Плоские зубчатые механизмы Ситников К.А. Федеральное государственное бюджетное образовательное учреждение высшего профессионального образования «Владимирский государственный университет имени Александра Григорьевича и Николая Григорьевича Столетовых» Владимир, Россия Flat gear units KA Sitnikov Federal State Educational Establishment Higher Professional Education "Vladimir State University named after Alexander G. and Nicholas G. Stoletovs" Vladimir, Russia
Transmission Transmission device is serving for power transmission and mechanical movement over a distance and conversion of the motion parameters. The programs produce energy distribution, rise and fall speed, mutual transformation of types of motion, such as a rotary to linear and vice versa. The gear speed control, start, stop, reverse. Gear transmission mechanisms They are intended for transmitting rotation from one shaft to another, there is a change in the magnitude and direction of angular velocity with simultaneous change of the magnitude of torque. Needs to increase speed appeared in ancient times, when the source of the movement were the wind and water. Then there cogwheels. There is a need to reduce the speed With the advent of the electric drive. Compact engines were produced at higher speeds. Currently, the gears have an enormous spread. In engines transmission from the crankshaft to the other shafts (valve mechanism, magnetos. Generator). The machines - Transmission. All transmissions of building and lifting machinery cranes, excavators, loaders - is turning mechanisms of movement, ladle drive chains, rotors, cutters. Various geared motors and drives power tools have gears. In these programs contact is specially shaped side surfaces of the teeth. The pressure of the rotating driving wheel is transferred to the driven gear teeth, realizing the rotation. Gear mechanism, which is a reduction of the angular velocity in the transmission of motion from the input member to the output, called a downshift or reducers. Toothed mechanisms in which the angular velocity increases, called overdrive multiplier. In engineering, more often it is necessary to lower the speed the use of gear, so the calculation and design of gear is given special attention. Requirements to be met by a gear reducer, are in obtaining the necessary gear ratios (often very large) with highquality indicators, which are the efficiency, kinematic accuracy, torsional rigidity, with perhaps small overall dimensions, weight, and high reliability of the gearbox.
Basic terms and definitions. Gear ratio - the ratio of the angular velocities of the two rotation-cleaning units. Fig. 1 is a diagram of a simple three-tier gear mechanism. Two mobile unit (gears a and b) are rotated relative to the third is second, a fixed link (rack c) The gear ratio denoted «i» letter with indexes, for example (C) AB i. The superscript (in parentheses) indicates which of the links of the mechanism Holy linked coordinate system, which defines the angular velocity (and the very transition datochnoe ratio), and the lower - input and output link between them The gear ratio is considered. By definition, for two links «a» and «b», with the system of coordinates associated with the link cangular vye speed (C) wa and (C) wb Angular speed and gear ratios found in the coordinate system ordinates associated with the mechanism of the counter are considered absolute; superscript index in their notation can be omitted. When calculating the transmission Relations are generally used modules of the angular velocity, so i> 0. If the two links are rotated about parallel axes, not substituted units and projection (with sign) of the angular velocity on the axis parallel to them. In this case, maybe i <0 when the rotation links in different directions. rack The gear - three-link mechanism in which two movable link are gears forming the turning pairs. Assists with wheels instead of one of the rack, there will not be considered. Gearing - the kinematic pair formed by toothed transmission wheels. Block of gears - link formed by several, rigidly interconnected gears with a common axis of rotation. complex ( Multi-tier) gear units are divided into rows and planetary mechanisms. A number of gears - the mechanism, all the gears that rotate about fixed axes. The planetary gear mechanism - the mechanism, which is composed of gears with movable axes of rotation. Gears and planetary gear units may be included in as steps in the multistep mechanisms. The total gear ratio multistage mechanism calculate according to the formula 1,n =i 12 i 2.3 i n
Parameters of cylindrical helical gears The helical wheels unlike spur tooth axes make an angle β with the axis of the wheel. The magnitude of this angle is recommended to choose at 10, 12, 16 and 20. Work in a pair of wheels may only equal angles of inclination of the teeth, but with a different (left and right) direction of the helices. The axes are parallel helical gears. Helical transmission have a number of advantages compared with the spur: thanks to the inclination angle β teeth come into engagement along its length gradually b, which provides a more uniform and smooth operation, and naturally the noise reduction mechanism due to the greater the overlap ratio. Helical gears have a minimum number of teeth zk min, at which trimming occurs is smaller than the spur (zk min = zmincos3β). Helical transmission allow to pick up at a given center distance by changing the angle of inclination β pair of wheels with a standard module. The disadvantages of the helical gear is necessary to carry a more complex manufacture of wheels compared to the appearance and spur additional axial force transmitted to the bearings. In order to eliminate the axial force can be applied herringbone gears. Crown chevron wheel consists of plots with the right and left direction of the teeth. The teeth of the wheels may be cut on one rim or crown consists of a rigid connection of two helical gears with different directions of inclination of teeth. Chevron wheel more difficult to manufacture helical. Distinguish rotation mechanical section in t-t and the normal plane of the wheel n-n - in the plane perpendicular to the direction of the tooth. Parameters defining the dimensions of helical gears in both sections, are not the same, so they are assigned different indices: the parameters in the face section - t, normal - n. District AC step in the face section pt = πmt, and in the normal section AB is a step pn = πmn, where mt and mn - Allen and normal modules. Of ABC follows that pt = pn / cosβ, so mt = mn / cosβ. When cutting helical gears tool axis tilted with respect to the wheel axis by an angle β. The standard is a normal module mn, and the tooth profile size in the normal section (pn = πmn; ha = mn; hf = (1 + + c *) mn; h = (2 + c *) mn; S = πmn / 2). Module mt at the end face plane circular pitch pt, pitch diameter (base) of the circle d = mtz helical gears depends on the angle β of inclination of the longitudinal axes of the teeth. Dimensions helical wheels through a standard module as follows: pitch diameter d = (mnz) / cosβ; diameter protrusions teeth da = d + 2mn; diameter cavities df = d - (2
+ 2c *) mn; tooth length b = (3... 15) mn; crown wheel width b '= bcosβ. Note that the width of the crown wheel affects the amount of overlap coefficient as tooth angle β. When cutting helical gears tool axis tilted with respect to the wheel axis by an angle β. The standard is a normal module mn, and the tooth profile size in the normal section (pn = πmn; ha = mn; hf = (1 + + c *) mn; h = (2 + c *) mn; S = πmn / 2). Module mt at the end face plane circular pitch pt, pitch diameter (base) of the circle d = mtz helical gears depends on the angle β of inclination of the longitudinal axes of the teeth. Dimensions helical wheels through a standard module as follows: pitch diameter d = (mnz) / cosβ; diameter protrusions teeth da = d + 2mn; diameter cavities df = d - (2 + 2c *) mn; tooth length b = (3... 15) mn; crown wheel width b '= bcosβ. Note that the width of the crown wheel affects the amount of overlap coefficient as tooth angle β. Construction materials and gears The size and shape depend on the gear unit, the number and length of the teeth, the material and manufacturing method, the diameter of the shaft. When designing the wheels tend to give a form that would satisfy the high stiffness, low weight, manufacturability and other requirements. Typical designs of gears shown in Figure Small gears can be manufactured with the shaft. If the diameter of the gears differs only slightly from the diameter of the shaft and its teeth are cut on the shaft or the rod is pressed into it. The size and shape depend on the gear unit, the number and length of the teeth, the material and manufacturing method, the diameter of the shaft. When designing the wheels tend to give a form that would satisfy the high stiffness, low weight, manufacturability and other requirements. Typical designs of gears shown in Figure Small gears can be manufactured with the shaft. If the diameter of the gears differs only slightly from the diameter of the shaft and its teeth are cut on the shaft or the rod is pressed into it The central part of the gear is designed as a hub sleeve which conditions of manufacture and convenience of assembly is often one-sided. The diameter of the hub shall be equal to two diameters of the shaft and its length - 10 mm for wheels with m 0,6 and 1.5... 2 with shaft diameters larger module. When the outer diameters of 50 mm to facilitate the wheels and reducing their moments of inertia in the wheels provide recesses and holes.
For large diameter (80 mm) and small width of the fine-grained manufacturing crown wheels of a workpiece it becomes uneconomical. In this case, the wheels are produced without the hub and is secured to the shaft with screws and slot or make teams. Construction of modular wheels are also used in the application of non-ferrous alloys and plastics for the manufacture of the ring gear. wheel mounting hub provides an interference fit, flare and punching, with screws and using the slot. To eliminate backlash in the gears reverse responsible use special cutting wheel with backlash between the teeth of the sampling devices The split gear comprises two toothed disks 1 and 4, one of which (4) is rigidly associated with the shaft through the hub, and the other is connected to the first springs 2 to enable it to rotate relative to the first, and thus to choose side clearances in meshing. Washer 3 prevents axial displacement of the disc 1. Cutting split wheels are made simultaneously for drives 1 and 4, the position of which is fixed by two cylindrical pins 5. After cutting teeth pins are removed. Construction of plastic wheels have some specifics. Fixing them on the shafts preferably carried out by means of dowels. The main method of attachment is fine-grained wheels mount tapered pin. To implement it in the hub at an angle of 90 makes two-sided holes: a locking screw threaded and smooth, with a diameter equal to the smaller diameter of the pin. When assembling the wheel fixed to the screw shaft through a smooth bore in the hub is a hole through the shaft to the other side of the hub. The hole is then deployed under the pin. The pin is driven into the hole and the screw is removed. To protect the pins from falling out, especially in the high-speed mechanisms and in the presence of vibration, use additional safety (spring) of the ring. As materials for the manufacture of steel gears are used, based on the nonferrous metals, alloys, plastics. The choice of material is determined by the purpose of the transfer, the peculiarities of its work, the method of manufacturing the wheel. The teeth of the wheels must have good wear resistance, endurance under the influence of the variables of contact and bending stresses. In the manufacture of cylindrical and bevel gears are the basic material is heat treated steel. In the district of teeth speeds of up to 3 m / s are used quality steel 20, 30, 35, and at higher peripheral speeds - have become 45, 50, tool steel U8A, U10A and alloy steel 20X, 40X, 40KhN, 30KhGSA, 12HN3A with appropriate heat treatment (normalizing, hardening, improving - quenched and tempered). Recommended hardness gear teeth (they are loaded) to choose (20... 50) HB greater hardness gear teeth. So I try to take the gear material more durable than that of the wheel.
At light loads the gears are made of aluminum alloy D16T, B95-T1. More widely in the manufacture of fine-grained gears, especially worm, used bronze BrOF10-1, BrAZh9-4, BrAMts9-2. These materials have good sliding properties. Due to the high cost of its bronze used only in the production of crown wheels. Metal gears are manufactured by cutting, rolling, extrusion. Widely used as the material of plastic gears (PCB PTC, getinaks, polyamides), possess good wear resistance, damping capacity, corrosion resistance. Plastics absorb shocks well, have the ability to repay the mechanical vibrations and noise. Their use reduces noise by up to 70%. Typically in the manufacture of the plastic wheel, the pinion is made of metal for removal of heat generated due to friction in the gearing. To avoid uneven wear of the plastic gear teeth, make wider the metal gear wheels. With less mass, inertia, plastic wheels reduce the dynamic loads that occur when you create a start-stop-speed technical devices. Gears of polyamides (nylon, nylon) can be operated without lubrication. The wheels are made from plastic as a slicing (of thermosets) and injection molding (thermoplastics). Bevel gears For transmitting rotary motion between shafts whose axes intersect at an angle Σ, bevel gears are used. They distinguish between direct, oblique or helical tooth. Mostly used straight bevel wheels and only when you can not use cylinder. This is explained by the greater complexity of the manufacturing and assembly of bevel gears. One of the wheels of the bevel gear of the intersection of the axes of the shaft is a cantilever, which creates additional difficulties in the construction of towers. In addition, support shafts and loaded not only radial but also axial forces. The use of more sophisticated supports results in reduced efficiency and greater noise than with cylindrical gears. In terms of movement, engaging bevel gears can be represented as rolling over each other without slip cones, touching the generators. These cones are called the initial, their tops are at the point of intersection of the geometric axes of the wheels and the installation it is necessary to provide. There are dividing and cones, which are the base for determining the elements of the teeth and their size; cones vertices bounding the teeth on the opposite side of the gear body and cones hollows separating the teeth of the wheel body. In the manufacture of bevel gears fix the height of the teeth is virtually absent. Therefore the initial pitch and cones coincide. Angles separating cones wheels denoted by δ1 and δ2, and the cross angle - through Σ. Its value (Σ = δ1 + δ2) often equals 90
In terms of movement, engaging bevel gears can be represented as rolling over each other without slip cones, touching the generators. These cones are called the initial, their tops are at the point of intersection of the geometric axes of the wheels and the installation it is necessary to provide. There are dividing and cones, which are the base for determining the elements of the teeth and their size; cones vertices bounding the teeth on the opposite side of the gear body and cones hollows separating the teeth of the wheel body. In the manufacture of bevel gears fix the height of the teeth is virtually absent. Therefore the initial pitch and cones coincide. Angles separating cones wheels denoted by δ1 and δ2, and the cross angle - through Σ. Its value (Σ = δ1 + δ2) often equals 90. Circle diameters d1 (d2), obtained by dividing the intersection of cones and additional gear (wheels) are called the pitch circle of bevel gears. According to these circles it is determined by the engagement module bevel gears. It is administered from constructive and technological conditions of manufacture and assembly, or according to strength calculation. Toothing is limited inner and outer ends. The teeth on the bevel gears are of variable length and height of the thickness. Standardized dimensions of the teeth, their unit and step on the outer end, and they are Indicated by the index e (me, pe, DE, dae, dfe). Gear ratio i bevel gear is determined from the rolling conditions without slipping initial cones. Hence i = d2 / d1 = sinδ2 / sinδ1 or Σ = 90 i = tgδ2 = ctgδ1. The value of the gear ratio u for kinematic gear is recommended to take no more than 7.5, for security - not more than 3 (u = z2 / z1). The geometrical calculation of bevel gear are in the following relationships: an external divider wheel diameter de = mez; corners separating wheels cones δ2 = arctgi, δ1 = 90 - δ2; outer cone distance Re = (mez) / (2sinδ); the width of the ring gear b = (0,25... 0,3) Re or b = (4... 10) me; the mean cone distance R = Re - 0,5b; Intermediate Circuit module m = (mer) / Re; external height of the tooth head hae = me; outer tooth flank height hfe = (1 + c *) me, where the radial clearance ratio c * = 0.45 ME 0,5 or in 0.3 * = 0,5 <me <1 and x = 0 2 at me 1,0;
outer diameter tooth top dae = de + 2haecosδ; the outer diameter of the teeth cavities dfe = de - 2hfecosδ. When calculating the strength calculation is the average module m, which is calculated on me external module. Bevel wheels of small size (de <70 mm) made from a solid disk. For large diameters to reduce the mass and moment of inertia in the drive wheels provide for boning, otverstiya. Stupitsu wheel on the opposite side a pitch cone. The wheels on the back of the hub can be used provided that the hub does not protrude beyond the cone depressions, it is necessary to exit the tool while cutting zubev. Zubchatye wheels are made of steels 35, 45, 50. If the requirements of low weight and small loads used for the manufacture of alloys D16T, V95T and plastic - PCB PTC brand, nylon. Wheels of plastic provide quiet operation.