The Gear System - Report Example

Experiment 2: THE GEARED SYSTEM AND THE GEAR BOX. Introduction. This experimental set up is a rubric of a functional gear as applied in Physics and in other disciplines. It gives a reflection of how the gear system operates, how sizes and numbers of teeth in any given gear system relate, as well as, how the naming of the gear system is achieved. Theory has it that the larger the gear the less the revolution and the reverse are also true. But can this be explained experimentally? Questions that are of fundamental and the experiment seek answers to are: what is the gear system? What does the gear system entail? And last but not least, what objectives define this experiment? A gear is a common device that is used in transmission of power in engineering. It is an essential component in running of automobiles and machinery (Uicker 67). A geared system includes any system that is toothed and designed for transmission or receiving of motion by means of using successive engaged teeth. The wheel is called the larger wheel where as the pinion is referred to as a smaller gear. A gear is used in engineering situations. It facilitates the rotational speed, the transmission of power (torque) and the direction of output and input shaft. Simpler gear specifications occurs in a gear ratio whereby the ratio of the number of hearing teeth that are the driving gears to the numbers of hearing teeth on the driven gear could be more or less than one. In cases where value of the ratio is more than one, this will lead to a reduced driving rotational speed, and in cases where it is less than one, it could give an increased speed. This experiment seeks to study different gear arrangements and some uses of the gear system. An automotive gear is a gear system that is used in the automotive industry (Uicker 92). This gear gives out a high torque and converts the mechanical energy in a smooth and noiseless way. Turbine gears, on the other hand, are used in minimization of power and noise. Worm gears are gears that are used in driving of the tooth wheel rim that is positioned on the turbines bearing. The objectives set for this experiment was to study different arrangements of gears including worm gearboxes, automobile gear boxes, as well as, turbine reduction gear boxes. Theory. The important specification of the parameters of the gears includes the number of the gears teeth (z), the circular pitch diameter of the gear (d), and the module (m). The module, m, can, therefore, be given by the following equation; m= d/z, d is the path diameter which could transmit equal motion as that of the actual gear by a pure rolling. The gear ratio or the torque ratio can also be termed as the mechanical advantage. For a basic gear train that has two gears, input gear drives output gear. The teeth of the gear are normally made in a manner that the pitch circles of one gear rolls on another without slipping (Uicker 42). The speed (v) of the contact point of the pitch circles are equal and are given by the following equation; V = r A w A = r B w B, where the input gear (GA) has a radius (r A) and an angular velocity (w A), where as the output gear (GB) has a radius (r B) and angular velocity (w B). The radius of the pitch circle is directly proportional to the number of teeth in gear. This, therefore, implies that the number of teeth’s ratio is equal to the radii’s ratio, that is W A/ w B= r B/ r A = N B/N A. Where N A is the input gear’s total number of teeth where as N B is the output gear’s number of teeth. Therefore, the gear ratio for a basic gear train is equal to; R= w A/ w B = N B/ N A. This equation implies that if the number of teeth in the input gear is smaller than that of the output gear, then the input gear has to go through a faster rotation in comparison with the output gear. Observations. The different types of the gear teeth were observed in the laboratory and their names and diameter recorded in the table shown below. Name of the gear Diameter of the gear(cm) 1st gear 13.50 2nd gear 7.25 3rd gear 4.05 4th gear 3.25 5th gear 2.05 Reverse gear 13.00 The three gear teeth observed include the parallel teeth (Spur), teeth under an angle (helical), the V-shape teeth (herring bone). The schematic drawing of one of the gear boxes was drawn as shown in figure 1.0. Figure 1.0: Schematic drawing of a Gearbox (Uicker 64). DISCUSSION. Gear ratio of the turbine reduction gearbox = w A/ w B= N B/N A = r B / r A since the ratio N B to N A is directly proportional to the ratio of the gear box. That is R = r B / r A= 13.5/2.05 = 6.585 The calculation of the gear ratio of the worm gear box can be done by getting the ratio of the number of teeth that are on the worm wheel to those that are on the worm. That is the worm acts as a single tooth gear so that its ratio is; Number of the teeth on the worm wheel/1. A worm drive can only be driven from worm to gear because, despite the size of the worm, the gear ratio would always be the gear size to one. If given a start worm that is single, a worm with twenty teeth would reduce the speed in a ratio of 20:1. Considering a gear with 20 teeth, the module of the turbine reduction gearbox will be. M= d/z =7.183/20 = 0.3592. Where d is the average diameter. The pitch circle diameter of a worm gear can be obtained by use of the diagram shown below. Figure 1.1, diagram representing the measurement of pitch circle diameter (Uicker 76). Pitch diameter is a defined diametric position in a gear in cases where by the Pressure angle, helix angle and tooth thicknesses are defined. A standard pitch diameter is one with basic dimensions, which can be measured, but is normally a location in which the other measurements are made. This value relies on the number of teeth, normal module or the normal diameter pitch and helix angle. This is calculated as: d = N mn /Cos Ψ in metric units Or, D = N/Pd Cos Ψ in imperial units. M is a scale factor used in metric gears having units in millimetres. Its effect is to enlarge the gear tooth sizes where as the module deals with increment and reduction of the sizes when the module decreases. Conclusion. Apparently all the experimental objectives were achieved. The gear systems were classified into five classes. These are the first gear, the second gear, the third gear, the fourth gear, and the reverse gear. Basing on the teeth appearances, there exist three types. These are the spur, the helical, and the V-shape teeth. The gear rations of the three gear boxes were also determined, and hence the success of this experiment as can be seen from the discussion was fully achieved. ABSTRACT. This Experiment helped reveal the different types of gears, the radius, as well as, their names. The gears were grouped into five groups as first gear, second, gear, third gear, fourth gear, and finally the reverse gear. These gears were later grouped according to the appearance of the teeth. These are teeth (Spur), teeth under an angle (helical), and the V-shape teeth (herring bone). Additionally, Gear ratio of the turbine reduction gearbox was also determined, as well as, the pitch circle diameter. The experimental objective was set as the study of different arrangements of gears including worm gearboxes, automobile gear boxes, as well as, turbine reduction gear boxes. The experiment was successful and yielded much of the expected. Work cited Uicker, J. Theory of Machines and Mechanisms, New York: Oxford University Press, 2003. Print. Read More