DESIGN OF CANTILEVER GEAR-RACK DRIVING SYSTEM ON JACK-UP DRILLING PLATFORM

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1 ARCHIVES OF MECHANICAL, ELECTRICAL AND CIVIL ENGINEERING Vol.2, No.2, DESIGN OF CANTILEVER GEAR-RACK DRIVING SYSTEM ON JACK-UP DRILLING PLATFORM WANG Longting *, XU Xingping and LIU Guangdou *College of Mechanical and Electronic Engineering, China University of Petroleum (East China), Qingdao, , China. ABSTRACT In order to realize a continuous and smooth sliding of the cantilever on jack-up drilling platform, Gear-Rack system is adopted to drive the longitudinal movement of the cantilever. Taking a certain jack-up drilling platform as an example, the overall structure of the cantilever was designed firstly. The mode called motor & gearbox & a small drive wheel & rack was adopted to drive the longitudinal movement of the cantilever. The required thrust to move the cantilever was determined by the cantilever structure and weight & center of gravity of the equipment on the cantilever. The geometric parameters of the cantilever Gear-Rack were designed, and the strength of Gear-Rack structure was checked using finite element analysis. The results show that the parameters of Gear-Rack are reasonable; the strength meets the design requirements. Keywords: Jack-up drilling platform, Cantilever beam, Gear-Rack, Structure design, Strength checking. 1. INTRODUCTION Cantilever jack-up drilling platform is the main equipment in offshore petroleum exploration and development [1-3], which can drill cluster wells with the help of longitudinal and transverse movement of drilling module. There are mainly three kinds of cantilever in jack-up platforms: classic cantilever, X-Y cantilever and rotating cantilever [4-6]. Traditional cantilever, which is that cantilever slips along the platform base longitudinally and drilling module slips along transverse girder on the cantilever laterally, is favored by platform design and manufacturing company due to technical maturity and relatively low cost. Nowadays, the mostly widely used cantilever slipping modes on jack up platform are pawl skidding mode, hinge pin skidding mode of hydraulic displacement, Gear-Rack skidding mode [7]. Traditional cantilever is generally moved by the aid of hydraulic power, which is named hydraulic cylinder & pawl mode [8]. The mode is relatively mature and reliable in the technique, and it can be achieved step-slip. Relying on the intermittent reciprocating driving of the hydraulic cylinder, the cantilever moves slowly, and the ballast blocks need to be pulled manually. So the operation is complicated, the working efficiency is low. In addition, the manufacture and installation of the hydraulic driving system is difficult. The application of Gear-Rack mode is relatively narrow, but it can achieve continuous steady slipping, and the slipping velocity can be adjusted according to need. So the research of convenient movement, easily to manufacture of the Gear- Rack skidding cantilever can improve the efficiency of offshore drilling. 2. CALCULATION OF MAXIMUM THRUST TO MOVE THE CANTILEVER Cantilever system, as a longitudinal movement structure for platform drilling and workover, mainly composed of the cantilever, driving system, cantilever base, cantilever locking mechanism and other components. The main design parameters of the cantilever beam system are as follows: Maximum Design Combined Load of Cantilever and Drill Floor: 540t; Maximum Cantilever Longitudinal Outreach of Rotary Table Center: 40ft/12m; Maximum Transverse Movement of Drill Floor: +/- 12ft/3.66m; Derrick Foot Dimensions: 30ft 30ft/9.144m 9.144m. The cantilever is designed as a box-shaped cross-sectional configuration, i.e., Ⅱ" shaped structure, is 30m length and 4.7m high. The width and thickness of the upper and lower flange beams are 950mm and 50mm, respectively. The web of the cantilever has four kinds of thickness: 26mm, 28mm, 32mm and 36mm. The web is very high, therefore, the stiffener, whose cross section is T-shaped structure, should be located at both ends to prevent web buckling. The width of the cantilever base is 15m. Two transverse guide rails, whose centre is 5.3m to the stern, connect to the upper of box girder. In the process of moving the cantilever, the supporting force of the stern and bow are constantly changing. Obviously, while the cantilever outreach to the most distal end and the drill floor move maximum distance transversely, the supporting force is the maximum, and at this time, the 15

2 drill floor move maximum distance transversely, the supporting force is the maximum, and at this time, the thrust to move the cantilever will be needed most [9]. Weight and drill floor move to the maximum (origin is supposed at the centre of the stern of the cantilever). centre of gravity of the cantilever rig are shown in Figure 1 when the cantilever outreach to the most distal end and the Figure 1. Schematic diagram of loads applied on cantilever beam In Figure 1, refers to weight of the drill floor, refers to weight of transverse rails, refers to weight of cantilever beam, and refers to weight of pipe rack. When the drill floor traverse to the far left, the left cantilever will bear the maximum load, so the force analysis of the left cantilever only need to be researched. Among them, the weight of the cantilever beam and the pipe rack evenly distributed load in the left cantilever beam at corresponding position (point H and point K in Figure 1); the four points A, B, C and D evenly bear the weight of transverse rail; the four points M, N, P, and Q evenly bear the weight of the drill floor. The transverse guide rails is simplified as a Simplysupported beam, so the equivalent supported force applied on the point A, B of the weight of the drill floor and the transverse rail can be depicted as follows: (1) In Eq.(1) and Eq.(2), QD, ND, BD, PC, MC and AC are denoted the length between point Q and point D, point N and point D, point B and point D, point P and point C, point M and point C, point A and point C, respectively. So the forced applied on the left cantilever beam can be gotten, as shown in Figure 2. (2) Figure 2. Schematic diagram of loads applied on left cantilever beam 16

3 So the supported force applied on the point E of stern of vessel and point G of forehead of cantilever is t and t, respectively. The contact between lower faceplate of cantilever and HOLD-DOWN on the forehead of cantilever and PUSH-UP on the stern of vessel belongs to rigid friction, the friction coefficient is 0.12(lubricate). So the minimum thrust need to move cantilever is: (3) 3. GEAR-RACK DESIGN Broken, spot corrosion, worn and plastic deformation constitutes the main failure mode of gear [10]. In order not to make the gear failure, gear must have sufficient bearing capacity. The main two design criteria for gear failure are the bending fatigue strength of tooth roots and contact fatigue strength of tooth surfaces [11]. The known conditions designing Gear-Rack structure are: moving velocity of cantilever is 0.03m/s; the minimum thrust need to move cantilever is 157.3t; and drive motor and power machine work steadily. First, the parameters of Gear- Rack are designed in accordance with the bending fatigue strength of tooth roots, and then check the strength of Gear- Rack according to the above two criteria based on the relevant parameters. 3.1 Material Selection Materials must meet the work requirements, and need to consider the size of gears, gear manufacturing molding process; normalized carbon steel gear can t withstand severe shock loads, and it can only work under conditions of mild shock or smooth; tempering carbon steel gear can withstand moderate shock loads; and the alloy can withstand high-speed, heavy and shock loads; The cantilever gear should withstand heavy loads, so alloy steel hardened gear is applied on the cantilever. The Gear- Rack material in this case is hardened steel 20CrMnTi, which is treated by carburizing, quenching, tempering, nitriding. The main characteristic parameters are as shown in Table 1. Table 1. Gear-Rack characteristic parameters Gear-Rack Material 20CrMnTi Elastic Modulus E 20600MPa Tensile Strength 1079MPa Yield Strength 834MPa Contact Fatigue Strength Limit of Tooth Surfaces 1500MPa Bending Fatigue Strength Limit of Tooth Roots 500MPa Hardness 57-63HRC 3.2 Parameters Design of Gear-Rack In conditions of steady load, hard-toothed surface, opengear, heavy duty drive, the number of teeth range from 17 to 24, so the number of gear teeth ( ) should be chose small value 17. Undercutting of Gear-Rack can be avoided by applying modified gear; and the strength of the tooth surface contact and tooth root bending strength can be improved; the antibonding capacity and wear resistance of the tooth surface can be also improved. Modification coefficient is taken as 0.32 according to teeth and variable coefficient selection principle [11]. Loads vary not much, and the hardness of Gear-Rack is greater than 350HBW, so that coefficient of tooth width is taken as, primarily taken as Module of gear is designed according to the bending fatigue strength of tooth roots. In Eq.(4), each symbol values are shown in Table 2. (4) 17

4 Table 2. Gear-Rack calculation parameters Symbol Name Value Symbol Name Value Loading Factor 1.2 Number of Gear Teeth 17 Torque of Gear Gear Form Factor 4.23 Coefficient of Tooth Width 12 Allowable Bending Stres 800MPa The data in Table 2 substituted in Eq.(4), is gotten to be So is taken as 32 according to the modulus selection principle. Thus, the geometric size of Gear-Rack is shown in Table 3. Table 3. Geometric size of Gear-Rack Name Calculating Formula Code & Value Name Calculating Formula & Code Value Number of Gear Teeth 17 Modification Coefficient 0.32 Modulus Helix Angle 32mm Tooth Rack 240mm 0 Width Gear 250mm Pressure Angle 20 Coefficient of Tooth Width 0.44 Addendu m Coefficien t 1 Standard Diameter Pitch 544mm Tip Clearance Coefficien t Fatigue Strength Checking of Gear-Rack Fatigue strength of Gear-Rack is checked according to criteria bending fatigue strength of tooth roots and contact fatigue strength of tooth surfaces, respectively. Allowable contact stress, allowable bending stress, actual calculated contact stress and actual calculated bending stress of gear are calculated shown in Eq.(5) to Eq.(8) below. In the above Formulas, the value and significance of the symbols are shown in Table 4. (5) (6) (7) (8) 18

5 Table 4. Fatigue strength calculation parameters of Gear-Rack Item & Name Value Item & Name Value Impact Factor affected by Lubricant Film 1.0 Node Area Coefficient 2.5 Tooth Surface Work Hardening Coefficient 1.0 Elasticity Coefficient Dimensional Factor 1.0 Coincidence Coefficient 0.89 Life Factor Helix Angle Factor 1 Minimum Safety Factor Width of Tooth Service Factor 240mm 1.10 Stress Modification Coefficient 2 Dynamic Load Factor 1.01 Contact Fatigue Strength Limit 1500MPa Load Sharing Coefficient, Bending Fatigue Strength 500Mpa Load Sharing Coefficient 1.0 Relative Notch Sensitivity Factor 1.0 Composite Tooth Coefficient 4.23 Coefficient of the Relative Gear Root Surface Condition 1.0 Helix Angle Factor 1.0 Dimensional Factor 0.85 Coincidence Coefficient 0.71 Single Tooth Contact Ratio 1.0 Note1: Gear speed, mesh times of same tooth surface per revolution. Supposed 50 years of working years, a 12-year moving wells, each well movement spending two hours, so gear working life, Load cycles ; Note2: Gear cantilever supported, so coefficient of tooth width,. Based on the above values, substituted, got,,,,., and, so Strength of Gear-Rack meets the requirements. The parameters of Gear- Rack are determined as: the material is 20CrMnTi, accuracy class is 6; gear modulus is 32mm; number of teeth is 17; modification coefficient is 0.32; width of gear is 250mm, width of rack is 240mm. the maximum stress and maximum deformation of Gear-Rack structure meet the requirements. 4 STRENGTH FINITE ELEMENT ANALYSIS OF GEAR-RACK According to the calculation of Gear-Rack parameters seen from the previous section, the contact finite element model of Gear-Rack is build using finite element analysis software ANSYS [12]. Under the conditions: the bore of gear is fully constrained, the movement in the vertical direction of rack is constrained, the rack is loaded t horizontal external force, the stress distribution of Gear-Rack will be calculated. Figure 3 shows the equivalent stress distribution. As can be seen from Figure 3, besides the significantly stress concentration of contact of the tooth root, the larger stress area is concentrated in contact between the teeth. So as can be seen from the analysis results, Figure 3. Equivalent stress distribution of Gear-Rack 5. CONCLUSIONS In combination with a cantilever jack-up drilling platform structure, steps and methods are given for Gear-Rack structure design of cantilever longitudinal slip system. Strength checking results and finite element analysis results show that cantilever Gear-Rack slip system is feasible. The Gear-Rack slip system can achieve continuous steady slipping, and the slipping velocity can be adjusted according to need. 19

6 ACKNOWLEDGMENTS The authors wish to thank the members of Shandong Offshore Petroleum Drilling Equipment Engineering Technology Research Center, College of Mechanical and Electronic Engineering, China University of Petroleum (East China) for their support and help. This work was supported by the Fundamental Research Funds for the Central University (No. 14CX02078A, No. 14CX02129A). REFERENCES 1. Chen Hong & Li Chen-Xiang, Introduction of Development in Jack-Up Drilling Platform. China Offshore Platform, 22(6), pp. 1-6, Zhang Yong-De & Yuan Xue-Qiang, Development Trend and Status of Offshore Drilling Platform in China. Oil Field Equipment, 37(9), pp , Ma Zhi-Liang &. Luo De-Tao. Mobile offshore platform, Beijing. Ocean Press, Chi Yu, Duan De-Xiang, Wang Yan-Feng, Zhu Li-Jun, Jiang Xing-Xun, Meng Xiang-Long & Wang Fu-He, Selection Technical Analysis of Cantilever Jack-Up. Drilling Platform. China Petroleum Machinery, 39(10), pp , Information on 6. Ren Xian-Gang, Bai Yong & Jia Lu-Sheng, Cantilever Beam Study of Offshore Jack-up Drilling Rig. Chuan Bo Li Xue/Journal of Ship Mechanics, 15(4), pp , Wang Long-Ting, Wang Xi-Lu, Liang Hui-Gao, Xu Xing-Ping & Wang Gang, Structure Characteristics of Foreign Cantilever Beams of the Jack-up Drilling Platform. Offshore Oil, 29(4), pp , Zhang Xiao-You & Sun Yong-Tai, A Study on the Cantilever & Moving System of Shengli No.3 Workover Platform. China offshore Platform, 18(4), pp , Gao Hua, Moving Device Design of Cantilever Jack-up Drilling Platform. China Science and Technology Expo, 32, pp. 8-9, Chen Miao-Qing, Gear Failure Analysis and Improvement Measures. Manufacturing Automation, 33(4), pp , Editorial of gear handbook, Gear handbook, Second ed., Beijing: China Machine Press, Kent Lawrence, ANSYS Workbench Tutorial Release 14, SDC Publications,