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Simple Machines

Simple Machines. Simple Machines. Work done = Force x distance moved (in direction of the force) In this case the effort move the same distance as the load The effort force is equal to the load force (weight of load). Effort. Load. Simple Machines. Force multipliers

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Simple Machines

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  1. Simple Machines

  2. Simple Machines Work done = Force x distance moved (in direction of the force) In this case the effort move the same distance as the load The effort force is equal to the load force (weight of load) Effort Load

  3. Simple Machines • Force multipliers • Work done = Force x distance moved (in direction of the force) • Work done by effort = work done on load • F x d (effort)= F x d (Load) • The further the distance moved by the effort force compared to the distance moved by the load means that a smaller effort force can move a larger load force

  4. Simple Machines Effort Load In the case of a lever the effort force moves further than the load so the less effort can lift a larger load

  5. Simple Machines Diameter 400mm Diameter 200mm Driven pulley 10 RPM Driver pulley 20 RPM

  6. Simple Machines A wheel and axle assembly used as a hoist the effort force again moves further than the load force 100mm 400mm Load Effort

  7. Simple Machines (equations) The mechanical advantage (MA) of a system = load /effort The velocity ratio (VR) = Distance moved by effort/ distance moved by load

  8. Simple Machines (equations) • In the case of the hoist shown in the diagram the effort moves a distance of 400π(Circumference of wheel) • And the load moves by 100π(circumference of the axle) • The velocity ratio = 400π/100π • = 4

  9. Simple Machines (equations) • The efficiency (η) of the for a system for any set of values is found by the equation • η = (MA x100)/VR x 100 • The limiting efficiency • =100/(VR x a) (a = gradient of graph)

  10. Simple Machines (equations) • The Law of the machine (in the form of y = mx + c) E= aW+ b Where W is the weight (load force) • E is the Effort Force • a and b are found by plotting the graph of load against effort

  11. Simple Machines (a) is the gradient of the graph (0.31) W = aE + b E kN (y) W kN (x) b is where the line crosses the y axis

  12. Simple Machines MAmax ≈ 3.24 Maximum (ideal) MAmax is found by plotting MA against W (load) and estimating the value for MA where the line is horizontal MA W kN

  13. Simple Machines Plotting the graph of Friction effort against the load (W) shows that the friction effort decreases with increasing load The efficiency of the system increases with increasing load F Friction effort W kN

  14. Simple Machines • Friction effort is calculated using the equation • F = E- (W/MAmax)

  15. Simple Machines

  16. Simple Machines

  17. Simple Machines • Limiting efficiency 1 ÷ (a x VR) • = 1 ÷ (0.31 x4) • 80.6% • A machine can never reach limiting efficiency because of friction losses in the system

  18. Simple Machines A 0.3m C D 0.8m B 0.2m 0.6m

  19. Simple Machines • In the above belt drive system, the input power is 10kW at a speed of 480 rpm and the efficiency is 85% • Power output = η x 10000 • = 0.85 x 10000 = 8500W • =8.5kW

  20. Simple Machines • Calculate the speed at pulley D • Speed at A = 480/60 = 8 rev/sec • Speed at B = 8 x (8/3) = 21.3 rev/sec • Speed at C= 21.3rev/sec • Speed at D =21.3 X (6/2) = 63.9 rev/sec

  21. Simple Machines • Calculate the output torque at D • Torque = power/ (2π x number of turns (per sec)) • = 8500/ (2π x 63.9) • 21.17Nm

  22. Simple Machines • The ratio of tensions in the output belt is 5:1. • Calculate the effective tension in the belt and show that the maximum tension the belt is subjected to is less than 400N. • Effective tension = ( T1 – T2) • = torque/ radius of pulley D • =21.17/0.1 • (T1 - T2)= 211.7N

  23. Simple Machines • T1/T2 = 5/1 • T1 - T2 = 5-1 = 4 • T2 = 211.7/4 = 52.93N • T1 = 52.93 x 5 • = 264.63 N

  24. Simple Machines • If higher speeds or greater power transmission is required vee belts used with vee grooves in the will be more effective because they provide a larger surface area which will give a better grip to prevent slip.

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