Federal State Autonomous Educational

institution of higher education

"St. Petersburg State Polytechnic University"

Institute of Metallurgy, Mechanical Engineering and Transport

________________________________________________________

Department "Technological processes and equipment of automated machine-building industries"

Methods for selecting interchangeable gears for metal-cutting machines

Guidelines for laboratory work

Direction: 15.03.05 - "DESIGN AND TECHNOLOGICAL SUPPORT OF MACHINE-BUILDING PRODUCTIONS"

Profile: 15.03.05_05 - "Technology, equipment and automation of machine-building industries

St. Petersburg

Methods for selecting interchangeable gear wheels for metal-cutting machines. Guidelines for laboratory work for students in the direction of 15.03.05. They contain a description of the device and methods for tuning guitars with interchangeable gears.

Compiled by:

Doctor of Technical Sciences, Professor Kalinin E.P.

Candidate of Technical Sciences, Associate Professor Portnov S.V.

Art. teacher Nikitin A.V.

Reviewers:

The guidelines were approved at a meeting of the department "Cutting, machines and tools" "" ________ 20__ protocol No. ___

Scientific editor - Doctor of Technical Sciences, Professor D.V. Vasilkov

1. The purpose of the work

The study of the device and methods of tuning guitars with interchangeable gears.

2. General information about replacement wheel guitars

Replaceable gears are used to change the gear ratios of various kinematic chains. Devices with interchangeable gears are called guitars. Depending on the number of pairs of interchangeable wheels installed in the guitar, single-pair, two-pair and three-pair guitars are distinguished. The wheels are mounted on the ends of the shafts, the axes of which are fixed in space or can be rearranged. The use of guitars with an adjustable shaft or axle makes it possible to select interchangeable gears regardless of the center distance (within certain limits). At the same time, the number of wheels with different numbers of teeth that can be installed in the guitar increases, the accuracy of selecting the required gear ratio increases.

3. Single-pair guitars

Rice. 1. Scheme of a single-pair guitar

The number of teeth of wheels 1 and 2 of a single-pair guitar is determined from the equations:

(1)

(2)

a - dividing center distance, mm; m - module, mm.

When designing single-pair guitars, the total number of teeth z c is usually set from a number of 60, 72, 90, 120. Since the number of unknowns z 1 and z 2 is equal to the number of equations, the desired number of teeth is uniquely determined from these equations. The number of teeth of the wheels can only be integers. However, when solving these equations, depending on the value of i 21 and z c, the values ​​of z 1 and z 2 can be obtained in the form of integers or mixed numbers. The latter are rounded to whole numbers. Therefore, it is difficult in most cases to obtain a precisely set gear ratio when using a single-pair guitar.

Example 1. Determine the number of teeth of the replaceable wheels of a single-pair guitar with z c =72 with i 21 = 1/3.

From the equations:

and

we get:
and
, a

Examination:

In this case, the numbers of teeth z 1 and z 2 are obtained as integers, since the value z c = 72 is divided without a remainder by the sum of the numerator and denominator (1+3) of the required gear ratio.

Example 2. Determine the number of teeth of the replaceable wheels of a single-pair guitar with z c \u003d 72 and i 21 \u003d 0.329.

From the equations:
and

we get:
and
, a

Accept: z 1 = 18 and z 2 = 54

Examination:

With the selected wheels, the given gear ratio is reproduced approximately.

Single-pair guitars are used when the number of required gear ratios is small and when there are no high requirements for the accuracy of the given gear ratio. They are used in the drives of the main movement of automatic machines, semi-automatic machines and special machines, as well as in the feed drives of some machines, for example, gear hobbing.

When calculating the gear ratio of a guitar, division is made on a slide rule. Leaving the engine motionless, move the sight and find the risks that match on the engine and the ruler.

Example. i = 0,34

On the ruler scale we find:

We use the second ratio as the most accurate one:

Factorization method

This method is applicable for small values ​​of the numerator and denominator of the gear ratio.

The essence of the method is as follows:

The numerator and denominator are factorized and, multiplying by the next number, the number of teeth of replaceable gears is found.

Example. We have: we decompose the fraction into factors.

multiplying the numerator and denominator, for example, by 10, we get (the total factor for each fraction can be any):

,

(Such gears are included with the machine).

Bibliography

1. Avraamova T.M., Bushuev V.V., Gilovoy L.Ya. etc. Metal-cutting machines. T.1. - M .: Mashinostroenie, 2011. - 608s.

2. Avraamova T.M., Bushuev V.V., Gilovoy L.Ya. etc. Metal-cutting machines. T.2. - M .: Mashinostroenie, 2011. - 608s.

3. Acherkan N.S. Metal cutting machines. - M .: Mashinostroenie, 1965, vol. 1. - 764 S., vol. 2. – 628 p.

4. Kovalev N.M., Perelomov N.G. Milling machines. - L.: Mashinostroenie, 1964. - 110 p.

5. Kucher A.M., Kucher I.M., Anserov Yu.M. Lathes and fixtures. - L .: Mashinostroenie, 1969. - 376 p.

6. Kucher A.M., Kivatitsky M.M., Pokrovsky A.A. Metal-cutting machines, - L .: Mashinostroenie 1972. - 305 p.

7. Metal-cutting machines: Textbook for engineering colleges / Edited by V.E. Push. – M.: Mashinostroenie, 1985. – 256 p.

8. Metal-cutting machines and automatic machines: Textbook for engineering colleges / Ed. A.S. Pronikova. – M.: Mashinostroenie, 1981. – 479 p.

10. Metal-cutting machines. Tepinkichiev V.K., Krasnichenko L.V., Tikhonov A.A., Kolev N.S. - M.: Mashinostroenie, 1970. - 464 p.

11. Metal-cutting machines: Textbook for universities in the specialty “Technology of mechanical engineering, metal-cutting machines and tools” / N.S. Kolev, L.V. Krasnichenko, N.S. Nikulin and others - M .: Mashinostroenie, 1980. - 500 p.

12. Nazarikov S.V. Adjustment of dividing heads. - L .: Mashinostroenie, 1967. - 72 p.

13. Gulyachkin K.N. Laboratory work on the course Metal-cutting machines. - M.: Mashinostroenie, 1963. - 230 p.

14. Guide to laboratory work on the course Metal-cutting machines / Ed. P.G. Petrukha. - M .: Higher. school, 1973. - 150 p.

15. GOST 12.4.113-82 SSBT. Educational laboratory works. General safety requirements. - M .: Publishing house of standards, 1982. - 32 p.

16. GOST 12.4.026-76. Signal colors and safety signs. - M.: Publishing house of standards, 1976. - 36 p.

17. GOST 2.770-68. ESKD. Conditional graphic designations in schemes. - M .: IPK Publishing house of standards, 2001. From 64 - 76.

18. GOST 2.701-84. ESKD. Rules for the execution of schemes. - M.: USSR State Committee for Standards, 1987. - 136 p.

HOW TO USE THE TABLES / PROGRAM

For the selection of replacement wheels, the desired gear ratio is expressed as a decimal fraction with the number of digits corresponding to the required accuracy. In the "Basic tables" for the selection of gears (p. 16-400) we find a column with a heading containing the first three digits of the gear ratio; for the rest of the numbers we find a line on which the numbers of teeth of the driving and driven wheels are indicated.

It is required to pick up replacement guitar wheels for a gear ratio of 0.2475586. First, we find a column with the heading 0.247-0000, and below it, the closest value to the subsequent decimal places of the desired gear ratio (5586). In the table we find the number 5595, corresponding to a set of interchangeable wheels (23*43): (47*85). Finally we get:

i \u003d (23 * 43) / (47 * 85) \u003d 0.2475595. (one)

Relative error compared to the given gear ratio:

δ = (0.2475595 - 0.2475586) : 0.247 = 0.0000037.

We strictly emphasize: in order to avoid the influence of a possible typo, it is necessary to check the obtained ratio (1) on a calculator. In cases where the gear ratio is greater than one, it is necessary to express its reciprocal value as a decimal fraction, using the value found in the tables, find the number of teeth of the driving and driven replacement wheels and swap the driving and driven wheels.

It is required to select replacement guitar wheels for the gear ratio i = 1.602225. We find the reciprocal of 1:i = 0.6241327. In the tables for the nearest value 0.6241218 we find a set of interchangeable wheels: (41*65) : (61*70). Considering that the solution was found for the reciprocal of the gear ratio, we swap the driving and driven wheels:

i = (61*70)/(41*65) = 1.602251

Relative selection error

δ = (1.602251 - 1.602225) : 1.602 = 0.000016.

It is usually required to select wheels for gear ratios expressed to the sixth, fifth, and in some cases even to the fourth decimal place. Then the seven-digit numbers given in the tables can be rounded up to the corresponding decimal place. If the existing set of wheels differs from the normal one (see page 15), then, for example, when setting up the differential or break-in chains, you can select a suitable combination from a number of adjacent values ​​\u200b\u200bwith an error that satisfies the conditions set out on pages 7-9. In this case, some numbers of teeth can be replaced. So, if the number of teeth of the set is not more than 80, then

(58*65)/(59*95) = (58*13)/(59*19) = (58*52)/(59*76)

The "heel" combination is pre-transformed as follows:

(25*90)/(70*85) = (5*9)/(7*17)

and then, according to the obtained multipliers, the number of teeth is selected.

DETERMINING THE PERMISSIBLE SETTING ERROR

It is very important to distinguish between absolute and relative tuning errors. The absolute error is the difference between the received and required gear ratios. For example, it is required to have a gear ratio i = 0.62546, and received i = 0.62542; the absolute error will be 0.00004. Relative error is the ratio of the absolute error to the required gear ratio. In our case, the relative error

δ = 0.00004/0.62546 = 0.000065

It should be emphasized that it is necessary to judge the accuracy of the adjustment by the relative error.

General rule.

If any value A obtained by tuning through a given kinematic chain is proportional to the gear ratio i, then with a relative tuning error δ, the absolute error will be Aδ.

For example, if the relative error of the gear ratio δ = 0.0001, then when cutting a screw with a pitch t, ​​the deviation in the pitch, depending on the setting, will be 0.0001 * t. The same relative error when setting the gear hobbing machine differential will give an additional rotation of the workpiece not to the required arc L, but to an arc with a deviation of 0.0001 * L.

If a product tolerance is specified, then the absolute size deviation due to the inaccuracy of the setting should be only a certain fraction of this tolerance. In the case of a more complex dependence of any value on the gear ratio, it is useful to resort to replacing the actual deviations with their differentials.

Adjusting the differential circuit when processing screw products.

The following formula is typical:

i = c*sinβ/(m*n)

where c is the circuit constant;

β is the angle of inclination of the helix;

m - module;

n is the number of cutter runs.

Differentiating both parts of the equality, we obtain the absolute error di of the gear ratio

di = (c*cosβ/m*n)dβ

then the allowable relative setting error

δ = di/i = dβ/tgβ

If the permissible deviation of the helix angle dβ is expressed not in radians, but in minutes, then we get

δ = dβ/3440*tgβ (3)

For example, if the angle of inclination of the helix of the product β = 18°, and the allowable deviation in the direction of the tooth dβ = 4 "= 0", 067, then the allowable relative setting error

δ \u003d 0.067 / 3440 * tg18 \u003d 0.00006

On the contrary, knowing the relative error of the gear ratio taken, it is possible by formula (3) to determine the error in the helix angle in minutes. When establishing the permissible relative error, in such cases it is possible to use trigonometric tables. So, in formula (2) the gear ratio is proportional to sin β. According to the trigonometric tables for the taken numerical example, it can be seen that sin 18 ° \u003d 0.30902, and the difference of the sines per 1 "is 0.00028. Therefore, the relative error per 1" is 0.00028: 0.30902 \u003d 0.0009. The permissible deviation of the helix is ​​0.067, therefore the permissible error of the gear ratio is 0.0009 * 0.067 = 0.00006, the same as in the calculation by formula (3). When both mating wheels are cut on the same machine and using the same differential chain setting, then the errors in the direction of the tooth lines are allowed to be much larger, since the deviations for both wheels are the same and only slightly affect the side clearance when the mating wheels are engaged.

Setting up the running chain when machining bevel gears.

In this case, the setup formulas look like this:

i = p*sinφ/z*cosу or i = z/p*sinφ

where z is the number of teeth of the workpiece;

p is the constant of the running circuit;

φ - the angle of the initial cone;

y is the angle of the pedicle of the tooth.

The radius of the main circle turns out to be proportional to the gear ratio. Based on this, it is possible to establish the permissible relative error of the setting

δ = (Δα)*tanα/3440

where α is the engagement angle;

Δα - permissible deviation of the engagement angle in minutes.

Setting when processing screw products.

Setting Formula

δ = Δt/t or δ = ΔL/1000

where Δt is the deviation in the pitch of the propeller due to tuning;

ΔL - accumulated error in mm per 1000 mm thread length.

The value of Δt gives the absolute pitch error, and the value of ΔL characterizes essentially the relative error.

Adjustment taking into account the deformation of the screws after processing.

When cutting taps, taking into account the shrinkage of the steel after subsequent heat treatment, or taking into account the deformation of the screw due to heating during machining, the percentage of shrinkage or expansion directly indicates the required relative deviation in the gear ratio compared to what would have happened without taking into account these factors. In this case, the relative deviation of the gear ratio in plus or minus is no longer a mistake, but a deliberate deviation.

Setting up dividing circuits. Typical tuning formula

where p is a constant;

z is the number of teeth or other divisions per revolution of the workpiece.

A normal set of 35 wheels provides an absolutely accurate setting up to 100 divisions, since the number of teeth of the wheels contains all simple factors up to 100. In such a setting, the error is generally unacceptable, since it is equal to:

where Δl is the deviation of the tooth line at the width of the workpiece B in mm;

pD is the length of the initial circle or the corresponding other circle of the product in mm;

s - feed along the axis of the workpiece for one of its revolutions in mm.

Only in rough cases, this error may not play a role.

Setting up gear hobbing machines in the absence of the required multipliers in the number of teeth of replaceable wheels.

In such cases (for example, at z \u003d 127), you can tune the dividing guitar to approximately a fractional number of teeth, and make the necessary correction using the differential. Typically, tuning formulas for division, pitch, and differential guitars look like this:

x = pa/z; y=ks; φ = c*sinβ/ma

Here p, k, c are, respectively, constant coefficients of these chains; a is the number of cutter runs (usually a = 1).

We tune the indicated guitars according to the formulas

x = paA/Az+-1 ; y=ks; φ" = pc/asA

where z is the number of teeth of the processed wheel;

A is an arbitrary integer, chosen so that the numerator and denominator of the gear ratio are decomposed into factors suitable for the selection of replacement wheels.

The sign (+) or (-) is also chosen arbitrarily, which facilitates factorization. When working with a right-hand cutter, if the (+) sign is selected, the intermediate wheels on the guitars are set as they are done according to the manual for working on this machine for a right-handed workpiece; if the sign (-) is selected, the intermediate wheels are set, as for a left-handed workpiece; when working with the left cutter - vice versa.

It is advisable to choose A within

then the gear ratio of the differential chain will be from 0.25 to 2.

It is especially necessary to emphasize that with replacement wheels taken for a guitar of feeds, the actual feed must be determined in order to be substituted into the differential tuning formula with great accuracy. It is better to calculate it according to the kinematic diagram of the machine, since the constant factor k in the feed setting formula in the machine manual is sometimes given approximately. If this instruction is not followed, the teeth of the wheel may turn out to be noticeably beveled instead of straight.

Having calculated the feed, the fine tuning is practically obtained according to the first two formulas (4). Then the allowable relative error in tuning the differential guitar is

δ = sA*Δl/pmb (5)

de b - the width of the gear rim of the workpiece;

Δl - permissible deviation of the direction of the tooth on the width of the crown in mm.

In the case of cutting wheels with helical teeth, it is necessary to use the differential to give the cutter an additional rotation to form a helix and an additional rotation to compensate for the difference between the desired number of divisions and the number of divisions actually set. The tuning formulas are obtained:

x = paA/Az+-1 ; y=ks; φ" = c*sinβ/ma +- pc/asA

In the formula for x, the sign (+) or (-) is chosen arbitrarily. In these cases:

1) if the direction of the screw at the cutter and the workpiece is the same in the formula for φ "take the same sign as is chosen in the formula for x;

2) if the direction of the screw of the cutter and the workpiece is different, then in the formula for φ "they take the sign opposite to that chosen for x.

Intermediate wheels on guitars are placed, as indicated in the instructions for this machine, according to the direction of the helical teeth. Only if it turns out that φ"

Non-differential tuning.

In some cases, when processing screw products, more rigid non-differential machines can be used if a secondary pass of the processed cavities is not required from the same installation and with an exact hit in the cavity. If the machine is set up at a predetermined feed, due to a small number of interchangeable wheels or the presence of a feed box, then the setting of the dividing chain requires great accuracy, i.e., it must be done as precision. Permissible relative error

δ = Δβ*s/(10800*D*cosβ*cosβ)

where Δβ is the deviation of the helix of the product in minutes;

D is the diameter of the initial circle (or cylinder) in mm;

β is the angle of inclination of the workpiece tooth to its axis;

s - feed for one revolution of the workpiece along its axis in mm.

To avoid time-consuming precision adjustment, proceed as follows. If a sufficiently large set of wheels (25 or more, in particular a normal set and the tables in this book) can be used for a guitar of feeds, then the given feed s is first considered indicative. Having set up the division chain and considering the setting to be quite accurate, they determine what the axial feed s should be for this.

The usual division chain formula is rewritten as follows:

x = (p/z)*(T/T+-z") = ab/cd (6)

where p is a constant fission chain factor;

z is the number of product divisions (teeth, grooves);

T \u003d pmz / sinβ - pitch of the helix of the workpiece in mm (it can be determined in another way);

s" - tool feed along the axis of the workpiece for one revolution in mm. The sign (+) is taken for different directions of the screw of the cutter and the workpiece; the sign (-) for the same.

Having selected, in particular, according to the tables of this book, the driving wheels with the numbers of teeth a and b, and the driven wheels with the numbers of teeth c and d, from the formula (6) we determine exactly the required feed

s" = T(pcd - zab)/zab(7)

We substitute the value s "into the feed setting formula

The relative error δ of the feed setting causes a corresponding relative pitch error T of the helix. On the basis of this, it is easy to establish that when tuning the guitar pitch, you can make a relative error

δ = Δβ/3440*tgβ (9)

From the comparison of this formula with formula (3), it can be seen that the allowable in this case tuning error of the pitch guitar is the same as it is with the usual setting of the differential circuit. It should be emphasized again the need to know the exact value of the coefficient k in the feed formula (8). If in doubt, it is better to check it by calculating the kinematic diagram of the machine. If the coefficient k itself is determined with a relative error δ, then this causes an additional deviation of the helix by Δβ, which is determined for a given β from relation (9).

GRIP CONDITIONS FOR REPLACEMENT WHEELS

In machine tool manuals, it is useful to give graphs by which it is easy to estimate in advance the possibility of adhesion of a given combination of wheels. On fig. 1 shows the two extreme positions of the guitar, defined by circular grooves B. In fig. Figure 2 shows a graph in which arcs of circles are drawn from points Oc and Od, which are the centers of the first driving wheel a and the last driven wheel d (Fig. 3). The radii of these arcs in the accepted scale are equal to the distances between the centers of interlocking interchangeable wheels with the sums of the numbers of teeth 40, 50, 60, etc. These sums of the numbers of teeth for the first pair of interlocking wheels a + c and the second pair b + d are affixed at the ends corresponding arcs.

Let a set of wheels (50*47) : (53*70) be found from the tables. Will they link up in the order 50/70 * 47/53 ? The sum of the number of teeth of the first pair is 50 + 70 = 120 The center of the pin should lie somewhere on the arc marked 120 drawn from the center of Oa. The sum of the number of teeth of the wheels of the second pair is 47 + 53 = 100. The center of the pin should be on an arc marked 100 drawn from the center of Od. As a result, the center of the finger will be set at point c at the intersection of the arcs. According to the diagram, wheel traction is possible.

For a combination of 30/40 * 20/50, the sum of the numbers of teeth of the first pair is 70, the second is also 70. Arcs with such marks do not intersect inside the figure, therefore, wheel traction is impossible.

In addition to the graph shown in Fig. 2, it is desirable to also draw the outline of the box and other details that may interfere with the installation of gears on the guitar. For the best use of the tables in this book, it is advisable for the guitar designer to observe the following conditions, which are not strictly necessary, but are desirable:

1. The distance between the fixed AXES Oa and Od must be such that two pairs of wheels with a total of 180 teeth can still mesh. The most desirable distance Oa - Od is between 75 and 90 modules.

2. A wheel with at least 70 teeth should be installed on the first drive shaft, up to 100 on the last driven shaft (if the dimensions are acceptable, up to 120-127 can be provided for some cases of refined settings).

3. The length of the guitar slot at the extreme position of the finger must ensure the adhesion of the wheels located on the finger and on the axle of the guitar with a sum of teeth of at least 170-180.

4. The extreme angle of deviation of the guitar groove from the straight line connecting the centers Oa and Od must be at least 75-80°.

5. The box must have sufficient dimensions. Adhesion of the most unfavorable combinations should be checked according to the schedule attached to the machine manual (see fig. 2).

The tuner of the machine or mechanism must use the graph given in the manual (see Fig. 2), but, in addition, take into account that the larger the gear wheel on the first drive shaft (at a given torque), the less force on the teeth of the first pair; the larger the wheel on the last driven shaft, the less force on the teeth of the second pair.

Consider slow transmissions, i.e. the case when i

z1/z3 * z2/z4 ; z2/z3 * z1/z4 (10)

The second combination is preferable. It provides a lower moment of forces on the intermediate shaft and allows you to meet the additional conditions imposed (see Fig. 3):

a+c > b+(20...25); b + d > с+(20...25) (11)

These conditions are set to prevent the stop of the replacement wheels in the corresponding shafts or fasteners; the numerical term depends on the design of the given guitar. However, the second of the combinations (10) can only be accepted when the wheel Z2 is mounted on the first drive shaft and if the gear z2/z3 is decelerating or does not contain much acceleration. It is desirable that z2/z3

For example, the combination (33*59) : (65*71) is better to use in the form 59/65 * 33/71 But in a similar case, the ratio 80/92 * 40/97 is not applicable if the wheel z = 80 is not placed on the first shaft. Sometimes inconvenient combinations of wheels are given in the tables to fill in the corresponding gear ratio intervals, for example 37/41 * 92/79 Condition (11) is not met in this order of wheels. It is impossible to swap the driving wheels, since the wheel z = 92 is not placed on the first shaft. These combinations are indicated for cases where, by any means necessary, a more accurate gear ratio must be obtained. You can also resort to the methods of refined settings in these cases (p. 401). For acceleration transmissions (i > 1), it is desirable to divide i = i1i2 in such a way that the factors are as close as possible to one another and the increase in speed is more evenly distributed. Moreover, it is better if i1 > i2

MINIMUM REPLACEMENT WHEELS PACKAGES

The composition of sets of replacement wheels, depending on the field of application, is given in Table. 2. For particularly fine settings, see page 403.

table 2

The tables supplied by the factory can be used to set the dividing heads. More difficult, but you can choose the appropriate heel combinations from the "Basic Tables for Selecting Gears" given in this book.

GUITAR MACHINE

Kinematic node. metal cutting settings machine, consisting of interchangeable gears. Guitars usually contain one, two or three pairs of wheels and are used to change the spindle speed or pitch (see picture).

Big encyclopedic polytechnic dictionary. 2004 .

See what "STANK'S GUITAR" is in other dictionaries:

GUITAR machine tool, machine tool assembly to reduce or increase the feed rate. Replaceable gears are installed on the guitar shafts, the selection of which expands the possibilities of regulating the speeds of movements created by the machine ... encyclopedic Dictionary

guitar- uh. guitarre f., Spanish guitarra. 1. music. Kitara. 1719. // Perspective. Harlequin, seeing the Guitar, took it and began to play it. It. com. 347. In the evening, alone with a guitar, she sang, sitting under the window. Moore. Art. 197. What feelings you infuse, Guitar! In the soul… … Historical Dictionary of Gallicisms of the Russian Language

Machine tool assembly of a metal cutting machine to reduce or increase the feed rate. Replaceable gears are installed on the guitar shafts, the selection of which expands the possibilities of regulating the speeds of movements created by the machine ... Big Encyclopedic Dictionary

s; and. [Spanish] guitarra] A stringed plucked musical instrument with a resonator body in the form of a figure-eight and a long neck (first appeared in Spain in the 13th century). Seven-string, six-string d. Orchestral d. Electronic d. Sing along with the guitar. ... ... encyclopedic Dictionary

Dormi amore, la situazione non è buona ... Wikipedia

- (power transmission) in mechanical engineering, a set of assembly units and mechanisms connecting the engine (motor) to the driving wheels of the vehicle (car) or the working body of the machine, as well as systems that ensure the operation ... ... Wikipedia

transcript

1 Ministry of Education and Science of Russia Federal State Budgetary Educational Institution of Higher Education “Volgograd State Technical University” Kamyshinsky Technological Institute (branch) of the Federal State Budgetary Educational Institution “Volgograd State Technical University” Department “Technology of Engineering and Applied Mechanics” Methods of Selection of Excessive Tough Rail to perform laboratory and practical work on the course "Metal-cutting machines" and "Technological equipment" Volgograd 206

2 UDC 62906(0758) М 54 METHODS OF SELECTION OF REPLACEMENT GEARS: guidelines for the implementation of laboratory and practical work on the course "Metal-cutting machines" and "Technological equipment" / Compiled by N.I. Nikiforov; VolgGTU Volgograd, c. Descriptions of various methods for selecting gears in guitars Intended for students studying in the direction of "Design and technological support of machine-building industries" and the specialty of SPO "Technology of mechanical engineering" Native Published by decision of the editorial and publishing council of the Volgograd State Technical University Volgograd State Technical University, 206 2

3 General information about guitars with interchangeable wheels A guitar is a mechanism with interchangeable gears designed for stepwise change in the gear ratio of the calculated kinematic chain. They are mainly used in rarely tunable chains with a large range and the number of gear ratios of the design chain tuning body. These mechanisms are simple in design. Main disadvantage guitars, the complexity of tuning Guitars are one, two, less often three-pair In speed boxes, single-pair guitars are usually used In the vast majority of cases, either a single-pair or two-pair guitar is sufficient to obtain the required feed values. application in machines for high-volume production with infrequent adjustments They are compact, simplify the structure and design of the drive Two-pair guitars with adjustable distance between the axes have a movable intermediate shaft and make it possible to engage gears with any number of teeth, which makes it possible to adjust the gear ratio with a high degree of accuracy. Figure shows a two-pair guitar schematically.

4 General series of teeth numbers z for turning milling backing General series of teeth numbers z for turning milling backing Sets of interchangeable wheels for groups of machines (recommended) gear-cutting gear-cutting Distance A between the driving shaft (wheels a) and the driven 2 (wheels d) is unchanged On the driven shaft freely the slope of the guitar is planted 3 In the slope there are radial and arc grooves In the radial groove, the axis of 4 wheels b and c is attached By moving the axis along the groove, you can change the distance B between wheels c and d Due to the presence of an arc groove in the slope, it is possible to change the distance C between wheels a and c b, turning the incline on the shaft 2 In the required position, the inclination is fixed with a bolt 5 2 Selection of the number of teeth of interchangeable gears The task of selecting interchangeable gears is to determine the number of teeth of these wheels to ensure the required gear ratio Each guitar of the machine is equipped with a certain set of interchangeable wheels (table) Quantity wheels in the set and their number of teeth are different and are determined by the possible variety of gear ratios that are required to be carried out during the operation of the machine, as well as the degree of accuracy with which the selection of gear ratios is required

6 All methods for selecting replacement gears can be divided into exact and approximate. Let's consider several methods for selecting the number of teeth of replaceable wheels are decomposed into simple factors After factorization, the first ratio of factors is taken and the numerator and denominator of this ratio are multiplied by the same number to obtain numbers in the numerator and denominator equal to the number of teeth of the wheels in the set. Similarly, they do the second ratio of factors (for a two-pair guitar ) and with the third (for a three-pair) Consider the example i a b c d, 63 a 36, ​​b 20, c 30, d 63 (The factors in parentheses are indicated by which we multiply the numerator and denominator) 22 The method of continued fractions The ratio a / b of any integers can be expressed as a continued fraction: a a b a 2 a3 a4 an, an where a, a2, a3, a4, a n ; an - quotients of division performed as follows: first a is divided by b, it turns out a, then b is divided by the remainder of the first division, it turns out a2 and so on, each previous remainder is divided by the next until the remainder is zero 6

7 In the continued fraction thus obtained, a is the roughest approximation; more precisely the approximation a a2 a ; adding each subsequent term a2 a2 of the fraction gives a more accurate approximation. First, they stop at some term of this fraction and determine the gear ratio, decomposing it into factors and select the wheels according to the first method we have considered. After selecting the wheels, check the tuning error. If it goes beyond the permissible error, then they again calculate, taking a larger number of terms of a continued fraction. Example Select gears for a gear ratio, 765 Let's turn the number, 765 into a continued fraction, for this you need to divide the numerator by the denominator, we get the first quotient and the first remainder, 765: \u003d (private) 765 (th remainder), then divide the denominator by the -th remainder: 765 = 8 (2nd quotient), (2nd remainder) Divide the first remainder by the second remainder 765: = (3rd quotient) 5885 (3rd remainder) Divide the second remainder by the third remainder: 5885 = 7 (4th quotient) 5835 (4th remainder) Divide the third remainder by the fourth remainder 5885: 5835 = (5th quotient) 50 (5th remainder) Divide the fourth remainder to the fifth remainder 5835: 50 = 6 (6th quotient) 35 (6th remainder) member, all members are discarded and the fraction interrupted in this way is converted into an ordinary one: 9); 2) 8 8 7

8 To get the next suitable fraction, you need to multiply the numerator and denominator of the previous suitable fraction by the denominator of the last term of the interrupted fraction and add the numerator to the numerator of the product, and the denominator of the second previous suitable fraction to the denominator of the product 3) (9) 0 8 (8) 9 4) ( 0 7) (9 7)) (79) (6)) (89 6) (70 6) Thus, a series of convergent fractions is obtained: ; ; ; ; ; For the selection of interchangeable gears, you can use any suitable fraction, but since each subsequent fraction will be closer to the value of the continued fraction, then taking the next suitable fraction, the selection error will be less. 25.4; and 25, 4 are replaced by approximate values ​​(Table 2), which make it possible with sufficient accuracy 25.4 8

9 get gear ratios This method is used, for example, on screw-cutting lathes when cutting inch threads in the absence of a set of wheels with the number of teeth z=27 Example 2 Select replacement gears for cutting inch threads with the number of threads per inch k=0 screw-cutting lathe with a screw pitch Pxv = 6 mm and a constant gear ratio i post We solve this example using table 2: a c Pp 25, b d i post Pxv in determining the setup error 25.4 Table 2 Table of replacement values; 25.4; and 25, 4 25.4 25.4 25.0 0, 0.2 0.4 0.23 0. 0 0.45 0.2 0.6 0, Note In brackets inaccuracies of linear movement are indicated in millimeters per m of length 24 The logarithmic method is based on finding the logarithm of the gear ratio (if the gear ratio has the form of an improper fraction, take the logarithm of the value, 9

10 inverse gear ratio) and according to the corresponding table VASHishkov determine the number of teeth of replaceable gears. This method is based on the principle of logarithm of the gear ratio and gives the gears of the heel set with a very small error. The gear ratio of the gears a c of the guitar i after logarithm is b d lg i lg ac lg bd a c For example, for gear ratio i 2.76; b d lg 2.76=0.425 lg i a c b d gear ratios is less than one, so for i you need to take the logarithm of the reciprocal of the gear ratio: 0

11 i i t abl Selection of the number of teeth of the wheels on a slide rule The edge of the slide rule engine is set against the number corresponding to the gear ratio By moving the sight find the risks that match on the engine and on the ruler The risks must correspond to integers that give the value of the gear ratio when divided Then select the number of teeth interchangeable gears, for example, by the method of decomposition into prime factors:, 885 i 0.629 3 Leaving the engine in the resulting position, move the sight until the risks on the engine and on the ruler match Then i 0, This method of selection and wheels when cutting threads as a rule, it cannot be used, since its accuracy is usually not high. to gear ratios the reduction ratio in the form of a simple proper fraction, inconvenient for conversion, must first be converted to a decimal fraction with six decimal places. If the fraction is incorrect, then it is necessary to divide its denominator by the numerator to get a decimal fraction less than one. equal to the one obtained or closest to it, and next to it the simple fraction corresponding to it. Having received a simple fraction, then the number of teeth of the replaceable wheels is selected in the usual way

12 Table 4 Fragment of the MVSandakov table 0, For example, i, from where 0, i From the MVSandakov table we have 0, Due to the fact that the gear ratio before converting to a decimal fraction has the numerator and denominator swapped, the approximate number does the same Then i Selected wheels available in a set for gear-cutting machines If it is not possible to select the necessary gears, then another nearest value is taken from the table (for example, see the fragment of the table 0.64340 or another) 27 Knappe method This method is based on the fact that the numerator and denominator of fractions, close to one, you can add (or subtract) an equal number of units without significantly changing the value of the fraction Let i Divide this fraction, we get Then we can write: i We got a factor in the form of a fraction close to one 335 Using the above rule, we can write:

13 i We have obtained a fraction that is easily decomposed into factors Now, using the previously considered method, we will select gears: (5) i (5) This method is recommended to be used in the absence of tables specifically designed for selecting interchangeable wheels. It is also convenient when selecting three-pair guitars. 3 Determining the error settings When using approximate methods for selecting interchangeable gears, it is especially important to correctly estimate the error with which the exact gear ratio is replaced by an approximate one. Knowing the setting error, you can determine its effect on the accuracy of the workpiece. required i gear ratios: i i Relative error is the ratio of the absolute error to the required gear ratio: i buildable kinematic chain For example, when cutting a thread, this will be the pitch of the thread being cut t p ; when setting up the differential chain of a gear hobbing machine, such a movement will be an additional rotation of the workpiece by a certain arc 3

14 Guitar gear engagement conditions After selecting the number of teeth of the guitar wheels that satisfy the required gear ratio accuracy, it is necessary to check the possibility of installing them in the guitar, taking into account the dimensions of the guitar body and the distance between the axes of the first and last wheels Let us denote a, b, c, d the number of replaceable teeth wheels (Fig. 2), D is the diameter of the gear shafts, mm; m - wheel module, mm; hr tooth head height, mm To be able to install wheels a and b, it is necessary that the sum of their radii is greater than the radius of wheel c, plus the tooth head of wheel c, plus the radius of the shaft of wheel a Similarly, to install wheels c and d, it is necessary that the sum of their radii was greater than the radius of the wheel b, plus the head of the wheel teeth b, plus the radius of the wheel shaft d The above can be written as inequalities: D D ra rb rc hr ; rc rd rb hr 2 2

15 For most guitars, the diameter of the wheels is constructively taken equal to D 3 m Height of the head of the teeth h r m Then the inequalities can be written as follows: a m b m c 2 m 3 m ; c m d m b 2 m 3 m, from which we obtain the adhesion conditions: a b c 5 and c d b 5 22 If the condition is not met, then it is necessary to swap the gears in the numerator or denominator and check them for adhesion again. If in this case the adhesion conditions are not met, then it is necessary to repeat the calculation of the number of teeth, taking other additional factors. Textbook for engineering colleges - M: Mechanical engineering, s, ill. 2 Petrukha PG Processing technology for structural materials: Textbook for universities M: Higher school, s, ill. 3 Sandakov M V et al. V Sandakov VD Wegner M: Mechanical engineering, with illustration 4 Basics of machine tool science: Lab work / Comp: VA Vanin, VK Fidarov, VK Luchkin Tam Bov: Publishing House of Tambgos Technological University, p. 5

16 Compiled by: Nikolai Ivanovich Nikiforov METHODS OF SELECTION OF INTERCHANGEABLE GEARS Guidelines for the implementation of laboratory and practical work on the course "Metal-cutting machines" and "Technological equipment" Edited by the author Templan 206 g, pos 5K Signed for printing g Format / 6 Sheet paper Offset printing Conv. print 0.93 Uch-izdl 0.7 Circulation 00 copies Order Volgograd State Technical University, Volgograd, Lenina pr., 28, building Printed in KTI, Kamyshin, Lenina st., 5 6

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