Dynamic Systems
The figure below shows a three-disc rotational mechanical system.
Three moments of inertia (J1, J2 and J3), torsional stiffness (k1 and k2) and torsional viscous friction (b1 and
It is combined with flexible shafts modeled with b2) elements. Angular location of three disks
displacements are measured from untwisted shaft positions. Electric motor torque, direct second
it affects the motor inertia in the disk. Free body of a three-disc rotational mechanical system
Find the diagram and mathematical model.
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MatLab analysis preferred, but please show the process. II) 3-DOF Torsional System Using matrix algebra, analyze...
MatLab analysis preferred, but please show the process.
II) 3-DOF Torsional System Using matrix algebra, analyze the natural frequencies of the following 3-DOF shaft system. First setup the equations of motion, express the system in matrix form, and then use MATLAB to calculate the natural frequencies and the mode shapes. K2 K3 K4 J1 J2 J3 Data: J: = 500 lb.in.s- J2 750 lb.in.s2 J3 1000 lb.in.s? K1-2x106 lb.in/rad K2 106 Ib.in/rad K3 106 Ib.in/rad K4 2x106 lb.in/rad
3. A motor with torque T and inertia Jm drives a load of inertia Joad via a shaft which may be assumed to have infin...
3. A motor with torque T and inertia Jm drives a load of inertia Joad via a shaft which may be assumed to have infinite stiffness and viscous damping b. Determine the transfer function between the torque T and the shaft speed w. 4. Find the transfer function X2(s)/F (s) of the spring-mass system shown in Figure 4. The system moves over a frictionless surface X2 X1 b k2 k1 M2 M1 Figure 4. A 2 DOF spring-mass system over...
Modelling of mechanical dynamic systems Exercice 1 An disc of an inertia J and radius r...
Modelling of mechanical dynamic systems Exercice 1 An disc of an inertia J and radius r is attached to a fixed axis of rotation A as shown below. The disc is in contact with a mass M attached via a spring of stiffness K to a fixed wall. The inertia-mass contact is subject to viscous friction of coefficientſ. The motion of the mass with respect to the horizontal floor is subject to the same viscous friction coefficient f.. The system...
Consider the mechanical dynamics of a 2DOF rotary motion system shown below, where the torque is...
Consider the mechanical dynamics of a 2DOF rotary motion system shown below, where the torque is applied to the right shaft but the angular position of the left shaft is to be controlled, k is the stiffness of the linear rotary spring and bi, b2 are the viscous friction coefficients of the ball bearings that support the left and right shafts respectively and act as linear viscous dampers with rotary motion. PLEASE show all mathematical steps explicitly. (I1=Iz=1kgm², bi=b2=0.9Nms/rad, k=4Nm/rad)...
Q 1- 08 Pts) Figure below is a diagram of a DC motor connected in parnllel to a current source i,...
Q 1- 08 Pts) Figure below is a diagram of a DC motor connected in parnllel to a current source i,. The torque and back-EMF constants of the motor are Ko K respectively, the motor resistance is R, also modeled as connected in parallel, the motor inertia is 1- (not shown), and the motor inductance is negligible. The motor load is an inertia J with compliance (stiffness) K and viscous friction coefficient b, and it is attached a gear pair...
Follwoing the ssumptions above we are able to model the force transmission process in a fashion...
Follwoing the ssumptions above we are able to model the force transmission process in a fashion of rotational mass-damper-spring as shwon below. We can assume the shaft 1 is massless. J is the mass moment of inertia for the set of motor, shaft 2 and driving gear and J2 for the driven gear, shaft 3 and prop eller. Assume the mechanical system is initially at rest a Governing Equations With the prescribed applied torque by the motor T(t), set up...
01- (08 Pts) Figure below is a diagram of a DC motor connected in parallel to...
01- (08 Pts) Figure below is a diagram of a DC motor connected in parallel to a current source is the torque and back-EMF constants of the motor are K. K respectively, the motor resistance is R, also modeled as connected in parallel, the motor inertia is I. (not shown), and the motor inductance is negligible. The motor load is an inertia compliance (stiffness) K and viscous friction coefficient b, and it is attached to the motor via a gear...
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical...
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical system subjected to fluctuations (t) at the wall is provided in figure 2. Spring k, is interconnected with both spring ka and damper Os at the nodal point. The independent displacement of mass m is denoted by 1, the independent displacement of mass m, is denoted by r2, and the independent displacement of the node is denoted by ra. Assume a linear force-displacement/velocity relationship...
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s...
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s)X2 (s)/F(s) (b) Does the system oscillate with a unit step input (f (t))? Explain the reason (c) Decide if the system(x2 (t)) is stable with a unit step input (f (t))? Explain the reason 1. 320) 8 kg 2 N/m 4N-s/m 2N-s/m Fig. 1 2. There are two suspensions for a car as shown in Fig. 2 (a) Find the equations of each...
MatLab analysis preferred, but please show the process.
II) 3-DOF Torsional System Using matrix algebra, analyze the natural frequencies of the following 3-DOF shaft system. First setup the equations of motion, express the system in matrix form, and then use MATLAB to calculate the natural frequencies and the mode shapes. K2 K3 K4 J1 J2 J3 Data: J: = 500 lb.in.s- J2 750 lb.in.s2 J3 1000 lb.in.s? K1-2x106 lb.in/rad K2 106 Ib.in/rad K3 106 Ib.in/rad K4 2x106 lb.in/rad
3. A motor with torque T and inertia Jm drives a load of inertia Joad via a shaft which may be assumed to have infinite stiffness and viscous damping b. Determine the transfer function between the torque T and the shaft speed w. 4. Find the transfer function X2(s)/F (s) of the spring-mass system shown in Figure 4. The system moves over a frictionless surface X2 X1 b k2 k1 M2 M1 Figure 4. A 2 DOF spring-mass system over...
Modelling of mechanical dynamic systems Exercice 1 An disc of an inertia J and radius r is attached to a fixed axis of rotation A as shown below. The disc is in contact with a mass M attached via a spring of stiffness K to a fixed wall. The inertia-mass contact is subject to viscous friction of coefficientſ. The motion of the mass with respect to the horizontal floor is subject to the same viscous friction coefficient f.. The system...
Consider the mechanical dynamics of a 2DOF rotary motion system shown below, where the torque is applied to the right shaft but the angular position of the left shaft is to be controlled, k is the stiffness of the linear rotary spring and bi, b2 are the viscous friction coefficients of the ball bearings that support the left and right shafts respectively and act as linear viscous dampers with rotary motion. PLEASE show all mathematical steps explicitly. (I1=Iz=1kgm², bi=b2=0.9Nms/rad, k=4Nm/rad)...
Q 1- 08 Pts) Figure below is a diagram of a DC motor connected in parnllel to a current source i,. The torque and back-EMF constants of the motor are Ko K respectively, the motor resistance is R, also modeled as connected in parallel, the motor inertia is 1- (not shown), and the motor inductance is negligible. The motor load is an inertia J with compliance (stiffness) K and viscous friction coefficient b, and it is attached a gear pair...
Follwoing the ssumptions above we are able to model the force transmission process in a fashion of rotational mass-damper-spring as shwon below. We can assume the shaft 1 is massless. J is the mass moment of inertia for the set of motor, shaft 2 and driving gear and J2 for the driven gear, shaft 3 and prop eller. Assume the mechanical system is initially at rest a Governing Equations With the prescribed applied torque by the motor T(t), set up...
01- (08 Pts) Figure below is a diagram of a DC motor connected in parallel to a current source is the torque and back-EMF constants of the motor are K. K respectively, the motor resistance is R, also modeled as connected in parallel, the motor inertia is I. (not shown), and the motor inductance is negligible. The motor load is an inertia compliance (stiffness) K and viscous friction coefficient b, and it is attached to the motor via a gear...
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical system subjected to fluctuations (t) at the wall is provided in figure 2. Spring k, is interconnected with both spring ka and damper Os at the nodal point. The independent displacement of mass m is denoted by 1, the independent displacement of mass m, is denoted by r2, and the independent displacement of the node is denoted by ra. Assume a linear force-displacement/velocity relationship...
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s)X2 (s)/F(s) (b) Does the system oscillate with a unit step input (f (t))? Explain the reason (c) Decide if the system(x2 (t)) is stable with a unit step input (f (t))? Explain the reason 1. 320) 8 kg 2 N/m 4N-s/m 2N-s/m Fig. 1 2. There are two suspensions for a car as shown in Fig. 2 (a) Find the equations of each...
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