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DanielleElmas [232]
3 years ago
5

A 24-tooth gear has AGMA standard full-depth involute teeth with diametral pitch of 12. Calculate the pitch diameter, circular p

itch, addendum, dedendum, tooth thickness and clearance. All dimensions must be taken to 4 decimal places to account for manufacturing tolerances.
Engineering
2 answers:
torisob [31]3 years ago
5 0

Answer:

Explanation:

Given:

Tooth Number, N = 24  

Diametral pitch pd = 12

pitch diameter, d = N/pd = 24/12 = 2in

circular pitch, pc = π/pd  = 3.142/12 = 0.2618in

Addendum, a  = 1/pd = 1/12 =0.08333in

Dedendum, b = 1.25/pd = 0.10417in

Tooth thickness, t = 0.5pc = 0,5 * 0.2618  = 0.1309in

Clearance, c = 0.25/pd = 0.25/12 = 0.02083in

Oduvanchick [21]3 years ago
4 0

Answer:

• Pitch diameter = 2.0000in

• Circular pitch = 0.2618in

• Addendum = 0.0833in

• Dedendum = 0.1042in

• Tooth thickness = 0.1309 in

• Clearance = 0.02083 in

Explanation:

We are given:

Total number, N = 24

Diametral pitch, pd = 12 in

•to calculate pitch diameter, we use:

d = \frac{N}{pd} =\frac{24}{12} = 2.0000 in

•to calculate circular pitch, we have:

P_c= \frac{pi}{pd} = P_c = \frac{3.142}{12}= 0.2618in

•To calculate addendum:

Addendum, a= \frac{1.0000}{pd} => \frac{1.0000}{12} = 0.0833in

•Dedendum:

b= \frac{1.2500}{pd}=> \frac{1.2500}{12} =0.1042in

•Tooth thickness, t :

t = 0.5*pc

= 0.5*0.2618 = 0.1309in

•Clearance, c:

c = \frac{0.2500}{pd} => \frac{0.2500}{12} = 0.2083in

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Answer:

Explanation:

Given that:

<u>At state 1:</u>

Pressure P₁ = 20 bar

Volume V₁ = 0.03 \mathbf{m^{3}}

From the tables at saturated vapour;

Temperature T₁ = 212.4⁰ C  ; v_1 = vg_1 = 0.0996 \mathbf{m^{3}} / kg

The mass inside the cylinder is m = 0.3 kg, which is constant.

The specific internal energy u₁ = ug₁ = 2599.2 kJ/kg

<u>At state 2:</u>

Temperature T₂ = 200⁰ C

Since the 1 - 2 occurs in an isochoric process v₂ = v₁ = 0.099 \mathbf{m^{3}} / kg

From temperature T₂ = 200⁰ C

v_f_2 = 0.0016 \ m^3/kg  

vg_2 = 0.127 \ m^3/kg  

Since  vf_2 < v_2 , the saturated pressure at state 2 i.e. P₂ = 15.5 bar

Mixture quality x_2 = \dfrac{v_2-vf_2}{vg_2 -vf_2}

x_2 = \dfrac{(0.099-0.0016)m^3/kg}{(0.127 -0.0016) m^3/kg}

x_2 = \dfrac{(0.0974)m^3/kg}{(0.1254) m^3/kg}

\mathsf{x_2 =0.78}

At temperature T₂, the specific internal energy u_f_2 = 850.6 \ kJ/kg , also ug_2 = 2594.3 \ kJ/kg

Thus,

u_2 = uf_2 + x_2 (ug_2 -uf_2)

u_2 =850.6  +0.78 (2594.3 -850.6)

u_2 =850.6  +1360.086

u_2 =2210.686 \ kJ/kg

<u>At state 3:</u>

Temperature T_3=T_2 = 200 ^0 C ,

V_3 = 2V_1 = 0.06 \ m^3

Specific volume v_3 = 0.2  \ m^3/kg

Thus; vg_3 =vg_2 = 0.127 \ m^3/kg ,

SInce v_3 > vg_3, therefore, the phase is in a superheated vapour state.

From the tables of superheated vapour tables; at v_3 = 0.2  \ m^3/kg and T₃ = 200⁰ C

The pressure = 10 bar and v =0.206 \ m^3/kg

The specific internal energy u_3 at the pressure of 10 bar = 2622.3 kJ/kg

The changes in the specific internal energy is:

u_2-u_1

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= (2622.3 - 2210.686)  kJ/kg

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≅ 410 kJ/kg  

We can see the correct sketches of the T-v plot showing the diagrammatic expression in the image attached below.

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Explanation:

Outer di ameter d_{0}=400 \mathrm{mm}[tex] Thickness of the cylinder [tex]t=10 \mathrm{mm}

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d_{1}=380 \mathrm{mm}

Given loading on the cylinder P=300 \mathrm{kN} Helix an gle of the weld form \theta=20^{\circ}

(i) Normal stress on the plane at angle \theta=20^{\circ} is

\sigma=\frac{P \cos ^{2} \theta}{A_{0}}

\text { Where } A_{0}=\frac{\pi}{4}\left(d_{0}^{2}-d_{1}^{2}\right)

\quad=\frac{\pi}{4}\left(400^{2}-380^{2}\right)

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\sigma=\frac{-300 \times 10^{2} \times \cos ^{2} 20}{12.25221 \times 10^{-1}}

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(ii) Shear stress along an angle of \theta=20^{\circ} is \tau=\frac{P}{A_{0}} \cos \theta \sin \theta

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2 years ago
Q9. A cylindrical specimen of a metal alloy 54.8 mm long and 10.8 mm in diameter is stressed in tension. A true stress of 365 MP
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Answer:

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Explanation:

The relation between true stress and true strain is given as:

σ = k εⁿ

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σ = true stress = 365 MPa

k = constant

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ε = (61.8 - 54.8)/54.8 = 0.128

n = strain hardening exponent = 0.2

Therefore,

365 MPa = K (0.128)^0.2

K = 365 MPa/(0.128)^0.2

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σ = true stress = ?

k = constant = 550.62 MPa

ε = true strain = Change in Length/Original Length

ε = (64.7 - 54.8)/54.8 = 0.181

n = strain hardening exponent = 0.2

Therefore,

σ = (550.62 MPa)(0.181)^0.2

<u>σ = 391.2 MPa</u>

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3 years ago
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