Chapter 9 Rigidity
15
Chapter 9
Rigidity
Rigidity and backlash of the drive system greatly affects the performance of the servo system. A detailed
review of these items is required before designing the equipment and selecting a model number.
Rigidity
Fixing the input side (wave generator) and applying torque to the
output side (flexspline) generates torsion almost proportional to
the torque on the output side. Figure O18-1 shows the torsional
angle quantity on the output side when the torque applied on the
output side starts from zero, increases up to +T0 and decreases
down to –T0. This is called the “Torque – torsional angle diagram,”
which normally draws a loop of 0-A-B-A’-B’-A. The slope described
in the “Torque – torsional angle diagram” is represented as the
spring constant for the rigidity of Harmonic Drive (unit: Nm/rad).
As shown in Figure 020-2, this “Torque – torsional angle diagram”
is divided into 3 partitions, and the spring constants in the area are
represented as K1, K2 and K3.
K1 – The spring constant when the torque changes from [zero] to
[T1]
K2 – The spring constant when the torque changes from [T1] to
[T2]
K3 – The spring constant when the torque changes from [T2] to
[T3]
Torsional angle can be calculated by the following formulas.
*
φ
: torsional angle
◆
Torque T is T1 or less:
◆
Torque T is between T1 and T2:
◆
Torque T is between T2 and T3:
The following table shows average values of T1 to T3, K1 to K3 and
θ
1 to
θ
2.
Spring constant
Model
No.
Sign
Unit
Reduction
ratio 30
Reduction
ratio 50
Reduction
ratio 100
3
T1
Nm
0.016
0.016
0.016
kgf m
0.0016
0.0016
0.0016
K1
Nm/rad
27
30
34
×10
-4
kgf m/arc min
8
9
10
θ
1
×10
-4
rad
5.9
5.3
4.7
arc min
2.0
1.8
1.6
T2
Nm
0.05
0.05
0.05
kgf m
0.005
0.005
0.005
K2
Nm/rad
40
47
54
×10
-4
kgf m/arc min
12
14
16
θ
2
×10
-4
rad
12.5
10.6
9.3
arc min
4.2
3.6
3.1
K3
Nm/rad
51
57
67
×10
-4
kgf m/arc min
15
17
20
3
2
2
K
T
T
−
+
θ
=
ϕ
2
1
1
K
T
T
−
+
θ
=
ϕ
1
K
T
=
ϕ
Figure 1
ね
じ
り
角
ヒステリシスロス
トルク
0
B’
B
A
+T
0
-T
0
A’
ね
じ
り
角
K
3
K
2
K
1
T
1
T
2
トルク
0
θ
1
θ
2
Tor
si
onal
an
gl
e
Tor
si
onal
a
ngl
e
Torque
Torque
Hysteresis
loss
