12.07.2023

Selection of replacement gears. Selection program

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§ 3. METHODS FOR SELECTING REPLACEMENT GUITAR WHEELS.

A guitar (Fig. 2) is a device that ensures correct engagement of replaceable gears.

Rice. 2. Two-pair guitar diagram

The distance L between driving shaft 1 and driven shaft 2 remains unchanged. Guitar tilt 3 is freely mounted on the driven shaft, secured with bolt 4. Axle 5 is intermediate wheels b,c can be moved along the radial groove, thereby changing the distance A between the centers of the wheels c and d. The arc groove allows you to adjust size B. To ensure that the selected replacement gears do not rest against the shaft bushings 1, 2, it is necessary to comply with the conditions for their adhesion:

a+b>c+(15-:-20); с+d>b+(15-:-20).

When selecting wheels, it is necessary to take into account the permissible limits of gear ratios of pairs of replacement wheels 1/5<= i <= 2,8. Каждой гитаре придается определенный набор сменных колес. Нормальные комплекты сменных зубчатых колес для различных станков приведены в книгах , .

There are several ways to select the number of teeth of replacement wheels.

Factorization method simple and accurate. This method is used when the numerator and denominator of the gear ratio can be factorized into simple factors.

For example:

Checking the adhesion of gear wheels:

a + b>c+(15-:-20) or 60+70>40+15;

c+d>b+(15-:-20) or 40+80>70+15.

A way to replace common numbers with approximate fractions lies in the fact that the numbers π and 25.4 (numerical value of an inch) often encountered when cutting inch threads, worms and in other cases are replaced with approximate values convenient for selecting replacement wheels, for example:

1"" ≈ 25.4 mm =127/5 mm; π≈22/7≈(19*21)/127, etc.

The resulting error should not exceed that specified by the condition. Absolute adjustment error

∆i=i cm -i" cm;

relative adjustment error

where i cm is the specified gear ratio; i" cm - the resulting gear ratio of the replacement wheels.

Method for selecting replacement wheels using a slide rule least accurate. The edge of the slide rule slider is set against the number corresponding to the gear ratio of the replacement wheel guitar. By moving the slider, you find the marks that coincide on the slider and on the ruler. Based on the new integers obtained, which give the same quotient values when divided, the number of teeth of the replacement gears is selected.

Transcript

1 MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERAL STATE BUDGETARY EDUCATIONAL INSTITUTION OF HIGHER EDUCATION "VOLGOGRAD STATE TECHNICAL UNIVERSITY" KAMYSHIN TECHNOLOGICAL INSTITUTE (BRANCH) OF THE FEDERAL STATE BUDGET ETHNIC EDUCATIONAL INSTITUTION OF HIGHER EDUCATION "VOLGOGRAD STATE TECHNICAL UNIVERSITY" Department of "MECHANICAL ENGINEERING TECHNOLOGY AND APPLIED MECHANICS" METHODS FOR SELECTION OF REPLACEMENT GEAR WHEELS Guidelines to perform laboratory and practical work at the course “Metal-cutting machines” and “Technological equipment” Volgograd 206

2 UDC 62906(0758) M 54 METHODS FOR SELECTION OF REPLACEMENT GEARS: guidelines for performing laboratory and practical work on the course “Metal-cutting machines” and “Technological equipment” / Compiled by N I Nikiforov; VolgSTU Volgograd, with Descriptions are provided various methods selection of gears for guitars Intended for students studying in the field of “Design and technological support of mechanical engineering production” and the specialty of secondary vocational education “Mechanical Engineering Technology” Il 2 Table 4 Bibliography: 4 titles Reviewer: kt n V I Vykhodets Published by decision of the editorial and publishing council Volgograd State Technical University Volgograd State Technical University, 206 2

3 General information about guitars with interchangeable wheels A guitar is a mechanism with replaceable gears, designed for stepwise changes in the gear ratio of the calculated kinematic chain. They are used mainly in rarely reconfigured chains with a large range and number of gear ratios of the tuning element of the calculated chain. These mechanisms are distinguished by their simplicity of design. The main disadvantage of guitars is the complexity of tuning Guitars can be one, two, less often three-pair. In gearboxes, single-pair guitars are usually used. In the vast majority of cases, either a single-pair or a double-pair guitar is sufficient to obtain the required feed values. Double-pair guitars of interchangeable wheels can be made with a constant and variable distance between the wheel axes. They are used in machine tools for large-scale production with rare tuning They are compact, simplify the structure and design of the drive Double-pair guitars with an adjustable distance between the axles have a movable intermediate shaft and make it possible to engage gears with any number of teeth, which allows you to adjust the gear ratio with a high degree of accuracy. In Fig. schematically shows a two-pair guitar Fig. Two-pair guitar with replaceable gears 3

4 General number of teeth z of turning milling backing General number of teeth z of turning milling backing Sets of replacement wheels for groups of machines (recommended) gear-working gear-working Distance A between the drive shaft (wheel a) and driven 2 (wheel d) is unchanged The driven shaft is free the slope of the guitar is seated 3. The slope has radial and arc grooves. The radial groove holds the axis of 4 wheels b and c. 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 b, turning the slope on the shaft 2 In the required position, the slope is secured with a bolt 5 2 Selection of the numbers of teeth of replacement gears The task of selecting replacement gears is to determine the numbers of teeth of these wheels to ensure the required gear ratio. Each guitar of the machine is equipped with a certain set of replacement wheels (table) Quantity wheels in a set and the number of their teeth are different and are determined by the possible variety of gear ratios that need 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 Table Normal sets of replacement gears for machines of various types Sets of replacement wheels for machine groups (recommended)

6 All methods for selecting replacement gears can be divided into exact and approximate. Let's consider several methods for selecting the numbers of teeth of replacement wheels 2Method of decomposing the gear ratio into simple factors This method is accurate and the simplest and is used when the gear ratio is a simple fraction, the numerator and denominator of which are decomposed into simple factors. After decomposition into factors, take the first ratio of factors and multiply the numerator and denominator of this ratio by the same number to obtain numbers in the numerator and denominator equal to the numbers of wheel teeth available in the set. Do the same with the second ratio of factors (for a two-pair guitar ) and with the third (for three-pair) Consider the example i a b c d , 63 a 36, b 20, c 30, d 63 (The factors by which we multiply the numerator and denominator are indicated in parentheses) 22 Method of continued fractions The ratio a / b of any integers can be expressed as a continued fraction: a a b a2 a3 a4 an, an where a, a2, a3, a4, a n; an - quotients from division performed as follows: first a is divided by b, we get a, then b is divided by the remainder of the first division, we get 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 selecting the wheels using the first method we considered. After selecting the wheels, check the setting error. If it goes beyond the permissible error, then they carry out the calculation again, taking a larger number of terms of the continued fraction Example Select gears for the gear ratio, 765 Let's turn the number, 765 into a continued fraction, for this we need to divide the numerator by the denominator, we get the first quotient and the first remainder, 765: = (quotient) 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) 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 by fifth remainder 5835: 50 = 6 (6th quotient) 35 (6th remainder) The continued fraction is determined, To select the dividing gears, the continued fraction is converted into a suitable one, those continued fractions in which, starting from some term , discard all terms and transform the fraction interrupted in this way into an ordinary one: 9) ; 2) 8 8 7

8 To obtain 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 number of suitable fractions are obtained: ; ; ; ; ; To select replacement 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 subsequent suitable fraction, the error in selection will be less. The method of replacing frequently occurring numbers with approximate fractions is that frequently occurring numbers; 25.4; and 25.4 are replaced by approximate values (Table 2), making it possible with sufficient accuracy 25.4 8

9 obtain gear ratios This method is used, for example, on screw-cutting lathes when cutting inch threads if there is no wheel with the number of teeth z = 27 in the set. Example 2 Select replacement gears for cutting inch threads with the number of threads per inch k = 0 per screw-cutting lathe with a screw pitch Pxв=6 mm and a constant gear ratio i post We solve this example using Table 2: a c Pp 25, b d ipost Pxв When using approximate methods for selecting replacement wheels, the resulting gear ratio differs from the specified one, so the need arises in determining the adjustment 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 parentheses the 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 improper fraction, take the logarithm of the value, 9

10 inverse gear ratio) and according to the corresponding VASHISHKOV table, the number of teeth of replaceable gears is determined. This method is based on the principle of logarithmization of the gear ratio and gives gears of the heel set with a very small error. The gear ratio of gears a c of guitar i after logarithmation has the form b d lg i lg ac lg bd a c For example, for the gear ratio i 2.76; b d lg 2.76=0.425 lg i a c b d Table 3 Fragment of VASHISHKOV’S table lg i a c b d 0, , , In the corresponding column of VASHISHKOV’S tables we find a close value of the logarithm lg i, which corresponds to replaceable guitar gears with a gear ratio of 25 5 i table In VASHISHKOV’S table the values are given gear ratios are less than one, so for i you need to take the logarithm of the reciprocal of the gear ratio: 0

11 i i t table Selection of numbers of wheel teeth using a slide rule The edge of the slide rule slider is set against the number corresponding to the gear ratio. By moving the viewfinder, the marks that coincide on the slider and on the ruler are found. The risks must correspond to integers that, when divided, give the value of the gear ratio. Then the number of teeth is selected replaceable gear wheels, for example, by the method of decomposition into simple factors: as a rule, cannot be used, since its accuracy is usually not high 26 Selection of the numbers of teeth according to MVSandakov tables Very often, the gear ratio contains fractional numerators and denominators or factors that are not multiples of the set of wheels. In this case, it is convenient to select the number of teeth of gear wheels according to MVSandakov tables containing to gear ratios The given gear ratio in the form of a simple regular fraction, inconvenient for conversion, must first be converted into a decimal fraction with six decimal places. If the fraction is irregular, then it is necessary to divide its denominator by the numerator to obtain a decimal fraction less than one. After this, in the table find a decimal fraction equal to the received one or closest to it, and next to it the corresponding simple fraction. Having received a simple fraction, then the numbers of teeth of the replacement wheels are selected in the usual way

12 Table 4 Fragment of MVSandakov’s table 0, For example i, from where 0, i From MVSandakov’s table we have 0, Due to the fact that the numerator and denominator of the gear ratio were swapped before turning into a decimal fraction, the approximate number does the same Then i Selected wheels are included in the kit for gear-processing machines. If it is not possible to select the required gears, then another closest 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 to 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 received a multiplier in the form of a fraction close to one 335 Using the rule formulated above, we can write: 2

13 i We have obtained a fraction that can easily be decomposed into factors. Now, using the previously discussed method, we will select gears: (5) i (5) This method is recommended for use in the absence of tables specifically designed for selecting replacement wheels. It is also convenient when selecting three-pair guitars 3 Determination of error settings When using approximate methods for selecting replacement gears, the correct assessment of the error with which the exact gear ratio is replaced by an approximate one becomes especially important. Knowing the adjustment error, you can determine its effect on the accuracy of the workpiece. Distinguish between absolute and relative adjustment errors. Absolute error is the difference between the obtained i and required i gear ratios: i i Relative error is the ratio of the absolute error to the required gear ratio: i The error in setting the kinematic chain will be equal to: П L, where L is the length of movement carried out by the adjusted kinematic chain. For example, when cutting a thread, this will be the pitch of the thread being cut t p ; when adjusting the differential chain of a gear hobbing machine, this movement will be an additional rotation of the workpiece to a certain arc 3

14 Conditions for the adhesion of guitar gears After selecting the numbers of teeth of the guitar wheels that satisfy the required accuracy of the gear ratio, 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 (Figure 2), D - diameter of gear shafts, mm; m - wheel module, mm; hr height of the tooth head, mm To be able to install wheels a and b, it is necessary that the sum of their radii be greater than the radius of wheel c, plus the head of the teeth 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 teeth of the wheel b, plus the radius of the wheel shaft d. The above can be written in the form of inequalities: D D ra rb rc hr ; rc rd rb hr 2 2 Fig2 Guitar diagram for calculating adhesion conditions 4

15 For most guitars, the diameter of the wheels is structurally assumed to be 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 In heavily loaded gears, the diameters of the wheel shafts are taken equal to 20 m, then the term instead of 5 will be equal to 22 Therefore, in the literature, adhesion conditions are given in the form: a b c 5 22 ;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 again for adhesion. If in this case the adhesion conditions are not met, then it is necessary to repeat the calculation of the numbers of teeth, taking other additional factors. List of used literature Chernov NN Metal-cutting machines: Textbook for mechanical engineering colleges - M: Mechanical Engineering, p., ill. 2 Petrukha PG Technology of processing of structural materials: Textbook for Universities M: Higher School, p., ill. 3 Sandakov M. V., etc. Tables for selecting gears: Handbook 6th ed., additional M V Sandakov VD Wegner M: Mechanical engineering, p. 4 Fundamentals of machine tool science: Lab work / Compiled by: VA Vanin, VKh Fidarov, VK Luchkin Tambov: Tambgos Technical University Publishing House, p. 5

16 Compiled by: Nikolai Ivanovich Nikiforov METHODS OF SELECTION OF REPLACEMENT GEARS Methodical instructions for performing laboratory and practical work in the course “Metal-cutting machines” and “Technological equipment” Edited by the author Templan 206 g, pos. 5K Signed for printing Format / 6 Sheet paper Offset printing Usl print l 0.93 Educational publication l 0.7 Circulation 00 copies Order Volgograd State Technical University, Volgograd, Lenina Ave., 28, building Printed in KTI, Kamyshin, Lenin St., 5 6

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A guitar is a mechanism with replaceable gears designed for stepwise changes in the gear ratio of the calculated kinematic chain. They are used mainly in rarely reconfigured circuits with a large range and number of gear ratios of the tuning element of the design circuit. These mechanisms are characterized by their simplicity of design. The main disadvantage of guitars is the complexity of tuning.

The machines use guitars with one, two and three pairs of replaceable gears. A guitar with one pair of replaceable gears (see Fig. 1.2) is used mainly in circuits that do not require precise tuning (tuning elements i v And i s). Guitars with two and three pairs of replaceable gears are used, as a rule, for precise tuning of kinematic chains (tuning elements i x, i y and so on.). In Fig. Figure 2.19 shows guitars with two and three pairs of interchangeable gears.

Guitar with two pairs of wheels (Fig. 2.19, A) consists of a plate 1, an axis 2, a fixing bolt 3 and replaceable gears a, b, c, d. Since the sum of the teeth of the engaged wheels is different for different settings, a groove is provided in the guitar plate that allows you to move the axis 2 and thus engage the replacement wheels c And d various diameters. Bolt 3 fixes the guitar plate in the required position for wheel traction A And V.

To select gears, use a single equation with four unknowns

Where i– gear ratio obtained from the FN; a, b, c, d- the number of teeth of the guitar wheels.

The number of solutions to equation (*) is limited by the following factors:

Available set of replaceable gears;

Adhesion conditions

a + b > c + (15…20) (**); from +d > to + (15…20) (***).

To select replacement gears, the following two methods are mainly used: main and additional.

Rice. 2.19. Guitar Replacement Gears: A– with two pairs

replaceable wheels; b– scan of a guitar with two pairs of interchangeable

wheels; V- guitar with three pairs of interchangeable wheels

Basic method– decomposition into prime factors. Used when i is expressed as a simple fraction, the numerator and denominator of which are decomposed into simple factors convenient for selecting wheels. For example,

Let us assume that the set of replaceable gear wheels of the machine contains wheels with numbers of teeth that are multiples of five from 20 to 100. Then,

We check the adhesion conditions (**) according to the permissible value

30 + 70 = 85 + 15.

It is possible that the gear wheel will cut the driven shaft (Fig. 2.19, b) and, therefore, mounting the wheels is impossible. Let's swap the wheels in the numerator or denominator. For example,

We check the adhesion conditions more acceptable value: (**) 85 + 70 > 30 + 20; (***) 30 + 65 > 70 + 20.

The adhesion conditions confirm the possibility of installing the selected replacement gears in the guitar.

Additional method- approximate selection. In this case, the method of continued fractions or, more often, the tabular method is used.

Let according to the setting formula i= 0, 309329. Using the tables (see, for example, M.V. Sandakov et al. Tables for selecting gears: Handbook. - 6th ed. M.: 1988. - 571 p.) we select the simple one corresponding to this decimal fraction fraction. After transformations we obtain the number of teeth of replacement wheels

Such gears are found in the normal set of replacement gears, such as gear hobbing machines. We check the adhesion conditions: (**) 21 + 65 > 45 + 20; (***) 45 + 47 > 65 + 20.

In a number of machines, for example gear hobbing machines, as a rule, a wider range of kinematic settings is provided. Therefore, such machines use guitars with three pairs of replaceable gears. In these guitars (Fig. 2. 19, V) an additional pair of gears is used, and its plate has two or three grooves for intermediate axes. To select gears, an equation with six unknowns is used

Gear wheels e And f change much less frequently than wheels a,b,c,d. As a rule, their gear ratio is constant and equal to 1; 1/2; 2. This allows for a given pair of wheels to use only four replaceable gears, for example with numbers of teeth 40, 60, 60, 80.

Wheels a, b, c, d are selected according to the rules for selecting wheels for a two-pair guitar, and one more thing is added to the adhesion conditions

e + f > d + (15…20)

For different groups of machines, the sets of replacement gears are different. However, all sets are created based on the general number of teeth of replacement wheels: 20 – 23 – 25 – 30 – 33 – 34 – 37 – 40 – 41 – 43 – 45 – 47 – 50 – 53 – 55 – 58 – 59 – 60 – 62 – 65 – 67 – 70 – 71 – 73 -75 – 79 – 80 - 83 – 85 – 89 – 90 – 92 – 95 – 97 – 98 – 100 – 105 – 113 – 115 – 120 – 127 - 44 wheels in total.

For screw-cutting lathes, a set of wheels is adopted, the number of teeth of which is a multiple of five (there are 22 wheels in a set).

The set of gears for gear cutting machines is limited to a wheel with 100 teeth. In backing machines, the set of wheels is similar to the general one, but it does not have a wheel with 113 teeth. For milling machines (for setting dividing heads), the set consists of wheels with the number of teeth: 25 – 25 – 30 – 35 – 40 – 50 – 55 – 60 – 70 – 80 – 90 – 100 (12 wheels in total).

With cone gears and ring gear (Norton cone).

II union wheel Z 0 can be alternately engaged with wheels mounted on the shaft I.

I- drive shaft; II- driven shaft

When moving the housing along the shaft II union wheel Z 0 can be alternately engaged with wheels mounted on the shaft I.

I- drive shaft;

II- driven shaft

The transmission of motion from the drive shaft to the driven shaft is carried out through a gear wheel 2 , rotating on a finger 5 lever 4 , Which can

rise or fall, thereby the wheel 2 or engages with the wheel 3 or disengages from it.

Flaws:

1. Low efficiency, because An intermediate link is constantly involved in the work.

2. More complex design.

3. Under the action of the expansion force arising in the gearing, the mechanism can open, so additional devices are required to fix the lever.

4. The mechanism is used to transmit small torques.

5. Low rigidity.

Used in screw-cutting lathes. Up to 12 gears can be placed in one row.

At TO transfer required K+2 wheels.

Guitar- a machine unit designed to change the feed speed. Interchangeable wheel guitars give you the ability to adjust the pitch to any degree of precision.

a, b, c, d- number of teeth of replacement wheels.