Belt Actuator Sizing Tool

Belt Actuator

Unit

Select the unit

Load and linear guide

Total weight mass of loads and conveyor belt

W m

= lb kg

Friction coefficient of the belt and linear guide

μ

=

Drive pulley specifications

Drive pulley diameter

Dp

= in mm

Drive pulley weight mass

Wp mp

= lb/pc kg/pc

If you are not sure about the weight

Drive pulley length

Lp

= in mm

 

Drive pulley material

ρ

=

Number of drive pulleys

n

= pc

Efficiency

η

= %

External force

FA

= lb N

Direction of Operation

Transmission belt and pulleys or gears (Leave the fields blank if a direct coupling structure is used) 

Primary pulley (gear) pitch circle diameter (PCD) or diameter

Secondary pulley (gear) pitch circle diameter (PCD) or diameter

Dp1

=   in mm

Dp2

=   in mm

Primary pulley (gear) weight mass

Secondary pulley (gear) weight mass

Wp1 mp1

=   lb kg

Wp2 mp2

=   lb kg

 

 

If you are not sure about the weight mass

If you are not sure about the weight mass

Primary pulley (gear) thickness

 

Secondary pulley (gear) thickness

Lp1

=   in mm

 

Lp2

=   in mm

Primary pulley (gear) material

 

Secondary pulley (gear) material

ρp1

=

 

ρp2

=

Mechanism Placement

Mechanism angle

α

= °

Angle of Operation

Other requirement(s)

It is necessary to hold the load even after the power supply is turned off.
→ You need an electromagnetic brake.

It is necessary to hold the load after the motor is stopped, but not necessary to hold after the power supply is turned off.

Operating conditions

Operating speed

V1

=

  in mm /s

 

Acceleration/Deceleration

t1

=

  s

Operating speed

V1

=

  in mm /s

V2

=

  in mm /s

 

Acceleration/Deceleration

t1

=

  s

 

Rotor inertia

JO

=

  oz·in kg·m 2

 

Gear ratio

i

=

 

 

If the rotor inertia and the gear ratio are unknown, the acceleration torque will be calculated with an inertia ratio of 5:1 (see the motor selection tips that will appear on the result window for the detail).

Positioning

 

Positioning distance

L

=

in mm

 

Positioning time

t0

=

 s    

Stopping time

ts

=

 s

If a specific acceleration / deceleration time is required

t1

=

 s

If a specific operating speed is required

V

=

  in mm /s

If Positioning distance is given and acceleration/deceleration is unknown, it is calculated as one fourth of Positioning time.

Stopping accuracy

Stopping accuracy

±

in mm

Safety factor

Safety factor


The following is the estimated requirements. Please contact 1-800-468-3982 ( from overseas 1-847-871-5931 ) for assistance or questions.

Sizing Results

 

Load Inertia 

JL

= [oz·in [kg·m 2]

 

 

Required Speed 

Vm

= [r/min]

 

 

V2

= [r/min]

 

 

Required Torque 

T

= [lb·in] = [oz·in] [N·m]

 

 

RMS Torque 

Trms

= [lb·in] = [oz·in] [N·m]

 

 

Acceleration Torque 

Ta

= [lb·in] = [oz·in] [N·m]

 

 

Load Torque

TL

= [lb·in] = [oz·in] [N·m]

 

 

Required Stopping Accuracy

Δθ

= [deg]

 

 

Other Requirement(s)

To print the calculation report, click    Full Report
To view the motor selection tips, click    Tips


×

Call 1-800-GO-VEXTA(468-3982) or 1-847-871-5931

Print

- given information -

Load and linear guide

 

Total weight mass of loads and table

W m

[lb] [kg]

 

Friction coefficient of the guide

μ

 

Drive pulley specifications

 

Drive pulley diameter

Dp

[in] [mm]

 

Drive pulley weight mass

Wp mp

[lb/pc] [kg/pc]

 

Drive pulley length

Lp

[in] [mm]

 

Drive pulley material

ρ

[oz/in [kg/m 3]

 

Number of drive pulleys

n

[pc]

 

Efficiency

η

[%]

External force

 

FA

[lb] [N]

Transmission belt and pulleys or gears

 

Primary pulley (gear)

Secondary pulley (gear)

 

pitch circle diameter (PCD)

Dp1

= [in] [mm]

Dp2

= [in] [mm]

 

weight mass

Wp1 mp1

= [lb] [kg]

Wp2 mp2

= [lb] [kg]

 

thickness

Lp1

= [in] [mm]

Lp2

= [in] [mm]

 

material

ρp1

= [oz/in [kg/m 3]

ρp2

= [oz/in [kg/m 3]

 

Mechanism Placement

 

Mechanism angle

α

= [°]

Other requirement(s)

 

Is it necessary to hold the load even after the power supply is turned off?

 

Is it necessary to hold the load after the motor is stopped, but not necessary to hold after the power supply is turned off?

Operating conditions

 

Fixed speed operation

Operating speed

V1

=

[in/s] [mm/s]

 

 

Acceleration / deceleration time

t1

=

[s]

Operating conditions

 

Variable speed operation

Operating speed

V1

=

[in/s] [mm/s]

 

V2

=

[in/s] [mm/s]

 

 

Acceleration / deceleration time

t1

=

[s]

Operating conditions

 

Positioning operation

Rotor inertia

JO

=

[oz·in kg·m 2]

 

Gear ratio

i

=

 

Positioning distance

L

=

[in] [mm]

 

Positioning time

t0

=

[s]

 

Stopping time

ts

=

[s]

 

Acceleration / deceleration time

t1

=

[s]

 

Specified speed

V

=

[in/s] [mm/s]

Stopping accuracy

 

Stopping accuracy

Δl

= [in] [mm]

Safety factor

 

Safety factor

S·F

=


- calculated result -

Load Inertia

 

JW Jm

=   W × 16 × ( Dp / 2 )2 m ×( (Dp×10-3 ) / 2 )2

 

=   × 16 × ( ( ×10-3)  / 2)2

= [oz·in [kg·m 2]

 

JDp

=   (π/32) ρ Lp Dp4 n =   (1/8) Wp ×16 × Dp2 n =   (π/32) ρ Lp Dp4 n =   (1/8) mp (Dp × 10-3)2 n

 

=  ( 3.14 / 32 ) × × ( ×10-3)  × ( ×10-3) 4  × =  (1/8) × × 16 × () 2  × =  ( 3.14 / 32 ) × × ( ×10-3)  × ( ×10-3) 4  × =  (1/8) × × ( × 10-3) 2  ×

= [oz·in [kg·m 2]

 

JDp1

=  ( 1 / 8 ) Wp1 × 16 × Dp1 mp1 × (Dp1×10-3) 2

 

=   ( 1 / 8 ) ×  × 16 × ( ×10-3) 2

= [oz·in [kg·m 2]

 

JDp1

=   ( π / 32 ) ρp1 ( Lp1 ×10-3) ( Dp1 ×10-3) 4

 

=   ( 3.14 / 32 ) ×  × ( ×10-3)  × ( ×10-3) 4

= [oz·in [kg·m 2]

 

JDp2

=   ( 1 / 8 ) Wp2 × 16 × Dp2 mP2 × (DP2×10-3) 2

 

=   ( 1 / 8 ) ×  × 16 × ( ×10-3) 2

= [oz·in [kg·m 2]

 

JDp2

=  ( π / 32 ) ρp2 ( Lp2 ×10-3) ( Dp2 ×10-3) 4

 

=   ( 3.14 / 32 ) ×  × ( ×10-3)  × ( ×10-3) 4

= [oz·in [kg·m 2]

 

JL

=   ( JW Jm + JDp + JDp2 ) ( Dp1 / Dp2 )2 + JDp1

 

= (  +  +  ) × (  /  )2 +

[oz·in [kg·m 2]

 

JL

=   JW Jm + JS

 

=  (  +  )

[oz·in [kg·m 2]

Required Speed

 

Vm

=   V1 ( 60 /( π Dp ))   ( Dp2 / Dp1 )

 

=    × ( 60 / (3.14 × ) ) × (  /  )

= [r/min]

 

Vm1

=   V1 ( 60 /( π Dp )) ( Dp2 / Dp1 )

 

=    × ( 60 / (3.14 × )  ) × (  /  )

= [r/min]

 

Vm2

=   V2 ( 60 / π Dp ) ( Dp2 / Dp1 )

 

=    × ( 60 / (3.14 × )  ) × (  /  )

= [r/min]

 

Vm

=   ( V / ( π × Dp ) ) × 60 × ( Dp2 / Dp1 )

 

= (  / (3.14 × )  ) × 60 × (  /  )

= [r/min]

 

Vm

=   ( L / ( π × Dp ) ) × ( 60 / ( t0 - t1 ) ) × ( Dp2 / Dp1 )

 

= (  / (3.14 × )  ) × (60 / ( - )) × (  /  )

= [r/min]

Required Torque

 

T

=   ( Ta + TL ) ( Safety Factor )

 

= (  +  ) ×

= [lb·in] [N·m]

 

= [oz·in]

RMS Torque

 

Trms

=

√(((( Ta + TL )2 × t1 ) + ( TL2 × (t0 - 2 × t1 )) + (( Ta - TL )2 × t1 )) / ( t0 + ts )) × (Safety Factor)

 

=

√ ((((  +  )2 ×  ) + ( 2 × (  - 2 ×  )) + ((  -  )2 ×  )) / (  +  )) ×

=

[lb·in] [N·m]

 

 

= [oz·in]

Acceleration Torque

 

Ta

=

( JL / 386 ) ( Vm / ( 9.55 × t1 )) ( 1 / 16 )

 

=

(   / 386 ) × (  / ( 9.55 ×  )) × ( 1 / 16 )

=

[lb·in] [N·m]

 

 

= [oz·in]

 

Ta

=

( JL / 386 ) ( Vm / ( 9.55 × t1 )) ( 1 / 16 )

 

=

(  / 386 ) × (  / ( 9.55 ×  )) × ( 1 / 16 )

=

[lb·in] [N·m]

 

 

= [oz·in]

 

Ta

=

(( JO i2 + 1.2 × JO + JL ) / 386 ) ( Vm / ( 9.55 × t1 )) ( 1 / 16 )

 

=

((  × 2 + 1.2 × +  )  / 386 )  × (   / ( 9.55 ×  ))  × ( 1 / 16 )

=

[lb·in N·m]

 

 

= [oz·in]

Load Torque

 

F

=   FA + W (m × 9.8) ( sinα + μcosα )

 

=    + (  × 9.8)  ( sin  +  × cos  )

[lb N]

 

TL

=   ( F × Dp ×10-3 ) / (2 η × 0.01 )   ( Dp1 / Dp2 )

 

=   (  ×   ×10-3 ) / ( 2 × × 0.01 )   × (  /  )

= [lb·in] [N·m]

 

=   [oz·in]

Required Stopping Accuracy

 

Δθ

=  Δl ( 360° / π Dp ) ( Dp2 / Dp1 )

 

=    × ( 360 / (3.14 × )  ) × (  /  )

[deg]

Other requirement(s)

 

 


- end of the report -

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Friction coefficient table (reference)

Materials

Dry

Lubricated

Aluminum

Aluminum

1.0

0.3

Aluminum

Steel

0.6

 

 

Brass

Steel

0.5

 

 

Graphite

Steel

0.1

0.1

Polythene

Steel

0.2

0.2

Polystyrene

Steel

0.3

0.3

Rubber

Steel

0.4

 

 

Steel

Steel

0.8

0.2

Teflon

Steel

0.04

0.04

Wood

Wood

0.5

0.2

Positioning operation

Step 1 :

Leave the rotor inertia Jo and the gear ratio i blank if you have not selected any motor (or geared motor) yet. Then, fill in the rest of the form. The software will temporary calculate the acceleration torque with a load/rotor inertia ratio of 5:1.

Step 2 :

Select a product based on the required torque and the required speed. Then, confirm the inertia ratio to be within the recommendation. (See the motor selection tips that will appear on the result window for the detail)

Step 3 :

Return to the form and enter the rotor inertia Jo and the gear ratio i of the product you have selected to calculate the torque requirement using that particular product. If you selected a round shaft type motor (without gearhead), leave i blank or enter 1.

Roter inertia Jo :

This value is found in the specification tables for stepping motor products.

Gear ratio i :

This value is the gear ratio of the geared motor product you selected.
* These values are only used to calculate a more accurate acceleration torque.

This number includes the driver pulleys and idler pulleys being rotated as the motor turns.