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EXAMINATION FOR ME3112E โ Mechanics of Machine (Semester I: 2012/2013)
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Based above formula and compare with SolidWorks simulation result, we can see that the theoretical result matches with Simulation quite well, especially when L becomes longer. Table 1: Max Angular Acceleration: Theoretical vs. SolidWorks simulation. (
0.6
0.9
1.2
1.5
1.8
2.1
2.4
4.8
9.6
(
7
10.5
14
17.5
21
24.5
28
56
112
(
9
9
9
9
9
9
9
9
9
Calculated Angular Acc
18.033
12.426
9.571
7.826
6.642
5.783
5.128
2.733
1.434
Simulated Angular Acc
16.405
11.948
9.378
7.732
6.591
5.752
5.108
2.731
1.433
9.93%
4.00%
2.06%
1.21%
0.78%
0.54%
0.38%
0.06%
0.01%
Difference:
Page 1 of 3
I also performed SolidWorks Simulation for Pinned disk case, here are the results: Table 2: Max Angular Acceleration: Theoretical vs. SolidWorks simulation. (
Surprisingly, the simulation result based on pinned disk matches with theoretical calculation perfectly! Which means the previously derived formula for maximum angular acceleration
(
is perfectly applicable for pinned disk case! But what should be the appropriate formula for welded disk case??? SolidWorks Motion Simulation output example:
Displacement vs. Time
Velocity vs. Time
Acceleration vs. Time
Page 2 of 3
For welded disk, the moment of inertia caused by disk should be calculated based on parallel axis theorem:
where: is the moment of inertia of the object about an axis passing through its centre of mass; is the object's mass; is the perpendicular distance between the axis of rotation and the axis that would pass through the centre of mass. Hence the equation of max acceleration will become: (
(
)
(
)
(
Table 3: Max Angular Acceleration: Theoretical vs. SolidWorks Motion simulation. (
This time, the calculated result matches with SolidWorks Motion simulation perfectly! Conclusion: When the disk is welded, we should use parallel axis theorem to calculate its moment of inertia. While when the disk is pinned, it is acting like a point mass at the end of rod. I wish I had figure this out during exam,
