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This study presents a MATLAB-based analysis comparing the impact of various pitting shapes on the mesh stiffness of a spur gear. The focus is on circular, rectangular, and elliptical pitting defects, with an examination of their effects on total deformation. The research highlights the critical role of mesh stiffness in the dynamic behavior of gear systems, particularly under high-load conditions.
Gear systems are integral to the operation of numerous mechanical devices, where precise transmission of power is critical. The mesh stiffness of gears, a key factor in their dynamic performance, can be significantly affected by surface defects such as pitting.
Pitting, a form of surface wear, occurs due to fatigue and manifests in various shapes depending on the conditions. This study employs MATLAB to analyze how different pitting shapes influence spur gear mesh stiffness, a property crucial to gear design and maintenance.
The following points were noted while checking the satellite images and maps:
5 (204)
“ She followed all my directions. It was really easy to contact her and respond very fast as well. ”
From this information we should conclude that the drill site must be cleared and leveled, and access roads needs to be built. Heavy equipment needs to be transported to the drill site, therefor the roads should be stronger, and the climatic conditions must be considered while building the roads and preparing the drill site.
The noise from the drill site and vehicles will not be a big problem because there are no residential areas nearby. This is a forest area, so we must consider the environmental impacts and what the local people of the Fort Nelson think about the site. (BC Oil and Gas Commission, 2013)
The study models tooth pitting in three shapes: circular, rectangular, and elliptical, using MATLAB for the analysis. The gear parameters considered include force, pressure angle, number of teeth, and material properties like modulus of elasticity and Poisson's ratio. The mesh stiffness calculations incorporate bending stiffness, axial stiffness, shear stiffness, and Hertzian contact stiffness, accounting for the geometry and dimensions of each pitting shape.
Surface casing outside diameter =16 inches (given)
Surface casing inside diameter =15.125 inches (API Casing chart, 2012)
Weight of the casing = 75 lb/ft (API Casing chart, 2012)
True vertical depth = 2200 meters (given)
Total depth of the well = 5900 meters
We planned to do surface casing up to 600 meters
One joint of casing = 40 feet = 12 meters
One meter is 3.28 feet
Number of surface casing required = 600/12= 50 Casing
Therefore, we need 50 casing for 600 meters of depth.
Weight of one casing = 75 lb/ft 40 feet = 3000 lbs.
Weight for 50 casing = 3000 lb 50 = 150000 lbs = 75 ton.
Casing price for 50 surface casing = Price 75 ton = 1500 75 = 112500 $
Annular volume =6003.28(20/12)2-(16/12)2
= 1544.88 ft3
= 275.1548 barrels
Annular Capacity = Dh2- Dl2/1029.6
= 202-162/1029.6
= 0.139 barrels/feet
That is the cement between the Casing and hole = annular capacity length of casing
= 0.139 600 3.28
= 273.552 barrels
Intermediate casing
Diameter of Intermediate hole = 12 inches (given)
Outside diameter of Intermediate casing = 10 inches (given)
Inside diameter of intermediate casing = 9.95 inches (API Casing chart, 2012)
Weight of the intermediate casing used = 45.5 lb/ft (API Casing chart, 2012)
Intermediate casing is given up to 2200 meters.
Number of casing required for intermediate hole = 2200/12 = 184 casing
Weight of each casing = 45.5 lb/ft 40 ft
= 1820 lbs
Weight of 184 casing = 184 1820
= 334880 lbs
Total intermediate casing weight = 334880/2000 = 167.44 ton 168 ton
Price of intermediate casing = 1500$ per ton
Price of 168-ton intermediate casing = 252000 $
Annular volume = /4 2200 328 [(12/12)2 – (10/12)2]
= 1345.23 ft3
= 239.61 barrels
Annular capacity = Dh2- Dc2/1029.6
= 12.252- 10.752/1029.6
= 150.06 – 115.56/1029.6
= 0.033 barrel/feet
Production Casing
Diameter of Main hole = 9.5 inches
Inner diameter of production casing = 7.125 inches (API Casing chart, 2012)
Weight of the casing = 26.4 lbs/ft (API Casing chart, 2012)
Number of production casing = 5900/12 = 429 casings
Total weight = 4924026.4 = 519200 lbs
= 260 ton
Annular volume = 3.14/4(59003.28(9.5/12)2 – (7.125/12)2 = 1041.364 ft3
= 185.475 barrels
Annular capacity = (9.52 – 7.1252) / 1029.4
= 0.031barrel/ft
Calculation of cement volume = 0.03159003.28
= 603.63 barrels.
Additive need to be added is barite having specific gravity 4.2. Barite is added to the drilling fluid to increase the mud weight. It also increases the hydrostatic pressure of the drilling mud to compensate for high pressure zones experienced during drilling. (Industrial mineral association north america , 2019) Now, we found that the pressure gradient of our formation will be 13 kpa/m or 0.57 psi/feet (BC oil and gas commission, 2012). We have decided to choose ENVIROTHERM NT water-based mud as our drilling fluid, because it has minimum environmental impact in high temperature applications. (Schlumberger , n.d.)
Equivalent hydrostatic pressure gradient = 0.433 psi/ ft
Hydrostatic pressure of the true vertical depth (2200 meters) = hydrostatic pressure TVD
= 0.433 2200
= 3125.32 psi
The formation pressure at true vertical depth by using the estimated pressure gradient (0.57 psi/ feet) (BC oil and gas commission, 2012)
Therefore, formation pressure = 0.57 2200 3.28
= 4113.12 psi
Now, equivalent mud weight for hydrostatic pressure MW1 =
= 8.33 ppg
Now require mud weight MW2 =
= 10.96 ppg
Barite to add (ppg) = 35.05 (MW2- MW1)/ 35.05- MW2
=35.05 (10.96- 8.33)/ 35.05- 10.96
=3.82 ppg
Therefore, quantity of barite that needed to our water-based mud to get the required mud weight is 3.82 ppg.
We decided to give the contract to company to provide barite on our site.
Volume of barite needed to get the desired mud weight
Volume of the production casing = volume of the casing – volume of the string
= 3.14/4 {(6.97/12)2- (4.5/12)2 5900 3.28
= 2988.66 feet3
= 22351.8 gallons
We assume mud volume needed on the site should be 150% more than the hole volume
Therefore, hole volume = 22351.8 gallons
Mud volume = hole volume 150%
= 33527.7 gallons
Therefore, barite on site needed = 33527.7 3.82
= 128075.814 pounds
= 64.037 ton
Price of barite (Voyageur Minerals, 2017) =426 per Ton
Total Price = 27690 CAD
We decided to give contract TWH oilfield services Ltd located in Fort Nelson area. (TWH oil field services ltd, 2018)
We have selected size of the drill string as 4.5 inches and having a grade of S135. Each drill pipe will have 30 feet or 10 meters.
Weight of the drill pipe = 20 lb/ft (Quail tools, 2013)
Total drill string weight in air = 20 x 5800 x 3.28
=190.24 ton
Weight of drill string in mud = BF x 190.24
BF = 65.5- MW/ 65.5
=0.83
So, the weight of drill string in mud = 0.83 x 190.24
= 157.89 ton 158 ton
We are taking 10 collars for additional weight on the bit
Weight of 1 collar = 98 lb/feet (Quail tools, 2017)
Weight of 10 collars = 10 x 92 x 30
= 27600 lb/feet
= 14 ton
Drag force = N
Let = 0.22- 0.35
N= Length of drill pipe x weight of drill pipe
Therefore, drag force = 0.2 x 2200 x 20
= 8800 lb = 5 ton
This is a high pressure high temperature well, so the LWD & MWD tools should have the capacity to withstand temperature more than 150 degree Celsius and a well requiring pressure control equipment with a working pressure more than 10000 psi (Petrowiki, 2013). We have decided to choose Eco Scope HT LWD tool and Telescope HT MWD tool by Schlumberger. The maximum operating Temperature of these tools is 175 degC and 30000 psi (Schlumberger, 2015).
High and fluctuating bottom-hole pressure and temperature adversely affect the mud properties like viscosity gel strength, tool life, potential stuck pipe events, life of LWD/MWD tools etc. By reducing the temperature, we could reduce the cost, improve mud pump life, bit life and enhance hole cleaning. Automated land mud cooler can be used to cool down the mud (Dorry, Coit, Gutierrez, Woolums, & Herrington, 2015). We have decided to use TUNDRA MAX Land Mud Chiller supplied by National Oilwell Varco. This equipment can reduce the bottom-hole temperature by 12 degree Celsius (Scott, 2017).
We decided to take 8 inches drilling motors having a lobe configuration 5/6 for drilling intermediate well. This is because as per the competency chart, ground hog formation have less competency. (Baker Hughes, 2002)
Weight on bit (8 inch motor) = 67400 lbs = 34 ton (Baker Hughes, 2002)
We decided to take 6 3/4 inches drilling motors having a lobe configuration of 7/8 for drilling intermediate well. This is because as per the competency chart, elkstone formation has high competency. (Baker Hughes, 2002)
Weight on bit (6 ¾ inch motor) = 36000 lbs = 18 ton
Hook Load (W) = 158 + 5 + 34 + 18 = 215 ton = 213927.43 daN
Pump Selection
Critical annular capacity = 0.20 barrels/ft
Flow Rate (Q)
Q = Annular velocity x critical annular capacity
= 28.61 x 42x 0.20
= 240 gpm
So, we decided to choose triplex mud pump having liner size 5 inches and 100 stokes per min which will displace 255 gallons per min of our desired mud. (American petroleum institute 7K, 2009)
This MATLAB-based analysis underscores the importance of considering pitting shape in the assessment of spur gear mesh stiffness. The findings contribute to a deeper understanding of gear dynamics, aiding in the design and maintenance of more reliable gear systems. Future work could extend this analysis to other gear types and operational conditions, broadening the applicability of these insights.
Analyzing Pitting Shapes' Impact on Spur Gear Mesh Stiffness via MATLAB. (2024, Feb 21). Retrieved from https://studymoose.com/document/analyzing-pitting-shapes-impact-on-spur-gear-mesh-stiffness-via-matlab
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