Determination of gear ratios of various gears in theoretical mechanics

Explosion-proof versions of gearmotors

Geared motors of this group are classified according to the type of explosion-proof design:

• “E” – units with an increased degree of protection. Can be used in any operating mode, including emergency situations. Enhanced protection prevents the possibility of ignition of industrial mixtures and gases.
• “D” – explosion-proof enclosure. The housing of the units is protected from deformation in the event of an explosion of the gear motor itself. This is achieved due to its design features and increased tightness. Equipment with explosion protection class “D” can be used at extremely high temperatures and with any group of explosive mixtures.
• “I” – intrinsically safe circuit. This type of explosion protection ensures the maintenance of explosion-proof current in the electrical network, taking into account the specific conditions of industrial application.

Reliability indicators

The table below shows the service life standards for the main parts of the gearmotor during long-term operation of the device with constant activity.

Resource

How to calculate gear ratio

The gear and wheel have a different number of teeth with the same module and proportional diameters. The gear ratio shows how many revolutions the driving part will make to turn the driven part a full circle. Gears have a rigid connection. The transmitted number of revolutions in them does not change. This negatively affects the operation of the unit under conditions of overload and dust. The tooth cannot slip like a belt on a pulley and breaks.

Calculation without resistance

When calculating the gear ratio, the number of teeth on each part or their radii are used.

Where u12 is the gear and wheel gear ratio;

Z2 and Z1 are the number of teeth of the driven wheel and drive gear, respectively.

The “+” sign is placed if the direction of rotation does not change. This applies to planetary gearboxes and gears with teeth cut along the inner diameter of the wheel. If there are parasites - intermediate parts located between the drive gear and the ring gear, the direction of rotation changes, as with an external connection. In these cases, “–” is placed in the formula.

When two parts are externally connected by means of a parasite located between them, the gear ratio is calculated as the ratio of the number of teeth of the wheel and gear with the “+” sign. The parasite does not participate in the calculations, it only changes the direction, and accordingly the sign in front of the formula.

Typically, the clockwise direction of movement is considered positive. The sign plays a big role in the calculations of multi-stage gearboxes. The gear ratio of each gear is determined separately according to the order in which they are located in the kinematic chain. The sign immediately shows the direction of rotation of the output shaft and the working unit, without additional diagramming.

Calculation of the gear ratio of a gearbox with several gears - multi-stage, is defined as the product of gear ratios and is calculated by the formula:

The gearing is rigid. The parts cannot slide relative to each other, as in a belt drive, and change the ratio of the number of rotations. Therefore, the output speed does not change and does not depend on overload. The calculation of the angular speed and the number of revolutions turns out to be correct.

Gear efficiency

To actually calculate the gear ratio, additional factors must be taken into account. The formula is valid for angular velocity; as for the moment of force and power, they are much less in a real gearbox. Their value is reduced by the resistance of transmission moments:

• friction of contacting surfaces;
• bending and twisting of parts under the influence of force and resistance to deformation;
• losses on keys and splines;
• friction in bearings.

Each type of connection, bearing and assembly has its own correction factors. They are included in the formula. Designers do not make calculations for the bending of each key and bearing. The directory contains all the necessary coefficients. If necessary, they can be calculated. The formulas are no different from simplicity. They use elements of higher mathematics. The calculations are based on the ability and properties of chromium-nickel steels, their ductility, tensile strength, bending, fracture and other parameters, including the dimensions of the part.

As for bearings, the technical reference book from which they are selected contains all the data for calculating their operating condition.

When calculating power, the main indicator of gearing is the contact patch, it is indicated as a percentage and its size is of great importance. Only drawn teeth can have an ideal shape and touch throughout the entire involute. In practice, they are manufactured with an error of several hundredths of a mm. When the unit operates under load, spots appear on the involute in places where the parts interact with each other. The more area on the tooth surface they occupy, the better the force is transmitted during rotation.

All coefficients are combined together and the result is the gearbox efficiency value. The efficiency is expressed as a percentage. It is determined by the ratio of power on the input and output shafts. The more gears, connections and bearings, the less efficiency.

General definition

A clear example of changing the number of revolutions is most easily observed on a simple bicycle. A man pedals slowly. The wheel rotates much faster. The change in the number of revolutions occurs due to 2 sprockets connected in a chain. When the large one, which rotates with the pedals, makes one revolution, the small one, standing on the rear hub, rotates several times.

Torque transmissions

The mechanisms use several types of gears that change torque. They have their own characteristics, positive qualities and disadvantages. Most common transmissions:

• belt;
• chain;
• serrated

Belt drive is the simplest to implement. It is used when creating homemade machines, in machine tools to change the speed of rotation of the working unit, in cars.

The belt is tensioned between 2 pulleys and transmits rotation from the driver to the driven. Performance is poor because the belt slides on a smooth surface. Thanks to this, the belt assembly is the safest way to transmit rotation. When overloaded, the belt slips and the driven shaft stops.

The transmitted number of revolutions depends on the diameter of the pulleys and the coefficient of adhesion. The direction of rotation does not change.

The transitional design is a belt gear drive.

There are protrusions on the belt and teeth on the gear. This type of belt is located under the hood of the car and connects the sprockets on the axles of the crankshaft and carburetor. When overloaded, the belt breaks, since it is the cheapest part of the unit.

The chain consists of sprockets and a chain with rollers. The transmitted speed, force and direction of rotation do not change. Chain drives are widely used in transport mechanisms and on conveyors.

Gear Characteristics

In a gear drive, the driving and driven parts interact directly through the meshing of teeth. The basic rule for the operation of such a node is that the modules must be identical. Otherwise, the mechanism will jam. It follows that the diameters increase in direct proportion to the number of teeth. Some values ​​can be replaced by others in calculations.

Modulus is the size between identical points of two adjacent teeth.

For example, between axes or points on an involute along the center line. The module size consists of the width of the tooth and the gap between them. It is better to measure the module at the point of intersection of the base line and the axis of the tooth. The smaller the radius, the more the gap between the teeth along the outer diameter is distorted; it increases towards the top from the nominal size. Ideal involute shapes can practically only be found on a rack. Theoretically, on a wheel with a maximally infinite radius.

The part with fewer teeth is called a gear. Usually it is leading, transmitting torque from the engine.

The gear wheel has a larger diameter and is driven in a pair. It is connected to the working unit. For example, it transmits rotation at the required speed to the wheels of a car or the spindle of a machine tool.

Typically, gearing reduces the number of revolutions and increases power. If in a pair there is a part with a larger diameter, the drive gear, at the output, the gear has a greater number of revolutions and rotates faster, but the power of the mechanism decreases. Such gears are called downshifts.

Why do we need a parasite?

When the gear and wheel interact, several quantities change at once:

• number of revolutions;
• power;
• direction of rotation.

Only in planetary units with teeth cut along the inner diameter of the ring, the direction of rotation is maintained. With external gearing, two identical gears are placed in a row. Their interaction does not change anything except the direction of movement. In this case, both gear parts are called gears, the wheel is not. The second, intermediate, is called “parasitic”, since it does not participate in the calculations and only changes its sign.

Types of gear connections

Gearing can have different tooth shapes on parts. This depends on the initial load and the location of the axes of the mating parts. There are types of gear movable joints:

• straight teeth;
• helical;
• chevron;
• conical;
• screw;
• worm

The most common and easiest to perform is spur gearing. The outer surface of the tooth is cylindrical. The arrangement of the gear and wheel axes is parallel. The tooth is located at right angles to the end of the part.

When it is not possible to increase the width of the wheel, but a large force must be transmitted, the tooth is cut at an angle and thereby increases the contact area. The calculation of the gear ratio does not change. The unit becomes more compact and powerful.

The disadvantage of helical gearing is the additional load on the bearings. The force from the pressure of the leading part acts perpendicular to the contact plane. In addition to the radial force, an axial force appears.

The chevron connection allows you to compensate for the stress along the axis and further increase the power. The wheel and gear have 2 rows of oblique teeth directed in different directions. The transmission number is calculated similarly to a spur gear according to the ratio of the number of teeth and diameters. Chevron gearing is difficult to implement. It is installed only on mechanisms with a very heavy load.

In a bevel gear transmission, the axes are located at an angle. The working element is cut along a conical plane. The gear ratio of such pairs can be equal to 1, when it is only necessary to change the plane of action of the force. To increase power, a semicircular tooth is cut. The transmitted number of revolutions is calculated only by tooth; the diameter is mainly used when calculating the dimensions of the unit.

The helical gear has a tooth cut at an angle of 45⁰. This allows the axes of the working elements to be positioned perpendicularly in different planes.

A worm gear does not have a gear; it is replaced by a worm. The axes of the parts do not intersect. They are located perpendicularly in space, but in different planes. The gear ratio of a pair is determined by the number of thread starts on the worm.

In addition to those listed, other types of gears are also produced, but they are extremely rare and are not standard.

Multi-stage gearboxes

How to choose the right gear ratio. The engine usually produces several thousand revolutions per minute. At the output - the wheels of the car and the spindle of the machine, such a rotation speed will lead to an accident. The power of the actuating mechanism is not enough for the working tool to cut metal and the wheels to move the car. One pair of gears will not be able to provide the required reduction, or the driven part must be of enormous size.

A multi-stage knot with several pairs of gears is created. The gear ratio is calculated as the product of the numbers of each pair.

Uр = U1×U2 × … ×Un;

Where:

Uр – gear ratio;

U1,2,n – each of the pairs.

Before choosing the gear ratio, you need to decide on the number of pairs, the direction of rotation of the output shaft, and do the calculation in reverse order, based on the maximum permissible wheel dimensions.

In a multi-stage gearbox, all the gear parts located between the drive gear at the input to the gearbox and the driven ring gear on the output shaft are called intermediate. Each individual pair has its own gear, gear and wheel.

Gearbox and gearbox

Any gearbox with gears is a gearbox, but the reverse is not true.

The gearbox is a gearbox with a movable shaft on which gears of different sizes are located. Shifting along the axis, it includes first one or another pair of parts in the work. The change occurs due to the alternate connection of various gears and wheels. They differ in diameter and transmitted number of revolutions. This makes it possible to change not only the speed, but also the power.

Car transmission

In the machine, the translational movement of the piston is converted into rotational movement of the crankshaft. The transmission is a complex mechanism with a large number of different components interacting with each other. Its purpose is to transmit rotation from the engine to the wheels and regulate the number of revolutions - the speed and power of the car.

The transmission includes several gearboxes. This is, first of all:

• gearbox - speeds;
• differential.

The gearbox in the kinematic diagram is located immediately behind the crankshaft and changes the speed and direction of rotation.

By switching - moving the shaft, the gears on the shaft are connected alternately to different wheels. When the reverse gear is engaged, the direction of rotation changes through the parasite, and as a result the car moves backwards.

The differential is a bevel gear with two output shafts located in the same axis opposite each other. They look in different directions. The gear ratio of the gearbox - differential is small, within 2 units. It changes the position of the axis of rotation and direction. Due to the arrangement of bevel gears opposite each other, when engaged with one gear, they rotate in one direction relative to the position of the vehicle's axle, and transmit torque directly to the wheels. The differential changes the speed and direction of rotation of the driven tips, and behind them the wheels.

Primary requirements. Modern tendencies

The main gears are subject to many requirements, the main ones being:

• Reliability;
• Minimal maintenance required;
• High efficiency indicators;
• Smooth and silent;
• Minimum possible overall dimensions.

Naturally, there is no ideal option, so designers have to look for compromises when choosing the type of final drive.

It is not yet possible to abandon the use of final drives in transmission designs, so all developments are aimed at increasing performance indicators.

It is noteworthy that changing the operating parameters of the gearbox is one of the main types of transmission tuning. By installing gears with a changed gear ratio, you can significantly influence the dynamics of the car, maximum speed, fuel consumption, load on the gearbox and power unit.

Finally, it is worth mentioning the design features of dual-clutch robotic gearboxes, which also affects the final drive design. In such gearboxes, paired and unpaired gears are separated, so there are two secondary shafts at the output. And each of them transmits rotation to its own drive gear of the main gear. That is, in such gearboxes there are two driving gears, and only one driven gear.

DSG gearbox diagram

This design feature allows you to make the gear ratio on the gearbox variable. To do this, only drive gears with different numbers of teeth are used. For example, when using a number of unpaired gears, to increase traction, a gear is used that provides a larger gear ratio, and the gear of a paired row has a lower value of this parameter.

The main gear of a car is a transmission element, in the most common version, consisting of two gears (driven and driven), designed to convert the torque coming from the gearbox and transmit it to the drive axle. The design of the main gear directly affects the traction and speed characteristics of the vehicle and fuel consumption. Let's consider the device, principle of operation, types and requirements for the transmission mechanism.

Frequency regulation

Special devices, frequency converters (other names: inverter, frequency converter, driver), are connected to an electrical machine. By rectifying the supply voltage, the frequency converter internally generates the required frequency and voltage values ​​and supplies them to the electric motor.

The converter calculates the necessary parameters for blood pressure control independently, according to internal algorithms programmed by the device manufacturer.

Advantages of frequency regulation

The only drawback that you can put up with is the need to purchase a frequency converter. The prices for such devices are absolutely sky-high, and within 150 euros, you can get a converter for a 2 kW motor.

Effect of gear ratio on dynamics

The gear ratio is a calculated value; it is found by the ratio of the number of teeth of the driven gear to the number of the driving gear. The higher this value, the faster the engine will turn the required number of revolutions and accelerate the car more rapidly. “Super!” - you will say, but you will be mistaken in the main thing - the maximum speed in this case will be lower, and you will have to change gears much more often. Therefore, manufacturers adhere to average gearbox ratios when creating multi-stage designs.

At first, gearbox designs contained 3 shafts, where the 3rd gear was direct and made it possible to reach maximum speed. Subsequent speed adjustment was reduced to reducing engine speed through the fuel supply; in this case, the effect of speed control was achieved, but the efficiency of the car was completely lost. Therefore, the number of gears was increased, and the former straight third became fourth or fifth, and then reached higher levels.

The gear ratios of the manual transmission of the most common 5-speed gearbox are in the following ranges:

• 1st gear – from 3 to 4;
• 2nd gear – from 2 to 2.9;
• 3rd gear – from 1.2 to 1.9;
• 4th gear – from 0.9 to 1.2;
• 5th gear – from 0.7 to 0.9;
• reverse gear - from 3 to 4.

If the automatic transmission gear ratios are set incorrectly, you will not be able to achieve a comfortable driving experience. But in an automatic transmission, if the gear ratios are unbalanced, they can turn the uniform movement of the car into riding a stubborn donkey, accompanied by constant jerking and unreasonably high fuel consumption.

Experts consider the optimal values ​​to be values ​​located close to each other, then the car will accelerate without jerking when changing gears. Such fragmentation cannot be achieved if there are few gears, so the more gears, the better for your driving comfort. This is especially true for cars with an automatic transmission: if there is a choice, then an automatic transmission with 5, 6, 7 speeds will be much preferable to a 4-speed automatic transmission. Here the automation switches the speed for you, and the more often it does this, the faster the expensive mechanisms will fail.

Gear ratios are often indicated in the vehicle specifications. Behind these numbers is the manufacturer’s scrupulous selection of optimal values. There are no ideal values, as in the assessment of other parameters, here. Therefore, it is impossible to call one value bad and another good, since gearboxes affect the dynamics of the car, and the type of driving and preferences of car owners are often radically different, and it is difficult to consider the gearbox separately from the entire “organism” of the car.

All speed modes and recommendations from the manufacturer are formed only after determining the gear ratios, because they must take into account such nuances as:

• comfort in driving, eliminating frequent gear changes both manually and automatically;
• good vehicle dynamics;
• all gears must work harmoniously so that not a single travel mode deviates from the given rhythm;
• fuel consumption should be normal and commensurate with the declared displacement, there should be no over-gasping;
• a long last gear can accelerate the car to maximum speed;
• there must be complete compatibility of the engine and gear ratios.

Let us explain the last point in a little more detail. For each engine, developers create a box with specified gear ratios, so when thinking about replacing the gearbox, the option of a non-original gearbox should not even be considered. With this modification you can get a lot of problems. If the new gearbox is taken from the same engine, but more powerful, then you are guaranteed more engine wear and not very convenient gear shifting, but you can get used to this over time, but premature engine wear is not a pleasant thing.

The situation is no better when replacing it back - the box was taken from a pair where the engine was weaker. With this modification you will deprive yourself of the potential of the car and increase fuel costs for the trip.

Thus, for the car to fully operate, it must have its original transmission. But car tuning craftsmen have already learned how to change the gear ratio in the car, using new gears in the rows and obtaining other characteristics of the model. Such modifications are often carried out with VAZ cars. The consequence of this is more intense acceleration of the car, but you have to sacrifice maximum speed.

The gear ratio of racing cars is also very different from production models, because they face different operating tasks.

Efficiency

The numbers in this section refer to the efficiency of the transmission, including the transmission means and any gear system.
In this context, efficiency refers to how much power is delivered to the wheel compared to the power of the pedals. For a well-maintained transmission system, efficiency is typically between 86% and 99%, as detailed below. Factors other than gearing that affect performance include rolling resistance and air resistance:

• Rolling resistance can vary by a factor of 10 or more depending on tire type, tire size, and tire pressure.
• Air resistance increases significantly with speed and is the most important factor at speeds above 10–12 miles (15–20 km) per hour (the drag force increases with the square of the speed, so the power required to overcome it increases with the cube of the speed).

Human factors can also play a role. Rohloff argues that in some cases overall efficiency can be improved by using a slightly less efficient gear ratio when this results in greater human efficiency (in converting food into pedal power) since a more efficient pedaling speed is used.

Review

An encyclopedic overview can be found in Chapter 9 of Bicycle Science, which covers both theory and experimental results. Some details drawn from these and other experiments are presented in the following subsection with links to the original reports.

Factors that have been shown to affect transmission efficiency include the type of transmission system (chain, shaft, belt), type of gearing system (fixed, derailleur, hub, continuously variable), size of sprockets used, amount of power input, pedaling speed and chain rust level. For a given gear train, different gear ratios usually have different efficiencies.

Some experiments used an electric motor to drive the shaft to which the pedals are attached, while others used averages from a number of real cyclists. It's unclear how the steady power delivered by the motor compares to the cyclic power provided by the pedals. Rohloff argues that constant motor power should match peak pedal power, not average (which is half of peak power).

Little independent information is available regarding the efficiency of belt drives and continuously variable gear drives; even the manufacturers/suppliers are reluctant to provide any numbers.

Details

Switch-type mechanisms of a typical mid-range product (the type used by serious hobbyists) achieve 88% to 99% mechanical efficiency at 100 watts. In gearshift mechanisms, the highest efficiency is achieved through larger sprockets. Efficiency generally decreases as sprocket and chainring sizes are reduced. Switch efficiency is also reduced due to cross circuit or transition from

large ring to large sprocket or from small ring to small sprocket. This cross connection also results in increased wear due to the lateral deflection of the chain.

Chester Kyle and Frank Berto reported in Human Power 52 (Summer 2001) that tests of three shift systems (4 to 27 gears) and eight hub transmissions (3 to 14 gears) performed at 80 watts, 150 Watts, 200W inputs gave the following results:

Testing the efficiency of bicycle gears is complicated by a number of factors - in particular, all systems tend to perform better at higher power ratings. 200W will power a typical bike at 20mph, while athletes can reach 400W, with efficiency claimed to be “close to 98%”.

At a more typical power rating of 150 watts, hub gears are typically about 2% less efficient than a shift system if both systems are in good condition.

Determination methods

There are several ways to determine the gear ratio:

• theoretical;
• practical;
• calculated

The first, simplest, method is theoretical. Usually, in order to find out the necessary information, you just need to look at the car’s instructions, where detailed tables are indicated. Most cars contain such information in the Vin number, where it is encrypted, but it is easy to find out. Russian-made cars usually have a standard set of standard gearbox models. This greatly simplifies the replacement process.

It's a different matter when it is necessary to replace only a separate part of the assembly. Usually, when a car has had several owners, it is not known how many times the gearbox has been replaced and what model is currently installed. This is often quite easy to do, since they try to put the necessary information in places that are most convenient for viewing.

The practical method of determining the gear ratio is more complex and requires direct intervention in the vehicle mechanism. Let's look at the detailed step-by-step instructions:

1. The first thing you need to do is find out what model is installed on your car. There are several types that differ depending on the type of gear transmission, there are gear, chain, screw, hypoid, wave and fractional. In any case, the gear ratio is calculated as the ratio of the rotation speed of the driven and drive shafts. If the above data is known, you will have to resort to disassembling the node.
2. It is necessary to disconnect the gearbox from the housing and related components and open the cover to have an overview of the structural elements. With the help of such manipulations, you can find out exactly which element of the gearbox you should start from when calculating.
3. Then calculate the gear ratio based on the type of unit. If the transmission is geared, then the calculation is quite easy; in this case, the calculated indicator is equal to the ratio of the number of teeth of the driven gear to the teeth of the drive gear. You just need to calculate the specified parameters.
4. If the transmission is belt driven, the calculation is made by the ratio of the diameter of the drive pulley to the driven one, or vice versa. The calculation is always carried out from the larger number. With a chain drive, you need to count the number of teeth of the drive and driven sprocket, and calculate the ratio of the larger to the smaller. With a worm gear, the number of runs on the worm and the teeth on the worm wheel are counted, after which the ratio of the second number obtained to the first is calculated.

To do this, you need to use a special measuring device - a tachometer, which measures the rotation speed of the engine drive shaft and the shaft that drives the wheels. The ratio of the first indicator to the second will help to accurately determine the gear ratio.

You can do this easier by calculating the torque of the gearbox by rotating the wheel. The drive axle must be raised on supports. The initial position of the wheel and drive shaft is recorded; this can be done using simple marks. Then you should rotate the wheels until the marks coincide and separately count the number of revolutions of the shaft and wheel. For these purposes, it is rational to use someone else's help.

After collecting all the necessary information, you need to divide the number of revolutions of the drive shaft by the number of rotations of the wheel. To get an accurate result, you need to carefully consider each stage of the procedure, since even the slightest inaccuracy in measurement can critically affect the final result.

Asynchronous motors with wound rotor

The main way to control an IM with a wound rotor is to change the amount of slip between the stator and the rotor.

Voltage regulation

Through special LATR autotransformers, by changing the voltage on the motor windings, the shaft speed is adjusted.

This method is also suitable for IMs with a squirrel-cage rotor.

In this way, it can be adjusted from the minimum to the nominal parameters of the engine.

Installing active resistance in the rotor circuit

A variable rheostat or set of resistances in the rotor circuit affects the rotor current and field. Thus changing the amount of slip and the number of engine revolutions.

The greater the resistance, the less the current, the greater the sliding value of the blood pressure and the lower the speed.

How to calculate gear ratio

The gear and wheel have a different number of teeth with the same module and proportional diameters. The gear ratio shows how many revolutions the driving part will make to turn the driven part a full circle. Gears have a rigid connection. The transmitted number of revolutions in them does not change. This negatively affects the operation of the unit under conditions of overload and dust. The tooth cannot slip like a belt on a pulley and breaks.

Calculation without resistance

When calculating the gear ratio, the number of teeth on each part or their radii are used.

u12 = ± Z2/Z1 and u21 = ± Z1/Z2,

Where u12 is the gear and wheel gear ratio;

Z2 and Z1 are the number of teeth of the driven wheel and drive gear, respectively.

The “+” sign is placed if the direction of rotation does not change. This applies to planetary gearboxes and gears with teeth cut along the inner diameter of the wheel. If there are parasites - intermediate parts located between the drive gear and the ring gear, the direction of rotation changes, as with an external connection. In these cases, “–” is placed in the formula.

When two parts are externally connected by means of a parasite located between them, the gear ratio is calculated as the ratio of the number of teeth of the wheel and gear with the “+” sign. The parasite does not participate in the calculations, it only changes the direction, and accordingly the sign in front of the formula.

Typically, the clockwise direction of movement is considered positive. The sign plays a big role in the calculations of multi-stage gearboxes. The gear ratio of each gear is determined separately according to the order in which they are located in the kinematic chain. The sign immediately shows the direction of rotation of the output shaft and the working unit, without additional diagramming.

Calculation of the gear ratio of a gearbox with several gears - multi-stage, is defined as the product of gear ratios and is calculated by the formula:

u16 = u12×u23×u45×u56 = z2/z1×z3/z2×z5/z4×z6/z5 = z3/z1×z6/z4

The gearing is rigid. The parts cannot slide relative to each other, as in a belt drive, and change the ratio of the number of rotations. Therefore, the output speed does not change and does not depend on overload. The calculation of the angular speed and the number of revolutions turns out to be correct.

Gear efficiency

To actually calculate the gear ratio, additional factors must be taken into account. The formula is valid for angular velocity; as for the moment of force and power, they are much less in a real gearbox. Their value is reduced by the resistance of transmission moments:

• friction of contacting surfaces;
• bending and twisting of parts under the influence of force and resistance to deformation;
• losses on keys and splines;
• friction in bearings.

Each type of connection, bearing and assembly has its own correction factors. They are included in the formula. Designers do not make calculations for the bending of each key and bearing. The directory contains all the necessary coefficients. If necessary, they can be calculated. The formulas are no different from simplicity. They use elements of higher mathematics. The calculations are based on the ability and properties of chromium-nickel steels, their ductility, tensile strength, bending, fracture and other parameters, including the dimensions of the part.

As for bearings, the technical reference book from which they are selected contains all the data for calculating their operating condition.

When calculating power, the main indicator of gearing is the contact patch, it is indicated as a percentage and its size is of great importance. Only drawn teeth can have an ideal shape and touch throughout the entire involute. In practice, they are manufactured with an error of several hundredths of a mm. When the unit operates under load, spots appear on the involute in places where the parts interact with each other. The more area on the tooth surface they occupy, the better the force is transmitted during rotation.

All coefficients are combined together and the result is the gearbox efficiency value. The efficiency is expressed as a percentage. It is determined by the ratio of power on the input and output shafts. The more gears, connections and bearings, the less efficiency.

Power

During rotational movements of the working parts of the mechanisms, resistance arises, which leads to friction - abrasion of the units. With the right choice of gearbox in terms of power, it is able to overcome this resistance. Therefore, this point is of great importance when you need to buy a gearmotor for long-term purposes.

The power itself - P - is calculated as a quotient of the force and speed of the gearbox. The formula looks like this:

• where: M – moment of force;
• N – revolutions per minute.

To select the desired gearmotor, it is necessary to compare the power data at the input and output - P1 and P2, respectively. output power of the geared motor

• where: P – gearbox power; Sf is the operating factor, also known as the service factor.

At the output, the power of the gearbox (P1 > P2) should be lower than at the input. The norm of this inequality is explained by the inevitable losses in performance during engagement as a result of friction between parts.

When calculating capacity, it is imperative to use accurate data: due to different efficiency indicators, the probability of selection error when using approximate data is close to 80%.

Gearbox type

The presence of a kinematic drive diagram will simplify the choice of gearbox type. Structurally, gearboxes are divided into the following types:

Single-stage worm gear with crossed input/output shaft arrangement (angle 90 degrees).

Two-stage worm gear with perpendicular or parallel arrangement of the axes of the input/output shaft. Accordingly, the axes can be located in different horizontal and vertical planes.

Cylindrical horizontal with parallel input/output shafts. The axes are in the same horizontal plane.

Cylindrical coaxial at any angle. The shaft axes are located in the same plane.

In a bevel-helical gearbox, the axes of the input/output shafts intersect at an angle of 90 degrees.

IMPORTANT! The spatial location of the output shaft is critical to a number of industrial applications.

• The design of worm gearboxes allows them to be used in any position of the output shaft.
• The use of cylindrical and conical models is often possible in the horizontal plane. With the same weight and dimensional characteristics as worm gearboxes, the operation of cylindrical units is more economically feasible due to an increase in the transmitted load by 1.5-2 times and high efficiency.

Table 1. Classification of gearboxes by number of stages and type of transmission

Operational coefficient (service factor)

Service factor (Sf) is calculated experimentally. The type of load, daily operating duration, and the number of starts/stops per hour of operation of the gearmotor are taken into account. The operating coefficient can be determined using the data in Table 3.

Table 3. Parameters for calculating the service factor

Advantages and disadvantages

Worm final drive Each type of gear connection has its pros and cons. Let's look at them:

• Cylindrical main gear. The maximum gear ratio is limited to 4.2. A further increase in the tooth ratio leads to a significant increase in the size of the mechanism, as well as an increase in the noise level.
• Hypoid main gear. This type is characterized by low tooth load and reduced noise level. In this case, due to the displacement in the meshing of the gears, sliding friction increases and efficiency decreases, but at the same time it becomes possible to lower the driveshaft as low as possible. Gear ratio for passenger cars – 3.5-4.5; for freight – 5-7;.
• Bevel main gear. Rarely used due to its large size and noise.
• Worm main gear. This type of gear connection is practically not used due to the complexity of manufacturing and the high cost of production.

Epilogue

For all their advantages, asynchronous machines have a significant drawback: the rotor jerks when voltage is applied. Such modes are dangerous both for the engine itself and for the drive mechanisms. Since during the start of the IM, the current in the motor windings is equivalent to a short circuit. And the jerk of the shaft breaks bearings, splines, and transmission devices. Therefore, they try to start the IM with a smooth start. Namely:

• Launch via LATR.
• Acceleration and operation of the IM, through switching the motor windings star-delta.
• Use of control devices such as frequency converter.

Belt drive ratio

A belt drive refers to two pulleys that are connected by a belt, as shown in the figure. It is possible that it was one of the first methods used by man. The material used to make the belt changed, its shape changed, but the gear ratio remained unchanged, defined as the frequency of dividing the speed of the drive shaft by the speed of the driven one, or as a result of dividing the number of revolutions of these shafts (n1/n2 or ω1/ω2). For a belt drive, it can be calculated using the diameters (radii) of the pulleys. The gear ratio in this case is also determined as the quotient of the division of revolutions.

If, during energy conversion, the speed decreases, that is, the gear ratio is greater than 1, then the transmission will be reduction, and the device itself is called a gearbox. If the result is less than one, then the device is called a multiplier, although it also functions as a reducer, only a step-down one. The gear ratio of the gearbox allows you to reduce the number of revolutions (angular velocity) coming from the drive shaft to the driven shaft, while increasing the transmitted torque.

This property of the gearbox makes it possible for engineers, when designing various devices, to change the parameters of the transmitted energy, and the gear ratio of the gearbox serves as a powerful tool in solving the problem.

Despite its considerable age, the belt drive is still used on cars; it is used as a drive for a generator, a gas distribution mechanism, and also in some other cases.

Preliminary preparation

Before you begin creating this device, you must have general knowledge of mechanics, be able to use repair tools and equipment, and know the operating principle and structure of this unit.

In addition, you need to initially determine:

• the type of future gearbox and its version;
• the gear ratio that will need to be converted and determined at the output;
• indicators of dynamic loads that will affect the working parts of the device;
• weight and dimensions of the future device;
• installation angle;
• temperature limits that will occur in the device during its operation;
• switching cycle – full or variable;
• intensity of operation.

Varieties

The gearboxes with which walk-behind tractors are equipped seem identical only at first glance. In fact, these devices can be divided into three groups. The differences lie in the design features of the gearboxes. Let's get to know the representatives of this family in more detail.

Angular

Angle-type gearboxes are elementary structures that serve to connect the transmission to the power plant of the unit.

Due to the absence of complex components, some farmers install homemade versions of angular gearboxes on walk-behind tractors.

The structure of this node looks like this:

1. Mechanism body.
2. Belt drive pulley with fastening.
3. Rotor shaft.
4. Flange complete with mounting and bearing.
5. Washer and fixing key.

Gear

This is a more complex mechanism, which is impossible to recreate at home without special skills and knowledge.

Gear reducers are called reduction gearboxes. Thanks to its design features, the mechanism reduces the engine speed, simultaneously increasing the power output of the walk-behind tractor.

Such gearboxes have a long service life, so they are suitable for performing various jobs, and do not suffer mechanical damage even under peak loads.

Unlike angular models, reduction gearboxes require additional cooling.

Where is the device used?

A reduction gearbox has many advantages. Its design allows you to increase the productivity and profit of large industrial enterprises. It can also be considered an indispensable assistant in the household.

Experts highlight the following areas of application of the device:

• in industry;
• in car gearboxes;
• in various electrical equipment.

At large enterprises this product is used quite widely. In various machines for metal processing, the gearbox is used as a rotary transmission unit, which increases the number of revolutions. In gearboxes for automobile transport, a device is installed that reduces the engine speed. The softness and smooth running of the machine directly depends on the quality of adjustment of the gears of the gearbox.

This product is widely used in electrical equipment and household appliances, such as rotary hammers, drills or mixers. Gearboxes can be considered the main parts of ventilation, planetary, pumping and cleaning systems, because they are able to maintain optimal operating pressure.