Frame NVH (Part - 1) | Skill-Lync | Workshop — Transcript
Full transcript
- 0:00[Music]
- 0:07everyone
- 0:07and welcome to the webinar on the topic
- 0:09introduction to frame nvh
- 0:11i would like to go through the following
- 0:13contents in the webinar
- 0:15uh which would be a quick revision of
- 0:18what we have studied in vibrations in
- 0:20our engineering days
- 0:21then we look into what is nvh uh what
- 0:24are the different areas of nvh and how
- 0:26is in which applied to
- 0:28a frame then what do we do with respect
- 0:31to a frame
- 0:31analysis from in which point of view and
- 0:34we break it up into different steps
- 0:36that is modal analysis frequency
- 0:37response functions stiffness and control
- 0:40etc and once we are done with that part
- 0:43we'll focus on what is the fear approach
- 0:45which is used in the industry
- 0:47and also we look into certain set of
- 0:49tools which are
- 0:50which are in demand and which are used
- 0:52in the industry for carrying out nvh
- 0:54analysis
- 0:55and on concluding remarks i would like
- 0:58to discuss
- 0:59regarding the industry open
- 1:00opportunities for students who are fresh
- 1:02passouts
- 1:03and what roles they would be playing and
- 1:05also
- 1:06what all industries they can target for
- 1:08nvh related roles
- 1:10and then that will be followed up by a q
- 1:12a session where
- 1:13i would like to clear most of your
- 1:15doubts related to the image area
- 1:18yeah let's start with vibrations
- 1:21so all of us have
- 1:25have studied vibrations i believe in our
- 1:27engineering courses
- 1:29and i also understand that it was
- 1:30probably one of the most difficult
- 1:32subjects to understand
- 1:34so let me try to give a small revision
- 1:37of vibrations before we go into nvh
- 1:39because
- 1:40these concepts are very very essential
- 1:43in going forward to carry out nvh
- 1:45analysis
- 1:46so vibration in in the simplest terms
- 1:50is nothing but a motion that repeats
- 1:52itself
- 1:54from time to time or within an interval
- 1:56of time
- 1:57and its most simplest representation
- 2:00would be a sine wave
- 2:02and a sine wave when you plot it on the
- 2:03x and y axis
- 2:05you can you can read it as alternate
- 2:08crests and drops
- 2:10and that is how a usual vibration system
- 2:13is
- 2:14visualized in a mechanical engineering
- 2:17world
- 2:18coming to the layman terms if you see
- 2:21around us or if you
- 2:22take the human body itself you will be
- 2:24surprised to know that
- 2:26vibration plays a very vital role in
- 2:28most of the
- 2:29our day-to-day activities but to name a
- 2:32few
- 2:33we are able to hear only because of
- 2:35vibrations and how is that
- 2:37that is because our eardrums vibrate
- 2:39whenever there is
- 2:40there are sound waves which are going to
- 2:41come and impinge on the eardrums
- 2:44and the eardrum is going to resonate and
- 2:46that is going to send signals to the
- 2:47brain
- 2:48and that is how our brain perceives
- 2:50sound which is going to be
- 2:52which is going to affect us then
- 2:57even breathing for example if you take
- 3:00so it is nothing but
- 3:01a compression and relaxation of the
- 3:02lungs of the human body
- 3:04that will also constitute a type of
- 3:06vibration
- 3:07and even speaking for that matter is
- 3:10also a kind of
- 3:12is also an output from the vibration of
- 3:14the larynx in the throat
- 3:15of the human body so human body itself
- 3:19has so many areas where vibrations are
- 3:22involved and coming out of the human
- 3:25body and if you want to look at the
- 3:26surroundings
- 3:27you can find vibrations in almost every
- 3:29every part or every region of it
- 3:32for example there are numerous machines
- 3:34which exhibit vibrations
- 3:36there are engineering there are
- 3:38buildings and structures which undergo
- 3:39vibrations
- 3:40there are if you take automotive sector
- 3:42almost all of the automotive sector
- 3:45engines and bodies go undergo vibrations
- 3:47so hence vibration
- 3:49is a very interesting branch of study
- 3:51and it becomes all the more interesting
- 3:53when you want to
- 3:54analyze a system for a given vibration
- 3:57and how is it going to behave
- 3:58for a given set of forces what will be
- 4:01the response of the system
- 4:03so that's that's a very interesting uh
- 4:06part of study
- 4:07and in order to understand vibrations in
- 4:09a better way
- 4:10what we had studied in engineering was
- 4:12that
- 4:13it will get we can divide the vibration
- 4:15systems into
- 4:16a single degree of freedom system uh 2
- 4:18degree of freedom system
- 4:19and multiple degree of freedom systems
- 4:21and the respective examples for them
- 4:23would be spring mass systems
- 4:25a double pendulum and a railway bracket
- 4:28in other terms if you want to define
- 4:30vibration you can actually bring in the
- 4:32spring damper analogy spring mass damper
- 4:35analogy
- 4:36that is each and every system or each
- 4:38and every body
- 4:40can be subdivided into a spring mass and
- 4:42damper
- 4:44and by spring mass and damper to speak
- 4:46in very simplistic terms
- 4:48they are nothing but forms of energies
- 4:50where spring will represent the
- 4:51potential energy
- 4:52mass will represent the kinetic energy
- 4:54and damper will represent the
- 4:56dissipation energy
- 4:57so what happens usually whenever there
- 5:00is vibration happening is
- 5:02the potential energy and the kinetic
- 5:04energy are interchanging themselves
- 5:06and the dissipation energy or the damper
- 5:08is going to act as
- 5:10the as the force of the source which is
- 5:12going to reduce the potential in the
- 5:14kinetic energy in every cycle
- 5:16so if you can take a look at the image
- 5:17which is on the right you can see that a
- 5:19pendulum is
- 5:20continuously clocking across the
- 5:22midpoint so if you see here when it is
- 5:25at the midpoint
- 5:26its potential energy is going to be at
- 5:28the highest and the kinetic energy is
- 5:29going to be
- 5:30zero and let us say if you just strike
- 5:33the pendulum once
- 5:34then the pendulum is going to start
- 5:36clocking itself
- 5:37and at the extreme end of it we can say
- 5:40that the potential energy is going to be
- 5:42zero
- 5:42but it is going to have maximum kinetic
- 5:44energy and
- 5:46that is how the potential and the
- 5:47kinetic energies are going to
- 5:48interchange themselves
- 5:50and help the pendulum to keep on rocking
- 5:53and where does damping come here
- 5:54so now if this pendulum is allowed to
- 5:57freely
- 5:59rock on itself rock by itself then it's
- 6:02going to come to rest after certain
- 6:03point of time
- 6:04and that is because of the internal
- 6:06friction forces and also because of the
- 6:08air which is going to offer resistance
- 6:09to the movement of the pendulum
- 6:11and that is how damping is perceived in
- 6:14nature
- 6:16then some terminologies which we learned
- 6:19with respect to vibrations where
- 6:21natural frequencies then damping
- 6:23different equations of motion
- 6:25what are the different types of free and
- 6:27forced responses so
- 6:28all of them are nothing but means to
- 6:31characterize the vibration
- 6:33vibratory system natural frequencies
- 6:36define the characteristic
- 6:38moments of the system then damping will
- 6:40define
- 6:41how good the system is with respect to
- 6:43dissipating the vibration energy
- 6:45equations of motions were derived to
- 6:48simplify the actual vibration vibratory
- 6:50system into mathematical models
- 6:52and mathematical terminologies and the
- 6:54solution of
- 6:55those equations of motion will actually
- 6:58give you the vibration parameters which
- 6:59are needed to solve
- 7:01or which are needed to characterize the
- 7:04system
- 7:05and we have different types of
- 7:07vibrations that is
- 7:09what are free vibrations what are forced
- 7:11vibrations how is the system going to
- 7:13behave with a free and a forced
- 7:15vibration under a free enforced
- 7:17vibrations etc
- 7:19and then we also spoke about
- 7:21transmissibility
- 7:22so whenever there is a vibration set up
- 7:26into a system
- 7:26there is definitely going to be a force
- 7:28involved
- 7:30and when the four and when the force
- 7:31excites the system
- 7:33the system is going to vibrate with some
- 7:35energy
- 7:36and this energy is going to get
- 7:38transmitted to all the connected members
- 7:40of the body
- 7:41and that is the area of interest which
- 7:44engineer would be looking into
- 7:46what how much amount of force is getting
- 7:48transmitted to another body
- 7:50is that force under limits is is however
- 7:53how am i going to control that force is
- 7:55that force necessary or is it unwanted
- 7:58so those were the areas which we have
- 8:00studied
- 8:01previously in engineering and
- 8:04that was a quick brush up of the
- 8:07fundamentals of vibrations and also the
- 8:08terminologies which are used in
- 8:10vibrations
- 8:12now let's take a quick look at the
- 8:15nvh perspective of the entire whole
- 8:18thing of the
- 8:18whole thing so what do you mean by nvh
- 8:22nvh is an acronym for noise vibration
- 8:24and harshness
- 8:25and why are they used together let's
- 8:28come to that
- 8:29so in the previous slide when we spoke
- 8:31about a force which is going to induce
- 8:33certain
- 8:34vibration into a machine what are going
- 8:36to be the side effects or what are going
- 8:38to be the
- 8:39further effects of that forcing function
- 8:41which is going to induce vibrations
- 8:43in most of the cases that vibration
- 8:46which is
- 8:47induced into the system is going to
- 8:50interact with the surrounding medium and
- 8:52it is going to radiate
- 8:54energy into the surrounding medium and
- 8:56let us say if it is
- 8:57air that the energy which is radiated
- 9:01into the surrounding medium
- 9:02is going to go in forms of pressure
- 9:04waves and these pressure waves are
- 9:06nothing but what we call it as
- 9:08sound waves so vibration is going to
- 9:11give rise
- 9:12to sound and whatever sound is generated
- 9:16if it is going to go beyond a level or
- 9:19if it is going to go beyond the limit of
- 9:21human ear perception
- 9:23then we call it as noise so vibration
- 9:26unwanted vibration is going to lead to
- 9:28unwanted sound
- 9:29which we call it as noise and if the
- 9:32unwanted
- 9:33vibrations reaches a peak or what we
- 9:35call it
- 9:36at resonant frequencies then it is the
- 9:39sound which or the noise which is
- 9:40generated
- 9:41is going to be much more irritating and
- 9:44unpleasant to the human ears
- 9:45and that is what we call it as harshness
- 9:48so
- 9:49nvh that is noise vibration and rashness
- 9:51are all interrelated
- 9:53the source being the vibration which is
- 9:55in turn going to generate the noise
- 9:57and from noise whatever is the level of
- 10:00perception of the human ear we can
- 10:01classify it as
- 10:02harshness so what would our engineer
- 10:06typically do when we say nvh engineer
- 10:09nvh analyst etc the typical role of an
- 10:12engineer
- 10:12would be to reduce the vibrations at the
- 10:15source
- 10:16so that whatever noise is going to
- 10:19come into the system that is reduced to
- 10:22an extent
- 10:23and also in turn that is going to reduce
- 10:25the amount of unpleasant
- 10:27things which which the user is going to
- 10:29experience
- 10:30also it can be in the reverse way uh
- 10:33sound source can generate structural
- 10:34vibrations
- 10:36and that can also be very unpleasant and
- 10:38that is also another area of study
- 10:41wherein an acoustic source is going to
- 10:43generate
- 10:45a vibration in the structure but since
- 10:47we're talking about frame nvh let's
- 10:48focus on
- 10:50the frame frame itself acting as a
- 10:52source as a vibratory source
- 10:54and also as a path to transfer different
- 10:56forces from
- 10:57one part of the car body to another so
- 11:01an engineer's duty would be to
- 11:03understand how vibrations are generated
- 11:05from where the vibrations are going to
- 11:07come onto the frame
- 11:09and how much of a vibration is too much
- 11:13there are certain set of standards which
- 11:14the industry uses to
- 11:17identify what what level is good and
- 11:18what level is bad
- 11:20and also how much of sound or noise
- 11:23is required inside automotive cabin or
- 11:26how much is the desired level for a
- 11:28human
- 11:29being so if you can see the images here
- 11:33the one on the right side that's the
- 11:35image of a shaker
- 11:37which is uh which is having a forced
- 11:38induced vibration
- 11:40so if you can uh if you can
- 11:44make it analogous to something like a
- 11:47cup of water
- 11:48so that is how the vibrations are going
- 11:49to look if you can
- 11:52transfer those vibrations or if you keep
- 11:53a glass of water on the shaker and
- 11:56that's how the water would vibrate
- 11:57so that's the transmissibility which i
- 11:59was talking about in the previous slide
- 12:01and if you look at the left side here
- 12:03there's a small there's a graph which
- 12:05has two plots in it
- 12:06so the top one would be called as music
- 12:10uh because it's it's quite repetitive
- 12:12and it's quite smooth
- 12:13whereas the one below it would be called
- 12:15as noise and that would be our area of
- 12:17interest
- 12:18when we try to reduce this unwanted
- 12:21noise and harshness
- 12:22which are going to get generated because
- 12:23of the undue vibrations
- 12:25in the body yeah so
- 12:28uh i would i would like to stick to a
- 12:32car body a car model
- 12:34whenever we talk about frame in vh but
- 12:36you can also extend it to
- 12:37different other areas because the
- 12:39technical concepts and the
- 12:41workload almost remain the same so
- 12:45whenever let us say you are sitting in a
- 12:46car and whenever you start the car
- 12:49so you are going to experience certain
- 12:52vibrations for example say add the
- 12:55stirring wheel
- 12:56on the gear pedal on the clutch pedal on
- 12:58the floor of the car
- 13:00etc so and also when you start
- 13:03when you close off your windows of the
- 13:05car and let us say you're cruising at
- 13:06around 80 or 100 kilometers per hour
- 13:08you are also going to hear some noise
- 13:11inside the car cable
- 13:12so there can be different sources of
- 13:15uh of those vibrations as well as noise
- 13:18so
- 13:19what can they be they can be it can be a
- 13:22road noise which are going to get
- 13:23generated because of the
- 13:25rolling of the tires on the road and
- 13:26then those in turn will be affecting the
- 13:28suspension systems and the suspension
- 13:29systems will be transferring
- 13:31the energies to the frame and the frame
- 13:34on which the
- 13:36on which the seats of the car are fixed
- 13:39so
- 13:39there you will be the driver will be
- 13:41experiencing the vibrations on the seat
- 13:43of the car
- 13:44and also the steering system is
- 13:46connected to the main body
- 13:48so the driver will be experiencing
- 13:50certain set of vibrations on the
- 13:51steering wheel
- 13:52and also the gear similarly with the
- 13:54gear pedal and
- 13:55the floor of the car and also all of
- 13:58this
- 13:58in combination will also add to the
- 14:01sound which is going to be
- 14:02experienced inside the cabin of a car so
- 14:06all of this would constitute the
- 14:09understanding of noise and vibrations
- 14:11inside a car body
- 14:12inside a car caving as such and our area
- 14:15of interest
- 14:16in today's webinar would be to
- 14:17understand what we do to reduce the
- 14:19vibrations in a frame
- 14:21and how do we go about understanding the
- 14:24different aspects and parameters of
- 14:27analyzing a frame from nvh perspective
- 14:32so in the previous slide the image which
- 14:34i had shown was quite
- 14:36simple and it was for a very layman
- 14:38approach
- 14:39but for an nvh engineer whenever he we
- 14:42speak about nvh
- 14:44analysis we have to divide the system
- 14:47into different areas or different
- 14:48levels and then we need to analyze the
- 14:51system and understand the nvh behavior
- 14:53so usually an automotive component
- 14:57would be divided into different levels
- 15:00wherein you
- 15:00you can just work on only the dream body
- 15:03of the car
- 15:04which will have only the frame and the
- 15:06body of the car with some other
- 15:07components
- 15:08or you can start working especially only
- 15:10with sub components
- 15:12which we usually call it as a component
- 15:14level or system level
- 15:16wherein you analyze a a simple component
- 15:20along with its uh inbound accelerace and
- 15:23also system level
- 15:25where you define a complete system and
- 15:27then you try to figure out what are what
- 15:29is the
- 15:30for what are the causes of vibrations
- 15:32what are the forces which are going
- 15:33to come onto the machine and also you
- 15:35can have the full vehicle analysis and
- 15:37try to understand
- 15:38how much of vibrations are going to get
- 15:40transferred in a complete vehicle
- 15:42and what is the sound level which is
- 15:44going to get generated
- 15:46inside the cabin of the car so in our
- 15:48study now
- 15:49we are going to work talk more about the
- 15:51system level
- 15:52and here the system under consideration
- 15:54would be the frame of the car
- 15:56which i would say would like we usually
- 15:59work with
- 16:00three distinct areas whenever we do
- 16:03analysis of that
- 16:04and that would be divided broadly into a
- 16:07modal analysis
- 16:08then a forced response analysis which
- 16:10involves frequency response functions
- 16:12and then the vibration control wire
- 16:14stiffness
- 16:15different stiffness methods
- 16:19let's start looking at each of them in
- 16:21detail
- 16:23modal analysis so i am sure pretty sure
- 16:26that most of you all have heard this
- 16:28term moral analysis natural frequencies
- 16:31mood shapes
- 16:32and blah blah blah so let's quickly see
- 16:34what what model analysis
- 16:36is how important it is to understand
- 16:40the frame nvh and how is it going to
- 16:43help the engineer to
- 16:45make the frame nvh better so
- 16:48modal analysis is a broad area wherein
- 16:53we study that we study the component
- 16:55behavior or we study the
- 16:57behavior of the model under test for its
- 16:59modal characteristics
- 17:01and by modal characteristics i mean what
- 17:03are its natural frequencies
- 17:05in a free free state what are its
- 17:06natural frequencies in a constrained
- 17:08state
- 17:09what what what what frequency will it
- 17:12resonate
- 17:13uh what types of displacements it's
- 17:16going to have what types of moments it
- 17:17is going
- 17:18to have is it a
- 17:21lateral mode or is it a torsional mode
- 17:23etc so
- 17:26when i say natural frequency it's
- 17:28nothing but of
- 17:29the fundamental frequency of the body at
- 17:31which it will
- 17:33start vibrating when you when you excite
- 17:36it and you leave it
- 17:37so for example if you take a guitar a
- 17:40string of a guitar
- 17:42you pluck the string of the guitar and
- 17:44you leave it so the guitar is going to
- 17:46vibrate at
- 17:47a certain frequency and that frequency
- 17:50is known as the fundamental frequency of
- 17:52the guitar
- 17:53and that is going to remain constant so
- 17:56this is very important
- 17:57this the fundamental frequency is a
- 18:00characteristic
- 18:01of the system or characteristics of the
- 18:04body
- 18:05so it is like young's modulus or
- 18:08stiffness so it is not going to change
- 18:11unless and until you
- 18:12change certain boundary conditions or
- 18:15certain constraints
- 18:16the natural frequency is going to remain
- 18:18the same
- 18:19especially in a free free analysis so if
- 18:23you can see the image here
- 18:24there's a tuning fork which has uh
- 18:28for which an uh free free run has been
- 18:30uh given
- 18:32and it is go uh a customer has been
- 18:34given and it is go
- 18:35it is showing its small shape so you can
- 18:38see that the two prongs
- 18:41moving away from each other and that
- 18:43this is one of the fundamental
- 18:45frequency modes of the tuning fork
- 18:48coming to resonance so whenever any body
- 18:52is subjected to a forcing
- 18:54frequency and the body has a certain set
- 18:57of natural frequencies associated with
- 18:59it
- 18:59and the forcing frequency overlaps or
- 19:03matches the fundamental frequency of the
- 19:05body
- 19:06then the amplitude which is generated
- 19:09will be quite high
- 19:10and that phenomenon we call it as a
- 19:12resonance
- 19:13a resonance can be both advantageous and
- 19:15disadvantageous
- 19:17and with respect to frame and we're
- 19:20concepts or with respect to frame in
- 19:21which
- 19:23analysis i would say we are at a
- 19:24disadvantage whenever we talk about
- 19:26resonance
- 19:27so this is very important to
- 19:30understand and we also need to identify
- 19:33at what
- 19:34forcing functions and or what flow
- 19:35forcing frequencies the
- 19:37resonance is going to happen next coming
- 19:40to mode shape
- 19:41mode shape is nothing but the direction
- 19:44of displacement of the body
- 19:46and which is going to help us understand
- 19:48at a particular frequency
- 19:51in what direction the body is going to
- 19:53displace itself
- 19:54and that will really help the engineer
- 19:57to
- 19:58make corrections to the design and to
- 20:01also
- 20:03stiffen the body or make the body more
- 20:06durable
- 20:06so that the frequencies are not excited
- 20:09and the
- 20:10particular mode shape is not attained
- 20:13so the different types of mode shapes
- 20:16which are
- 20:17the different terminologies being rigid
- 20:19modes
- 20:20then you have the lateral modes you have
- 20:21the torsional modes
- 20:23you can have vertical mode there is
- 20:25something called as local and global
- 20:26modes
- 20:28which usually are applied to the whole
- 20:30body
- 20:31so global modes are the ones where you
- 20:34can say 85 to 90 percent of the body
- 20:36is having a displacement and local are
- 20:39usually where the only one one part of
- 20:41the body is going to have
- 20:42certain displacements that is which is
- 20:45usually observed at higher frequencies
- 20:46and
- 20:47global modes are of more interest at
- 20:49lower frequencies
- 20:51the formula for natural frequency
- 20:53mathematically would be given by
- 20:54omega n is equal to root k by m where
- 20:58k would be the stiffness of the body and
- 21:00m would be the mass of the body
- 21:02and omega n usually denotes the natural
- 21:04frequency
- 21:05and omega n would be the undamped
- 21:09natural frequency of the body so
- 21:12let us quickly try to understand uh what
- 21:16are these different mode shapes and how
- 21:17do they
- 21:18help us so if you can see here a plate
- 21:21has been subjected to
- 21:23a free free analysis model analysis and
- 21:26these are the different mode shapes
- 21:27which the plate will undergo at
- 21:29different
- 21:31natural frequencies and each of them if
- 21:34you plot each of them those are called
- 21:35as modes
- 21:36and the more shapes will help the
- 21:38engineer to understand the behavior of
- 21:40the system
- 21:40better so in a practical application let
- 21:44us say
- 21:44you can consider that if this is the
- 21:47frame of the car
- 21:48okay and this is the excitation of the
- 21:51first mode and let us say it has
- 21:53a certain frequency or single digit
- 21:55frequency of say
- 21:57four or five hertz and
- 22:00at this point above it you have you have
- 22:03located the
- 22:04seat of the driver so
- 22:07what does this mean is if the road
- 22:10frequency or say even the excitation
- 22:12frequency from the
- 22:13engines is going to match the frequency
- 22:17which is going to
- 22:18get transmitted to the frame and it is
- 22:21going to be off 5 hertz
- 22:23this is the amplitude the amplitude
- 22:25would be magnified to a greater extent
- 22:28and the person and the model or the body
- 22:32which is attached to it that is the seat
- 22:33would experience very heavy vibrations
- 22:36and that would cause great discomfort to
- 22:38the driver
- 22:39and this would be then the area of
- 22:41interest
- 22:42for the engineer to arrest the
- 22:44vibrations of this mode
- 22:45either move the vibrate either move the
- 22:47fundamental frequency to a lower grade
- 22:49or a higher
- 22:50band and then try to again rerun the
- 22:53analysis and see if
- 22:54the driver's seat is not is experiencing
- 22:57lower or moderate vibrations which are
- 22:58under the
- 23:00regulated guidelines
- 23:04yeah going further let's talk more about
- 23:08damping and what is done exactly in a
- 23:11eigen value analysis or a modal analysis
- 23:14so
- 23:15damping is nothing but dissipation of
- 23:18energy from a system
- 23:19and as discussed in the first slide
- 23:21itself it's going to play a
- 23:24major role in terms of attenuating the
- 23:28amplitude of vibration so if you can
- 23:32if you can see the image on the right
- 23:33side here
- 23:35there are three different dampings which
- 23:36are provided so the first one
- 23:40has a very light damping the second one
- 23:43has
- 23:43a critical damping and the third one has
- 23:46heavy dumping what do you mean by
- 23:48those three terms so if the first one
- 23:51by light damping it means that the
- 23:53system is free to vibrate
- 23:55okay and it is going to come to rest in
- 23:58a slow
- 23:58and a phased manner and if you can plot
- 24:01a graph of it
- 24:02this is how the behavior will be and it
- 24:04will come slowly to rest
- 24:06okay and critical damping is the one
- 24:09where
- 24:11the vibration will come to rest in the
- 24:13minimum or the shortest possible time
- 24:15and that is what you can see here that
- 24:17the vibration started
- 24:19and then it damped out and there is no
- 24:21hydration now there is no amplitude
- 24:23and the third one is heavily damped
- 24:27okay so here the
- 24:30rate at which it is going to come to
- 24:32zero is going to be very very slow
- 24:34so all the three have different set of
- 24:37applications in the industry
- 24:39uh one of the applications for the or
- 24:41the heavy dumping case which i can give
- 24:43is the
- 24:45the dampers which we use on the doors in
- 24:47offices so if you have seen them
- 24:49whenever you open the door and you leave
- 24:51it so it will come back
- 24:54slowly and it will respect to its
- 24:55original position and that is one of the
- 24:57examples of
- 24:59heavily damped system so critically
- 25:03damped systems uh
- 25:05the example which i can give would be
- 25:06those of
- 25:08missile systems wherein after the
- 25:09missile is shot or after the after the
- 25:11gunshot
- 25:12the system has to quickly recoil and
- 25:14come back to its original position
- 25:17otherwise imagine what would happen if
- 25:18it keeps on recoiling like this
- 25:21the soldiers will never be able to
- 25:22reload it back
- 25:24so different damping conditions help in
- 25:27arresting
- 25:28the amplitude of vibration to the
- 25:30desired level
- 25:31so there are different mathematical
- 25:33equations which are formed
- 25:35for the damping and how is damping going
- 25:38to
- 25:39play a role in analysis so what we saw
- 25:42in the previous slide was the
- 25:44natural frequency omega n and
- 25:48that was nothing but is equal to root of
- 25:50k by m
- 25:52but whenever you talk about damping
- 25:54damping is
- 25:55going to reduce the natural frequency to
- 25:58a certain level and that formula is
- 26:00given by
- 26:01the last one here the damping frequency
- 26:03is going to be
- 26:04omega natural frequency multiplied by
- 26:06root of 1 minus
- 26:07tau of tau square and what is tau tau is
- 26:10nothing but
- 26:11the damping factor divided by the
- 26:12critical damping
- 26:14and if you closely observe now critical
- 26:16damping is nothing but a function of
- 26:17constant multiplied by root of again
- 26:20mass
- 26:21and spring stiffness so
- 26:25they're all interrelated everything is
- 26:27going to revolve around
- 26:28the mass and stiffness of the body and
- 26:32damping as damping is going to play a
- 26:35important role
- 26:36as per this equation which is provided
- 26:39now coming down to eigenvalue analysis
- 26:42what what
- 26:43are the different types of analysis that
- 26:45can be carried out
- 26:47here in modal analysis you can carry out
- 26:49a free free analysis
- 26:51of the body so what do you mean by free
- 26:53free analysis here
- 26:54in a preview analysis there is no
- 26:55forcing function or no force involved
- 26:58you are just going to allow the body to
- 27:00freely vibrate
- 27:01and then you are you are going to figure
- 27:04out what are the natural frequencies of
- 27:05the system
- 27:06and what are the different mode shapes
- 27:07which are going to be exhibited by the
- 27:09system uh one of the main applications
- 27:12of a free free analysis especially in
- 27:14assembly setting is to understand
- 27:17the model integrity so let us say you
- 27:20have number of
- 27:21components of automated components
- 27:23connected to each other and if you run a
- 27:25free free analysis
- 27:27you should get six rigid modes for the
- 27:29complete
- 27:30component or complete body or the
- 27:32complete assembly of the vehicle
- 27:34if you get more than that it means that
- 27:36there is there is some mismatch
- 27:38in the way you have connected the
- 27:40different components with each other and
- 27:42that is going to make your complete
- 27:45whole of the analysis
- 27:46uh to be invalid so a free free run will
- 27:50usually give you
- 27:51the the six rigid modes and your seventh
- 27:54mode will be
- 27:55by rigid modes i mean that the frequency
- 27:57will be tending almost standing to zero
- 28:00and from the seventh mode onwards you
- 28:02will have a positive
- 28:03frequency value which will be termed as
- 28:04the first fundamental frequency of the
- 28:07system under test
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