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1、Technical guide No.7-Basic formulas基本公式,Road show 3Jukka Juottonen,Technical guide No.7-Basic formulas,Purpose of the presentation 内容Show the typical formulas used in basic dimensioning 说明基本选型公式The targets of the presentation are that you:目的Can do also manual calculations of basic dynamical systems(
2、e.g.acceleration time)动态系统的手工计算,Purpose and targets of the presentation内容和目的,Technical guide No.7-Basic formulas,Motors mechanical output power can be calculated from speed and torque:通过速度和力矩计算电机的输出功率,AC motor-Power 交流电机的功率,Motors input power can be calculated from voltage,current and power factor:通
3、过电压，电流和功率因数计算电机输入功率,Technical guide No.7-Basic formulas,Motors efficiency is output power divided by input power:电机效率是输出功率/输入功率,AC motor-Power 交流电机的功率,At nominal point AC motors output power is:电机额定点的输出功率,or,Electric power input电磁功率输入,Mechanical power output机械功率输出,Thermalpower losses热损耗,轴头电功率,轴头机械功率
4、,Technical guide No.7-Basic formulas,One of the fundamental equations for an electric motor is:电机转子的加速规律,AC motor-Mechanical laws of rotational motionAC电机的转动原理,Motor torque consists of dynamic and load component.Dynamic component changes the speed:电机力矩包含动态力矩分量和负载力矩分量,Technical guide No.7-Basic formu
5、las,Dynamic torque component changes the motor speed:动态力矩分量影响电机转速,In practice the dynamic component is calculated as follows:动态分量的工程计算,The total torque needed in acceleration is thus:加速过程中总的力矩是,AC motor-Mechanical laws of rotational motionAC电机的转动原理,Technical guide No.7-Basic formulas,Example:AC moto
6、rs and loads total moment of inertia is 3 kgm2.Constant load torque is 50 Nm.举例：电机和负载的总转动惯量是3 kgm2，恒定负载力矩50 NmA)What is the torque needed to accelerate the motor from 0 rpm to 1000 rpm speed in 10 seconds?问题A)：电机转速在10秒内从0加速到1000rpm，需要多大力矩？B)If the electric supply is switched off at 1000 rpm speed ho
7、w fast will the motor decelerate to 0 rpm speed?问题B)：如果电机运行在1000rpm时，停止供电，那么电机减速至0rpm要多少时间？,AC motor-Mechanical laws of rotational motionAC电机的转动原理,Technical guide No.7-Basic formulas,Solution:答案A)The total torque needed for acceleration is the sum of dynamic and load components.加速过程中总力矩是动态和负载力矩之和,B)
8、The motor decelerates because of the load torque(50 Nm)，Actual motor torque is zero.Then:减速过程中，仅靠负载力矩起作用(50 Nm)，电机本身没有任何力矩起作用,AC motor-Mechanical laws of rotational motionAC电机的转动原理,Technical guide No.7-Basic formulas,Moment of inertia&gears惯性矩和齿轮箱的因素,Inertia(moment of inertia)is important to know in
9、 many dimensioning cases.选型时必须知道惯性(转动惯量)。Generally Jkgm2 can be given by motor and machine manufacturers.制造厂通常给出转动惯量：Jkgm2Sometimes it can be calculated quite easily.For a cylinder shape the moment of inertia is proportional to mass and quadratically proportional to radius of the cylinder:J=m*r2.转动惯
10、量很容易计算。圆筒型的转动惯量与其质量和半径的平方成正比：J=m*r2Energy stored to a rotating mass is:E=0.5*J*w2 旋转体储存的能量是：E=0.5*J*w2,Technical guide No.7-Basic formulas,Moment of inertia&gears惯性矩和齿轮箱的因素,When gear is used power,torque,moment of inertia,spring constant of a shaft,etc.must be reduced.使用齿轮箱时，功率，转矩，转动惯量，轴的弹性系数等必定会减小,
11、h,Technical guide No.7-Basic formulas,Calculation example 计算举例,A fan has following load characteristics 一个风机有如下的负载特性,Technical guide No.7-Basic formulas,Calculation example 计算举例,A following motor has been selected:电机选型如下Pn=110 kWUn=400 V In=202 Acos(fn)=0.83nn=991 rpmJmotor=5 kgm2,Fans moment of ine
12、rtia is Jfan=995 kgm2 风机转动惯量：Jfan=995 kgm2,Technical guide No.7-Basic formulas,Calculation example计算举例,Task 1:What is the nominal torque of the motor?What is the nominal efficiency of the motor?电机的额定力矩是多少？电机的额定效率是多少？Task 2:Estimate the starting time from 0 to 100%speed if accelerating is done with n
13、ominal torque.如果以额定力矩加速，估算电机转速从0上升到100%的额定速度的起动时间。,Solution,Technical guide No.7-Basic formulas,Calculation example,Task 3:Estimate the deceleration time from 100%to 0%speed if it is assumed that the average braking torque over the whole speed range(in generating mode,flux braking is utilised)is 4.5
14、%.Hint:Divide the speed range into sectors and calculate the times over the sectors.,Technical guide No.7-Basic formulas,Calculation example-Solution,Nominal efficiency of the motor is:电机的额定效率,Task 1:,Nominal torque of the motor is:电机的额定力矩,Technical guide No.7-Basic formulas,Calculation example-Solu
15、tion,Speed range is divided into 10 sectors.速度范围分成10段Acceleration time for each sector is calculated using formula:每一段的加速时间用下列公式计算,Task 2:,In each sector average value of load torque is used.For example in sector 1 the average load torque is(20+12.9)/2%=16.45%and the dynamic accelerating torque(Tn-T
16、load)is 100%-16.45%=83.55%.每段都使用负载力矩的平均值。例如第一部分的平均力矩是：(20+12.9)/2%=16.45%，动态加速力矩(Tn-Tload)是：100%-16.45%=83.55%.,Technical guide No.7-Basic formulas,Calculation example-Solution,Task 2:,Technical guide No.7-Basic formulas,Calculation example-Solution,Task 2:,Technical guide No.7-Basic formulas,Calcul
17、ation example-Solution,Task 2:,The total acceleration time is the sum of all sector times:186.8 seconds!总时间为每段时间之和,Sector width affects the accuracy of this kind of approximation.每一部分的宽度影响近似类型的精度,Technical guide No.7-Basic formulas,Calculation example-Solution,Speed range is divided into 10 sectors.
18、Deceleration time for each sector is calculated using formula(T=-4.5%):,Task 3:,In each sector average value of load torque is used.For example in sector 10 the average load torque is(90+72.9)/2%=81.45%and the dynamic decelerating torque is 81.45%+4.5%=85.95%.,Technical guide No.7-Basic formulas,Cal
19、culation example-Solution,Task 3:,Technical guide No.7-Basic formulas,Calculation example-Solution,Task 3:,Technical guide No.7-Basic formulas,Calculation example-Solution,Task 3:,The total deceleration time is the sum of all sector times:383.7 seconds!,Sector width affects the accuracy of this kind of approximation.,
