Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_78

⚡ Mecademy AIENG정역학 · ch6  Problem Statement An automobile disk brake consists of a flat-faced rotor and a caliper which contains a disk pad on each side of the rotor. For equal forces behind the two pads with the pressure uniform over the pad, show that the moment applied to the hub is independent of the angular span of the pads. Would pressure variation with change the moment? Problem 6/78 (a) Show that the moment applied to the hub is independent of the angular span ● Calculation Process 1. Present Final Formula: The total friction moment is the sum of the moments from both pads. For uniform pressure , the clamping force on one pad and the friction moment are given by: The total moment for two pads is . 2. Substitute Values: First, evaluate the clamping force for a uniform pressure : From this, the pressure is . Now, evaluate the moment for one pad: 3. Partial Operations: Substitute the expression for into the total moment equation : Pp β θ β M pP M pad P= p r d r d θ∫ 0 β ∫ R i R o M = pad μp r d r d θ∫ 0 β ∫ R i R o 2 M=2M pad Pp P= p d θ r d r = ∫ 0 β ∫ R i R o p⋅β⋅ = [ 2 r 2 ] R i R o ( R − 2 pβ o 2 R ) i 2 p= β(R −R ) o 2 i 2 2P M = pad μp d θ r d r = ∫ 0 β ∫ R i R o 2 μp⋅β⋅ = [ 3 r 3 ] R i R o ( R − 3 μpβ o 3 R ) i 3 p M=2M pad 4. Final Calculation: Simplify the expression: ● Final Conclusion: Since the angular span cancels out in the final expression relating total moment to the clamping force , the moment is independent of the angular span of the pads. (b) Effect