Jahangirabad Institute Of Technology Assistant Prof. MD Gulfaraz Alam Dynamics of Machines Semester VI, 2015-16 MASTER SCHEDULE Class 1 Monday, January 18 Unit-I Introduction Week 1 Class 3 Wednesday, January 20 Force analysis: Static force analysis D Alembert s Principle, Week 2 mechanisms, Class 5 Friday, January 23 Class 2 Tuesday, January 19 Importance of dynamics of machine Class 4 Thursday, January 22 of dynamics of rigid link in plane motion, Class 6 Monday, January 25 dynamic force analysis of planar mechanisms,moment on crankshaft due to force on piston, piston force and crank effort Class 7 Thursday, January 28 Class 8 Friday 29 Unit-II Turning moment diagrams for single cylinder ur stroke IC engine and multi-cylinder engines, double acting steam engine, Week 3 Class 9 Class 10 Monday Feb. 1 Saturday January 30 Turning moment diagrams for single cylinder Fluctuation of speed, Flywheel. Class 11 Tuesday, Feb. 2 Class 12 Thursday Feb. 4 Space motion of rigid bodies, Gyroscope: introduction. Week 4 Class 13 Friday, Feb. 5 angular momentum, gyroscopic couples, Class 15 Monday, Feb. 8 ship stabilization, Class 17 Thursday, Feb.11 Week 5 Continue.. moving on curved paths. Class 19 Saturday, Feb.13 Mech. Vibrations: Unit-III Class 21 Tuesday, Feb.16 Week 6 Longitudinal Vibration Friday, Feb.19 Week 7 Class 23 Single degree free and damped vibration Class 14 Saturday, Feb. 6 gyroscopic stabilization, Class 16 Tuesday, Feb. 9 stability of four wheel and two wheel vehicles Class 18 Friday, Feb. 12 Mech. Vibrations: Class 20 Monday, Feb.15 Degrees of freedom Class22 Thursday Feb.18 Numerical Class 24 Saturday, Feb.20 Forced vibration of single degree under harmonic excitation Class 26 Tuesday, Feb.23 Monday, Feb. 22 Unit-IV Class 25 Cont. Forced vibration of single degree under Vibration isolation. Whirling of shaft and critical harmonic excitation speed. Thursday, Feb.25 Class 28 Friday, Feb 26 Week 8 Class 27 Unit test Balancing: introduction. Class 29 Saturday, Feb. 27 Introduction, static balance, dynamic balance, Week 9 Class 31 Wednesday, March 18 balancing of rotating masses Class 33 Friday, March20 balancing of single cylinder engine Class 30 Monday, March 17 balancing of rotating masses Class 32 Thursday, March 19 graphical and analytical methods, balancing of reciprocating masses. Class 34 Monday, March23 balancing of multi cylinder inline engines.
Tuesday, March 24 Week 10 Class 35 Numerical Class 37 Thursday, March26 Introduction, types of governors Class 39 Monday, March 30 Gravity controlled and spring centrifugal governors Class 41 Wednesday,April 1 hunting of centrifugal governors, Class 36 Wednesday, March 2 Unit test 2 Class 38 Friday, March 27 characteristics of centrifugal governors Class 40 Tuesday,March 31 controlled Gravity controlled and spring controlled centrifugal governors Class 42 Friday, April 3 inertia governors Class 43 Monday,April 6 Effort and Power of governor, Class 44 Tuesday,April 7 Controlling force diagrams for Porter governor Class 45 Wednesday April 8 And spring controlled governors. Class 46 Thursday April 9 Numerical Class 47 Friday, April 10 Brakes and dynamometers: Class 49 Tuesday, April 14 and types of lubrication, Class 51 Thursday,April 16 effect of braking on rear Class 53 Monday,April 20 dynamometers, Class 55 Wednesday,April 22 torsion dynamometer, Class 48 Monday,April 13 Introduction, Law of friction Class 50 Wednesday, April 15 types of brakes, Class 52 Friday,April 17 and front wheels of a four wheeler Class 54 Tuesday,April 21 belt transmission dynamometer, Class 56 Thursday, April 23 hydraulic dynamometer Class 57 Friday,April 24 Numerical Details are found in the following sections: General Information, Class Schedule, and Project Schedule. GENERAL INFORMATION Teaching Staff: MD GULFARAZ ALAM Assist Prof, JIT ME, gulfaraz1986@gmail.com Course Web Site: Class Meetings: JIT Room 205 GOALS: The main goal is to contribute to the further development of the Science and Technology of dynamics of machines, which is of fundamental importance for the future Dimensional and integrate resources. Usually required to consider physical, human and financial resources at high efficiency and low cost, yet considering the possibility of continuous further improvement; Make proper use of math and statistics to model production systems during decision making process;
Design, implement and refine products, services, processes and systems taking in consideration that constraints and particularities of the related communities; Course Objectives: To understand the method of static force analysis and dynamic force analysis of Mechanisms To study the undesirable effects of unbalance in rotors and engines. To understand the concept of vibratory systems and their analysis To understand the principles of governors and gyroscopes. Classes and Topics Class 1 Introduction Monday, January 18 This subject is a continuation of statics and dynamics, which is taken by students in their freshman or sophomore years. In kinematics and dynamics of machines and mechanisms, however, the emphasis shifts from studying general concepts with illustrative examples to developing methods and performing analyses of real designs. This shift in emphasis is important, since it entails dealing with complex objects and utilizing different tools to analyze these objects Class 2 Class 2 Tuesday, January 19 Importance of dynamics of machine The design process starts with meeting the functional requirements of the product. The basic one in this case is the proper opening, dwelling, and closing of the valve as a function of time. To achieve this objective, a corresponding cam profile producing the needed follower motion should be found. The rocker arm, being a lever, serves as a displacement amplifier/reducer. The timing of opening, dwelling, and closing is controlled by the speed of the camshaft. The function of the spring is to keep the roller always in contact with the cam. Class 3 Thursday, January 22 Dynamics of rigid link in plane motion, Reduced delivery times Reduced set-up costs Reduced set-up times Reduced transportation costs Reduced investment in stock Reduction in batch sizes Improved quality Improved reliability Technological In order to understand a firm s technological competitiveness, a periodic technology assessment needs to be performed to chart the deterio-ration of technology and to benchmark a firm srelative position against a competitor. Class 4 Wednesday, January 20 Force analysis: Static force analysis of A force is characterized by its magnitude and direction, and thus is a vector. In an (x, y)-plane the force vector, F, can be represented in different forms F = [Fx, Fy] = F [cosα, sinα]t = F (i cosα + j sinα) where Fx, Fy are the x- and y-components of the vector (Figure 3.1), α indicates force direction (positive α is measured counterclockwise), and i and j are the unit vectors directed along the x- and yaxis, correspondingly. A moment of the force F with respect to a point A is a vector found as a crossproduct of two vectors: M = ra F Class 5, Thursday, January 22 Dynamics of rigid link in plane motion, It consists of four rigid bodies (called bars or links), each attached to two others by single joints or pivots to form closed loop. Four-bars are simple mechanisms common in mechanical engineering
machine design and fall under the study of kinematics. Dynamic Analysis of Reciprocating engines. Inertia force and torque analysis by neglecting weight of connecting rod. Velocity and acceleration of piston. Angular velocity and Angular acceleration of connecting rod. Force and Torque Analysis in reciprocating engine neglecting the weight of connecting rod. Equivalent Dynamical System Determination of two masses of equivalent dynamical system. Class 6 Monday, January 25 moment on crankshaft due to force on piston, Class 7 Thursday, January 28 Turning moment diagrams for single cylinder double acting steam engine. The turning moment diagram is graphical representation of the turning moment or crank effort for various positions of crank.
Class 8 Friday 29 Four stroke IC engine and multi-cylinder engines, Class 9 Saturday January 30 Fluctuation of speed of Flywheel. The difference in the kinetic energies at the point is called the maximum fluctuation of energy.
Class 10 Monday Feb. 1 Turning moment diagrams for single cylinder Class 11 Tuesday, Feb. 2 Gyroscope: introduction. A gyroscope is a device for measuring or maintaining orientation, based on the principles of conservation of angular momentum. A mechanical gyroscope is essentially a spinning wheel or disk whose axle is free to take any orientation. This orientation changes much less in response to a given external torque than it would without the large angular momentum associated with the gyroscope's high rate of spin. Since external torque is minimized by mounting the device in gimbals, its orientation remains nearly fixed, regardless of any motion of the platform on which it is mounted. Gyroscopes based on other operating principles also Exit, such as the electronic, microchip-packaged MEMS gyroscope devices found in consumer electronic devices, solid state ring lasers, fiber optic gyroscopes and the extremely sensitive quantum gyroscope. Applications of gyroscopes include navigation (INS) when magnetic compasses do not work (as in the Hubble telescope) or are not precise enough (as in ICBMs) or for the stabilization of flying vehicles like radio-controlled helicopters or UAVs. Due to higher precision, gyroscopes are also used to maintain direction in tunnel mining.
Class 12 Thursday Feb. 4 Space motion of rigid bodies, Diagram of a gyro wheel. Reaction arrows about the output axis (blue) correspond to forces applied about the input axis (green), and vice versa. Within mechanical systems or devices, a conventional gyroscope is a mechanism comprising a rotor journal led to spin about one axis, the journals of the rotor being mounted in an inner gimbals or ring, the inner gimbals is journal led for oscillation in an outer gimbals which is journal led in another gimbals. So basically there are three gimbals. Class 13 Friday, Feb. 5 Angular momentum, gyroscopic couples, Class 14 Saturday, Feb. 6 Gyroscopic stabilization, The behavior of a gyroscope can be most easily appreciated by consideration of the front wheel of a bicycle. If the wheel is leaned away from the vertical so that the top of the wheel moves to the left, the forward rim of the wheel also turns to the left. In other words, rotation on one axis of the turning wheel produces rotation of the third axis. Class 15 Monday, Feb. 8 Ship stabilization, Steering is the turning of a complete ship in a curve towards left or right, while it moves forward, considers the ship taking a left turn, and rotor rotates in the clockwise direction when viewed from the stern, as shown in Fig. below. The effect of gyroscopic couple on a naval ship during steering taking left or right turn may be obtained in the similar way as for an aero plane as discussed in Art. Class 16 Tuesday, Feb. 9 Stability of four wheel and two wheel vehicles. Effect of Gyroscopic couple on a 4-wheel drive:
Class 17 Thursday, Feb.11 Continue. Moving on curved path.
Class 18 Friday, Feb. 12 Mech. Vibrations: When a system is subjected to an initial disturbance and then left free to vibrate on its own, the resulting vibrations are referred to as free vibrations.free vibration occurs when a mechanical system is set off with an initial input and then allowed to vibrate freely. Examples of this type of vibration are pulling a child back on a swing and then letting go or hitting a tuning fork and letting it ring. The mechanical system will then vibrate at one or more of its "natural frequencies" and damp down to zero. Class 19 Saturday, Feb.13 Mech. Vibrations: Basic elements of vibration system Mass or Inertia Springiness or Restoring element Dissipative element (often called damper) External excitation Causes of vibration: Unbalance: This is basically in reference to the rotating bodies. The une the unbalance. A good example of unbalance related vibration would be the vibrating alert in our mobile weight is rotated by a motor causing the vibration which makes the mobile phone to vibrate. occurring in your front loaded washing machines that tend to vibrate during the spinning mode. Misalignment: This is another major cause of vibration particularly in machines that are drive rotating shaft that is bent also produces the vibrating effect since it losses it rotation capability machine always tend to produce vibration, mainly due to their meshing. Though this may be ma fast and fails quickly, but before this is noticed it damages the remaining components in the mac gone wrong with the other components leading to the bearing failure. Controlled to some extent, ease. Bearings: Last but not the least, here is a major contributor for vibration. In majority of
propagates to the rest of the members of the Class 20 Monday, Feb.15 Degrees of freedom The minimum number of independent coordinates required to specify the motion of a system at any instant is known as D.O.F of the system. Single degree of freedom system Two degree of freedom system Class 21 Tuesday, Feb.16 Longitudinal Vibration When the particles of the shaft or disc moves parallel to the axis of the shaft, then the vibrations known as longitudinal vibrations. Class22 Thursday Feb.18 Numerical
Solve the numerical relative to above theory. Class 23 Friday, Feb.19 Single degree free and damped vibration. It is the resistance to the motion of a vibrating body. The vibrations associated with this resistance are known as damped vibrations. Types of damping: (1)Viscous damping (2) Dry friction or coulomb damping (3) Solid damping or structural damping (4) Slip or interfacial damping. Class 24 Saturday, Feb.20 Forced vibration of single degree under harmonic Forced vibration is when an alternating force or motion is applied to a mechanical system. Examples of this type of vibration include a shaking washing machine due to an imbalance, transportation vibration (caused by truck engine, springs, road, etc), or the vibration of a building during an earthquake. In forced vibration the frequency of the vibration is the frequency of the force or motion applied, with order of magnitude being dependent on the actual mechanical system. Steady State Response due to Harmonic Oscillation Consider a spring-mass-damper system as shown in figure. The equation of motion of this system subjected to a harmonic force can be given by
Class 25 Monday, Feb. 22 Cont Forced vibration of single degree under harmonic excitation. Forced vibration with damping In this section we will see the behavior of the spring mass damper model when we add a harmonic force in the form below. A force of this type could, for example, be generated by a rotating imbalance. If we again sum the forces on the mass we get the following ordinary differential equation: The steady state solution of this problem can be written as: The result states that the mass will oscillate at the same frequency, f, of the applied force, but with a phase shift φ. Class 26 Tuesday, Feb.23 Vibration isolation. Whirling of shaft and critical The speed, at which the shaft runs so that the additional deflection of the shaft from the axis of rotation becomes infinite, is known as critical or whirling speed. No shaft can ever be perfectly straight or perfectly balanced. When an element of mass is a distance from the axis of rotation, centrifugal force, will tend to pull the mass outward. The elastic properties of the shaft will act to restore the straightness. If the frequency of rotation is equal to one of the resonant frequencies of the shaft, whirling will occur. In order to save the machine from failure, operation at such whirling speeds must be avoided. Class 27 Thursday, Feb.25 Unit test
Class 28 Friday, Feb 26 Balancing:-introduction. Balancing is the process of eliminating or at least reducing the ground forces and/or moments. It is achieved by changing the location of the mass centers of links. Balancing of rotating parts is a well known problem. A rotating body with fixed rotation axis can be fully balanced i.e. all the inertia forces and moments. For mechanism containing links rotating about axis which are not fixed, force balancing is possible, moment balancing by itself may be possible, but both not possible. We generally try to do force balancing. A fully force balance is possible, but any action in force balancing severe the moment balancing. Class 29 Saturday, Feb. 27, Introduction, static balance, dynamic balance. Balancing of rotating masses The process of providing the second mass in order to counteract the effect of the centrifugal force of the first mass is called balancing of rotating masses. Static balancing: The net dynamic force acting on the shaft is equal to zero. This requires that the line of action of three centrifugal forces must be the same. In other words, the centre of the masses of the system must lie on the axis of the rotation. This is the condition for static balancing. Dynamic balancing: The net couple due to dynamic forces acting on the shaft is equal to zero. The algebraic sum of the moments about any point in the plane must be zero. Class 30 Wednesday, March 18, balancing of rotating masses Balancing of a single rotating mass by single mass rotating in the same plane. n the different plane.
Class 31 Wednesday, March 18, balancing of rotating masses
Class 32 Thursday, March 19, graphical and analytical methods, balancing of reciprocating masses.
Class 33 Friday, March20 Balancing of single cylinder engine A single cylinder engine produces three main vibrations. In describing them we will assume that the cylinder is vertical. Firstly, in an engine with no balancing counterweights, there would be an enormous vibration produced by the change in momentum of the piston, gudgeon pin, connecting rod and crankshaft once every revolution. Nearly all single-cylinder crankshafts incorporate balancing weights to reduce this. While these weights can balance the crankshaft completely, they cannot completely balance the motion of the piston, for two reasons. The first reason is that the balancing weights have horizontal motion as well as vertical motion, so balancing the purely vertical motion of the piston by a crankshaft weight adds a horizontal vibration. The second reason is that, considering now the vertical motion only, the smaller piston end of the connecting rod (little end) is closer to the larger crankshaft end (big end) of the connecting rod in mid-stroke than it is at the top or bottom of the stroke, because of the connecting rod's angle. So during the 180 rotation from mid-stroke through top-dead-center and back to mid-stroke the minor contribution to the piston's up/down movement from the connecting rod's change of angle has the same direction as the major contribution to the piston's up/down movement from the up/down movement of the crank pin.
Class 34 Monday, March23, balancing of multi cylinder inline engines. In multi-cylinder engines the mutual counteractions of the various components in the Crank shaft assembly are one of the essential factors determining the selection of the Crank shafts configuration and with it the design of the engine itself. The inertial forces are Balanced if the common centre of gravity for all moving crankshaft-assembly components lies at the crankshaft's midpoint, i.e. if the crankshaft is symmetrical (as viewed from the front). The crankshaft's symmetry level can be defined using geometrical representations of 1st- and 2nd-order forces (star diagrams). The 2nd order star diagram for the four-cylinder in-line engine is asymmetrical, meaning that this order is characterized by substantial free inertial Forces. Class 35 Tuesday, March 24 Numerical. Class 36 Wednesday, March 2 Unit test 2
Class 37 Thursday, March26 Introduction, types of governors. A centrifugal governor is a specific type of governor that controls the speed of an engine by regulating the amount of fuel (or working fluid) admitted, so as to maintain a near constant speed whatever the load or fuel supply conditions. It uses the principle of proportional control. It is most obviously seen on steam engines where it regulates the admission of steam into the cylinder(s). It is also found on internal combustion engines and variously fuelled turbines, and in some modern striking clocks. Class 38 Friday, March 27 Characteristics of centrifugal governors Classification of governors: Governors are classified based upon two different principles. These are: 1. Centrifugal governors 2. Inertia governors Height of governor It is the vertical distance between the centre of the governor halls and the point of intersection between the upper arms on the axis of spindle is known as governor height. It is generally denoted by h. Sleeve lift The vertical distance the sleeve travels due to change in the equilibrium Speed is called the sleeve lift. The vertical downward travel may be termed as Negative lift Isochronisms This is an extreme case of sensitiveness. When the equilibrium speed is constant for all radii of rotation of the balls within the working range, the governor is said to be in isochronisms. This means that the difference between the maximum and minimum equilibrium speeds is zero and the sensitiveness shall be infinite. Class 39 Monday, March 30 Gravity controlled and spring controlled centrifugal governors
Class 40 Tuesday, March 31, gravity controlled and spring controlled centrifugal governors
Class 41 Wednesday, April 1, hunting of centrifugal governors. The phenomenon of continuous fluctuation of the engine speed above and below the mean speed is termed as hunting. This occurs in over- sensitive or isochronous governors. Suppose an isochronous governor is fitted to an engine running at a steady load. With a slight increase of load, the speed will fall and the sleeve will immediately fall to its lowest position. This shall open the control valve wide and excess supply of energy will be given, with the result that the speed will rapidly increase and the sleeve will rise to its higher position. As a result of this movement of the sleeve, the control valve will be cut off; the supply to the engine and the speed will again fall, the cycle being repeated indefinitely. Such a governor would admit either more or less amount of fuel and so effect would be that the engine would hunt. Class 42 Friday, April 3
Inertia governors Class 43 Monday, April 6 Effort and Power of governor, Class 44 Tuesday, April 7 Controlling force diagrams for Porter governor Class 45 Wednesday April 8 And spring controlled governors.
Class 46 Thursday April 9 Numerical Class 47 Friday, April 10 Brakes and dynamometers: A brake is a device by means of which artificial frictional resistance is applied to a moving machine member, in order to retard or stop the motion of a machine. In the process of performing this function, the brake absorbs either kinetic energy of the moving member or potential energy given up by objects being lowered by hoists, elevators etc. The energy absorbed by brakes is dissipated in the form of heat. This heat is dissipated in the surrounding air (or water which is circulated through the passages in the brake drum) so that excessive heating of the brake lining does not take place. The design or capacity of a brake depends upon thefollowing factors : Class 48 Monday,April 13 Introduction, Law of friction In order to determine the coefficient of friction for well lubricated full journal bearings, the following empirical relation established by McKee based on the experimental data, may be used. Class 49 Tuesday, April 14 And types of lubrication,
The lubricants are used in bearings to reduce friction between the rubbing surfaces and to carry away the heat generated by friction. It also protects the bearing against corrosion. All lubricants are classified into the following three groups : 1. Liquid, 2. Semi-liquid and 3. Solid. Class 50 Wednesday, April 15 types of brakes, The brakes, according to the means used for transforming the energy by the braking element, are classified as : 1. Hydraulic brakes e.g. pumps or hydrodynamic brake and fluid agitator, 2. Electric brakes e.g. generators and eddy current brakes, and 3. Mechanical brakes. Class 51 Friday,April 17 and front wheels of a four wheeler The energy absorbed by the brake and transformed into heat must be dissipated to the surrounding air in order to avoid excessive temperature rise of the brake lining. The *temperature rise depends upon the mass of the brake drum, the braking time and the heat dissipation capacity of the brake. The highest permissible temperatures recommended for different brake lining materials are given as follows 1. For leather, fiber and wood facing = 65 70 C 2. For asbestos and metal surfaces that are slightly lubricated = 90 105 C 3. For automobile brakes with asbestos block lining = 180 225 C Class 52 Friday, April 17 Band & shoe brake
Class 53 Monday, April 20 Dynamometers, A dynamometer is an instrument for measuring the power exerted by a source or the amount of power consumed by a load. Absorption type: This type of dynamometer measures torque (and power) by dissipating mechanical energy and are suitable for power measurement of engines (such as internal combustion and gas turbine engines) and electrical motors (ac and dc motors). Driving type: This type of dynamometer measures torque (and power) and supply energy to operate the device being tested. Class 54 Tuesday, April 21 Belt transmission dynamometer,
Water-brake dynamometer is similar to a Prony brake but employs fluid friction (rather than dry friction) to dissipate energy. Class 55 Wednesday, April 22 Torsion dynamometer, Torsion dynamometers in combination with inertia less indicators are preferable to those of the pendulum type for use in machines intended for high-speed loading and deformations. Pendulum dynamometers are preferably used in the best machines for testing materials with static loads. The existing designs of torsion dynamometers have as yet no substantial advantages as compared with those of the pendulum type. Class 56Thursday, April 23 Hydraulic dynamometer The hydraulic brake system consists of a hydraulic pump (usually a gear-type pump), a fluid reservoir, and piping between the two parts. Inserted in the piping is an adjustable valve, and between the pump and the valve is a gauge or other means of measuring hydraulic pressure. In simplest terms, the engine is brought up to the desired RPM and the valve is incrementally closed. As the pumps outlet is restricted, the load increases and the throttle is simply opened until at the desired throttle opening. Unlike most other systems, power is calculated by factoring flow volume (calculated from pump design specifications), hydraulic pressure, and RPM. Brake HP, whether figured with pressure, volume, and RPM, or with a different load cell-type brake dyno, should produce essentially identical power figures. Hydraulic dynos are renowned for having the quickest load change ability, just slightly surpassing eddy current absorbers. The downside is that they require large quantities of hot oil under high pressure and an oil reservoir. Class 57 Friday, April 24 Numerical..