12-6 shows a planetary gear train.The numbers of teeth of gears are z1、z2、z3 respectively.The mass centers of these gears are coefficient with
10、 their rotating centers,and the moments of inertia of gears 1,2 and the arm about their centers are J1、J2、JH.The mass of the planetary gear is m2.We assume the gear 1 to be the equivalent link.Determine the equivalent moment of inertia.Fig.12-6Planetary gear train(行星轮系)Example 12-2 Fig 12-7 shows a
11、Scotch yoke mechanism.The crank has a length of l1,and the moment of inertia about its rotating center A is J1.The link 2 and 3 have masses of m2、m3.The resistance acting on the link 3 is F3.Determine the equivalent moment of inertia,when the crank is the equivalent link,and equivalent resistance ac
12、ting on the crank.Fig.12-7Scotch-yoke mechanism(正弦机构)1.Kinetic Equations of the Equivalent Link12.3 Kinetic Equations of Mechanism SystemsRearranging the above equations，we have：considering the border conditions,we obtain:considering the border conditions,we obtain:2.Solution of the Kinetic Equation
13、(1)The equivalent moment of inertia and equivalent moment are constants This is suitable for machines with constant ratio and constant force or moment,such as a gear hoist.(2)The equivalent moment of inertia and equivalent moment are functions of position When the equivalent moment of inertia and eq
14、uivalent moment are analytical forms,we can use the integrating equation to solve this problem.Example 12-3 Fig.12-8 shows a mechanism system in which the electric motor rotates at 1440r/min,and the ratio of the gear reducer is i=2.5.The shaft B is selected as an equivalent link,and its equivalent m
15、oment of inertia Je=0.5kgm2.If the shaft B has been braked,the hoist must be stopped within three seconds.Determine the braking moment supplied to the shaft B.Fig.12-8Simple mechanical system(简单的机械系统)1.Work and Energy in a Steady Running PeriodFig.12-9Equivalent moment diagram(等效力矩线图)12.4 Periodic S
16、peed Fluctuation and Regulation in a Machine Fig.12-9 shows a diagram of equivalent driving moment Md and equivalent resistant moment Mr.When MdMr,the kinetic energy of the machine increases,and the angular velocity increases too.When MdMr,the kinetic energy of the machine decreases,and the angular
17、velocity decreases too.2.Fluctuation of Speed When a flywheel is mounted in a machine spindle,the total kinetic energy is the sum of the kinetic energy of the flywheel and the kinetic energy of the machine.So we have:Suppose the moment of inertia of the flywheel is J f,the maximum kinetic energy Efm
18、ax and the minimum kinetic energy E fmin of the flywheel are as follows：As we know,the moment of inertia consists of two portions：one portion is constant and the other is various.The kinetic energy of the equivalent link can be written as：Because when the kinetic energy is maximum the speed is maxim
19、um,and when the kinetic energy is minimum the speed is minimum.Rearranging these equations，we have：The moment of inertia of the flywheel is based on that the flywheel is mounted to the equivalent link.If the flywheel is fixed to the other link,such as x link,rather than the equivalent link,its momen
20、t of inertia Jx can be determined according to the same energy supplied by the flywheel.This can be written as:Fig.12-10Dimensions of flywheels(飞轮尺寸)3.Dimensions of Flywheels There are two shapes of flywheels：the one is disk,and the other is disk with web.Fig 12-10 shows these flywheels.The inertia
21、of a flywheel is provided by the hub,web and the rim.However,the inertia due to the hub and the web is very small,usually it is ignored.Example 12-4 The equivalent link is selected as the crank shaft of a shaper,and its average speed is 60r/min.The operating period of steady motion is 2.The allowabl
22、e coefficient of speed fluctuation=0.1.The diagram of the equivalent resistant moment Mr versus angle is shown as Fig12-11,and the equivalent driving moment Md is a constant.If the moment of inertia of the machine has been ignored,determine the moment of inertia of the flywheel.Fig.12-11The diagram
23、of Equivalent moment of the shaper(刨床等效力矩图)12.5 Aperiodic Speed Fluctuation and Regulation in a MachineFig 12-12 shows a diagram of a governor.The governor shaft 1 is rotated by the engine W1 and a sleeve 2 carried on the shaft is positioned by the ball crank lever.When the rotating speed of the sha
24、ft increases,the centrifugal forces acting on the two balls increase too,the sleeve will move up.The oil supply will be reduced,and the electric power generated will be reduced due to the reduction of the rotating speed.Fig.12-12Centrifugal governor(离心调速器)1shaft(主轴)2sleeve(套筒)3、5、7Rod(杆件)4ball(重球)6spring(弹簧)
