Page 1600 - MISUMI SINGAPORE Economy Series

[Technical Data]
Selection of Ball Screws 4

10. Driving Torque ①Constant Speed Torque Exerted on the Motor Output Thread
This selection provides a guide for selecting ball screw frictional properties and This is the amount of torque required to drive the output thread against the applied external load, at a constant speed.
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
T1 : Driving Torque at Constant Speed (N·cm)
When rotational force is converted into axial force (Forward Action)
P : External Axial Load (N)
P＝F＋OMg
1-O tan ı
˝＝ F : Thrust Reaction Produced in Cutting Force (N)
1＋O/tan ı
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)Referto Formula10-2-③
PL : Preload(N)
10-2.Load Torque Z1 : Number of Pinion's Teeth
The load torque (constant velocity torque) required for the drive power source (motor, etc.) selection is as follows. Z2 : No. of Gear's Teeth
①Forward Action
Torque required when converting rotational force into axial force
②Acceleration Torque Exerted on the Motor Output Thread
PL This is the amount of torque required to drive the output shaft against the external load during acceleration.
T＝ (N·cm)
2Q˝
2QN
Where: T2＝ JM˛ ＝ JM ×10 -3 (N·cm)
T : Load Torque (N·cm) 60t
Z1
2
P : External Axial Load (N) JM＝ J1＋J4 ＋ (J2＋J3＋J5＋J6) (kg·cm )
( )｛ ｝
2
L : Ball Screw Lead (cm) Where: Z2
˝ : Ball Screw Efficiency (0.9) T2 : Driving Torque in Acceleration (N·cm)
˛ : Motor Thread Angular Acceleration (rad/s )
2
-1
②Reverse Action N : Motor Thread Rotational Speed (min )
External axial load when converting axial force into rotational t : Acceleration Time (S)
JM : Moment of Inertia Exerted on the Motor (kg·cm )
2
2Q T J1 : Moment of Inertia Exerted on Pinion (kg·cm ) 2
P＝ (N) J2 : Moment of Inertia Exerted on Gear (kg·cm ) 2
˝ 'L

Where: J3 : Moment of Inertia Exerted on Ball Screw (kg·cm ) 2
P : External Axial Load(N) J4 : Moment of Inertia Exerted on Motor's Rotor (kg·cm ) 2
T : Load Torque(N·cm) J5 : Moment of Inertia of Moving Body (kg·cm ) 2
2
L : Ball Screw Lead(cm) J6 : Moment of Inertia of Coupling (kg·cm )
M : Masses of Table and Work Piece (kg)
˝ ' : Ball Screw Efficiency(0.9) L : Ball Screw Lead (cm)
Moment of inertia exerted on cylinders as screws and cylinders such as Gears
③Friction Torque Caused by Preloading (Calculation of J1~J4, J6)
This is a torque generated by preloading. As external loads increase, the preload of Qγ 4 2
32
the nut is released and therefore the friction torque by preloading also decreases. J＝ D R(kg·cm )
Where:
Under No load D : Cylinder Outer Diameter (cm)
PLL R : Cylinder Length (cm)
TP＝ K (N·cm)
2 Q γ : Material Specific Gravity
K＝0.05(tanı) - 2 1 γ ＝7.8×10 (kg/cm ) 3
-3

( )
2
L
Where: J5＝M (kg·cm )
2
PL : Preload(N) 2 Q
L : Ball Screw Lead (cm)
K : Coefficient of Internal Friction ③Total Torque Exerted on the Motor Output Thread
L
ı : Lead Angle ı≈tan ( ) Overall torque can be obtained by adding results from formulas ①and②.

-1
QD
( )
PL (3PL-P) Z1 2 QN
D : Thread Outer Diameter 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: T1 : Driving Torque at Constant Speed(N·cm)
1.Ensure a marginal force sufficient to counter the load torque 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, sufficient to
counter the moment of inertia exerted on the motor's output thread. 1.effective torque,
2.acceleration constant and
Table F Work Piece
W 3. motor overload properties and heat tolerance during repeated
Gear J2 starting, stopping. It is necessary to ensure a sufficient margin for
Z 2
these parameters.
Ball Screw J3 Pinion J1
Z 1 Motors
1595 1596