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1 ME 302 DYNAMICS OF MACHINERY GEAR FORCE ANALYSIS Dr. Sadettin KAPUCU © 2007 Sadettin Kapucu

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Gaziantep University 2 GEAR FORCE ANALYSIS Gears are used to transmit force and motion from one shaft to the other.

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Gaziantep University 3 Spur Gear l In theory, one blank transmit force and motion via the friction force occurring at the pitch point. There must be no slip between the two blanks at the pitch points. Blanks roll but do not slip with respect to each other. Input /output relationship for circular gear is linear. So:

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Gaziantep University 4 Spur Gear l Magnitudes of friction forces are generally small. So, if we want to transmit larger amounts of forces, friction becomes inadequate and slip occurs. To prevent slip, we make the joint between links 2 and 3 “form closed”. This is obtained by putting teeth around the periphery of the gear blanks. For fitting these details, we need some space. We simply separate the gear blanks apart a bit. This separation causes the transmitted force to at an angle called “pressure angle”, denoted by. Pressure angle is standardized; In imperial system In international system

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Gaziantep University 5 Spur Gear Characteristic dimension for the tooth is either the number of teeth on the blank or the length of the portion of the pitch circle within the tooth body.

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Gaziantep University 6 Helical Gear To improve the force carrying capacity of the gears the teeth are cut in a helix. This increase the tooth thickness, so helical gears are stronger. Also they operate with less noise. Force acting normal to the tooth surface, hence it makes an angle of (helix angle) with the gear axis of rotation and with the common tangent.

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Gaziantep University 7 Bevel Gear Bevel gears are conical in shape and used to couple the shafts not parallel but intersecting. Point of intersection of shafts is called the apex. Gear force acts as distributed over the whole tooth thickness, but we can assume a resultant single force acting on the mid point of the tooth thickness.

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Gaziantep University 8 Example 1 The gear train shown in the figure is composed of 6 diametral pitch spur gears and 20 degrees pressure angle. Link 2 is the driving gear, delivering 25 Hp at a CCW speed of 900 rpm. Gear 3 is an idler and gear 4 carries the external load. Draw freebody diagrams of the gears, show all the forces acting and calculate their magnitudes. Given:

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Gaziantep University 9 Example 1 F’ 3t F’ 3r F 3x F 3y F 3t F 3r F 4t F 4r F 2r F 2t F 2x F 2y F 4x F 4y 44 22 x y + 33

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Gaziantep University 10 Example 1 F 2r F 2t F 2x F 2y 44 x y + From second gear freebody diagram:

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Gaziantep University 11 Example 1 F’ 3t F’ 3r F 3x F 3y F 3t F 3r x y + From third gear freebody diagram: 33

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Gaziantep University 12 Example 1 F 4t F 4r F 4x F 4y 44 x y + From fourth gear freebody diagram: Radius of the gears can be calculated following formulas:

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Gaziantep University 13 Example 1 Gear forces of the second gear become: Speed of the fourth gear is: Then, gear forces of the fourth gear become: Using the equations unknowns become: F’ 3t F’ 3r F 3x F 3y F 3t F 3r F 4t F 4r F 2r F 2t F 2x F 2y F 4x F 4y 44 44 x y +

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