ENGINEERING COLLEGE

A 26-tooth pinion rotating at a uniform 1800 rpm meshes with a 55-tooth gear in a spur gear reducer. Both pinion and gear are manufactured to a quality level of 10. The transmitted tangential load is 22 kN. Conditions are such that Km = 1.7. The teeth are standard 20-degree, full-depth. The module is 5 and the face width 62 mm. Determine the bending stress when the mesh is at the highest point of single tooth contact.

Answers

Answer 1

Answer:

Answer:

The bending stress of the face tooth is $\sigma _(bg) = 502.82 MPa$

Explanation:

From the question we are told that

The number of tooth of the pinion is $N_t = 26 \ tooth$

The velocity of rotation is given as $\omega_p = 1800 rpm$

The number of tooth is of the gear is $N_g = 55 \ tooth$

The quality level is $Q_r = 10$

The transmitted tangential load is $F_T = 22\ kN$ = $22 KN * (1000N)/(1KN) = 22*10^3 N$

$k_m = 1.7$

The angle of the teeth is $\theta_t = 20^o$

The module is $M= 5$

The face width is $W_f = 62mm$

The diameter of the pinion is mathematically represented as

$d_p = M * N_t$

Substituting the values

$d_p = 5 *26$

$= 130 mm = (130)/(1000) = 0.130m$

The pitch line velocity is mathematically represented as

$V_t = (d_p )/(2) (2 \pi \omega_p)/(60)$

Substituting values

$= (0.130)/(2) * (2 * 3.142 * 1800 )/(60)$

$= 12.25\ m/s$

Generally the dynamic factor is mathematically represented as

$K_v = [(A)/(A +√(200V_t) ) ]^B$

Now B is a constant that is mathematically represented as

$B = ((12 -Q_r )^(2/3))/(4)$

substituting values

$= ((12- 10 )^(2/3))/(4)$

$=0.3968$

A is also a constant that is mathematically represented as

$A = 50 + 56(1 -B)$

Substituting values

$= 50 +56 (1- 0.3968)$

$= 83.779$

Substituting these value into the equation for dynamic factor we have

$K_v = [(83.779)/(83.779 + √(200 * 12.25) ) ]^(0.3968)$

$= 0.831$

The geometric bending factor for a 20° profile from table

"AGMA Bending Geometry Factor J for 20°, Full -Depth Teeth with HPSTC Loading , Table 2-9"

That corresponds to 55 tooth gear meshing with 26 pinion is

$J_g = 0.41$

the diameter pitch can be mathematically represented as

$p_d = (1)/(M)$

Substituting values

$p_d = (1)/(5)$

$=0.2mm^(-1)$

The mathematically representation for gear tooth bending stress in the teeth face is as follows

$\sigma_(bg) = (F_T \cdot p_d )/(W_f * J_g)(K_a K_(dt) )/(K_v) K_s K_B K_t ----(1)$

Where $W_t$ is the tangential load

$W_f$ is the face width

$K_a$ is the application factor this is obtained from table "Application Factors, Table 12-17 " and the value is $K_a$ = 1

$K_(dt)$ is the load distributed factor

$K_s$ is the size factor

$K_B$ is the rim thickness factor which is obtained for M which has a value 1

$K_t$ is the idler

Substituting values into equation 1

$\sigma_(bg) = (22*10^3 *0.2)/(62 * 0.41) * (1 * 1.7 )/(0.831) * 1 *1 *1.42$

$= 502.82 N/mm^2$

$= 502.82 * 1000 * (N)/(m^2)$

$= 502.82 MPa$

Related Questions

Which of the following expressions causes an implicit conversion between types? Assume variable x is an integer, t is a float, and name is a string.Group of answer choices7.5 + (x / 2)x + 2 * x"Hello, " + str(name)print(str(t))
Cody’s car accelerates from 0m/s to 45 m/s northward in 15 seconds. What is the acceleration of the car
The cost of hiring new employees outpaces the raises for established employees is A. Salary compression B. Occupational based payC. Merit payD. Need for Achievement
Which property of real numbers is shown below?3 + ((-5) + 6) = (3 + (-5)) + 6 commutative property of addition identity property of multiplication associative property of addition commutative property of multiplication
The pressure in an automobile tire depends on thetemperature of the air in the tire. When the air temperature is25°C, the pressure gage reads 210 kPa. If the volume of the tire is 0.025 m3, determine the pressure rise in the tire whenthe air temperature in the tire rises to 50°C. Also, determinethe amount of air that must be bled off to restore pressure toits original value at this temperature. Assume the atmosphericpressure to be 100 kPa.

Webster is giving a speech on the benefits of moving toward the use of windmill energy instead of having to rely on fossil fuels. Most likely, he will select which method of arrangement?

Answers

Answer:

the netuon arrangment

Explanation:

A technician has been dispatched to assist a sales person who cannot get his laptop to display through a projector. The technician verified the video is displaying properly on the laptop's built-in screen. Which of the following is the next step the technician should take?

Answers

Answer:verify proper cable is hooked between laptop and projector. HDMI ports or 15 pin video output to input.

And laptop is selected to output to respective video output.

Explanation:

B. Suppose R1 is a fuse which burns out due to a sudden surge of current, thus, it essentially becomes an open switch. How do the currents change after this?

Answers

Answer:

The currents becomes 0

Explanation:

when the fuse burns out due to a sudden surge of current and becomes an open switch (with a resistance of Infinity ∞) this automatically reduces the currents through it to zero

A test bottle containing just seeded dilution water has its DO level drop by 0.8 mg/L in a 5-day test. A 300 mL BOD bottle filled with 30 mL of wastewater and the rest with seeded dilution water experiences a drop of 7.3 mg/L in the same period (5-day). Calculate the BOD5 of the wastewater.

Answers

Answer:

BOD_5 = =65.8 mg/l

Explanation:

dilution water DO level = 0.8 m/l

BOD level drop to 7.3 mg/l

we know that BOD at 5th day can be clculated by using following relation $BOD_5 = ((D_1 -D_2) -(B_1-B_2)(1-P))/(P)$

$D_1 -D_2$ - DO drop in BOD bottle

$B_1-B_2$ - dilution water drop

P= 30/300 = 0.1

$BOD_5 = ((7.3) -(0.8)(1-0.1))/(0.1)$

$BOD_5 = =65.8 mg/l$

Clothing made of several thin layers of fabric with trapped air in between, often called ski clothing, is commonly used in cold climates because it is light, fashionable, and a very effective thermal insulator. So, it is no surprise that such clothing has largely replaced thick and heavy old-fashioned coats. Consider a jacket made up of six layers of 0.1 mm thick synthetic fabric (k = 0.026W/m.K) with 1.2 mm thick air space (k = 0.026 W/m.K) between the fabric layers. Assuming the inner surface temperature of the jacket to be 25˚C and the surface area to be 1.25 m2 , determine the heat loss through the jacket when the temperature of the outdoors is -5˚C and the heat transfer co-efficient of outer surface is 25 W/m2 .K. What would be the thickness of a wool fabric (k = 0.035W/m.K) if the person has to achieve the same level of thermal comfort wearing a thick wool coat instead of a jacket. (30 points)

Answers

Answer:

Q=127.66W

L=9.2mm

Explanation:

Heat transfer consists of the propagation of energy in the form of heat in different ways, these can be convection if it is through a fluid, radiation through electromagnetic waves and conduction through solid solids.

To solve any problem related to heat transfer, the general equation is used

Q = delta / R

Where

Q = heat

Delta = the temperature difference

R = is the thermal resistance by conduction, convection and radiation

to solve this problem we propose the previous equation

Q = delta / R

later we find R

$R=[tex]r=(6L1)/(AK1) +(5L2)/(AK2)+(1)/(Ah)$

$R=(6(0.0001))/((1.25)(0.026)) +(5(0.012))/((1.25)(0.026))+(1)/((25)(1.25)) =0.235 K/w$

Q=(25-(-5))/0.235=127.66W

part b

we use the same ecuation with Q=127.66

Q = delta / R

Δ $R=(L)/(KA) +(1)/(hA) \nR=(L)/((0.035)(1.25)) +(1)/((25)(1.25))\n R=22.85L+0.032\nQ=(T1-T2)/R\n\n127.66=(25-(-5))/(22.85L+0.032)\nsolving for L\nL=9.2mm$

The Clausius inequality expresses which of the following laws? i. Law of Conservation of Mass ii. Law of Conservation of Energy iii. First Law of Thermodynamics iv. Second Law of Thermodynamics

Answers

Answer:

(iv) second law of thermodynamics

Explanation:

The Clausius inequality expresses the second law of thermodynamics it applies to the real engine cycle.It is defined as the cycle integral of change in entropy of a reversible system is zero. It is nothing but mathematical form of second law of thermodynamics . It also states that for irreversible process the cyclic integral of change in entropy is less than zero

Other Questions

An automobile engine consumes fuel at a rate of 27.4 L/h and delivers 55 kW of power to the wheels. If the fuel has a heating value of 44,000 kJ/kg and a density of 0.73 g/cm3, deter- mine the efficiency of this engine in percentage(

Where should the Q point of an amplifier be on a DC load line to have the LARGEST linear output?

In response to the market revolution:the legal system worked with local governments to find better ways to regulate entrepreneurs.Chief Justice John Marshall ruled that legislatures could not alter or rescind charters and contracts that previous legislatures had created.local judges protected businessmen from paying property damages associated with factory construction and from workers seeking to unionize.Massachusetts Chief Justice Lemuel Shaw held in Commonwealth v. Hunt that workers had no right to organize.corporations proved less able to raise capital than chartered companies did.

The 50mm diameter cylinder is made from Am 1004-T61 magnesium (E = 44.7GPa, a = 26x10^-6/°C)and is placed in the clamp when the temperature is T1 = 15°C. If the two 304-stainless-steel (E =193GPa, a = 17x10^-6/°C) carriage bolts of the clamp each have a diameter of 10mm, and they holdthe cylinder snug with a negligible force against the rigid jaws, determine the temperature at whichthe average normal stress in either the magnesium or steel becomes 12 MPa.