Page 1679 - MiSUMi 2025

7. Screw Shaft Mounting Arrangements 9. Rigidity
Representative ball screw mounting arrangements are shown below. To improve positioning accuracy and control response of a
machine, considerations must be given to the rigidity of feed screw
Mounting Methods Application Example elements. Rigidity of feed screw system can be expressed with the
following formula.
Supported Span Distance (Critical Speed: Fixed – Supported )
P
Fixed Fixed Supported K＝ (N/Om)
δ
· Typical method Where:
· Medium ~ High Speeds
· Medium ~High Accuracy P : Axial Load Applied on Feed Screw System (N)
δ : Elastic Deformation of Feed Screw System (µm)
Additionally, the following relationship exists between the feed screw
Load Applicable Span Distance (Buckling Load: Fixed – Fixed) system rigidity and other various construction element rigidity.
1 1 1 1 1
Supported Span Distance (Critical Speed: Fixed – Fixed) K ＝ KR ＋ Kn ＋ Kb ＋ Kh
Fixed Fixed Fixed Where:
KR : Screw Shaft Compressive/Tensile Rigidity
· Medium Speeds Kn : Nut Rigidity
· High Accuracy Kb : Support Bearing Rigidity
Kh : Nut and Bearing Mount Rigidity
Load Applicable Span Distance (Buckling Load: Fixed – Fixed)
•Screw Shaft Compressive/Tensile Rigidity : KR
Supported Span Distance (Critical Speed: Fixed – Free) P
KR＝ (N/Om)
Fixed Fixed Free δℓ
Where:
· Low Speeds P : Axial Load (N)
· For Short Screw Shafts δR : Screw Shaft Expansion/Contraction (µm)
· Medium Accuracy
The expansion and contraction are expressed in the following formula.
Load Applicable Span Distance (Buckling Load: Fixed – Fixed) The expansion and contraction will directly appear as ball screw backlash.
➀ Fixed-Free Arrangement
8. Temperature and Life
When ball screws are continuously used at 100°C or higher, or
used momentarily at very high temperatures, Basic Dynamic/
Static Load Rating will be reduced according to the temperature
rise due to changes in material compositions. ℓ
However, there will be no effect up to 100°C. Basic Dynamic Fixed Free
Load Rating C" and Basic Static Load Rating Co" at 100°C or 4Pℓ
3
higher with the temperature factors ft and ft' can be expressed δR＝ ×10 (Om)
EQd
2
with the following formula. Where:
P : Axial Load (N)
C"＝ftC(N) E : Young's Modulus (2.06x10 N/mm )
5
2
C0"＝ft'C0(N)
d : Screw Shaft Root Diameter (mm)
Temperature °C 100 or less 125 150 175 200 225 250 350 R : Load Applicable Span Distance (mm)
ft 1.0 0.95 0.90 0.85 0.75 0.65 0.60 0.50 ➁ Fixed-Fixed Arrangement ℓ
ft' 1.0 0.93 0.85 0.78 0.65 0.52 0.46 0.35 L
E Normal usage range is -20 ～ 80℃ . For application in high Fixed Fixed
temperature, use of heat resistant grease as well as heat resistivity of
other components should be evaluated.
ℓ ℓ’
L
Fixed Fixed
4Pℓℓ'
δR＝ ×10 (Om)
3
2
EQd L
Where:
P : Axial Load(N)
5
E : Young's Modulus (2.06x10 N/mm ) 2
d : Screw Shaft Root Diameter (mm)
R,R ' : Load Applicable Span Distance (mm)
L : Mounting Span Distance (mm)
L

The formula produces the max. value whenR＝R '＝
2
( )
PL
δR＝ ×10
3
EQd
2
Therefore, the max. shaft expansion and contraction will be 1/4 of
Fixed-Free arrangement.
B-034