Rotary and reciprocating compressors are both components of gas transfer systems. They both have the same purpose–to bring a gas into the system, inhale exhaust, then repeat the process. They both do this by changing the pressure at certain points in order to force gas in and exhaust out.
One key difference is that reciprocating compressors use pistons while rotary compressors do not. A reciprocating compressor has a piston move downwards, reducing pressure in its cylinder by creating a vacuum. This difference in pressure forces the cylinder door to open and bring gas in. When the cylinder goes back up, it increases pressure, thus forcing the gas back out. The up-and-down motion is called a reciprocating motion, hence the name.
Rotary compressors, on the other hand, use rollers. They sit slightly off-center in a shaft, with one side always touching the wall. As they move at high speeds, they accomplish the same goal as the reciprocating compressors–one part of the shaft is always at a different pressure than the other, so gas can come in at the low pressure point and exit at the high pressure point.
Advantages and Disadvantages
Reciprocating compressors are marginally more efficient than rotary compressors, generally being able to compress the same amount of gas with between 5 and 10 percent less energy input. However, since this difference is so marginal, most small-to-medium level users are best off using a rotary compressor. Reciprocating compressors are more expensive and require more maintenance, so it is often not worth the extra cost and headache for such a small difference in efficiency.
Large users, however, are generally best-served by reciprocating compressors. These are users for whom 5 percent represents a substantial figure, often substantial enough to justify the added expense.
Comparison Between Reciprocating and Rotary Compressors
Comparison between Reciprocating and Rotary Compressors can be done in aspects like pressure ratio, handled volume, speed of compressor, vibrational problem, size, air supply, purity of compressed air, compression efficiency, maintenance, mechanical efficiency, lubrication, initial cost, flexibility and suitability.
|S.no || |
|1 ||Pressure Ratio ||Discharge Pressure of air is high. The pressure ratio per stage will be in the order of 4 to 7. ||Discharge pressure of air is low. The pressure ratio per stage will be in the order of 3 to 5. |
|2 ||Handled Volume ||Quantity of air handled is low and is limited to 50m3/s. ||Large measure of air handled can be handled and it is about 500 m3/s. |
|3 ||Speed of Compressor ||Low speed of compressor. ||High speed of compressor. |
|4 ||Vibrational Problem ||Due to reciprocating section, greater vibrational problem, the parts of machine are poorly balanced. ||Rotary parts of machine, thus it has less vibrational problems. The machine parts are fairly balanced. |
|5 ||Size of compressor ||Size of Compressor is bulky for given discharge volume. ||Compressor size is small for given discharge volume. |
|6 ||Air supply ||Air supply is intermittent. ||Air supply is steady and continuous.. |
|7 ||Purity of compressed air ||Air delivered from the compressor is dirty, since it comes in contact with lubricating oil and cylinder surface. ||Air delivered from the compressor is clean and free from dirt. |
|8 ||Compressed efficiency ||Higher with pressure ratio more than 2. ||Higher with compression ratio less than 2. |
|9 ||Maintanence ||Higher due to reciprocating engine. ||Lower due to less sliding parts.. |
|10 ||Mechanical Efficiency ||Lower due to several sliding parts.. ||Higher due to less sliding parts. |
|11 ||Lubrication ||Complicated lubrication system. ||Simple lubrication system. |
|12 ||Initial cost ||Higher. ||Lower. |
|13 ||Flexibility ||Greater flexibility in capacity and pressure range. ||No flexibility in capacity and pressure range. |
|14 ||Suitability ||For medium and high pressure ratio. |
For low and medium gas volume.
|For low and medium pressures. |
For large volumes.
The laws of thermodynamics dictate energy behavior, for example, how and why heat, which is a form of energy, transfers between different objects. The first law of thermodynamics is the law of conservation of energy and matter. In essence, energy can neither be created nor destroyed; it can however be transformed from one form to another. The second law states that isolated systems gravitate towards thermodynamic equilibrium, also known as a state of maximum entropy, or disorder; it also states that heat energy will flow from an area of low temperature to an area of high temperature. These laws are observed regularly every day.
Melting Ice Cube
Every day, ice needs to be maintained at a temperature below the freezing point of water to remain solid. On hot summer days, however, people often take out a tray of ice to cool beverages. In the process, they witness the first and second laws of thermodynamics. For example, someone might put an ice cube into a glass of warm lemonade and then forget to drink the beverage. An hour or two later, they will notice that the ice has melted but the temperature of the lemonade has cooled. This is because the total amount of heat in the system has remained the same, but has just gravitated towards equilibrium, where both the former ice cube (now water) and the lemonade are the same temperature. This is, of course, not a completely closed system. The lemonade will eventually become warm again, as heat from the environment is transferred to the glass and its contents.
Sweating in a Crowded Room
The human body obeys the laws of thermodynamics. Consider the experience of being in a small crowded room with lots of other people. In all likelihood, you’ll start to feel very warm and will start sweating. This is the process your body uses to cool itself off. Heat from your body is transferred to the sweat. As the sweat absorbs more and more heat, it evaporates from your body, becoming more disordered and transferring heat to the air, which heats up the air temperature of the room. Many sweating people in a crowded room, “closed system,” will quickly heat things up. This is both the first and second laws of thermodynamics in action: No heat is lost; it is merely transferred, and approaches equilibrium with maximum entropy.
Taking a Bath
Consider a situation where a person takes a very long bath. Immediately during and after filling up the bathtub, the water is very hot — as high as 120 degrees Fahrenheit. The person will then turn off the water and submerge his body into it. Initially, the water feels comfortably warm, because the water’s temperature is higher than the person’s body temperature. After some time, however, some heat from the water will have transferred to the individual, and the two temperatures will meet. After a bit more time has passed, because this is not a closed system, the bath water will cool as heat is lost to the atmosphere. The person will cool as well, but not as much, since his internal homeostatic mechanisms help keep his temperature adequately elevated.
Flipping a Light Switch
We rely on electricity to turn on our lights. Electricity is a form of energy; it is, however, a secondary source. A primary source of energy must be converted into electricity before we can flip on the lights. For example, water energy can be harnessed by building a dam to hold back the water of a large lake. If we slowly release water through a small opening in the dam, we can use the driving pressure of the water to turn a turbine. The work of the turbine can be used to generate electricity with the help of a generator. The electricity is sent to our homes via power lines. The electricity was not created out of nothing; it is the result of transforming water energy from the lake into another energy form.
Basic terms for Mechanical Engineering
List of basic terms for Mechanical Engineering
1. Torque or Turning Force
7. Specific Weight
8. Specific Volume
9. Specific Gravity
10. Specific Heat
13. Discharge of Fluid
14. Bernoulli’s Equation
15. Device for Fluid
16. Mach Number
17. Hydraulic Machine
18. Draft Tube
19. Thermodynamics Laws
- zeroth law
- First law
- second law
21. calorific value of fuel
22. Boiler/Steam Generator
24. Air Preheater
25. Boiler Draught
32. Rating of fuel-
33. Stoichiometric Mixture/ Stoichiometric Ratio
34. Heat Transfer
35. Thermal Conductivity
36. Heat Exchanger
38. 1 tonne Refrigeration
41. Gear Train
42. Gyroscopic Couple
43. Heat Treatment
45. Non-ferrous metal
52. Nuclear Fission
53. Nuclear Fussion
55. Machine Tool
56. Cutting Tool
Torque or Turning Force:
It is the total amount of force which is required to create acceleration on moving substance.
Two forces those acts on equally,parallely & oppositely on two separate points of same material.
It is the amount of moving effect which is gained for action of turning force.
It is the force that can prevent equal & opposite force. That means, it is the preventing force. If one force acts on outside of a material, then a reactive force automatically acts to protest that force. The amount of reactive force per unit area is called stress. e.g. Tensile Stress, Compressive Stress, Thermal Stress.
If a force acts on a substance, then in that case if the substance would deform. Then the amount of deformation per unit length of that substance is called strain.
It is one type of device which is being distorted under certain amount of load & also can also go to its original face after the removal of that load.
- To store energy.
- To absorb energy.
- To control motion of two elements.
Load per unit deflection. The amount of load required to resist the deflection.
Weight per unit volume of the fluid.
Volume per unit mass of the fluid.
It is the ratio of specific weight of required substance to specific weight of pure water at 4 degree centigrade temperature.
The amount of heat required to increase 1 unit temperature of 1 unit mass.
The amount of resistance of one layer of fluid over other layer of fluid.
It is the ratio of dynamic viscosity to density.
When a body is immersed in a liquid, it is lifted up by a force equal to weight of liquid displaced by the body. The tendency of liquid to lift up an immersed body is buoyancy. The upward thrust of liquid to lift up the body is called buoyancy force.
P/γ +V²/2g +Z = Constant
Where, P = pressure,V = velocity,Z = Datumn Head
Devices for fluid:
It measures discharge of fluid.
It measures discharge of fluid.
It measures discharge of fluid.
Pitot tube :
It measures velocity of fluid.
It is the ratio of the velocity of fluid to the velocity of sound.
M=1 —————– Sonic flow
M> (1-6) ———– Super-Sonic flow
M>6 —————- Hyper-Sonic flow
Fluid discharge/Fluid flow:
Quantity of fluid flowing per second.
(through a section of pipe/ through a section of channel)
where, V= velocity of fluid,A= cross-sectional area of pipe/channel
Note: 1m³ = 1000 L1 cusec = 1 ft³/sec1 ft = 0.3048 m
It attaches with reaction turbine . Its function is to reduce energy loss from reaction turbine & it also reduce pressure at outlet which is must blow the atmospheric pressure.
If two body are in thermal equilibrium with a third body then these two body are also in thermal equilibrium with each other.
First Law of Thermodynamics:
In a closed system, work deliver to the surrounding is directly proportonal to the heat taken from the surrounding.And also, In a closed system, work done on a system is directly proportonal to the heat deliver to the surrounding.
Second Law of Thermodynamics:
It is impossible to make a system or an engine which can change 100 percent input energy to 100 percent output.
It is a thermodynamic property.
ds = dq/T
where, ds = change of entropy, dq = change of heat, T = Temperature.
In adiabatic process, entropy can not change. Actually,lacking or mal-adroitness of tranfering energy of a system is entropy.
Calorific Value of fuel:
It us the total amount of heat obtained from burning 1 kg solid or liquid fuel.
It is a clossed vessel which is made of steel. Its function is to transfer heat to water to generate steam.
It is a part of boiler. Its function is to heat feed water which is supplied to boiler.
It is a part of boiler. Its function is to increase temperature of steam into boiler.
It is a part of boiler. Its funtion is to preheats the air to be supplied to furnace and it recover heat from exhaust gas.
It is an important term for boiler. It is the difference of pressure above and below the fire grate. This pressure difference have to maintain very carefully inside the boiler. It actually maintains the rate of steam generation. This depends on rate of fuel burning. Inside the boiler rate of fuel burning is maintained with rate of entry fresh air. If proper amount of fresh air never entered into the boiler, then proper amount of fuel inside the boiler never be burnt. So, proper fresh air enters into the boiler only by maintaining boiler draught.
Nozzle is a duct of varying cros-sectional area. Actually, it is a passage of varying cross-sectional area. It converts steam’s heat energy into mechanical energy. It is one type of pipe or tube that carrying liquid or gas.
It is the process of removing burnt gas from combustion chamber of engine cylinder.
Actually, power output of engine depends on what amount of air enter into the engine through intake manifold. Amount of entry air if increased, then must be engine speed will increased. Amount of air will be increased by increasing inlet air density. The process of increasing inlet air density is supercharging. The device which is used for supercharging is called supercharger. Supercharger is driven by a belt from engine crankshaft. It is installed in intake system.
Turbocharging is similar to the supercharging. But in that case turbocharger is installed in exhaust system whereas supercharger is installed in intake system. Turbocharger is driven by force of exhaust gas. Generally, turbocharger is used for 2-stroke engine by utilizing exhaust energy of the engine, it recovers energy otherwise which would go waste.
Its function id to regulate mean speed of engine when there are variation in the load. If load incrases on the engine, then engine’s speed must decrease. In that case supply of working fluid have to increase. In the otherway, if load decrease on the engine, then engine’ speed must increase. In that case supply of working fluid have to decrease.Governor automatcally, controls the supply of working fluid to the engine with varying load condition.
It is the one of the main parts of the I.C. engine. Its main function id to store energy in the time of working stroke or expansion stroke. And, it releasesenergy to the crankshaft in the time of suction stroke, compression stroke & exhaust stroke. Because, engine has only one power producing stroke.
Rating of fuel:
Octane number. Octane number indicates ability of fuel to resist knock.
Cetane Number. Cetane number indicates ability of ignition of diesel fuel. That means, how much fast ignites diesel fuel.
It is the chemically correct air-fuel ratio by volume. By which theoretically sufficient oxygen will be gotten to burn all combustible elements in fuel completely.
It is a science which deals with energy transfer between material bodies as a result of temperature difference.There are three way to heat transfer such as-ConductionConvectionRadiation
It is the quantity of heat flows between two parts of solid material by conduction. In this case following consideration will be important fact-
- Time—— 1 sec
- Area of that solid material——– 1 m²
- Thickness of that solid material—— 1m
- Temperature difference between two parts of that material—— 1k
It is one type of device which can transfer heat from one fluid to another fluid. Example- Radiator, inter-cooler, preheater, condenser, boiler etc.
It is the process of removing heat from a substance. Actually, extraction of heat from a body whose temperature is already below the temperature of its surroundings.
1 tonne of refrigeration:
It is amount of refrigeration effect or cooling effect which is produced by uniform melting of 1 tonne ice in 24 hours from or at 0 degree centigrade or freezing 1 tonne water in 24 hours from or at 0 degree centigrade.
It is the addition of moisture to the air without change dry bulb temperatur.
It is the removal of moisture from the air without change dry bulb temperature.
Meshing of two or more gear. It can transmit power from one shaft to another shaft.
Operation involving heating and cooling of a metal in solid state for obtaining desirable condition without being changed chemical composition.Its object-increase hardness of metal.increase quality of metal ( heat, corrosion,wear resistance quality )improve machinability.
1. Cast Iron – (2-6.67)%C, Si, Mn, P, S
2. Steel – (0-2)%C
3. Wrought Iron – 99.5% Fe
1. Brass – (Cu+Zn)
2. Bronze –
(Sn+Cu) —— Tin Bronze
(Si+Cu) ——- Silicon Bronze
(Al+Cu) ——- Aluminium Bronze
It is the difference between basic dimension of mating parts. That means, minimum clearance between mating parts that can be allowed.
It is the difference between upper limit of dimension. It is also the permissible variation above and below the basic size. That means maximum permissible variation in dimensions.
It is the difference in size between mating parts. That means, in that case the outside dimension of the shaft is less than internal dimension of the hole.
It is the ability to resist deformation.
It is the property to resist fracture.
When a material is subjected to repeated stress below yield point stress, such type of failure is fatigue failure.
It is a nuclear reaction by which one big nucleous divided into two or more nucleous.
It is also a nuclear reaction by which one big nucleus will produced by adding two small nucleus.
It is the process of joining two similar or dissimilar metal by fusion.
Arc Welding –
* need D.C current
* produced (6000-7000) Degree Centegrade Temperature
Gas Welding –
* Oxy – acetylene flame join metals
* Oxygen & acetylene gas works
* produced 3200 Degree Centegrade Temperature
It is the power driven tool. It cut & form all kinds of metal parts.
Example – 1. Lathe 2. Drill Press 3. Shaper 4. Planer 5. Grinding 6. Miling 7. Broaching 8. Boring
Tool Materials for Cutting Tool:
1. High Carbon Steel
2. High Speed Steel (W+Cr+V)
3. Carbide (W Carbide+Ti Carbide+Co Carbide)
It is the method of dividing periphery of job into equal number of division. Actually, it is the process of dividing circular or other shape of workpiece into equal space, division or angle.
It is one type of device which hold & locate workpiece and also guide & control cutting tool. It uses in drilling, reaming and tapping.
It is one type of device which hold and locate workpiece. It uses in miling, grinding, planning & turning.
The usual need to look up values from various tables and charts makes the conventional hand calculation
quite laborious, time consuming and prone to errors and inaccuracies because of the tendency to simplify
truncate or interpolate tabulated values. Listed below are the suggested applications and methodology of
two computer programs Elite CHVAC and TRACE 700 that may be used in the cooling and heating load
CHVAC is a commercial Heating, Ventilation and Air Conditioning software platform developed by Elite
Software. This computer program calculates the maximum heating and cooling loads in commercial and
Listed below are capabilities of CHVAC:
- Calculates peak heating and cooling loads
- Calculates both heating & cooling airflow CFM requirements
- Calculates run out and main trunk duct sizes
- Automates compliance with ASHRAE Standard 62
- Provides overall building envelope report
- Spreadsheet file compatibility
- Performs complete psychrometric analysis
- Prints bar graphs and exploded pie charts
- Exterior shading handles overhangs, fins, & glass tilt
- Uses exact ASHRAE CLTD procedures
- Built-in design weather data for hundreds of cities
- Analyzes up to 12 months per calculation
- Calculates 24 hours per design day
- Allows unlimited number of zones per project
- Zones may be grouped under 100 air handlers
- Zones may be optionally grouped under VAV boxes
- Allows 12 walls, 12 windows, and 5 roofs per zone
- Allows simultaneous infiltration and ventilation
- Allows different summer and winter air rates
- Allows varying indoor conditions within a project
- Allows 6 master roof types,8 master wall types, 8 master partition types, and 20 master glass types
- Allows glass to be tilted from 0 to 180 degrees
- Allows for roof and wall color effects
- Provision for both VAV and constant volume systems
- Proper handling of return air plenum loads
- Accounts for people diversity in total building load
- Computes supply fan horsepower and heat gains
- Accounts for both draw-thru and blow-thru fans
- Calculates reheat requirements if necessary
- Computes supply and return duct gains and losses
- Allows direct specification of supply CFM quantities
- Allows specification of minimum supply air quantities
- Allows heating only, cooling only, or both
- Excess supply air can be handled as reheat, reserve capacity, or by adjusting the leaving coil conditions
- Leaving coil conditions can be specified with a desired dry bulb temperature or a relative humidity
- Calculates chilled and hot water coil flow rates
- Allows for pretreated outside air
- Allows heating and cooling safety factors
- Lighting & equipment watts along with no. of people can be entered directly or on a per square foot basis
CHVAC performs calculations using the CLTD/CLF procedures described in the ASHRAE Handbook of Fundamentals. The programs use exact CLTD and MSHGF table values where possible, otherwise direct
calculations are made. This calculation technique allows the programs to calculate for any building
orientation and still produce output results that can be easily verified by hand.
CHVAC is a true Windows program that uses all the latest data entry techniques such as toolbars, hyper linked help, and form tabs. All input data is checked at the time of entry so that no improper data can be entered. Five types of data are requested: general project data, outdoor design data, building material data, air handler data, and specific zone data. The general project data includes the project and client name, designer, building opening and closing hours, internal operating load schedules, and any desired safety factors. The outdoor design data includes the summer and winter outdoor design conditions (automatically looked up for you if a city reference is given) and the desired ventilation and infiltration rates. The building material data includes the definition of master building material types for roofs, walls, partitions, glass sections, and exterior shading. A user defined material library is available for saving the data on common material types. The air handler data includes the fan and terminal type, the desired heating and cooling supply air temperatures and data for duct heat gains and losses. The zone data includes the zone name, floor length and width, number of people, equipment watts, lighting watts, external shading data, and specific roof, wall, partition, floor, and glass data.
The CHVAC program provides eleven types of reports,which can be selectively previewed onscreen or printed as desired. CHVAC supports all printers that work with Windows and numerous full color reports are available.The reports are: General Project Data, Air Handler Input Data, Zone Input Data, Detailed Project Zone Loads, Air System Zone Summary, Total Building, Air System, and Zone Load Profiles, Air System Total Load Summary, Air System Psychrometric Analysis, Overall Building Envelope Report, Pie Charts, Bar Graphs, and the Total Building Load Summary. Air system summary data can be exported to your favorite spreadsheet.
TRACE ® 700
The TRACE Load ® 700 program is a commercial Heating, Ventilation and Air Conditioning software platform developed by Trane’s CDS Group.
The Load phase of the program computes the peak sensible and latent zone loads, as well as the block sensible and latent loads for the building. In addition, the hourly sensible and latent loads, including weather-dependent loads, are calculated for each zone, based on the weather library. The building heating/cooling load calculations, used in the load phase of the program for annual energy consumption analysis, are of sufficient detail to permit the evaluation of the effect of building data such as orientation, size, shape and mass, heat transfer characteristics of air and moisture, as well as hourly climatic data. The Design phase of the TRACE program calculates the design supply air temperatures, heating and cooling capacities, and supply air quantities given the peak load files generated by the Load phase. For applications where the building design parameters are known, you can override the calculation of these values using optional entries to the System phase. This gives you the ability to simulate existing buildings
with installed equipment that may not be sized according to the loads calculated in the program’s Load Phase.
Beyond this, the calculations used to simulate the operation of the building and its service systems through a full-year operating period, are of sufficient detail to permit the evaluation of the effect of system design, climatic factors, operational characteristics and mechanical equipment operating characteristics on annual energy usage. Manufacturers’ data is used in the program for the simulation of all systems and equipment. The calculation procedures used in TRACE are based upon 8,760 hours of operation of the building and its service system. These procedures use techniques recommended in the appropriate ASHRAE publications or produce results that are consistent with such recommended techniques. The following are the program features:
Project Navigator View
- Organizes entries by task to lead you through the modeling process
- Displays the status of each modeling step
- Accommodates up to 4 alternatives per project
Project Tree View
- Organizes all rooms, systems, and plants in a hierarchical list
- Displays all information about a system, zone, or room on 1 screen
- Supports cut, copy, and paste to save entry time
- Displays cooling set point for every room in the project on 1 screen
- Makes it easy to check and edit your work
Task-oriented display guides you through the modeling process as follows:
Select weather information
- Provides both design and typical weather data by location
- Choose from 400 climate locations
- Import standard weather files for a full-year (8760) analysis
- Describe the construction, airflows, thermostat settings, heat sources, and schedules by room
Create airside systems
- Choose from more than 30 methods of air distribution
- Add energy recovery, economizers, and dedicated ventilation/makeup air
Assign rooms to systems
- Create thermal zones and assign them to systems
- Determine airflows, coil loads, and fan sizes for each airside system
If the only requirement is to calculate the cooling and/or heating loads and the project does not require energy analysis and economic evaluation, it is recommended that the Program Load ® 700 be utilized instead of Full TRACE 700.The only difference is that Trace Load ® 700 users only have access to the Load Design section (from Project Information to Assign Rooms to Systems). Full TRACE 700 users will have full access to the Load, Energy and Economic sections.
The advantage of using only Trace Load ® 700 is that all the added features and capabilities (applicable to load design) in full TRACE 700 program are also available to the Trace Load ® 700 users. Also, same file extensions and libraries will enable users of both programs to transfer archived files back and forth without any additional steps needed.
The fundamentals of Sound and Vibrations are part of the broader field of mechanics, with strong connections to classical mechanics, solid mechanics and fluid dynamics.
Dynamics is the branch of physics concerned with the motion of bodies under the action of forces.
Vibrations or oscillations can be regarded as a subset of dynamics in which a system subjected to restoring forces swings back and forth about an equilibrium position, where a system is defined as an assemblage of parts acting together as a whole. The restoring forces are due to elasticity, or due to gravity.
The subject of Sound and Vibrations encompasses the generation of sound and vibrations, the distribution and damping of vibrations, how sound propagates in a free field, and how it interacts with a closed space, as well as its effect on man and measurement equipment. Technical applications span an even wider field, from applied mathematics and mechanics, to electrical instrumentation and analog and digital signal processing theory, to machinery and building design. Most human activities involve vibration in one form or other. For example, we hear because our eardrums vibrate and see because light waves undergo vibration. Breathing is associated with the vibration of lungs and walking involves (periodic) oscillatory motion of legs and hands. Human speak due to the oscillatory motion of larynges (tongue).
In most of the engineering applications, vibration is signifying to and fro motion , which is undesirable. Galileo discovered the relationship between the length of a pendulum and its frequency and observed the resonance of two bodies that were connected by some energy transfer medium and tuned to the same natural frequency. Vibration may results in the failure of machines or their critical components. The effect of vibration depends on the magnitude in terms of displacement, velocity or accelerations, exciting frequency and the total duration of the vibration.
Free Vibration– In Free vibration, the object is not under the influence of any kind of outside force.
In free vibration the body at first is given an initial displacement and the force is withdrawn. The body starts vibrating and continues the motion of its own accord. No external force acts on the body further to keep it in motion. The frequency of free vibration is known as free or natural frequency.
The free vibration of an elastic body can further be of three types:
a)Longitudinal vibration: when the particles of the body move parallel to the axis of the body, the vibration is known as longitudinal vibration.
b)Transverse vibration: when the particles of the body move nearly perpendicular to the axis of the body, the vibration is known as transverse vibration.
c)Torsional vibration: When the particles of the body move in a circle about the axis of the body, the vibration is known as torsional vibration.
Forced Vibration– In forced vibration, the object is under the influence of an outside force.
This can be understood more clearly by the following example:-
When a pendulum vibrates it is free vibration because it does not depend on any outside force to vibrate whereas when a drilling machine vibrates, it depends on a force from outside. Therefore, it is an example of forced vibration.
A linear system is defined as one in which the relationship between the input and output signals can be described by a linear differential equation.
Often in Vibrations and Acoustics, the calculation of the effect of a certain physical quantity termed as the input signal on another physical quantity, called the output signal.
An example is that of calculating vibration velocity v(t), which is obtained in a structure when it is excited by a given force F(t). That problem can be solved by making use of the theory of linear time- invariant systems. A linear time-invariant system describes the relationship between an input signal and an output signal. For example, the input signal could be a velocity v(t), and the output signal a force F(t), or the input signal an acoustic pressure p(t) and the output signal an acoustic particle velocity u’(t). If the coefficients are, moreover, independent of time, i.e., constant, then the system is also time invariant.
Discrete System Components A system is defined as an aggregation of components acting together as one entity. The components of a vibratory mechanical system are of three different types, and they relate forces to displacements, velocities, and accelerations. The component relating forces to displacements is known as a spring. For a linear spring the force Fs is proportional to the elongation or
where k represents the spring constant, or the spring stiffness, and x2 and x1 are the displacements of the end points.
Viscous damper or a dashpot The component relating forces to velocities is called a viscous damper or a dashpot. It consists of a piston fitting loosely in a cylinder filled with liquid so that the liquid can flow around the piston when it moves relative to the cylinder. The relation between the damper force and the velocity of the
piston relative to the cylinder is
in which c is the coefficient of viscous damping; note that dots denote derivatives with respect to time. Finally, the relation between forces and accelerations is given by Newton’s second law of motion:
where m is the mass.
The spring constant k, coefficient of viscous damping c, and mass m represent physical properties of the components and are the system parameters.
Note that springs and dampers are assumed to be massless and masses are assumed to be rigid.
Equivalent spring constant Springs can be arranged in parallel and in series. Then, the proportionality constant between the forces and the end points is known as an equivalent spring constant and is denoted by keq, as shown in Table below:
Certain elastic components, although distributed over a given line segment, can be regarded as lumped with an equivalent spring constant given by keq = F/δ, where δ is the deflection at the point of application of the force F. A similar relation can be given for springs in torsion. Table given above lists the equivalent spring constants for a variety of components.
Equation of Motion The dynamic behavior of many engineering systems can be approximated with good accuracy by the mass-damper spring model. Using Newton’s second law in conjunction with equations for Fs, Fd and Fm given above and measuring the displacement x(t) from the static equilibrium position, we obtain the differential equation of motion as below:
which is subject to the initial conditions x(0)=x0, ẋ(0)=v0, where x0 and v0 are the initial displacement and initial velocity, respectively.
Equation given above is in terms of a single coordinate. namely x(t) is therefore said to be a single-degree-of-freedom system.
Free Vibration of Undamped Systems Assuming zero damping and external forces and dividing above equation through by m, we obtain
In this case, the vibration is caused by the initial excitations alone. The solution of above equation is
which represents simple sinusoidal, or simple harmonic oscillation with amplitude A, phase angle ф, and frequency .
The time necessary to complete one cycle of motion defines the period.
The reciprocal of the period provides another definition of the natural frequency,namely,
where Hz denotes hertz[1 Hz = 1 cycle per second (cps)].
Free Vibration of Damped Systems Let F(t)=0 and divide through by m.Then, Equation of motion reduces to
ξ is the damping factor, a non-dimensional quantity. The nature of the motion depends on ξ. The most important case is that in which 0<ξ<1.
In this case, the system is said to be underdamped and the solution of above equation is
ωd is the frequency of damped free vibration and is the period of damped oscillation.
The case ξ=1, represents critical damping, and Cc is the critical damping coefficient,although there is nothing critical about it. It merely represents the borderline between oscillatory decay and aperiodic decay. In fact, Cc is the smallest damping coefficient for which the motion is aperiodic. When ξ>1, the system is said to be overdamped.
Logarithmic Decrement Quite often the damping factor is not known and must be determined experimentally. In the case in which the system is underdamped, this can be done conveniently by plotting x(t)
versus t, and measuring the response at two different times separated by a complete period.
Whirling of Rotating Shafts Many mechanical systems involve rotating shafts carrying disks. If the disk has some eccentricity, then the centrifugal forces cause the shaft to bend, as shown in Figure (a) below. The rotation of the plane containing the bent shaft about the bearing axis is called whirling. Figure (b) below shows a disk with the body axes x, y rotating about the origin O with the angular velocity ω.
The geometrical center of the disk is denoted by S and the mass center by C.The distance between the two points is the eccentricity e. The shaft is massless and of stiffness keq and the disk is rigid and of mass m. The x and y components of the displacement of S relative to O are independent from one another and, for no damping, satisfy the equations of motion
Resonance occurs when the whirling angular velocity coincides with the natural frequency. In terms of rotations per minute, it has the value
where fc is called the critical speed.
- Marks’ Standard Handbook for Mechanical Engineers Eleventh Edition.
- Fundamentals of Sound and Vibrations by KTH Sweden.
The Cooling Load
The cooling load on refrigerating equipment seldom results from any one single source of heat. Rather, it is the summation of the heat usually evolves from several different sources.
Cooling load calculations may be used to accomplish one or more of the following objectives:
- Provide information for equipment selection, system sizing and system design.
- Provide data for evaluating the optimum possibilities for load reduction.
- Permit analysis of partial loads as required for system design, operation and control.
Commonly used terms relative to heat transmission and load calculations are defined below in accordance with ASHRAE Standard 12-75, Refrigeration Terms and Definitions.
Space – is either a volume or a site without a partition or a partitioned room or group of rooms.
Room – is an enclosed or partitioned space that is usually treated as single load.
Zone – is a space or group of spaces within a building with heating and/or cooling requirements sufficiently similar so that comfort conditions can be maintained throughout by a single controlling device.
British thermal unit (Btu) – is the approximate heat required to raise 1 lb. of water 1 deg Fahrenheit, from 59°F to 60°F. Air conditioners are rated by the number of British Thermal Units (Btu) of heat they can remove per hour. Another common rating term for air conditioning size is the “ton,” which is 12,000 Btu per hour and Watts. Some countries utilize one unit, more than the others and therefore it is good if you can remember the relationship between BTU/hr, Ton, and Watts.
- 1 ton is equivalent to 12,000 BTU/hr. and
- 12,000 BTU/hr is equivalent to 3,516 Watts – or 3.516 kW (kilo-Watts).
Cooling Load Temperature Difference (CLTD) – an equivalent temperature difference used for calculating the instantaneous external cooling load across a wall or roof.
Sensible Heat Gain – is the energy added to the space by conduction, convection and/or radiation.
Latent Heat Gain – is the energy added to the space when moisture is added to the space by means of vapor emitted by the occupants, generated by a process or through air infiltration from outside or adjacent areas.
Radiant Heat Gain – the rate at which heat absorbed is by the surfaces enclosing the space and the objects within the space.
Space Heat Gain – is the rate at which heat enters into and/or is generated within the conditioned space during a given time interval.
Space Cooling Load – is the rate at which energy must be removed from a space to maintain a constant space air temperature.
Space Heat Extraction Rate – the rate at which heat is removed from the conditioned space and is equal to the space cooling load if the room temperature remains constant.
Dry Bulb Temperature – is the temperature of air indicated by a regular thermometer.
Wet Bulb Temperature – is the temperature measured by a thermometer that has a bulb wrapped in wet cloth. The evaporation of water from the thermometer has a cooling effect, so the temperature indicated by the wet bulb thermometer is less than the temperature indicated by a dry-bulb (normal, unmodified) thermometer. The rate of evaporation from the wet-bulb thermometer depends on the humidity of the air. Evaporation is slower when the air is already full of water vapor. For this reason, the difference in the temperatures indicated by ordinary dry bulb and wet bulb thermometers gives a measure of atmospheric humidity.
Dew point Temperature – is the temperature to which air must be cooled in order to reach saturation or at which the condensation of water vapor in a space begins for a given state of humidity and pressure.
Relative humidity – describes how far the air is from saturation. It is a useful term for expressing the amount of water vapor when discussing the amount and rate of evaporation. One way to approach saturation, a relative humidity of 100%, is to cool the air. It is therefore useful to know how much the air needs to be cooled to reach saturation.
Thermal Transmittance or Heat Transfer Coefficient (U-factor) – is the rate of heat flow through a unit area of building envelope material or assembly, including its boundary films, per unit of temperature difference between the inside and outside air. The U-factor is expressed in Btu/ (hr °F ft²).
Thermal Resistance(R) – is the reciprocal of a heat transfer coefficient and is expressed in (hr °F ft²)/Btu. For example, a wall with a U-value of 0.25 would have a resistance value of R = 1/U = 1/0.25=4.0. The value of R is also used to represent Thermal Resistivity, the reciprocal of the thermal conductivity.
Sizing Of Air-Conditioning System
Concepts and fundamentals of air conditioner sizing is based on heat gain, and/or losses in a building. It is obvious that you will need to remove the amount of heat gain – if it is hot outside. Similarly, you’ll need to add in the heat loss from your space – if outside temperature is cold. In short, heat gain and loss, must be equally balanced by heat removal, and addition, to get the desired room comfort that we want.
The heat gain or heat loss through a building depends on:
- The temperature difference between outside temperature and our desired temperature.
- The type of construction and the amount of insulation is in your ceiling and walls. Let’s say, that you have two identical buildings, one is build out of glass, and the other out of brick. Of course the one built with glass would require much more heat addition, or removal, compared to the other – given a same day. This is because the glass has a high thermal conductivity (U-value) as compared to the brick and also because it is transparent, it allows direct transmission of solar heat.
- How much shade is on your building’s windows, walls, and roof? Two identical buildings with different orientation with respect to the direction of sun rise and fall will also influence the air conditioner sizing.
- How large is your room? The surface area of the walls. The larger the surface area – the more heat can lose, or gain through it.
- How much air leaks into indoor space from the outside? Infiltration plays a part in determining our air conditioner sizing. Door gaps, cracked windows, chimneys – are the “doorways” for air to enter from outside, into your living space.
- The occupants. It takes a lot to cool a town hall full of people.
- Activities and other equipment within a building. Cooking? Hot bath? Gymnasium?
- Amount of lighting in the room. High efficiency lighting fixtures generate less heat.
- How much heat the appliances generate. Number of power equipments such as oven, washing machine, computers, TV inside the space; all contribute to heat.
The air conditioner’s efficiency, performance, durability, and cost depend on matching its size to the above factors. Many designers use a simple square foot method for sizing the air-conditioners. The most common rule of thumb is to use “1 ton for every 500 square feet of floor area”. Such a method is useful in preliminary estimation of the equipment size. The main drawback of rules-of-thumb methods is the presumption that the building design will not make any difference. Thus the rules for a badly designed building are typically the same as for a good design.
It is important to use the correct procedure for estimating heat gain or heat loss. Two groups—the Air Conditioning Contractors of America (ACCA) and the American Society of Heating, Refrigerating, and Air Conditioning Engineers (ASHRAE)—publish calculation procedures for sizing central air conditioners.
Reputable air conditioning contractors will use one of these procedures, often performed with the aid of a computer, to size your new central air conditioner.
Heating Load V/s Cooling Load Calculations
As the name implies, heating load calculations are carried out to estimate the heat loss from the building in winter so as to arrive at required heating capacities. Normally during winter months the peak heating load occurs before sunrise and the outdoor conditions do not vary significantly throughout the winter season. In addition, internal heat sources such as occupants or appliances are beneficial as they compensate some of the heat losses. As a result, normally, the heat load calculations are carried out assuming steady state conditions (no solar radiation and steady outdoor conditions) and neglecting internal heat sources. This is a simple but conservative approach that leads to slight over estimation of the heating capacity. For more accurate estimation of heating loads, one has to take into account the thermal capacity of the walls and internal heat sources, which makes the problem more complicated.
For estimating cooling loads, one has to consider the unsteady state processes, as the peak cooling load occurs during the day time and the outside conditions also vary significantly throughout the day due to solar radiation. In addition, all internal sources add on to the cooling loads and neglecting them would lead to under estimation of the required cooling capacity and the possibility of not being able to maintain the required indoor conditions. Thus cooling load calculations are inherently more complicated.
In determining the heating load, credit for solar heat gain or internal heat gains is usually NOT included and the thermal storage effects of building structure are generally ignored. Whereas in cooling load calculations, the thermal storage characteristics of the building play a vital role because the time at which the space may realize the heat gain as a cooling load will be considerably offset from the time the heat started to flow.
Heat Flow Rates
In air-conditioning design, four related heat flow rates, each of which varies with time, must be differentiated:
- Space heat gain —————-How much heat (energy) is entering the space?
- Space cooling load ————-How much energy must be removed from the space to keep temperature and relative humidity constant?
- Space heat extraction———–How much energy is the HVAC removing from the space?
- Cooling load (coil)—————How much energy is removed by the cooling coil serving various spaces plus any loads external to the spaces such as duct heat gain, duct leakage, fan heat and outdoor makeup air?
Space Heat Gain
This instantaneous rate of heat gain is the rate at which heat enters into and/or is generated within a space at a given instant. Heat gain is classified by:
The manner in which it enters the space –
- Solar radiation through transparent surfaces such as windows
- Heat conduction through exterior walls and roofs
- Heat conduction through interior partitions, ceilings and floors
- Heat generated within the space by occupants, lights, appliances, equipment and processes
- Loads as a result of ventilation and infiltration of outdoor air
- Other miscellaneous heat gain
Whether it is a sensible or latent gain –
Sensible heat – Heat which a substance absorbs, and while its temperature goes up, the substance does not change state. Sensible heat gain is directly added to the conditioned space by conduction, convection, and/or radiation. Note that the sensible heat gain entering the conditioned space does not equal the sensible cooling load during the same time interval because of the stored heat in the building envelope. Only the convective heat becomes cooling load instantaneously. Sensible heat load is total of
- Heat transmitted thru floors, ceilings, walls
- Occupant’s body heat
- Appliance & Light heat
- Solar Heat gain thru glass
- Infiltration of outside air
- Air introduced by Ventilation
Latent Heat Loads – Latent heat gain occurs when moisture is added to the space either from internal sources (e.g. vapor emitted by occupants and equipment) or from outdoor air as a result of infiltration or ventilation to maintain proper indoor air quality. Latent heat load is total of
- Moisture-laden outside air form Infiltration& Ventilation
- Occupant Respiration & Activities
- Moisture from Equipment & Appliances
To maintain a constant humidity ratio, water vapor must condense on cooling apparatus at a rate equal to its rate of addition into the space. This process is called dehumidification and is very energy intensive, for instance, removing1 kg of humidity requires approximately 0.7 kWh of energy.
Space Heat Gain V/s Cooling Load (Heat Storage Effect)
Space Heat Gain is ≠ to Space Cooling Load
The heat received from the heat sources (conduction, convection, solar radiation, lightning, people, equipment, etc…) does not go immediately to heating the room air. Only some portion of it is absorbed by the air in the conditioned space instantaneously leading to a minute change in its temperature. Most of the radiation heat especially from sun, lighting, people is first absorbed by the internal surfaces, which include ceiling, floor, internal walls, furniture etc. Due to the large but finite thermal capacity of the roof, floor, walls etc., their temperature increases slowly due to absorption of radiant heat. The radiant portion introduces a time lag and also a decrement factor depending upon the dynamic characteristics of the surfaces. Due to the time lag, the effect of radiation will be felt even when the source of radiation, in this case the sun is removed.
Differences between Space Heat Gain and Space Cooling Load
Differences between instantaneous heat gain and cooling load is due to heat storage affect.
The relation between heat gain and cooling load and the effect of the mass of the structure (light, medium & heavy) is shown below. From the figure it is evident that, there is a delay in the peak heat, especially for heavy construction.
Actual cooling load and solar heat gain for light, medium and heavy Construction
Space Cooling V/s Cooling Load (Coil)
Space cooling is the rate at which heat must be removed from the spaces to maintain air temperature at a constant value. Cooling load, on the other hand, is the rate at which energy is removed at the cooling coil that serves one or more conditioned spaces in any central air conditioning system. It is equal to the instantaneous sum of the space cooling loads for all spaces served by the system plus any additional load imposed on the system external to the conditioned spaces items such as fan energy, fan location, duct heat gain, duct leakage, heat extraction lighting systems and type of return air systems all affect component sizing.
- Principles of Refrigeration, Second edition by Roy J. Dossat
- Cooling load calculations and principles by A. Bhatia