Trifilar Suspension Lab Sheet
Laboratory Sheet for the Experiment
Trifilar Suspension Course (s)B58EC, B58ED–Mech. Eng. Sci. 3, 4 | Year2 | SubjectDynamics | Semester (s)1 and 2 | Laboratory TitleTrifilar Suspension |
Objective:
To calculate the polar moment of inertia of an assembly and using the result to predict the periodic time of a trifilar suspension of the assembly.
Theory:
The moment of inertia of a solid object is obtained by integrating the second moment of mass about a particular axis. The general formula for inertia is:
where Ig = inertia in kg.m2 about the mass centre m = mass in kg k = radius of gyration about mass centre in m. In order to calculate the inertia of an assembly, the local inertia Ig needs to be increased by an amount mh2. where m = local mass in kg h = the distance between parallel axis passing through the local mass centre and the mass centre for the overall assembly. The Parallel Axis Theory has to be applied to every component of the assembly. Thus
The polar moments of inertia for some standard solids are:
Cylindrical solid | | Circular tube | | Square hollow section | |
An assembly of three solid masses on a circular platform is suspended from three chains to form a trifilar suspension. For small oscillations about a vertical axis, the periodic time is related to the Moment of Inertia.
1
3
L
O
3
2
1
Ø600
2
Figure 1. Trifilar suspension
From Figure 1, the equation of motion is:
(1)
Comparing this to the standard equation (2nd order differential equation) for Simple Harmonic Motion (SHM),
(2) the frequency in radians/sec and the period T in seconds can be calculated by:
(3) and (4)
Assuming the general solution for the equation (1) is , solve the differential equation (1) to obtain equation (3) and use frequency to obtain equation (4). Show the derivation in your report.
Trifilar Suspension Course (s)B58EC, B58ED–Mech. Eng. Sci. 3, 4 | Year2 | SubjectDynamics | Semester (s)1 and 2 | Laboratory TitleTrifilar Suspension |
Objective:
To calculate the polar moment of inertia of an assembly and using the result to predict the periodic time of a trifilar suspension of the assembly.
Theory:
The moment of inertia of a solid object is obtained by integrating the second moment of mass about a particular axis. The general formula for inertia is:
where Ig = inertia in kg.m2 about the mass centre m = mass in kg k = radius of gyration about mass centre in m. In order to calculate the inertia of an assembly, the local inertia Ig needs to be increased by an amount mh2. where m = local mass in kg h = the distance between parallel axis passing through the local mass centre and the mass centre for the overall assembly. The Parallel Axis Theory has to be applied to every component of the assembly. Thus
The polar moments of inertia for some standard solids are:
Cylindrical solid | | Circular tube | | Square hollow section | |
An assembly of three solid masses on a circular platform is suspended from three chains to form a trifilar suspension. For small oscillations about a vertical axis, the periodic time is related to the Moment of Inertia.
1
3
L
O
3
2
1
Ø600
2
Figure 1. Trifilar suspension
From Figure 1, the equation of motion is:
(1)
Comparing this to the standard equation (2nd order differential equation) for Simple Harmonic Motion (SHM),
(2) the frequency in radians/sec and the period T in seconds can be calculated by:
(3) and (4)
Assuming the general solution for the equation (1) is , solve the differential equation (1) to obtain equation (3) and use frequency to obtain equation (4). Show the derivation in your report.