Page 1680 - MiSUMi 2025

[Technical Data]
Selection of Ball Screws 4

10. Driving Torque ➀Constant Speed Torque Exerted on the Motor Output Thread
This selection provides a guide for selecting ball screw frictional This is the amount of torque required to drive the output thread against
the applied external load, at a constant speed.
properties and the driving motor. PL (3PL-P) Z1
( )
10-1.Friction and Efficiency T1＝ ＋TP (N·cm)
2Q˝ 3PL Z2
When the friction coefficient is O , and lead angle is ı , ball screw's
efficiency ˝ is indicated by the following formulas. Where: P≤3PL
When rotational force is converted into axial force (Forward Action) T1 : Driving Torque at Constant Speed (N·cm)
P : External Axial Load (N)
1-O tan ı P＝F＋OMg
˝＝
1＋O/tan ı F : Thrust Reaction Produced in Cutting Force (N)
M : Masses of Table and Work Piece (kg)
When axial force is converted into rotational force (Reverse Action) O : Coefficient of Friction on Sliding Surfaces
g : Gravitational Acceleration (9.8m/s ) 2
1-O/tan ı
˝'＝ L : Ball Screw Lead (cm)
1＋O tan ı ˝ : Mechanical Efficiency of Ball Screw or Gear
TP : Friction Torque Caused by Preloading (N·cm) Refer to
10-2.Load Torque Formula 10-2-➂
The load torque (constant velocity torque) required for the drive power PL : Preload (N)
source (motor, etc.) selection is as follows. Z1 : Number of Pinion's Teeth
➀Forward Action Z2 : No. of Gear's Teeth
Torque required when converting rotational force into axial force
PL ➁Acceleration Torque Exerted on the Motor Output Thread
T＝ (N·cm) This is the amount of torque required to drive the output shaft against
2Q˝
Where: the external load during acceleration.
T : Load Torque (N·cm) 2QN
P : External Axial Load (N) T2＝ JM˛ ＝ JM ×10 -3 (N·cm)
60t
L : Ball Screw Lead (cm) JM＝ J1＋J4 ＋ (J2＋J3＋J5＋J6) (kg·cm )
2
Z1
2
( )｛ ｝
˝ : Ball Screw Efficiency (0.9) Z2
Where:
T2 : Driving Torque in Acceleration (N·cm)
➁Reverse Action ˛ : Motor Thread Angular Acceleration (rad/s ) 2
External axial load when converting axial force into rotational N : Motor Thread Rotational Speed (rpm)
2Q T t : Acceleration Time (s)
P＝ (N) JM : Moment of Inertia Exerted on the Motor (kg·cm ) 2
˝ 'L

Where: J1 : Moment of Inertia Exerted on Pinion (kg·cm ) 2
2
P : External Axial Load (N) J2 : Moment of Inertia Exerted on Gear (kg·cm ) 2
J3 : Moment of Inertia Exerted on Ball Screw (kg·cm )
T : Load Torque (N·cm) J4 : Moment of Inertia Exerted on Motor's Rotor (kg·cm )
2
L : Ball Screw Lead (cm) J5 : Moment of Inertia of Moving Body (kg·cm ) 2
˝ ' : Ball Screw Efficiency (0.9) J6 : Moment of Inertia of Coupling (kg·cm ) 2
M : Masses of Table and Work Piece (kg)
L : Ball Screw Lead (cm)
➂Friction Torque Caused by Preloading Moment of inertia exerted on cylinders as screws and cylinders such as Gears
This is a torque generated by preloading. As external loads increase,
the preload of the nut is released and therefore the friction torque by (Calculation of J1~J4, J6)
Qγ
preloading also decreases. J＝ D R(kg·cm ) 2
4
32
Under No load Where:
PLL D : Cylinder Outer Diameter (cm)
TP＝ K (N·cm) R : Cylinder Length (cm)
2 Q
K＝0.05(tanı) - 2 1 γ : Material Specific Gravity
γ ＝7.8×10 (kg/cm ) 3
-3
Where: L 2
( )
PL : Preload (N) J5＝M (kg·cm )
2
2 Q
L : Ball Screw Lead (cm)
K : Coefficient of Internal Friction
ı : Lead Angle ➂Total Torque Exerted on the Motor Output Thread
( ) Overall torque can be obtained by adding results from formulas ➀and➁.
D : Thread Outer Diameter PL (3PL-P) Z1 2 QN
( )
TM＝T1＋T2＝ ＋TP ＋JM ×10 (N·cm)
-3
2Q˝ 3PL Z2 60t
11. Selecting the Driving Motors Where:
When selecting a driving motor, it is necessary to satisfy the following TM : Total Torque Exerted on the Motor Output Thread (N·cm)
conditions:
1. Ensure a marginal force sufficient to counter the load torque T1 : Driving Torque at Constant Speed (N·cm)
exerted on the motor's output thread. T2 : Driving Torque at In Acceleration (N·cm)
2. Enable starting, stopping at prescribed pulse speeds, sufficiently
powered to counter the moment of inertia exerted on the motor's
output thread. Once you have temporarily found the type of motor you need, check
3. Obtain the prescribed acceleration and deceleration constants, 1.effective torque,
sufficient to counter the moment of inertia exerted on the motor's 2.acceleration constant and
output thread. 3. motor overload properties and heat tolerance during repeated
Table F Work Piece starting, stopping. It is necessary to ensure a sufficient margin for
W these parameters.
Gear J2
Z 2
B-035 Ball Screw J3 Pinion J1 1 Motor
Z