GATE Past Year Questions: Brakes, Clutches & Ropes | Design of Machine Elements - Mechanical Engineering PDF Download

Q1: A band brake shown in the figure has a coefficient of friction of 0.3 . The band can take a maximum force of 1.5kN. The maximum braking force (F) that can be safely applied is _____ N. (rounded off the nearest integer).  [GATE ME 2024]
Ans: 115 to 119
Data given, μ = 0.3
F = 1.5kN = 1500 N
θ = 180º = π
F.B.D. of system is
∑M₀ = 0
F × 1000 − T₂ × 200 = 0
F = T₂/5

T₂ = 584.492 N
So, F =
= 116.9 N ≈ 117 N

Q1: The braking system shown in the figure uses a belt to slow down a pulley rotating in the clockwise direction by the application of a force P. The belt wraps around the pulley over an angle α = 270 degrees. The coefficient of friction between the belt and the pulley is 0.3. The influence of centrifugal forces on the belt is negligible.
During braking, the ratio of the tensions T₁ to T₂ in the belt is equal to __________. (Rounded off to two decimal places)
Take π = 3.14.  [GATE ME 2023]
Ans: 4.05 to 4.15
μ = 0.3
α = 270º = 3π/2
T₁/T₂ = e^μα 
So, 

Q1: A short shoe drum (radius 260 mm) brake is shown in the figure. A force of 1 kN is applied to the lever. The coefficient of friction is 0.4.
The magnitude of the torque applied by the brake is ________N.m (round off to one decimal place).    [GATE ME 2021 SET-1]
Ans: 199 to 201
Taking moment about 'O'
R_N(500) + F_γ[310 − 260] - 1000 x 1000 = 0
R_N(500) + 0.4(R_N)(50) - 1000 x 1000 = 0
R_N = 1923.076 N
F_r = µR_N = 769.23 N
T_f = F_r x R = 200 N - m

Q1: A helical spring has spring constant k. If the wire diameter, spring diameter and the number of coils are all doubled then the spring constant of the new spring becomes   [GATE ME 2020 SET-2]
(a) k/2
(b) k
(c) 8k
(d) 16k
Ans: (b)
k_{(sping )} = Gd⁴/8D³n
k_new =

Hence k_new = k

Q2: In a disc-type axial clutch, the frictional contact takes place within an annular region with outer and inner diameters 250 mm and 50 mm, respectively. An axial force F₁ is needed to transmit a torque by a new clutch. However, to transmit the same torque, one needs an axial force F₂ when the clutch wears out. If contact pressure remains uniform during operation of a new clutch while the wear is assumed to be uniform for an old clutch and the coefficient of friction does not change, then the ratio F₁/F₂ is_________ (round off to 2 decimal places).  [GATE ME 2020 SET-1]
Ans: 0.85 to 0.89
T = μW × R_m
T_new = μ × W × R_new
T_new = μ × W_new x

T_odd = μ × W × R_old
T_new = T_dd
W_new

 = 0.871

Question for GATE Past Year Questions: Brakes, Clutches & Ropes

Try yourself:For the brake shown in the figure, which one of the following is TRUE?

 [2016,Set-2]

 

• A.

  Self energizing for clockwise rotation of the drum
• B.

  Self energizing for anti-clockwise rotation of the drum
• C.

  Self energizing for rotation in either direction of the drum
• D.

  Not of the self energizing type

Explanation

Taking moment about hinge in clockwise
N_b – Fl – μNc = 0
F = N(b - μc)/l
Self energizing if b > mc so for clockwise rotation of drum the brake is self energizing.

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Question for GATE Past Year Questions: Brakes, Clutches & Ropes

Try yourself:A force of 400 N is applied to the brake drum of 0.5 m diameter in a band brake system as shown in figure, where the wrapping angle is 180°. If the coefficient of friction between the drum and the band is 0.25, the braking torque applied, in Nm is

[2012]

• A.

  100.6
• B.

  54.4  
• C.

  22.1
• D.

  15.7

Explanation

As the drum is rotating in anti clock wise direction, T₁ will be right side & T₂ will be clock side.
T₁/T₂ = e^μθ  = e^0.25 x π = 2.19
⇒ T₂ = 182.375 N
Braking torque = (T₁ – T₂)r
= 54.4 N – m

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