Page 1600 - MISUMI Thailand Economy Series

[Technical Data]
Selection of Ball Screws 4

10. Driving Torque ①Constant Speed Torque Exerted on the Motor Output Thread ■Conveyer belts selection procedure
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 following steps for selection is based on the case that sizes of head pulley and tail pulley are same.
the driving motor. ( ) (Follow the steps 1 -3 even when sizes of head pulley and tail pulley are different)
PL (3PL-P) Z1
10-1.Friction and Efficiency T1＝ ＋TP (N·cm) Use a head pulley as a driving pulley.
For belt installation and tension control, make the structure of the driven side to be
2Q˝ 3PL Z2
When the friction coefficient is O , and lead angle is ı , ball screw's efficiency ˝ is adjustable of alignment and center distance with set screws.
indicated by the following formulas. Where: P≤3PL ※ Head Pulley: The front of the pulley against traveling direction
Tail Pulley: The rear end of the pulley against traveling direction
T1 : Driving Torque at Constant Speed (N·cm)
When rotational force is converted into axial force (Forward Action) [Step 1] Calculate effective tension (Te).
P : External Axial Load (N)
1-O tan ı P＝F＋OMg Traveling Direction Head pulley (Driving Pulley)
˝＝ 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 H
g : Gravitational Acceleration (9.8m/s )
2
1-O/tan ı L : Ball Screw Lead (cm)
˝'＝ C
1＋O tan ı ˝ : Mechanical Efficiency of Ball Screw or Gear Tail pulley
TP : Friction Torque Caused by Preloading(N·cm)Referto Formula10-2-③
PL : Preload(N) Table 1. Typical Friction Coefficient of Belt versus Table
10-2.Load Torque Z1 : Number of Pinion's Teeth Table Material Steel Stainless Aluminium UHMW Teflon
The load torque (constant velocity torque) required for the drive power source (motor, etc.) selection is as follows. Z2 : No. of Gear's Teeth Friction coefficient: O 0.65 0.68 0.42 0.31 0.21
①Forward Action [Step 2] Calculate design tension (Td).
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. Td＝K·Te Td (N) Design Tension

K
Overload Coefficient
T＝ (N·cm) Te (N) Effective Tension
2Q˝
2QN
Where: T2＝ JM˛ ＝ JM ×10 -3 (N·cm)
T : Load Torque (N·cm) 60t K＝K1＋K2＋K3 K1 Correction factors for daily operation hours
Belt length correction coefficient
K2

2
Z1
P : External Axial Load (N) JM＝ J1＋J4 ＋ (J2＋J3＋J5＋J6) (kg·cm ) 2 K3 Belt speed correction coefficient
( )｛ ｝
L : Ball Screw Lead (cm) Where: Z2 Table 2. K1 Correction Factors for Daily Operation Hours Unit: hour
˝ : Ball Screw Efficiency (0.9) T2 : Driving Torque in Acceleration (N·cm) ～5 5～8 8～12 12～16 16～24
˛ : Motor Thread Angular Acceleration (rad/s ) 2 1.0 1.1 1.2 1.3 1.4
-1
②Reverse Action N : Motor Thread Rotational Speed (min ) Table 3. K2 Belt Length Correction Factors Unit : mm
External axial load when converting axial force into rotational t : Acceleration Time (S)
JM : Moment of Inertia Exerted on the Motor (kg·cm ) 2 ～1500 1501～3000 3001～4500 4501～
2Q T J1 : Moment of Inertia Exerted on Pinion (kg·cm ) 2 0.3 0.2 0.1 0.0
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 Table 4. K3 Belt Speed Correction Factors Unit : m/min
P : External Axial Load(N) J4 : Moment of Inertia Exerted on Motor's Rotor (kg·cm ) 2 ～60 61～90 91～120
0.2
0.1
0.0
T : Load Torque(N·cm) J5 : Moment of Inertia of Moving Body (kg·cm ) 2 [Step 3] Select belt type, belt width and pulley dimension.
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) ①Select from Table 5 a belt type and a width which have a greater allowable tension than the designed tension.
Moment of inertia exerted on cylinders as screws and cylinders such as Gears Table 5. Allowable Tension of Joint Belts
③Friction Torque Caused by Preloading (Calculation of J1~J4, J6) Belt Belt Width(mm)
Qγ
This is a torque generated by preloading. As external loads increase, the preload of J＝ D R(kg·cm ) 2 Type 6 9 10 12 15 20 25 30 40 50
4
the nut is released and therefore the friction torque by preloading also decreases. 32 S3M 70 80 110
Where: － － － － － － －
Under No load D : Cylinder Outer Diameter (cm) S5M － － 165 － 230 － 400 － － －
PLL R : Cylinder Length (cm) S8M － － － － 240 － 450 530 650 －
TP＝ K (N·cm) T5 － － 150 － 200 270 350 － － －
2 Q γ : Material Specific Gravity T10 320 440 640 720 960 1280
－
K＝0.05(tanı) - 2 1 γ ＝7.8×10 (kg/cm ) H3M 70 － － － － － － － － －
3
-3

80
90
－
( )
2
L
Where: J5＝M (kg·cm ) 2 H5M － 165 － － 230 － 400 － － －
PL : Preload(N) 2 Q H8M － － － － － 360 450 530 650 －
L : Ball Screw Lead (cm) ②Select a pulley with a larger number of teeth than the minimum allowable number in Table 6 for both of driving and driven pulley.
K : Coefficient of Internal Friction ③Total Torque Exerted on the Motor Output Thread
ı : Lead Angle ı≈tan ( ) Overall torque can be obtained by adding results from formulas ①and②. Belt Type Belt Nominal Width
L

-1
QD 025 037 050 075 100 150 200
( )
PL (3PL-P) Z1 2 QN
D : Thread Outer Diameter TM＝T1＋T2＝ ＋TP ＋JM ×10 (N·cm) XL 70 80 110 － － － －
-3
2Q˝ 3PL Z2 60t L － － 200 300 400 600 －
H － － － 300 400 600 800
11. Selecting the Driving Motors Where: Table 6. Number of Minimum Allowable Number of Teeth for Pulleys
When selecting a driving motor, it is necessary to satisfy the following TM : Total Torque Exerted on the Motor Output Thread(N·cm) Belt Type XL L H S3M S5M S8M T5 T10 H3M H5M H8M
conditions: T1 : Driving Torque at Constant Speed(N·cm) Pitch (mm) 5.08 9.525 12.7 3 5 8 5 10 3 5 8
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) Min. No. of Pully Teeth 12 14 14 14 14 24 12 14 14 14 24
2. Enable starting, stopping at prescribed pulse speeds, sufficiently powered to Pully Diameter (mm) 19.40 42.45 56.60 13.37 22.28 61.12 19.10 44.56 13.37 22.28 61.12
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, Reference: Open End Belt Allowable Tension Table Unit : N
2.acceleration constant and Belt Material Belt Width(mm)
Table F Work Piece Type 6 9 10 12 15 20 25 30 40 50
W 3. motor overload properties and heat tolerance during repeated S3M Urethane 127 － 145 － 159 － － － － －
Gear J2 starting, stopping. It is necessary to ensure a sufficient margin for S5M Urethane － － 215 － 323 － 539 － － －
Z 2 S8M Urethane － － － － 647 － 1176 1412 1882 －
these parameters. T5 Urethane － － 196 － 291 394 497 － － －
Ball Screw J3 Pinion J1
T10 Urethane
Z 1 Motors H3M Urethane 127 145 － 150 523 695 926 1097 1509 1862
－
－
－
159
－
H5M Urethane － 215 － － 323 － 539 － － －
－
－
－
－
－
1595 H8M Urethane － － － － － 941 1176 1412 1882 － 1596
When using belts for other purpose than conveyance (e.g. transmission), for polyurethane belt S3M/H3M; design with 1/2 of the allowable tension in the table; for XL, L, H, S5M, S8M, T5, T10, H5M and H8M, design with approx. 2/3 of the allowable tension in the table.

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