ME 302 DYNAMICS OF MACHINERY INTRODUCTION Dr. Sadettin KAPUCU © 2007 Sadettin Kapucu

Introduction to Dynamics of Machinery ME 108 ME 208 ME 302 ME 301 Dynamics of machinery is an applied science which is used to understand the relationship between the motion of a machine and the forces which produce these motions.

Introduction to Dynamics of Machinery In this course, we study kinetics, the time-varying forces in machines and the resulting phenomena which must be considered in their design. Design is the process of prescribing the sizes, shapes, material compositions, and arrangements of parts so that the resulting machine will perform the prescribed task. Mechanism: A system of elements arranged to transmit motion in a predetermined fashion. Machine: A system of elements arranged to transmit motion and energy in a predetermined fashion.

Introduction to Dynamics of Machinery Joints Rigid Bodies Mechanism: Assemblage of resistant bodies (rigid) connected by movable joints, to form a closed kinematic chain with one link fixed and having the purpose of transforming motion. Kinematic Pair

D.O.F of a body in space Dof is defined as the number of independent parameters that is required to define the position of a body in space. P1(x1,y1,z1) l3 P3(x3,y3,z3) l1 l2 P2(x2,y2,z2) 9 parameter x1, y1, z1, x2, y2, z2, x3,y3,z3 9-3=6 But ;

4-1=3 D.O.F of a body in plane P1(x1,y1) l1 P2(x2,y2) The number of independent parameters that is required to define the position of a body in space. P1(x1,y1) l1 P2(x2,y2) 4 parameter x1, y1, x2, y2 4-1=3 But ;

Plane motion

Brief Review of Engineering Mechanics Fundamental principles of dynamics are Newton’s Laws of Motion. They cannot be proved arithmetically. No experimental evidence up till now has been observed to violate them. These are three laws:

Brief Review of Engineering Mechanics Newton’s First Law (Statics):A body at rest tends to stay at rest, and a body in motion tends to stay in uniform motion (direction & magnitude of the velocity not changing) unless a net non-zero force act on it. Newton’s first law is expressed as mathematically;

Brief Review of Engineering Mechanics Newton’s Second Law (Dynamics):When a net, non-zero force acts on a body, the body accelerates in proportion to and in direction of the acting force. Newton’s Second law is expressed as mathematically; Amount of mater Resistance of a body against motion

Brief Review of Engineering Mechanics Newton’s Third Law (Action-Reaction):Every force has a reaction; equal in magnitude, collinear, and opposite in direction to the original force. Newton’s third law is expressed as mathematically;

Brief Review of Engineering Mechanics Newton’s laws of motion will be the main starting point for the dynamic analysis of machinery. The basic quantities of dynamics are force, mass and time. Force can be define in terms of Newton’s first law as an action which tends to change the motion of a body Mass is the resistance of a body to motion. Time is a concept for ordering the flow of events.

Brief Review of Engineering Mechanics In this generally SI system of units will be used. Quantity name Symbol Lenght meter m Mass kilogram kg Force Newton N Time second s Work joule J Power watt W Frequency hertz Hz

Subject of ME 302 Subject of matter of ME 302 is to apply Newton’s laws to multi body, single or multi degree of freedom mechanical systems (mechanism) to understand their mechanical behaviour.

Static Force Analysis We start with simple problem where the bodies accelerations are zero. Then all the forces and moments will add to zero. This is the static condition. Every sub component of a static system is also static. If a mechanism is static each of its link are also static. Big problem of the whole mechanism is now broken into several simpler problems. Each body with all the acting forces is called a free body. Pictorial representation of a body is called the free body diagram.

Please remember that for a solution, Freebody Diagram Y Please remember that for a solution, a correct freebody diagram is essential. B 3 4 F C 2 t X A 1 3 2 t 4 F

Forces and Moments Force is a vectorial quantity that has manitude, direction and point of application.

Forces and Moments A force generates a moment (or torque) about a point which is not in its line of action moment is the turning effect of a force. Moment direction can be found by right hand rule. It is perpendicular to the plane formed by r and F.

Forces in Machine Systems External forces are generated by effects external to the mechanism, like actuation forces from a motor or actuator. Reactions of the external forces are outside our system boundary.

Forces in Machine Systems Constraint forces “constraint” means “limitation of freedom”, in our case, limitation of free motion. These forces are applied onto each link to prevent their free motion. Reactions of constraint forces are inside the system boundary.

Joint Types and Constraint Forces Revolute Joint Z X Y It has one degree of freedom, which is in rotation about z-axis.

Joint Types and Constraint Forces Revolute Joint Z X Y Z X Y Fx Fx Mx Mx Fz Fy Fz Fy My My It cannot transfer force or torque or angular motion about z-axis, but it transmits forces and torques and related motions in all the other remaining directions. These are; Forces in x, y and z directions, Torques about x and y-axis.

Joint Types and Constraint Forces Prizmatic Joint Y It has one degree of freedom, which is a translation along z axis. Z X

Joint Types and Constraint Forces Prizmatic Joint Z X Y Z X Y Fx Fx Mx Mx Fy Fy My Mz My Mz It cannot transmit a force in z axis, but it can transmit forces in x and y directions and moments x, y, and z axis.

Joint Types and Constraint Forces Cylindrical Joint X Y Z It has two degree of freedom; a translation along and rotation about the same axis, called the cylindrical axis.

Joint Types and Constraint Forces Cylindrical Joint Z X Y Z X Y Fx Fx Mx Mx Fy Fy My My No torque transmission about z-axis, no force transmission along z-axis is possible. In all other directions, there can be forces and moments transmitted, which are forces in x and y-axis and moments about y and z-axis.

Joint Types and Constraint Forces Screw joint X Y Z There are two apparent motions, which are translation along and rotation about z-axis, are not independent from each other. Therefore degree of freedom is only one. This is a rotation about z-axis.

Joint Types and Constraint Forces Screw Joint Z X Y Z X Y Fx Fx Mx Mx Fy Fz Fy My Fz My No torque transmission about z-axis, no force transmission along z-axis is possible. In all other directions, there can be forces and moments transmitted, which are forces in x and y-axis and moments about y and z-axis.

Joint Types and Constraint Forces Planar joint Y It has three degree of freedom, translation along x and z directions and a rotation about y-axis. Z X

Joint Types and Constraint Forces Planar Joint X X Fx Fx Mx Mx My Mz My Y Mz Y Z Z There are no forces and a torque transmission in these directions. In all other directions there can be force and moment transmitted, which are force in y-axis and moments x and z-axis.

Joint Types and Constraint Forces Spherical joint X Y Z It has three rotational degrees of freedom, so it cannot transmit any moments.

Joint Types and Constraint Forces Spherical Joint Z X Y Z X Y Fx Fx Fz Fy Fz Fy It can transmit forces in all directions.