SigmaSize+ HELP (Machine information)

Wizard sizing / Machine information

Machine information

The Machine information regarding the selected application is input.
In the case of load the data with Data load / delete and input them in that time. When data were load with Data load/ delete, or Machine Infomatino already inputted, the Machine Infomation that were already finished setting are displayed.

[Operation Procedure]

Input data in the data input column.
The saved data is loaded if necessary (Click the Load data button).
The Inertia calculation can calculate the inertia value.
The Transmission Calculate button is displayed beside the Gear Ratio input column.
Because this advances to Transmission Calculate when you click this button, you can calculate Gear ratio by setting Transmission.
The Inertia Calculate button is displayed beside the Inertia input column.
Because this advances to Inertia Calculate when you click this button, you can calculate Inertia.
Click "Next" to advance to the Velocity diagram.

     *Relations between movement direction of load and signs of velocity
          Here defines that right direction of the screen and upper direction of the movement of a load as "plus".
          In other word, when you input a plus value at speed parameter with Velocity diagram, a load moves to right direction or upper direction.
          Or, the external force of a load is defined a external force from a right direction or a upper direction as plus, and is defined a external force from a left direction or a lower direction as minus.

     *Relations between total efficiency and gear efficiency
          Total efficiency whole of mechanism dose not included gear efficiency.
          If you want to input efficiency of whole machine, you need to input it at the column of total efficiency, and to input 1 at the column of gear efficiency.

[Screen Structure]

Machine information Screen (Ball Screw <horizontal>)

Application Preview
A selected application is zoomed in.
Load Data button
The value of the Machine information is loaded from saved data.
The data loaded is converted to the current set unit.

Load data dialogue
1. Data list
  Data is displayed from the latest one at the date.
  Click and select the following page button if necessary.
2. Select the data loaded then click "OK".
  Goes to the previous screen without loading when click a "Cancel".

Data Input Column
In init state, all columns are blank.
When data is read or hold, the value at that time is displayed.

The number of maximum input beams of each input column is 12 figures(include such as a mark and a decimal point).
Example
Possible :1.0,-1.0,1.2345678912,-1.234567891,1.0e+100 etc.
Impossible;:1.00000000000,-1000000000,1.23456789123,1.000000e+001 etc.

Rotary type

Ball screw (horizontal)

Timing belt (horizontal)

Rack & pinion (horizontal)

Ball screw (vertical)

Timing belt (vertical)

Rack & pinion (vertical)

Roll feeder

Rotor

Rotation table

Linear type

Linear single axis

Transmission calculation button
The Transmission calculation window is open.
*Displays beside the gear ratio input column.
Inertia calculation button
The Inertia calculation window is open.
*Displays beside the inertia input column.
Back button
Returns to the Application.
Next button
Advances to the Velocity diagram.

[Mechanism Parameter and Equation in each application]

Constants

Gravity g

Circular constant π

Input without Mechanism parameter

Rotary type motor

Rotor moment of ienrtia J_M

Motor option moment of inertia J_MO

Linear type motor

Moving coil mass m_M

Ball screw (horizontal) [Back]

	1	Mass of load( m_W )
	2	Mass of table( m_T )
	3	Thrust( F )
	4	Coefficient of friction( μ )
	5	Gear ratio( R )
	6	Gear + coupling inertia( J_G )
		Gear efficiency( η_G )
	7	Pitch( P_B )
	8	Diameter( d_B )
	9	Length( l_B )
		Density( ρ )
		Total efficiency( η )

Frictional force	F_FR	= μ ( m_W + m_T )g	(N)
Constant external force	F_C	= F	(N)
Moment of inertia component
Mechanism moment of inertia (Ball screw)	J_MC	= πρ_B l_B d_B⁴ / ( 32 R² )	(kg.m²)
Load mass moment of inertia	J_W	= (m_W + m_T )( K_vn / 2π )²	(kg.m²)
Load moment of inertia	J_L	= J_MC + J_G + J_W	(kg.m²)
Total load moment of inertia	J_A	= J_L + J_M + J_MO	(kg.m²)
*	K_vn	= P_B / R	(m/rev)
Torque component
Torque by friction	T_FR	= F_FR K_vn / ( 2π )	(N.m)
Constant torque	T_C	= F_C K_vn / ( 2π )	(N.m)
Torque by force from forward	T_FW	= 0	(N.m)
Torque by force from backward	T_BW	= 0	(N.m)

Required torque

[Back]

Timing belt (horizontal) [Back]

	1	Mass of load( m_W )
	2	Thrust( F )
	3	Coefficient of friction( μ )
	4	Gear ratio( R )
	5	Gear + coupling inertia( J_G )
		Gear efficiency( η_G )
	6	Pulley inertia( J_P )
	7	Pulley diameter( d_P )
		Total efficiency( η )

Friction force	F_FR	= μ m_W g	(N)
Constant external force	F_C	= F	(N)
Momemnt of inertia component
Mechanism moment of inertia (Pulley)	J_MC	= J_P / R²	(kg.m²)
Load mass moment of inertia	J_W	= m_W ( K_vn / 2π )²	(kg.m²)
Load moment of inertia	J_L	= J_MC + J_G + J_W	(kg.m²)
Total load moment of inertia	J_A	= J_L + J_M + J_MO	(kg.m²)
*	K_vn	= π d_P / R	(m/rev)
Torque component
Torque by friction	T_FR	= F_FR K_vn / ( 2π )	(N.m)
Consntant torque	T_C	= F_C K_vn / ( 2π )	(N.m)
Torque by force from forward	T_FW	= 0	(N.m)
Torque by force from backward	T_BW	= 0	(N.m)

Required torque

[Back]

Rack & pinion (horizontal) [Back]

	1	Mass of load( m_W )
	2	Thrust( F )
	3	Coefficient of friction( μ )
	4	Gear ratio( R )
	5	Gear + coupling inertia( J_G )
		Gear efficiency( η_G )
	6	Mass of rack( m_R )
	7	Pinion inertia( J_PIN )
	8	Pinion diameter( d_PIN )
		Total efficiency( η )

Frictional force	F_FR	= μ ( m_W + m_R )g	(N)
Consntant external force	F_C	= F	(N)
Moment of inertia component
Mechanism moment of inertia (Pinion)	J_MC	= J_PIN / R²	(kg.m²)
Load mass moment of inertia	J_W	= ( m_W + m_R )( K_vn / 2π )²	(kg.m²)
Load moment of inertia	J_L	= J_MC + J_G + J_W	(kg.m²)
Total load moment of inertia	J_A	= J_L + J_M + J_MO	(kg.m²)
*	K_vn	= π d_PIN / R	(m/rev)
Torque component
Torque by friction	T_FR	= F_FR K_vn / ( 2π )	(N.m)
Constant torque	T_C	= F_C K_vn / ( 2π )	(N.m)
Torque by force from forward	T_FW	= 0	(N.m)
Torque by force from backward	T_BW	= 0	(N.m)

Required torque

[Back]

Ball screw (vertical) [Back]

	1	Mass of load( m_W )
	2	Mass of table( m_T )
	3	Mass of counter( m_WC )
	4	Thrust in ascending( F_VU )
	5	Thrust in descending( F_VD )
	6	Gear ratio( R )
	7	Gear + coupling inertia( J_G )
		Gear efficiency( η_G )
	8	Pitch( P_B )
	9	Diameter( d_B )
	10	Length( l_B )
		Density( ρ )
		Total efficiency( η )
*Reference When you consider the resistance that a load is moving in a lower direction. Input a plus value in the Thrust in descending column. When you consider the resistance that a load is moving in a upper direction. Input a minus value in the Thrust in ascending column.

Frictional force	F_FR	= 0	(N)
Constant external force(Thrust + Gravity)	F_C	= - ( m_W + m_T - m_WC )g	(N)
Force from forward	F_FW	= F_VU	(N)
Force from backward	F_BW	= F_VD	(N)
Moment of inertia component
Mechanism moment of inertia (Ball screw)	J_MC	= π ρ_B l_B d_B⁴ / ( 32 R² )	(kg.m²)
Load mass moment of inertia	J_W	= ( m_W + m_T + m_WC )( K_vn / 2π )²	(kg.m²)
Load moment of inertia	J_L	= J_MC + J_G + J_W	(kg.m²)
Total load moment of inertia	J_A	= J_L + J_M + J_MO	(kg.m²)
*	K_vn	= P_B / R	(m/rev)
Torque component
Torque by friction	T_FR	= F_FR K_vn / ( 2π )	(N.m)
Constant torque	T_C	= F_C K_vn / ( 2π )	(N.m)
Torque by force from forward	T_FW	= F_FW K_vn / ( 2π )	(N.m)
Torque by force from backward	T_BW	= F_BW K_vn / ( 2π )	(N.m)

Required torque

[Back]

Timing belt (vertical) [Back]

	1	Mass of load( m_W )
	2	Mass of counter( m_WC )
	3	Thrust in ascending( F_VU )
	4	Thrust in descending( F_VD )
	5	Gear ratio( R )
	6	Gear + coupling inertia( J_G )
		Gear efficiency( η_G )
	7	Pulley inertia( J_P )
	8	Pulley diameter( d_P )
		Total efficiency( η )

Frictional force	F_FR	= 0	(N)
Constant external force(Thrust+Gravity)	F_C	= - ( m_W + m_T - m_WC )g	(N)
Torque by force from forward	F_FW	= F_VU	(N)
Torque by force from backward	F_BW	= F_VD	(N)
Moment of inertia component
Mechanism moment of inertia (Pulley)	J_MC	= π ρ_B l_B d_B⁴ / ( 32 R² )	(kg.m²)
Load mass moment of inertia	J_W	= ( m_W + m_T + m_WC )( K_vn / 2π )²	(kg.m²)
Load moment of inertia	J_L	= J_MC + J_G + J_W	(kg.m²)
Total load moment of inertia	J_A	= J_L + J_M + J_MO	(kg.m²)
*	K_vn	= P_B / R	(m/rev)
Torque component
Torque by friction	T_FR	= F_FR K_vn / ( 2π )	(N.m)
Constant torque	T_C	= F_C K_vn / ( 2π )	(N.m)
Torque by force from forward	T_FW	= F_FW K_vn / ( 2π )	(N.m)
Torque by force from backward	T_BW	= F_BW K_vn / ( 2π )	(N.m)

Required torque

[Back]

Rack & pinion (Vertical) [Back]

	1	Mass of load( m_W )
	2	Thrust in ascending( F_VU )
	3	Thrust in descending( F_VD )
	4	Gear ratio( R )
	5	Gear + coupling inertia( J_G )
		Gear efficiency( η_G )
	6	Mass of rack( m_{R )}
	7	Pinion inertia( J_PIN )
	8	Pinion diameter( d_PIN )
		Total efficiency( η )

Frictional force	F_FR	= 0	(N)
Constant force(Thrust+gravity)	F_C	= - ( m_W + m_R )g	(N)
Force from forward	F_FW	= F_VU	(N)
Force from backward	F_BW	= F_VD	(N)
Moment of inertia component
Mechanism moment of inertia (Pinion)	J_MC	= J_PIN / R²	(kg.m²)
Load mass moment of inertia	J_W	= ( m_W + m_R )( K_vn / 2π )²	(kg.m²)
Load moment of inertia	J_L	= J_MC + J_G + J_W	(kg.m²)
Total load moment of inertia	J_A	= J_L + J_M + J_MO	(kg.m²)
*	K_vn	= π d_PIN / R	(m/rev)
Torque component
Torque by friction	T_FR	= F_FR K_vn / ( 2π )	(N.m)
Constant torque	T_C	= F_C K_vn / ( 2π )	(N.m)
Torque by force from forward	T_FW	= F_FW K_vn / ( 2π )	(N.m)
Torque by force from backward	T_BW	= F_BW K_vn / ( 2π )	(N.m)

Required torque

[Back]

Roll feeder [Back]

	1	Tension( F )
	2	Press( F_P )
	3	Coefficient of friction( μ )
	4	Gear ratio( R )
	5	Gear + coupling inertia( J_G )
		Gear efficiency( η_G )
	6	Driving roller inertia( J_R1 )
	7	Driven roller inertia( J_R2 )
	8	Driving roller diameter( d_R )
		Total efficiency( η )
Reference when the movement direction of a load is a right direction and the tension against a load is a left direction. Input a plus value in the speed(v) column with Velocity diagram and a minus value in the Tension(F) column. when driven roller's diameter and driving roller's diameter are different. when there are a driven roller's inertia J'_R2* and its diameter d_R2 , driven roller inertia J_R2 is indicated as follows. J_R2 = J'_R2 ( d_R / d_R2 )²

Frictional force	F_FR	= μ F_P	(N)
Constant external force	F_C	= F	(N)
Moment of inertia component
Mechanism moment of inertia (Roller)	J_MC	= ( J_R1 + J_R2 ) / R²	(kg.m²)
Load mass moment of inertia	J_W	= 0	(kg.m²)
Load moment of inertia	J_L	= J_MC + J_G + J_W	(kg.m²)
Total load moment of inertia	J_A	= J_L + J_M + J_MO	(kg.m²)
*	K_vn	= π d_R / R	(m/rev)
Torque component
Torque by friction	T_FR	= F_FR K_vn / ( 2π )	(N.m)
Constant torque	T_C	= F_C K_vn / ( 2π )	(N.m)
Torque by force from forward	T_FW	= 0	(N.m)
Torque by force from backward	T_BW	= 0	(N.m)

Required torque

[Back]

Rotor [Back]

	1	Load inertia( J_WL )
		Friction torque( T_FL )
	2	Gear ratio( R )
	3	Gear + coupling inertia( J_G )
		Gear efficiency( η_G )
		Total efficiency( η )

Mechanism moment of inertia (Rotor)	J_MC	= J_WL / R²	(kg.m²)
Load mass moment of inertia	J_W	= 0	(kg.m²)
Moment of inertia component
Load moment of inertia	J_L	= J_MC + J_G + J_W	(kg.m²)
Total load moment of inertia	J_A	= J_L + J_M + J_MO	(kg.m²)
*	K_vn	= 1 / R
Torque component
Torque by friction	T_FR	= T_FL K_vn	(N.m)
Consntant torque	T_C	= 0	(N.m)
Torque by force from forward	T_FW	= 0	(N.m)
Torque by force from backward	T_BW	= 0	(N.m)

Required torque

[Back]

Rotation table [Back]

	1	Load inertia( J_WL )
	2	Mass of load( m_WL )
	3	Radius of load mass( r_WL )
	4	Coefficient of friction( μ )
	5	Gear ratio( R )
	6	Gear + coupling inertia( J_G )
		Gear efficiency( η_G )
	7	Mass of rotation table( m_T )
	8	Rotation table diameter( d_T )
	9	Holding shaft diameter( d_F )
	10	Main shaft diameter( d_S )
	11	Main shaft length( l_S )
		Main shaft density( ρ_S )
		Total efficiency( η )

Mechanism moment of inertia (Table + shaft)	J_MC	= (π ρ_S l_S d_S⁴ / 32 + m_T d_T² / 8 ) / R²	(kg.m²)
Load mass moment of inertia	J_W	= ( J_WL + m_WL r_WL² ) / R²	(kg.m²)
Moment of inertia component
Load moment of inertia	J_L	= J_MC + J_G + J_W	(kg.m²)
Total load moment of inertia	J_A	= J_L + J_M + J_MO	(kg.m²)
*	K_vn	= 1 / R
Torque component
Torque by friction	T_FR	= μ ( m_WL + m_T )g ( d_F / 2 ) K_vn	(N.m)
Constant torque	T_C	= 0	(N.m)
Torque by force from forward	T_FW	= 0	(N.m)
Torque by froce from backward	T_BW	= 0	(N.m)

Required torque

[Back]

Linear single axis [Back]

	1	Mass of load( m_W )
	2	Mass of table( m_T )
	3	Friction force( F_FR )
		Force margin( K_M )
		Total efficiency( η )
* Friction force( F_FR ) Please include the following thrust by which coefficient of friction is considered to the friction force. 1.The load required thrust by which the friction coefficient of machine part is considered, such as a linear guide. 2.Mass of linear motor movable required thrust by which the friction coefficient of machine part is considered, such as a linear guide. 3.The power-of-absorption part required thrust of the linear motor with core by which the friction coefficient of machine part is considered, such as linear guide. * Force margin( K_M ) This is a coefficient assuming the case which increases required force to accelerate or decelerate, on the structure of a machine. Input 1 or more value by the inertia between a moving coil and the center of gravity of load. Force to accelerate or decelerate is calculated as F = K_M m a.

Mass of load	m_L	= m_W + m_T	(kg)
Total mass of load	m_A	= m_L + m_M	(kg)

Required Force

[Back]

Required Torque/Force Equation

When you set speed such as chart below, there are equations of required torque and force.
In addition, It replace speed(v_i) with rotate speed(n_i) in the case of rotor or rotary table.

Velocity diagram

Section speed pattern	i	= 1 .. n
Section time	t_i		(s)
Section speed	v_i		(m/s)

Example for velocity diagram

Required torque (Rotary motor case)

Section rotation speed difference	n_Mdi	= ( v_i - v_i-1 ) / K_vn	(s^-1)

Section acceleration torque	T_Ai	= J_A ( 2π n_Mdi / ( t_i - t_i-1 ) )	(N.m)

Section torque	T_i		(N.m)
Normal ( n_Mi > 0 OR n_Mi = 0, n_Mi-1 > 0 )	T_i	= T_Ai - T_C - T_FW + T_FR	(N.m)
Reverse ( n_Mi < 0 OR n_Mi = 0, n_Mi-1 < 0 )	T_i	= T_Ai - T_C - T_BW - T_FR	(N.m)
Stopping ( n_Mi = 0)
\| T_C \| > T_FR
T_C > 0	T_i	= - T_C + T_FR	(N.m)
T_C < 0	T_i	= - T_C - T_FR	(N.m)
\| T_C \| <= T_FR	T_i	= 0	(N.m)

Effective torque	T_RMS	= √( ∑ⁿ_i=1 T_i² ( t_i - t_i-1 ) / t_n )	(N.m)

Required force(Linear motor type)

Section acceleration force	F_Ai	= K_M m_A ( v_i - v_i-1 ) / ( t_i - t_i-1 )	(N)

Section force	F_i		(N)
Normal (v_i > 0 OR v_i = 0, v_i-1 > 0 )	F_i	= F_Ai + ( F_FR / η )	(N)
Reverse (v_i < 0 OR v_i = 0, v_i-1 < 0 )	F_i	= F_Ai + ( - F_FR / η )	(N)
Stopping (v_i = 0, v_i = 0 )	F_i	= 0	(N)

Effective force	F_RMS	= √( ∑ⁿ_i=1 F_i² ( t_i - t_i-1) / t_n )	(N)

[Back]

Table of Contents

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[Mechanism Parameter and Equation in each application]

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