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[[image]]
Figure 9 A Finite Element Model of the SRMS Arm (shown in the Swung-Out Configuration, With the Shoulder Brace Unlatches)

9. In this model, the arm mass/inertia is ignored in comparison with the payload mass and inertia; and the flexibilities of the beam elements are added to yield a 6x6 arm flexibility matrix. The payload mass properties are represented by: 
[[image]] 
(1)
where m = payload mass 
I = 3x3 inertia matrix of the payload with respect to its centre of mass, expressed in a payload reference frame Fp. 

The arm flexibility matrix is represented by: 
[[image]]
(2)
where the summation is taken over all 24 beam elements representing the arm, 

Fi = 6x6 beam flexibility matrix, expressed in the local reference frame Fi, fixed to beam i,


Table 4
SRMS Arm Natural Frequencies for Diffeent [[Different]] Arm Configurations
[[9 Columned Table]]
|Payload (Kg)|Orbiter|Arm Configuration|Natural Frequencies (Hz) ω1|Natural Frequencies (Hz) ω2|Natural Frequencies (Hz) ω3|Natural Frequencies (Hz) ω4|Natural Frequencies (Hz) ω5|Natural Frequencies (Hz) ω6|
|---|---|---|---|---|---|---|---|
|0|Constrained|A|0.5351|0.6366|1.5273|2.0330|9.2957|12.4187|
|   |   |C|0.7093|0.8805|1.1223|1.7226|11.2366|13.2662|
|   |   |D|0.3726|0.4771|3.6883|4.4402|9.1770|9.9049|
|   |   |S|0.3463|0.4614|3.5544|4.2282|14.9813|15.1365|
|0|Unconstrained|A|0.5409|0.6386|1.5288|2.0388|9.2960|12.4190|
|   |   |C|0.7115|0.8813|1.1257|1.7253|11.2394|13.2752|
|   |   |D|0.3734|0.4779|3.6913|4.4422|9.1983|9.9190|
|   |   |S|0.3547|0.4633|3.5571|4.2296|14.9954|15.1395|
|14615|Constrained|A|0.0365|0.0427|0.0684|0.1669|0.2014|0.2717|
|   |   |B|0.0434|0.0569|0.0859|0.0992|0.1593|0.3315|
|   |   |C|0.0448|0.0520|0.0737|0.1470|0.2515|0.3534|
|   |   |S|0.0274|0.0329|0.0578|0.1399|0.4383|2.9758|
|14615|Unconstrained|A|0.0494|0.0684|0.0726|0.1755|0.2261|0.3009|
|   |   |B|0.0473|0.0596|0.0897|0.1166|0.1694|0.3567|
|   |   |C|0.0469|0.0546|0.0784|0.1612|0.2653|0.3630|
|   |   |S|0.0439|0.0591|0.0719|0.1431|0.4405|3.4987|

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