Deviation- algebraic difference between the size (limit or actual) and the corresponding nominal size.

To simplify the sizing in the drawings, instead of limiting dimensions, limit deviations are affixed: upper deviation- algebraic difference between the largest limit and nominal sizes; lower deviation - algebraic difference between the smallest limit and nominal sizes.

The upper deviation is indicated ES(Ecart Superieur) for holes and es- for shafts; the lower deviation is indicated El(Ecart Interieur) for holes and ei- for shafts.

According to definitions: for holes ES=D max -D; EI=Dmin-D; for shafts es=d max -d; ei= d mln -d

The peculiarity of deviations is that they always have a sign (+) or (-). In a particular case, one of the deviations can be equal to zero, i.e. one of the limiting dimensions may coincide with the nominal value.

admission size is called the difference between the largest and smallest limit sizes or the algebraic difference between the upper and lower deviations.

The tolerance is designated IT (International Tolerance) or T D - hole tolerance and T d - shaft tolerance.

According to the definition: hole tolerance T D =D max -D min ; shaft tolerance Td=d max -d min . Dimension tolerance is always a positive value.

The size tolerance expresses the spread of actual dimensions from the largest to the smallest limit dimensions, physically determines the amount of the officially permitted error of the actual size of the part element in the process of its manufacture.

Tolerance field is a field bounded by upper and lower deviations. The tolerance field is determined by the tolerance value and its position relative to the nominal size. With the same tolerance for the same nominal size, there may be different tolerance fields.

For a graphical representation of the tolerance fields, which makes it possible to understand the ratio of nominal and maximum dimensions, maximum deviations and tolerance, the concept of a zero line has been introduced.

Zero line the line corresponding to the nominal size is called, from which the maximum deviations of dimensions are plotted in the graphic representation of the tolerance fields. Positive deviations are laid up, and negative deviations are laid down from it (Fig. 1.4 and 1.5)

Rice. 1.5. Shaft tolerance fields layout

The smaller the tolerance, the more accurately the part element will be made. The larger the tolerance, the coarser the detail feature. But at the same time, the smaller the tolerance, the more difficult, more difficult and hence more expensive the production of an element of parts; the larger the tolerances, the easier and cheaper it is to manufacture a part element.

SURFACE ROUGHNESS.

BASIC CONCEPTS.

Surface roughness called a set of surface irregularities with relatively small steps, selected using the base length.

The considered microroughnesses are formed in the process of machining by copying the shape of cutting tools, plastic deformation of the surface layer of parts under the influence of the processing tool, its friction against the part, vibrations, etc.

The surface roughness of parts has a significant impact on wear resistance, fatigue strength, tightness and other performance properties.

Surface roughness in the form of a profilogram in fig. 1.44.

Rice. 1.44. Surface profilogram

To separate the surface roughness from other irregularities with relatively large steps (deviations in shape and waviness), it is considered within a limited area, the length of which is called the base length L. The base length L is normalized depending on the roughness parameters within the range: 0.01; 0.03; 0.08; 0.25; 0.8; 2.5; 8; 25, i.e. the more microroughness, the greater the base length.

The line on which the set of surface irregularities stands out is called the base line. The base line is a line of a given geometric shape, drawn in a certain way relative to the profile and used to evaluate the geometric parameters of surface irregularities. The appearance of this line depends on the surface type of the part element. Thus, the base line of the surface of the part element has the form of a nominal profile line and is located equidistantly from this profile.

The center line is used as a baseline for evaluating surface irregularities, which is the baseline for the profile deviation.

ROUGHNESS PARAMETERS.

1. Arithmetic mean profile deviation Ra- arithmetic mean of the absolute values ​​of profile deviations within the base length:

where l is the base length;

n is the number of selected profile points on the base length;

y is the distance between any point of the profile and the middle line (profile deviation).

2. Height of profile irregularities by ten points Rz- the sum of the average absolute values ​​of the heights of the five largest protrusions of the profile and the depths of the five largest depressions of the profile within the base length:

or

where H imax , H imin are determined relative to the midline;

h jmax , h imin - relative to an arbitrary straight line parallel to the midline and not intersecting the profile.

3. The greatest height of the profile irregularities R max - distance between the line
protrusions of the profile and a line of profile depressions within the base length.

4. Average step of profile irregularities S m - arithmetic mean
step of profile irregularities within the base length:

where S mi is the pitch of the profile irregularities, equal to the length of the midline segment enclosed between the intersection points of adjacent protrusions and depressions of the profile with the midline.

5. The average step of profile irregularities along the vertices S- average
the value of the profile roughness step along the vertices within the base length:

where S i is the pitch of the profile irregularities, equal to the length of the midline segment enclosed between the projections onto it of the highest points of two adjacent local protrusions of the profile.

6. Relative profile reference length t p - the ratio of the reference length of the profile to the base length:

where hp - profile reference length- the sum of the lengths of the segments cut off at a given level in the profile material by a line equidistant to the midline t within the base length.

Of the listed roughness parameters, the most commonly used parameters are Ra and Rz. The parameter Ra is preferred, since it is determined from a significantly larger number of profile points than Rz. The use of the Rz parameter as a control is largely determined by the methods of measuring the parameters in question. Ra values ​​are preferably measured using instruments equipped with diamond needle probes. The determination of Ra on rough surfaces is associated with the risk of breakage of the diamond needle, and on very smooth surfaces - with low reliability of the results due to the fact that the radius of the end of the needle cannot fix very small irregularities. Therefore, it is recommended to use Rz for uneven heights of 320 ... 10 and 0.1 ... 0.025 µm, in other cases - Ra.

When calculating critical movable and press joints, it is necessary to take into account the parameter Rz, while in the drawings, in most cases, Ra values ​​are specified. In these cases, you can use the dependency

Where K=4 at R a =80...2.5 µm; K=5 at Ra=1.25…0.02 µm.

Table 1.3 Correspondence of the numerical values ​​of Ra, Rz, Rmax with the numerical values ​​of the base length

For rubbing surfaces of critical parts, the parameters Ra (or Rz), t p are assigned and the direction of irregularities is set, for surfaces of cyclically loaded parts - R max , S m (or S) and the direction of irregularities, for interference connections - only Ra (Rz). For non-critical parts, you can not specify the roughness parameters, in which case it is not subject to control.

Table 1.4 Types of direction of roughness roughness.

ON THE DRAWINGS.

The designation of roughness in the drawings establishes the designations of surface roughness and the rules for applying them to product drawings.

Three signs are used in the designation of roughness:

When designating roughness only by parameter, a sign without a shelf is used.

The values ​​of all roughness parameters are indicated after the corresponding symbol, and the height parameters Ra, Rz, Rmax are indicated in micrometers, the step parameters Sm, S - in millimeters, the shape parameter t p - in percent.

1. Signs indicating the requirements for surface irregularities - roughness, are located (Fig. 1.46):

a) on the contour lines of the detail elements,

b) on extension lines, while being as close as possible to the dimension line,

c) on the shelves of lines - callouts,

d) on dimension lines or on their extensions with a lack of space, while it is allowed to break the extension line.

2. Signs indicating the requirements for roughness and having a shelf should be located relative to the main inscription of the drawing (stamp), as
shown in fig. 1.47.

4. If the requirements for surface irregularities are the same for all elements of the part, then the roughness mark is applied once and placed in the upper right corner of the drawing, and not applied to the surface of the elements of the part (Fig. 1.48).

This means that surfaces on which the requirement for roughness is not indicated are not processed at all according to this drawing, i.e. these surfaces will have irregularities that the workpiece has.

The signs that indicate the requirements for roughness and placed in the upper right corner of the drawing should have dimensions and line thickness approximately 1.5 times greater than the signs applied directly to the surface of the part,

Rice. 1.50

6. When the surface of a part element has little space for placing a sign, it is allowed to apply a simplified designation to surface irregularities (Fig. 1.) with an explanation of this designation in the technical requirements on the drawing of the part.

7. When the surface of the part is a contour, for example, a polyhedral figure, and the requirements for surface irregularities must be the same, then the roughness mark is applied once.

THREADED CONNECTIONS.

BASIC CONCEPTS AND CLASSIFICATION OF THREAD.

A threaded connection is a connection of two parts using a thread, i.e. elements of parts that have one or more evenly spaced helical protrusions of a thread of constant cross section formed on the side surface of a cylinder or cone.

The contour of the section of grooves and protrusions in a plane passing through the axis of the thread, common to external and internal threads, is called the thread profile.

Thread classification.

A variety of conditions for the use of threads led to the diversity of their types in terms of design features and purpose.

Depending on the shape of the surface on which the threads are formed:

Cylindrical; - conical threads;

According to the profile of the section (i.e., from the type of figure in the section), the threads are divided into:

Rice. 1.51.

Triangular (Fig. 1.51 a)

Trapezoidal (Fig. 1.51 b)

Sawtooth (Fig. 1.51 c)

Round (Fig. 1.51 d)

Rectangular (Fig. 1.51 e)

by the number of visits:

Single start; - multiple

in the direction of the turns:

Right; - left;

by the unit of measurement of linear quantities

For metric; - inch.

By appointment, the threads are divided into general-purpose threads and special threads.

TO general purpose include fastening, kinematic, pipe and reinforcement.

Mounting threads used for detachable fixed connections of machine parts. Their main purpose is to ensure the strength of the joints and maintain the density (non-opening) of the joint during operation.

Kinematic threads used for movable joints in screw-nut type gears (lead screws and screws of calipers of metal-cutting machines, screws of measuring instruments, screws of presses, jacks, etc.).

Pipe and rebar threads, having a triangular profile, are used for pipelines and fittings with the main purpose of ensuring the tightness of joints.

To threads special purpose include those that are used only in certain products of some industries (for example, threads for sockets and sockets of electric lamps, backlash-free threads in the lead screws of jig boring machines, etc.).

General requirements are complete interchangeability, those. ensuring unconditional make-up of parts forming a threaded connection during their independent manufacture without fitting or selection, and reliable performance of the prescribed operational functions.

METRIC THREADS.

The basics of this system of tolerances and fits, including degrees of accuracy, accuracy classes of threads, standardization of make-up lengths, methods for calculating tolerances for individual thread parameters, designation of accuracy and fit of metric threads in drawings, control of metric threads and other issues.

Degrees of accuracy and accuracy classes of threads.

Metric thread is defined by five parameters: average, outer and inner diameters, pitch and angle of the thread profile.

Tolerances are assigned only for two parameters of the external thread (bolt); medium and outer diameters and for two parameters of internal thread (nuts); medium and inner diameters. For these parameters for metric threads, the degrees of accuracy are 3 ... 10 (Table 1.5).

Table 1.5. Degrees of accuracy of external and internal thread diameters.

In accordance with established practice, the degrees of accuracy are grouped into 3 accuracy classes:

precise (3-5 degree of accuracy),

medium (5-7 degree of accuracy),

rude. (7-9 degree of accuracy),

The concept of accuracy class is conditional. When assigning degrees of accuracy to the accuracy class, the length of the make-up is taken into account, since in manufacturing the difficulty of ensuring the specified accuracy of the thread depends on the length of the make-up that it has.

Installed three groups of make-up lengths:

S - short ( less than normal)

N - normal ( make-up lengths from 2.24Pd 0.2 mm to 6.7Pd 0.2 mm),

L - long(more than normal).

WHEELS AND GEARS.

Each of the groups according to the operational purpose is characterized by its main indicator of accuracy. Yes, for counting gears the main accuracy requirement is kinematic accuracy; for high-speed - smoothness of work; for heavy-duty slow-moving- fullness of contact teeth; for reverse(especially reference) - limiting the magnitude and fluctuations of the side clearance.

Taking into account the operating conditions in the standards for tolerances for gear and worm gears, accuracy standards are established:

- kinematic accuracy,

- smoothness of work;

- tooth contact;

- side clearance.

According to the accuracy of manufacturing, all gears and gears are divided into 12 degrees.

Transmission smoothness

This transmission characteristic is determined by the parameters, the errors of which appear repeatedly (cyclically) per revolution of the gear wheel.

The cyclic nature of the errors that disturb the smooth operation of the transmission, and the possibility of harmonic analysis, made it possible to determine and normalize these errors according to the spectrum of the kinematic error.

Under the cyclic transmission error f zkor(Fig. 1.72, but) And gear wheel f zkr(Fig. 1.72, b) understand the doubled amplitude of the harmonic component of the kinematic error, respectively, of the transmission or wheel. To limit the cyclic error, tolerances are set:

□ fzok- on the cyclic transmission error;

□ fzk- on the cyclic error of the gear.

Rice. 1.73

To limit the cyclic error with a repetition rate equal to the frequency of engagement of the teeth fzzor And f zzr tolerances for the cyclic error of the tooth frequency in the gear were established fzzo And f zz . These tolerances depend on the frequency of the cyclic error (equal to the number of teeth of the wheels z), the degree of accuracy, the coefficient of axial overlap ε β and the modulus T.

Rationing of dimensional accuracy in mechanical engineering

Basic concepts of sizes, deviations and fits

The creators of mechanisms and machines, based on the purpose of the parts, on the basis of calculations of a different nature and the results of experimental studies, determine the geometric parameters of the elements of the parts. The degree of possible, from the point of view of the performance of each part, deviations of its geometric parameters from the given ones is determined by the designer. Naturally, some elements of parts need to be performed more accurately than others in accordance with their purpose.

At the same time, it is known that it is impossible to manufacture the geometric elements of a part with absolute accuracy due to a number of reasons inherent in any technological process.

1. Size - numerical value of a linear quantity (diameter, length, etc.) in the selected units of measurement. In other words, the size of a detail element is the distance between two characteristic points of this element.

2. The size of the element, established by the measurement with a permissible error, is called actual size . The actual size is determined experimentally (by measurement) with an allowable error, which is determined by any regulatory documents. The actual size is found in cases where it is required to determine the conformity of the dimensions of the elements of the part with the established requirements. When such requirements are not established and measurements are not carried out for the purpose of accepting products, it is possible to use the term measured size, i.e., the size obtained as a result of measurements.

3. true size - the size obtained as a result of manufacturing and the value of which we do not know, although it exists. We are approaching the value of the true size as the accuracy of measurements increases, therefore the concept of "true size" is often replaced by the concept of "actual size", which is close to the true one under the conditions of the goal.

4. Nominal size - the size relative to which deviations are determined. For the parts that make up the connection, the nominal size is common to the hole and the shaft. The nominal size is determined by the designer as a result of calculations for strength, stiffness, when determining dimensions, etc. or taking into account design and technological considerations. This size is indicated on the drawing.

5. Taking into account the processing error, the constructor specifies not one size, but two maximum allowable sizes of the element, between which the actual size must be (or be equal to). These two sizes are called the largest size limit (the largest allowable size of a part element) and the smallest size limit (the smallest allowable size of a part element). The difference between the largest and smallest limit sizes is called the processing tolerance or tolerance, denoted by T d:

;

.

Tolerance is an essentially positive value, it cannot be negative. This is the interval of dimension values ​​between which the size of a valid part element must lie.

; .

Therefore, the tolerance shows, as it were, the permitted processing error, foreseen in advance and reflected in the drawing of the part. In this case, suitable and interchangeable parts will be those in which the size obtained after processing is within tolerance.

The smaller the tolerance, the more accurately the normalized element of the part must be made and the more difficult, more complex and therefore more expensive its manufacture. The larger the tolerance, the rougher the requirements for the element of the part and the easier and cheaper it is to manufacture.

Thus, to establish (normalize) the accuracy of a size means to indicate its two possible (permissible) limit values.

The correctness of obtaining dimensions during processing is checked by measuring them.

To measure a size means to compare its value with a value taken as a unit (for linear dimensions, the unit of measurement is a meter).

All instruments and devices used for measurements have a common name - measuring instruments. Measurement errors are possible, and therefore it is impossible to accurately determine the size of the part.

Measurement error is the deviation of the measurement result from the true value of the measured quantity. The measurement error can be caused by: errors introduced by the installation measures and samples; inaccuracies of the SI or deterioration of its individual parts; temperature influences; errors related to the experience and skills of the person who takes the measurement, etc.

State educational institution of higher professional education

"TYUMEN STATE OIL AND GAS UNIVERSITY"

TECHNOLOGICAL INSTITUTE

DEPARTMENT "ENGINEERING TECHNOLOGY"

Test

Standardization of accuracy, tolerances and fit

Option number 16

Tyumen2010

Task#1

Given: Ш77, for the nominal size, build the location of the tolerance fields of three types of connections.

Determine and indicate on the diagram the value of the maximum deviations of dimensions, gaps and interference. Determine: tolerances, fits and within what limits the actual size of a suitable part can be.

one). Ш77Н8 ES=+0.046 mm

Ш77 d7 es= -0.100 mm

Limit dimensions:

Landing with clearance

for shaft from Ø76.900 to Ø76.870mm

2). Ш77Н8 ES=+0.046 mm

Ш77 n7 es= +0.050 mm

Limit dimensions:

landing transitional

clearance and tension

Actual dimensions of a suitable part:

for hole from Ø77.046 to Ø77.0mm

for shaft from Ш77.020 to Ш77.050mm

3). Ш77Н8 ES=+0.046 mm

Ш77 s7 es= +0.089 mm

Limit dimensions:

Interference landing

Actual dimensions of a suitable part:

for hole from Ø77.046 to Ø77.0mm

for shaft from Ø77.059 to Ø77.089mm

Task number 2

Given: type of keyed connection - C (free), shaft diameter Ш77

one). Choose the dimensions of the feather key:

22 x 14, length range from 63 to 250 mm

9mm shaft groove depth

5.4mm Groove Depth in Sleeve

2). We select the tolerance fields for the key and for the grooves, depending on the nature of the key connection:

for the key - 22h9 x 14h11 x 100h14

keyway width on the shaft - 22H9

groove width in the sleeve - 22D10

3). Key connection sketch

4). The layout of the tolerance fields of the key connection

five). Key designation:

2-22h9 x 14h11 x100h14 GOST23360-78

Task number 3

Given: spline connection 6x11x14, bushing hardened.

one). We accept the method of centering the spline connection - centering on the inner diameter of the bushing d.

2). We find from the table the width of the tooth - b = 3 mm.

For size d = 11

For size b= 3

4). Sketch of spline connection:

five). The layout of the tolerance fields of the spline connection

6). Symbol for spline connection

d - 6 x 11 x 14 x 3

Similar abstracts:

Interchangeability, standardization and technical measurements

Tolerances and fits of cylindrical joints.

Rationing of accuracy in mechanical engineering

Tolerances and fits of smooth cylindrical mates and gauges for controlling their joints. Selection of rolling bearing fits. The concept of roughness, deviation of the shape and location of surfaces. Straight-sided and involute splined and keyed connection.

Metrology calculation of typical connections

Choice of fit for connection with gap depending on diameter and speed of rotation. Calculation of fit for a sleeve pressed into the body. Calculation of a threaded connection, determination of the executive dimensions of gauges. Selection of rolling bearing fits.

Rationing of the main parts and assemblies

Features of the calculation and selection of landings. Rationing of the accuracy of bolted and studded connections, the accuracy of the diametrical size of the bushing and shaft at normal temperature. Determination of landings under bearings, key connections. Calculation of the dimensional chain.

Calculation of the elements of the feed mechanism of a metal-cutting machine

Calculation of smooth cylindrical joints of the metal-cutting machine feed mechanism. Method for determining calibers to control the details of the connection. Selection and calculation of rolling bearings, threaded and keyed connections. Drawing up a diagram of a dimensional chain.

Calculations of means of technical measurements and control

Determination of interface elements, conditional designation of landings and qualifications in the drawings and calculation of calibers. Selection of clearance fits for fluid friction bearings. Calculation of tolerances and landings of keyed connections. Selection of parts for rolling bearings.

Interchangeability, tolerances and fits

Features of the choice of tolerance and fit for smooth cylindrical joints, the choice of tolerance fields for parts mating with rolling bearings. The choice of tolerances and landings of keyed, splined connections. Calculation of dimensional tolerances of a given dimensional chain.

Determining the parameters of the main typical connections

Method for calculating the parameters of interfaces: smooth cylindrical, threaded, keyed and splined connections. Construction of schemes for the location of tolerance fields for parts and their interfaces in accordance with the requirements of the Unified System for Design Documentation.

Smooth cylindrical connection. Determination of elements of connections subjected to selective assembly

Basic parameters of a smooth cylindrical connection. Group tolerances of shaft and hole. Compiling a sorter map. Calculation and selection of tolerance fields for parts mating with rolling bearings. Tolerances and fit of keyed and splined connections.

Calculations of machine parts

Selection of fittings for smooth cylindrical joints, for keyed joints, for splined joints with a straight tooth profile. Calculation of the dimensions of the parts of the bearing unit, limit and average interference and clearances. Check for radial clearance.

Metrology, interchangeability, standardization, certification

Justification, appointment and analysis of fits for typical connections of machine parts of a given assembly unit, their calculation. Calculation of the executive dimensions of the caliber-bracket and the caliber-cork. Execution of working drawings of the shaft and gear.

Features of the choice of landings for smooth cylindrical and keyed joints of a gearbox used to reduce engine speed and increase torque. Methodology for calculating the dimensional chain by the method of complete interchangeability and the probabilistic method.

Matings with clearance and interference

Landing characteristics with clearance and interference, upper and lower deviations, largest and smallest limit dimensions, clearance and interference tolerance. Locations of tolerance fields for mates. Designation of limit deviations on the assembly and working drawings.

Selection and calculation of landings of typical connections

Calculation of a smooth cylindrical connection 2 - gear - shaft. Calculation of gauges for the control of smooth cylindrical joints. Choice of normal geometric accuracy. Determination of bearing connection, landings of keyed and splined connections.

Analysis of the quality of engineering products

Calculation and selection of an interference fit for connecting a gear to a shaft. Analysis of the resulting fit and construction of a tolerance field layout. Designation of fit of the connection and tolerance fields of mating parts, correction to the calculated interference.

Calculation, selection and justification of landing connections

Standardization and unification of parts and assembly units: speeding up and reducing the cost of designing, manufacturing, operating and repairing machines. The choice of landings for smooth cylindrical mates, keyed and splined joints, rolling bearings.

Calculation, selection and justification of landings of gearbox connections

The choice of landings for smooth cylindrical joints located on a low-speed shaft, the rationale for choosing a system and qualifications. Calculation and selection of interference fit. The solution of linear dimensional chains by the method of complete interchangeability and the probabilistic method.

Drawing up schemes for the location of tolerance fields of standard mates. Calculation of the connection of a rolling bearing with a shaft and a housing. Calculation of dimensional chains

Schemes of location of tolerance fields of standard mates. The connection of the rolling bearing with the shaft and housing. Calculation of dimensional chains. Solving the problem by the maximum-minimum method. Solution of the problem by the probabilistic method (method of equal qualifications).

Landings and tolerances

Calculations of calibers and counter-calibers of bearing ring fits, dimensional control and calculation for the probability of gaps. Parameters of a spur gear and calculation of the dimensional chain of a given master link. Dimensions and limit deviations of connections.

Tolerances and landings

Deciphering the landing by lettering or other parameters. Designation of a system in which a hole and a shaft are designated. The letter designation of the dimensions of the shaft and hole. Calculation of the maximum size of the shaft and hole S (N) max and min fit tolerance.

Send your good work in the knowledge base is simple. Use the form below

Students, graduate students, young scientists who use the knowledge base in their studies and work will be very grateful to you.

Federal Agency for Education

Siberian State Aerospaceuniversitythem. Academician M.F.Reshetnev

Department of UKS

Course work on the course

« Rationing of accuracy in mechanical engineering»

Option number 14

Completed: student

Checked by teacher:

Krevina T.E.

Krasnoyarsk 2008

• Introduction 3
• 4
• 1.1 Rationing of interference fits 4
• 1.2 transitional landings 7
• 11
• 3. Selection of landings for spline connection 15
• 4. Serrated connections 18
• 5. Calculation of dimensional chains 21
• 5.1 Calculation by the method of complete interchangeability 21
• 5 .2 24
• References 28

Introduction

Mechanical engineering is the most important leading branch of industry. But mechanical engineering plays an equally important role in other areas such as science, culture, education, public utilities and housing. Mankind is growing and developing, thereby giving food for the development of mechanical engineering and expanding its range. The main emphasis today is on electrification, as well as mechanization and automation of production and labor, in general, everything is done to facilitate the physical labor of a person.

Course work on the course "Rationing of accuracy in mechanical engineering" is the first independent design work of the student. Course work allows you to consolidate the theoretical provisions of the course, presented in lectures, instills the skills to use reference material, ESKD standards, introduces students to the main types of calculations.

An important place in the course work is occupied by issues related to ensuring the accuracy of interchangeable parts of assembly units. The accuracy standards for the interchangeability of joints of all types are regulated by a unified system of tolerances and fits (ESDP).

The purpose of the course work is to instill the skills of assigning the accuracy of parts and assemblies and the skills of designating it on the drawings.

When performing the course work, the main standards for tolerances and landings of typical mates are worked out, issues of dimensional control and technical requirements are touched upon.

1. Smooth cylindrical joints

1. 1 Rationing of landings with an interference fit

Nominal connection diameter, mm……………………………..75;

Maximum limit tightness N max р, micron………………………80;

Minimum limit tightness N min p , µm………………………..60.

The calculated nominal diameter d = 75 mm corresponds to the Ra40 series and does not need to be rounded off.

We determine the average tightness of the limit tightness given in the problem:

where N max p and N min p are the calculated limit interference data in the task, microns.

According to the average tightness, we select the fit in any system (shaft system or hole system) according to Table 5 and write out the tabular tightness N max T \u003d 72 microns and N min T \u003d 40 microns of the selected fit.

where N max T and N min T - tabular limit interference, microns.

The tabular average tightness is close to the calculated one and the fit in the hole system corresponds to it

We find deviations for the tolerance fields of the hole and shaft according to tables 6,9,14.

We write down the combined landing designation with deviations

We build the layout of the tolerance fields of the selected fit. Specify tension. Deviations on the tolerance diagram are put down in micrometers.

Fig.1 . Tolerance fields for interference fit

We calculate the maximum and minimum tightness (check) for the selected fit, according to the scheme of tolerance fields according to the formulas:

where ES, es, EI, ei- upper and lower deviations of the hole and shaft, respectively.

The obtained limit interferences coincide with the tabular limit interferences.

Define shaft tolerance and hole tolerance:

The fit is chosen so that if the tolerances of the shaft and the hole are not the same, the tolerance at the hole is greater.

Rice. 2 . Connection sketch

TN \u003d TD + Td \u003d N max -N min \u003d 72-40 \u003d 32

Connection immobility under load is not guaranteed.

1. 2 Transitional settlementski

Given:

Rated di connection diameter ……………………………… 209 mm;

Maximum limit interference N nb ……………………………40 µm;

Maximum limit clearance S nb ………………….……........ 14 µm

Solution:

1) Round the specified connection diameter to a value of 210 mm, corresponding to the Ra40 series according to GOST 6636-69

2) Tabular values ​​of transitional landings:

N nm = - S nb N nb =40 µm N nm = -14 µm

These values ​​correspond to the fit in the shaft system

3) Limit deviations of the hole and shaft:

210

210h5

4) The layout of the tolerance fields in the landing:

S nb \u003d ES - ei S nb \u003d -8 - (-20) \u003d 12 microns

S nm = EI - es S nm = -37 - 0 = - 37 µm

S nm = - N nb N nb = 37 µm

The table values ​​of the gap and preload are the same as the specified ones

Rice. 3 . Tolerance fields for transitional fit

5) Full landing designation:

6) Transition fit tolerance:

T(S,N) = TD + Td

T(S,N) = (-0.008-(-0.037))+(0-(-0.02)) = 0.029+0.02 = 0.049 µm

7) The tolerance of the hole is greater than the tolerance of the shaft, which means that the hole is made less accurately than the shaft.

9) Calculations for building a Gaussian curve:

a) landing standard deviation:

b) zone of dispersion of gaps of tensions and maximum ordinate:

c) relative deviation:

true ordinate deviation with zero clearance

d) the probable number of mates with a gap:

e) probable number of interfacing with interference:

10) Gaussian Curve:

On the y-axis, we plot the number of conjugations, i.e. number of landings.

On the x-axis - dispersion of gaps or interference. On this curve, the center of the landing grouping corresponds to the center of the landing N cf.

Rice. 4 . Gaus curve

On distance X=12.5 µm from the center of grouping is the ordinate corresponding to zero tightness (clearance). Let us agree to count this ordinate to the left of the grouping center when the transition fit has an average clearance and to the right with an interference fit. The entire area under the curve, bounded along the ordinate by the scattering interval R, corresponds to the total number of mates of a given fit, i.e. the probability is from 1 to 100%. The probability of occurrence of mates with interference corresponds to the shaded area on the left, with a gap - shaded on the right.

2. Calculation of landings for rolling bearings

Given:

Bearing 97516, accuracy class 60, inner ring rotating, radial load 30,000 N, moderate, low vibration, axial load 10,000 N, =0.6

Solution:

1) Bearing type: tapered ball bearing, double row, light series.

Dimensions: d=80mm, D=140mm, T=80mm,

The inner ring rotates, therefore, it is circulation-loaded.

2) The shaft is solid, the body is thin-walled, as the ratios are indicated

3) Radial load intensity:

a) R=30000 N, radial load

b) b=0.08 m, ring width

c) -coefficient depending on the nature of the load. =1

d) - coefficient taking into account the weakening of the fit interference with a hollow shaft or thin-walled housing. =1.1, since the problem contains a solid shaft and a thin-walled body. e) is the coefficient of uneven distribution of the radial load R between the rows of rollers in double-row bearings. To find, we calculate the expression

, then =2

e) calculate:

4) Tolerance field for the mounting hole:

The load of 825 and the diameter of the outer ring D=140 mm corresponds to the tolerance field G. Since, according to the condition, the accuracy class of the bearing is 6, then the quality for the hole in the housing is 7, then we write G7

5) Tolerance field for circulation-loaded inner ring:

Shaft diameter 80mm corresponds to k6 shaft fit

6) Deviations for the tolerance fields of the landing hole:

ES=+54; EI= 14 µm

7) Deviations for a circulation-loaded ring:

es=21; ei=2 µm

8) Deviations for the tolerance fields of the inner and outer rings of the rolling bearing:

For inner ring: ES=0; EI= -15µm

For outer ring: es=0; ei= -12 µm

10) Fit for inner ring-shaft connection:

80, where L0 is the tolerance field of the inner ring (0 is the designation of the accuracy class)

11) Fit for body bore - outer ring connection: 140, where l 0-tolerance field of the outer ring (0-class accuracy)

12) The layout of the tolerance fields of the connection "shaft - inner ring":

13) The layout of the tolerance fields of the connection "hole in the body - the outer ring":

Since, the body will not rotate.

14) Sketch of the housing and shaft for the rolling bearing:

3. Choice nprecipitate for spline connection

Determine the type of centering, accuracy and nature of mating for a spline connection.

Build a layout of tolerance fields indicating deviations, determine the maximum dimensions of all interface elements.

1) Number of splines Z=10, inner diameter d=72, outer diameter D=82

2) Tooth (spline) width b=12mm, smallest inner diameter d 1 \u003d 67.4 mm, the series is medium.

3) Type of centering: centering on b (tooth flanks)

4) According to the table. 3.1 looking for a fit for the centering parameter b .

Since the connection is movable, we choose a fit with a gap

5) For non-centering diameters d and D choose landing 5, according to the table. 3.4.] For D - , for inner diameter d: for sleeve H 11, and for the shaft we find the tolerance d - d 1.

6). Let's find the deviations for all parameters, using the table. 6, 7, 12.

for H 12ES = +350 micron ; EI= 0 (D=82 mm)

forH 11 ES =+ 190 micron , EI= 0 (d=72 mm);

for F8 ES = +43 micron ; EI= +16 (b =12 mm)

for f 87 es = - 16 micron ; ei = - 43 micron (b =12 mm);

fora11 es = -380 micron ; ei = -600 micron (D = 82 mm);

for the inner diameter of the shaft we findd - d 1 \u003d 72- 67.4 \u003d 4.6 mm = 4600 microns.

7) We build the layout of the tolerance fields:

8) Let's write down the symbol of the spline connection given in the problem with the corresponding landings.

where b - type of centering; 10 - number of teeth; 72 - internal diameter of the connection. Landing in the designation is not affixed, since there is no tolerance field in the denominator; 82 - outer diameter of the connection;

Fit for the outside diameter of the connection; 12 - tooth width (splines);

Fit for slot width.

Let's write the designations for the splined shaft and the splined sleeve separately

Sleeve designation

In this designation, the inner diameter d = 72 mm bushing tolerance field H 11.

Shaft designation.

4. Serrated connections

Type of gears - cylindrical, spur, uncorrected. Parameters : m =4, Z 1 = 60, Z 2=35. Appointment - aircraft wheels.

1. According to the purpose of the gear train, we determine that the contact of the teeth and the backlash are a group of indicators of smooth operation, which is of the greatest importance for this gear (see subsection 4.1 3).

2. Determine the degree of accuracy for the selected group of indicators according to Table. 24 5. From the same table, write out the circumferential speed.

The degree of accuracy for the smoothness group is 6, the circumferential speed is 15 m/s.

3. In this problem, for the groups of accuracy and contact of the teeth, we assign the same degrees of accuracy one lower than for the smoothness group, i.e., the degree of accuracy is 7.

4. Based on the circumferential speed, we determine the type of conjugation, given that the smallest side clearance is assigned to low-speed gears, and the largest - to high-speed gears.

In this task, the transmission is high-speed, since the speed is 15 m/s , Therefore, we choose the type of conjugation B

5. Using the table. 4.1, assign a tolerance for side clearance and indicate the deviation class of the center distance.

Lateral clearance tolerance -b, center distance deviation class -V.

6. Let's write down the designation of the accuracy of the spur gear:

7-7-6 B GOST 1643-81,

where 7 - the degree of accuracy of the contact of the teeth of indicators; 7 - degree of accuracy of the accuracy group; 6 - degree of accuracy of the smoothness group; B - type of conjugation; b- tolerance for side clearance.

7. For one group of smoothness indicators, which is of the greatest importance for a given transmission, we determine the normalized indicators. We write out the indicators according to tables 28 and 29 1. For this, it is necessary to calculate the pitch diameters of the two data in the wheel problem d 1 and d 2 ,width of each gear b 1 and b 2 , transmission center distance a w . We set the width of the gear rim equal to 1/3 of the pitch diameter.

According to the table 28 5 determine the total contact patch along the height and length of the tooth, tolerances for parallelism f, axle misalignment f y and tooth tension F .

The total contact spot for the 6th degree of accuracy is not less than 50 for the height of the teeth, and not less than 70 for the length of the teeth.

To determine the following indicators, we calculate the pitch diameters d 1 And d 2 .

d 1 = mz 1 = 4 60= 240mm ;

d 2 = mz 2 = 4 35 = 140 mm

Gear ring width

b 1 = 1/3d 1 ;

b 2 = 1/3d 2 ;

b 1 = 80 mm ;

b 2 = 46,6 mm,

For the 6th degree of accuracy f x 1 = 12 micron, f x 2 = 12 µm f y 1 = 6.3 µm; f y 2 = 6.3 µm

F 1 = 10 micron, F 2 = 10 µm.

According to the table 29 5 write out the values ​​of the guaranteed side clearance j n min and deviations of center distance f a. To do this, we calculate the center distance.

Type of conjugation IN, center distance class V, its value equal to 190mm, center distance deviation f a = ± 90 µm, corresponds to the guaranteed side clearance j n min = 185 µm.

Operation smoothness standards: kinematic error µm, tolerance for profile error µm, pitch deviations µm.

5 .Calculation of dimensional chains

5 .1 Paymentmefull interchangeability method

Given:

;; ; ; ; ; ;

Solution:

1) Nominal size of master link:

,

where is A? - closing link, A I B - increasing size, A I UM - decreasing size, m- the number of increasing links, n - the number of constituent links.

Table 1

2) Average Accuracy Ratio a:

where TA is the tolerance of the closing link; I- tolerance unit; n- the number of constituent links.

For this task i 1 =i 2 =1.31µm; i 3 = 1.56 µm; i 4 \u003d i 5 \u003d 1.31, i 6 =1.86µm; i 7 = 2.17 µm; i 8 = 3.23 µm.

3) Tolerance units for size intervals are entered in the table

4) Accuracy grade 7

5) The values ​​​​of the tolerances of the constituent links according to the quality and size are entered in the table

6) Tolerance check:

; µm;

The sum of the tolerances of the constituent links is less than the tolerance of the closing link, therefore, an adjustment is necessary.

In this case (when? TA i < ТА?) рекомендуется провести корректировку следующим образом. Поскольку вычисленное значение среднего коэффициента but was between 7 and 8 qualifications, then part of the tolerances can be taken according to 8 qualifications and thus increased? TA i to the required value.

For example, let's assign tolerances for dimensions A 6 according to the 8th grade (see Table 5.4).

In this case, TA 6 = 46, then? TA i = 238 µm.

?TA i < ТА? на 0.8 % , что находится в пределах допустимого.

7) The dimensions of the reducing links with deviations are entered in the table. Since dimensions from to are covered, we assign deviations as for shafts.

8) Dimensions of the increasing link:

We will consider the deviation of the closing link to be symmetrical, that is

;

;

5 .2 Calculation by the theoretical and probabilistic method

Draw a diagram of the dimensional chain with the designation of increasing and decreasing sizes. To do this, analyze and identify decreasing and increasing sizes.

Nominal dimensions, mm: ;; ; ; ; ; ; .

Distribution laws A 1 =3; A 2 =3; A 3 =2; A 4 =2; A 5 =1; A 6 =1; A 7 =1; And 8 \u003d 1.

Closing link tolerance TA = 240 µm.

1) We compile a table in which we enter the dimensions of the links and the numerical values ​​​​of the units of tolerance of the constituent links

table 2 .

2) The average accuracy coefficient is calculated by the formula

where is the average accuracy factor;

TA - tolerance of the closing link;

The coefficient corresponding to the law of distribution;

Tolerance unit.

1-for the law of normal distribution;

2-for the law of equal probability;

3 for the triangle law.

3) The denominator of the expression for but will look like this:

Substituting the tolerance values, we get

4) According to the average coefficient of accuracy but we find the quality (see table 5.3 3). We choose 9 qualifications.

5) According to the quality and dimensions of the links, we find the tolerances for the component dimensions (Table 5.4 3) and enter them in the table.

6) We check according to the formula

The sum of the tolerances of the constituent links may be less than the tolerance of the closing link by 5 ... 6%, which is not fulfilled under these conditions.

We are making adjustments. To do this, we assign tolerances for the 13th grade to the dimensions A 4, A 5 and put down the values ​​​​of these tolerances in the table. We check again.

The check showed compliance with the condition.

7) We put down the dimensions with deviations in table 2 (except for the increasing link), using the following rule: we assign deviations for all covered dimensions (as for shafts) with tolerances of "minus". These are the dimensions A 1 ... A 7

Deviations for the increasing link A8, we count. To do this, we determine the average deviations for decreasing sizes from A1 to A7:

where? from A - the average deviation of the size; ES A i, - upper limit deviation of the size; EI A i, - lower limit deviation of the size.

The calculation is carried out taking into account the signs of deviations in microns:

8) For the closing link (A?), let's set the upper deviation equal to the tolerance, and the lower one - equal to 0. ES A? =TA? = 1300 µm; EI A? = 0. Then the average deviation for the closing link

The average deviation for the increasing size A 8 is found by the equation

where c Ay m . - the sum of the average deviations of the reducing links;

c A y m \u003d (- 75) * 2 + (- 125) + (-230) * 2 + (- 175) + (-200) \u003d -1110 microns;

c A 8 = - 1110 + 650 = - 460 µm.

9) The upper and lower deviations for the increasing size A 8 are determined from the following equations:

E S A8= c A8 + 1/2TA8; EI A8= c A8 - 1/2TA8 .

Take the tabular tolerance for A 8 according to table 2. Then

the calculated values ​​of the deviations of the link will be:

ES A 8 \u003d - 460 + 1/2570 \u003d -175 microns; EI A 8 \u003d - 460 - 1/2570 \u003d - 745 microns.

Let's write down the size A 8 with the calculated deviations in table 2.

Tolerances calculated by the method of complete interchangeability are less stringent, i.e., the accuracy is lower than when calculating by the probabilistic method.

Bibliography

1. Tolerances and landings: Handbook: At 2 pm / M.A. Paley, A.B. Romanov, V.A. Braginsky. -8th ed., revised. and additional - St. Petersburg: Mashinostroenie, 2001. - Part 1.

2. Tolerances and landings: Handbook: At 2 pm / V.D. Myagkov, M.A. Paley, A.B. Romanov, V.A. Braginsky. -8th ed., revised. and additional - St. Petersburg: Mashinostroenie, 2001. - Part 2.

3. Metrology, standardization and certification: Guidelines for the implementation of course work for students of technical specialties of a given form of education / Comp.: Belik G.I., Pshenko E.B.; SibGAU.- Krasnoyarsk, 2003.

4. Metrology, standardization and certification: Handout for course work for students of all forms of education / Comp.: Belik G.I., Pshenko E.B.; SAA.-2002.

5. Rationing of accuracy in mechanical engineering. Collection of reference materials / Comp. G. I. Belik. - Krasnoyarsk: CAA, 1998..

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