1. Gears
1.1 Constructions
2. Wear and repair of gears
2.1 Replacement and repair of gear wheels
2.2 Methods for the rapid repair of gears
List of used literature
1. GEARS
1.1 Constructions
Gear drives are used in almost all mechanisms with which metallurgical workshops are equipped (cranes and hoists, roller tables, overhead winches, stand drives, etc.)
The main parts of gears are gears (gears). They serve to transfer rotation from one shaft to another when the shafts are not on the same axis.
Depending on the relative position of the shafts, gears are used: cylindrical, conical and helical.
A cylindrical gear transmission serves to transfer rotation from one to another parallel shaft (Fig. 1, a).
The bevel gear is used to transfer rotation from the shaft to the shaft, located with intersection of the axes (Fig. 1.6).
The helical gear is used to transfer rotation from the shaft to the shaft located with intersecting but not intersecting axes (Fig. 1, c).
Rice. 1. Gear drives: a - cylindrical: b - bevel: c - helical: g-chevron gear.
A gear wheel and a rack are used to convert rotary motion into translational and return
The teeth of cylindrical wheels can be straight (Fig. 1, a and b), oblique and chevron (herringbone) - Fig. 1, d.
The chevron gear consists of two helical gears connected together.
When gears with straight teeth are operating, one or two teeth are meshed at the same time, as a result of which the transmission operation is accompanied by some jolts.
Smoother operation of the gear transmission is achieved by using oblique or chevron teeth, since the number of teeth participating in the engagement increases.
Gear wheels are made from steel forgings, steel castings and rolled products, or from cast iron castings. For critical gears (for example, hoisting machines), the use of cast iron gears is not allowed.
Classification of gears. Depending on the purpose of the gear, the type of tooth and the speed of rotation, gears are divided into four classes of gear accuracy according to manufacturing and assembly tolerances (Table 119).
Table 1 Classification of gears
| Class | Allowable | |||
| exactly- | Gear type | Type of | district speed | Note |
| sti | tooth | height, m / s | ||
| 4 | Cylindrical | Straight | Up to 2 | Let's apply where the accuracy |
| Oblique | »3 | and smoothness do not have | ||
| values as well as in | ||||
| Conical | Straight | " 1 | manual and unloaded | |
| transmissions | ||||
| 3 | Cylindrical | Straight | »6 | |
| Oblique | " eight | |||
| Conical | Straight | »2 | ||
| Oblique | " 5 | |||
| 2 | Cylindrical " | Straight | " ten | |
| Oblique | " eighteen | |||
| Conical | Straight | " 5 | ||
| Oblique | " ten | |||
| 1 | Cylindrical | Straight | Above 8 | 1 When required, |
| Oblique | " 15 | 1 smoothness of transmission | ||
| Conical | Straight | " 5 | whether, as well as in the countdown | |
| Oblique | " ten | mechanisms |
Gear drives are made open, half-open and closed.
Open gears are those that do not have a casing (reservoir) for an oil bath; such gears are periodically lubricated with grease. Usually these transmissions are slow-speed and are mainly used in simple machines and mechanisms.
Semi-open gears differ from open ones by the presence of a reservoir for a liquid oil bath.
Closed gears are gears that, together with bearings, are mounted in special housings.
The gears of the reducer are lubricated in various ways:
1) at peripheral speeds of the gears above 12-14 m / sec - by the jet method with the supply, the jet into the zone of the beginning of the engagement of the gear wheels;
2) at peripheral speeds of gears below 12 m / s - by dipping method.
Consider the following when dipping lubrication:
a) the larger gear of the pair should be immersed in oil two to three times the height of the tooth;
b) if the gearbox has several stages, then the oil level is determined taking into account the speed of the gears.
In the latter case, level b (Fig. 2) is allowed when the gear wheel 1 of the low-speed stage rotates at low speed. In gearboxes with medium and large
Rice. 2. Jet lubrication of gears.
Rice. 3. Scheme of lubrication of gears by dipping.
the speed of low-located wheels, the latter are immersed to two to three times the tooth height of the larger wheel, and oil is poured to level a. greases of the first stage put an auxiliary gearwheel 3 with a narrow tooth, which supplies lubricant to the impeller.
The viscosity of the oil poured into the gearbox is selected depending on the speed and load - usually from 4 to 12 ° E at a temperature of determining the viscosity of 50 ° C. temperature conditions in which the unit operates; when the temperature rises, an oil of a higher viscosity is used, and when the temperature is low, a lower viscosity is used.
Open gears are usually lubricated with greases (grease, constantin, etc.).
The packing of the seals provided (in the drawings) in the bearings and along the joint line of the gearbox housing should be done very carefully to avoid oil leakage and dust ingress into the gearbox.
2. Gear wear and repair
Gear wheels fail for two main reasons: tooth wear and tooth breakage.
Wear usually results from 1) incomplete adhesion and 2) increased friction (progressive wear).
Wear in the first case is mainly the result of poor assembly and correct assembly(strict observance of the radial clearance) is usually absent. However, a change in the radial clearance can also be a consequence of the depletion of the bearing shells, and as a result of the depletion of the bearings, there can be both an increase in the radial clearance and its decrease (work in the thrust).
If the load on the liners is transferred to the sides opposite to the clutch during operation, as the liners wear out, an increase in the radial clearance is possible.
If the load on the liners is transferred to the side of the cord (for example, at the gear wheels of crane runners, during operation, as the liner depletes (in this example, the liner of the runner), the radial clearance may decrease.
In both cases, after replacing the bushings, the radial clearance is restored.
Gradual wear from increased friction depends on a number of conditions, including the hardness of the material from which the gears are made, heat treatment, the correct selection of lubricant, insufficient oil purity and untimely oil change, gear overload, etc.
Correct installation and good supervision during operation are the main conditions for a long and trouble-free operation of the equipment.
Breakage of gear teeth occurs for the following reasons: gear overload, one-sided (from one end of the tooth) load, tooth undercut, invisible cracks in the workpiece material and microcracks, as a result of poorly conducted heat treatment, weak metal resistance to shocks (in particular, as a result of failure to anneal castings and forgings), increased impacts, falling between the teeth of solid objects, etc.
Rice. 4. Repair of teeth using screwdrivers followed by welding
As a rule, gear wheels with worn out and broken teeth should not be repaired, but replaced, and it is recommended to replace both wheels at the same time. However, when the large wheel in engagement is many times the size of the small wheel, it is necessary to replace the small wheel in time, which wears out faster than the large one approximately by the ratio of the gear ratio. Replacing the small wheel in time will protect the large wheel from wear.
The wear of the teeth of the gear wheels should not exceed 10-20%: the thickness of the tooth, counting along the arc of the initial circle. In low-critical gears, tooth wear is allowed up to 30% of the tooth thickness, in gears of critical mechanisms, it is much lower (for example, for load lifting mechanisms, wear should not exceed 15%: tooth thickness, - and for gear wheels of crane lifting mechanisms transporting liquid and hot metal - to 10%").
Gears with cemented teeth should be replaced when the cemented layer is worn over 80% 1 of its thickness, as well as cracking, chipping or peeling of the cemented layer.
In case of broken teeth, but no more than two in a row in not particularly critical gears (for example, mechanisms for moving cranes), their restoration is allowed, which is done in the following way: the broken teeth are cut down to the base, two or three holes are drilled along the width of the tooth and a thread is cut in them, make studs and screw them tightly into the prepared holes, weld the studs to the gear and electrically weld the metal, giving it the shape of a tooth, on a gear-cutting, milling or planing machine or manually filing the deposited metal into a tooth shape, after which the restored profile is checked by adhesion to the mating part and by template.
Types of gears
Types of gears: a, b, c - cylindrical gears with external gearing; d - screw-nut transfer; d - cylindrical gear with internal gearing; e - gear screw; g, h, i - bevel gears; k - hypoid transmission
Gears and wheels are classified according to the following criteria
Picture 1
Picture 2
Involute profile tooth shapes
Forms of teeth of an elliptical profile (new gear transmission by G.P. Grebenyuk).
Forms of teeth in gears with gearing M.L. Novikova
Multi-stage.
7. Depending on the relative nature of the movement of the shafts distinguish between privates and planetary.
Planetary gear.
The standard provides 12 degrees of accuracy. In practice, transmissions of general engineering are made from the sixth to the tenth degree of accuracy. Gears made according to the sixth degree of accuracy are used for the most critical cases.
Of the gears listed above, the most widespread are cylindrical spur and helical gears, as the easiest to manufacture and operate. Gears with involute teeth are predominantly used. The advantage of the involute engagement is that it is insensitive to fluctuations in the center-to-center distance.
Other types of engagement are used to a limited extent. So, cycloidal gearing, in which the operation of gears with a very small number of teeth (2-3) is possible, cannot, unfortunately, be manufactured by a modern high-performance running method, therefore the gears of this gearing are laborious and expensive to manufacture; Novikov's new spatial engagement has not yet received mass distribution, due to its high sensitivity to fluctuations in the center-to-center distance.
Straight-toothed wheels (about 70%) are used at low and medium speeds, when dynamic loads from manufacturing inaccuracies are small, in planetary, open gears, as well as when axial displacement of the wheels is necessary.
Helical wheels (more than 30%) have a great smoothness and are used for critical mechanisms at medium and high speeds.
Chevron wheels have the advantages of helical gears plus balanced axial forces and are used in highly loaded gears.
Bevel gears are used only in cases where it is necessary according to the conditions of the layout of the machine; screw - only in special cases.
3. Let's consider in more detail some types of transfers
Helical gear.
The helical gear (a kind of helical gear) consists of two helical cylindrical wheels. However, unlike helical spur gears with parallel shafts, the tangency between the teeth here occurs at a point and at significant sliding speeds. Therefore, under significant loads, helical gears cannot work satisfactorily.
Helical gear
Bevel gear
Bevel gear consists of two bevel gears and serves to transmit torque between shafts with intersecting axes at an angle. Bevel gear wheels are made with straight, oblique, circular teeth.
Hypoid transmission.
A bevel gear transmission for transmitting torque between cross-axle shafts is called hypoid. This transmission is used in cars.
Hypoid transmission.
Worm gears
A worm gear is a gear that consists of a screw called a worm and a worm wheel. A worm gear is used to transfer rotation from one shaft to another when the axes of the shafts intersect. The crossing angle is 90 ° in most cases. The worm gear belongs to the gear - screw, in contrast to the helical gear, the worm rim has a concave shape, this contributes to the fitting of the worm and, accordingly, the length of the contact line, the worm thread can be single-threaded or multi-threaded, as well as right or left.
Worm-gear
Worms are distinguished by the following features: by the shape of the surface on which the thread is formed - cylindrical and globoid; in the shape of the thread profile - Archimedean and involute cylindrical worms. The Archimedes worm has a trapezoidal thread profile in the axial section, in the end section the threads are outlined by an Archimedean spiral.
Cylindrical and globoid views.
An involute worm is a helical gear with a small number of teeth and a large angle of their inclination. The profile of the turn in the end section is outlined by an involute.
Archimedean worms are most widely used in mechanical engineering, since the technology for their production is simple and the most developed.
The profile of the teeth of worm wheels in gears is involute. Therefore, the engagement in a worm gear is an involute engagement of a gearwheel with a toothed rack.
Planetary gear
The most common gear single-row planetary transmission. It consists of a central wheel 1 with external teeth, a stationary (central) wheel 2 with internal teeth and a carrier on which the axes of the planetary wheels (or satellites) are fixed.
Planetary gear
Wave gear transmissions.
Wave transmissions are based on the principle of transmission of rotational motion due to the traveling wave deformation of one of the gear wheels.
This transmission was patented by the American engineer Masser in 1959.
Wave gear transmission
Kinematically, these gears are a kind of planetary gear with one flexible gear. The figure shows the main elements of the wave transmission: a stationary wheel with internal teeth, a rotating elastic wheel with external teeth and a carrier h. The stationary wheel is fixed in the housing and is made in the form of a conventional gearwheel with internal gearing. The flexible gear wheel has the shape of a glass with an easily deformable thin wall: teeth are cut in the thickened part (left), the right part has the shape of a shaft. The carrier consists of an oval cam and a special bearing.
When the oval carrier rotates, two waves are formed. This transmission is called two-wave transmission. There are three-wave transmissions, below is a diagram of such a transmission.
involute helical gear
Wave transmissions have a large load capacity (there are a large number of pairs of teeth in engagement) and a high gear ratio (< 300 для одной ступени) при сравнительно малых габаритах. Это основные достоинства этих передач. Передача может работать, находясь в герметизированном корпусе, что очень важно для использования волновых передач в химической, авиационной и других отраслях техники.
Disadvantages of wave transmission: practically individual, expensive, very laborious manufacturing of a flexible wheel and a wave generator; the possibility of using these gears only at a relatively low angular speed of the generator shaft; limited revolutions of the drive shaft (to avoid large centrifugal forces of inertia of the non-circular wave generator; small tooth modules 1.5-2 mm)
Gears with Novikov engagement.
Gears with Novikov gearing consist of two cylindrical helical gears or bevel gears with helical teeth and are used to transfer torque between shafts with parallel or intersecting axes. The peculiarity of the Novikov engagement is that in this engagement the initial linear contact is replaced by a point contact, which turns under load into a contact with a good fit. The simplest tooth profiles that provide such contact are profiles outlined along an arc of a circle or a curve close to it.
Tooth profiles in gears with M. L. Novikov's gearing
In the Novikov gearing, the contact of the teeth is theoretically carried out at a point; in the involute gearing, the contact of the teeth occurs along the line. However, with the same overall dimensions transmission, the contact of the teeth in the Novikov gearing is much better than the contact in the involute gearing.
Unfortunately, in this case, one has to sacrifice the main advantage of involute engagement - rolling of the tooth profiles over each other and, accordingly, get high friction in the teeth. However, for slow-moving cars, this is not so important.
The advantages of Novikov gearing include the possibility of using it in all types of gears: with parallel, intersecting and crossing wheel axes, with external and internal gearing, constant and variable gear ratio. Friction losses in this gearing system are approximately 2 times less than those in involute gearing, which increases the transmission efficiency.
The main disadvantages of gears with Novikov gearing include: the technological laboriousness of wheel manufacturing, the width of the wheels must be at least 6 modules, etc. At present, gears with Novikov gearing are used in large gearboxes.
The vast majority of mechanical transmissions are based on gears. In other words, in a gear train, the force is transmitted due to the engagement of a pair of gears (gear pair). Gear drives are actively used, allowing you to change the speed of rotation, direction, moments.
The main task is to transform rotary motion, as well as change the arrangement of elements and a number of other functions that are necessary for the operation of units, assemblies and mechanisms. Next, we will look at the types of gears, their features, as well as the advantages and disadvantages of gears.
Read in this article
As already mentioned, gearing (gearing transmission) allows you to effectively implement the transmission of rotary motion that comes from the engine.
In parallel, the transformation of motion is carried out, the frequency of rotation, the magnitude, direction of the axes of rotation, etc. change. To accomplish such tasks, there are different types of transmissions. First of all, it is customary to classify them according to the peculiarities of the arrangement of the axes of rotation.
In the case when the gear is driving, and the gear ratio is greater than one, such a gear is a reduction, since the gear will rotate at a lower frequency than the gear. Also, at the same time, subject to a decrease in the angular velocity, an increase in the torque on the shaft occurs. In the case when the gear ratio is less than one, such a gear will be overdrive.
There is also a central wheel, as well as a carrier with satellites. These elements move around the circumference of the stationary wheel, due to which they rotate the central wheel. In this case, rotation is transferred from the carrier to the central wheel or vice versa.
Gears can be external or internal engagement. If everything is clear with the outer one (in this case, the gearing scheme assumes that the teeth are located on top), then with internal gearing, the teeth of the larger wheel are located on the inner surface. Also rotation is only possible in one direction.
Having considered above the main types of gearing (gears), it should be added that in this case, these types can be used in different combinations taking into account the peculiarities of certain kinematic schemes.
First of all, these teeth are cut with a simple rack and pinion tool. The specified engagement has a constant gear ratio, which does not depend in any way on the degree of displacement of the center-to-center distance. The only disadvantage of the engagement is that, during high power transmission, a small contact patch in the two convex tooth surfaces is affected. The result is surface destruction and other material defects.
We also add that circular gearing differs in that the convex gear teeth are meshed with the concave wheels. This makes it possible to significantly increase the contact patch, however, the friction force in these pairs also increases greatly.
Helical gears are best used if the rotational speed is very high. This decision allows you to achieve smoothness and noise reduction. The downside is considered to be a large load on the bearings, since axial forces arise.
Chevron wheels have a number of advantages inherent in helical pairs. First of all, they do not create additional load on the bearings by axial forces (forces are multidirectional).
Curved wheels are usually used when maximum gear ratios are required. Such wheels create less noise during operation, and also work more efficiently in bending.
As a rule, steel is the basis of the gear wheel. In this case, the gear must have greater strength, since the wheels themselves can have different characteristics in terms of strength.
For this reason, gears are made from different materials, and such products also undergo additional heat treatment and / or complex chemical and temperature treatment.
For example, gears that are made of alloy steel also undergo a surface hardening process that can be used to achieve the desired characteristics (nitriding, carburizing or cyanidizing). If carbon steel is used to make the gear, this material is surface hardened.
As for the teeth, surface strength is extremely important for them, and the core must be soft and tough. These characteristics allow avoiding fracture and rapid wear of the working loaded surface. We also add that the wheelsets of mechanisms, where there are no heavy loads and high rotational speed, are made of cast iron. You can also find bronze, brass and even all kinds of plastic as a material for the manufacture of wheelsets.
The gears themselves are made from a cast or stamped blank. Then the teeth cutting method is applied. Slicing is carried out by using the methods of copying, rolling. The running-in method makes it possible to produce teeth of different configurations using one tool (chisel, hob cutters, rack).
Finger cutters are required to perform ripping slicing. After cutting, heat treatment is performed. If high-precision gearing is required, grinding and running-in are additionally performed after such heat treatment.
First of all, among the advantages of the gear transmission are:
The disadvantages of the gear train are also distinguished:
Finally, we note that during maintenance, the mechanism must be inspected by checking the condition of gears, gears and teeth for damage, cracks, chips, etc.
The engagement itself and its quality are also checked (paint is often used, which is applied to the teeth). The application of paint allows you to study the size of the contact patch, as well as the location in relation to the height of the tooth. To adjust the gearing, spacers are used, which are placed in the bearing assemblies.
As you can see, the gear transmission is a fairly common solution that is used in various units, assemblies and mechanisms. Given the fact that there are several types of such transmissions, before using one or another type, in the design, designers take into account the kinematic and power characteristics of the operation of various mechanisms and assemblies.
Taking into account a number of features and loads, the type of gear transmission, its dimensions, and the degree of load are determined. After that, the selection of materials for the manufacture of gear pairs is carried out, as well as the methods of the necessary processing and cutting of teeth. The calculations separately take into account the gearing modulus, displacement values, the number of teeth of the gear and wheel, the distance between the axles, the width of the rims, etc.
In this case, the main conditions that determine the service life of the gear transmission and its resource are considered to be the general wear resistance of the surfaces of the teeth, as well as the bending strength of the teeth. In order to obtain the desired characteristics, special attention is paid to these features in the design of the production of gear mechanisms.
Read also
Hypoid gear in a car transmission device: what is a hypoid gear, what are its features and differences, as well as advantages and disadvantages.
Toothedtransmission. Generalintelligence
A gear transmission is a three-link mechanism in which two movable gear links form a rotational or translational pair with a fixed link. The gear link of the transmission can be a wheel, sector or rack. Gears are used to convert rotary motion or rotary motion into translational motion.
All terms, definitions and designations relating to gears used here and hereinafter correspond to GOST 16530-83 "Gears", GOST 16531-83 "Cylindrical gears" and GOST 19325-73 "Bevel gears".
The gearing is a higher kinematic pair, since the teeth theoretically touch each other along lines or points, with the smaller gear of the pair called a gear, and the larger gear. A sector of a spur gear of an infinitely large diameter is called a rack.
Gears can be classified in many ways, namely: by the arrangement of the axes of the shafts(with parallel, intersecting, crossing axes and coaxial); by working conditions(closed - working in an oil bath and open - running dry or periodically lubricated); by the number of steps(single-stage, multi-stage); by the mutual arrangement of the wheels(with external and internal gearing); by changing the frequency of rotation of the shafts(lowering, raising); by the shape of the surface, on which the teeth are cut (cylindrical, conical); peripheral speed wheels (low-speed at speeds up to 3 m / s, medium-speed at speeds up to 15 m / s, high-speed at speeds above 15 m / s); by the location of the teeth relative to the generatrix of the wheel (spur, helical, chevron, with curved teeth); according to the shape of the tooth profile(involute, circular, cycloidal).
In addition to the above, there are transmissions with flexible gears, called wave.
The main types of gears (Fig.) with parallel axes: a - cylindrical spur, b- cylindrical helical, v- chevron, G- with internal gearing; with intersecting axes: d- conical spur, e - tapered with tangential teeth, f - conical with curved teeth; with crossed axes: s- hypoid, and- screw; To- rack and pinion spur (hypoid and screw gears belong to the category of hyperboloid gears).
A gear train, the axes of which are located at an angle of 90 °, is called orthogonal.
The advantage of gears lies primarily in the fact that, with the same characteristics, they much more compact compared to other types of transmission. In addition, the gear drives have a higher efficiency (up to 0.99 in one stage), maintain a constant gear ratio, create a relatively small load on the shaft supports, have greater durability and reliability in wide power ranges (up to tens thousand kilowatts), peripheral speeds (up to 150 m / s) and gear ratios (up to several hundred).
Disadvantages of gears: the complexity of making precise gears, the possibility of noise and vibrations with insufficient precision in manufacturing and assembly, the impossibility of stepless regulation of the driven shaft rotation frequency.
Gear drives are the most common types of mechanical transmissions and are widely used in all branches of mechanical engineering, in particular in metal-cutting machines, automobiles, tractors, agricultural machines, etc .; in instrument making, watch industry, etc. The annual production of gear wheels in our country is estimated at hundreds of millions of pieces, and their overall dimensions are from fractions of a millimeter to ten or more meters. Such wide use gears necessitates a great deal of research and development work on the design and manufacturing of gears and comprehensive standardization in this area. Currently, the terms, definitions, designations, elements of gears and gearings, the main parameters of the gears, the calculation of geometry, the calculation of cylindrical involute gears for strength, the tool for cutting teeth, and much more are standardized.
The main kinematic characteristic of any gear transmission is the gear ratio, defined by the standard as the ratio of the number of teeth of a wheel to the number of teeth of a gear and designated and, hence,
The definition of the gear ratio remains the same as for other mechanical transmissions, i.e.
Energy losses in gear drives depend on the type of transmission, the accuracy of its manufacture, lubrication and is the sum of friction losses in the gearing, in the shaft bearings and (for closed gears) losses due to mixing and oil splashing. The lost mechanical energy is converted into thermal energy, which in some cases makes it necessary to calculate the thermal transfer.
Losses in engagement are characterized by a coefficient, losses in one pair of bearings - by a coefficient and losses due to mixing and oil splashing - by a coefficient. Total efficiency of one-stage closed transmission
Approximately = 0.96 ... 0.98 (closed gears), = 0.95 ... 0.96 (open gears), = 0.99 ... 0.995 (rolling bearings), = 0.96 .. .0.98 (sleeve bearings), = 0.98 ... 0.99.
The surfaces of interacting teeth of the wheels that provide a given gear ratio are called conjugate. The process of transmitting motion in a kinematic pair formed by gear wheels is called gearing.
Cylindricalspur-toothedbroadcast
In fig. depicts a cylindrical wheel with straight teeth. The part of the gear that contains all the teeth is called the rim; the part of the wheel that fits onto the shaft is called the hub. Pitch circle diameter d divides the tooth into two parts - the tooth head is high h a and the leg of the tooth in height h f , tooth height h = h a + h f . The distance between similar profiles of adjacent teeth, measured along the pitch circle arc, is called the circumferential pitch of the teeth and is denoted R. Tooth pitch is made up of the circumferential thickness of the tooth s and the width of the cavity e. The chord length corresponding to the circumferential thickness of the tooth is called the chord thickness and is denoted. A linear value that is one times smaller than the circumferential pitch is called the circumferential pitch module of the teeth, denoted T and is measured in millimeters (henceforth we will omit the words "circumferential pitch" in terms)
Tooth modulus is the main parameter of the gear wheel. For a pair of meshed wheels, the module must be the same. Tooth modules for cylindrical and bevel gears are regulated by GOST 9563-60 *. The values of standard modules from 1 to 14 mm are given in table.
Modules, mm
1st row 1; 1.25; 1.5; 2; 2.5; 3; 4; 5; 6; eight; ten; 12
2nd row 1.125; 1.375; 1.75; 2.25; 2.75; 3.5; 4.5; 5.5; 7; nine; eleven; fourteen
Note... When assigning modules, the 1st row should be preferred to the 2nd.
All basic parameters of gears are expressed in terms of modules, namely: tooth pitch
pitch circle diameter
The last formula allows you to determine the modulus as the number of millimeters of the pitch circle diameter per one tooth of the wheel.
According to the standard reference contour for spur gears, tooth head height h a = t, tooth pedicle height h f = 1.25t. Height of teeth of cylindrical wheels
h = h a + h f = 2,25m.
Tooth tip diameter
d a = m(z + 2),
cavity diameter
d f = m(z – 2,5).
The distance between the ends of the teeth of the wheel is called the width of the rim. The contact of a pair of spur gear teeth theoretically occurs along a line parallel to the axis; the length of the contact line is equal to the width of the crown. During the operation of the transmission, a pair of teeth engages immediately along the entire length of the contact line (which is accompanied by the impact of the teeth), after which this line moves along the height of the tooth, remaining parallel to the axis.
Center distance of cylindrical gear with external and internal gearing
called the pitch center distance (minus sign for internal gearing). If the center distance differs from the pitch, then it is denoted a w .
GOST 1643-81 for tolerances for spur gears and gears are established twelve degrees of accuracy, indicated by numbers (the first degree is the highest). For each degree of accuracy, norms have been established: kinematic accuracy, smoothness of operation and contact of teeth of wheels and gears.
In the process of manufacturing gears, errors in the pitch, thickness and profile of the teeth are inevitable, radial runout of the rim, fluctuation of the center distance with a clearance-free engagement of the controlled and measuring wheels, etc. All this creates a kinematic error in the angles of rotation of the driven wheel, expressed by a linear quantity, measured along the arc of the pitch circle. The kinematic error is defined as the difference between the actual and calculated angle of rotation of the driven wheel. The norms of kinematic accuracy regulate the tolerances for the kinematic error and its components for a full revolution of the wheel. Smoothness standards establish tolerances for the cyclic (repeated many times in one revolution) kinematic error of the wheel and its components. The contact rates establish the dimensions of the total contact spot of the gear teeth (as a percentage of the teeth dimensions) and the tolerances for the parameters affecting this contact.
In mechanical engineering, general-purpose gears are manufactured according to the 6-9th degrees of accuracy. Cylindrical spur gears of the 6th degree of accuracy are used at circumferential wheel speeds up to 15 m / s; 1st degree - up to 10 m / s; 8th degree - up to 6 m / s; 9th - up to 2 m / s.
Consider the forces acting in the engagement of a spur gear transmission. With the contact shown in this figure, a pair of teeth in a pole NS sliding (hence, friction) is absent, the engagement will be single-pair and the force interaction of the wheels will consist in transmission along the pressure line (normal NN) forces of normal pressure . We expand this force into two mutually perpendicular components and , called, respectively, circumferential and radial forces, then
, ,
where is the engagement angle.
If the transmitted torque is known T and diameter d pitch circle, then
(since = 20 °, then ).
Force , causes rotation of the driven wheel and bends the wheel shaft in the horizontal plane, the force G bends the shaft in a vertical plane.
Cylindricaltransmissionwithoblique andchevronteeth
Helical gears are called wheels in which the theoretical pitch line of the tooth is part of a helical line of constant pitch (the theoretical pitch line is the line of intersection of the lateral surface of the tooth with the pitch cylindrical surface). The tooth line of helical gears may have right and left the direction of the helix. The angle of inclination of the tooth line is indicated.
The parallel-axis helical gear has opposite direction of teeth drive and driven wheels and belongs to the category of cylindrical gears, since the initial surfaces of such gears are the lateral surface of the cylinders. A gear with helical gears, the axes of which are crossed, has the same direction of the teeth of both wheels and is called a helical gear, which belongs to the category of hyperboloid gears, since the initial surfaces of such gears are parts of a single-sheet hyperboloid of revolution; the dividing surfaces of these wheels are cylindrical.
In helical gears, the contact lines are inclined with respect to the tooth line, therefore, unlike straight ones, the helical teeth do not engage immediately along the entire length, but gradually, which ensures smooth engagement and a significant reduction in dynamic loads and noise during transmission operation. Therefore, helical gears, in comparison with spur gears, allow significantly higher limiting peripheral speeds of the wheels. So, for example, helical gears of the 6th degree of accuracy are used at a peripheral speed of up to 30 m / s; 7th degree - up to 15 m / s; 8th degree - up to 10 m / s; 9th - up to 4 m / s.
Normal pressure force in the engagement of helical wheels can be decomposed into three mutually perpendicular components (Figure 7.10, b): circumferential force, radial force and axial force , equal:
where T- transmitted torque; - the angle of engagement.
The presence of axial force is a significant disadvantage of helical gears. In order to avoid large axial forces in the helical gear, the angle of inclination of the tooth line is limited to the values = 8 ... 20 °, despite the fact that with an increase the strength of the teeth increases, the smooth operation of the gear, and its load capacity.
In modern gears, helical gears are predominantly used.
A cylindrical gear wheel, the crown of which in width consists of sections with right and left teeth, is called chevron. The part of the crown with teeth of the same direction is called a half-chevron. For technological reasons, chevron wheels are made of two types: with a track in the middle of the wheel (a) and no track (b). In the chevron wheel, axial forces on half-chevrons, directed in opposite directions, are mutually balanced inside the wheel and are not transmitted to the shafts and shaft bearings. Therefore, for chevron wheels, the angle of inclination of the teeth is taken in the range = 25 ... 40 °, as a result of which the strength of the teeth, the smooth operation of the transmission and its load capacity increase. Therefore, chevron wheels are used in powerful high-speed enclosed gears. The disadvantage of chevron wheels is their high labor intensity and production cost.
Geometric, kinematic and strength calculations of the chevron and helical gears are similar.
Materials (edit)cylindrical wheels
Materials for the manufacture of gears in mechanical engineering - steel, cast iron and plastic; in instrument making gears are also made of brass, aluminum alloys, etc. The choice of material is determined by the purpose of the gear, its operating conditions, wheel dimensions and even the type of production (single, serial or mass production) and technological considerations.
The general modern trend in mechanical engineering is the desire to reduce the material consumption of structures, increase the power, speed and durability of the machine. These requirements lead to the need to reduce weight, dimensions and increase the load capacity of power gears. Therefore, the main materials for the manufacture of gears are heat-treated carbon and alloy steels, which provide high volumetric strength of teeth, as well as high hardness and wear resistance of their active surfaces.
Criteriaoperability of gearwheelsand
Under the action of normal pressure and friction forces, the wheel tooth experiences a complex stress state, but two factors have a decisive influence on its performance: contact stresses and bending stresses , which act on the tooth only while it is in engagement and are thus re-variables.
Repeatedly alternating bending stresses cause fatigue cracks in the stretched fibers of the tooth base (the place of stress concentration), which over time lead to it breakdown(rice. a, b).
Repeatedly alternating contact stresses and frictional forces lead to fatigue wear of the active tooth surfaces. Since the resistance to fatigue wear of the leading surfaces is higher than that of the lagging ones, then the load capacity of the tooth heads is higher than that of the legs. This explains the flaking and chipping of material particles on the active surface of the teeth legs (Fig. v) in the absence of visible fatigue damage to the heads. Fatigue wear of the active surfaces of the teeth is characteristic for the operation of closed gears.
In open gears and gears with poor (contaminated) lubrication, fatigue wear is preceded by abrasive wear of the active surfaces of the teeth (Fig. D).
In heavily loaded and high-speed gears, a high temperature occurs in the contact zone of the teeth, which contributes to the rupture of the oil film and the formation of metal contact, as a result of which the teeth become seized (Fig. e), about threaded connections Threaded connection is called a connection ... thread pitch, like the pitch of the teeth toothed wheels, we will denote by a lowercase letter ..., persistent, rectangular) are used for transmission movements and are applied in gears screw - nut that will ...
... toothed gears 1.1 General intelligence V toothed transmission the movement is transmitted by the engagement of the pair toothed wheels (Fig. 1, a - c). Less toothed... oils. 2 CYLINDRICAL OBJECT TRANSFERS 1.1 General intelligence Cylindrical wheels with ...
Interference (press connections) General intelligence The connection of two parts .... Therefore, below are brief intelligence about contact voltages and ... losses inherent in both toothed transmission and transmission screw nut. General K.P.D. worm transmissionη, (5.25) ...
And the axes. General intelligence Shaft is a part of machines intended for transmission torque along ... parts rotating with them ( toothed wheels, pulleys, sprockets, etc. shafts may interfere with normal operation toothed wheels and bearings, therefore ...
Gear drives are widely used both in industrial units and in household appliances... They act as an intermediate link between the source of rotational-translational motion and the unit that acts as the final consumer of this energy. Moreover, the transmitted power can be calculated both in negligible units (clock mechanisms and measuring instruments), and by enormous efforts (turbines of power plants).
The engine that generates energy and the final unit that consumes it often differ in such characteristics as rotation speed, power, force angle. In addition, one source of rotational energy can be used to drive several different units or assemblies at once. To ensure the delivery of torque in such conditions, intermediate modules are needed that would transmit this force with minimal losses.
If, as a result of such a distribution or transformation, the revolutions of the drive shaft become greater than that of the driven shaft, then it is customary to talk about a reduction gear. In this case, the loss of speed is compensated by an increase in the load on the driven axle and an increase in the power of the consuming unit. In the event that an increase in the number of revolutions is ultimately observed, such a gear will be overdrive. Accordingly, this will be accompanied by a decrease in the force on the driven shaft.
Belt transmission assumes the presence of an intermediate link between the pulleys on the connected shafts - a flexible belt. The gear mechanism differs from such a connection by the presence of engagement teeth on the surface of the mating parts. They are identical in profile and size.
The tooth head of the wheel engages with a groove on the gear that follows its profile. When the drive shaft rotates, the slave turns in the opposite direction. Between them, the design provides the smallest possible gap, which provides sliding, thermal expansion and lubrication to prevent jamming. In this case, the leading part of the paired mechanism is called a wheel, and the driven part is called a gear.
In a belt drive, the plane of engagement of the belt with the pulley is at least one third of the circumference. In the gear mechanism, one pair of teeth is in constant contact between the drive wheel and the driven gear under load. Wheels and gears on shafts are usually keyed.
Gear drives are widespread. They are durable and reliable, subject to permissible load levels and the proper level of maintenance. The small-sized mechanism provides a high efficiency and can be used for a wide range of speed changes.
The presence of the teeth of the engagement makes it possible to achieve constancy of the gear ratios between the mating shafts due to the absence of the possibility of their slipping. In this case, the loads on the shafts do not exceed the permissible limits.
Gear drives also have a number of features that can be attributed to their disadvantages. In terms of operation, such a mechanism makes noise at high rotational speed. It cannot react flexibly to changing loads, since it is a rigid structure with precise adjustment.
In technological terms, it is the complexity of the manufacture of pairs of engagement wheels. This type of transmission requires increased accuracy, since the teeth are in mesh with a constantly changing stress. In such conditions, fatigue damage to the material is possible.
This happens when the permissible loads are exceeded. Teeth can be chipped, partially or completely broken. Broken-off fragments fall into the mechanism, damage the adjacent mating sections, which leads to jamming and failure of the entire unit.
The most widespread is a cylindrical gear transmission. It is used in assemblies and mechanisms with parallel shaft arrangement. According to their design features, teeth with a straight, oblique and chevron profile are distinguished.
For intersecting shafts, a worm, helical cylindrical transmission is used, and for intersecting shafts, a bevel gear is used. The rack and pinion transmission differs in that the gear in the common paired mechanism is replaced by the working plane. At the same time, teeth are cut on it, identical in the profile of the wheel. As a result, the rotary motion is converted into translational motion.
The gears are also divided according to the speed of rotation: low-speed, medium and high-speed. According to their purpose, they are divided into power and kinematic (not transmitting significant power). In addition, gears can be classified according to the size of the gear ratio, the mobility of the axles (ordinary and planetary), the number of degrees, the accuracy of the engagement (12 classes), and the manufacturing method. The shape of the tooth profile can be involute, cycloidal, pinned, circular.
All kinds of gears are widely used in various industries. The annual production of various wheelsets is in the millions. The scope of their application is so extensive that a rare device, mechanism or unit that uses rotary motion in its work does not include one or another type of gear movable connection.
A spur gear train is used to convert rotary motion with a decreasing or increasing factor. Examples: internal combustion engines, gearboxes in rolling stock, machine tools, drilling, metallurgy, mining and all types of industries.
Bevel gear is used to a lesser extent due to the complexity of the wheelset manufacturing process. It is used in complex and combined mechanisms, where there is a rotary motion with variable angles and changing loads. Bevel gears are commonly used in special gearboxes. Examples: drive axles of cars, agricultural machinery, locomotives, wheelsets of conveyors, drives of various industrial equipment.
They are most widely used, since the technology for manufacturing wheelsets is relatively simple and proven. A spur gear train is used to transmit torque between parallel shafts. They differ in the shape of the teeth: straight, oblique and chevron. In rare cases, when shafts cross and light loads, a screw profile is used.
Straight teeth are the most used. They are used to transmit torque with low or medium load, as well as in cases where there is a need to shift the wheels during operation along the shaft axis. Oblique teeth are used for smooth running. They are used for critical mechanisms and at increased loads. The chevron profile (two rows of oblique teeth along the edges, located in the shape of a herringbone) is distinguished by a high balance of axial displacement forces, which are a disadvantage of helical wheelsets.
Spur gears can be open and closed type... In the latter case, the teeth of one of the wheels are located not on the outer, but on the inner surface of the circle.
In conditions where the torque from the source to the consuming unit needs to be delivered with an angular displacement, intersecting shafts are used. Their axes are most often at an angle of 90 degrees. In such cases, a bevel gear is usually used.
It is called so because of design features pairs of gears. They have the shape of a cut cone and mate with their side planes, on which the teeth are cut. Along the profile, they are higher at the base and decrease towards the top.
The ring gear can have a straight, tangential or curvilinear cut. If along the profile it is made in the form of a helical spiral, and the shafts, in addition to the intersection, also have axial displacement, then such a bevel gear is called hypoid. It has a smooth running and low noise level, but has an increased tendency to seize, so special lubricants are used for it.
In comparison with cylindrical gears, bevel gears can provide only 85% of their bearing capacity. In terms of manufacturing and assembly technology, they are the most complex. However, the ability to transmit torque with angular displacement makes them indispensable in complex assemblies and mechanisms.
When it is necessary to convert rotary motion into translational motion or vice versa, one of the wheels is replaced by a plane with serrated teeth. Rack and pinion transmission are distinguished by simplicity of manufacture and installation, reliability and good load characteristics. Used in machine tools and drives where it is used translational motion: slotting machines, variable feed conveyors.
The toothed belt drive is a hybrid model that incorporates the positive qualities of both types. Differs in the constancy of the gear ratio due to the absence of slippage. Quiet operation at high speeds and loads is achieved by using flexible core belts. Often used in electric motor drives.
On the paired pulleys of the unit assembly and on the elastic belt that binds them, there are teeth that are identical in profile. The transmission does not work on the principle of friction, but an engagement mechanism is used. At the same time, on the one hand, there is no need for strong tension between the pulleys and fine adjustment, on the other hand, there is no need for lubrication between mating metal parts.
Gears must have robustness in a robot at different speeds and loads, strength of teeth, their durability and the ability to resist galling. Steel is the main material for wheelsets. It can be heat treated or contain alloying additives and impurities. As a material for low-speed mechanisms with large dimensions and open type construction, cast iron may protrude.
To prevent jamming, paired wheels are made of materials of different strength. If high carbon steel is used for the wheel and gear, then different degrees of heat treatment are used. Bronze, brass, caprolon, textolite, plastics and formaldehydes are also used.
Billets for gear wheelsets can be made by casting or stamping. In the future, they are subjected to additional processing, and the teeth are cut. Disc and finger cutters, shaped grinding wheels are used for this.
The bevel-type gear mechanism cannot be manufactured by finishing cutting with a milling cutter or grinding, since the profile of the protrusions and valleys is not constant. This can only be done at the initial stage of roughing. Further refinement is carried out on machines in the process of running in with gearing. For this, a twin wheel made of high-strength material is used, which repeats the main profile. It acts as a cutting tool.
Carbon steels are hardened, carburized, nitrided or cyanidized. For irrelevant units, heat treatment can be carried out after cutting the teeth. High precision wheelsets require additional finishing grinding or running-in.
During normal operation, the gear mechanism runs smoothly, and the process is accompanied by a monotonous moderate noise. The presence of extraneous sounds and uneven rotation indicate wear of the engaging surfaces or a violation of the adjustment.
During the Maintenance when inspecting, check for cracks, tooth breakage or chipping. Particular attention is paid to the correct engagement of the wheelsets and the absence of clearances. During operation, check the end runout and control the friction surfaces.
Correct engagement is determined by applying paint to the gear teeth. Until it has dried, the shafts are turned several times and the contact points of the working surfaces are inspected. The shape of the print (it should be in the form of an ellipse) determines the overall state of the transmission.
Pay attention to the touch points. They should be approximately in the middle of the tooth height. A spot of paint should occupy 70 - 80% of its length. Adjustment is mainly limited to increasing or decreasing the thickness of the spacers under the bearings.
Depending on the type of unit, lubrication of the open mechanism can be carried out periodically by hand with a plastic material. For closed structures, it is carried out forcibly by spraying or dipping a part of the impeller crown into a grease bath.
To characterize the gearing mechanism, the diameters of the pitch and main circle, the center distance and the possible displacement of the shafts are determined. The relationship between the number of teeth of the driving and driven wheels determines the gear ratio. Based on the initial data, it allows you to calculate the revolutions for a pair of engagement.
A gear wheel is initially characterized by the number of teeth and modulus. It is standardized and displays the pitch circle per tooth. Determine the diameters of the protrusions and depressions. Calculate the total length, height and thickness of the tooth, as well as its individual parts - the head and legs.
The pitch diameter is calculated. The ratio of the width of the ring gear is used. In the case of bevel teeth, they are determined with their angle of inclination. It should be borne in mind that it is different in bevel and cylindrical gears.
In addition to the above, the profile angle, the coefficient of end overlap and displacement, the line of engagement are also used. For worm gears, the number of turns, the diameter and type of the worm are calculated.
Before designing, you should study the initial data and determine the conditions for the planned operation of the mechanism. The original contour, the type and type of transmission, its location in the node are taken into account, permissible loads, material for wheelsets and their heat treatment. At this stage, the speed of rotation of the shafts and their diameters, torque, gear ratio are taken into account.
To calculate the gear train, you need to determine the overall gearing modulus, the number of teeth for the gear and wheel, their profile, angle of inclination and location. The center distance is determined, the width of the gear rims of the pair is selected.
The geometric parameters of the machine gearing are calculated, for which the gear transmission is designed. The drawing must display at least two projections: frontal and side views from the left with the applied measurements. Additionally, a table of the main geometric and design parameters is compiled, graphs are built.
The values are calculated using formulas, tables, coefficients and ratios are used, while the original data of the wheel and gear are used. The calculation algorithm for individual transmissions can contain up to fifty or more steps and logical stages. The optimal solution to the issue of detailed design is the use of a specialized computer program.
The dimensions of the grooves for keys or splines are selected according to standards. In general terms, a drawing for mounting wheels on shafts is developed separately.
Are the gears normalized? GOST, currently in force, defines the permissible deviations for finished wheelsets. The accuracy of the workpieces is set depending on technological features and can be adjusted for each industry or manufacturer separately.
For each type of gear, there are standards of interchangeability. Some standards have lost their relevance altogether, some are valid only in certain regions. However, the norms developed earlier are used for general terminology, designations, the procedure for developing documentation and building drawings.
GOSTs regulate the parameters for calculating the geometry of gear wheelsets, their modules, initial contours, degrees of accuracy and types of mates. Other regulations set standards for individual elements of parts, and still others - for ready-made components and assemblies.
