Page 1597 - MISUMI SINGAPORE Economy Series

5. Allowable Rotational Speed
Ball screw rotational speed is determined by required feed speed and the given screw lead, and needs to be less than the Allowable Maximum Rotational Speed.
Ball screw rotational speed is evaluated based on the shaft's critical speed and ball recirculation speed limitation DmN value.
5-1. Critical Speed
Allowable rotational speed is defined as a speed 80% or less of the Critical Speed where the rotational speed coincides with a natural resonant frequency of the screw shaft.
The Allowable Rotational Speed can be obtained by the following formula.
Additionally, approximate Allowable Rotational Speeds can be obtained from Table 2. Allowable Maximum Rotational Speed Graph.
•Allowable Rotational Speed (rpm)
Allowable Rotational Speed Calculation Example
3
2
60λ EI×10 d
7
Nc＝fa ＝ g 10 (min －1 ) Find the Allowable Maximum Rotational Speed for Fig.2
2 Q R A R 2
2
Where: <How to use>
ℓ: Distance of Supports (mm) ·Thread shaft diameterF15,Lead 5
fa: Safety Factor (0.8) ·Mounting method Fixed-Support
·Distance between Points of Buckling Load R 2 790mm
5
E: Young's Modulus (2.06×10 N/mm ) 2
I: Min. Geometrical Moment of Inertia of Across Root Thread Area (mm ) 4 <Calculations>
Q
I＝ d 4 g＝15.1， since the mounting method is Fixed-Supported,
64 the Allowable Rotational Speed (Nc) is,
d: Thread Root Diameter (mm)
12.5
d
: Specific Gravity (7.8×10 kg/mm ) 3 Nc＝ g 10 7 (min －1 ) ＝ 15.1 × M 10 7 (min －1 ) ＝ 3024(min －1 )
-6
A: Root Thread Section Area (mm ) 2 l 2 790 2
Q Therefore, the rotational speed will need to be 3024min －1 or less.
A＝ d 2
4 Table.2
g, λ: Coefficient Determined by Method of Screw Support
Method of Screw Support g λ Distance of Supports (Critical speed : Fixed-Support)ℓ2
Support - Support 9.7 Q
Fixed - Support 15.1 3.927
Fixed - Fixed 21.9 4.73
Fixed- Free 3.4 1.875
•Figure2. Allowable Rotational Speed Graph
Allowable Rotational Speed Calculation Example
4
3 2 1.5 10 8 Ø10 Thread outer diameter(mm) <Requirements>
1.5 10 4 · Thread outer diameter 20
2 8 6 5 Ø15 · Distance of Supports 1500mm
1.5 10 4 6 4 Ø20 · Mounting method Fixed-Support
8 6 5 4 5 4 3 3 2 Ø25 Ø32 <Calculations>
10
3
Allowable Rotational Speed (rpm) 6 5 4 3 2 1.5 3 2 3 1.5 2 8 3 1.5 8 6 5 3 ② The value 1076min －1 on the Fixed-Supported scale (Y-Axis) that
①From Table 1., find an intersection of a vertical line from Supported
8
Span Distance 1500mm and Screw Shaft O.D. F20 line.
corresponds to the intersection of (1) above is the Allowable Maximum
10
Speed.
10
Screw Shaft Dia. Calculation Example
10
1.5
10
· Distance of Supports 2000mm
· Maximum Rotational Speed 1000min －1
8 2 8 6 5 6 5 4 3 4 3 2 <Requirements>
6 4 1.5 · the max. axial load Fixed-Fixed
5 3 2
4 1.5 10 2 <Calculations>
3 2 8 ①From Table 2., find a intersection of a vertical line from Supported
Span Distance 2000mm and a horizontal line from Fixed-Fixed max.
1.5 10 2 6 speed scale (Y-Axis) at 1000min －1 .
2 5
1.5 10 2 8 6 4 ②A line that reaches down to the intersection in (1) is the 25 ball screw
8 5
10 6 4 3 that satisfies the required speed of 1000min －1 .
8 5 2
3 10 2 1.5 2 3 4 5 6 7 8 910 3 1.5 2 3 4 5 6 7
Fixed- Fixed- Fixed- Support -
Free Fixed Support Support Distance of Supports (mm)
Method of Screw Support
5-2. DmN Value
The DmN value represents a ball recirculation (orbit) speed limit within a ball nut.
If this vale is exceeded, the recirculation components will be damaged.
•Allowable Rotational Speed (rpm)
DmN≤70000(Precision Ball Screws)
DmN≤50000(Rolled Ball Screws) Ball Dia. A Value
1.5875 0.3
Where: 2.3812 0.6
Dm: Thread outer diameter(mm)＋A Value 3.175 0.8
1.0
4.7625
－1
N : Maximum Rotational Speed(min ) 6.35 1.8
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