Weight and Damper Motor
Let’s consider a very simple motor drive system that contains a source of torque (such as a falling weight or
a torsion spring), a rotary damper, and the output shaft. Let’s also assume that the torque source (S) is
connected to the damper (D) through a gear train and that the damper is connected via a gear train to the
output shaft (O). A block diagram of this system could be as follows:
Torque
Source
Gears
Output
Shaft
Damper
Gears
The torque source supplies the torque to be provided to the system. The damper constrains the angular
velocity of the system. The angular velocity of the damper has a linear relationship between the torques
applied to the damper, i.e.

Torque Rating
K = Torque Rating / Max Speed

Maximum Speed
This implies that the larger the torque applied to the damper, the faster it will run until it hits its torque
rating and its maximum speed. Running the damper at higher torques than the rating may cause damage to
the damper so that it will no longer function correctly. Since the damper constrains relationship between its
torque and speed, the damper defines the relationship between the output torque and output rotational
velocity. We will use this in selecting a damper for our system.
Now, we select the components (damper, gears, torque source) of the motor assembly system to give us the
desired torque and angular velocity on the output shaft for our sculpture. First, we need to compute the
torque and angular velocity needed to power the sculpture. Let’s call these known variables, o and o.
STEP 1: Pick gear ratio between damper and output
First we will pick the gear ratio between the damper and the output G do based on the desired output velocity
that we would like. We know that here is a maximum allowable angular velocity we can drive the damper
without breaking down the fluid in the damper, i.e.
 d   d max
So we will pick a gear ratio to make sure that we are operating at 75% or less of the maximum allowable
angular velocity by:
God 
0.75 *  d max
o
STEP 2: Pick the damper constant and damper
To pick a damper, we want to match the ratio of the desired output torque and velocity with the damper the
torque-angular velocity ratio, K. We know that the damper constrains its torque and angular velocity to
have the following relationship:
d
K
d
The relationship between the torque of the damper and the output torque is given by the gear ratio:
o
 God
d
Similarly, the relationship between the angular velocity of the damper and the output angular velocity is
given by the inverse gear ratio:
o
1

 d God
Therefore:
o
2 
2
 God d  God K
o
d
So we should choose the damper that has the K closest to:
K
o
2
God  o
STEP 3: Pick the gear ratio between the output and the source torque.
Finally, we choose the gear ratio between the output and the torque source to give the correct output torque
to the system, i.e.,
Gos 
o
s
Potential Dampers
For the McMaster-Carr rotary dampers,
 d max  10rpm
The following table summarizes the dampers available from McMaster Carr :
Torque Rating
in-oz
(specs)
0.28
0.56
0.83
1.39
2.78
4.17
6.94
13.89
17.36
20.83
Torque Rating
in-lb
(in-oz/16)
0.0175
0.035
0.051875
0.086875
0.17375
0.260625
0.43375
0.868125
1.085
1.301875
K
in-lb/rpm
(torque rating/wdmax)
0.00175
0.0035
0.0051875
0.0086875
0.017375
0.0260625
0.043375
0.0868125
0.1085
0.1301875
Calculations for Bubbles on Waves
Max angular velocity of damper
Desired angular velocity
Desired output torque
Gear ratio between damper and output
Damper constant
Gear ratio between source and output
wdmax
wo
to
God=0.75*wdmax/wo
K=to/(God^2*wo)
Gos=to/ts
10
7.5
1
1
0.13
1
rpm
rpm
in-lb
in-lb/rpm
From these calculations, we can power our sculpture with a very simple drive system. We will create a
source torque from a weight on a string rotating a shaft. If we design this to deliver 1 in-lb of torque (what
we computed our sculpture needs to move) then we can eliminate the gear train and have the weight and
string mounted directly on the output shaft. In addition, since the speed at which we want to run our
sculpture is perfectly within the range of the operating speed of the dampers, we do not need a gear train
between the damper and the output shaft either. Therefore, for Bubbles on Waves, torque source, damper
can all share a single shaft (i.e. the output shaft.)