Lab #14
Determination of gear ratios of gears
Goal of the work– study different kinds gears, learn to determine the type and type of gears, their gear ratios and gear ratios.
Gear
Gear - a three-link mechanism in which two moving links are gears that form a rotational or translational pair with a fixed link (Fig. 1).
Fig.1. External Gear
Paired gear - gear wheel of a transmission, considered in relation to another gear wheel of this transmission. Gear wheel 2 (Fig. 1) is paired with wheel 1, gear wheel 1 is paired with wheel 2.
Gear - a transmission gear with a smaller number of teeth.
Wheel - a transmission gear with a large number of teeth.
gear ratio gear train is the ratio of the angular velocity of the driving gear to the angular velocity of the driven gear .
Drive gear - a transmission gear that communicates movement to a paired gear.
driven gear - a transmission gear driven by a paired gear.
gear ratio(sometimes the notation) is determined with drive wheel 1, gear ratiodetermined if wheel 2 is leading:
Fig.2. Types of gears: external (left) and internal
Gear ratio gear ratio is the ratio of the number of teeth on the driven gear to the number of teeth on the drive gear. The gear ratio of the gear train is determined by the formula:
where and - the number of teeth of wheels 1 and 2, respectively.
The “+” sign is taken for external gearing (Fig. 1 and Fig. 2), the “-” sign for internal gearing. Types of engagements are shown in Fig.2. Signs are taken into account only for gears with parallel axes of rotation of the wheels.
Gear types
spur gear (shown in Fig. 3, its kinematic diagram - in Fig. 1) - gear train with parallel axes, y gear wheels which axoid, initial and dividing surfaces are cylindrical. In these gears, the relative location of the axes of rotation of the wheels is determined only by the center distance.
Axoid surface of the gear - each of the surfaces described by the instantaneous axis of relative motion of the transmission gears, related to this gear. In cylindrical and bevel gears, the initial surfaces coincide with the axoid ones.
bevel gear (shown in Fig.3) - a gear train with intersecting axes, the gears of which have axoid, initial and dividing surfaces that are conical. In these gears, the relative location of the axes of rotation of the wheels is determined only by the angle between the axles.
Orthogonal gear train (shown in Fig.3) - bevel gear, the angle between the axes of which is 90 °.
non-orthogonal gearing - bevel gear, the angle between the axes of which is different from 90 °.
Fig.3. Gear types (left), bevel (center), helical gear
Crossed gears wheel rotation(fig.3) - a gear train in which the relative location of the axes of rotation of the wheels is determined by the center distance and the angle between the axles. There are many variants of such mechanisms. Figure 3 shows a helical gear, the angle between the axes of which is 90 ° . Another transmission option with an angle between the axes of 90 ° - worm gear (Fig. 4). The worm gear is called worm (pos.1 in Fig.4) , and the wheel worm wheel (pos.2 in Fig.4) . The second gear, shown in Figure 4, is called hyperboloid. The axoids of its gears are single-sheeted hyperboloids of revolution.
For bevel and cross-axle gears gear ratio determined by the same formulas as for cylindrical gears, but without signs.
Fig.4. Worm gear (left) and hyperboloid gear train
Types of gears
Fig.5. Types of gears: cylindrical helical (left), chevron (center),
conical spur
Depending on the type of teeth, the gear wheels of cylindrical gears are divided into spur gears (Fig. 3 on the left), helical and chevron gears (Fig. 5). gear wheels bevel gears- on spur (Fig. 5), tangential, with a circular tooth (Fig. 3 in the center), with a curved tooth.
Depending on the profile of the teeth, the gears and gears are divided into involute (Fig. 2, Fig. 6), cycloidal, Novikov spur gears (Fig. 6), the tooth profiles of which contact along the arc of a circle.
Fig.6. Types of gears: with an involute tooth profile (left),
Novikov transmission gears
MULTI-STAGE GEARS
Gears with fixed axes of wheel rotation
Fig.7. Two-stage gear transmission and its kinematic scheme
The simplest gear mechanism (Fig. 1) consists of two gears driving and driven, which are both input and output, respectively. To obtain the necessary gear ratios in machines and devices, complex gear mechanisms are often used, which, in addition to the input and output wheels, have several intermediate wheels, each of which rotates around its own axes. The use of complex mechanisms is explained by various reasons. For example, the axes of the input and output wheels are far apart. In this case, the direct transmission of rotation using two wheels would require the creation of a transmission with large dimensions. In another case, the gear ratio can be very large or very small, then it is convenient to have intermediate wheels with their own axles between the input and output wheels. By transferring rotation from the input wheel to the intermediate wheels and from them to the output wheel, we are, as it were, sequentially separate steps we change the rotation speed of the links, resulting in the required gear ratios between the input and output wheels.
Thus, the complex transmission mechanism can be divided into separate parts − steps, each of which is two wheels forming a gearing. In accordance with the above, there are single- and multi-stage transmissions, for the most part two- and three-stage (Fig. 7). The number of steps is equal to the number of gears formed by the gears of the mechanism. One wheel can be included in several steps (Fig. 8). Any stage can be cylindrical, conical, worm, globoid, etc. transmission. Figure 8 shows a multi-stage mechanism containing cylindrical and conical stages.
Fig.8. Multi-stage gear
Overall gear ratio (ratio) of the gear train with a series connection of steps is equal to the product of the gear ratios of the steps included in them. For transmission in Fig.7:
planetary gears
In some multi-stage gears, the axles of the individual wheels are movable. Such gear mechanisms with one degree of freedom are called planetary gears (Fig. 9), and with two or more degrees of freedom - differential mechanisms or simply differentials. In these mechanisms wheels with movable axes of rotation are called satellites (link 2 in Fig. 9), and link in which satellites are installed - carrier. In the diagrams, the carrier is usually denoted by the letter H. Gears whose axes coincide with the axis of rotation of the carrier are called central(links 1 and 4 in Fig. 9) . Satellites are single-crown (left figure) and multi-crown.
The gear ratio of the planetary mechanism is determined by the formula:
Where - gear ratios of steps (including signs) with the carrier stopped.
Figure 10 shows the formulas for determining the gear ratios of planetary mechanisms. The gear ratios between the movable central wheel and the carrier are related by the ratio:
Fig.10. Determination of gear ratios of planetary mechanisms
When choosing the number of teeth of the wheels of planetary gears, the following conditions are checked for them:
1. Alignment condition, ensuring the coincidence of the axes of the central gears and carrier: (fig.10). The conditions shown in Fig. 10 are obtained for planetary gears, the gears of which have the same module.
2. Neighbor condition, providing joint placement of several satellites along a common circumference in the same plane, without contact of the tops of the teeth of adjacent satellites:
Where - maximum number teeth of the gear rim of the satellite, k - number of satellites
The neighborhood condition was obtained for planetary gears, in which the satellites are located evenly around the circumference of the carrier.
3. Build condition transmission gears, which determines the possibility of assembling the transmission when using several satellites:
Where P- number of full turns of carrier 0,1,2,3..., C- integer 1,2,3, ...
Equipment
Models of cylindrical, bevel, worm, multi-stage and planetary gear mechanisms.
Work order
1. Get the assignment and laboratory layouts from the teacher.
Each student must determine the gear ratio and gear ratio of five gears:
1) spur gear;
2) bevel gear;
3) gear transmission with crossed axes;
4) multi-stage transmission with fixed wheel axles;
5) planetary gear.
2. For each transmission:
2.1. Draw a kinematic diagram.
2.2. Give the full name of the gear (determine its type and type). For example, the mechanism shown in Figure 7 is called cylindrical helical involute gearing.
2.3. Determine the mobility of the transmission using the Malyshev formula for flat mechanisms.
2.4. Empirically determine the gear ratio of the gear. To do this, calculate the number of revolutions of the driving wheel corresponding to the whole number of revolutions of the driven wheel.
2.6. For a planetary gear, check that the conditions for alignment, proximity and assembly are met.
2.7. Compose a complex gear by connecting in series three of the considered gears. Draw its kinematic diagram and determine the total gear ratio.
2.8. Record all results in a lab report.
Control questions
1. List the links included in the simplest gear mechanisms.
2. List the links included in complex gear mechanisms.
3. The purpose of using multi-stage gears.
4. List the main types of gears.
5. Write a formula for determining the gear ratio of a multi-stage gear.
6. Write a formula for determining the gear ratio of a single-stage gear.
7. What are the advantages and disadvantages of spur and helical gears?
8. What is the difference between a planetary gear and a non-planetary gear?
9. Why install several satellites in the planetary gear?
10. How to determine the gear ratio of a planetary gear?
11. What conditions are checked for the planetary gear? What is their meaning?
12. When are gear ratio signs of gear stages taken into account?
Types of gears
Gears are a type mechanical gears operating on the principle of engagement. They are used to transmit and convert rotational motion between shafts.
Gears are characterized by high efficiency (for one stage - 0.97-0.99 and higher), reliability and long service life, compactness, stability of the gear ratio due to the absence of slippage. Gears are used in a wide range of speeds (up to 200 m/s), power (up to 300 MW). The dimensions of the gears can be from fractions of a millimeter to several meters.
The disadvantages include the relatively high complexity of manufacturing, the need for cutting teeth with high accuracy, noise and vibration at high speeds, high rigidity, which does not allow compensating for dynamic loads.
Gear ratios in gear drives can reach 8, in open transfers- up to 20, in gearboxes - up to 4.
According to the arrangement of the teeth, gears with external and internal gearing are distinguished.
Structurally, gear transmissions are mostly closed in a common rigid housing, which ensures high precision assemblies. Only slow gears (v< 3 м/сек) с колесами значительных размеров, нередко встроенных в конструкцию машин (например, в механизмах поворота подъемных кранов, станков), изготавливаются в открытом исполнении.
Most often, gears are used as retarders (reducers), i.e. to reduce the speed and increase the torque, but also successfully used to increase the speed of rotation (multipliers).
Lubrication is used to protect the working surfaces of the teeth from seizing and abrasive wear, as well as to reduce friction losses and the associated heating. Enclosed gears are usually lubricated with liquid mineral oils, wheel dipping, or forced oil supply to the meshing teeth. Open gears are lubricated with grease periodically applied to the teeth.
about the location of the teeth, gears are distinguished with external (Fig. 2.1a - c) and internal gearing (Fig. 2.1d).
According to the profile of the teeth of the gears, the gears are divided into: gears with involute gearing, in which the tooth profiles are outlined
involutes; on transmissions from cycloidal profile; on transmissions from Novikov's link. Further in the manual, only involute profile gears with external gearing will be described.
A gear is a transmission gear with a smaller number of teeth (most often a drive gear). A wheel is a transmission gear with a large number of teeth. The term "gear wheel" can be applied to both the pinion and the gear wheel.
Cylindrical gears are straight,
helical and chevron.
Spur wheels(fig. 2.1a) are used mainly at low and medium circumferential speeds, with high tooth hardness (when dynamic loads from manufacturing inaccuracies are small compared to useful ones), in planetary gears, in open gears, and also if axial movement of the wheels is necessary (in gearboxes).
worm gears
A worm gear (or screw) can be thought of as a single tooth gear
Worm gears have some special properties that make them different from other gears. First, they can achieve very high gears in a single movement. Because most worm gears has only one loaded tooth, the gear ratio is simply the number of teeth per gear connection. For example, a worm gear pair paired with a 40-
toothy helical gearbox has a ratio of 40:1. Second, worm gears have much higher friction (and lower efficiency) than other types of gears. This is because the tooth profile of the worm gears is constantly sliding over the teeth of the mating gears. This friction gets higher, the greater the load on the transmission. Finally, a worm gear cannot work backwards. In the animation below, the worm gears on the green axle are driven by the blue gears on the red axle. But if you turn on the red axle as the leading one, then the worm gears will not work. This transmission property can be used to stop - block things in a certain place, without rolling back, for example, a garage door.
LINEAR GEARS
It is a means of converting rotational motion from an axis of rotation or gear into translational motion. gear rack. The gear rotates and pushes the rack forward as the gear teeth move in it. It is regulated, for example, by a smaller number of teeth on the drive gear and more on the rack. the movement in the racks will be proportional to the number of teeth on the gear
DIFFERENTIAL GEAR
A differential is a mechanical device that transmits torque from one source to two independent consumers in such a way that the angular speeds of rotation of the source and both consumers can be different relative to each other. Such transmission of torque is possible due to the use of the so-called planetary mechanism. In the automotive industry, the differential is one of the key parts of the transmission. First of all, it serves to transmit torque from the gearbox to the wheels of the drive axle.
Why does this require a differential? In any turn, the path of a wheel on an axle moving along a short (inner) radius is less than the path of another wheel on the same axle traveling along a long (outer) radius. As a result, the angular velocity
rotation of the inner wheel must be less than the angular velocity of rotation of the outer wheel. In the case of a non-driving axle, this condition is quite simple to fulfill, since both wheels may not be connected to each other and rotate independently. But if the axle is driving, then it is necessary to transmit torque to both wheels simultaneously (if you transmit torque to only one wheel, then the ability to drive the car by modern concepts will be very bad). With a rigid connection of the wheels of the drive axle
and the transfer of torque to a single axis of both wheels, the car could not turn normally, since the wheels, having equal angular velocity, would tend to go the same way in the turn. The differential solves this problem: it transmits torque
moment on separate axles of both wheels (half shafts) through its planetary mechanism with any ratio angular velocities half shaft rotation. As a result, the vehicle can move and steer normally both in a straight line and in a turn.
Technical.machine.docx
1. Types of gears.Spur wheels- the most common type of gears. The teeth are a continuation of the radii, and the contact line of the teeth of both gears is parallel to the axis of rotation. In this case, the axes of both gears must also be strictly parallel.
helical gears are an improved version of straight teeth. Their teeth are located at an angle to the axis of rotation, and form part of a spiral in shape. The engagement of such wheels is smoother than that of spur gears, and with less noise.
During the operation of the helical gear, a mechanical moment arises along the axis, which necessitates the use of thrust bearings to install the shaft;
An increase in the friction area of the teeth (which causes additional power losses for heating), which is compensated by the use of special lubricants.
In general, helical gears are used in applications that require high torque transmission at high speed or have severe noise restrictions.
^ Double helical wheels (chevron ) solve the axial moment problem. The teeth of such wheels are made in the form of the letter “V” (or they are obtained by joining two helical wheels with opposite teeth). The axial moments of both halves of such a wheel are mutually compensated, so there is no need to install axles and shafts in special bearings. Gears based on such gears are commonly referred to as "chevron" gears.
With severe restrictions on dimensions, in planetary mechanisms, in gear pumps with internal gear, in the tank turret drive, wheels with a ring gear cut with inside. The drive and driven wheels rotate in the same direction. In such a transmission, there is less friction loss, that is, higher efficiency.
sector wheel is part of an ordinary wheel of any type. Such wheels are used in cases where the rotation of the link for a full turn is not required, and therefore it is possible to save on its dimensions.
^ Wheel based transmission with circular teeth (Novikov's transmission) has even higher driving performance than helical gears - a high engagement load capacity, high smoothness and quietness of operation. However, they are limited in use by reduced, under the same conditions, efficiency and service life, such wheels are noticeably more difficult to manufacture. Their tooth line is a circle of radius, selected for certain requirements. The contact of the surfaces of the teeth occurs at one point on the line of engagement, located parallel to the axes of the wheels.
In many machines, the implementation of the required movements of the mechanism is associated with the need to transfer rotation from one shaft to another, provided that the axes of these shafts intersect. In such cases, apply bevel gear. There are types of bevel gears that differ in the shape of the tooth lines: with straight, tangential, circular and curved teeth. Straight tooth bevel gears, for example, are used in automotive differentials used to transfer torque from the engine to the wheels.
2. The degree and norms of accuracy of gears.
GOST 1643-81 applies to involute spur gears and gear drives of external and internal gearing with spur, helical and chevron gears with a diameter pitch circle up to 6300 mm, tooth module from 1 to 55 mm, gear rim or half-chevron width up to 1250 mm. The involute tooth profile is obtained by machining workpieces by rolling (without sliding) with a gear-cutting tool. At the same time, the profile geometric parameters gear teeth must comply with GOST 13755-81.
For gears and gears, twelve degrees of accuracy are established, indicated in descending order of accuracy by Arabic Numerals from 1 to 12. For degrees of accuracy 1 and 2, tolerances and limit deviations are not given in GOST 1643-81, since these degrees are provided for future development, when gear cutting technology can provide such accuracy.
With a degree of accuracy of 3 - 5, measuring gears are used to control gears; wheels used in highly precise dividing mechanisms; cutting tool. Gears of degrees of accuracy 5 - 8 are widely used in aviation, automotive and other industries. The most widespread in mechanical engineering are gears of the 7th degree of accuracy, obtained by rolling on precision machines with subsequent finishing for wheels undergoing hardening (grinding, honing). Such wheels are widely used in machine tools, high-speed gearboxes, automobiles and tractors. Gears of degree of accuracy 8-11 are used in lifting mechanisms and agricultural vehicles. According to the 12th degree of accuracy, irresponsible wheels are made with teeth that are not machined, for example, cast.
The calculated degree of accuracy is the sixth degree. Tolerances were calculated for this degree of accuracy, and for other degrees numerical values
The tolerances were determined by multiplying or dividing the tolerances of the 6th degree by the conversion factors. Within the same degree of accuracy, the tolerances and limit deviations for various accuracy indicators are interconnected by analytical dependencies given in the standard.
The choice of the degree of transmission accuracy is made by the designer based on the specific operating conditions of the transmission and the requirements that apply to it (circumferential speed, transmitted power, operating mode, etc.).
When choosing degrees of accuracy, one of three methods is used: calculation, precedents (analogues) or similarity (tabular).
The preferred method is a calculation method in which the required degree of accuracy is determined based on the kinematic calculation of the errors of the entire transmission, the calculation of the dynamics of the transmission, the vibration and noise requirements of the transmission, the calculation of contact strength and durability.
With the precedent method, the degree of accuracy of the newly designed transmission is assumed to be similar to the degree of the working transmission, for which there is a positive operating experience.
With the similarity method, generalized recommendations and tables are used to select the degree of accuracy, which contain approximate values of peripheral speeds for each degree of accuracy.
For each degree of accuracy, accuracy indicators are established, which are summarized in three groups, called accuracy standards: kinematic accuracy standards, smoothness and tooth contact. This separation is due to the fact that, depending on the purpose and operating conditions of gears and gears, there are different requirements for the accuracy of their elements.
This allows you to combine degrees of accuracy in one gear, that is, to assign different degrees of accuracy according to accuracy standards, and it is advisable in cases where, according to the conditions of operation of the gearing, some accuracy indicators are more important than others. For example, for low-speed power transmissions, tooth contact rates are assigned according to more than high degrees accuracy than the norms of kinematic accuracy and smooth operation of the wheel, and for
Gears of reference mechanisms of the contact norms are taken rougher than the norms of kinematic accuracy.
The combination of accuracy standards in terms of degrees of accuracy allows you to set higher requirements for important functional parameters, and lower requirements for manufacturing accuracy for secondary ones, which also determines the choice of finishing operations for tooth profiles. Finishing operations significantly increase the accuracy of the wheel only in relation to indicators of one type of norm. For example, tooth grinding increases mainly kinematic accuracy, shaving increases smoothness of operation, and lapping and running in increases tooth contact.
There is a certain relationship between the accuracy indicators of gears, therefore it is practically impossible to manufacture wheels with a significant gap in the degrees of accuracy for individual indicators. The standard establishes restrictions when combining standards of different degrees of accuracy: the standards for smooth operation of gears and gears can be no more than two degrees more accurate or one degree rougher than the norms of kinematic accuracy; tooth contact norms can be assigned to any degree, more accurate than the smooth operation norms of gears and gears, as well as one degree coarser than the smoothness norms.
If the operational requirements for the transmission are the same for all indicators, then for all wheel accuracy indicators (accuracy standards) one degree of accuracy is assigned.
At symbol standardized indicators of accuracy according to the standards of accuracy adhere to the following rules. The indicators for gears are specified by adding subscripts: 1, 2 and 0 refer to gear, wheel and gear, respectively. When measuring the accuracy indicators of manufactured gears and assembled gears, the letter r is added to the end of the index. If it is not in the designation, then the numerical values \u200b\u200bof the corresponding indicators are standard, not measured.
The presence in the symbol of the accuracy indicator of one stroke in the degree means that the control of this indicator should be carried out with a single-profile engagement, the presence of two strokes obliges to carry out control with a two-profile engagement. The unstreaked readings are mainly tested on individual gears out of mesh. The indicators of gear wheels are checked in engagement with a measuring, more accurate wheel, and gears - in engagement with a paired impeller.
Types of gears.
Degree and norms of accuracy of wheels.
Used Books
Danilevsky V.V. Mechanical engineering technology: Textbook for technical schools. – 5th ed., revised. And additional - M., Higher School, 1984.
Ministry of Education and Science of the Russian Federation
Federal Agency for Education
FGOU SPO "TTK VAZ"
external student
By discipline: "Technology of mechanical engineering"
Group: TM-06-41
Completed by: Kravchenko I.I.
Checked by: Nazaikinskaya I.V.