510E
Permissible Rotational Speed
[Dangerous Speed of the Screw Shaft]
When the rotational speed reaches a high magnitude, the Ball Screw may resonate and eventually
become unable to operate due to the screw shaft’s natural frequency. Therefore, it is necessary to
select a model so that it is used below the resonance point (dangerous speed).
Fig.13 on A15-34 shows the relationship between the screw shaft diameter and a dangerous
speed.
If determining a dangerous speed by calculation, it can be obtained from the equation (7) below.
Note that in this equation, a safety factor of 0.8 is multiplied to the result.
60 • λ1
2
2π •ℓb
2
N1 =
N1
ℓb
E
I
I=
E 10 • I
γ•A
3
0.8 = λ2 •
: Permissible rotational speed determined
by dangerous speed
(min-1)
: Distance between two mounting surfaces
(mm)
: Young’s modulus
(2.06×105 N/mm2)
: Minimum geometrical moment of inertia
of the shaft
(mm4)
π
d14
d1: screw-shaft thread minor diameter (mm)
64

A
A=
d1
7
• 10
2
ℓb
: Density (specific gravity)
(7.85×10-6kg/mm3)
: Screw shaft cross-sectional area (mm2)
π
d12
4
1, 2 : Factor according to the mounting method
Fixed - free
1=1.875 2=3.4
Supported - supported
1=3.142 2=9.7
Fixed - supported
1=3.927 2=15.1
Fixed - fixed
2=21.9
1=4.73
A15-32
………（7）
510E
Point of Selection
Permissible Rotational Speed
[DN Value]
The permissible rotational speed of the Ball Screw must be obtained from the dangerous speed of
the screw shaft and the DN value.
The permissible rotational speed determined by the DN value is obtained using the equations (8) to
(16) below.
Model SBK
(SBK3636, SBK4040 and
SBK5050)
N2 =
210000
………（8-1）
D
Model SBK
(For cases other than the above model
numbers and small size model SBK*)
N2 =
160000
………（8-2）
D
Models SBN, HBN and SBKH
130000
N2 =
D
Model WHF
N2 =
120000
………（10）
D
N2 =
70000
D
Large Lead
Caged Ball
Precision
Standard lead
Super Lead
FullComplement
Ball
Model WGF
Large Lead
Models BLW, BLK, DIR and BLR
Standard lead
Models BIF, DIK, BNFN, DKN,
BNF, BNT, DK, MDK, MBF,
BNK, BNS and NS
Standard lead
Models EBA, EBB, EBC, EPA,
EPB and EPC
100000
N2 =
D
Model WHF
N2 =
100000
………（13）
D
N2 =
70000
D
Super Lead
Rolled
Models WTF and CNF
FullComplement
Ball
Large Lead
Models BLK and BLR
Model BTK-V
100000
N2 =
D
Models JPF, BNT and MTF
N2 =
Standard lead
50000
D
………（11）
………（12）
………（14）
………（15）
………（16）
: Permissible rotational speed determined by the DN value (min-1(rpm))
: Ball center-to-center diameter
(indicated in the specification tables of the respective model number)
Of the permissible rotational speed determined by dangerous speed (N1) and the permissible rotational speed
determined by DN value (N2), the lower rotational speed is regarded as the permissible rotational speed.
For small size SBK (SBK1520 to 3232) and SDA, the permissible rotational speed (N2) is the maximum permissible rotational speed shown in the dimensional tables.(See dimensional tables on
pages A15-74 to A15-75, and A15-78 to A15-79)
If the service rotational speed exceeds N2, contact THK.
N2
D
A15-33
Ball Screw
Full-Complement Ball
(DIN Standard Compliant)
………（9）
510E
10000
8000
Distance between two mounting surfaces (mm)
6000
4000
2000
1000
φ 100
φ 80
φ 70
φ 63
φ 55 φ 50
φ 45 φ 40
φ 36
φ 32 φ 30
φ 28 φ 25
φ 20
φ 18 φ 16 φ 15
φ 14 φ 12
φ 10
φ8
φ6
800
600
400
200
Fixed - free
Fixed - supported
4
6
2
Fixed - fixed
4
8 102
2
4
6
6
8 103
4
8 103
6
2
2
8 103
4
4
6
Mounting method
Rotational speed (min-1)
Fig.13 Permissible Rotational Speed Diagram
A15-34
2
6
8 104
8 104
2