# INTERPRETATION OF STIFFNESS AND DAMPING

## Dynamic & Control

### INTRODUCTION

This sheet gives some insight about stiffness and damping and their effect on the dynamics of mechanical systems.

###### Influence of stiffness

Stiffness increases the tracking behavior the displacement of the end-effector (mass m) in relation to the input (a stiff actuator). Moreover, it decreases the influence of the external force Fe, which is often a disturbance to the system.

###### Influence of damping

Damping is difficult! Damping can be regarded as loss of energy. However, the positive effect of damping is that it damps oscillations and resonances.

###### Damping prediction

The damping of mechanical systems is hard to predict. Rule of thumb: damping decreases with increasing frequency. Joints and other system impurities increase damping.
with viscous damping ratio

Systemζ [-]
Metals in elastic range0.01
Continuous metal structures0.02 - 0.04
Metal structures with joints0.03 - 0.07
Plastics (hard - soft)0.02 - 0.05
Rubber0.05
Sintered material (piezos)0.05
Airpots (vibration isolation tables)0.07
###### Response to the external force:

Properties:

• Eigen frequency:
• Gain at :
###### Schematic overview

1 mass m, 1 spring c, 1 damper d, input xin, external force Fe

###### Tracking – design rule

When designing a system that has to track the input xin and that needs to be insensitive to disturbance force Fe, then design ‘light and stiff’.

###### Vibration isolation – design rule

When designing a system that needs to be insensitive to vibrations xin (such as ground vibrations), then design ‘heavy and weak’.

###### Eigen frequency

At this point the spring energy is converted into kinetic energy: hence: and thus:

###### Response to the input:

Properties:

• Eigen frequency:
• 2nd cross-over frequency:

(from hence:   and thus: )

• Gain at : dB