電機的選型計算選編

電機的選型計算作者:Michel

COUPATM8

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Sizer目錄I關(guān)于機械的背景知識II再生能量IIIIV電機選型計算的步驟

施耐德伺服的計算VSummaryM8

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Sizer練習(xí)電機和驅(qū)動器的選型計算I關(guān)于機械的背景知識單位機械公式慣量的計算運動學(xué)摩擦慣量的比例II再生能量IIIIV電機選型計算的步驟

施耐德伺服的計算VSummaryM8

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Sizer練習(xí)單位SummaryM8

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Sizer關(guān)于機械的背景知識米制單位3個基本單位:國際單位制(SI)質(zhì)量:m單位:千克(kg)長度:l單位:米(m)時間:t單位:秒(s)推導(dǎo)單位:角度:單位

:

弧度

(rad)360°

=

2

radrlθSummaryM8

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Sizer運動學(xué)線速度:l

t-1單位:米每秒(m/s

or

m.s-1)角速度:t

-1單位:弧度每秒(rd/s

or

s-1)W

x

in

mW

t

in

sW

D

in

mW

t

in

sWinradiansW

ω

in

rd/sW

N

in

rpmSummaryM8

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Sizer米制單位運動學(xué):線加速度:l

t

-2單位:米每秒平方(m/s/s

or

m.s-2)角加速度:t

-2單位:弧度每平方秒(rad.s-2

or

s-2)W

v

in

m/sW

t

in

sW

t

in

sW

ω

in

rd/sSummaryM8

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Sizer米制單位運動學(xué):力:m

l

t

-2單位:牛頓(N)力等于質(zhì)量與加速度的乘積:F=m

γ重量W:m

l

t

-2單位:牛頓(N)W=m.g(g:重力加速度=9,81m/s2)力矩M:m

l2

t

-2單位:牛米(Nm)力與長度的乘積:M=F

r(力與長度的方向垂直時)運動力矩:M=J

’

(J:轉(zhuǎn)動慣量kg.m2)能量:m

l2

t

-2單位:焦耳(J)力與位移的乘積:

E

=

F

L或轉(zhuǎn)矩與角度的乘積:

E

=

MrF米制單位SummaryM8

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SizerW

E

in

JouleW

t

in

sW

F

in

NewtonW

V

in

m/sW

M

in

NmSummaryM8

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SizerWin

rad/s米制單位運動學(xué):功率:m

l2

t

-3單位:Watt

(W)*直線運動:P

=

F

v1

W

=

1

J/s*角運動:P

=

M英制單位SummaryM8

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Sizer質(zhì)量,重量,力:單位:磅(lb)[盎司(oz):1

lb

=16

oz]長度:[1英尺(ft)=12英寸-1碼(yd)=3英尺]單位:英寸(in)時間:單位:秒(s)線速度:單位:英寸每秒(in/s)線加速度:單位:英寸每平方秒(in/s2)力矩:單位:英寸磅(in.lb)慣量:單位:英寸磅平方秒(in.lb.s2)等效的米制和英制單位SummaryM8

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Sizer重量:1

pound

(lb)

=

453,59237

g

=

0,45359237

kg

=

4,44822

N長度:1

inch

(in)

=

2,54

cm

=

0,0254

m力矩:1

inch

pound

(in.lb)

=

0,1130234

Nm慣量:1

inch

pound

second

square

(in.lb.s2)

=

0,112961

kg.m2重力加速度:g

=

386

in/s2

=

32,12

ft/s2

=

9,81

m/s2機械公式SummaryM8

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Sizer關(guān)于機械的背景知識直線運動:角度運動:機械公式SummaryM8

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SizerW

E

in

JoulesW

J

in

kg.m2Win

rad/s直線運動:轉(zhuǎn)動:W

E

in

JoulesW

m

in

kgW

v

in

m/sSummaryM8

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Sizer動能慣量的計算SummaryM8

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Sizer關(guān)于機械的背景知識密度:單位:千克每立方米(Kg/m3)磅每立方英尺(lb/in3)某個體積承載的重量取決于構(gòu)成的材料.W

m:質(zhì)量in

Kg

or

lbW

V:體積in

m3

or

in3W

:密度in

Kg/m3

or

lb/in3常見材料的密度:SummaryM8

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Sizero

鋼

:7750

Kg

/

m30,286

lb

/

in3o

鋁

:2720

Kg

/

m30,098

lb

/

in3o

黃銅:8170

Kg

/

m30,295

lb

/

in3o

紫銅:8910

Kg

/

m30,322

lb

/

in3o

塑料:1110

Kg

/

m30,040

lb

/

in3密度長方體(if

h

and

W

<<

L)SummaryM8

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Sizer實心圓柱體SummaryM8

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Sizer空心圓柱體SummaryM8

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Sizer力臂和質(zhì)量SummaryM8

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SizerRm1J

?r1J

=

m

R2

+

m1

r12m力臂和質(zhì)量SummaryM8

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Sizer不同類型的機械SummaryM8

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Sizer關(guān)于機械的背景知識減速機JM

:電機的轉(zhuǎn)動慣量JL

:負載的慣量JL

M

:反映到電機的負載慣量ML

:負載轉(zhuǎn)矩JR

:反映到輸入側(cè)的減速機慣量R:機械系數(shù)ηR

:減速機效率JMJLθL,

ωL,

MLθM,

ωMJL

MJR,

R,

ηR總的慣量:按照能量守恒定律:反映到電機的轉(zhuǎn)矩:SummaryM8

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Sizer皮帶和鏈條減速器JMJLθL,

ωL,

MLθM,

ωMJPM,

DPM,

NTMJPL,

DPL,

NTLJM

:電機的慣量JL

:負載的慣量ML

:負載轉(zhuǎn)矩JPM

:電機傳動輪慣量DPM

:電機傳動輪直徑NTM

:電機傳動輪的齒數(shù)JPL

:負載傳動輪的慣量DPL

:負載傳動輪的直徑NTL

:負載傳動輪的齒數(shù)η

:減速器的效率mB

:皮帶的質(zhì)量MB總的慣量:折算的慣量:折算到電機的轉(zhuǎn)矩:SummaryM8

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Sizer齒輪箱JMJLθL,

ωL,

MLθM,

ωMJGM,

NTMJGL,

NTL總的慣量:折算的慣量:JM

:電機的慣量JL

:負載的慣量ML

:負載轉(zhuǎn)矩JGM

:電機側(cè)的齒輪慣量NTM

:電機側(cè)的齒輪齒數(shù)JGL

:負載側(cè)的齒輪慣量NTL

:負載側(cè)的齒輪齒數(shù)η

:減速器的效率折算到電機的轉(zhuǎn)矩:SummaryM8

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Sizer導(dǎo)螺桿JM

:電機的慣量JC

:耦合慣量mL

:負載的質(zhì)量XL

:負載的位移VL

:負載的速度mT

:工作臺的質(zhì)量FP

:力Fg

:重力

Ffr

:摩擦JS

:螺桿的慣量p:螺距(mm/rev)α

:軸向的角度

η

:螺桿的效率

μ:摩擦系數(shù)g:重力加速度JMJS,

pθM,

ωMmLJCαFfrXL

,

VL

FP

,

FgmTSummaryM8

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Sizer折算的慣量:根據(jù)能量守恒定律:導(dǎo)螺桿總的慣量:JMSummaryM8

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SizerJS,

PθM,

ωMMLJCα如果我們考慮到螺桿,負載,工作臺的數(shù)據(jù)和效率:FfrXL

,

VL

FP

,

FgMT

折算到電機的轉(zhuǎn)矩:按照能量守恒定律:導(dǎo)螺桿JMθM,

ωMMLJCαFfrXL

,

VL

FP

,

FgJS,

PMT如果我們考慮到螺桿,負載,工作臺的數(shù)據(jù)和效率:SummaryM8

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Sizer傳送帶JMJP3,

D3θM,

ωMmLαFfrXL

,

VL

FP

,

FgMBJP2,

D2JP1,

D1

NTP1,

pJM

:電機的慣量mL

:負載的質(zhì)量XL

:負載的位移VL

:負載的速度mT

:工作臺的質(zhì)量FP

:力Fg

:重力

Ffr

:摩擦JPx

:傳動輪的慣量Dx

:傳動輪的直徑

NTP1

:主傳動輪的齒數(shù)p:齒條的節(jié)距(mm/tooth)CP1

:主傳動輪的周長α

:軸向的角度η

:皮帶傳動輪的效率μ:摩擦系數(shù)g:重力加速度SummaryM8

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Sizer傳送帶JMJP3,

D3θM,

ωMmLαXL

,

VL

FP

,

FgFfrmBJP2,

D2JP1,

D1

NTP1,

PJP1,JP2,JP3

根據(jù)實心柱體計算.折算的慣量:總的慣量:折算到電機的轉(zhuǎn)矩:SummaryM8

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SizerRack

and

pinionJMθM,

ωMMLαFfrXL

,

VLFP

,

FgMTDGJG,

NTG,

PGJM

:電機的慣量mL

:負載的質(zhì)量XL

:負載的位移VL

:負載的速度FP

:力Fg

:重力

Ffr

:摩擦JG

:齒輪的慣量DG

:齒輪的直徑NTG

:齒輪的齒數(shù)pG

:齒的節(jié)距(mm/tooth)CG

:齒輪的周長α

:軸的角度

η

:齒輪的效率μ:摩擦系數(shù)g:重力加速度SummaryM8

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SizerRack

and

pinionJMθM,

ωMMLαFfrXL

,

VLFP

,

FgMTDGJG,

NTG,

PG折算的慣量:總的慣量:折算到電機的轉(zhuǎn)矩:SummaryM8

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Sizer機械效率SummaryM8

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Sizer常見的機械的效率:阿基米德螺桿(帶銅襯套)

:

from

0.35

to

0.65阿基米德螺桿(塑料襯套):from

0.50

to

0.85滾珠絲杠:預(yù)加載滾珠絲杠:正齒輪:錐齒輪:蝸輪:鏈輪:調(diào)速皮帶:軸承:from

0.75

to

0.85from

0.85

to

0.95~

0.75from

0.90

to

0.95from

0.45

to

0.85~

0.95,

0.98~

0.96,

0.98~

0.98摩擦SummaryM8

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Sizer關(guān)于機械的背景知識摩擦SummaryM8

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Sizer摩擦:當(dāng)一個物體在另一個物體上滑動時,兩個物體之間的作用力.取決與兩個物體之間的相對速度.摩擦力的方向與滑動的方向相反摩擦的公共模型有三個組成部分:滑動摩擦(Coulomb):幅值大致不變.零速時的粘滯摩擦(靜摩擦).????從零速到滑行的摩擦過渡不明顯.僅僅在很低的速度下發(fā)生.對系統(tǒng)有不穩(wěn)定的影響,會造成粘滑運動的現(xiàn)象.This

phenomenon

is

exacerbated

with

compliantcouplings.與速度成正比的粘滯阻尼.摩擦Fcoulomb(滑動摩擦)Fviscous(Nm/rpm)摩擦力(N)粘滯效應(yīng)Fstiction(靜摩擦)ωSummaryM8

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Sizer摩擦SummaryM8

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Sizer典型的滑動摩擦系數(shù):鋼對鋼:鋼對鋼(涂脂):鋁對鋼:黃銅對鋼:紫銅對鋼:塑料對鋼:~

0.58~

0.15~

0.45~

0.35~

0.58~

0.15,

0.25慣量系數(shù)SummaryM8

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Sizer關(guān)于機械的背景知識電機規(guī)格的選擇SummaryM8

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Sizer低慣量電機還是高慣量電機?負載和電機之間的慣量匹配?低慣量SummaryM8

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Sizer低慣量=高加速度因為牛頓定律告訴我們,對于一個旋轉(zhuǎn)的系統(tǒng):M=J

ω’

這里M:轉(zhuǎn)矩(Nm)J:慣量(Kg.m2)ω’:角加速度rd/s2ω’

=

M

/

J(加速度=轉(zhuǎn)矩/慣量)低慣量電機:允許高動態(tài)系統(tǒng).增加系統(tǒng)帶寬.但是增加了負載與電機的不匹配不同慣量下系統(tǒng)的響應(yīng)SummaryM8

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Sizer2

13

44象限概念4-象限調(diào)節(jié):象限系指以轉(zhuǎn)速轉(zhuǎn)矩為坐標(biāo)軸所畫圖的4個區(qū)域?正速度方向:順時針.MotorSummaryM8

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SizerMotorGeneratorGenerator當(dāng)速度與轉(zhuǎn)矩方向相同時，為電動狀態(tài)(1和3象限)2，4象限，電機處于制動狀態(tài).?電機工作于發(fā)電機狀態(tài).電機再生的能量必須被消耗.?制動電阻的計算SummaryM8

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Sizer產(chǎn)生的能量制動電阻的指標(biāo):Ohm

值.SummaryM8

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Sizer?驅(qū)動器的容量決定了最小的阻值.峰值功率.?由最小電阻和直流母線電壓決定.持續(xù)功率.?與工作循環(huán)有關(guān).制動電阻制動電阻的計算需要:系統(tǒng)慣量,工作循環(huán)表.制動電阻計算指導(dǎo)nStep1:對每個工作循環(huán)畫速度-時間圖和力矩-時間圖n無需畫出力矩的幅值,只需畫出力矩的方向.Step

2:確定每個部分的工作狀態(tài),是否減速/速度力矩是否方向相反.SummaryM8

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SizerGuideline

for

resistor

calculationSummaryM8

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SizerStep

6:計算峰值功率,將每一段需要消耗的動能除以這一段的減速時間P

peak

=

E

dissipated

/

ti

deceleration(s)

??當(dāng)然,還要檢查最大峰值功率如果最大峰值功率超出了驅(qū)動器的最大過載能力,則需放大驅(qū)動器.Step

7

:

Calculate

the

continuous

power

dissipated

by

the

braking

resistorby

totaling

all

the

dissipated

energy

and

dividing

it

by

the

total

cycle

time.P

continuous

=

E1dissipated

+

E2dissipated

+…+

Ei

dissipated)/T

cycleCheck

in

the

drive

characteristic

table

if

we

have

to

use

an

external

resistor.Note

:

All

the

steps

of

this

guideline

are

when

using

single

axis

connected

onDC

Bus

voltage.Motor

and

Drive

SizingIMechanical

remindersIIEnergy

regeneratedIIIDifferent

stages

of

sizingMachine

dataStatic

sizingDynamic

sizingThermal

verificationInertia

ratioBraking

resistorSchneider

Motion

SizerIVVSummaryM8

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SizerExercisesStage

1

:Machine

dataPerformance

requirementsSummaryM8

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SizerDifferent

stages

of

sizingMachine

dataSummaryM8

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SizerTo

size

correctly

a

motor

and

drive

association

we

need

any

data

fromthe

customer

about

the

machine

kinematics

:Type

of

axis

:Rotary

or

linear

axis

?Horizontal

or

vertical

?

Angle

?Type

of

kinematics

:Type

and

size

of

kinematics.

(Conveyor,

lead

screw,

rack

and

pinion,nip

roll,

….)Type

of

guidance.

(Slide,

bearings,

roll,

…)

To

estimate

friction.Type

and

ratio

for

gearboxes.

(Gear,

belt-pulley,

…)Load

size

:Load

dimensions.Mass

to

move.Performances

requirementsSummaryM8

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SizerThe

customer

also

must

define

all

his

requirements

for

the

performancesof

the

motion

:Maximal

speed

of

the

axis.Working

forces

or

torque.Optimum

working

cycle

:Time

of

cycle,Acceleration

and

deceleration

times,Distances

of

moving,…Stage

2

:Static

sizingSummaryM8

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SizerDifferent

stages

of

sizingStatic

sizingSummaryM8

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SizerELEMENTS

TO

DEFINE

:Maximal

speed

of

the

motor

:

nMAX.From

all

the

data

of

the

kinematics,

calculate

the

maximal

speed

of

the

motorto

reach

the

speed

requirements.Working

torque

Mt.From

the

working

force

required

and

the

data

of

the

kinematics,

calculate

thenecessary

working

torque.Friction

torque

Mf.Calculate

or

evaluate

if

possible

the

friction

torque

on

the

axis.FIRST

APPROACH

OF

MOTOR

CHOICE

:Nominal

speed

:

nN

>

nMAX.Nominal

torque

:

MN

>

Mt

+

Mf.Stage

3

:Dynamic

sizingSummaryM8

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SizerDifferent

stages

of

sizingELEMENTS

TO

DEFINE

:Acceleration

torque

:

MACC

=

Jω’.From

all

the

data

of

the

kinematics,

calculate

the

torque

to

reach

theacceleration

requirements.Friction

torque

Mf.Calculate

or

evaluate

if

possible

the

friction

torque

on

the

axis.FIRSTAPPROACH

OF

DRIVE

CHOICE

:Maximal

torque

:

MMAX

>

MACC

+

Mf.The

maximal

torque

available

on

the

motor

is

defined

by

the

maximal

currentavailable

on

the

drive.SummaryM8

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SizerDynamic

sizingStage

4

:Thermal

verificationSummaryM8

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SizerDifferent

stages

of

sizingThermal

verificationFrom

the

first

motor

-drive

association

definedpreviously,

it

isnecessary

to

check

itsappropriateness

withthe

working

cycle.n

Plot

speed

versustime

and

torque

versustime

for

the

entiremotion

cycle.SummaryM8

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SizerThermal

verificationCalculating

the

average

speed.During

the

acceleration

and

deceleration

times

:Calculating

the

equivalent

thermal

torque.SummaryM8

lex15

Lexium

Sizerên

(rpm)MthnavgContinuous

regionnavgThermal

verificationACompare

the

calculation

results

with

the

Torque

curve

of

motor

:Case

A

:

Motor

well

sized

for

the

working

cycle.Case

B

:

Choose

another

motor

with

higher

continuous

torque.M

(Nm)Intermittent

region?BMthSummaryM8

lex15

Lexium

SizerStage

5

:Inertia

ratioSummaryM8

lex15

Lexium

SizerDifferent

stages

of

sizingInertia

ratioSummaryM8

lex15

Lexium

SizerFrom

machine

data

calculate

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

:from

1:1

to

3:1

-

for

robotic

applications.from

4:1

to

7:1

-

for

machine

tool

type

applications.from

8:1to

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.Higher

if

we

only

need

stop

accuracy

without

time

cycle

constraint.Stage

6

:Braking

resistorSummaryM8

lex15

Lexium

SizerDifferent

stages

of

sizingInertia

ratioSummaryM8

lex15

Lexium

SizerCheck

if

anexternalbraking

resistance

is

required

:See

chapter

II.Schneider

Motion

SizerIMechanical

reminderIIEnergy

regeneratedIIIDifferent

stages

of

sizingIVSchneider

Motion

SizerVSummaryM8

lex15

Lexium

SizerExercisesWhy

a

Motion

Sizer

?Help

to

choose

the

right

motor

-

drive

association

from

:Kinematics

definition.Velocity

profile

of

the

cycle.Help

to

choose

the

best

ratio

of

inertia

between

motor

and

load.SummaryM8

lex15

Lexium

SizerSetup

unitsSummaryM8

lex15

Lexium

SizerChoose

the

units

of

works

:Metric

units.US

standards

(Anglo-Saxon

units).Motor

selection

:

safety

factorsTo

define

the

limits

of

value

for

selecting

motors

:SummaryM8

lex15

Lexium

SizerMotor

selectionList

of

motorsselectedInertia

ratio

:

Message

“Gearbox

?”

is

noted

if

inertia

ratio

>

10SummaryM8

lex15

Lexium

SizerMotorselection

:

braking

resistorHere

is

indicated

ifan

external

brakingresistor

is

requestedSummaryM8

lex15

Lexium

SizerPerformances

curvesSelect

the

best

inertia

ratio

can

induce

to

choose

an

higher