Design Procedure for Screw Jack – Power Screws – Design of Machine


Hello friends here in this video we will see the design procedure for a Screw Jack and for that purpose here we have a diagram now screw jack is a machine which we call it a simple machine which is used to lift heavy loads by applying comparatively small amount of efforts basically when I talk about screw jack it is used to lift vehicles now here as we can see in the diagram W indicates the load which is kept on this screw jack and where this load is kept that part is called as Cup then we have the most important part of the screw jack which is called as the screw spindle which is here the screw spindle is in between whenever we have a screw spindle that screw will rotate inside a nut so here we have a nut and screw spindle they are in contact next we have a handle which we can rotate then we have the body here this is the outer body of the screw jack along with the base next there is head of the screw jack which is attached to the cup so these are some of the principal or important parts of a screw jack now when we are talking about the design of a screw jack in that case the most important part which is to be designed or you can say that is the heart of the screw jack it is the screw spindle so while designing the screw jack the most important part screw spindle because it is it carries the load directly the load which we are keeping on the screw jack for example it can be a car which is lifted with the help of a screw jack so the entire weight of the car will be acting on this screw spindle next here we can see some of the dimensions I just explained some of them like for example here there is DC and do DC indicates the core diameter or the minimum diameter of the screw do indicates the outer diameter of the screw next here we have capital D which we can take it as the diameter of handle D 1 capital D 1 it is the diameter of you can say outer diameter of nut next D 2 it is the diameter of nut collar D 3 it is the outer diameter of head or you can say the bigger diameter D 4 is the small diameter for the head then we have D 5 which is the diameter on the outside for the body d 6 is the internal diameter at the base and D 7 is the external diameter at the base so these are some of the diameters then capital H it indicates the height of head small H indicates the height of nut as it is visible from the diagram then we have T 1 as the thickness of nut collar t 2 as the thickness of base or we can say the thickness of the body next if the thickness of base is T 2 the thickness of body is taken as T 3 then here we have lifting height lifting height indicates the height of the screw in its maximum upward position that is by how much amount it will lift and lifting height is equal to the amount by which the load would be lifted to its maximum position then we have the entire height of the body of the screw jack which is called as the body height here we have handle length I can denote it by L so these are some of the description of the parts of a screw jack now let us get started with the design for the screw jack you’re the heading is design procedure of is creo jack now in the design procedure of screw jack I’ll divide it into number of steps the first step is step number one it is called as design of screw spindle now if I look at the diagram of a screw jack then suppose it is lifted completely and then the load is acting over the screw jack as we can see the bottom end of the screw jack is fixed and here the load is applied so the kind of loading which the screw is subjected to that would be called as compressive load because on that screw the load which is kept it will try to compress this screw spindle so for the design of screw spindle I will say that considering screw spindle under compression now when I am considering the screw spindle and a compression first I will draw the frailing area where it will fail Here I am drawing the section now this I will term it as the diameter here I’ll denote it as BC called as a Cole diameter now why we are considering Cole diameter here since we are having a screw spindle I will just draw the profile of a screw so that I can explain it in a better way here I am drawing the profile of a screw now when we have a screw as it is clear from this diagram that four screw we do not have the diameter constant at one end that is here we are having a bigger value of diameter this is called as do the outer diameter and here we have the minimum diameter this is called as a coal diameter DC so failure will always start at the minimum diameter now if I compare out of do and DC DC is the minimum diameter and when this screw is subjected to compression from both the sides there is compressive load because of this compressive load there are chances of this screw to break along its minimum diameter DC it will break here so now you’re considering the screw spindle under compression it will fail along its thread at the minimum diameter which is DC so this is the resisting area so now I’ll write it down there for resisting area capital a that will be equal to it is a circular area PI by 4 into DC square where DC is a minimum diameter of the screw thread so I will write down there for compressive strength because I am considering the failure under compression so compressive strength of screw spindle now strength as we know it is written in the form of load is equal to stress into area here I am getting stress as compressive so Sigma see area is capital a so therefore the strength equation W is equal to area PI by 4 DC square multiplied by Sigma C this I’ll keep it as equation number one this equation gives us the load carrying capacity of a screw jack that is if we know how much is the coal diameter of a screw spindle if we know the value of crash compressive stress then we can calculate how much is the load carrying capacity for the screw jack and similarly if we know the value of load if we know Sigma C we can calculate the coal diameter so I will say that therefore from equation number one DC can be calculated so this was considering the spindle or screw spindle under compression now after this once I have considered it in the first step now as we can see because of compression this screw spindle can fail along the coal diameter minimum diameter at the same time this screw is subjected to a torque because we are holding this handle and then we are rotating it so when we rotate this handle and at the same time load is kept so here this crew spindle is subjected to torsional shear stress because of the rotation of handle so here I will say that considering torsional shear stress for screw spindle now when I am considering the torsional shear stress first crow spindle I know the formula of torsion I will say that there for t1 I’ll write it as T 1 is equal to PI by 16 DC cube into tau Here I am having this equation this equation I will call it as the second equation and this has come from strength criteria the strength criteria which we are using for the design of shafts because we can consider the screw spindle as a rotating shaft and when it rotates there are chances of torsional shearing so here this equation indicates the torsional shear stress tau I write down therefore tau will be equal to 16 into T 1 upon PI into DC cube now your from this equation we can get the value of shear stress but we should also note even here so I will say that where T 1 your T 1 is equal to torque required to rotate the screw and this torque required to rotate the screw it can be calculated by using the formula t1 is equal to W into tan alpha plus Phi multiplied by D by 2 so from this formula we can get t1 once we know t1 we can easily calculate the value of shear stress now one more important concept here is that since we can see from the diagram that this screw jack is subjected to compressive load from the top load is kept and then the screw is rotated with the handle so there are two stresses which are acting at the same time on this screw and those stresses are at first because of the load there is compressive stress and because of the rotation of handle there is torsional shear stress so whenever a particular member or any screw like in this figure it is subjected to two stresses at that at the same time so we can write it as considering maximum sheer stress theory now from this theory we can write it as tau max is equal to half of under root Sigma C whole square plus 4 into tau square because here as the screw is subjected to two kinds of stresses at the same time so we can get this maximum shear stress from maximum shear stress theory and similarly I can write down considering maximum normal stress theory in this we can write down Sigma C max that is maximum compressive stress will be equal to half into bracket Sigma C plus under root Sigma C square plus 4 into tau square so now you’re in step number one we have reached at this stage where we are getting the maximum shear stress tau Max and we are getting the maximum normal stress that is Sigma C max which is called as maximum compressive stress so we can check these values from this formula for the screw spindle and here with this we have completed the step number one that is the design of screw spindle next as we see into this screw jack after screw spindle the next part which we have to design is the nut now here we are having this nut we need to design it so I will write down here that as step number second it is design of nut now in the design of night the first consideration is considering bearing failure of night when we are considering the berry bearing failure here I’ll draw the diagram of the resisting area this is the area which is subjected to bearing outer diameter is do inner diameter is DC now how this bearing failure takes place since screw and nut they are in contact so there is there are chances when we see screw in net they are in which they are in contact so there are chances of rubbing between the screwin net because of the compressive load and because of rotation there is continuous continuous rubbing off screwin net and because of that rubbing what happens is that the portion of the nut it can crush like this so here if I can explain it in a more simplified manner here I’ll draw the profile and explain this is the screw profile which I am drawing screw and nut now this portion is the nut and here we have a screw so when both are in contact there are chances of rubbing of the portion here that is metal powders would be formed because of this bearing action so the area which is resisting bearing that I have drawn here this is the resisting area so therefore resisting area capital a it is equal to area of a hollow circle PI by 4 d square minus D C square and now I can say that therefore bearing strength of nut it is equal it is w is equal to area multiplied by bearing pressure so therefore W is equal to here the area is I will write it down PI by 4 into d o square minus DC square now this is the area of contact between one pair of screw and nut like this we have n number of pairs so I will write down it is into small n multiplied by bearing pressure now after this I can say that therefore from above equation small N and what is small n it is number of threads in contact so from the equation here I can get the number of threads in contact it can be calculated and once I know the number of threads in contact here I can even calculate the height of not here which is small H so I can say that therefore height of nut small H is equal to n multiplied by P where this P indicates pitch of screw thread and this pitch will be in terms of mm so now once we have designed the coal diameter of the nut we have designed the outer diameter for the nut and we have designed the height of the nut so this was considering bearing now the second consideration is considering tensile failure of 90 this design procedure is quite lengthy considering tensile failure of nut now when we are considering tensile failure as we can see from the diagram of the nut which I have drawn here here this is the maximum diameter called as do and nut will fail along this maximum diameter that is along do so what happens is that when the compressive load is acting this screw spindle is in contact with the nut so there are chances of this screw spindle to stretch stretch the nut and then the nut will be failing because of tension so here I will say that considering tensile failure of nut the area which is resisting tension that area I am drawing here next considering tensile failure of note here I’ll write the outer diameter as this is d1 and here the failing area is this section Here I am marking this diameter it is d-ohh which is the outer diameter or we can say major diameter and that will fail along this diameter so here is the resisting area so considering tensile failure of nut resisting area capital a that is equal to PI by 4 D 1 square minus d square that is area of this hollow circle therefore tensile strength of nut it is w is equal to area multiplied by tensile stress therefore W is equal to area is PI by 4 into d1 square – do square into Sigma T therefore we can say that from this equation d 1 that is the outer diameter for naught here as we can see the diagram this d1 can be calculated so here we complete the second point in step number 2 that is the design of nut here what are the things we have designed I will just give an overview in step number 2 we have designed the height of nut and we have designed this outer diameter of that d1 now next here I will be designing the thickness of this nut collar and for that I will consider the shearing of nut collar the next consideration is considering sheering failure of nut collar now there are chances that this nut which is having outer diameter d1 when the load is applied screw will pull this end and what can happen is the nut can shear at this Junction so here I’ll write the shearing area that will be PI into D 1 which is the circumference at this location multiplied by thickness T 1 that gives us the shearing area so therefore shearing area capital A it is equal to PI into D 1 multiplied by T 1 and therefore shearing strength of night that is w is equal to area x shear stress tau therefore W is equal to area is PI into D 1 multiplied by T 1 into tau so now I can say that from this equation T 1 that is the thickness of nut column it can be calculated next upsetter considering the shear failure of the nut collar there are chances that even the thread between the screw and nut as they are in contact so this thread they can share of for the nuts so I will say that first I’d considered sharing failure of nut collar now I’ll write down considering sheering failure for threads in not now when I am considering the sharing failure I’ll draw the diagram here and explain I am growing the profile of the nut it is in contact with the screw Here I am drawing the profile of screw and thread the notes which are in contact now as we can see in this diagram here this is the nut and here we have screw so there are chances that when the load is applied there can be shearing of this nut along its major diameter it can failure which is called as do so the failing area is I’ll write down since resisting area it is also called as the failing area that will be equal to PI do which is the circumference multiplied by T which is the thickness of threads and therefore I can say that from this shearing strength of night now that strength is equal to area multiplied by shear stress because we want shearing strength so therefore W is equal to area is PI do into T multiplied by tau where T is equal to thickness of each thread and it is taken as pitch by two distance in terms of mm so here I will say that from this equation T which is the thickness of thread can be calculated or if we know the thickness of thread then we can check the value of shear stress from this equation after designing the nut the third component that we will design in step number three that is the handle so your step number three in which we have design of handle now when we are designing the handle at that time we should know how much is the torque torque means torsion or we can say the quantity which causes the rotation so how much is the rotation effect produced so I will see that in the design of handle the first step is total torque applied at the handle so that total torque applied at the handle it will be capital T is equal to t1 plus t2 I’ll give this as equation capital a so here I’ll mention what are these terms where t1 is the torque required to rotate the screw and t2 it is the torque required to overcome friction between not collar or year I can say that we are overcoming the friction since we are placing this cup because of this cup here as we can see there is some bearing area so we need to overcome the friction here because cup is placed on top of the head to prevent the rotation of the load and when we are applying the torque here some value goes into the rotation of the screw and some amount of torque is required to avoid the rotation of load here so we are overcoming the torque here which is T 2 so it is to overcome friction between cup and head so here I will mention the values that there for T 1 torque required to rotate the screw the formula is w into tan alpha plus Phi multiplied by D by 2 where D is the mean diameter next T 2 it is equal to MU W R M which is the torque required to overcome friction between cup and head so R M I’ll write it down here where all the values I will denoted where mu here I have written it is mu w RM I’ll denote it by mu 1 to differentiate between the coefficient of friction because mu will be the coefficient of friction between screw and nut mu 1 will be the coefficient of friction between cup and head at the surface so coefficient of friction have two different values so your mu1 is equal to coefficient of friction between cup and head next w as we know it is the load which is kept on Scrooge AK now the term R suffix M it is called as mean radius and for RM we have two different values so I will write down the first value R M is equal to here d4 is the minimum diameter and d3 is the maximum diameter so from the centre if I take the distance R 3 B comes from here Taylor R 3 is the major diameter and r4 will be the smaller diameter so this section is hollow so for that I will explain it here this is the bearing area your outer radius that is our three inner radius is our 4 so our M is equal to it is our 3 cube minus r4 cube upon our 3 square minus r4 square so this formula which I have written it is by uniform pressure theory and in this same formula after the writing this I will have to write it as RM multiplying it by 2 by 3 and this is the complete formula so now after I have written the formula by uniform pressure theory next I’ll write the formula by uniform layer theory and that will be R 1 plus R 2 by 2 or here R 1 is nothing but R 3 and R 2 is nothing but R 4 so it is R 3 plus R 4 by 2 and that is by uniform wear theory so once I have written both these formulae I can easily calculate the value of torque T 2 and once T 1 T 2 are known we can put them in equation number 1 and get the value of T so now after this since we are designing the handle I can say that therefore total torque after getting the value of total torque it can be written as P multiplied by L where P indicates the effort capital P it is the effort applied at the handle and a normal person can apply a load of around 300 to 400 Newton by his hand so here I’ll take this value of P it can be from 300 Newton to 400 Newton next once I know the value of P and total torque I can say that therefore capital L which is the length of handle it will be T upon P so in this equation I will say that from this equation L can be calculated that is here we can get the length of handle next after getting the length of handle I can say that therefore bending moment is given by the formula of bending moment is M is equal to PI by 32 D cube into Sigma B and from this bending moment equation here we can get from this equation diameter of handle which is d it can be calculated so your in this step number three we have designed the length of handle and the diameter of handle this diameter we have designed denoted by small D so here we complete the step number three design of handles now the last step which is there in case of the design of screw jack now we will this we will write the value of load at which this screw will try to buckle which is called as a critical load C what is the meaning of buckle is that when the screw is lifted to its topmost position that is about this entire lifting height here in the diagram we can see the screw jack in the bottom most position now when it is in the topmost position this end of this end of the nut here will be attached here and this screw would be entirely lifted so when it is completely lifted and when the load is applied over the screw then it is a case of buckling the screw will buckle in the lateral direction so for that I’ll write down in step number four checking buckling of screw spindle now in this case I’ll write down therefore buckling load or crippling load is given by here I have the formula that buckling load or I can say it is crippling load it is W suffix ER and that is AC into Sigma Y 1 minus Sigma Y upon 4 C PI square into capital e multiplied by effective length upon K square this is the formula of buckling load here I will say that I will define the terms where a suffix C AC is the cross sectional area of screw at core diameter unit will be in terms of mm square Sigma Y it is called as yield stress next L II it is called as effective length of screw spindle see it is called as an fixity coefficient and its value is 0.25 then K it is called as radius of gyration and radius of gyration it can be written as root of moment of inertia upon area so from this value here we can get from this formula the value of critical load and that critical load is the load when which is applied to the screw jack this crew spindle will buckle and the meaning of buckle is that this crew spindle will bend in the lateral direction forming a curve so that condition needs to be avoided so here once we know this critical load we will divide it by factor of safety and get a safe load which would be the design load for the screw jack so here in this video in four simple steps we have seen how to design a screw jack starting with the screw spindle then we had gone on to the nut after that we had designed the handle and at last we had designed the critical load which the screw jack can carry I hope everything is understood in this video

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