Cylindrical gear transmission

The gear transmission used to transmit power and motion between parallel shafts. The transmission power and speed of cylindrical gear transmission have a wide range of applications. The power can range from less than one thousandth of a watt to 100000 kW, and the speed can range from very low to 300 m / s. The transmission has the advantages of reliable operation, long service life, high transmission efficiency (up to more than 0.99), compact structure and simple operation and maintenance. However, machining some gears with high precision requires special or high-precision machine tools and cutting tools, so the manufacturing process is complex and the cost is high; Low precision gears often produce noise and vibration without overload protection.

According to the relative relationship between gear teeth and gear axis, cylindrical gear transmission can be divided into spur gear transmission, helical gear transmission and herringbone gear transmission. According to the meshing form, it can be divided into: external meshing gear transmission, which is composed of two meshing external gears, and the two wheels turn opposite; Internal meshing gear transmission, composed of an internal gear and an external gear, with the same steering of the two wheels; The gear rack meshing transmission is composed of an outer gear and a rack, which can change the rotation of the gear into the linear motion of the rack, and the pitch circle circumference speed of the outer gear is equal to the moving speed of the rack.

The tooth profile is formed. When the plane s is pure rolling along the base cylinder with radius Rb, the involute surface formed by the track of a straight line KK parallel to the base cylinder bus NN is the tooth surface of the involute spur cylindrical gear. If the straight line KK is at an angle to the bus NN β b. Then the trajectory formed is an involute helical surface, that is, the tooth surface of involute helical cylindrical gear, β B is the helix angle on the base cylinder. The meshing characteristics can be seen from the formation process of the tooth profile surface. When the involute spur cylindrical gear is meshed, the contact line of the tooth profile surface is a straight line parallel to the axis. In the meshing process, the whole tooth width enters and exits the meshing at the same time, and the force on the tooth is suddenly added or removed, so the transmission stability is poor and the impact and noise are large. During the meshing of involute helical cylindrical gears, the contact line on the tooth surface gradually changes from short to long, and then from long to short until it is out of meshing. The force on the teeth also gradually increases from small to large, and then from large to small. At the same time, there are many pairs of meshing teeth, so the transmission is relatively stable and the impact and noise are small. It is suitable for high-speed and heavy-duty transmission. However, the axial component FX is generated when the helical cylindrical gear is driven, which is borne by the shaft and bearing. In order to reduce the axial component force FX during transmission, the helix angle should not be too large. Generally, the helix angle on the indexing cylinder is taken β= 8°~15°。 Part of the tooth width of herringbone cylindrical gear is right spiral tooth, and the other part is left spiral tooth. According to different manufacturing methods, there are two structures between the left and right spiral teeth with and without tool withdrawal groove. The former can be processed on ordinary hobbing machine, while the latter needs special equipment. In addition to the advantages of helical gear, herringbone gear can make the axial force FX offset each other because the left and right helix angles of its two parts of teeth are the same and the direction is opposite; But manufacturing is a little more difficult. Herringbone cylindrical gear transmission is often used in heavy machinery transmitting high power and torque, and its helix angle can be larger than that of helical gear: β= 15 ° ~ 45 °, usually about 30 °.

The correct meshing condition of a pair of involute standard spur gears is that the pressure angles on the indexing circles of the two gears are equal, α 1= α 2= α; Modulus is equal, M1 = M2 = M. In addition to these two conditions, helical gears should also meet the following requirements: during external meshing, the helix angle on the indexing cylinder of the two gears is equal and the direction is opposite, β 1=- β 2; During internal meshing, the helix angle is equal in size and direction, β 1= β 2。

There are two methods for calculating the geometric dimensions of gears: modular system and diameter control. Modular system is used in China.

The main parameters of involute standard spur gear are module M and pressure angle α、 Number of teeth Z, addendum height coefficient h and radial clearance coefficient C *. Except for the number of teeth Z, there are standards for these five parameters. Modulus M = P / π, P is the circumferential pitch, and the radial size of the gear is made into a multiple of the modulus, so the modulus is the most important parameter for calculating the size of the gear. pressure angle α It usually refers to the pressure angle on the gear indexing circle, which is stipulated in Chinese standards α= 20 °, and 25 ° pressure angle is also allowed. Other countries also use pressure angles of 14.5 °, 15 ° and 22.5 °. The tooth height of the gear is taken as the multiple of the module. In the standard gear, the tooth top height h a = HFM and the tooth root height H F = HA + C = h m + cm are taken. Chinese standard stipulates that normal teeth HF = 1, short teeth HF = 0.8; The clearance between the top gear and the other gear is C = m, which is used to avoid the contact between the top gear and the other gear. Chinese standard stipulates that normal tooth C = 0.25 and short tooth C = 0.3.

The main parameters of involute helical cylindrical gear are basically the same as those of spur cylindrical gear, but when machining helical cylindrical gear, the cutter is fed along the tooth direction, so the normal surface parameters are taken as the standard value. The relationship between end face parameters and normal face parameters is corresponding to the footmarks T and N, which represent the parameters of end face and normal face. The relationship between the number of teeth Z of helical gear and the equivalent number of teeth Zn of normal tooth profile is Zn = Z / cos3 β。

The main dimensions of involute external meshing standard spur gear are: indexing circle diameter d = MZ; Diameter of tooth tip circle Da = D + 2ha; Root circle diameter DF = d-2hf. Structure type when the diameter of the addendum circle is small (damn), the shaft gear structure shall be adopted. When the diameter of the addendum circle is large (DA > 400 ~ 600mm), the cast gear, ring gear, welded gear and even sectioned gear can be used. The number of spokes and teeth of the sectioning gear shall be an even number, which shall be sectioned between the teeth.

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