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In this topic, we shall discuss about the geometry of gears and then consider three different aspects of gearing namely elastohydrodynamic lubrication, tooth contact phenomena, and wear of gears. Gears are machine elements, which are required to transmit power between shafts rotating at different rotational speeds. By adding teeth of the proper shape on disk, power can be transmitted without slip at uniform rate. These types of geometrics are known as external gears. Internal gears are generally more efficient since the sliding velocity along the profile is lower than equivalent external gears.
It operates at closer center distance with its mating pinion than external gears of the same size, which often permits a more compact design. The internal gears eliminates the use of an idler gear, where it is necessary to have two parallel shafts rotate in the same direction.
In manufacturing point of view also, external gears are simpler than internal gears. Often gears are treated as pitch cylinder, which roll together without slip as shown in Fig. Smaller gear is known as pinion and larger mating gear is called gear. Generally, a gear pair acts as a speed reducer aiming torque amplification at output shaft.
Generally tooth profile is designed so that velocity ratio does not change due to inaccuracies in center distance. Tooth curves of the mating teeth need to be tangent to each other as shown in Fig. On changing center distance, line of action still remains tangent to both base circles but slope changes.
Nominal pressure angle is given by : The lower pressure angle has the advantage of smoother and quieter tooth action because of larger profile contact ratio. In addition, lower loads are imposed on the support bearings because of a decrease radial load component. Pressure angle at base circle is zero. Backlash : Difference between tooth space and tooth thickness is known as backlash. It prevents jamming of teeth and compensates for thermal expansion of teeth.
The amount of speed reduction is simply the ratio of pitch diameters of the larger gear to the smaller gear. There is no limit to the speed reduction ratio that can be achieved using gearing; but larger ratio must be obtained using multi-stage reduction. In simple gear mesh, a maximum ratio in order of to should not be exceeded. The limit on velocity ratio depends on gear pair for example :. For high speed reduction, two stage or three stage construction are preferred, otherwise gear wheel size increases, which increases the gearbox size.
For high speed reduction, compound gear trains are required. In such trains as shown in Fig. An efficient method of achieving high reduction ratios in minimum space is the use of planetary gearing. Helical gearing, in which the teeth are cut at an angle with the axis of rotation, was developed after spur gearing and has the advantages that has the smoother action and tends to be quieter Fig.
In helical angle greater than 15 degrees, the tooth bending capacity generally begins to drop off due to the fact that the tooth thickness decreases rapidly. In addition, helical gears causes axial thrust force and impose load on bearings. Rolling and sliding in gears : Ideally, rolling gears are required.
In practice, sliding comes along rolling action. Typical gear pair having high sliding is shown in Fig. Worm gears have crossed axes Fig.
Helical crossed axes Fig. Hypoid gears Fig. Hypoid gears are widely used in many power trains to transfer power between two non-intersecting crossed axes. Their most common and highest-volume applications can be found in front and rear axles of rear-wheel-drive or all-wheel-drive vehicles.
It is interseting to note that even spur gears experience sliding ,as depicted in Fig. For rolling action, tangential velocities at point of contact must be equal to make sliding zero. This happens at pitch point. At all other contact points as shown in Fig. Friction between gear pair occurs due to sliding between meshed teeth and churning of lubricant. In absence of lubricant additives and antifriction coating, gears will be subjected to direct friction.
This is hypothetical situation which occurs rarely in extreme conditions. A worst situation from tribology point of view i. In normal atmospheric conditions, all engineering metallic surfaces are primarily coated with some adsorbed gas Fig. They thus protect the surface of the base material from excessive wear and subsequent destruction. This favorable behavior is utilized by intentionally creating protective surface coating.
Following two coatings as solid lubricants are used to reduce friction. This friction process is aided by the presence of small quantities of lubricant, at the point of friction. This friction process is characterized by solid-body friction as well as by fluid friction Fig. In this regime, friction and wear are influenced by the ability of lubricant to create protective boundary films on gear tooth with chemical and physical reactions, and by its viscous characteristics.
Interface shear strength in mixed lubrication can be given by;. It is interesting to note that oil sample collected after 3 hours of operating gear at rpm no load conition show wear Fig. This means mild wear is bound to occur in gear operations. With involute profile of gears, only one contact position experiences pure rolling.
As contact moves towards or away from pitch point, sliding occurs. Due to sliding, power loss occurs and transmission efficiency decreases. Typical values of gear efficiencies are listed in Table 6. Table 6. In a geared system, the total power loss is comprised of two groups of losses: i load-dependent friction induced mechanical power losses and ii load-independent viscous spin losses.
Sliding and rolling friction losses at the loaded gear meshes and at the bearings largely define the load-dependent mechanical power losses. The total mechanical loss is then given as the sum of losses from all gear meshes and bearings. The sliding friction losses are related to the coefficient of friction, normal load and sliding velocity on the contact surfaces, while the rolling friction losses occur due to the formation of an elastohydrodynamic EHL film.
It is interesting to note that coefficient of friction is variable and it depends on operating conditions. Friction losses can be divided into two major categories: Loss due to load and loss due to speed. In high speed units, the churning losses may exceed the friction losses; therefore, the type and amount of lubricant are critical.
Normal gear load W n for a given application depends on pitch diameter and face width. These dimensions are determined on the basis of tooth stresses, which are imposed by the transmitted tooth load. The tooth load is simply the torque on a given gear divided by the gear pitch radius.
Torque is calculated from the horsepower transmitted and the speed of rotating component in question. Composite roughness depends on gear manufaturing process as given in Table 6. Gear life depends on effective lubrication, which can be quatified by minimum film thickness to R composite , as shown in Fig. Following empirical formulae are used to estimate effective temperature T F.
Higher value of T f cause scuffing failure of gears. To reduce the value of T f , effective lubrication that maintains low friction coefficient is desirable. But sometime failure of lubrication pump failure, filter chocking, excessive leakage occurs and gear materials must be able to handle such extreme situations. By using parameters shown in Table 6.
So N-S is prefferable. But for home applications, we use N-N gear pair, where rate of heat generation is relatively low. To estimate the working life of gears, it is essential to analyze the destructive forces at work, and knowledge of the ability of chosen gear materials to withstand those forces. To design gear, we need to estimate W n Fig. Properly designed gear-sets should never fail but must be expected to eventually fail by wear of one of surface.
Insufficient backlash is sometimes the cause of excessive heat and wear. If sufficient backlash has not been provided to take care of the differential thermal expansion, the teeth will bind, with disastrous results. Inadequate lubrication may also be a source of excessive heat and wear. Surface failure of gear tooth occurs due to very high local contact stresses. Maximum contact pressure at the contact point between two cylinders is given by :. Maximum contact stress is equal to p max.
Therefore, contact stress is;. Bore diameter of pinion is 17 mm, and bore dia of gear is 20 mm. Using AGMA pitting equation formula, determine the maximum contact stress. The Fig. Most gears are in the hardness range of approximately Rc 30 to Rc 38 or Rc 55 to Rc Too much or too less lubricant is harmful for gear operation. Usually, following two types of lubrication mechanisms are commonly used for gear lubrication.
Following empirical formulae are availiable for splash lubrication system to minimize churning losses. With increase in pitch line velocity, lubricant used should be less viscous in order to min.
Kinematics of Mechanisms and Machines
Five of the seven topics listed under the heading Kinematics of Machine belongs to dynamics. These are:. Breaks and dynamometers ii. Inertia force analysis iii. Governors iv.
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