1、Petroleum Science 2005 Vol.2 No.3Applications of the Finite Element Method to PDC Mold Design Zhou Sizhu(School of Mechanical Engineering,Yangtze University,Jingzhou,Hubei 434102,China)Received May 8,2005 Abstract:This paper describes the structure of the molds for making polycrystalline diamond com
2、pact(PDC)drilling bits.It represents the mold shapes by using the Finite Element technique,and compares the analytical results with available experimental data.Based on the results of Finite Element analysis,some areas of stress concentrations are determined,and modifications made,to the PDC(polycry
3、stalline diamond compact)mold.A displacement plot and several stress contour plots are presented.Techniques of the mold design are discussed.Key words:Finite Element Method，PDC，mold，design 1.Introduction Since their introduction in the early 1970s,PDC bits have almost completely replaced three-cone
4、bits for use in relatively soft,nonabrasive formations.They sometimes replace three-cone bits in harder or slower drilling intervals,if the section is uniform.It is fair to say,however,that drillers do not normally consider selecting a PDC bit when drilling goes on in harder formations or even in so
5、ft formations with infrequent hard streaks.The problem is that the service life of the bit is too short.A PDC bit consists of a crown,a shank and a pin.The crown contains all the structural components necessary to drill the formation(Gaddy,1999).The key component necessary to better durability of th
6、e bit is polycrystalline diamond compact(PDC)(Fig.1,from Gaddy,1999).Fig.1 Polycrystalline diamond compact The PDC manufacturer must use a procedure similar to a Die-cast or plastic-injection molding process used in toy and automobile industries.The PDC mold design is very important.The need for a h
7、igher pressure and temperature in the PDC manufacturing process today has led to very intricate designs of the mold(Fig.2).Fig.2 PDC mold（1-mold,2-steel belts）The exotic alloys and complex geometries used require sophisticated analytical methods to optimize mold design.Finite Element Analysis,based
8、on the principle of minimization of total potential energy,is becoming widely accepted as a powerful design tool.This technique is being successfully used to eliminate excess weight and to accurately predict stresses.2.Theory of three-dimensional Finite Element Analysis A brief summary of the theory
9、 follows.For more details refer to the appendix(Zienkiewicz,1971).The finite element method involves solving k=R (1)where all variables in brackets are matrices.k represent a n n matrix containing the stiffness constants for each variable in the system of n linear equations.is the nodal displacement
10、 matrix of all the nodes after dividing the PDC mold into finite Petroleum Science 200512 elements.The matrix R is the 1n column matrix representing the reactions or loads on the system.Solving the Eq.(1),the displacements and stresses can be obtained.The element-stiffness matrix of the three-dimens
11、ional element is that =zyxBDBkdddT (2)where x,y,z unified coordinates ,local coordinates J Jacobian matrix D elastic matrix B strain matrix 3.Finite element modeling Fig.2 shows the PDC mold without any modifications.Based on this configuration a three dimensional model is established.A complete gri
12、d is established(1/4)in Fig.3,and,for a better perspective,a hidden line plot is shown in Fig.4.In the Finite Element model,the three dimensional iso-parametric 8 nodal solid element is used(Flugg,1960;Zhou,1997;1998).The total number of elements is 180 corresponding to 308 nodes.Fig.4 Hidden line p
13、lot Fig.4 Hidden line plot of the mold 4.Stress analysis Finite Element Analysis combined with tests can give the pressure distribution on the internal wall and external surface of the PDC mold.Fig.5 shows the pressure distribution.Fig.5 The pressure distribution Figs.6 and 7 are the tangent stress
14、contours and radial stress contours.The maximum stress value is shown in the Fig 6.Fig.6 The tangent stress contours Fig.7 The radial stress contours Fig.3 Grid generated for the PDC mold(1/4)=111111TBdddJBDApplications of the Finite Element Method to PDC Mold Design Vol.2 No.3 13Fig.8 is a displace
15、ment plot of the PDC mold,and Fig.9 shows a hidden initial geometric plot.Fig.8 The displacement plot Fig.9 The hidden initial geometry plot Table 1 Encloses the analytical result and experimental data at key points.The location of the measured points is shown in Fig.10.Table 1 The analytical result
16、s and experimental data at key points Times 1 2 3 1 MPa(1)/4 MPa t MPa Error%1 732 220-75 444.63 2 720 190-132 435.34 3 724 168-154 435.53 4 728 179-188 438.41 438.47 404.63 7.72 Fig.10 The position of the point measured In the table t is the analytical main stress based on the Finite Element Analysis,1 the measured stress according to the experimental data.The equation of the measured stress can be expressed as where E and are the elastic coefficients of the steel used for the PDC Mold.E=597.8
