Circular Round pitch is the distance from a point on 1 molar to the corresponding betoken on the next tooth measured along the pitch circle as shown in Figure 57.32. Its value is equal to the circumference of the pitch circumvolve divided past the number of teeth in the gear. While virtually common-size gears are based on diametric pitch, big-diameter gears are oft made to circular pitch dimensions.

The pitch-circle bore and the diametric pitch of a 4-inch pitch-circle bore gear are illustrated in Figure 57.33. For this 4-inch gear, there are four 3.1416-inch circumference segments. Note that for a three-inch gear, at that place are 3 3.1416-inch segments.

These concepts may be better visualized and dimensions more hands obtained with the rack teeth presented in Figure 57.34. This clearly shows that at that place are x teeth in three.1416 inches and, therefore, the rack illustrated is a 10 diametric-pitch rack.

Effigy 57.35 illustrates a similar measurement forth the pitch circle of a x diametric-pitch gear.

Notes:

1.

Materials eight to 22, the bones allowable angle stress (South _BO ), used in estimating load chapters of gears depends on the ratio of the depth of the hard pare at the root fillets to the normal pitch (circular pitch) of the teeth.

$S_{BO}=S_{BOS}or\frac{S_{BOC}}{[1-\mathrm{vii.5}\text{(depth}\text{of}\text{skin}\text{)}\text{/}\text{normal}\text{pitch]}}$

whichever is the less.

2.

Materials viii to 22, values of Due south _co are reliable merely for peel thicker than:

0.003 d × D (d+ D)

3.

Materials 1 to 8, the value of Due south _B0 is approx:

$S_{BO}=600\times \text{Ult}\text{Tensile}\text{−}\frac{\text{Ult}\text{.}{\text{Tensile}}^{\mathrm{three}}}{\mathrm{lx}}$

4.

Gear cutting becomes hard if BHN exceeds 270.

Gear calculations:

$\text{Pitch}-\text{circle}\text{diameter}=\text{module}\times \text{no}.\text{of}\text{teeth}=12\times 25=300\text{mm}$

$\text{Addendum}=\text{module}=12\text{mm}$

$\text{Clearance}=0.25\times \text{module}=0.25\times 12=3\text{mm}$

$\text{Dedendum}=\text{addendum}+\text{clearance}=12+3=15\text{mm}$

$\text{Circular}\text{pitch}=\pi \times \text{module}=\pi \times 12=37.68\text{mm}$

Molar thickness = ½ (round pitch) = 18.84 mm

An advanced tube type BWR [108], which utilizes 54 rod bundle as a fuel chemical element has been considered for CFD simulations for flow and void distribution within rod packet inside the pressure level tube. Station Blackout (SBO) conditions were faux for the reactor with organisation lawmaking RELAP5 [109, 110] and boundary weather condition for the rod parcel at various pseudo steady-state instances were obtained for simulating the multidimensional flow over heated rod bundle during decay rut conditions. This written report reveals the conditions of the void and temperature distribution inside pressure tube and hence facilitates the identification of the hot spots, if present anywhere within the pressure tube. The 54 fuel pins of the heated rod cluster are bundled in three concentric circular pitches forming a fuel rod bundle chosen as 54 rod parcel. It is a rod bundle with 11.2   mm OD fuel pins having heated length of 3.five   m. Fig. 3.10 shows arrangement of the fuel rod bundle inside the coolant channel. The rod bundle is having 1/12th symmetry. However, in a 1/12th section, some the rods contribute only half of their surface expanse to the subchannel. In this report, we have considered a 1/sixth sector of the rod package, which consists of 9 full fuel pins of the bundle equally seen in Fig. 3.11.

CFD simulations are carried out to investigate the wellness of the rod bundle during decay heat removal on a 1/6th sector of the packet. This can exist confirmed with the estimation of the void, temperature and catamenia field inside the rod bundle. Fig. 3.12 shows the Principal Oestrus Transport System (MHTS) depressurization curve along with the variation of period every bit predicted by RELAP5. 4 cases marked as case #1 to case #4 are studied for occurrence of any local hot spot. Instance #1 falls in a region of subcooled boiling, while rests of the betoken fall in the single-stage flow region.

For understanding the catamenia behaviour within the rod bundle during these two different regimes, two cases, i.e. case #1 and instance #4 are presented here. Table 3.2 shows the initial and purlieus conditions obtained from RELAP5 which are simulated and studied with CFD. An axial and radial menstruation profile is applied to the fuel rods that simulate the decay heat for the considered instances during SBO. Fig. three.13A and B shows the heat flux as applied to the fuel rods in 3 radial rings known equally inner, middle, and outer rings.

Many practical rotating disc applications involve protrusions and features, such as bolts and hooks, fastened to either the stationary disc or the rotating disc in a rotor-stator crenel. The protrusions tin significantly influence the local period and estrus transfer in the vicinity of the features, and as a issue the ability required to overcome sticky drag. A typical rotating disc configuration with fixing bolts is illustrated in Effigy five.xx.

•

class elevate

•

boundary layer losses

•

pumping losses

The tangential velocity of the bolts on the disc is larger than the speed of the fluid in the cadre in the rotor-stator gap, giving a relative speed differential between the bolts and the fluid. This results in a drag loss, which can be determined by

(5.128) $\Delta C_{\mathrm{thou},form}=\mathrm{Northward}{C}_D\left(1-{\beta }^2\right){\left(\frac{r}{b}\right)}^3\frac{H{d}_{bolt}}{b^{\mathrm{ii}}}{K}_f$

where Northward is the number of bolts, C_D is the drag coefficient of the bolts in the undisturbed flow, β is the cadre rotation factor in the centre of the cavity (i.e., at z   =   s/2), r is the pitch circle radius for the bolts, b is the outer radius of the disc, H is the height of the bolts or cover, d_bolt is the diameter of the bolts, and Thou_f is a class elevate correction gene due to the interference with the wakes from adjacent bolts (Taniguchi, Sakamoto, and Arie, 1982). For a rotational Reynolds number of four   ×   10⁶ and a nondimensional throughflow of Cw  =   2.6   ×   ten^iv, the swirl ratio was causeless to exist 0.42 based on test evidence and 0.6 in the absence of throughflow.

The boundary layer losses can be accounted for using the von Kármán relationship for turbulent menses over a rotating ring of inner radius r_i and outer radius r_o :

(5.129) $C_m=0.073{\mathrm{Re}}_{\phi }^{-\mathrm{0.two}}{\left(\frac{r_o}{b}\right)}^{\mathrm{iv.half\; dozen}}{\left[1-{\left(\frac{r_i}{r_o}\right)}^{\mathrm{v.7}}\right]}^{0.8}$

If the bolts are assumed to act as the blades for a radial compressor, the pumping losses tin be modeled using the Euler turbomachine equation,

(5.130) $Pow\mathrm{east}r=\Omega \dot{m}\left(u_{\phi ,\mathrm{two}}{r}_o-u_{\phi ,1}{r}_i\right)$

where $\dot{m}$ is the mass flow pumped by the bolt heads, u_φ,1 is the tangential velocity of the bolt-driven fluid at the inner bolt radius, and u_φ,2 is the tangential velocity of the bolt-driven fluid at the outer bolt radius.

Millward and Robinson (1989 performed a series of experiments to quantify the consequence of both static and rotating protrusions and recesses. For a range of conditions with Re_φ   ≤   1   ×   10⁷ and Cw  ≤   1   ×   10⁴ and a range of pitch to diameter ratios between 3 and 20, they developed the post-obit correlation to account for the additional frictional drag over and above that of the plainly disc.

(five.131) $C_{\mathrm{thou}}=2.3{\left(\frac{\dot{m}/\mu r}{\rho \Omega r^2/\mu }\right)}^{\left(\mathrm{ane.four}-r/\mathrm{three}a\right)}{\left(\frac{l_{pitch}}{d_{bolt}}\right)}^{0.44}\frac{r^{\mathrm{three}}\mathrm{Due\; north}A}{b^{\mathrm{v}}}$

where r is the radius of the bolt pitch circumvolve, l_pitch is the pitch of the protrusions, d_bolt is the diameter of the bolts, N is the number of the bolts, and A is the projected cross-sectional area of the protrusion, a is the inner radius of the rotating disc, and b is the outer radius of the disc.

This equation can be restated in terms of the local nondimensional menstruation charge per unit and local rotational Reynolds number equally

(5.132) $C_m=\mathrm{2.iii}{\left(\frac{C{w}_{local}}{R{\mathrm{east}}_{\phi ,\mathrm{50}ocal}}\right)}^{\left(\mathrm{i.4}-r/\mathrm{iii}a\right)}{\left(\frac{l_{pitch}}{d_{bolt}}\right)}^{0.44}\frac{r^{\mathrm{iii}}\mathrm{Northward}A}{b^{\mathrm{five}}}$

The recommended limits for the correlation (Equation five.131 or 5.132) are:

(five.133) $1.5<\frac{r}{a}<\mathrm{two.25}$

(five.134) $0.001<\frac{C{w}_{\mathrm{fifty}ocal}}{R{\mathrm{east}}_{\phi ,local}}<\mathrm{0.i}$

(5.135) $3<\frac{l_{pitch}}{d_{bolt}}<20$

i.

Electrical gear-driven device

Because these jack-upwards drilling rigs all take three legs, the entire platform has nine electric gear-driven devices, and each one is composed of the four same units, equally shown in Figure ii-17. Each unit is composed of an alternating-current motor, gear reducer, equally well as a small gear for output. The components of the entire device are as follows.

a.

Motor

The motor tin can be alternating current or direct current. The three-phase alternating current motor with a power of xiv.72 kW, voltage of 600 Five, and frequency of 600 Hz is by and large used. The power is transferred from motor to reducer.

b.

Gear reducer

The gear reducer is a ii-stage reduction. The first reduction is from a 12-molar gear to a 76-molar gear. The second reduction is from a 17-tooth gear to a 54-tooth gear. Except for the driving gear and driven gear, other gears are all sealed in oil.

c.

Rack

Every bit shown in Figure ii-17, racks are welded on two sides of the cylinder legs. The racks are used to mesh with the output gear of the reducer so as to make the legs move up and down. By and large the norm length of a rack is 10 meters, the distance of the circular pitch is 254 millimeters, and the thickness is 127 millimeters. The gears and racks equally well every bit the axis are all made of alloy steel treated past heating.

d.

The spring plate friction disc safety restriction

This is a shaft safety brake mounted on the motor. A brake plate friction disc is mounted on the motor shaft. The friction plate is pressed by a fork, and fork motion functions through the suction of an electromagnet; the energized electromagnet is connected to the motor switch. Thus, when the motor is turned off, the electromagnet is energized to produce suction, promoting the fork while pressing the friction plate. The motor shaft is completely broken to ensure prophylactic. When the electromagnet is de-energized, the friction plate is supported past spring strength.

eastward.

Shock cushion

In that location are spring steel pad shock absorbers, and each pile leg is connected to the platform with them, with a setup more often than not composed of seven elastic steel pads. The purpose is to reduce the impact of legs on the platform deck when legs initially contact the seabed.

f.

Solid pile wedge

This aims at fixing the platform with the pile legs. There are viii wedges on each leg of one thigh, with four on the upper side and four on the lower side. Consequently, in that location are 72 wedges on the entire platform with three legs and 9 thighs.

Figure 2-17. Electrically driven gear lifting device.

2.

Lifting functioning of electric gear-driven device

Pinions from the gearbox are symmetrically arranged in pairs on both sides of the cylindrical thigh and are meshed with the rack on both sides of the thigh at the same meridian, to offset the horizontal component force. Each thigh has iv pinions meshing with the rack simultaneously from top to bottom. There are 36 pairs of pinions on the entire platform with three legs and nine thighs meshing with the rack on the thigh, and thus when the motor synchronizes, the three pile legs of the platform are synchronically transmitted through the gears and racks, gradually lifting upwards. The unabridged platform lifting performance of the motor can be mainly controlled by the platform command room, and also by each pile leg. Legs tin drop downwards due to their gravity, merely they should control the rate of refuse by the brakes to ensure condom. The platform itself rises to a certain height on the surface of the water and downwardly to the water in the conditions of pile legs fixed to the seabed. Because the motor and gearbox unit of the lifting device are installed on the platform deck, it even so uses an electrical gear manual method, which is the aforementioned principle as the pile lifting its leg to operate.

The wear load F_w is

(2.54) $F_{\mathrm{westward}}=d_{p}BKQ,$

where dp is the pitch diameter of the smaller gear (pinion), G is the stress gene for fatigue, Q = 2N _g/(Np + Ng), Ng is the number of teeth on the gear, and Northward_p is the number of teeth on the pinion.

The stress factor for fatigue has the expression

$\mathrm{Thousand}=\frac{{\mathrm{southward}}_{es}^{\mathrm{two}}(sin\varphi )(\mathrm{i}/\mathrm{Eastward}p+1/\mathrm{Eastward}g)}{\mathrm{i.four}},$

where s_es is the surface endurance limit of a gear pair (psi), E_p is the modulus of elasticity of the pinion material (psi), E_g is the modulus of elasticity of the gear material (psi), and ϕ is the pressure bending. An estimated value for surface endurance is

${\mathrm{southward}}_{es}=(400)(\text{BHN})-\mathrm{10,000}\text{psi},$