Power screw Page Power Screw Strength Equations
Strength considerations for Power Screws|
The following notes are provided for general guidance. In practice power
screws are provided by specialist suppliers who provide technical literature which
includes all the necessary data for selecting power screws from their range.
The notes below are general in nature and cannot provide detailed information about precise
strength levels because there are limitations on the understanding of the stress levels in screws.
Calculations assume that loading is distributed along the whole length of the engaged screw.. In practice this
is not the case and the loading is actually mainly taken by the first two threads. These
may yield a little to distribute the load along the thread.
The bearing stress results from the crushing force between the screw surface and the adjacent nut surface developed by lifting and supporting the load W.
σ B = W / ( π . dm. h.n )
Table of Safe Bearing Pressures
The maximum bending stress occurs at the root of the thread. It is calculated
by assuming the thread is a simple cantilever beam built in at the root. The load is
assumed to act at mid point on the thread.
For an ISO metric screw thread b = 3p /4 ... for a square single start thread b = p /2Shear Stress
Both the nut and screw threads are subject to traverse shear stress resulting from the bending forces. For a rectangular section the maximums shear stress occurs at the neutral axis and equals
Screw...τ = 3.W /2.A = 3.W /(2.π.d r.n.b )
Tensile /Compressive stresses
A loaded power screw is subject to a direct tensile or compressive load.. This is simply calculated
as the load / tensile stress area.
σ t or c = W /A...
Based on maximum shear stress theory...
The shear stress τ caused by torque on the screw =
The value of the combined stress is therefore
This equation always applies when the screw is in tension. When a screw is in compression and the length is greater than 8 time the root diameter then the buckling stress has to be considered..
Buckling stress..ref Simple Struts
When the screw is longer than 8 times the root diameter it must be considered a column.
Long columns with are dealt with using the Euler equation.
Columns with slenderness ratios of less than 100 are considered as short columns. The slenderness
ratio is the length (between supports) / Least radius of gyration of the section.
For a column the maximum stress at the concave side of the column
σ co should not exceed the design compressive strength of
the screw material..
The above equation applies only the screws with purely axial loads. When the load is eccentric from the screw centre line by distance e. Then the following variation of the Ritter equation applies.
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