Application of Engineering Principles - Coursework Example

a) Mud cleaners are used to remove particles of drilled solids that are suspended in the barite and fluid suspension. Usually a combination of centrifugal force by hydrocyclones, and vibratory screens are used in combination. Linear motion mud cleaners have linear motion vibrating screens. A schematic of a mud cleaner is shown in Figure 1. Figure 1. Mud Cleaner As seen from the figure, the fluid with the suspended drilled solid particles that need to be removed is fed through the inlet. It passes through a rotating hydrocyclone. Hydrocyclone is cylindrical on the upper side and conical in the lower side. Due to centrifugal force, clean mud overflows, and the waste particles (together with some amount of fluid) enters the mesh through the bottom outlet of the hydrocyclone. The vibrating mesh further sieves the unwanted particles out, leaving only the pure mud suspension to pass through it. Hence pure mud suspension is obtained. The efficiency of the mud cleaner and the range of sizes of the waste particles that may be sieved out, depends on many factors like cone angle, diameter of the inlet, diameter of overflow pipe, diameter of the bottom outlet of hydrocyclone, the fineness of the mesh, vibration characteristics of the mesh, viscosity and density of the fluid, density and size of the waste particles etc. b) The three components where angular motion is involved are: hydrocyclone, pump, drill pipe. Hydrocyclone Here, the centrifugal force that is a characteristic of a system having angular motion is utilized to separate coarser and finer suspended particles. In hydrocyclones, viscous forces are also produced by the angular motion. Because of the difference in densities of the suspended waste particles and the fluid, there will be difference in the centrifugal forces each of these subjected to. This difference in the centrifugal force is responsible for the separation of coarser waste particles and finer (required) particles that are suspended in the fluid. Motor and pump A pump is needed to circulate the liquid in the drilling pipe. A motor is needed for the pump. Usually, both the motor and pump have rotating parts as their core components. Design of both motor and pump should stress on the angular motion of these components; the balancing has to be done properly, bearings have to be selected properly, lubrication should be taken care of, centrifugal forces (and centrifugal stresses) should be considered while designing the components, blade reactions have to be considered for pumps. Drill pipe Many a times drill pipes rotate and the rotation is greatly responsible for the cutting. But sometimes, even when the rotation of the drill pipe is not the main force behind drilling, a slight rotation of the drilling pipe is necessary for a successful drilling. As with any rotating components (which have angular motion), balancing has to be considered while designing drilling pipes. In addition, buckling should also be taken note of. c) Velocity distribution in a drill pipe during the first stage is given by (cm/s) (1) Differentiating (1); The acceleration, (2) (i) When acceleration is minimum, Hence, from (2), (3) Solving (3), When acceleration is minimum, Hence, Hence, (ii) Assuming that the acceleration is proportional to the velocity during the whole period; Final velocity in a further 35 second = Final velocity after (20 + 35) second = Final velocity after 55 second = (12%/20)*55 = 33% increase in the velocity (iii) To get the displacement profile for the first stage, integrating (1); Displacement (4) where c is a constant The displacement profile is a fourth order polynomial during the first stage. The displacement profile may be obtained by plotting (4) using MATLAB. The profile looks similar to Figure 2. Figure 2. Displacement Profile for the First Stage To get the velocity profile for the second stage, acceleration proportional to velocity during the whole period of the second stage implies that the velocity variation during this stage is exponential. The profile looks similar to Figure 3. Figure 3. Velocity Profile for the Second Stage 2. a) Difference between circular motion and angular motion: (i) Circular motion refers to a body moving in a circular path. Angular motion refers to a body rotating about an axis. (ii) In circular motion, most of the times, refers to particles. Angular motion, most of the times, refers to rigid bodies. (iii) When a rigid body undergoes angular motion about a fixed axis, all of its particles undergo circular motion. (iv) A particle on a rigid body under constant angular velocity is subjected to acceleration. (v) Circular motion considers just the centre of mass of the body under motion. Angular motion considers every particle on the body under motion. b) Length of a drill pipe is very large compared to its diameter. Hence the pipes are vulnerable to buckling. Drilling pipes should exert compressive forces and they are also subjected to torsion. Torsion and buckling occurring together is very dangerous and can cause very early fatigue failure. Hence to reduce or eliminate compressive stresses in drilling pipes, a very heavy component called drill collar is screwed onto the bottom of the drill pipe assembly just above the bit. It provides the necessary weight and prevents buckling of drill pipes above them. Also, drill collars concentrate the weight on the rotating bit. The drill pipe above the collars kept in tension also helps to maintain a vertical bore. There are many types of drill collars available. The two most popular drill collar types are shown in Figure 4 and Figure 5. Figure 4. Pin End Type Drill Collar Figure 5. Slip Recess Type Drill Collar Also, as far as possible, it is better if the drill pipe itself is dynamically balanced. c) (i) Space diagram showing the angular positions of masses as well as their planes are shown in Figure 6 and Figure 7. The planes where balancing masses (mX and mY) are to be placed are denoted by X and Y. Both the balancing masses revolve at a radius of 100 mm. Problem is to find the magnitudes of mX and mY and their angular positions. ?A, ?B, ?C and ?D are the angular positions of masses mA, mB, mC and mD from the position of the mass mA. rA, rB, rC and rD are the radii at which the masses mA, mB, mC and mD are located. lA, lB, lC and lD are the distance of the planes in which the masses mA, mB, mC and mD are located, reckoned from the plane in which the mass mA is located. ?X and ?Y are the angular positions of the balancing masses that are located on the planes X and Y. rX and rY are the radii at which the balancing masses are located in the planes X and Y. lX and lY are the distances of the planes X and Y reckoned from the plane in which the mass mA is located. Figure 6. Angular Positions of Masses Figure 7. Positions of Planes (ii) The numerical values of the masses, angles, distance between the planes etc. is shown in Table 1. Table 1 also calculates the quantities that are necessary to calculate the balancing masses and their orientations. Table 1 is the data table. Table 1. Data Table Planes Corresponding to Masses Mass, m (kg) Radius, r (mm) Plane Location, l (mm) Angle, ? (degree) m*r m*r*l A 250 85 0 0 21250 0 X mX 100 100 ?X 100mX 10000mX B 325 75 300 45 24375 7312500 C 450 60 400 115 27000 10800000 Y mY 100 500 ?Y 100mY 50000mY D 270 85 700 235 22950 16065000 For dynamic balancing, sum of forces along both the horizontal and vertical directions should be equal to zero. In addition, sum of couples along both the horizontal and vertical directions should be equal to zero. These conditions are enough to obtain the magnitudes and angular positions of balancing masses. From these conditions, we have, ? mrcos?=0 and ? mrsin?=0 (5) Also, ? mrlcos?=0 and ? mrlsin?=0 (6) Solving (5) and (6) using data from Table 1 gives the results. Result is: mX = 110.1 kg at 34.7 degrees, and mY= 43.4 kg at 87.2 degrees. (iii) The force polygon and the couple polygon are shown in Figure 8 and Figure 9. Figure 8. Force Polygon Figure 8. Couple Polygon (iv) The result (refer to Figure 7 and Figure 8) should be the same as the one obtained using (5) and (6). The slight error observed in the graphical method is due partly to the inaccurate scaling and partly due to the inability of the graphical method to accurately represent forces and couples. 3. a) The quick return mechanism that is used in conventional drilling, planning and shaping machines is shown in Figure 9. Figure 9. Quick Return Motion Mechanism This type of mechanism cannot be used for removing drill pipes after completing the drill process. The reason is that the drill pipes are very long, and during return stage of the quick return mechanism, the drill pipe has to travel a very large distance. This necessitates some of the links of the quick return mechanism to be very long which is in feasible. Even if one is ready to fabricate these very long links, the quick return mechanism may not have the required mobility that can be determined using suitable mobility criteria. Hence, the mechanism may not be able to do the job for which it is built. b) The mechanism shown is nothing but the quick return mechanism shown in Figure 9. (i) The number of instantaneous centre is given by the formula N = n (n-)/2 (7) where n is the total number of links. For the given mechanism, n= 6. Hence, N = 6*(6-1)/2 = 15. (ii) The velocity diagram is shown in Figure 10. Figure 10. Velocity Diagram (iii) The linear velocity of D = ?DBDB, where DB = 45 mm, and ?DB is found from (iv) below. Substituting the value of ?DB (from (iv) below) in the expression, the linear velocity of the slider D = 0.138 * 45 = 6.21 mm/s. (iv) The angular velocity of link BD = ?DB = ?BD = (Linear velocity of point B) * (Distance of the instantaneous centre from the point B). This distance is noted from the velocity diagram, Figure 10, (by taking normal to each of the links in the current configuration and considering their intersection). Of course, the current configuration is fully known, i.e., length of all links and all angles are given in the problem itself. Substituting these values, ?DB = 7.9 degree/second = 0.138 rad/s Read More