noc18-me60 Lec15

Welcome to the course on Smart Materials and Intelligent System Design and now we are coming into the realm of the final part in this course that is the intelligent systems and this is the round one talk on this intelligent systems. Now, what we have studied till the previous lecture is that we have talked about forward and reverse transformations related to SMA and we have talked about the constitutive models, Brinson model and SMA ware actuation. And if you consider the entire last module, we have devoted ourselves to the piezoelectric materials modeling okay and in fact, you can do the terfanol D magnetostrictive the same way by using induced train actuation model, induced train actuation and then we have also talked about if you have SMA which is not generally bonded like PZT and MS in a plate like way but it is more we fix wares of SMA you know and we attach it either on the top of our structure or inside the structure. So, however, after doing all these things, the question that will come is that fine through this we can control the shape of a beam, we have mostly shown you the controlling of the shape of a beam but can I make now a little more complex system out of it that is what brings us to today's lecture, where we will first talk about that how do we develop high bandwidth low strain what we call HVLS smart actuators, we will also talk about multi layering technique of piezoelectric materials because whenever we would like to use materials like piezoelectric which is now commercially available in the form of actuators and we will find that a major limitation that would come in its use is in terms of its you know the actuation strain. So, in order to enhance that generally the multi layer technique is used and there we will see that when you are doing the multi layering there is some issue, there are some issues related to series and parallel modeling and both for mechanical as well as electrical systems. Then we will talk about piezoelectric actuator modeling, we will talk about advantages of multi layered piezoelectric actuators and also how these multi layers are generally developed. So, at the end of the talk I think you will get an idea about how to develop a typical smart actuator. I would like to show you that how in some of these common smart actuators these kind of smart materials are used and you can develop the actuator out of it. Now if you look at the first simple example that is this thin disc buzzer which is used in every bicycle buzzer. So, if you are a little bit aware of your surroundings you will see this application very common and what you will be having here is that you can see the metal disc that the broad one and then on top of it there is a piezoelectric disc and in fact there is a shining layer on top of it which is the electrode actually. So this through this electrode you supply power to the piezoelectric disc and this piezoelectric disc by supplying variable current you can actually deform this piezoelectric disc axially as well as circumferentially and radially and once you do that then that vibration will generate actually vibration on this metallic disc. So, let us just see that how this whole thing would work. So here you can see that how does a buzzer work and you can see it here that you have these you know system that you are attaching to the power and that whole system has a piezoelectric element in it that is the piezo ceramic element that is there in the center and this is the plate which is going to vibrate because of the effect of the piezo ceramic element. So instead of a beam or a plate now it is a disc that you are vibrating and we are applying this current the alternating current and through that we can actually vibrate it. As we change the frequency of this current we can actually change the frequency of the buzzer. It is very simple system and that you know is used to form the simplest actuator that is the piezoelectric buzzer system. Now if you look at some of the other systems which is very common is like these digital single lens reflector system. So every SLR so to say camera if you look at it, it will be having an actuator inside something like this it would work as you can see that the simple actuator is actually creating an up and down motion of the system as an excitation system. So there also the piezoelectric actuator is integrated in the form of you know to build up an actuator which is used in your single lens reflector. Somewhat more you can actually increase the effect of it if you look at the amplified piezo actuator. So in this particular case you see how it works that how you can increase the effect the small amount of deformation that you get from a piezoelectric material how you can amplify it. As you can see that there is this core here which is a piezoelectric stack there are n number of this you know piezoelectric materials in the core. And it is connected to this oval shape and this is where is the output as you can see. And the resonance in this case you know is coming at 245 hertz. So you can vary it and you can design it accordingly. So you are basically applying the force along the center and along the semi minor axis you are actually getting this particular you know vibration of the system. So that is what is a amplified piezo actuator. Also I have earlier talked about Epson printers. The printers is a good place where you know this kind of technologies are applied. So if you look at it that how that is applied in the printing technology. So you can see that you know this is the piezo element for example as you are applying voltage you know in a pulse you are getting this motion in the system. So if you have two systems like a unimorph where one is active one is passive then you can get even bending in the system. So that is what you look for if there is a bending then that will push actually the ink and you see the inks are coming out and many of these inks together actually form the printing pattern. So you know now that how you know you can actually develop such kind of actuators using smart materials. This just gives us a glimpse of the whole thing. Now let us see that what are the issues here. Well the automotive electronics is full of such actuation systems. For example piezo fuel actuator or piezoelectric pressure sensors or piezo level sensors and air transducers and if you look at all of them they are not simply unimorph or bimorph or disks. They are something which is more complex than a simple system like that. So how this kind of simple piezoelectric actuators or rheological fluids are actually built up into a system to develop something like a fuel injection control or motion control that is very interesting. If you look at for example this particular piezoelectric fuel injector application this is the cut out of this actuation system. So essentially what it does is that it actually helps us to inject fuel into the system during combustion not just at a particular point but at multiple points and at multiple intensity level. So this gives you a fantastic control over the combustion process and you can see it from the cut out that this is the nozzle here so and there is a switch valve here, there is a coupler module and the piezo actuator is right here at the back end. So it is this is what is the muscle of the entire system. So if this gets shrinken then actually it pulls the switch valve and then from the nozzle the fuel gets sprayed into the system. So let us see there is a typical Bosch system you know how does it work. So this is a piezo injector system as you can see and you can see that you know how this is getting injected in a combustion system if you look at it. So this is where for example is the piezoelectric you know multilayered stack actuator you can see a quick flashing so that is what is that quick motion that is happening. The response time is what is the essence of it because with if you use you know something like say for example solenoid system you can also control this but that will be much slower. This is like one tenth of a millisecond whereas using solenoid it will be in the millisecond range. So you can very nicely control the fuel injection process which will make the combustion to be more efficient there will be less actually you can see that the whole thing is coming out. So there will be less actually you know pollution if you use this piezoelectric fuel injection system. Now if I compare between all these different actuators then you can see that pneumatic actuators give you a response of about 10 seconds level and the accuracy is in terms of degrees if it is motor that you can have plus minus 1 degree kind of accuracy. Hydraulic actuator again degrees level of accuracy response time is about 1 second faster than pneumatic actuator. Electromagnetic actuator likes stepper motors or solenoids etc. 0.1 second response time. Pneumatic actuator can go up to 0.0001 second of course the particular system that I have shown you has more delay because it has to work with so many other mechanical systems with it and that is the complete systems response that I told you. But on its own the piezoelectric actuator is enormously fast compared to that magnetostrictive actuator is little slow but still it is much better than hydraulic counterparts and ultrasonics is also of the same level. So this gives us an idea that as actuator how fast we are talking about. Now you want to go fast there must be some price you have to pay. So you know for anything if you want to excel you have to pay some prices. So in case of this smart material also there are some prices that you have to pay. So what are the issues that you know is important that you have to actually tackle in order to build such actuators. First of all a relatively high electric field is generally necessary to develop an equivalent system which is associated with a high voltage requirement. Say for example if I take a PZT block of height about 1 millimeter I need to apply a field of about 1 kilovolt which is very dangerous and considering the D33 of about 600 meter per picovolt I will get a strain which is about 6 into 10 to the power minus 4 which means something like 600 micron strain. So 600 micron strain. So that you know you can think of it that if you take suppose a meter of a system so 6 this is 600 into 10 to the power minus 6 and times if you take a meter of a particular rod then you are going to see it to be 600 into 10 to the power minus 3 you know meter kind of thing. So that means it will be something like 600 millimeter. So it is something which is and this is if you take it of course in a 10 cube meter level. So that means if you take 1000 meter which is about a kilometer actually. If you take a kilometer of this particular system and apply say a 1 kilovolt field and you are then going to see something like this type of a deflection in the system which is enormously low in the whole system. Now how we can actually get around this application of high voltage? Well how about if I go in terms of multilayering of this piezoelectric material? So suppose I have actually chopped as you have seen that that particular you know piezoelectric fuel injector have given us some clue that they have used blocks of such things. So suppose I make such small small disks and make you know n number of such disks. So in that case what will be the displacement that will be available from the system? Well each one of them individually if that same voltage is what I am using then it is not over the whole thickness but over that thickness divided by n. So that electric field intensity increases n times. That means the finer you are going to make the higher it will be. You can see that your displacement is directly proportional to the number of layers. So if you can cut your disk very very thin you are certainly going to get advantage out of it. Now cutting a thin piezoelectric disk is not very simple. I would later on tell you that this is what actually brings us to the domain of what you call MEMS systems to make it enormously thin something like 10 micron to 100 micron kind of thickness. You need special technologies to do that. Now if we consider this kind of a multi-layer actuator how does it really stand? So typically you consider a layer thickness which is about 50 micron meter let us say strain available is about 0.1 percent. So for a 100 millimeter stack actuator if you have 2000 such piezoelectric layers because each one is of 50 micron meter and your total thickness is 100 so it will come out to be about 2000 layers and you apply only 100 volt no more you are applying a kilo volt. You apply only 100 volt you are going to get you know a displacement of about 200 micron meter. So your hair is close to 100 micron meter of thickness. So double the hair you know kind of you can think of it. So that is what is the displacement. Blocking force however is quite high about 100 kgm and the lifetime is 10 to the power 11 cycles. Now this is if you can cut your layer of 50 micron the finer you will make the better it will be and if you can apply slightly higher voltage you will get even better deformation out of the system. Now once you are making such blocks there are many ways in which you can actually stack them. First of all if you stack them in a way in which it is like a spring system then what is the K equivalent of this system? The K equivalent would actually depend on each K let us say each one of them are having same mechanical compliance I have identically cut them then for n layers it will be K by n. So naturally what it tells us is that the more the spring in series the more flexible will be the system and the force that you will be getting is something like this where you have AC as the actuator constant all these constants that we have earlier talked about and stiffness of the component is K which you can find out for a disk very easily and then you have the V as the voltage which is applied across the component. So you can see that through this system you can achieve a very compliant you know mechanical model. Now if you want to make a stiff mechanical system then you do not keep these stacks in series. So a typically series stacking will be with respect to the loading something like this so you do not you should not do it rather you should keep them in parallel. So if this is the way in which you are actually you know applying this system in that case these are in parallel. So this kind of a system if you use compressive or tensile load here your K equivalent will be n times each of the K. So that means you are n number of times you are increasing the stiffness. So the more the stiffness you are getting this is higher stiffness in comparison to this one so let us say I call it as K series let us say I call it as KP. So definitely your you know KP will be much much higher than the K in series and then you know you are also gaining in terms of the voltage intensity because you know you would be able to give less voltage but you would be able to get actually a good you know force out of the system. So this is a stiff model where you want to get more force out of the system. Now if I put them electrically also because a piezoelectric material is a electromechanical system if I consider each piezoelectric material if piezoelectric block to be a parallel plate capacitor just like you consider the disc you know so each block as a parallel plate capacitor then of capacitance C then you have you can either keep them electrically connected in series or you can connect them in parallel. So if I connect them in series then we find that actually this is the you know kind of the voltage that we are getting that more the number of you know layers you are getting the voltage applied across the component which will be coming down so the you need lesser voltage in the system and on the other hand if you actually and this may in fact give you a faster response but if you actually put it in a parallel model you would see that this is the force that you will be getting in the system where it is the force is directly proportional to the voltage of the system. So thus you know you can actually get various types of you know combinations in order to design your actuator. Now for parallel modeling of the electrical system the voltage drop across element would be equal to the voltage drop across the stack and this is the force that you will be getting and for series modeling of both mechanical and electrical system both are in series, so you can have four combinations basically three combinations you can say that mechanical and electrical system so both are the first case that I have talked about case 1. So case 1 is both are parallel okay and case 2 is that series modeling so both are in series and case 3 could be that one in series and one in parallel. So you can see that corresponding to the second case where series modeling of both mechanical and electrical system this is what will be the force. So for this case with the typical value of AC, K and V, N varying from 10 to 100 if you get the plot P versus N keeping V constant you will get you know with respect to the number of springs the linear plot it actually tells us as you know too many springs in this parallel model of mechanical and series is not good in terms of the force point of view you need lesser but if you go for other systems for example here it is increasing parallel modeling of both mechanical and electrical system you are getting an increased value of the force as you are increasing the number of the spring. So you can make many such type of simulations of the system. Now if you you know look at the commercial piezoelectric actuator they actually exploit on it for example high mechanical compliance you would see this type of actuators okay that is available in the market. High mechanical stiffness you will get this group of actuators. Low response times which means that definitely the capacitors were in series you will get this type of you know actuators and high robustness to electrical disturbances which for which you need to have the capacitances in parallel you will get this type of actuators. So thus you know you can actually from the characteristics of the commercial actuators you would be knowing that what is there inbuilt in these multi-layer stacks. So what are the governing criteria for us? The piezoelectric actuators which show higher mechanical compliance higher mechanical compliance should be modeled as a series assembly of springs okay. So those with higher stiffness can be modeled as parallel assembly of springs. So this point we have to keep in our mind. In the electrical domain piezoelectric actuators having faster response time should be modeled with a series assembly of capacitors and for higher robustness should be modeled with a parallel circuit. So this is the final governing criteria that we are talking about. If you model such piezoelectric element in this case we made a two port model we call it that this top part is actually electric field displacement and this is the strain and here is the stress and the electric field that you are applying to the system. Then you can actually for a only longitudinal direction you can reduce it to this simple you know relationship you do not have to go to that big you know matrix relationship just these two relationships along the three direction that is along this direction the thickness direction this will give you the electric field displacement and the strain and then you know you can consider that plane strain as a you know stress assumption. So your S33 will be simply 1 over E p and the strain also you can find out. So using these simple relationship you can actually find out the relationship between force voltage and the electric field displacement okay and that you can actually use in terms of the piezoelectric stack you know and what is the force that it is giving out. So you can see that the force that you are coming getting in this system is actually related to the connectivity spring constant and the deflection you know at the actuator end and also the active displacement of the system. So this kind of system is typically like if you look at any intelligent system then it must be having actually an active part. So let us just show it say for example like this, this is an active part then there must be some mechanical compliance in the system so that is K connectivity and then you have a mechanism. This mechanism could be many you can think of a simple mechanism like this gripper okay so which is considered to be rigid. If you consider flexibility then this model will be little more difficult that is all. So this you know kind of a system where an actuator is connected with a spring and it is at this point where the output you are looking at then you know the force that you will be getting in the system will be like this where the connectivity you can simply model as you know kind of a mechanical axial members you know spring constant. So this is how you can actually model such a system for a real life actuator. Now if you do that and if you do that with a series modeling for both electrical and mechanical domains okay then we already know that the voltage wise you know we are doing a series modeling so Vst will be Nv okay. We also know that what is the force expression. Now using all these things together okay you know what is the delta Lst so you can actually get this force Fst that output force that this actuator will be actually giving to the system. So what can we see from here well we can see that say for example these number of actuating layer okay in this particular case when there is a series modeling the number of actuating layer is somewhat inversely proportional to the force that you are getting from the system. So for series modeling because it is a compliance driven model right. On the other hand you can see that the voltage that you are getting and if you actually for proportional to the voltage in this system. So you can also think of it that if I keep the same force I leave it as an exercise for you what will be the expression of Vst as a function of Fst and what are the parameters that actually you know would be important there and there you will see what will be the role of these you know multi-layered stacks. Now if you consider a case in which you are having series model for electrical and parallel modeling then your Vst is n times V, Fst is n times F. So again you can find out the expression for the total deflection in the system and if you use that you will be getting your Fst in this case which is like some you know parameter times Z, Z is that deflection at the actuator end and another parameter times Vst. So it is a somewhat different way in which you will be getting the force voltage relationship. So thus you can also develop I leave it as an exercise for you that how it will be for series electrical let us say and parallel model in the mechanical domain. Like you know parallel model if you consider in the electrical and series model in the mechanical domain then because you know parallel model in electrical so Vst is the V the voltage that you are applying so and then Fst is F and you can find out this deflection you will see this kind of a relationship in the system. Parallel model for both electrical and mechanical domains if you try to do you would see that once again with respect to this assumptions that you know you will be able to get Vst as V, Fst as nF and delta Lst as delta L because this is a parallel model you are going to get this force which is defined by two parameters alpha 4 and beta 4. So you can develop various such combinations based on your requirement. In fact we have carried out many optimization studies of such systems which you will see in the reference. So as a summary if your this side is mechanical system and this side is electrical system then you can see that for series what is the force expression okay and for parallel what will be the force expression and what is the force expression when it is mechanically in parallel electrically and series and when it is mechanically in parallel and electrically in parallel. You can see little little differences like from electrically parallel to series when you are changing series to parallel this you know 1 by n is not appearing anymore okay. So like that you can see here also there is a n multiplication that is happening in the system. So this will change the characteristic behavior of the system. Another important factor in this design issue is the resonating frequency. So for high frequency application this is important because the resonating frequency would vary with respect to the length, density and the compliance modulus. So for example for a 1 centimeter sample it will resonating frequency will come out somehow at about 100 kilohertz level. So this is important for ultrasonics or motor like applications. Now what are the advantages of this multilayer piezoelectric actuators? Well it requires less voltage, produces larger deformation or displacement and safer to use, high life cycle, lighter and more compact and it is a concurrent engineering because you are thinking of it from the mechanical standpoint also there is electrical standpoint and it is to be it is a product of a fascinating product of these two concurrent technology. There are two common techniques of developing multilayers. One is called cut and bond and another is called a tape casting technique. In cut and bond technique PZT wafers are cut typical thickness of 0.2 millimeter and then bound with intermittent metallic foils. So that is one way and another way is that you actually go for a tape casting where you first prepare the ceramic green sheets and print them with the electrodes and then you co-fire all these electrodes together. So that is you know another way of developing the multilayers. So if you look at the flow diagram cut and bond system you have the sintered bulk to begin with. So you already have the piezoelectric material as a bulk one then you cut it and you polish it you electrode it bond these things together to get a stacked actuator. On the other hand in tape casting you start with powder you do not have the bulk you mix this powder make a slurry then you slip cast it and you get a green sheet. Again you have to go for this part that is this part electroding and then lamination cutting firing and you get the device. So this is where we will put an end. In the next lecture we will learn about various electrode configurations that you can develop in this manner. What are the design issues, electrode configurations, we will touch also a little bit of pyroelectricity and later on we will talk about intelligent MEMS devices. Thank you.