 Welcome to today's lecture entitled, Flow Force Compensation and Spool Design. This is continuation of the lectures on electrohydrolytic valves. I have put this into a special topics, miscellaneous topics, because this is some detailed idea about how to design a spool and how to compensate the flow force. Now, it is already established that steady state flow force has substantial contribution towards the stroking force. If you look into this figure, which you have seen in earlier lecture that how the flow force is working on the spool. If we look into the spool, then let us consider the flow is coming like this and it is going out like this. This is full rectangular port. This means that there is a groove here and so if we consider the length of this orifice will be pi into this diameter and width is the opening, which is x v. Now, for this configuration, we know this flow will neither touch this wall nor touch this land. With some sufficient velocity or in other words at very low speed and some configuration, it may touch this land or this wall. Otherwise, it will make an angle to this path, which is theta and it is possible to predict this angle theoretically. Now, what is happening? If we consider this spool, on that spool, there is a force on this wall. This is the pressure force. Similarly, the same pressure force is in the opposite direction, in opposite face of another land. Then, we should consider, then these two will be balanced. But if we consider this jet, then definitely there is a force. There is a force because this oil is moving in this direction. If we follow the Newton's laws, then there will be force and that force if we resolve, this will have one in the lateral direction and another in the axial directions of this spool. Now, this force is called flow force. This flow force I mean at the steady state conditions, if we look into this flow force, direction of this force acting on the spool is in this direction. That means, it is trying to close this path. Now, while we are estimating what is the force required to move this spool, then this flow force having a substantial contribution towards this total force. Apart from the other this force, when this spool is accelerating, we have to consider the mass of that and if there is pressure imbalance anywhere, we have to consider that force also. So, total force is calculated in that way, but this force may be 30 percent, 50 percent of the total force. So, if we can reduce this force, definitely then control of this spool because we have to drive this spool with some force, with some actuator. That actuator, if it is a hydraulic actuator, then there is less problem, but if it is solenoid drive, that means electrical drive in that case to generate that force and control of that is difficult. So, better to reduce this force if we cannot eliminate. Now, this force, this F 1, which is the steady state flow force can be estimated like this, which we have shown earlier. Now, C D is the coefficient of discharge, C V is the velocity coefficient, A 0 is the orifice area, P 1 and P 2 is the pressure difference and cos theta is the jet angle, that derivation is shown earlier. Now, this is important I have already discussed, this force will try to close the port. Now, let us consider a large valve. Again it is 4-way, 4-way valve of spool diameter 25 millimeter. Once we say that spool diameter, this means this larger diameter, other is called stem. So, spool diameter means this is 25 millimeter. Stroke of 0.5 millimeter, that is the X V is 0.5 millimeter at pressure 7 megapascals, then the force, the stroking force may be estimated as large as 80 Newton. This considering the acceleration of this spool also. If this spool has constant velocity, then there is no force, but when this is accelerating or decelerating, there will be additional force. So, summing up all such force, it is 80 Newton. So, with hydro mechanical devices for stroking, handling such a force is not a problem. However, for electromechanical devices, it is nearly the upper limit of available generated force. Now, upper limit this term, although we have used, we can go for bigger solenoid, but looking into the size of this spool, normally the size of the drive solenoid should not be very big than the valve. So, in that case, whatever the solenoid size we can provide with these dimensions, we can see that this is almost, the 80 Newton is almost the upper limit of the available generated force. In designing direct drive valves, because this valve may be, this is the mains spool, may be direct drive, which are gaining popular for more reliability in some areas like an aircraft applicable, it becomes crucial. This means that sometimes, why sometimes in many operations instead of pilot operated valve, the direct drive valve is preferred, the response is better. Now, pilot operated valve, as I have mentioned, that is called two stage. So, that is like, it is like that, when there will be some signal to move that the spool will move the pilot stage. Now, through this pilot stage, this may look identical like spool valve, but small spool, then there will be a small force, which will be diverted to this, either this end or in the opposite end, which will generate this force, may be say 80 Newton or that level to move that spool. So, that can be done, but response of such valve is much less. So, in many cases, direct drive valve is required. Then for direct drive valve, we cannot use this or even if we use that hydraulic, again some controllability problem will be there. So, in that case, if we would like to use the solenoid, better to reduce this force. This is the only area, which we can reduce, that I have mentioned. Therefore, reaction of flow force is desired both for direct drive, single stage and also if in case of pilot operated, it is better, if you can reduce this force. Now, proposed methods of steady state flow force compensation by modifying this spool design are generally employed. So, one is that we can move this design of such spool as well as may be the sleeve, because this is not the direct body of the valve, usually this will be a sleeve. So, we can modify design to reduce such force. It increases the manufacturing cost, definitely if you want to, this is very simple thus just a step down. Instead of that, if you would like to modify this profile, naturally the manufacturing cost will be more and even increase non-linearity in controlling the force. Sometimes due to this curve or may be some profile, which I will show non-linearity will increase, but still reduction of this force is required. Now, so there are one can think of many methods, but all may not be acceptable due to the non-linearity in control or too much increase in the cost of manufacturing, but there are some popular design, which are accepted for flow force compensation. Now, one is that jet angle modification. Say for example, if we can make this angle 90 degree, that means straight directly it is going in the upward directions, say then definitely there will be no component in this directions and one can see this, you may ask that, but f 2 will be there, f 2 will be large, but f 2 is uniformly distributed over the circumference. If not uniformly distributed, it might be discrete, but at a certain angle equal amount of force. So, that we will cancel each other. So, we can make this theta 90 degree to make this flow force 0, but it is not possible by providing this group design. One way of making the jet angle 90 degree, not even not exactly 90 degree, but close to that is that instead of making the rectangular groove for port in the bulb sleeve, say this is the rectangular port, very common for that rectangular port, because this machining may not be that difficult. So, flow can go like this. So, this is the 90 degree, sorry, this is the jet angle. So, for full rectangular port, we cannot reduce this theta to 90 degree, reduce or may be we would say that to make it 90 degree, it is not possible. Then what we can do? We can provide the rectangular hole at different positions, may be 4 at a 90 degree, may be 6 at 60 degree or more, but making such rectangular hole on this sleeve is difficult. Say one is that electro hydraulic, sorry, that is non-conventional machining, electro discharge machining or something can be provided, but for mass scale, obviously it can be done with the use of broaching. How it is done? That first we will make an hole, circular hole by drilling. Say, if it is a 90 degree, just two cross hole we can provide there and then using a broaching tool we can make this. So, but it is seen that if we make such square hole, then this flow jet angle may be 90 degree, very close to that. So, and if we can make it is 90 degree, because cos theta will be 0 in that case and there will be no component in this axial directions. It is to be noted that the rectangular holes are better, but the circular holes in compensation of linearity also serve the purpose. This means that as I told, we make a circular hole, then we broach it. Instead of that we can have a circular hole there also, that will serve the purpose. That means that we will compensate the force. However, this will, there will be more linearity due to that. Now, larger spool and diameter is also another solution. What it is? We can make this land diameter is more, also the stem diameter as you see here is more than what is at the middle. Now, in that case what happens that due to, we have to make this groove depth and here also depth in such a way, we can see this angle is more than is normal angle. It is close to 90 degree and the flow force is reduced, not fully compensated, but it is reduced. But this is to increase the flow rate and thus the pressure drop in the opposite side of the flow force to have more force opposing the flow force. This means that usually larger diameter means there is a orifice opening because this length is more. So, for a same stroke orifice size will be more, there will be more flow and the pressure drop will be more in that case the pressure is compensated. It reduces the flow force to some extent. However, this is effective only for large flow valve valves. That means if we use such a, say for example, as I told the 25 millimeter diameter that may be around 25 liter per minute flow rate, very high flow rate. For that valve, it is 25 millimeter is a large dimension if we think of this valve design, spool design and therefore, it is possible to compensate to some extent this force. Moreover, such compensation named as pressure drop compensation, it is we call it large spool and diameter from the end diameters. This is from the spool configuration, but actual the mechanism is that pressure drop compensation is not effective for partial orifice pore to valve. So, that means if we use that rectangular ports, a few rectangular ports instead of full port, it will not work. Another method is that re-circulation land for compensation. Now, in that case, let us look in this valve what is happening. This spool end lands are made of specific profile. This profile is made like this. Now, also the sleeve groove is made like this, but still if you look into this, the port is the orifice is rectangular, full rectangular because orifice area is calculated this stroke length into pi into this diameter. So, this is rectangular, but instead of rectangular groove, this is somewhat spherical groove inside. Now, for that what we see that whatever flow is coming, due to this profile it is re-circulating. Once it starts re-circulating, then this although here is the jet angle, but due to this flow there is another force. So, that force counteract to each other and in that case the total flow forces reduces, but if you look into this, this is a obviously special design not as simple as this. For that what we will have? What we will have? Such lands re-circulate the flows before their way to final return path from the valve that I have discussed as a result and opposing force to the flow for flow is generated. Now, but this design again usually made for very large flow because for small spool giving such profile is difficult and also non-linearity arises and apart from the cost giving a special profile. Now, another possibility is that we can generate some negative force by designing the port accordingly. Now, for that what we find? So, we will have negative force port is designed providing specific spool end profiles and land length dimensions and the grooves in the sleeve. If we look into this in comparison to the earlier one, there it was a spherical instead of that it is stiff and inclined surface. Due to that as you look into this instead of flow moving in this directions, here it is of course moving in this directions. On the other hand it is moving in the from here to here it is moving in this directions and there is a re-circulating due to that the force is negative. It becomes it can be calculated design can be made such that flow force is negative that means this will try to open the valve and ultimately to move a spool in this direction total force will be less. Now, it gives better compensation in the expense of manufacturing cost. If we can use this type of port then it is better, but manufacturing cost is high. Now, these are the few methods which I have shown for specific amount of compensation care must be taken in design. Say if we this means that we can optimize something it is not always expected that the flow force will be 0. We can have some flow force and designing the drive that means designing the solenoid or any other drive and keeping the compensation force to a limit we can have some optimum design. Now, using such methods what type of compensation may be available this is described here. Say for example, that this is uncompensated that means if we take this type of valve directly then what we find that this flow force will increase with this valve stroke length. This is almost linear for this type of port. Now, if it is compensated a good compensated valve is something like this. Now, this say for example, negative port sometime it may become over compensated. Now, over compensated is having a difficulties because this due to this flow force in that case the it is trying to open. What we are giving the we are giving the force in the direction of the stroke, but if flow force over compensated mean flow force is trying to open the valve. That means if we keep the valve without any force due to the flow force if there is leakage that will try to move. So, controlling of over compensated valve is difficult. Non-linearity and the stability are two major criteria. Now non-linearity we understand say for example, this type of when it will come that we what we will find the force not always a constant. It is varying again not linearly varying then controlling of such force will be difficult. I mean it is non-linear control we have to introduce and stability is another point. Stability means that when we are moving the spool it has dynamics. Then we have to stop the spool at a particular position because we want a definite movement of the spool, but what happens at that condition starting at the starting point particularly and the stopping point it will try to vibrate. So, we have to consider about that part also. It might be sometimes that flow force is better from the control point of view of the stability. Now apart from this the linear force there is also lateral force on spool valve. Now as I have described if I consider this force z force then this is having two components F 1 and F 2. F 1 is the flow force which we cannot balance we have to control we have to add we have to control this force by the drive, but there is also the lateral force F 2, but for the full rectangular port or for the uniformly distributed small rectangular ports or may not be rectangular also uniformly distributed. If we look into this F 2 ideally they are equal and opposite. So, they are cancelling each other. So, there is no chance that there will be lateral force, but there may be lateral force due to several reason. One is that say for example, instead of this full rectangular port we have used say small holes discrete rectangular holes they are uniformly distributed. Let us consider that 90 degree, but again due to the manufacturing error there might have they are not exactly opposite to each other two are opposite, but they are say for example, centre through these holes through holes is not coinciding with the centre of the slips. So, in that case there will be an imbalance this is from that point of view again if we consider this cylinder the cylindrical surface that cylindrical surface may have several defects one is that they are not perfect the surface is not parallel to the axis some taper is there or the centre of this and centre of this pool is shifted sleeve centre of the sleeve and centre of this pool is shifted. So, in that case what will happen there will be imbalance in this force this F 2 will not be properly balanced in that case this pool will try to move towards one side and it will touch the sleeve and touching the sleeve means we need more force to control. So, lateral force we must consider while we are designing the such lateral force. However, this is we cannot estimate such lateral force because these are due to the manufacturing defect and estimating such manufacturing defects and calculation of lateral force is very difficult only experimentally we can find out and we can provide some methods so that this force is also reduced. Now, lateral components of the steady state flow forces may not be evenly distributed around the periphery of the port openings are not evenly distributed this is due to this reason which I have already explained. Secondly, the leakage past this pool land causes lateral force say suppose this is slightly moved in this direction then leakage flow started and that flow is having some lateral force that will further push this pool in one direction. Thirdly and most crucial one is that due to taper land and or sleeve bore bore may be also tapered non-parallel cylindrical surface with central axis etcetera and this these are due to the machining error a lateral force is generated. Now, how it is generated we will see in the next slide. Now, this this is the ideal one which I have shown. Now, let us consider this land is like this instead of the cylindrical perfection is taper of course, this is an enlarged view it will never be like this, but there may have slight taper even that will cause substantial lateral force. Now, such lateral forces are normally not balanced and push this pool to sleeve this is obvious. Now, due to tapered duct what will have say this first of all this pool axis is not matching with the bore axis there might have some suppose let us consider a small amount of lateral force generated due to some reason. After that what will find that if you imagine a ring over the periphery then here might be the smallest distance here may be the largest distance. So, in that case this path of different area or we say varying area over the periphery. In that case if we look into that in case of parallel duct if this duct is parallel then P 1 is P 2 is like that pressure variation will be like that. If it is a taper duct then pressure variation will be like this and that definitely you can see that instead of parallel duct this will generate a force. You see this due to this non-linearity and other side if you look into other side then this is also some parabolic shape, but we can see that there is a difference. Difference is due to that opening area this means that due to this there will be definitely a lateral force in this directions, but if it is perfectly parallel due to this flow there will be no lateral force. This also not only for spool this happens any piston cylinder when the spool or piston is moved additional force is required to overcome internal friction force caused by the lateral force that is obvious. Now, how to compensate this what we can do we can provide a groove here. Now, providing this groove what happens let us see making a groove over the spool land the piston and piston the lateral push force can be reduced to some extent. How if we now look into the pressure distribution due to this groove this distribution will be something like this due to this what is happening whatever the pressure here this is connected to other side. Say if there is no such groove, but keep in mind this passage what we are looking into much much smaller than what we are looking into this is real sense that will be capillary passage because these are the sleeve and this spool they are very close fit and the difference in diameter may be only 20, 25 microns. However, if we make a groove like this this groove is having a substantial depth may be 0.5 millimeter or something like that this means that this path is directly connected. So, throughout this groove the pressure will be same and due to that this pressure curve will be like this say without groove this is the curve pressure distribution and with groove this is the pressure distribution curve. If we look into the other side of this spool what is there this side also difference in this pressure distributions. Now, here much I mean larger difference as this division was more in that case a little less, but ultimately what is happening if we now estimate at least at that portion the four differences force is very less that means totally the effect is that lateral force is reduced. So, this is the method of compensating the lateral force that is why if you observe a spool you will find on the spool there are grooves. This providing such grooves has other problem or merits are there say within this groove sometimes the dark particles are accumulated that gives a problems later. The result resultant push force affecting the spool effect of compensatory pressure equalizing and centering groove etcetera are these grooves these grooves are called pressure equalizing groove sometime that pressure compensation groove etcetera. Now, in spool valve design one widths of the porting lands must match with the corresponding port widths in the sleeves. Now, importantly say say for example, it is a critical center valve in that case this width must be equal to width of this land. So, in that case and critical center valve is preferred due to the quick response time over the null point. However, maintaining such dimension is always difficult because not only that, but also we have to maintain the distance between say for example, from this point on the sleeve from this point to this point what is the distance same distance may have to measure or the proportional distance has to be measured from one inch of the land the same similar edge in the other side. So, maintaining such dimension is difficult. However, we have to maintain that for better performance. Distances between lands must match with the corresponding dimensions between groove in the sleeve and finally, close tolerances must be held between the spool land diameter and corresponding sleeve bore diameter and on squareness in the land and the port groove edge. Now, this is another important factor is that this edges say from the movement point of view you may think of that we can provide a sample here, we can provide a sample here, but if we provide a sample there immediately valve performance drastically falls. This is because drastically reduces this is because of the reason that in that case at the time of opening this jet angle will be different and response will be much poorer than if we can maintain the sharp edge maintaining the sharp edge at the opening there will be the turbulent flow, but that turbulent flow is preferred from the response point of view. However, if these edges are very sharp in that case there is a problem that due to this lateral force it may get stuck there. So, to avoid that there is a small the breaking of such edge is done that means you may find if it is measured a small not sample you can says round off. It is done at these corners. However, it is better to keep this edges as sharp as possible it all at is off as you can see point naught naught 2 5 millimeter look at the tolerance this point 2 5 millimeter is typical for a high performance servo valve. You see this to get this tolerance not only this dimension control, but also the surface finish is required. So, you can imagine how accurate machining is required. However, it may be plus minus naught naught 7 5 millimeter in general cases say little lower performance low performance valve or may be general purpose valve, but these are for very accurate position control or velocity control. Vulp coefficient such as flow gain and pressure sensitivity at null point depend on these tolerances. Now, choice of ways this is what is way say if I say that 4 by 3 dc valve that means 4 port 3 position or 3 wave valve. So, that is called way now no 3 4 ports 3 position that means 4 way 3 position valve first one is the number of port or way and second one is the position, but here the way means that port or on the how many directions the flow occurs. So, how to select or I would say how to select say that where it should be 4 way or 3 way or 2 way that is an important factor we have to according to requirements we have to make a choice of that. Now, general choice is 4 way valve because 4 way valve is in it is easy to think of the system as well as may be for from control of point of view. However, this with the number of ways the cost also increases. Now, in some specific applications 3 way valve is better one actuator line of course, with linear actuator only is one example of the way. So, 3 way valve application less number of tolerance is required in such applications say with the linear actuator and with 3 way valve the system becomes simple compact and relatively it is also controllable. So, where we are moving this actuator frequently in opposite directions then through a valve is a good choice. Another factor is the number of lands in the spool with respect to the number of ports that is ways in the script and their locations. You see this I will show that 4 way may have 3 lands may have 4 lands or may have 2 lands also. So, it can be made like this, but they have own merits and demerits which I shall discuss. Now, various configurations as shown are possible first let us consider the 2 land 4 way spool valve. This is 2 land, but there are 4 way. What are the 4 way? If you see that this is the supply flow, let us consider this is a critical centre or even if over that valve, but still when it is a neutral positions this it is totally closed it cannot go in any directions this flow. So, that means flow is being bypassed through the relief valve may be. Now, if you move in this directions then oil will be supplied through this and this will go one end of the actuator and from the other end this oil will return back to tank. If I move in the opposite directions it will be vice versa. So, this is one configuration. Now, if we look into the other this is 3 land 4 way spool valve. In that case what is happening here the oil is directly coming to inside the valve inside this this spool stem and it can move in either direction, but if we consider this valve. So, this when we are moving in this directions the oil is going like this and the return oil is going back through this path and if I move in the opposite direction this will be opposite. Now, there is a question that why we should go for this we can make this is a very simple, but we will see that these two is having some differences also merits and demerits. However the another valve is that the 2 land 3 way valve that is with the actuator, but before that we will also see another valve that is if we say this is again 4 way, but we have 4 land you can say apart from these 2 land there are another 2 land through which the oil is going back. So, starting from this one this is the 2 land this is 3 land this is 4 land, but all are 4 way. So, which one we should choose and why if we can do the same job with this valve why we should go for 4 land or 3 land. Each of such spool sleeve arrangements has merits and demerits over the other. Now, if we look into that such merits and demerits then first of all if we consider 2 land valve that is 2 land 4 way, this is shorter in length simpler in construction statically unbalanced as in 2 written lines resistances are not identical for full port the lands may locked into the sleeve groups. Say in this case say for critical centre it might happen you can see that this simply can go inside say this is a full rectangular port. Now, this sleeve height or with whatever we call it is exactly ideally is equal to the group width. So, in that case for full port simply this can go inside and also when it opens we can see the some unbalanced force. Now, demerits force in balance tend to open the valve further in this case. So, stability even null point is difficult. Now, if we consider the other one that means which is as having the 3 land moderate in length statically balanced this is statically balanced say if we look into this, this will not try to move this or that way because this path is closed and these are widely used. Now, if I consider the other one that is the last one that is the 4 land and 4 way then operationally same as 2 land valve with 2 additional end lands preventing leakage and providing better support. So, if I if we had to compare then we can compare this one with this in that case also this is open directly flow is coming to the school. So, this unbalance will be there, but as there is a land support there is no chance it will go into the groove and also there will be the leakage will be less. In that case this directly this is open to the I mean outside and the leakage has to depend only on this seal in that case this path and then sealing. So, operationally this has these 2 are same, but this has much better performance whereas, this is slightly different configurations. However, from close observations it reveals that all such 4 way valves shown in the illustrations are required same number of tolerances. That means tolerances means say this width so maintaining such width and this length here this length here in relation to this length all has to relate with close tolerances. So, that means if we think in terms of tolerances it will be same for both, but obviously this will be more expensive than this one. Now, next step is the choice of the type of valve center that means valve center means that is a closed center open center or critical center. For linear flow gain with optimum or 0 dead band a critical center valve is the obvious choice. Open center valves are preferred for high temperature applications allowing flow at neutral zone. You say if we prefer that there is a high temperature and that temperature to be cooled in that case it is better to keep this center open at null positions, but the problem is that for quick action that means if we want we give a stroke the response will be delayed due to that and in many cases it is not tolerable it is not acceptable, but high flow gain at null zone deteriorates the response at that zone which I have mentioned just now. The power loss at null due to the central flow is another disadvantage. The closed center valve has dead band no flow gain at null resulting in loss of control loop at null. The valve area gradient is the principal parameter in the null flow gain one of the major criteria in valve selection. Now, I have given some also practical data the it is 6.5 10 to the power minus 6 meter cube per second that is it is 6.5 cc and 3.2 3.5 into 10 to the power minus 2 that is 35 3.5 liter perhaps per second flow gain per millimeter of stroke is usual range. This pool diameter is selected accordingly. Erectrohydraulic servo valve have stroke ranging from 0.12 to 0.25 millimeter just imagine how small it is 0.25 millimeter one fourth of a millimeter may be very large stroke to have 45 liter per minute to 200 liter per minute. You just imagine the orifice size it even if rectangular port say diameter may be 10 to 25 millimeter and width 0.25 such a small hole, but flow is 45 to 200 liter per minute higher stroke range from 2.5 millimeter to 4 millimeter for large flow range amounting 400 liter per minute to 1000 liter per minute approximately in 3 stage valve is found that is 3 stage valve you see this pilot stage then one main stage that main stage is operating the another main stage you can see this is for very high flow. Usually the maximum valve stroke is kept below 5 percent of this pool diameter for full periphery rectangular port to satisfy the flow saturations and valve strength conditions. This we should say that flow saturations means that I would say that with the stroke the flow is increasing, but we have to consider that too much non-negrity should not be there. So, from that point of view the flow saturations and also the valve strength is the I would call the how much is the strength is required to move this spool parallel to the flow. So, this is the flow saturation. Due to several reasons area gradient is given more attention than stroke length in valve design. Now, area gradient is the what is called the pi d is called area gradient that is more important than the stroke length. That means that decides what should be the diameter of this pool and we have followed this mainly I would say that hydraulic control system by Merritt that book we have followed as well from to know we have for better knowledge you can follow also Martin and McLeod particularly the orifice sizes it is discussed in the last lecture. And also in general terms if you have more idea about the valves and their applications etcetera you can follow this Blackburn report book also. However, the more the more the more the more the more the more the more the more the more the more the more the more mostly I have consulted the Merritt's book hydraulic control system. Thank you.