Ball Screw Motor Torque Calculation: Formulas thiab Piv txwv

Kev suav cov pob ntsia hlau lub cev muaj zog yuav tsum muaj ntau dua li hloov cov khoom txav mus rau hauv lub zog axial. Kev kwv yees txhim khu kev qha yuav tsum xav txog kev nrawm nrawm, txheej txheem quab yuam, kev taw qhia kev tiv thaiv, pob ntsia hlau ua haujlwm, rotating inertia, preload thiab qhov yuav tsum tau muaj kev nyab xeeb.

Txoj kev suav kuj hloov nrog kev taw qhia mounting. Kab rov tav axis feem ntau xav tau torque los ua kom lub zog txav mus los thiab kov yeej kev tawm tsam, thaum lub axis ntsug yuav tsum tsis tu ncua ua haujlwm tiv thaiv lub ntiajteb txawj nqus thaum lub zog nce.

Phau ntawv qhia no piav qhia txog cov qauv tseem ceeb thiab muab ob qho piv txwv rau kev ua ntej lub cev muaj zog. Qhov kawg xaiv lub cev muaj zog tseem yuav tsum tau kuaj xyuas qhov tseeb ntawm qhov profile, pob ntsia hlau specifications thiab lub cev muaj zog nkhaus.

1. Cov ntaub ntawv yuav tsum tau ua ua ntej xam torque

Sau cov ntaub ntawv kev khiav hauj lwm hauv qab no ua ntej xam cov pob ntsia hlau tsav torque:

Tsiv loj, nrog rau lub rooj, fixture, workpiece thiab lwm yam txav Cheebtsam
Kab rov tav lossis ntsug mounting orientation
Maximum linear ceev
Yuav tsum tau acceleration thiab deceleration
Pob ntsia hlau
Pob ntsia hlau kis tau tus mob efficiency
Qhia kev tiv thaiv, foob tsis kam thiab lwm yam kev sib txhuam quab yuam
Cov txheej txheem sab nraud, xws li txiav, nias lossis clamping quab yuam
Pob ntsia hlau thiab coupling rotational inertia
Pob ntsia hlau preload lossis pib torque, thaum muaj
Yuav tsum muaj lub voj voog ua haujlwm thiab kev nyab xeeb

Lub dynamic thiab zoo li qub load ratings nyob rau hauv lub pob ntsia hlau catalog tsis yog lub cev muaj zog torque qhov tseem ceeb. Lawv feem ntau yog siv los ntsuas lub pob ntsia hlau thauj khoom muaj peev xwm thiab kev pabcuam lub neej.

2. Basic Ball Screw Torque Formula

Tom qab txiav txim siab tag nrho cov axial quab yuam ua rau ntawm lub pob ntsia hlau, lub torque yuav tsum tau hloov cov lus tsa suab rau hauv cov lus tsa suab tuaj yeem kwv yees siv:

T_{kab tawm} = F × p ÷ (2π × η)

Qhov twg:

T_{kab tawm}= torque yuav tsum tau tsim axial quab yuam, N·m
F= tag nrho axial quab yuam, N
p= pob ntsia hlau, m/rev
η= pob ntsia hlau tsav tsheb efficiency

Cov txhuas yuav tsum tau hloov los ntawm millimeter mus rau meters ua ntej siv cov qauv no. Piv txwv li, 10 mm lead yog nkag mus rau 0.010 m / rev.

Pob ntsia hlau feem ntau muaj cov tshuab ua haujlwm siab, tab sis tus nqi tiag tiag yog nyob ntawm cov txiv ntoo tsim, preload, lubrication, seals, kev sib dhos thiab kev ua haujlwm. Siv cov kev ua tau zoo muab los ntawm lub pob ntsia hlau chaw tsim khoom thaum twg los tau es tsis txhob xav tias tus nqi universal.

3. Xam Axial Force rau kab rov tav axis

Rau kab rov tav axis, lub ntiajteb txawj nqus yog ib txwm txhawb nqa los ntawm cov kab qhia los yog cov qauv tshuab es tsis ua ncaj qha raws lub pob ntsia hlau. Yog li ntawd, lub zog axial feem ntau txiav txim siab los ntawm kev nrawm, kev coj ua haujlwm thiab kev ua haujlwm sab nraud.

F_{kab rov tav} = m × a + F_{tsis kam} + F_{txheej txheem}

Qhov twg:

m= tag nrho qhov hnyav, kg
a= linear acceleration, m/s²
F_{tsis kam}= phau ntawv qhia, foob thiab mechanical resistance, N
F_{txheej txheem}= sab nraud quab yuam tawm tsam kev txav, N

Yog tias cov chaw tsim khoom siv cov lus qhia ua haujlwm, siv tus nqi ntawd. Kev kwv yees tsis kam tsuas yog los ntawm kev sib txhuam coefficient feem ntau yuav tsis raug vim hais tias cov lus qhia ua ntej, cov ntsaws ruaj ruaj, lubrication thiab mounting alignment tuaj yeem hloov qhov kev tiv thaiv tiag tiag.

4. Kab rov tav Axis xam piv txwv

Xav txog kab rov tav automation axis nrog rau cov xwm txheej hauv qab no:

Tsiv loj	100 kg
Qhov siab tshaj plaws acceleration	1.0 m/s²
Qhia thiab foob tsis kam	40 N
Sab nraud txheej txheem quab yuam	200 N
Pob ntsia hlau	10 mm
Assumed tsav efficiency	0.90

Kauj Ruam 1: xam lub zog acceleration

F_{kev ceev} = 100 × 1.0 = 100 N

Kauj ruam 2: xam tag nrho cov axial quab yuam

F_{kab rov tav} = 100 + 40 + 200 = 340 N

Kauj Ruam 3: Hloov lub pob ntsia hlau

10 hli =0.010 m

Kauj ruam 4: xam lub torque rau axial quab yuam

T_{kab tawm} = 340 × 0.010 ÷ (2π × 0.90)

T_{kab tawm} ≈ 0.60 N·m

Qhov no 0.60 N·m tus nqi tsuas yog sawv cev rau lub zog uas yuav tsum tau ua kom muaj kev suav axial quab yuam. Nws tseem tsis tau suav nrog lub torque uas yuav tsum tau ua kom nrawm lub pob ntsia hlau, txuas txuas thiab lwm yam sib hloov.

5. Ntxiv qhov Rotational Inertia Torque

Lub cev muaj zog yuav tsum ceev ob lub rooj txav thiab cov khoom sib hloov. Txawm hais tias lub rooj acceleration twb muaj nyob rau hauv lub axial- quab yuam xam, kev sib hloov inertia ntawm lub pob ntsia hlau, coupling thiab lwm yam rotating qhov chaw yuav tsum tau xam cais.

T_tig = J ×

= 2π × a ÷ p

Qhov twg J yog qhov sib xyaw ua ke inertia hauv kg·m² thiab yog angular acceleration hauv rad/s².

Xav tias qhov sib xyaw inertia ntawm lub pob ntsia hlau thiab sib txuas hauv kab rov tav -axis piv txwv yog 0.0008 kg·m².

= 2π × 1.0 ÷ 0.010 ≈ 628.3 rad/s²

T_tig = 0.0008 × 628.3 ≈ 0.50 N·m

Yog tias muaj kev tso cai ntxiv 0.15 N·m rau pob ntsia hlau ua ntej, cov ntsaws ruaj ruaj thiab lwm yam tsis muaj kev tiv thaiv:

T_{xav tau} = 0.60 + 0.50 + 0.15 = 1.25 N·m

Siv cov kev pabcuam ua ntej ntawm 1.5:

T_xaiv = 1.25 × 1.5 ≈ 1.88 N·m

Rau qhov piv txwv no, lub cev muaj zog thiab kis tau tus mob yuav tsum muaj peev xwm muab tau yam tsawg kawg yog kwv yees li 1.88 N·m raws li qhov yuav tsum tau ua kom nrawm. Lub torque muaj yuav tsum tau kuaj xyuas ntawm qhov kev khiav hauj lwm ceev, tsis yog ntawm xoom ceev.

6. Xam Axial Force rau ib tug ntsug axis

Lub axis ntsug yuav tsum kov yeej qhov hnyav ntawm lub rooj sib txoos txav thaum lub sijhawm nce siab. Lub zog nce siab tshaj plaws tuaj yeem kwv yees li:

F_ntsug = m × g + m × a + F_{tsis kam} + F_{txheej txheem}

Qhov twggyog gravitational acceleration, ib txwm coj li 9.81 m/s².

Cov xwm txheej quab yuam hloov thaum lub sij hawm nce mus nce mus, downward taug kev, acceleration, deceleration thiab thaum muaj xwm ceev nres. Rau qhov pib ntawm lub cev muaj zog, kev nce nrawm yog feem ntau kuaj raws li ib qho kev tsav tsheb siab tshaj -torque. Lub voj voog ua tiav yuav tsum tau soj ntsuam nyias.

7. Vertical Axis xam piv txwv

Xav txog ib txoj hlua nqa ntsug nrog cov kev ua haujlwm no:

Tsiv loj	120 kg
Upward acceleration	0.5 m/s²
Mechanical resistance	60 N
Pob ntsia hlau	10 mm
Assumed tsav efficiency	0.90
Ua ke rotating inertia	0.0005 kg²

Kauj Ruam 1: xam lub ntiajteb txawj nqus

F_{lub ntiajteb txawj nqus} = 120 × 9.81 = 1,177.2 N

Kauj Ruam 2: xam lub zog acceleration

F_{kev ceev} = 120 × 0.5 = 60 N

Kauj Ruam 3: Xam tag nrho lub zog nce axial

F_ntsug = 1,177.2 + 60 + 60

F_ntsug = 1,297.2 N

Kauj ruam 4: Xam lub torque rau ntsug txav

T_{kab tawm} = 1,297.2 × 0.010 ÷ (2π × 0.90)

T_{kab tawm} ≈ 2.29 N·m

Kauj ruam 5: Ntxiv rotational inertia torque

= 2π × 0.5 ÷ 0.010 ≈ 314.2 rad/s²

T_tig = 0.0005 × 314.2 ≈ 0.16 N·m

Tso cai rau lwm 0.15 N·m rau preload, ntsaws ruaj ruaj thiab ntxiv kuj:

T_{xav tau} = 2.29 + 0.16 + 0.15 = 2.60 N·m

Siv qhov kev pabcuam ua ntej ntawm 1.5:

T_xaiv = 2.60 × 1.5 = 3.90 N·m

Yog li ntawd, lub cev muaj zog uas tau xaiv yuav tsum muaj peev xwm muab kwv yees li 3.90 N·m ntawm qhov yuav tsum tau ua kom nrawm thiab nrawm hauv qhov piv txwv no. Vim tias qhov no yog ib txoj kab ntsug, tuav nres, counterbalance lossis lwm yam khoom siv kev nyab xeeb kuj tseem yuav tsim nyog.

8. Xam qhov xav tau lub cev muaj zog ceev

Torque yuav tsum tau soj ntsuam ua ke nrog ceev. Lub cev muaj zog rotational ceev yog xam los ntawm linear ceev thiab pob ntsia hlau lead:

n = v × 60 ÷ p

Qhov twg:

n= pob ntsia hlau tig ceev, rpm
v= linear ceev, m/s
p= pob ntsia hlau, m/rev

Piv txwv li, yog tias kab rov tav axis yuav tsum tau linear ceev ntawm 0.5 m / s nrog 10 mm lead:

n = 0.5 × 60 ÷ 0.010 = 3,000 rpm

Yog li ntawd, lub cev muaj zog yuav tsum muab qhov xav tau torque ntawm 3,000 rpm. Lub cev muaj zog yuav muaj tsawg txaus - nrawm lossis siab tshaj torque tab sis tsis txaus torque ntawm qhov ceev no.

Kev ntsuas kev sib hloov ceev yuav tsum tau nyob hauv qab ntawm qhov tso cai pob ntsia hlau nrawm txiav txim siab los ntawm txoj kab uas hla ntawm cov ntsia hlau, qhov ntev uas tsis muaj kev txhawb nqa, kev txhawb nqa kev npaj thiab tsim kev ncig sab hauv.

9. Rated Torque, Peak Torque thiab RMS Torque

Kev xaiv lub cev muaj zog yuav tsum tsis txhob ua raws li tus nqi torque nkaus xwb. Peb cov xwm txheej yuav tsum tau kuaj xyuas:

Peak torque:yuav tsum tau thaum lub sij hawm acceleration, deceleration los yog ib tug luv luv txheej txheem - quab yuam ncov
Nruam los yog ntsuas torque:torque lub cev muaj zog tuaj yeem muab tsis tu ncua ntawm kev khiav hauj lwm ceev
RMS torque:thermal- sib npaug torque xam los ntawm kev ua haujlwm tiav

Lub cev muaj zog tuaj yeem ua tau raws li qhov ntsuas qhov siab tshaj plaws tab sis tseem overheat yog tias nws RMS torque tshaj qhov ntsuas tas li. Cov ntawv thov nrog kev nrawm nrawm, lub sijhawm luv luv lossis kev tsim khoom tas mus li yog li yuav tsum tau ua tiav lub luag haujlwm- lub voj voog suav.

10. Yog vim li cas ib tug ntsug axis xav tau ib tug nres

Pob ntsia hlau ua haujlwm tau zoo thiab ib txwm tuaj yeem rov qab tau- tsav. Thaum lub cev muaj zog torque raug tshem tawm, qhov hnyav ntawm ib txoj kab ntsug tuaj yeem tig cov ntsia hlau thiab ua rau lub axis nqis.

Servo tuav torque ib leeg yuav tsum tsis txhob raug kho raws li kev ntsuas kev nyab xeeb nkaus xwb. Nyob ntawm daim ntawv thov thiab qib kev pheej hmoo, ib txoj kab ntsug yuav xav tau:

Lub cev muaj zog tuav nres
Pneumatic counterweight los yog counterweight
Ib qho kev nyab xeeb txiv ntoo los yog cov tshuab xauv tshuab
Ib qho khoom siv nres thaum muaj xwm ceev
Kev thauj khoom - tuav nres lossis txwv tsis pub rov qab

Nyeem ntxiv txog ntsug-axis kev nyab xeeb hauvLub Pob Screw puas tuaj yeem tuav lub Load Vertical?

11. Common Ball Screw Torque xam yuam kev

Tsuas yog siv qhov hnyav txav

Loj hauv kilograms tsis tuaj yeem nkag ncaj qha rau hauv cov mis torque. Nws yuav tsum xub hloov mus rau hauv kev quab yuam, thiab lub zog xam nyob ntawm seb lub axis yog kab rov tav lossis ntsug.

Tsis quav ntsej acceleration

Lub nrawm- txav mus tab sis maj mam nrawm axis yuav xav tau lub siab tshaj plaws torque dua li lub axis qeeb nrog acceleration ceev heev. Ob qhov ceev thiab acceleration yuav tsum tau txhais.

Ignoring pob ntsia hlau inertia

Kev sib hloov inertia ntawm qhov ntev lossis loj -diameter pob ntsia hlau tuaj yeem yog qhov tseem ceeb. Qhov no tseem ceeb tshwj xeeb tshaj yog nyob rau hauv siab -acceleration applications.

Siv lub cev muaj zog tuav torque li khiav torque

Lub cev muaj zog torque ib txwm txo qis thaum ceev nce. Qhov xav tau torque yuav tsum tau kuaj xyuas lub cev muaj zog torque-ceev nkhaus ntawm qhov kev khiav hauj lwm ceev.

Xaiv cov hlau lead xwb los ntawm qhov yuav tsum tau ceev

Cov hlau lead loj txo cov ntsia hlau rpm xav tau rau ib qho kev sib tw ceev, tab sis nws kuj yuav tsum tau tsav tsheb ntau dua rau tib lub zog axial. Kev xaiv cov txhuas yuav tsum sib npaug ntawm qhov ceev, lub zog, qhov kev daws teeb meem thiab qhov tseem ceeb - txwv ceev.

Siv ib qho kev nyab xeeb yam tsis txaus ntseeg

Ib qho kev pabcuam pabcuam pabcuam suav nrog kev suav tsis tseeb tab sis tsis hloov cov ntaub ntawv engineering raug. Qhov loj dua qhov kev nyab xeeb tsis tuaj yeem kho cov txheej txheem qis qis, tsis tsim nyog lub cev muaj zog inertia piv lossis tsis txaus ntsug-axis nres.

12. Cov txheej txheem ua kom lub cev muaj zog

Txhais lub zog txav, axis orientation thiab sab nraud txheej txheem quab yuam.
Txhais lub siab tshaj plaws ceev, acceleration, deceleration thiab lub luag hauj lwm voj voog.
Xaiv lub pob ntsia hlau ua ntej txoj kab uas hla thiab txhuas.
Xam qhov siab tshaj plaws axial quab yuam rau txhua qhov kev txav chaw.
Hloov axial quab yuam rau hauv pob ntsia hlau tsav torque.
Ntxiv pob ntsia hlau, coupling thiab lwm yam rotating inertia torque.
Ntxiv cov ntaub ntawv pov thawj preload, foob thiab mechanical resistance.
Siv ib qho qauv tsim nyog.
Xam qhov xav tau pob ntsia hlau rpm.
Xyuas ncov torque, nruam torque thiab RMS torque tiv thaiv lub cev muaj zog nkhaus.
Xyuas qhov ceev ceev, buckling load thiab pob ntsia hlau kev pab cuam lub neej.
Ntxiv qhov tsim nyog tuav thiab kev ruaj ntseg system rau ntsug axes.

Xaus

Pob ntsia hlau lub cev muaj zog torque yog txiav txim siab los ntawm kev ua tiav cov lus tsa suab es tsis yog qhov txav txav ib leeg. Kab rov tav axis feem ntau yuav tsum tau torque rau acceleration, txheej txheem quab yuam thiab mechanical resistance. Lub axis ntsug yuav tsum kov yeej lub ntiajteb txawj nqus thiab ib txwm yuav tsum tau ntxiv load- tuav tiv thaiv.

Lub hauv paus axial - quab yuam torque formula muab qhov pib muaj txiaj ntsig, tab sis rotating inertia, pob ntsia hlau preload, lub cev muaj zog ceev, lub voj voog lub luag haujlwm thiab kev nyab xeeb yuav tsum tau soj ntsuam ua ntej xaiv lub cev muaj zog kawg.

DLY cov khoom sivpob screwsnyob rau hauv ntau txoj kab uas hla, txhuas, cov qib raug thiab cov txiv ntoo configurations. Txheem thiab kev cai kawg machining tuaj yeem muab rau kom phim lub cev sib txuas thiab BK / BF, FK / FF lossis EK / EF kev txhawb nqa.

Xav tau kev pab xaiv lub pob ntsia hlau rau koj cov lus tsa suab?

Xa peb lub load, stroke, ceev, acceleration, mounting orientation thiab yuav tsum tau raug.

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