8//0 hapter seven Laith atarseh are very important in power transmission between a drive rotor and driven rotor What are the functions of gears? - Transmit motion and torque (power) between shafts - Maintain constant speed ratios between power transmission shafts What is gear? In general, a gear is a circular disk with teeth along the circumference
8//0 Gear types are divided into four main types depending on the relation between the tooth axis and the gear axis this relation provide different form of transmission and these types are Rack and pinion gear Rack is gear that has infinite radius. This type is used to transform rotational torque into axial force Gear types Spur gear xis of the gear transmits motion between two parallel shafts. The teeth have straight line shape Helical gear The tooth axis is apart of helix about the gear axis. This type can transmit the power between two parallel or none parallel shafts
8//0 Gear types evel gear The tooth axis is apart of cone about the gear axis. This type can transmit the power between two intersecting shafts Worm gear Is a special case of helical gear and used to transmit power from high speed shaft to low speed shaft with different ratios gear train Gear train is a sequence of consecutive meshed gears such the one shown below When gears are meshed in gear train, one of the gears is drive (input) and the others are driven. However, one of the driven gears is called output
8//0 Gear parameters Problem: mention the types of gears shown in the figure Torque & Efficiency The power transmitted by a torque T -m applied to a shaft rotating at rev/min is given by: T P 60 In an ideal gear box, the input and output powers are the same so; T T P 60 60 T T T T GR Power out Power In T 60 T 60 T T
8//0 Problem: mention the types of gears shown in the figure Velocity ratio d mv d in out in out n... mv n Torque ratio m T d d out in out in m T n n n... n Problem: mention the types of gears shown in the figure Speed ratio Speed ratio is the ratio between the output gear angular velocity (ω o ) and the input gear velocity (ω i ) : speed ratio = ω o / ω i For example, the gear speed ratio for the gear train shown below if we assume gear is the drive and gear is the driven: : speed ratio = ω / ω 5
8//0 Problem: mention the types of gears shown in the figure Example [] gear box has an input speed of 500 rev/min clockwise and an output speed of 00 rev/min anticlockwise. The input power is 0 kw and the efficiency is 70%. Determine the following. i. The gear ratio; ii. The input torque.; iii. The output power.; iv. The output torque; v. The holding torque. Solution: G. R or VR Input speed Output T Input Power 60 500 5 speed 00 60Input Power T Problem: mention the types of gears shown in the figure Example [] 600000 Input torquet 7. m 500 ( egative clockwise) Output power 0.7 Inpu power Power Output 0.7 0 kw 60000 Output torquet 5. 6 m 00 Positive unticlockwise 6
8//0 Problem: mention the types of gears shown in the figure Example [] T T 7. 5.6 T T T 0 0 7. 5.6 8. m lockwise Problem: mention the types of gears shown in the figure Simple gear train x x x x The negative sign means change in the direction of rotation 7
8//0 Problem: mention the types of gears shown in the figure Simple gear train Example Take: ω = 500 RPM = 0 =50 =70 =5 Find ω? x x x 0 500 000RPM 5 x The negative sign means change in the direction of rotation Problem: mention the types of gears shown in the figure ompound Gear train Input ompound gears are simply a chain of simple gear trains with the input of the second being the output of the first. chain of two pairs is shown below. Gear is the output of the first pair and gear is the input of the second pair. and are locked to the same shaft and revolve at the same speed. GER '' GER '' D Output ompound GER '' GER 'D' 8
8//0 Problem: mention the types of gears shown in the figure ompound Gear train For large velocities ratios, compound gear train arrangement is preferred. The velocity of each tooth on and are the same so: Input D Output t = t -as they are simple gears. ompound GER '' Likewise for and D, t = D td. GER '' GER 'D' D D x x D x x D GER '' Problem: mention the types of gears shown in the figure ompound Gear train Example Take: ω = 500 RPM = 0 =50 =75 D =5 Find ω D? Input D Output ompound GER '' D D D x x x D x D GER '' x 0 75 500 x 500RPM 50 5 D GER '' GER 'D' 9
8//0 Gear operation The goal is to have constant speed ratio, it can be observed that is the motion transmit between gears teeth is a cam mechanism so, to guaranty the constant speed ratio, the intersection between the line of action and the line of center (k) is held constant in space,therefore the tooth profile must guaranty this requirement. This requires the line of action to be stationary in space and the tooth profile which guaranty this can be constructed by involute profile. Gear operation The involute profile is the resultant of the straight line motion of the point of contact along the common normal or line of action and the negative of the rotating motion of the observer attached to the gear at the base circle Pc = circular pitch = distance between two tooth along the pitch circle circumference of the pitch circle Pc umber of tooth d 0
8//0 Problem: mention the types of gears shown in the figure Length of action (Z) Z r a r cos r a r cos sin p p p g g g Problem: mention the types of gears shown in the figure Epicyclic or planetary gear train Some gears experience planetary motion, it revolves about its own axis and its axis revolves about fixed axis (sun gear).the planet gear is held in its orbit by an arm called the planet arm. the mobility of this set of gears is M = (-) -() - = (two inputs )
8//0 Epicyclic or planetary gear train Speed ratio To find the speed we must take the speed of arm and this can be done by observed the whole motion from the arm point view and for this process defined e which called the train value as observed by the arm e out in arm arm Epicyclic or planetary gear train Example ( problem 9.6): Find ω If = 50T, = 5T, = 5T, 5 = 0T, 6 = 0T, ω 6 = 0, ω arm = -50
8//0 Epicyclic or planetary gear train Solution Let to be input and 6 output 6 e arm arm arm arm 5 RPM 6 6 500 50 5 5 0 50 6 50 6