Paul E. Sandin - Robot Mechanisms and Mechanical Devices Illustrated (779750), страница 21
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Standard angles are 20 and 25º. The pressureangle affects the force that tends to separate mating gears. A high pressure angle decreases the contact ratio, but it permits the teeth to havehigher capacity and it allows gears to have fewer teeth without undercutting.Gear Dynamics Terminologybacklash: The amount by which the width of a tooth space exceeds thethickness of the engaging tooth measured on the pitch circle. It is theshortest distance between the noncontacting surfaces of adjacent teeth.gear efficiency: The ratio of output power to input power, taking intoconsideration power losses in the gears and bearings and from windageand churning of lubricant.gear power: A gear’s load and speed capacity, determined by geardimensions and type. Helical and helical-type gears have capacities toapproximately 30,000 hp, spiral bevel gears to about 5000 hp, and wormgears to about 750 hp.gear ratio: The number of teeth in the gear (larger of a pair) divided bythe number of teeth in the pinion (smaller of a pair).
Also, the ratio of thespeed of the pinion to the speed of the gear. In reduction gears, the ratioof input to output speeds.gear speed: A value determined by a specific pitchline velocity. It can beincreased by improving the accuracy of the gear teeth and the balance ofrotating parts.undercutting: Recessing in the bases of gear tooth flanks to improveclearance.Gear ClassificationExternal gears have teeth on the outside surface of a disk or wheel.Chapter 2Indirect Power Transfer DevicesInternal gears have teeth on the inside surface of a cylinder.Spur gears are cylindrical gears with teeth that are straight and parallel tothe axis of rotation. They are used to transmit motion between parallelshafts.Rack gears have teeth on a flat rather than a curved surface that providestraight-line rather than rotary motion.Helical gears have a cylindrical shape, but their teeth are set at an angleto the axis.
They are capable of smoother and quieter action than spurgears. When their axes are parallel, they are called parallel helical gears,and when they are at right angles they are called helical gears.Herringbone and worm gears are based on helical gear geometry.Herringbone gears are double helical gears with both right-hand andleft-hand helix angles side by side across the face of the gear. This geometry neutralizes axial thrust from helical teeth.Worm gears are crossed-axis helical gears in which the helix angle ofone of the gears (the worm) has a high helix angle, resembling a screw.Pinions are the smaller of two mating gears; the larger one is called thegear or wheel.Bevel gears have teeth on a conical surface that mate on axes that intersect,typically at right angles. They are used in applications where there areright angles between input and output shafts.
This class of gears includesthe most common straight and spiral bevel as well as the miter and hypoid.Straight bevel gears are the simplest bevel gears. Their straight teethproduce instantaneous line contact when they mate. These gears provide moderate torque transmission, but they are not as smooth runningor quiet as spiral bevel gears because the straight teeth engage withfull-line contact. They permit medium load capacity.Spiral bevel gears have curved oblique teeth. The spiral angle of curvature with respect to the gear axis permits substantial tooth overlap.Consequently, teeth engage gradually and at least two teeth are in contact at the same time.
These gears have lower tooth loading thanstraight bevel gears, and they can turn up to eight times faster. Theypermit high load capacity.Miter gears are mating bevel gears with equal numbers of teeth andwith their axes at right angles.Hypoid gears are spiral bevel gears with offset intersecting axes.8990Chapter 2Indirect Power Transfer DevicesFace gears have straight tooth surfaces, but their axes lie in planes perpendicular to shaft axes.
They are designed to mate with instantaneouspoint contact. These gears are used in right-angle drives, but they havelow load capacities.Designing a properly sized gearbox is not a simple task and tables ormanufacturer’s recommendations are usually the best place to look forhelp. The amount of power a gearbox can transmit is affected by gearsize, tooth size, rpm of the faster shaft, lubrication method, availablecooling method (everything from nothing at all to forced air), gear materials, bearing types, etc. All these variables must be taken into account tocome up with an effectively sized gearbox.
Don’t be daunted by this. Inmost cases the gearbox is not designed at all, but easily selected from alarge assortment of off-the-shelf gearboxes made by one of many manufacturers. Let’s now turn our attention to more complicated gearboxesthat do more than just exchange speed for torque.Worm GearsWorm gear drives get their name from the unusual input gear whichlooks vaguely like a worm wrapped around a shaft. They are used primarily for high reduction ratios, from 5:1 to 100s:1.
Their main disadvantage is inefficiency caused by the worm gear’s sliding contact with theworm wheel. In larger reduction ratios, they can be self locking, meaningwhen the input power is turned off, the output cannot be rotated. The following section discusses an unusual double enveloping, internally-lubricated worm gear layout that is an attempt to increase efficiency and thelife of the gearbox.WORM GEAR WITH HYDROSTATICENGAGEMENTFriction would be reduced greatly.Lewis Research Center, Cleveland, OhioIn a proposed worm-gear transmission, oil would be pumped at highpressure through the meshes between the teeth of the gear and the wormcoil (Figure 2-16). The pressure in the oil would separate the meshingsurfaces slightly, and the oil would reduce the friction between these sur-Chapter 2Indirect Power Transfer Devices91Figure 2-16 Oil would beinjected at high pressure toreduce friction in critical areas ofcontactfaces.
Each of the separating forces in the several meshes would contribute to the torque on the gear and to an axial force on the worm. Tocounteract this axial force and to reduce the friction that it would otherwise cause, oil would also be pumped under pressure into a counterforcehydrostatic bearing at one end of the worm shaft.This type of worm-gear transmission was conceived for use in thedrive train between the gas-turbine engine and the rotor of a helicopterand might be useful in other applications in which weight is critical.Worm gear is attractive for such weight-critical applications because (1)it can transmit torque from a horizontal engine (or other input) shaft to avertical rotor (or other perpendicular output) shaft, reducing the speed bythe desired ratio in one stage, and (2) in principle, a one-stage design canbe implemented in a gearbox that weighs less than does a conventionalhelicopter gearbox.Heretofore, the high sliding friction between the worm coils and thegear teeth of worm-gear transmissions has reduced efficiency so much92Chapter 2Indirect Power Transfer DevicesFigure 2-17 This test apparatussimulates and measures some ofthe loading conditions of the proposed worm gear with hydrostatic engagement.
The test datawill be used to design efficientworm-gear transmissions.that such transmissions could not be used in helicopters. The efficiencyof the proposed worm-gear transmission with hydrostatic engagementwould depend partly on the remaining friction in the hydrostatic meshesand on the power required to pump the oil. Preliminary calculationsshow that the efficiency of the proposed transmission could be the sameas that of a conventional helicopter gear train.Figure 2-17 shows an apparatus that is being used to gather experimental data pertaining to the efficiency of a worm gear with hydrostaticengagement.
Two stationary disk sectors with oil pockets represent thegear teeth and are installed in a caliper frame. A disk that represents theworm coil is placed between the disk sectors in the caliper and is rotatedrapidly by a motor and gearbox. Oil is pumped at high pressure throughthe clearances between the rotating disk and the stationary disk sectors.The apparatus is instrumented to measure the frictional force of meshingand the load force.The stationary disk sectors can be installed with various clearancesand at various angles to the rotating disk.
The stationary disk sectors canbe made in various shapes and with oil pockets at various positions. Aflowmeter and pressure gauge will measure the pump power. Oils of various viscosities can be used. The results of the tests are expected to showthe experimental dependences of the efficiency of transmission on thesefactors.It has been estimated that future research and development will makeit possible to make worm-gear helicopter transmission that weigh half asmuch as conventional helicopter transmissions do. In addition, the newhydrostatic meshes would offer longer service life and less noise. ItChapter 2Indirect Power Transfer Devicesmight even be possible to make the meshing worms and gears, or at leastparts of them, out of such lightweight materials as titanium, aluminum,and composites.This work was done by Lev.
I. Chalko of the U.S. Army PropulsionDirectorate (AVSCOM) for Lewis Research Center.CONTROLLED DIFFERENTIAL DRIVESBy coupling a differential gear assembly to a variable speed drive, adrive’s horsepower capacity can be increased at the expense of its speedrange. Alternatively, the speed range can be increased at the expense ofthe horsepower range. Many combinations of these variables are possible.
The features of the differential depend on the manufacturer. Somesystems have bevel gears, others have planetary gears. Both single anddouble differentials are employed. Variable-speed drives with differentialgears are available with ratings up to 30 hp.Horsepower-increasing differential. The differential is coupled sothat the output of the motor is fed into one side and the output of thespeed variator is fed into the other side.
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