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GATE SYLLABUS FOR MECHANICAL ENGINEERING

ENGINEERING MATHEMATICS
Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigen vectors.
Calculus: Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.
Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy’s and Euler’s equations, Initial and boundary value problems, Laplace transforms, Solutions of one dimensional heat and wave equations and Laplace equation.
Complex variables: Analytic functions, Cauchy’s integral theorem, Taylor and Laurent series. Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions.
Numerical Methods: Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson’s rule, single and multi-step methods fordifferential equations.
APPLIED MECHANICS AND DESIGN
Engineering Mechanics: Free body diagrams and equilibrium; trusses and frames; virtual work; kinematics and dynamics of particles and of rigid bodies in plane motion, including impulse and momentum (linear and angular) and energy formulations; impact.
Strength of Materials: Stress and strain, stress-strain relationship and elastic constants, Mohr’s circle for plane stress and plane strain, thin cylinders; shear force and bending moment diagrams; bending and shear stresses; deflection of beams; torsion of circular shafts; Euler’s theory of columns; strain energy methods; thermal stresses.
Theory of Machines: Displacement, velocity and acceleration analysis of plane mechanisms; dynamic analysis of slider-crank mechanism; gear trains; flywheels.
Vibrations: Free and forced vibration of single degree of freedom systems; effect of damping; vibration isolation; resonance, critical speeds of shafts.
Design: Design for static and dynamic loading; failure theories; fatigue strength and the S-N diagram; principles of the design of machine elements such as bolted, riveted and welded joints, shafts, spur gears, rolling and sliding contact bearings, brakes and clutches.
FLUID MECHANICS AND THERMAL SCIENCES
Fluid Mechanics: Fluid properties; fluid statics, manometry, buoyancy; control-volume analysis of mass, momentum and energy; fluid acceleration;differential equations of continuity and momentum; Bernoulli’s equation; viscous flow of incompressible fluids; boundary layer; elementary turbulent flow; flow through pipes, head losses in pipes, bends etc.
Heat-Transfer: Modes of heat transfer; one dimensional heat conduction, resistance concept, electrical analogy, unsteady heat conduction, fins; dimensionless parameters in free and forced convective heat transfer, various correlations for heat transfer in flow over flat plates and through pipes; thermal boundary layer; effect of turbulence; radiative heat transfer, black and grey surfaces, shape factors, network analysis; heat exchanger performance, LMTD and NTU methods.
Thermodynamics: Zeroth, First and Second laws of thermodynamics; thermodynamic system and processes; Carnot cycle. irreversibility and availability; behaviour of ideal and real gases, properties of pure substances, calculation of work and heat in ideal processes; analysis of thermodynamic cycles related to energy conversion.
Applications: Power Engineering: Steam Tables, Rankine, Brayton cycles with regeneration and reheat. I.C. Engines: air-standard Otto, Diesel cycles. Refrigeration and air-conditioning: Vapour refrigeration cycle, heat pumps, gas refrigeration, Reverse Brayton cycle; moist air: psychrometric chart, basic psychrometric processes. Turbomachinery: Pelton-wheel, Francis and Kaplan turbines — impulse and reaction principles, velocity diagrams.
MANUFACTURING AND INDUSTRIAL ENGINEERING
Engineering Materials: Structure and properties of engineering materials, heat treatment, stressstrain diagrams for engineering materials.
Metal Casting: Design of patterns, moulds and cores; solidification and cooling; riser and gating design, design considerations.
Forming: Plastic deformation and yield criteria; fundamentals of hot and cold working processes; load estimation for bulk (forging, rolling, extrusion, drawing) and sheet (shearing, deep drawing, bending) metal forming processes; principles of powder metallurgy.
Joining: Physics of welding, brazing and soldering; adhesive bonding; design considerations in welding.
Machining and Machine Tool Operations: Mechanics of machining, single and multi-point cutting tools, tool geometry and materials, tool life and wear; economics of machining; principles of non-traditional machining processes; principles of work holding, principles of design of jigs and fixtures
Metrology and Inspection: Limits, fits and tolerances; linear and angular measurements; comparators; gauge design; interferometry; form and finish measurement; alignment and testing methods; tolerance analysis in manufacturing and assembly.
Computer Integrated Manufacturing: Basic concepts of CAD/CAM and their integration tools.
Production Planning and Control: Forecasting models, aggregate production planning, scheduling, materials requirement planning.
Inventory Control: Deterministic and probabilistic models; safety stock inventory control systems.
Operations Research: Linear programming, simplex and duplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM.

Aerospace Flywheel Development

1) INTRODUCTION

Presently, energy storage on the Space Station and satellites is accomplished using chemical batteries; most commonly nickel hydrogen or nickel cadmium. A flywheel energy storage system is an alternative technology that is being considered for future space missions. Flywheels offer the advantage of a longer lifetime, higher efficiency and a greater depth of discharge than batteries. A flywheel energy storage system is being considered as a replacement for the traditional electrochemical battery system in spacecraft electrical power systems. The flywheel system is expected to improve both the depth of discharge and working life by a factor of 3 compared with its battery counterpart. Although flywheels have always been used in spacecraft navigation and guidance systems, their use for energy storage is new. However, the two functions can easily be combined into a single system. Several advanced technologies must be demonstrated for the flywheel energy storage system to be a viable option for future space missions. These include high strength composite materials, highly efficient high speed motor operation and control, and magnetic bearing levitation.2) COMPONENTS OF FLYWHEEL SYSTEM

The main components of the flywheel energy storage system are the composite rotor, motor/generator, magnetic bearings, touchdown bearings, and vacuum housing. The flywheel system is designed for 364 watt-hours of energy storage at 60,000 rpm and uses active magnetic bearings to provide a long-life, low-loss suspension of the rotating mass. The upper bearing of the unit is a combination magnetic bearing, providing suspension axially as well as radically. The lower magnetic bearing suspends the shaft in the radial direction only. At each end of the shaft there is also a touchdown bearing. This provides a back up bearing system should the magnetic bearings fail during testing.

The motor/generator unit is located at the lower end of the shaft. It consists of a two-pole rotor piece with surface mounted samarium cobalt magnets and a carbon fiber retaining wrap. On the stator side, there are three phase sinusoidally distributed windings in twelve slots. A water jacket around the stator provides cooling. Field orientation and a combination of mechanical sensor less techniques are used to control the motor from zero and low speed up to full speed operation. The self-sensing technique is used at zero and low speeds to start the machine, then the control is switched to a back-EMF based sensor less technique for the normal higher speed operating range of the machine.

A typical system consists of rotor suspended by bearings inside a vacuum chamber to reduce friction, connected to a combination electric motor/electric generator. On larger systems, the bearings are magnetic. The rotors are generally made of steel on smaller systems but large systems use high-tensile-strength fibers (such as carbon fibers) embedded in epoxy resins, or some other high-strength composite material. Energy is stored by using an electric motor to increase the speed of the spinning flywheel. The system releases its energy by using the momentum of the flywheel to power the motor/generator.

3) FLYWHEEL CONTROL

There are three modes of operation for the flywheel in a spacecraft power system

1) Charge

2) Charge reduction

3) Discharge

In charge mode, the solar array produces enough current to charge the flywheel at its set point and to provide the required load current. The solar array electronics regulate the DC bus voltage during charge mode.

In charge reduction mode, the solar array continues to provide load current but it can not provide enough current to charge the flywheel at its set point. When this occurs, the DC bus voltage regulation function is transferred to the flywheel system.

In discharge mode, the flywheel system provides the entire load current and regulates the DC bus voltage.

3.1) CHARGE, CHARGE REDUCTION AND DISCHARGE CONTROL

In charge mode, the flywheel charges at a constant power, constant DC current rate using the excess current from the solar array. The charge control algorithm regulates the acceleration of the flywheel motor so that the DC current is maintained at the commanded set point. There are two components to the controller: the proportional-integral (PI) and the feed-forward (FF). The feed-forward portion uses the DC charging current command and converts it into a motor current command. The measured DC bus voltage and the estimated rotor speed from the back EMF estimation algorithm. The PI portion makes up for any inaccuracies in the relationship and guarantees zero steady state error. Thus fast, accurate performance is achieved with relatively low gains.

In charge reduction and discharge modes, the flywheel motor must decelerate at the appropriate rate to maintain the DC bus voltage at the commanded value while supplying the necessary current to the loads Again, there are two components to the controller: the PI portion and a disturbance decoupling portion (DD). In the decoupling portion, the DC flywheel current is measured and used as an early indicator to the controller whether there has been an increase or decrease in load. If there is a sudden increase in load, the capacitor will initially maintain the bus voltage and there will be an increase in the DC current, Flywheel, to supply the new load. This increase in Flywheel is measured and used to calculate the corresponding motor current. Thus the motor responds by decelerating more quickly, even before a drop in the DC bus voltage causes the system is in charge mode (current regulation) when the solar array provides enough current to meet both the load demands and the charging current to the flywheel system. Otherwise, the system is in charge reduction or discharge mode which means the flywheel system is regulating the DC voltage bus.

The transition from current regulation to voltage regulation is accomplished in the following manner. The solar array regulates the bus voltage to a set point value higher than the flywheel regulation set point as long as the solar array current is sufficient to provide both the load and the charging current. Once the solar array current begins to drop off, the DC bus voltage begins to fall and the flywheel current, Flywheel, also drops. This transition is detected in the controller by comparing the difference between the actual DC bus voltage and the flywheel set point voltage to the "voltage transition constant", VTC.Once this difference is less than the VTC, the integrator in the PI portion of the controller is reset. This reduces the command at point 2 to a value slightly larger than Flywheel. This value is then compared to the charge current set point. If it is less than, which it will be if the solar array is not producing enough current, then the system transitions into charge reduction mode where the DC bus voltage is regulated by the flywheel system. Similarly, as the system moves from eclipse into sunlight, the solar array will produce more current. When the array produces enough current to meet the load demand, the command at point 2 in the controller will become positive. When it exceeds the charge current set point, the integrator in the current regulator portion of the controller is reset and the system transitions back into charge mode where the flywheel system regulates the current into the flywheel and the solar array system regulates the DC bus voltage.

The three modes of operation: charge, charge reduction and discharge, were defined based on a battery energy storage system. Because the flywheel system is intended to replace batteries, these modes were duplicated in the flywheel system control. However, the flywheel energy storage system is capable of regulating the DC bus voltage both when charging and discharging, obviating the need for multiple modes and the transition between them. Designing the flywheel system control to perform this regulation at all times would result in an overall simpler control strategy, even when considering the necessary provisions to prevent over-speed or over current operation. This is an area for future study.

4) AEROSPACE FLYWHEEL CHALLANGES

The primary factor preventing the application of flywheels to long-term energy storage is loss in the bearings. Any mechanical bearing with contact between the stationary and rotating parts will have enough loss to render the system uneconomical one solution to the problem is to use a non-contact active magnetic bearing that employs conventional electromagnets. The rotational loss of such a bearing is 1-10% that of a mechanical bearing under the same operating conditions. The problem, however, is that the bearing itself consumes power, which is dissipated as heat in the copper electromagnets, and the bearing and cooling system power consumption must be included in the calculation of the overall system efficiency. A reasonable magnetic bearing consumes a few watts for each kilogram of flywheel weight, depending on the structure of the bearing and the control system, and this loss is sufficient to make a system using copper electromagnets uneconomical. Superconducting magnetic bearings, on the other hand, have demonstrated losses of 10^-2 to 10^-3 watts per kg for a 2,000 rpm rotor. This translates to an overall one-day, "round-trip" system efficiency of 84%, which is acceptable.

5) FLYWHEEL ENERGY STORAGE (FES)

It works by accelerating a rotor to a very high speed and maintaining the energy in the system as inertial energy. Commercially available FES systems are used for small uninterruptible power systems. The rotors normally operate at 4000 RPM or less and are made of metal. Advanced flywheels are made of high strength carbon-composite filaments that spin at speeds from 20,000-100,000 RPM in a vacuum enclosure. Magnetic bearings are necessary as speeds increase to reduce the friction present when using conventional mechanical bearings. Quick charging is done in less than 15 minutes. Long lifetimes of most flywheels, plus high energy densities (~ 130 Wh/kg) and large maximum power outputs are positive attributes. The energy efficiency (ratio of energy out per energy in) of flywheels can be as high as 90%. Since FES can store and release power quickly, they have found a niche providing pulsed power.

6) ADVANTAGES AND DISADVANTAGES

Flywheels are not affected by temperature changes as are chemical batteries, nor do they suffer from memory effect. Moreover, they are not as limited in the amount of energy they can hold. They are also less potentially damaging to the environment, being made of largely inert or benign materials. Another advantage of flywheels is that by a simple measurement of the rotation speed it is possible to know the exact amount of energy stored. However, use of flywheel accumulators is currently hampered by the danger of explosive shattering of the massive wheel due to overload.

One of the primary limits to flywheel design is the tensile strength of the material used for the rotor. Generally speaking, the stronger the disc, the faster it may be spun, and the more energy the system can store. When the tensile strength of a flywheel is exceeded the flywheel will shatter, releasing all of its stored energy at once; this is commonly referred to as "flywheel explosion" since wheel fragments can reach kinetic energy comparable to that of a bullet. Consequently, traditional flywheel systems require strong containment vessels as a safety precaution, which increases the total mass of the device. Fortunately, composite materials tend to disintegrate quickly once broken, and so instead of large chunks of high-velocity shrapnel one simply gets a containment vessel filled with red-hot sand (still, many customers of modern flywheel power storage systems prefer to have them embedded in the ground to halt any material that might escape the containment vessel). Gulia's tape flywheels did not require a heavy container and reportedly could be rewound and reused after a tape fracture.

When used in vehicles, flywheels also act as gyroscopes, since their angular momentum is typically of a similar order of magnitude as the forces acting on the moving vehicle. This property may be detrimental to the vehicle's handling characteristics while turning. On the other hand, this property could be utilized to improve stability in curves. Two externally joined flywheels spinning synchronously in opposite directions would have a total angular momentum of zero and no gyroscopic effect.

7) APPLICATIONS

In the 1950s flywheel-powered buses, known as gyro buses, were used in Yverdon, Switzerland, and there is ongoing research to make flywheel systems that are smaller, lighter, cheaper, and have a greater capacity. It is hoped that flywheel systems can replace conventional chemical batteries for mobile applications, such as for electric vehicles. Proposed flywheel systems would eliminate many of the disadvantages of existing battery power systems, such as low capacity, long charge times, heavy weight, and short usable lifetimes. Flywheel systems have also been used experimentally in small electric locomotives for shunting or switching.

8) CONCLUSION AND FUTURE WORK

This paper has presented a new algorithm for regulating the charge and discharge modes of a flywheel energy storage system using a sensor less field orientation control algorithm to provide the inner loop torque control. The algorithm mimics the operational modes presently found in battery systems and would allow the flywheel system to replace batteries on future spacecraft. Experimental and simulation results show the successful control of the flywheel system permanent magnet motor in all modes of operation. Additionally, transition between modes and DC bus voltage regulation during step changes in load was also demonstrated. A future application of flywheel technology is to use flywheels to combine the energy storage and the attitude control functions on a spacecraft. A minimum of four flywheels would be needed to provide three axes of attitude control plus power during eclipse