The transmission ratio is the two rotating components in the mechanismangular velocityIs also called speed ratio.The transmission ratio of component a and component b is i=ω a/ω b=na/nb, where ω a and ω b are the angular velocities (radians/second) of component a and b respectively;Na and nb are the rotational speeds (r/min) of members a and b respectively.
When the angular velocity isInstantaneous valueThen the obtained transmission ratio is the instantaneous transmission ratio.When the angular velocity in the formula is the average value, the calculated transmission ratio is the average transmission ratio.Theoretically correct for most involute tooth profilesgear drive, the instantaneous transmission ratio is constant;aboutChain driveandFriction wheel driveThe instantaneous transmission ratio is variable.For meshing transmission, the transmission ratio can be expressed by the number of teeth Za and Zb of a and b wheels, i=Zb/Za; for friction transmission, the transmission ratio can be expressed by the diameters Da and Db of a and b wheels, i=Db/Da.
The ratio of the instantaneous input speed to the output speed in the mechanism is called the transmission ratio of the mechanism.
The ratio of angular velocity of two rotating components in the mechanism, also calledspeed ratio。The transmission ratio of component a and component b is I=ω a/ω b=na/nb, where ω a and ω b are the angular velocities (radians/second) of component a and b respectively;Na and nb are the rotational speeds (rpm) of members a and b respectively (note: a and b after ω and n are lower footmarks).When the angular velocity in the formula is the instantaneous value, the obtained transmission ratio is the instantaneous transmission ratio.When the angular velocity in the formula is the average value, the calculated transmission ratio is the average transmission ratio.For most correct tooth profilesgear driveandFriction wheel drive, the instantaneous transmission ratio is constant;aboutChain driveAnd non-circular gear transmission, instantaneous transmission ratio is variable.For meshing transmission, the transmission ratio can be expressed by the number of teeth Za and Zb of wheel a and wheel b, and i=Zb/Za; for friction transmission, the transmission ratio can be expressed by the radius Ra and Rb of wheel a and wheel b, and i=Rb/Ra. At this time, the transmission ratio generally represents the average transmission ratio;stayHydraulic transmissionIn, the transmission ratio of hydraulic transmission components generally refers to the ratio of turbine speed S to pump wheel speed B, that is,=S/B.Hydraulic transmission elements can also be connected withmechanical driveElement (various gears are generally usedgear train）It can be used together to obtain transmission ratios of different values (see gear train for transmission ratio of gear train).
computing method
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Transmission ratio=service torque ÷ 9550 ÷ motor power × motor power input revolutions ÷ service factor
Transmission ratio=the value of driving wheel speed divided by driven wheel speed=the reciprocal of their reference circle diameter ratio.That is, i=n1/n2=D2/D1
I=n1/n2=z2/z1 (gear)
For multi-stage gear transmission: 1. The transmission ratio between each two shafts shall be calculated according to the above formula.2. The total transmission ratio from the first shaft to the nth shaft is equal to the product of transmission ratios at all levels[1]。
Distribution principle
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The distribution of transmission ratios at all levels of a multi-stage reducer directly affects the bearing capacity and service life of the reducer, as well as its volume, weight and lubrication.The transmission ratio is generally distributed according to the following principles: make the bearing capacity of transmission at all levels approximately equal;Make the size and mass of reducer smaller;Make the circumferential speed of all gears smaller;When oil bath lubrication is adopted, the difference of immersion depth of big gears at all levels of gear pairs is small.
The low speed gear directly affects the size and weight of the reducer, reducing the transmission ratio of the low speed gear, that is, reducing the size and weight of the low speed gear and the body containing it.Increase the transmission ratio of the high-speed stage, that is, increase the size of the high-speed stage big gear, reduce the size difference with the low-speed stage big gear, which is conducive to the simultaneous oil bath lubrication of all gears;At the same time, after the size of the high-speed stage pinion is reduced, the circumferential speed of the high-speed stage and the following stages of gears is reduced, which is conducive to reducing noise and vibration and improving the smoothness of transmission.Therefore, under the condition of meeting the strength, the final transmission ratio is small and reasonable.
The bearing capacity and service life of the reducer depend on the strength of the weakest gear.It is often a great waste of bearing capacity and service life to be satisfied that the strength can pass without pursuing the approximate equal strength at all levels.In order to reduce the number of gears in the universal reducer, the gears with the same center distance and transmission ratio in single stage and multi-stage are generally taken as the same parameters.When a and i are densely set, it is easier to achieve equal strength distribution at all levels;When a and i are sparsely set, it is difficult to achieve equal strength.The bearing capacity of about half of the universal reducers designed according to equal strength can be increased by 10% - 20% compared with those not designed according to equal strength.
Compared with the strength, the principle of distribution is that the immersion depth of large gears at all levels is similar. Even if the high-speed large gears cannot be immersed in oil, they can be fully lubricated by the structural design.
Three stage transmission ratio distribution
For multi-stage reduction drive, the transmission ratio can be distributed according to the principle of "small front and large rear" (that is, gradually increasing from high speed stage to low speed stage), and the difference between two adjacent stages should not be too large.This distribution method can make intermediate shafts at all levels obtain higher speed and smaller torque, so the size and quality of shaft and parts on the shaft are reduced, and the structure is relatively compact.The speed increase transmission can also be distributed according to this principle.
In multistage gear reduction transmission, the distribution of transmission ratio will directly affect many technical and economic indicators of transmission.For example:
The overall size and quality of the transmission largely depend on the size of the low-speed stage big gear. The smaller transmission ratio of the low-speed stage is conducive to reducing the overall size and quality.
In closed transmission, gears are mostly lubricated by splashing oil. In order to avoid the large gear diameters at all levels being significantly different, the oil mixing loss will increase too much due to the large gear oil immersion depth. It is often hoped that the large gear diameters at all levels are similar.Therefore, properly increasing the transmission ratio of the high-speed stage is conducive to reducing the diameter difference of the big gears at all levels.
In addition, in order to make the transmission life of all levels close, the design shall be carried out according to the principle of equal strength. Generally, when the transmission ratio of the high-speed level is slightly higher than that of the low-speed level, it is easy to approach the equal strength.
From the above analysis, it can be seen that the adoption of a larger transmission ratio in the high-speed stage is beneficial to reducing the overall size of the transmission, reducing the mass, improving the lubrication conditions, and achieving equal strength design.
When the second levelCylindrical gear reducerWhen the transmission ratio is distributed according to the condition that the contact strength of the gear teeth is equal, the transmission ratio of the high speed stage should be taken.
The transmission ratio distribution of three-stage cylindrical gear reducer can also adopt the distribution principle of two-stage reducer.
Related concepts
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The transmission ratio is defined as the ratio of driving wheel speed to driven wheel speed.On cars, the total transmission ratio is equal to the engine speed/drive wheel speed, and also equal to the drive wheel torque/Engine torque, more equal totransmission caseTransmission ratio*main reducerTransmission ratio (commonly known as final transmission ratio).
Power, the work done per unit time.automobile enginePower is equal to engine torque * engine speed/9550. According to the above transformation of transmission ratio, it can also be equal to drive wheel torque * drive wheel speed.
Torque, explained by physicsmoment, equal to force*Lever arm(Since the force is proportional to the acceleration, the torque is proportional to the angular acceleration.) It is a parameter to measure the angular acceleration of an object.
speedIs the driving speed of the car.There are two kinds of speed, one is the engine speed, and the other is the driving wheel speed.The quotient of the two is the total transmission ratio, provided that the driving wheel runs on the road with good adhesion without slipping or locking.The conversion relationship between driving wheel speed and vehicle speed is: vehicle speed=driving wheel speed * 2 π * driving wheel radius/1000 * 60.[2]
