Industrial and Production Engineering

1.) Undamped vibrations:- In undamped vibrations, no resistive force acts on the vibrating object. As the object oscillates, the energy in the object is continuously transformed from kinetic energy to potential energy and back again, and the sum of kinetic and potential energy remains a constant value. In practice, it’s extremely difficult to find undamped vibrations. For instance, even an object vibrating in air would lose energy over time due to air resistance. Let us consider an object undergoing simple harmonic motion. Here, the objet experiences a restoring force towards the equillibrium point, and the size of this force is proportional to displacement. If the displacement of the object is given by x, then for an object with mass m in simple harmonic motion, we can write: This is a differential equation. A solution to this equation can be written in the form: Here,  If vibration is undamped, the object continues to oscillate sinusoidally. 2.) Damped vibratio

Degree of freedom is defined as the minimum number of independent variables required to define the position or motion of a system is known as degree of freedom. Degree of freedom is the property of kinematic chain which shows that in how many directions the connected links of the kinematic can move freely. It is also known by mobility. In 3-D space system an unconstrained rigid body possesses six degree of freedom. Total number of motions in space is six as 3 are rotary and 3 are translatory along x, y and z axis respectively. Here DOF can also be defined as the subtraction of total number of motions and the number of motions restraints or arrested (those motions which are not possible). DOF = 6 – Restraints In 2-D space system maximum 3 motions can be predicted as 2 translatory motion along x and y axis respectively and 1 rotary in perpendicular to x-axis i.e. z-axis. DOF = 3 – Restraint To determine DOF of 2-D planar mechanism, Kutzback was a scientist who gave the relatio

The Grashof’s law states that for a four-bar linkage system, the sum of the shortest and longest link of a planar quadrilateral linkage is less than or equal to the sum of the remaining two links, then the shortest link can rotate fully with respect to a neighboring link. Consider a four-bar-linkage. Denote the smallest link by S, the longest link by L and the & other two links by P and Q. If the Grashof’s Law condition is satisfied i.e S+L ≤ P+Q, then depending on whether shortest link ‘S’ is connected to the ground by one end, two ends, or no end there are 3 possible mechanisms. They are: Double-crank mechanism Double-rocker mechanism and Crank and rocker mechanism 1. Double crank mechanism In double crank mechanism, the shortest link ‘S’ is a ground link. Both input crank and output crank rotate at 360°. Grashof’s condition for double crank mechanism: s+l > p+ q Let:  ‘s’  = length of shortest link, ‘l’  = length of longest link, ‘p’  = length of one rema

BALANCING OF ROTATING MASSES When a mass moves along a circular path, it experiences a centripetal acceleration and a force is required to produce it. An equal and opposite force called centrifugal force acts radially outwards and is a disturbing force on the axis of rotation. The magnitude of this remains constant but the direction changes with the rotation of the mass. In a revolving rotor, the centrifugal force remains balanced as long as the centre of the mass of rotor lies on the axis of rotation of the shaft. When this does not happen, there is an eccentricity and an unbalance force is produced. This type of unbalance is common in steam turbine rotors, engine crankshafts, rotors of compressors, centrifugal pumps etc. BALANCING OF A SINGLE ROTATING MASS ROTATING IN THE SAME PLANE Consider a disturbing mass m1 which is attached to a shaft rotating at ω rad/s. Let r1 :- radius of rotation of the mass m1  distance between the axis of rotation of the shaft and the centr

Static Balance:- Static balance occurs when the centre of gravity of an object is on the axis of rotation. This allows the object to remain stationary, with the axis horizontal, without the application of any braking force. Static balance has no tendency to rotate due to the force of gravity. Dynamic Balancing:- Dynamic balancing is when the rotation does not produce any resultant centrifugal force or couple. The system will rotate without needing the application of any external force or couple, other than that required to support its weight. When a system or machine is unbalanced, to avoid stress being put upon the bearings, a counterbalancing weight is added. Dynamic balancing is a way to balance out machines by rotating parts quickly and then measuring the imbalance using electronic equipment. The imbalance calculated can then be added or subtracted from the weight until the vibration of the parts is reduced. Static balance refers to the ability of a stationary on object to i

In physics  and engineering,  a  free body diagram  (force diagram,  or FBD) is a graphical illustration used to visualize the applied forces, movements, and resulting reactions on a body in a given condition. They depict a body or connected bodies with all the applied forces and moments, and reactions, which act on the body(ies). The body  may consist of multiple internal members, (such as a truss  ), or be a compact body (such as a beam ). A series of free bodies and other diagrams may be necessary to solve complex problems. Free body diagrams are used to visualize the forces and moments applied to a body and calculate the resulting reactions, in many types of mechanics problems. Most free body diagrams are used both to determine the loading of individual structural components as well as calculating internal forces within the structure in almost all engineering disciplines from Biomechanics to Structural.   In the educational environment , learning to draw a free body diagram is an

Absolute motion :- An absolute motion is a motion to move a taught position without affected by the previous motion. In actual practice, there is no absolute motion, since an arbitrary set of axes or planes is always required to define a motion. However, the earth can be taken as a fixed reference plane and all motions relative to it are termed as absolute motions. Motion of a body with respect to another fixed body is called absolute motion. Relative Motion :- A relative motion is a motion to move by a taught distance from the current position. Since a relative motion sets its reference to the current position of the result of executing the previous motion command, the previous motion command affects the motion.