Mechanical transmissions, General information, Drive - Applied Mechanics

Mechanical transmissions


Mechanical transmissions are the mechanisms that transfer energy from the engine to the executive body of the machine, usually with the transformation of velocities, forces and moments, and sometimes the nature and law of motion. They are intended for the coordination of the type, parameters of movement and location of the engine and the executive body, when the speeds of the working elements of the machine are different from the speeds of standard engines, i.e. The operating body requires a torque greater or less than that on the motor shaft. In some cases, it is also necessary to change the spatial orientation of the transmission elements.

According to the method of transfer of motion from the leading link to the slave, there are different transfers:

friction : with direct contact - frictional, with flexible connection - belt;

gearing : with direct contact - gear, worm, with flexible coupling - chain.

Toothed gears are cylindrical, conical, planetary, wave, etc.

According to relative arrangement of shafts , mechanical transmissions can be parallel (for cylindrical gears, Fig. 4.4, a-c), intersecting (for bevel gears, Fig. 4.4 , r, d) and with crossed (for worm gears, figure 4.4, e) axes.

According to the nature of the motion of the shafts distinguish mechanisms with fixed axes of shafts and moving axes of shafts in planetary gears. In the latter movement of the satellite wheels mounted on the movable shafts is similar to the motion of the planets.

Mechanical transmissions also happen:

• with a constant gear ratio (reducers, multipliers);

• with variable gear ratio: stepped - gearbox and stepless - variators. Gearboxes allow you to adjust a number of speeds of the output shaft, and variators - to smoothly change the gear ratio.

In a number of mechanisms, it becomes necessary to fix the immovability of the output link under load

Fig. 4.4

or if there is no traffic at the entrance. The mechanism property, in which motion is transmitted in only one direction, is called irreversibility of motion or self-inhibition . Appropriate devices are used in hoisting machines.

Recently, a new direction has begun to develop - mechatronics. In it, mechanical power units are combined with electrical and electronic devices that provide control and communication between the elements of the entire system. Electronics converts the input signal from the control system, and the power electronics issues commands to the executive: electromechanical, hydraulic, etc. The latter convert the incoming signals into mechanical motion. In such systems it is expedient to use ready-made elements in the form of modules. The use of mechatronics allows to obtain low-mass drives with high accuracy of the output link and high efficiency. Such devices are already used in robotics and aircraft in flight control systems. They are also promising in other branches of engineering.


Drive - device for driving machines and mechanisms. It consists of an engine (power source), a transmission mechanism and a control system that controls the operation of the drive and usually includes electrical and electronic devices. Only two parts of the drive, the transmission mechanism with the engine, will be considered below.

Reducer - a gear that serves to lower the speed, increase torque, and sometimes the spatial orientation of the elements, made as a separate unit. It is an intermediate link between the input link - the motor and the output - the executive body, which can be a wheel, a robot arm, a screw, a screw, etc. The purpose of the reducer is to ensure the coordination of parameters (kinematic, power and geometric) between the engine and the executive. Reducers are widely used in industry.

Multiplicator - a mechanism that boosts the speed.

In Fig. 4.5, a shows the drive scheme consisting of a gearbox P with an electric motor D, where n b , n T - speed of high-speed and low-speed shafts. The reducer is connected to the motor by means of a clutch M, which transfers the torque from the engine to the output through the cylindrical gears z i and the shafts. Shafts The gears have bearings that are rolling or sliding bearings. The gears include wheels with a number of teeth z i. If you need to obtain the translational motion of the output link, you can use another version of the last stage - the transfer of the screw-nut.

There are different types of gearboxes, which are named according to what gears and how many stages they have. One stage consists of a pair of gears.

In Fig. 4.5, b the cylindrical reducer (with cylindrical gear wheels) is shown in Fig. 4.5, B - conical (with bevel gears), in Fig. 4.5, r - worm (with worm and worm wheel). There are combined reducers, for example, conical-cylindrical (Figure 4.5, d). For small gear ratios (for cylindrical gearboxes with ) use single-stage reducers (with one pair of gears, see figure 4.5, b), and for large (with) - two-stage with two pairs of wheels, figure 4.5, e). Application in the latter case instead of a two-stage single-stage transmission would increase the weight of the reducer. For large values ​​of the transmission ratios, transmissions with a large number of stages are used. In Fig. 4.5, a shows the reducer of the expanded scheme, and in Fig. 4.5, e - coaxial, when the shafts I and III coincide. Reducers coaxial scheme more compact than deployed. The mass and overall dimensions of the transmission decrease with the use of multi-stream transmissions, which is used, for example, in planetary mechanisms.

The main characteristics of the gearbox. These include the gear ratio , the rated torque on the slow-speed (output shaft, efficiency, overall dimensions and weight. standard reducers are listed in special reference books, and some of them are presented in Table 4.5.

The technical level of the gearbox is determined by the mass refinement factor -

Fig. 4.5

Table 4.5

Transmission type

Efficiency (η)

The gear ratio ( and )

Relative mass (q)

Toothed cylindrical




Toothed conical


























va - the ratio of the weight of the reducer m to the torque at the output . In the industry with a low level of perfection, and at a high level, in the widely used gearboxes, the working surface of the teeth of the wheels is reinforced (carburizing, nitriding, etc.), ∙ In aviation gearboxes . Such a high index for aviation gearboxes is achieved through the use of rational designs using high-strength materials and the manufacture of light alloy bodies (aluminum and magnesium).

To obtain the most reliable and perfect design of the reducer, the following requirements must be met:

• apply the most rational and reliable gearbox schemes that provide the necessary strength and rigidity of structures made of a material with a high specific strength and with a hardened working surface teeth of wheels at high loads;

• Reduce the material intensity due to the compactness of structures and the choice of the rational shape of parts;

• apply unification, use standard parts and ensure complete interchangeability of structural elements;

• ensure reliable locking of threaded connections and fixing of parts from displacement; low power consumption during operation by reducing friction losses and increasing efficiency; necessary lubrication and protection of parts from corrosion; resistance to mechanical and climatic influences; easy and convenient service with maximum automation;

• Use enclosed enclosures to prevent dust and moisture from getting inside;

• to achieve the maximum manufacturability of parts and assemblies in the manufacture, assembly and disassembly.

Fulfillment of the formulated requirements usually leads to reduction of the cost price of the reducer.

To assess the gearbox, you can also use the economic criterion - relative cost β = c/t (c - cost).

One of the ways to improve the design in engineering - the transition from the use of steel and cast iron casings to light alloy (aluminum, magnesium), non-metallic or composite materials. The latter is especially important in low-power gearboxes. In them, the mass of the hull can be determined by the technological capabilities of casting, when the wall thickness is greater than the necessary of the strength condition. Typically, the required wall thickness δ in low-power reducers (P <0.5> kW) of metal is no more than 2 mm. For castings in the earth of light alloys, the minimum wall thickness is δ = 3 div 4 mm, and with more advanced casting methods (casting into chill mold, investment or pressure models) is less. Molding of casings of cast iron has a thickness of at least 6 mm. Even with the same geometry of the hull, the transition from iron or steel (ρ = 7.8 g/cm3) to an aluminum alloy (ρ = 2.7 g/cm3) reduces the body weight by about 3 times, and taking into account the smaller wall thickness with the use of advanced casting technology, even more. For example, if the mass of the steel casing is 30% of the weight of the reducer, then changing its material to an aluminum alloy reduces the weight of the entire reducer by approximately 20%. Such a replacement is unacceptable in designs where high rigidity is required, for example in machine tool construction. The replacement of steel with an aluminum alloy reduces the rigidity by about 3 times. Cases of foundry aluminum and magnesium alloys are widely used in aviation, rocketry and transport, but less often in other industries. The lightest hulls are made from non-metals and composite materials, which are widely used even in household appliances. Hardening of the working surface of the teeth of the wheels significantly reduces the weight of the reducer. For example, changing the hardness of the working surface of the teeth of wheels with HB 250 by 11 RC. "60 reduces the weight of the two-stage cylindrical gearbox by approximately 40%. Usually, reducing the weight of the housing reduces the cost of the gearbox.

Drive Calculation Order

Consider the calculation procedure for the drive shown in Fig. 4.5, a.

Input. The initial data for the calculation should be specified in the TOR: kinematic scheme; cyclogram of loading (change of loading on time); T, ω - torque and angular velocity (instead of you can set n - rotation frequency) watt at the output. In the other case, if the output is a transfer that converts the rotary motion into translational motion, for example, screw-nut transmission, then set the force and speed of the screw movement at the output

Select the engine. 1. Determine the output power of the drive by the formula ; if there is a transfer screw-nut I, then by the formula

2. Calculate the required engine power , where - the efficiency of the entire reducer; in y - efficiency of each transmission stage (efficiency for different types of transmissions are given in Table 4.5); Πj - bearing loss (rolling slip with boundary friction); - The efficiency of screw-nut transmission - enters the formula only if it is available.

3. Select the engine and find its characteristics and .

Kinematic calculation of the transfer. 1. Determine the approximate value of the total gear ratio and break it up into steps ,

where - coefficient determined from optimization by one of the parameters (overall dimensions, inertia, accuracy, etc.); the index indicates that the rotation is transferred from the gear to the wheel ; - the number of transmission stages.

If the output is a screw-nut transmission, then - the speed of the shaft at the output of the gearbox, equal to the rotational speed of the screw (nuts, rpm), where P is the step, mm; ζ - number of threads; and - speed, m/s.

For cylindrical gears, the coefficient is adopted:

• from the condition minimum dimensions for the expanded scheme (the optimal option, when the wheels and gears of both stages have the same diameters) with a two-stage transmission with a three-stage , and for coaxial transmissions when, . The gear ratio of the last stage is found at from the image, when - from the expression ;

• from the minimum inertia condition for high-speed reverse drives at ; at

For high-precision transmissions, high requirements to the last stage (high accuracy and large gear ratio ) are required to ensure the appropriate accuracy. In this case, the accuracy of the drive will be determined by the last stage, and the errors of the previous stages will not have a significant impact on it.

2. Select the number of teeth of each wheel in the pair - the total number of teeth :

• for gears with a homogeneous structure ;

for small-sized (t & lt; 1) gears with a homogeneous structure ;

• for wheels with a hardened working surface (cementing, nitriding, etc.)

Number of gear teeth and wheels in a two-stage gear:

• for the first stage, is rounded to an integer);

for the second stage round to the nearest integer).

Refine the gear ratio

3. Determine the rotational speed of each shaft

Another variant of the kinematic calculation is possible, when the number of gear teeth . If the number of teeth is less than , to modify the cropping, you need to modify the profiles (contour shift), but take at least 12 .

Power transmission calculation. 1. Calculate the nominal torque of the engine (II-mm):

where - engine power, W; - rotation speed, rpm

2. Determine the calculated torque on each shaft:

where - coefficient of dynamic external load; - losses in bearings.

The design of the reducer. For ease of assembly and disassembly, the gear housing is made up of a composite, usually of two parts: the base O and the lid K. The lid on the body is fixed with pins and fixed to it with threaded parts (bolts, studs, nuts). Reducers come with axial (longitudinal) and radial (transverse) assembly (Figure 4.6).

Fig. 4.6

With the axial assembly, the body connector is made along a plane perpendicular to the axes of the shafts (Figure 4.6, a). Such a design is more technological and stiffer (easier casting, ).

Disadvantages: complex assembly and inspection of internal parts.

With the radial assembly, the body connector is made along the plane passing through the axis of the shafts (Figure 4.6, 6), which facilitates the assembly, disassembly and inspection of the internal cavities.

Disadvantages: the hull is more complex, the rigidity is different (the asymmetry of the hull), the sealing is more difficult (seal on the joint).

Application: Axial assembly is used to create strong and lightweight structures in aviation, rocketry, transport. However, this causes some operational inconvenience. Radial is used if the mass does not play a significant role and higher production cost is allowed for the sake of convenience of assembly and operation.

Such designs have become most common in general engineering.

Drives with high-speed engines (n = 6000 or 12,000 rpm) are widely used on space vehicles, as they are more economical and have less mass than slow-moving high-torque engines.

Two common schemes of drives of general engineering are shown in Fig. 4.7. In Fig. 4.7, a shows the connection between the electric motor D and the reducer P using the coupling M, and in Fig. 4.7, б - с using the belt transmission of the RP. At low powers, the gear can be mounted on the motor shaft. Such a design is used in motor-reducers consisting of an electric motor and a gear reducer. The mass and overall dimensions of the motor-reducers are much smaller than those shown in Fig. 4.7.

In gear units with a long service life, a continuous lubricant, is usually provided with a liquid lubricant. To do this, a part of the wheel is immersed in oil (crankcase lubrication) or fed by a jet (jet lubrication). A hydraulic system is used to feed the oil. Lubrication of bearings is often done by spraying oil with gears.

If a small amount of liquid or plastic lubricant is needed (low life, low speed and load), it is fed periodically with the help of a grease cup or a hand syringe. Sometimes a resource lubricant is used - once for the whole resource (for example, on missiles).

Typical for general engineering two-stage gearbox with radial assembly and cylindrical wheels (in different formations) is shown in Fig. 4.8. The case of the reducer is cast of cast iron. It consists of a base 5 and a removable cover 4. They are connected by bolts 6 and pins 9, which accurately fix the lid on the base. Cover 3 with vent 2 - for inspection and filling of liquid oil, plug 8 - for draining the oil, oil indicators 7 - for determining the oil level in the gearbox . The eyebolts 1 serve to carry the gear unit by a crane. In addition, the gearbox has a cogwheel 10, a slow-moving shaft 11,

Fig. 4.7

bearing cover 12, bearing 13, intermediate shaft 14, high-speed shaft with cut teeth 15

In Fig. 4.9 shows the aircraft reducer (in different projections) with axial assembly. The case of the gearbox from the magnesium alloy ML5 consists of two parts 2 and 3, connected with the studs 9 with the nuts. The studs are installed without a gap, which ensures an exact mutual position of the body parts. The design of the reducer is characterized by its minimum surface area, which ensures a minimum mass of the housing. To reduce the mass of the shafts 1, 5 and the axis 4 of -

Fig. 4.8

Fig. 4.9

Gotavlivayutsya hollow. The plug 6 prevents dirt and moisture from entering the housing. The holes 10 are intended for fastening the reducer on an airplane. The gear wheels 7 are made of 30Χ2HΒΛ steel with a hardened working surface.

thematic pictures

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