Analysis And Calculation About Axial Load Of Rotate Shoulder Connection

A study on axial load distributing law is a basis that analyzing outof action law of Rotate Shoulder Connection. Firstly, a standpoint is putforward about axial acting load and remains of prestrain force overlapeach other in this paper. By using the method of mathematical analysisand on the basis of prestrain force, the paper not only further analyzesthe distribution differences between pin and box under the condition ofaxial operating load, but also establishes the mathematical model forcompatibility relationship of deformation. Therefore the mathematicalvalue of distribution function of axial load is obtained by the methodsof mathematical analysis. At last, the characteristics of the distributionof the axial load are given as below.A Additivity between axial acting load and remain of prestrainforce each otherB Transmission by equal valueC Distribution differences between pin and boxD Reserve specialty of the axial load1. Prestrain force and critical axial loadWhen the operating load Fw is given to the thread, the shoulderperstrain force decreases to F'. The box is lengthened by the pullingforce while the pin's deformations can be divided into two types: one isthe lengthened deformation of operating load; the other is the decreaseddeformation of prestrain. An coordinating relationship among the abovethree can be derivate as belowThe axial load of the pin root isThe critical axial load of the gearing torque T2. The endurance of the thread under the axial operating load The relation of the start stop of the length of thread gearing is asbelowThe distribution of the axial operating load F is uneven betweenpin and box. However, on any position z within the length of the threadgearing, the resultant force of the axial force given to the pin and box isalwaysFw .The axial load Fw on any position of the thread gearing is equallytransmitted.The axial load is composed by the axial operating load andperstrain within the different ranges. The box and pin share the loadaccording to the proportion on the same section.The increment of the load acting on the shoulder of pin is less thanaxial operating load while the axial load of thread less than load limit.At the same time, the stress level of box decreases at the shoulder, butincreases at the small. The stress level goes to equality within range asthe redistribution of load. But the increase of the stress level is limited.After the axial load have been acted, as prestrain force, the loadacting on the shoulder of pin increases toClamping force acting on the shoulder of box decreases to F' F'=F-Fw Ab Ab +Ap Clamping force acting on the shoulder of pin increases form 0 toFw This means that the axial load acting on the shoulder of pin Apincreases by Ab +Ap ×100% only while the axial load Fw has beentransmitted by the fastened connection, the rest Ab Ab +Ap ×100% hasbeen counteracted by prestrain force.3. Distribution of Axial Operating Load in length of thread gearing Set Fbw(z) as the distribution load at the location z in length L ofbox Fw , similarly, set Fpw(z) as the distribution load at the location zin length L of box Fw , then Fbw(z)+Fpw(z) = Fw The axial stress σp and the axial stretching δpw are processedwhen the axial load Fpw(z) is functioned on the body of pin. There isthe compatibility condition of deformation between the total deflectionδtp(z) and δtb(z) on the teeth of pin and box is: δpw -δbw = ?? δtb(z)+δtp(z) ?? -?? δtb(0)+δtp(0) ?? ? ? ? ? deformation of the screw thread body δpw 4 -δbw = πE? ?z? ?? 1 1 + Fpw(z)dz?0 d 2 1p -id2 od2 -d21 b???deformation of the screw thread teeth ??? dFpw(z) δtb(z)+δtp(z) ?? -?? δtb(0)+δtp(0) ?? =??λp -λb? ? ? ? ? dz-λbFw so compatibility equation of deformation 4 πE?z???? 1 1 1? + Fpw(z) -Fw dz?0 ??d21 p-id2 od2 -d21b ??? od2 -d21b ??? dFpw(z) =??λp -λb? ? dz -λbFw Differentiate about z, equation's left hand is 4 1 1 1 πE ??????d1 + Fpw(z) -Fw 2 2 p -id2 od2 -d1 b??? od2 -d21 b ??? Equation's right hand is d2Fpw(z) dFpw(z) ?λp -λb? ? ' '? -λbFw ' ? dz2 +???λp -λb ?? dz Then load distributing Fw equation in joggle length d2Fpw(z) dFpw(z) + a(z) + b(z)Fpw(z) +c(z)=0 dz2 dz Boundary condition expressionz = 0,Fpw(0) = 0 z = L,Fpw(L) = Fw4. Load distribution of residual prestrain force The law of distribution load in joggle length of residual prestrainforce is the same, which means, compatibility condition of deformationhas no change. We should evaluate distribution load according to themethod of prestrain force. The boundary condition is: z = 0,F(0) = 0 z = L,F(L) =F'=F-Fw Ab Ab +Ap Then we come into possession of the distribution load F(z) ofresidual prestrain force of pin. Similarly, -F(z) of box.5. relation between two loads They are two different loads between the axial operating load andthe residual prestrain force. The axial operating load is an operatingload which acts on the drill-stem overall, and which be transmitted intantamount mode through random section of the pin and box. With thepin and box, the load distribution between the different sections of thethread is different in number but the same in directions. But the residualprestrain force which acts on the shoulder of thread are the same innumber but different in directions. The decisive range is additivity injoggle length of thread, the difference of load distribution is the resultof their additivity The load distribution of the pin Fp(z) = Fpw(z) +F (z) The load distribution of the box Fb(z) = Fbw(z) -F (z)6. Effect on the axial load by axial operating load With the action of axial operating load, as prestrain force F'>0andFw≤Fwc, shoulder of pin and box keep track, and as F'=0 , means...