Linearführungen2_E_Mechanik_Linearführungen.qxd 09.07.2012 11:57 Seite 2-41
Linear guides
Effective loading calculation
Various factors affect the calculation of the
loading of isel guides. This includes the
position of the
C of G of the load, tensile and compressive
forces, torques, load and acceleration forces.
For a linear bench on 4 bearings, the bearing
forces are calculated according to the force
application point for various load directions.
The dimension LL/2 is used as the dimension L (see dimensioned drawings for the
relevant guides).
The calculation can also be applied to a slide
configuration with 2 slides.
The load factor in this case is CO/2.
Combined load
F2
If the load alignment of an element does
not coincide with one of the main load
directions, then the equivalent load is calculated:
F1
P [N]
F [N]
F1 [N]
F2 [N]
C0 [N]
M [Nm]
M0(XYZ) [Nm]
F
P = F 1 + F2
If a force F and a torque M load an element simultaneously, then the dynamically
equivalent load is:
C
P=F+M. 0
M0(XYZ)
dynamically equivalent load
F 2
opposing force = 1 + F22
vertical component see sketch (4)
horizontal component see sketch (4)
static load factor
opposing torque
static torque in the direction of the
opposing torque
According to DIN, the dynamically equivalent load
should not exceed the value P = 0.5 . C.
Equivalent load calculation
Equivalent load
Operating conditions
A incremental change B uniform change
P P1
3
1 . 3.
3
3
3
(P1 L 1+P2 . L 2+P3 . L 3.....+Pn . L n)
L
P=
1 .
( Pm i n + 2 . Pm a x )
3
Pmax.
P2
Pm
P
Pn
L1
P=
P
P
P1...n
L
L1...n
Pmin.
Ln
L2
L
L
dynamically equivalent load [N]
Individual load [N]
Total travel [m]
Individual travel [m]
Pmin
Pmax
smallest load [N]
largest load [N]
Static safety
Operating conditions
S0
Normal motion
High speed
With impacts and vibration
1.0 - 3.0
2.0 - 4.0
3.0 - 5.0
S0 =
M0
C0
=
P0
M
S0
C0
P0
M0
M
static load safety
static load factor [N]
statically equivalent bearing loading [N]
static loading torque [Nm]
equivalent static torque [Nm]
Nominal working life
The nominal working life is achieved or
exceeded by 90% of an adequately large
quantity of identical bearings, before the
first signs of material fatigue become
apparent.
made by isel
®
L [m]
Lh [h]
C [N]
P [N]
H [m]
n0SZ [min]
v [m/min]
Linear guides
nominal working life in units of 100,000 m
nominal working life in hours run
dynamic load factor
dynamically equivalent load
single stroke of the oscillating motion
Number of double strokes per minute
average speed of movement
MECHANICS 2-41
mechanics
Operating loads calculation
Linearführungen2_E_Mechanik_Linearführungen.qxd 09.07.2012 11:57 Seite 2-42
mechanics
Linear guides
Operating loads calculation
Load vertical on the bench surface
Loading
Dimensioned figure
Load on a trolley
F
F
F
P1=
F F L1
F L2
+
+
4
2L
2a
P2=
F
4
2
P3=
F F L1
+
4
2L
F L2
2a
4
P4=
F
4
F L1
2L
F L2
2a
P2
P4
L
a
P1
P3
L
a
1
F
L2
3
L1
F L1
F L2
+
2L
2a
Load in direction of motion
Loading
Dimensioned figure
Load on a trolley
F
F
L6
P2
F
Pt1 P1
Pt3
Pt1
P
PPPt1t1t1t1
PPt1 Pt1
Pt2
P3
t1
P4
Pt4
Pt2
Pt2Pt4
PP
Pt2t2t2
Pt4
Pt2Pt2 PPt2P
Pt4t4t4
PPt4 Pt4
a
L
P1 ... P4 =
F L6
2L
Pt1 ... Pt4=
F L5
2L
F
t4
L5
1
2
3
4
Load at right angles to the direction of motion
Loading
Dimensioned figure
F
Load on a trolley
F
L4
P1
F
Pt1
P3
P2
PPt33
P4
P3
Pt3 PPPP3 33 P Pt2
P3 3 3
P
Pt44
Pt3
PP
Pt3t3t3
PP4
Pt3Pt3 Pt3
Pt4 PPP4 44 P
P4 4 4
Pt4
PP
Pt4t4t4
Pt4Pt4 Pt4
2-42
MECHANICS
a
P1 ... P4 =
F L4
2a
L
L3
F
Linear guides
1
2
3
4
Pt1=Pt3=
F
4
F L3
2L
Pt2=Pt4=
F
4
F L3
2L
made by isel
®