Belt Actuator Sizing Tool

Belt Actuator Sizing Tool

Unit

Load and linear guide

Drive pulley specifications

External force

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

Mechanism Placement

Other requirement(s)

Operating conditions

Stopping accuracy

Safety factor

Sizing Results

Load and linear guide

Drive pulley specifications

External force

Transmission belt and pulleys or gears

Mechanism Placement

Other requirement(s)

Operating conditions

Operating conditions

Operating conditions

Stopping accuracy

Safety factor

Load Inertia

Required Speed

Required Torque

RMS Torque

Acceleration Torque

Load Torque

Required Stopping Accuracy

Other requirement(s)

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Belt Actuator

Unit
Select the unit	Imperial Metric

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	=
Please enter the friction coefficient	μ	=

Drive pulley specifications
Drive pulley diameter	D_p	= in mm
Drive pulley weight mass	W_p m_p	= lb/pc kg/pc
If you are not sure about the weight
Drive pulley length	L_p	= in mm
Drive pulley material	ρ	=
Number of drive pulleys	n	= pc
Efficiency	η	= %

External force
F_A	= lb N

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
D_p1	= in mm	D_p2	= in mm
Primary pulley (gear) weight mass		Secondary pulley (gear) weight mass
W_p1 m_p1	= lb kg	W_p2 m_p2	= 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
L_p1	= in mm	L_p2	= in mm
Primary pulley (gear) material		Secondary pulley (gear) material
ρ_p1	=	ρ_p2	=

Mechanism Placement
Mechanism angle	α	= °

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

Fixed speed operation	Operating speed	V₁	=	in mm /s
	Acceleration/Deceleration	t₁	=	s

Variable speed operation	Operating speed	V₁	=	in mm /s	〜	V₂	=	in mm /s
	Acceleration/Deceleration	t₁	=	s

Positioning operation (Fill in the fields, if any)
	Rotor inertia	J_O	=	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 distance	L	=	in mm
	Positioning time	t₀	=	s	Stopping time	t_s	=	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.


Load Inertia	J_L	= [oz·in [kg·m ²]
Required Speed	V_m	= [r/min]
	V₂	= [r/min]
Required Torque	T	= [lb·in] = [oz·in] [N·m]
RMS Torque	T_rms	= [lb·in] = [oz·in] [N·m]
Acceleration Torque	T_a	= [lb·in] = [oz·in] [N·m]
Load Torque	T_L	= [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

- given information -


Total weight mass of loads and table	W m	= [lb] [kg]
Friction coefficient of the guide	μ	=


Drive pulley diameter	D_p	= [in] [mm]
Drive pulley weight mass	W_p m_p	= [lb/pc] [kg/pc]
Drive pulley length	L_p	= [in] [mm]
Drive pulley material	ρ	= [oz/in [kg/m ³]
Number of drive pulleys	n	= [pc]
Efficiency	η	= [%]

External force
	F_A	= [lb] [N]


	Primary pulley (gear)		Secondary pulley (gear)
pitch circle diameter (PCD)	D_p1	= [in] [mm]	D_p2	= [in] [mm]
weight mass	W_p1 m_p1	= [lb] [kg]	W_p2 m_p2	= [lb] [kg]
thickness	L_p1	= [in] [mm]	L_p2	= [in] [mm]
material	ρ_p1	= [oz/in [kg/m ³]	ρ_p2	= [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?	→


Fixed speed operation	Operating speed	V₁	=	[in/s] [mm/s]
	Acceleration / deceleration time	t₁	=	[s]


Variable speed operation	Operating speed	V₁	=	[in/s] [mm/s]
		V₂	=	[in/s] [mm/s]
	Acceleration / deceleration time	t₁	=	[s]


Positioning operation	Rotor inertia	J_O	=	[oz·in kg·m ²]
	Gear ratio	i	=
	Positioning distance	L	=	[in] [mm]
	Positioning time	t₀	=	[s]
	Stopping time	t_s	=	[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 -


J_W J_m	= W × 16 × ( D_p / 2 )² m ×( (D_p×10^-3 ) / 2 )²
	= × 16 × ( ( ×10^-3) / 2)²	= [oz·in [kg·m ²]
J_Dp	= (π/32) ρ L_p D_p⁴ n = (1/8) W_p ×16 × D_p² n = (π/32) ρ L_p D_p⁴ n = (1/8) m_p (D_p × 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]
J_Dp1	= ( 1 / 8 ) W_p1 × 16 × D_p1 m_p1 × (D_p1×10^-3) ²
	= ( 1 / 8 ) × × 16 × ( ×10^-3) ²	= [oz·in [kg·m ²]
J_Dp1	= ( π / 32 ) ρ_p1 ( L_p1 ×10^-3) ( D_p1 ×10^-3) ⁴
	= ( 3.14 / 32 ) × × ( ×10^-3) × ( ×10^-3) ⁴	= [oz·in [kg·m ²]
J_Dp2	= ( 1 / 8 ) W_p2 × 16 × D_p2 m_P2 × (D_P2×10^-3) ²
	= ( 1 / 8 ) × × 16 × ( ×10^-3) ²	= [oz·in [kg·m ²]
J_Dp2	= ( π / 32 ) ρ_p2 ( L_p2 ×10^-3) ( D_p2 ×10^-3) ⁴
	= ( 3.14 / 32 ) × × ( ×10^-3) × ( ×10^-3) ⁴	= [oz·in [kg·m ²]
J_L	= ( J_W J_m + J_Dp + J_Dp2 ) ( D_p1 / D_p2 )² + J_Dp1
	= ( + + ) × ( / )² +	= [oz·in [kg·m ²]
J_L	= J_W J_m + J_S
	= ( + )	= [oz·in [kg·m ²]

Required Speed

	V_m	= V₁ ( 60 /( π D_p )) ( D_p2 / D_p1 )
		= × ( 60 / (3.14 × ) ) × ( / )	= [r/min]

V_m1	= V₁ ( 60 /( π D_p )) ( D_p2 / D_p1 )
	= × ( 60 / (3.14 × ) ) × ( / )	= [r/min]
V_m2	= V₂ ( 60 / π D_p ) ( D_p2 / D_p1 )
	= × ( 60 / (3.14 × ) ) × ( / )	= [r/min]

V_m	= ( V / ( π × D_p ) ) × 60 × ( D_p2 / D_p1 )
	= ( / (3.14 × ) ) × 60 × ( / )	= [r/min]
V_m	= ( L / ( π × D_p ) ) × ( 60 / ( t₀ - t₁ ) ) × ( D_p2 / D_p1 )
	= ( / (3.14 × ) ) × (60 / ( - )) × ( / )	= [r/min]


T	= ( T_a + T_L ) ( Safety Factor )
	= ( + ) ×	= [lb·in] [N·m]
		= [oz·in]


T_rms	=	√(((( T_a + T_L )² × t₁ ) + ( T_L² × (t₀ - 2 × t₁ )) + (( T_a - T_L )² × t₁ )) / ( t₀ + t_s )) × (Safety Factor)
	=	√ (((( + )² × ) + ( ² × ( - 2 × )) + (( - )² × )) / ( + )) ×	=	[lb·in] [N·m]
				= [oz·in]

Acceleration Torque


F	= F_A + W (m × 9.8) ( sinα + μcosα )
	= + ( × 9.8) ( sin + × cos )	= [lb N]
T_L	= ( F × D_p ×10^-3 ) / (2 η × 0.01 ) ( D_p1 / D_p2 )
	= ( × ×10^-3 ) / ( 2 × × 0.01 ) × ( / )	= [lb·in] [N·m]
		= [oz·in]


Δθ	= Δl ( 360° / π D_p ) ( D_p2 / D_p1 )
	= × ( 360 / (3.14 × ) ) × ( / )	= [deg]

Other requirement(s)

- end of the report -

Unit Conversion

Length:

Mass:

Weight:

Inertia:

Torque:

Speed:

^°

° = For Stepper Motors input Step Angle

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.

( J_L / 386 ) ( V_m / ( 9.55 × t₁ )) ( 1 / 16 )

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

[lb·in] [N·m]