Linear Units

Deflection Calculations
How to calculate the deflection of the profile
Load Cases
1. 2. 3.
F F
Profile supported in both ends.
Profile fixed at both sides.
Profile supported in both ends.
Profile fixed at one side.
Permissible Profile Deflection Formula [mm]
fh = Lf × b
Profile Deflection Formulas [mm]
Load Case 1.
Load Case 2.
Load Case 3.
Lf
4
fmax = m’100 × g × Lf (mext
+
× mc) × g × Lf
100 × 384 × EAl × Iy 192 × EAl × Iy
fmax = m’100 × g × Lf (mext
+
× mc) × g × Lf
100 × 185 × EAl × Iy 48 × 5 × EAl × Iy
Conclusion Formulas
fh > fmax = deflection OK
4
4
fmax = m’100 × g × Lf (mext
+
× mc) × g × Lf
100 × 8 × EAl × Iy 3 × EAl × Iy
fh < fmax = deflection not OK, Lf must be shorter
198 www.danahermotion.com
Lf
3
3
3
F
Lf
Profile supported in one end.
Profile fixed at one side.
fh = permissible profile deflection [mm]
Lf = length of profile being bent [mm]
b = bending factor 1
fmax = deflection of the profile [mm]
m’100 = weight of every 100 mm of
stroke [kg] 2
mext = external load on carriage [kg]
mc = weight of carriage(s) [kg] 2
g = acceleration due to gravity [m/s 2 ]
Eal
= elastic modulus of aluminium
(70000 N/mm 2 )
Iy = geometrical moment of inertia of
the profile in Y direction [mm 4 ] 1
1 This value can be found in the additional
technical data tables.
2 This value can be found in the performance
specifications tables for each unit.