1. Mounting Methods Both the critical speed and column bucking load depend upon the method of mounting and the unsupported length of the shaft,the most common mounting methods for ball screws are shown in Fig.3.5 ~ 3.19. 
2. Buckling Load The safety of the screw shafy against buckling needs to be checked when the shaft is expected to receive buckling loads. Fig.3.20 shows a diagram which summarizes the allowable compressive load for buckling for each nominal outside diameter of screw shaft. (Calculate with the equation shown right when the nominal outside diameter of the screw shaft exceeds 125mm.)
Select the graduation of allowable axial load according to the method of ball screw support.
Remark: Allowable tensile/buckling load
Check the allowable tensile/buckling load (the formula shown below) and allowable load of the ball groove regardless of the mounting method when the mounting distance is short.
Where, 
 : Allowable tensile compressive stress (kgf/mm2)
A: Sectional area (mm2) of screw shaft root bottom diameter
dr: Screw shaft root diameter (mm)
Where,
 : Safety Factor ( = 0.5)
E: Vertical elastic modules (E=2.1 x 104kgf/mm2)
I: Min.secondary moment of screw shaft sectional area 
dr: Screw shaft root diameter (mm)
L: Mounting distance (mm)
m.N: Coefficient determined from mounting method of ball screw:
Simple-Simple m=5.1 (N=1)
Fixed-Simple m=10.2 (N=2)
Fixed-Fixed m=20.3 (N=4)
Fixed-Free m=1.3 (N=1/4) 
3. Critical Speed It is necessary to check if the ball screw rotation speed is resonant with the natural frequency of the screw shaft.
HSK has determined 80% or less of this critical speed as an allowable rotation speed.Fig.3.21 shows a diagram which summarizes the allowable rotation speed for shaft exceeds 125mm.) Select the graduation of allowable rotation speed according to the method of supporting the ball screw.
Where the working rotation speed presents a problem in terms of critical speed,it would be best to provide an intermediate support to increase the natural fuequency of the screw shaft.
dm.n value
The allowable rotation speed is regulated also by the dm.n value (dm:diameter of central circle of steel ball,n:Revolution speed,rpm)which expresses the peripheral speed.
Generally;
For precision (accuracy grade C7 to CO)
dm.n <= 70,000
For general industry (C10)
dm.n <= 50,000
Product exceeding the above limits can be produced,contact HSK. 
Where,
: Safety factor ( = 0.8)
E: Vertical elastic modules (E = 2.1 x 104kgf/mm2)
I: Min.secondary moment of screw shaft sectional area
I = ( /64) dr4 (mm4)
dr: Screw shaft root diameter (mm)
g: Acceleration of gravity ( = 9.8 x 103mm/s2)
Y: Density (Y = 7.8 x 10-6kgf/mm3)
A: Screw shaft sectional area (A = dr2/4mm2)
L: Mounting distance (mm)
f,  : Coefficient determined from the ball screw mountung method
Simple-Simple f = 9.7 ( = )
Fixed-Simple f = 15.1 ( = 3.927)
Fixed-Fixed f = 21.9 ( = 4.730)
Fixed-Free f = 3.4 ( = 1.875) (* Particular consideration is necessary for manufacturing when the screw length/shaft dia.Ratio is £`>70.In such an event,contact HSK) 
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