A STUDY ON JACK-UP GEARBOX DESIGN FOR DRILLSHIPS

International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 6, June 2018, pp. 948 959, Article ID: IJMET_09_06_107 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=9&itype=6 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 IAEME Publication Scopus Indexed A STUDY ON JACK-UP GEARBOX DESIGN FOR DRILLSHIPS HyoungWoo Lee Department of Aero Mechanical Engineering, Jungwon University, South Korea ABSTRACT A typical jack-up gearbox used in drillships is composed of a three-stage spur gearbox, which consists of gear chains, shafts and bearings, and a two-stage planetary gear. This study designed the components of the spur gearbox and planetary gear system, and assessed the carrier stability. A gear strength analysis was performed based on ISO 6336, and the system was verified as safe under a load of 18.5kW at 50hr, 100hr, and 150 hr. The shaft strength was calculated using a finite element analysis according to DIN 743, and the shafts had a satisfactory safety factor of at least 3.5 in all cases. The bearing safety factor met the standards of ISO 281 under a load of 18.5 kw at 150 hr. A structural analysis was conducted on the rack and pinion, and the stability of the assembly error was assessed. Keywords: Jack-up Gearbox, Drillships, Planetary Gear, Gear Strength, Shaft Strength, Bearing Safe Factor Cite this Article: HyoungWoo Lee, A Study on Jack-Up Gearbox Design for Drillships, International Journal of Mechanical Engineering and Technology, 9(6), 2018, pp. 948 959 http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=9&itype=6 1. INTRODUCTION With offshore petroleum accounting for a higher proportion of petroleum production, there has been an increase in the development and production of deepwater petroleum, along with rising oil prices. Key facilities used in oil drilling include jack-up rigs, drillships, and semisubmarines, and the use of drillships and semi-submarines has surged with the commercialization of deepwater oil. The growing demand for drillships has contributed to the development of deepwater oil, higher oil prices, and enhanced drillship productivity. With the shift in the oil drilling environment from coastal waters to the deep sea, drillships are being equipped with a Dynamic Positioning System (DPS), which uses thrusters to support on-site repair and maintenance. The structure of the proposed motorized thruster retrieving system is shown in Figure 1. As can be seen in the figure, when the thruster is in the normal operating position, each canister is firmly fixed to the ship using three locking pins. At the ends of each canister are two pairs of rack gears, which are elevated to the service position by four driving units. Each http://www.iaeme.com/ijmet/index.asp 948 editor@iaeme.com

A Study on Jack-Up Gearbox Design for Drillships driving unit consists of a motor, brake, spur gear reducer, planetary gear reducer, and pinion gear. Figure 1 Thruster retrieving system The jack-up gearbox is composed of a gear-rotor system, which includes gear chains, shafts, bearings, and a planetary gear system, and a casing unit. In past research, Lida [1] stated that the dynamic behavior of a reducer differs from that of the simplified model when the coupling between torsional and flexural vibrations is considered. Schwibinger [2] showed that coupling of torsional and lateral vibrations influences the stability of geared rotor systems. Choy [3] analyzed a three-stage gear transmission system with lateral and torsional coupling in the normal and transient state. Kahraman [8] calculated critical speeds with consideration of coupling between torsional and transverse vibrations, and applied the finite element method to obtain mass unbalances and the displacement transmission error. In research on one-stage helical gears, Umeza [4-5] performed a numerical analysis on rotational motion to reduce tooth errors. Neriya [6] examined the excitation to the system in the form of static transmission error with consideration of the coupling between torsional, flexural, rotational,` and axial motions, while Neriya [7] applied the Floquet theory to the coupled vibrations. Cheng-Ho [8] analyzed the kinematic structure of planetary gear trains with any number of degrees of freedom. M. Savage [9] proposed a reliability model for planetary gear trains with the sun gear as the input and the carrier as the output. In accordance with standard specifications of jack-up gearboxes used in drillships, this study designed a multi-stage gear train and supporting components, including bearings and shafts, and assessed the stability of the planetary gear system and carriers. The bending stress and contact stress of gear components were analyzed based on ISO 6336 standards [10], and the rack and pinion underwent a structural analysis followed by a stability assessment. 2. DESIGN AND ASSESSMENT OF JACK-UP GEARBOX 2.1. The Object of the Tooth Modification The gearbox was evaluated using the CAE software MASTA and finite element software. Basic powertrain elements such as gears, bearings, and shafts were modeled in MASTA. Other components such as carriers and housing were built in the finite element software, and then combined with powertrain elements in MASTA through the substructure synthesis method. Figure 2 shows the gear train modeling in MASTA, the housing and carriers built using the finite element method, and the combination of the various components. http://www.iaeme.com/ijmet/index.asp 949 editor@iaeme.com

HyoungWoo Lee (a) Gear train modeling for MASTA (b) Housing for FEM (c) Jack-up gearbox by MASTA & Finite element method Figure 2 Jack-up gearbox modeling Under a given input load of 18.5 kw, this study analyzed the system with consideration of deformation to the output shaft, comprised of the rack and pinion, due to normal force of the pinion. A finite element analysis was applied to displacement in the radial direction of the pinion and rack gear. The input speed was 1750 [rpm], and the forced displacement of the output shaft (x/y) was -121/230 ( ). Figure 3 shows the deformation analysis of the rack and pinion. Figure 3 Rack & pinion finite element method analysis 2.2. Design and Assessment of Jack-up Gearbox 2.2.1. Spur Gearbox As shown in Figures 4 and 5, the spur gear system was designed to have a reduction ratio of 97.54 and is composed of three stages. The rotational speed was 1750 [rpm] for the input shaft, 315.57 [rpm] for the two-stage shaft, 74.46 [rpm] for the three-stage shaft, and 17.94 [rpm] for the four-stage shaft. Figure 4 Spur gear system http://www.iaeme.com/ijmet/index.asp 950 editor@iaeme.com

A Study on Jack-Up Gearbox Design for Drillships (a) 1 step spur gear (b) 2 step spur gear (c) 3 step spur gear Figure 5 Spur gear pairs 2.2.2. Planetary Gearbox The planetary gear system has a total reduction ratio of 19.73, with an input of 17.94 rpm and an output of 0.9091 rpm. It comprises two stages, and the ring gear of each stage is fixed to the housing. The sun gear acts as the input and the carrier as the output. The input speed of the one-stage planetary gear is 17.942 [rpm], and the output speed of the two-stage planetary gear is 0.9091 [rpm]. The one-stage planetary gear train consists of three gears, and the two-stage planetary gear train of five gears. The two gear trains are shown in Figure 6. Figure 6 Planetary gear train The one-stage planetary gear train consists of three planetary gears, and the two-stage planetary gear train of five planetary gears. Figure 7 shows the cross-section of the planetary gear stages. (a) 1 stage planetary gear train (b) 2 stage planetary gear train Figure 7 Planetary gear stage The planetary gear is made from SCM415 materials, and the ring gear from SCM440 materials. The materials used for the ring gear have not received heat treatment. The gears were designed to satisfy various requirements such as strength, weight, interference with the objective function, and ease of assembly. http://www.iaeme.com/ijmet/index.asp 951 editor@iaeme.com

HyoungWoo Lee 2.2.3. Gear Strength Assessment For strength design of the jack-up device, this study examined the power delivery gear in terms of the two items below. i. Bending stress of tooth root: The gear tooth undergoes fatigue failure due to stress on the tooth root. ii. Contact stress of tooth surface: The tooth surface undergoes fatigue failure and exhibits pitting due to stress on the tooth surface. The delivered horsepower was determined by the minimum permissible load with consideration of the aforementioned items, and the gear strength was calculated based on ISO6336 standards [10]. Gear strength was assessed based on ISO 6336, and calculated under a load of 18.5 kw for 50hr, 100hr, and 150hr. As shown in Table 1, all safety requirements were met with the safety factor of contact stress and bending stress exceeding 1 and 1.5, respectively. Some caution is needed as the contact stress safety factor was 1.17 for the sun gear of the one-stage planetary gear train, 1.14 for the ring gear of the one-stage planetary gear train, and 1.12 for the ring gear of the two-stage planetary gear train. Table 1 Gear stress spur gearbox planetary gearbox stage stage1 stage2 stage3 stage1 stage2 Fatigue ( 18.5kW ) 150[hr] 100[hr] 50[hr] contact bending contact bending contact bending pinion 1.57 3.58 1.45 4.13 1.45 4.18 gear 1.69 3.35 1.74 3.50 1.83 3.76 pinion 1.72 4.07 1.64 4.55 1.73 4.92 gear 1.78 3.93 1.84 4.10 1.93 4.40 pinion 1.54 3.35 1.54 3.56 1.63 3.86 gear 1.69 3.18 1.74 3.32 1.75 3.58 sun 1.17 2.17 1.21 2.27 1.25 2.43 planet 1.36 1.53 1.36 1.60 1.36 1.72 ring 1.14 3.30 1.14 3.59 1.14 4.15 sun 1.36 2.41 1.36 2.51 1.38 2.39 planet 1.38 2.10 1.38 2.201 1.36 2.69 ring 1.12 4.68 1.12 4.99 1.12 5.53 2.2.4. Shaft Strength Assessment The shaft strength was assessed using DIN 743 standards[11] and a finite element analysis, and the safety factor was calculated under a load of 18.5 kw. The standards of DIN 743 were applied to general symmetrical shafts, and a finite element analysis was employed in evaluating carriers and other components. Under DIN743, the safety factor is calculated using tension, compression, bending, and torsion. : Stress amplitudes due to tension/compression, bending, torsion : Permissible stress amplitudes, strengths http://www.iaeme.com/ijmet/index.asp 952 editor@iaeme.com

A Study on Jack-Up Gearbox Design for Drillships Figure 8 and Figure 9 show the stress of the one-stage shaft and four-stage shaft of the spur gearbox, respectively. Figure 10 and Figure 11 show the stress of the one-stage planetary gear train input shaft and the two-stage planetary gear train output shaft, respectively. (a) Axial Stress (b) Bending Stress (c) Torsional Stress Figure 8 Stress of 1 stage input shaft (spur gearbox) (a) Axial Stress (b) Bending Stress (c) Torsional Stress Figure 9 Stress of 4 stage shaft (spur gearbox) http://www.iaeme.com/ijmet/index.asp 953 editor@iaeme.com

HyoungWoo Lee (a) Axial Stress (b) Bending Stress (c) Torsional Stress Figure 10 Stress of 1 stage input shaft (Planetary gearbox) (a) Axial Stress (b) Bending Stress (c) Torsional Stress Figure 11 Stress of 2 stage output shaft (Planetary gearbox) http://www.iaeme.com/ijmet/index.asp 954 editor@iaeme.com

A Study on Jack-Up Gearbox Design for Drillships Table 2 Shaft safety factor by DIN743 Shaft DIN 743 Static Safety Factor spur gearbox 1 stage input shaft 50 spur gearbox 2 stage shaft 12.94 spur gearbox 3 stage shaft 11.44 spur gearbox 4 stage shaft 9.18 planetary gearbox 1 stage input shaft 3.53 planetary gearbox 2 stage output shaft 4.12 As shown in Table 2, the gear support shaft for different stages had satisfactory safety factors of 50, 12.94, 11.44, and 9.18, respectively. The shafts in the planetary gear had a satisfactory safety factor of at least 3.5. 2.2.5. Carrier Stability Assessment A finite element analysis was performed using MASTA to calculate the load acting on the carriers. Figure 12 shows the stress distribution of the one-stage carrier and two-stage carrier. Under a load of 18.5 kw, both the one-stage carrier and two-stage carrier were found to be safe with a maximum stress of 44.6 Mpa and 89.4 Mpa, respectively. (a) 1 stage carrier (b) 2 stage carrier Figure 12 Finite element analysis of carrier 2.2.6. Bearing Safety Assessment The safety factor of bearing components was calculated using the standards on dynamic capacity provided in ISO 281[12]. The analysis was performed at a confidence interval of 99%, and the load conditions were 18.5[kw] and 150[hr]. Figure 13 shows the bearing position of the jack-up gearbox, and Table 5 presents the bearing safety factors. The bearings were verified to be safe with the minimum safety factor being 1.57. The support bearing of the one-stage and two-stage planetary gear trains had a minimum safety factor of 2.91 and 3.39, respectively. All bearings were safe and usable at 150hr or longer. stage1 stage2 stage3 stage4 Figure 13 Bearing of jack-up gearbox http://www.iaeme.com/ijmet/index.asp 955 editor@iaeme.com

HyoungWoo Lee Table 3 Bearing safety factor Spur gear box Planetary gear box load[n] life time[hrs] ISO 281 Fatigue Stage1 LH 763.3 4248 2.19 RH 1960 1016 1.57 Stage2 LH 7743 126723 7.06 RH 4935 562110 10.04 Stage3 LH 15872.5 447178 9.12 RH 22686 72077 6.56 Stage4 LH 17400 805477 11.41 RH 18128 475101 9.31 CB LH 2816.7 6941846 15.99 RH 2491.7 9808877 20.71 1P LH 61658.3 5593 2.91 RH 56439.6 7499 3.25 LH 72869.9 14912 3.39 2P C 51668.7 51588 4.76 RH 71238.2 14297 4.95 OB LH 487528.5 202950 25.96 RH 169633.9 407079 50 1S - 1710.8 1566025 15.67 2S - 9469.5 415228 9.54 3. DESIGN AND ASSESSMENT OF RACK AND PINION The output shaft of the jack-up gearbox consists of a rack and pinion, used to lift or lower canisters. The pinion, which rotates at approximately 0.9rpm, allows the rack to travel at one meter per minute. It is subject to a high torque at very low speed, and a structural analysis was performed to verify its design stability. The load applied was 18.5kw. 3.1. Finite Element Analysis A finite element analysis was conducted with consideration of various components such as the pinion, rack, output shaft, and bearing. One side of the rack and the outer wheel of the bearing were fixed to the ground. The spline of the output shaft was connected to a revolute joint, and a moment was applied. The pinion and rack gear were in frictionless contact, and the bearing and output shaft in no separation contact. Figure 14 shows the boundary condition used in the structural analysis of the rack and pinion. Figure 14 Rack and pinion boundary condition http://www.iaeme.com/ijmet/index.asp 956 editor@iaeme.com

A Study on Jack-Up Gearbox Design for Drillships The stability of the tooth root was analyzed based on the stress distribution. The analysis focused on tensile forces over compression as more cracks were associated with the former. The torque values were 80 tons and 140 tons. Maximum str ess (a) Moment 137,340Nm (80ton) (b) Moment 240,345Nm (140ton) Figure 15 Torque of rack and pinion As shown in Figure 15, the gear exhibits poor strength when tensile forces are generated at the tooth root. When a moment of 80 tons is applied, the tooth root experiences a stress of 188 877 MPa. When a moment of 140 tons is applied, the tooth root experiences a stress of 470 1530MPa, which exceeds the yield stress. Stress was found to be concentrated in the area connecting the pinion and shaft. Figure 16 shows the stress distribution of the rack and pinion. The pinion was observed for possible changes in the presence of holes, without holes, and with a block added. The three cases did not have any significant effect on the stress distribution. This shows that stress is mostly concentrated in the area joining the output shaft and pinion, and not the opposite side. (a) Hole (stress: 1531 Mpa) (b) No hole (stress: 1589 Mpa) (c) Add block (stress: 1423 Mpa) Figure 16 Stress of rack and pinion http://www.iaeme.com/ijmet/index.asp 957 editor@iaeme.com

HyoungWoo Lee To determine the effect of assembly error on the pinion and rack, the stress distribution was observed while offsetting the rack position in a range of 2mm to 2mm. Figure 17 Assembly error of rack and pinion Table4 shows the stress distribution of the pinion in relation to assembly error. Stress increased with an offset in the + and directions than when in the zero position. The changes were more significant for bending stress than contact stress. Since the gear is subject to a high torque of low speed and must be optimized for maximum bending stress, greater precision is required in the assembly of the rack and pinion. Table 4 Pinion stress by assembly error Offset Pinion Contact stress Bending stress -2mm 1785.6 924.25-1mm 1814.8 927.04 0mm 1714.5 872.1 1mm 1755.8 922.96 2mm 1759.9 925.66 4. CONCLUSION 1. This study modeled a jack-up gearbox, consisting of a three-stage spur gearbox and two-stage planetary gear system, and assessed its stability. 2. Gear strength analysis was performed based on ISO 6336, and the system was verified to be safe under a load of 18.5kW at 50 hr, 100 hr, and 150 hr. The contact stress of the spur gearbox and planetary gearbox was at least 1, and the safety factor of bending stress was at least 1.5. 3. The shaft strength was calculated using a finite element analysis according to DIN 743, and the shafts of the spur gearbox and planetary gearbox had a satisfactory safety factor of at least 3.5. 4. The bearing safety factor met the standards of ISO 281 under a load of 18.5 kw at 150hr. 5. A structural analysis was conducted on the rack and pinion, and the stability of assembly error was assessed. ACKNOWLEDGEMENT This work was supported by the Jungwon University Research Grant (2016-035). http://www.iaeme.com/ijmet/index.asp 958 editor@iaeme.com

A Study on Jack-Up Gearbox Design for Drillships REFERENCES [1] H. lida, A. Tamura and M. Oonishi, 1985, "Coupled Torsional-Flexural Vibration of a Shaft in a Geared System", Bull. JSME 28, pp. 2694~2698. [2] P. Schwibinger and R. Nordmann, 1988, "The Influence of Torsional-Lateral Coupling on the Stability Behavior of Geared Rotor System", Journal of Engineering for Gas Turbines and Power Vol. 110, pp. 563~571, OCTOBER. [3] F.K.Choy, Y.K.Tu, M.Savage And D.P.Townsend, 1991, "Vibration Signature and Modal Analysis of Multi-stage Gear Transmission", Jouranl of the Franklin Institure, Vol. 328, N0. 2/3, pp. 281~298. [4] K.Umezawa, T.Suzuki and T.Sato, 1986, "Vibration of Power Transmission Helical Gears (Approximate Equation of Tooth Stiffness)", Bulletine of JSME, Vol. 29, No. 251, pp. 1605 ~ 1611. [5] K.Umezawa, T.Suzuki and H.Houjoh, 1988, " Estimation of Vibration of Power Transmission Helical Gears by Means of Performance Diagrams on Vibration ", JSME International Journal Series Ⅲ, Vol.31, No. 3, pp. 598 ~ 605. [6] Neriya, S.V., Bhat, R.B., and Sankar, T.S., 1988, "On the Dynamic Response of a Helical Geared System Subjected to a Static Transmission Error in the Form of Deterministic and Filtered White Noise Input", ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 110, pp. 501 ~506. [7] Neriya, S.V., Bhat, R.B., and Sankar, T.S., 1989, "Stability analysis of force coupled in helical geared rotor systems", Proceedings of the Twelfth Biennial ASME Conference on Mechanical Vibration and Noise, Montreal, Canada, Sept. 17-21, pp. 225~229. [8] Cheng-Ho Hsu, Kin-Tak Lam,"Automatic Analysis of Kinematic Structure of Planetary Gear Trains", Joural of Mechanical Design, Vol. 115, pp. 631~638, 1993. [9] ] M. Savage, C. A. Paridon, "Reliability Model for Planetary Gear Trains", Journal of Mechanis, Transmissions and Automation in Design, Vol. 105, pp. 291~297, 1983. [10] INTERNATIONAL STANDARD ISO 6336-5, Calculation of load capacity of spur and helical gears -Part 5: Strength and quality of materials, pp. 1~43, 2003. [11] DIN 743, Calculation of load capacity for shafts and axles, 2012. [12] INTERNATIONAL STANDARD ISO 281, Rolling bearings - Dynamic load ratings and rating life, pp. 1~51, 2007 [13] E. Balaji, D. Mouli, P.Rajasekaran and S. Sudhakar, Reduction of Noise In ZF Gearbox, International Journal of Mechanical Engineering and Technology, 8(4), 2017, pp. 351-358. http://www.iaeme.com/ijmet/index.asp 959 editor@iaeme.com