23
1019658 11/2014
Selection Example: Stiffness Based Dimensioning
Resonance Frequency (Gear Output)
The formula
fn = Resonance frequency [Hz]
K1 = Gear torsional stiffness K1 [Nm/rad]
J = Load moment of inertia [kgm
2
]
allows the calculation of the resonance frequency at the gear output from the given torsional stiffness, K1, of the Harmonic Drive®
gear and the load‘s moment of inertia. The calculated frequency should correspond with the value provided in table 22.1. The
higher the load‘s moment of inertia, the more influence the application has on the gear selection. If the moment of inertia = 0,
the selected application has no numerical influence on the selection result.
Resonance Speed (Gear Input)
The resonance speed nn on the input side (motor side) can be calculated using the formula
n
n
= f
n
*30 [rpm]
During operation, we recommend that you pass the resonance speed rapidly. This can be achieved by selecting a suitable gear
ratio. Another possibility is to select suitable gear stiffness such that the resonance speed lies
beyond the required speed range.
Selection Example
HFUC-40-120-2A-GR preselected from “Selection Procedure” on page 20.
Intended application: milling head for woodworking
Moment of inertia at the gear output: 7 kgm
2
. Recommended resonance frequency from table 22.1: ≥ 30 Hz.
Resonance frequency using the preselected gear
HFUC-40-120-2A-GR:
According to stiffness based dimensioning, this gear size is too small for the application.
The larger gear HFUC-50-120-2A-GR results in a resonance frequency of:
Based on stiffness based dimensioning, the gear HFUC-50-120-2A-GR is recommended.
The resonance speed at the input (motor) amounts to:
n
n
= 30*30 = 900 [rpm]
Either, this speed should be passed without stopping when accelerating / braking, or it should
lie beyond the utilised speed range.
f
n
=
. = 22 [Hz]
1.3
.
10
5
7
1
2
�
f
n
=
. = 30 [Hz]
2.5
.
10
5
7
1
2
�
Equation 23.1
1
2
�
K
1
J
f
n
= [Hz]
