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