电机的选型计算

1、,电机的选型计算,作者: Michel COUPAT,目录,I 关于机械的背景知识 II 再生能量 III 电机选型计算的步骤 IV 施耐德伺服的计算 V 练习,Michel COUPAT,M8 lex15 Lexium Sizer,电机和驱动器的选型计算,I 关于机械的背景知识 单位 机械公式 惯量的计算 运动学 摩擦 惯量的比例 II 再生能量 III 电机选型计算的步骤 IV 施耐德伺服的计算 V 练习,Michel COUPAT,M8 lex15 Lexium Sizer,单位,关于机械的背景知识,Michel COUPAT,M8 lex15 Lexium Sizer,米制单位,3 个

2、基本单位 : 国际单位制 (SI) 质量 : m 单位 : 千克 (kg) 长度 : l 单位 : 米 (m) 时间 : t 单位 : 秒 (s) _ 推导单位 : 角度: 单位 : 弧度 (rad) 360 = 2rad,Michel COUPAT,M8 lex15 Lexium Sizer,运动学 线速度 : l t-1 单位 : 米每秒 (m/s or m.s-1) 角速度 : t -1 单位 : 弧度每秒 (rd/s or s-1),x in m t in s D in m,t in s in radians, in rd/s N in rpm,米制单位,Michel COUPAT,M

3、8 lex15 Lexium Sizer,运动学 : 线加速度 : l t -2 单位 : 米每秒平方 (m/s/s or m.s-2) 角加速度 : t -2 单位 : 弧度每平方秒 (rad.s-2 or s-2),v in m/s t in s,t in s in rd/s,米制单位,Michel COUPAT,M8 lex15 Lexium Sizer,运动学 : 力 : m l t - 单位 : 牛顿 (N) 力等于质量与加速度的乘积: F = m 重量 W : m l t - 单位 : 牛顿 (N) W = m.g (g : 重力加速度 = 9,81m/s ) 力矩 M : m l

4、 t - 单位 : 牛米 (Nm) 力与长度的乘积 : M = F r (力与长度的方向垂直时) 运动力矩 : M = J (J : 转动惯量 kg.m) 能量: m l t - 单位 : 焦耳 (J) 力与位移的乘积 : E = F L 或转矩与角度的乘积 : E = M ,米制单位,Michel COUPAT,M8 lex15 Lexium Sizer,E in Joule t in s,F in Newton V in m/s,M in Nm in rad/s,米制单位,运动学 : 功率 : m l t -3 单位 : Watt (W) 1 W = 1 J/s * 直线运动 : P =

5、F v * 角运动 : P = M ,Michel COUPAT,M8 lex15 Lexium Sizer,英制单位,质量,重量,力 : 单位 : 磅 (lb) 盎司 (oz) : 1 lb = 16 oz 长度 : 单位 : 英寸 (in) 1英尺 (ft) = 12 英寸 - 1 码 (yd) = 3英尺 时间 : 单位 : 秒 (s) 线速度 : 单位 : 英寸每秒 (in/s) 线加速度 : 单位 : 英寸每平方秒 (in/s) 力矩: 单位 : 英寸磅 (in.lb) 惯量 : 单位 : 英寸磅平方秒 (in.lb.s),Michel COUPAT,M8 lex15 Lexium

6、Sizer,等效的米制和英制单位,重量 : 1 pound (lb) = 453,59237 g = 0,45359237 kg = 4,44822 N 长度 : 1 inch (in) = 2,54 cm = 0,0254 m 力矩 : 1 inch pound (in.lb) = 0,1130234 Nm 惯量 : 1 inch pound second square (in.lb.s) = 0,112961 kg.m 重力加速度 : g = 386 in/s = 32,12 ft/s = 9,81 m/s,Michel COUPAT,M8 lex15 Lexium Sizer,机械公式,

7、关于机械的背景知识,Michel COUPAT,M8 lex15 Lexium Sizer,直线运动 : 角度运动 :,机械公式,Michel COUPAT,M8 lex15 Lexium Sizer,E in Joules J in kg.m2 in rad/s,直线运动 : 转动 :,E in Joules m in kg v in m/s,动能,Michel COUPAT,M8 lex15 Lexium Sizer,惯量的计算,关于机械的背景知识,Michel COUPAT,M8 lex15 Lexium Sizer,密度 : 单位 : 千克每立方米 (Kg/m3) 磅每立方英尺 (lb

8、/in3) 某个体积承载的重量取决于构成的材料. 常见材料的密度:,m : 质量 in Kg or lb V : 体积 in m3 or in3 : 密度 in Kg/m3 or lb/in3,钢 : 7750 Kg / m3 0,286 lb / in3 铝 : 2720 Kg / m3 0,098 lb / in3 黄铜 : 8170 Kg / m3 0,295 lb / in3 紫铜 : 8910 Kg / m3 0,322 lb / in3 塑料 : 1110 Kg / m3 0,040 lb / in3,密度,Michel COUPAT,M8 lex15 Lexium Sizer,长

9、方体,(if h and W Mt + Mf.,Michel COUPAT,M8 lex15 Lexium Sizer,Stage 3 : Dynamic sizing,Different stages of sizing,Michel COUPAT,M8 lex15 Lexium Sizer,ELEMENTS TO DEFINE : Acceleration torque : MACC = J. From all the data of the kinematics, calculate the torque to reach the acceleration requirements. F

10、riction torque Mf. Calculate or evaluate if possible the friction torque on the axis. FIRST APPROACH OF DRIVE CHOICE : Maximal torque : MMAX MACC + Mf. The maximal torque available on the motor is defined by the maximal current available on the drive.,Dynamic sizing,Michel COUPAT,M8 lex15 Lexium Siz

11、er,Stage 4 : Thermal verification,Different stages of sizing,Michel COUPAT,M8 lex15 Lexium Sizer,Thermal verification,From the first motor - drive association defined previously, it is necessary to check its appropriateness with the working cycle. Plot speed versus time and torque versus time for th

12、e entire motion cycle.,Michel COUPAT,M8 lex15 Lexium Sizer,Thermal verification,Calculating the average speed.,Calculating the equivalent thermal torque.,During the acceleration and deceleration times :,Michel COUPAT,M8 lex15 Lexium Sizer,Thermal verification,Compare the calculation results with the

13、 Torque curve of motor :,Case A : Motor well sized for the working cycle.,Case B : Choose another motor with higher continuous torque.,Michel COUPAT,M8 lex15 Lexium Sizer,Stage 5 : Inertia ratio,Different stages of sizing,Michel COUPAT,M8 lex15 Lexium Sizer,Inertia ratio,From machine data calculate

14、the inertia ratio between load and motor. If this ratio is to high (see typical ratio below) Either change eventually the kinematics (i.e. by using Gearbox), or use another motor with higher inertia. or both. Make a new sizing with the new inertia data. Typical ratios of load to motor inertia can be

15、 : from 1:1 to 3:1 - for robotic applications. from 4:1 to 7:1 - for machine tool type applications. from 8:1 to 10:1 - for other factory automation applications. More practically, we can advise to limit the inertia ratio to : 5:1 for dynamical and accurate machines. 10:1 for standard machines. High

16、er if we only need stop accuracy without time cycle constraint.,Michel COUPAT,M8 lex15 Lexium Sizer,Stage 6 : Braking resistor,Different stages of sizing,Michel COUPAT,M8 lex15 Lexium Sizer,Inertia ratio,Check if an external braking resistance is required : See chapter II.,Michel COUPAT,M8 lex15 Lex

17、ium Sizer,Schneider Motion Sizer,I Mechanical reminder II Energy regenerated III Different stages of sizing IV Schneider Motion Sizer V Exercises,Michel COUPAT,M8 lex15 Lexium Sizer,Why a Motion Sizer ?,Help to choose the right motor - drive association from : Kinematics definition. Velocity profile

18、 of the cycle. Help to choose the best ratio of inertia between motor and load.,Michel COUPAT,M8 lex15 Lexium Sizer,Setup units,Choose the units of works : Metric units. US standards (Anglo-Saxon units).,Michel COUPAT,M8 lex15 Lexium Sizer,Belt - Pulley,Axis Design : Kinematics definition,HELP !,Kin

19、ematics parameters to define Load Inertia,Conveyor,Disk,Gearbox,Lead screw,Rack - Pinion,Rotary table,Nip roll,Kinematics :,Michel COUPAT,M8 lex15 Lexium Sizer,Velocity profile,Definition of the velocity profile of cycle work :,Michel COUPAT,M8 lex15 Lexium Sizer,Motor selection : criteria of choice

20、,Select the best criteria to choose the motor :,Stability : select the best load/motor inertia match.,Dynamic : select the smallest motor.,Michel COUPAT,M8 lex15 Lexium Sizer,Motor selection : safety factors,To define the limits of value for selecting motors :,Michel COUPAT,M8 lex15 Lexium Sizer,Mot

21、or selection,List of motors selected,Inertia ratio : Message “Gearbox ?” is noted if inertia ratio 10,Michel COUPAT,M8 lex15 Lexium Sizer,Motor selection : braking resistor,Here is indicated if an external braking resistor is requested,Michel COUPAT,M8 lex15 Lexium Sizer,Report generator,Lexium size

22、r creates a professional looking application report for every axes.,Michel COUPAT,M8 lex15 Lexium Sizer,Performances curves,Select the best inertia ratio can induce to choose an higher motor than the cycle requests.,Michel COUPAT,M8 lex15 Lexium Sizer,Schneider Motion Sizer,I Mechanical reminder II

23、Energy regenerated III Different stages of sizing IV Schneider Motion Sizer V Exercises,Michel COUPAT,M8 lex15 Lexium Sizer,Ex.1 : Conveyor indexer,Machine Data : - Motor pulley (mp) : D : 14 cm m : 3,6 Kg - Gearbox pulley (gp) : D : 21 cm m : 10 Kg - Belt mass : 50 g - Gearbox Ratio : 8,25 Inertia

24、(gb) : 0,021 Kg.m Efficiency : 98% - Main pulley (md) : D : 20 cm m : 9,2 Kg - Load mass : 700 Kg - Belt conveyor mass : 4,5 Kg - Coefficient friction : 0,1,Michel COUPAT,M8 lex15 Lexium Sizer,Ex.1 : Conveyor indexer,1-1 : Calculate the inertia reflected to the motor shaft. 1-2 : Calculate the resis

25、tant torque to the motor shaft. 1-2-1 Horizontal axis 1-2-2 Vertical axis 1-2-3 Axis 45 1-2-4 Check the calculation with Schneider Sizer.,Michel COUPAT,M8 lex15 Lexium Sizer,Triangular Profile :,Ex.1a : Triangular profile,- Move distance : 6 m - Move time : 5 s - Dwell time : 0 s,1a-1 : Calculate th

26、e thermal torque for horizontal axis. 1a-2 : Check the calculation with Schneider Sizer.,Michel COUPAT,M8 lex15 Lexium Sizer,Trapezoidal Profile :,Ex.1b : Trapezoidal profile,- Move distance : 6 m - Move time : 5 s - Dwell time : 0 s,1b-1 : Check the calculation with Schneider Sizer.,Michel COUPAT,M

27、8 lex15 Lexium Sizer,Trapezoidal Profile :,Ex.1c : Trapezoidal profile,- Move Speed : 1 m/s - Move time : 5 s - Accel./Decel time : 0,2 s - Dwell time : 0 s,1c-1 : Calculate the thermal torque for horizontal axis. 1c-2 : Check the calculation with Schneider Sizer.,Michel COUPAT,M8 lex15 Lexium Sizer,Trapezoidal Profile :,Ex.1d : Constant speed,- Move distance : 6 m - Move time : 3600 s - Accel./Decel time : 60 s - Dwell time : 0 s,1d-1 : Check the c