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2. (20 pts.) The figure below shows a rotating drive system with a viscous-friction coefficient c...
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...
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...
Figure shows a disk with moment of inertia J=0.5 kg-m2 that is initially rotating at an...
Figure shows a disk with moment of inertia J=0.5 kg-m2 that is initially rotating at an angular velocity 0 0 = 40 rad/s. A flexible shaft with torsional spring constant k = 65 N-m/rad connected to the disk. The disk is subjected to friction, which is modeled by linear viscous friction torque bò, with friction coefficient b = 1.0 N-m-s/rad. The input torque in the clockwise direction is a step function Tin(t) = 3.0U(t) N-m. Flexible shaft, k Disk Viscous...
PROBLEM -2 An Inertia J of radius r attached to a fixed axis of rotation A as shown below. The inertia is in contac...
PROBLEM -2 An Inertia J of radius r attached to a fixed axis of rotation A as shown below. The inertia is in contact with a mass M attached via aspring of stiffness K to a fixed wall. The inertla- mass contact is subject to viscous friction of coefficient f. The motion of the mass with respect to the horlzontal floor is subject to the same viscous friction coefficient f..The system input is a horizontal force f(t) on the mass...
Q2 A rotational mechanical system is shown in Figure 2.1. T(t) is the external torque and...
Q2 A rotational mechanical system is shown in Figure 2.1. T(t) is the external torque and is the input to the system. 01(t) is the angular displacement of inertia Ji and O2(t) is the angular displacement of inertia J2. C and C are friction coefficients and K, and K2 are spring constants. (a) Draw the free-body diagrams for J; and Jz. (7 marks) (b) Derive the equations of motion for the system shown in Figure 2.1. (8 marks) (c) Using...
Consider the mass-spring-damper system depicted in the figure below, where the input of the system is...
Consider the mass-spring-damper system depicted in the figure below, where the input of the system is the applied force F(t) and the output of the system is xít) that is the displacement of the mass according to the coordinate system defined in that figure. Assume that force F(t) is applied for t> 0 and the system is in static equilibrium before t=0 and z(t) is measured from the static equilibrium. b m F Also, the mass of the block, the...
PROBLEM I- (3 pts) Figure below represents a suspension system of vehicle. It is composed by...
PROBLEM I- (3 pts) Figure below represents a suspension system of vehicle. It is composed by a rigid half axle that pivots about a fixed point o. A support, which consists of a massless spring (with stiffness k) and a damper (with damping coefficient b) coaxially placed, is pivoted on the half shaft at one end and the body at the other end. Neglect the masse of the half shaft and assume the equilibrium position of the system to be...
PARTS: a-c Problem 1 (40 points) The rotational system shown in this diagram has a single...
PARTS: a-c
Problem 1 (40 points) The rotational system shown in this diagram has a single torque input, T(t), and a single angular displacement output, (t). Also shown are the shaft polar moment of inertia, J, torsional spring constant, k, and rotational viscous damping coefficient, c. From the law of rotation (sum of the moments equal to polar moment of inertia times angular acceleration), we obtain: jä(t) + c)(t) + ko(t) = T(t). This ordinary differential equation is second-order, linear...
Problem-5 (20 pts): Consider the DC servo motor shown in Figure-5. Assume that the input of the s...
Problem-5 (20 pts): Consider the DC servo motor shown in Figure-5. Assume that the input of the system is the applied armature voltage ea and the output is the load shaft position θ2. Assume also the following numerical values for the components: Ra-) Armature winding resistance = 0.2Ω La → Armature winding inductance = 0.1 mH Kb-) Back emf constant 0.05 Vs/rad K > Motor torque constant 0.06 Nm/A Jr Moment of inertia of the rotor of the motor =...
3. The following figure shows the block diagram of a mechanical translational system k1 U3 m1...
3. The following figure shows the block diagram of a mechanical translational system k1 U3 m1 (a) Draw free body diagrams for each of the masses. Bearing in mind that the force due to spring is proportional to its length and the force due to friction is proportional to velocity, label each of the forces acting upon each body. (b) Develop the dynamical equations for the system.
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...
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...
Figure shows a disk with moment of inertia J=0.5 kg-m2 that is initially rotating at an angular velocity 0 0 = 40 rad/s. A flexible shaft with torsional spring constant k = 65 N-m/rad connected to the disk. The disk is subjected to friction, which is modeled by linear viscous friction torque bò, with friction coefficient b = 1.0 N-m-s/rad. The input torque in the clockwise direction is a step function Tin(t) = 3.0U(t) N-m. Flexible shaft, k Disk Viscous...
PROBLEM -2 An Inertia J of radius r attached to a fixed axis of rotation A as shown below. The inertia is in contact with a mass M attached via aspring of stiffness K to a fixed wall. The inertla- mass contact is subject to viscous friction of coefficient f. The motion of the mass with respect to the horlzontal floor is subject to the same viscous friction coefficient f..The system input is a horizontal force f(t) on the mass...
Q2 A rotational mechanical system is shown in Figure 2.1. T(t) is the external torque and is the input to the system. 01(t) is the angular displacement of inertia Ji and O2(t) is the angular displacement of inertia J2. C and C are friction coefficients and K, and K2 are spring constants. (a) Draw the free-body diagrams for J; and Jz. (7 marks) (b) Derive the equations of motion for the system shown in Figure 2.1. (8 marks) (c) Using...
Consider the mass-spring-damper system depicted in the figure below, where the input of the system is the applied force F(t) and the output of the system is xít) that is the displacement of the mass according to the coordinate system defined in that figure. Assume that force F(t) is applied for t> 0 and the system is in static equilibrium before t=0 and z(t) is measured from the static equilibrium. b m F Also, the mass of the block, the...
PROBLEM I- (3 pts) Figure below represents a suspension system of vehicle. It is composed by a rigid half axle that pivots about a fixed point o. A support, which consists of a massless spring (with stiffness k) and a damper (with damping coefficient b) coaxially placed, is pivoted on the half shaft at one end and the body at the other end. Neglect the masse of the half shaft and assume the equilibrium position of the system to be...
PARTS: a-c
Problem 1 (40 points) The rotational system shown in this diagram has a single torque input, T(t), and a single angular displacement output, (t). Also shown are the shaft polar moment of inertia, J, torsional spring constant, k, and rotational viscous damping coefficient, c. From the law of rotation (sum of the moments equal to polar moment of inertia times angular acceleration), we obtain: jä(t) + c)(t) + ko(t) = T(t). This ordinary differential equation is second-order, linear...
Problem-5 (20 pts): Consider the DC servo motor shown in Figure-5. Assume that the input of the system is the applied armature voltage ea and the output is the load shaft position θ2. Assume also the following numerical values for the components: Ra-) Armature winding resistance = 0.2Ω La → Armature winding inductance = 0.1 mH Kb-) Back emf constant 0.05 Vs/rad K > Motor torque constant 0.06 Nm/A Jr Moment of inertia of the rotor of the motor =...
3. The following figure shows the block diagram of a mechanical translational system k1 U3 m1 (a) Draw free body diagrams for each of the masses. Bearing in mind that the force due to spring is proportional to its length and the force due to friction is proportional to velocity, label each of the forces acting upon each body. (b) Develop the dynamical equations for the system.
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