Scaravella F.lli
3
CALCULATION OF APPLIED TORQUE
The value of C torque, necessary for the operation of a ball screw
to which an axial load F is applied is:
Ct = = kgm
F • p
2000 • π • η
where: F, is axial LOAD
p, is screw PITCH
η, is the yield of the helical pair (0,9).
To this should be added the inertia torque of the screw shaft and
the torque due to the PRELOAD of the screw nut.
CALCULATION OF LOADS
AND DURATION
The calculation of the permissible LOAD on the shaft can be set,
especially for long and thin screws, stuck at one end and free
from the other (heavier case), with the processes of the tip loaded
solids (Euler formulas)..
The LOAD to which the ball screw is subjected must be considered
applied in dynamic conditions, sometimes with shocks: therefore,
the sizing must take this condition into account.
It should also be noted that the sizing of the ball screw must
be carried out, taking into account not only the screw, but the
resistance of the screw-nut-ball assembly.
As for the duration of a screw, it is noted that it is correlated with
its resistance to fatigue, and with the number of times the sphere
touches a given point of the groove.
Therefore, the lifetime measurement of a ball screw is expressed
in number of rotations (10
6
revolutions, or millions of revolutions).
The coefcient L
din
of dynamic LOAD indicates the permissible
LOAD (in kg) for a duration T of 10
6
revolutions. The coefcient
L
stat
of static LOAD corresponds to the maximum permissible
load on the screw in resting conditions, or for very slow rotations.
Beyond this LOAD there is a permanent deformation on the
raceways of 0,0001 compared to the diameter of the ball.
For the choice of the screw it is necessary, however, to know the
medium load Fm: that is the load corresponding to the actual
use of the screw, which is determined by the conditions of use
of the screw itself and can be calculated approximately by the
following formula:
F
v
=
F
1
3
T
1
+
F
2
3
T
2
+...
+
F
n
3
T
n
T
3
where:
F
1
is the constant LOAD during T
1
rotations;
F
2
…F
n
, are the constant loads during T
2
…T
n
rotations;
T = T
1
+ T
2
+ … + T
n
, are the number the total number of rotations
during which the loads F
1
, F
2
, …, F
n
.
The calculation of the life of the screw:
where:
T
v
Screw life in number of revolutions
L
din
dynamic LOAD
(see Technical Data Tables, pages 10 ÷ 69)
F
m
medium operating working LOAD
For the calculation of the service life, the average value of the
load is considered for F
m
, the medium operating working LOAD,
which affects the service life raised to the third.
Still the report
it can be called λ and obtained according to the number of rotations
required by the screw.
OPERATIONAL LIFE
The nominal life of a ball screw is the number of hours of activity
at a constant speed (or the number of revolutions) that the screw
is able to withstand before the rst signs of fatigue (peeling) occur
on the rolling surfaces (screw and screw nut)..
Practical experience has shown that identical screws, working
under the same conditions, have different durability; hence
the concept of nominal life. The nominal life, according to
the ISO denition, is the life reached or exceeded by 90% of a
sufciently large number of identical screws working under the
same conditions (alignment, applied load, speed, acceleration,
temperature, lubrication and cleaning).
The service life is the lifespan of a specic screw before failure.
The failure is not normally caused by fatigue (peeling), but by the
wear of the recirculation system, corrosion, contamination and,
more generally, by the loss of functional characteristics.
To obtain a useful life equivalent to the nominal life, the screw
must be subjected to an real medium load not exceeding 80% of
the dynamic load along a stroke of not less than 4 times the pitch.
The determination of the “size” of the screw to obtain the required
durability is provided by the experience gained with similar
applications; it is also necessary to consider the specic structural
needs such as the robustness of the terminals (shanks) and the
attachments of the screw nut due to the efforts applied to these
elements.
Mounting
In order to ensure the expected life of the screw it is important to
ensure a correct alignment of the screw with the sliding guides.
Radial loads and eccentric thrusts are absolutely to be avoided
because they reduce in signicantly the service life of the screw.