When designing a Slot Car (track model), when it comes to choosing gears, we have a large assortment of modern market with basic modulus values of 0.3, 0.35 and 0.4. The main characteristics of a gear are the number of teeth, gear module, and gear ratio. If everything is clear with the number of teeth and gear ratio (the ratio of the number of teeth of the driven gear to the drive gear), then the concept of gear module is not entirely clear. Unfortunately, in schools the level of teaching the subject of drawing has not been the same for a long time, and in most cases this subject is not taught.
So what is a gear module? How is the gear modulus calculated and what determines it? A textbook helped us answer this question - Technical Drawing, published back in 1972 (oddly enough, in the vast modern Internet there is not much information on this issue).
Gears (in technical language - gears) serve to transmit movement from one element of the machine to another. Gears, depending on the nature of the engagement (external or internal), the relative position of the rotating shafts, transmission method, etc. may be the most various designs. The most common are spur and bevel gears.
Figure 1 - Elements gear wheel(gears)
And so, what elements does the gear (gear) shown in Figure 1, a consist of? The main element of the gear is a tooth (Figure 1, b) - a protrusion a certain shape, designed to transmit motion by acting on the protrusion of another gear element. The part of the gear wheel that does not include teeth is called the body of the gear wheel (Figure 1, c). The part of a gear wheel, consisting of all its teeth and some part of the wheel body connecting them, is called a ring gear.
A cavity is the space enclosed between the side surfaces of adjacent teeth and the surfaces of the tops and bases of the cavities (Figure 1, d).
The initial surface of a gear wheel (Figure 1, e) is a coaxial surface on which the same surface of another wheel meshed with the first rolls without sliding. The initial surface of the wheel divides the tooth into two parts - the head and the stem.
Figure 1, e shows a drawing of some of the main elements of the tooth. The projection of the surface of the protrusions onto a plane perpendicular to the axis of the gear is called the circle of the protrusions, the surface of the depressions - the circle of the depressions, the surface of the pitch surface - the pitch circle. This drawing shows the tooth height - h , tooth heads - h" and the legs of the tooth - h" " .
Butt step t3 is called the distance along pitch circle between similar profiles of adjacent teeth. Pitch circle diameter - dd , the diameter of the protrusion circle is De , depressions - Di .
Gear module m is called the ratio of the diameter of the pitch circle to the number of teeth Z :
m= dd/Z.
The module of a gear (gear) can also be expressed as the ratio of the mechanical pitch to the number π :
m= tз/π
The height of the tooth head of a normal gear is approximately equal to the module h"=m , and the height of the leg h""≈1.25 m . In accordance with these relationships, we can establish the following dependence of the diameter of the protrusions De on the module m and the number of teeth Z gear:
De = m (z + 2) .
To transmit motion between shafts whose axes intersect, bevel gears are used. A conventional image of a bevel gear is shown in Figure 2. In a section with a plane passing through the axis of the wheel, the teeth are shown unshaded. In the view obtained by projection onto a plane perpendicular to the axis of the wheel, the circles corresponding to the large and small protrusion of the teeth are depicted with solid lines and the circle of the large base of the pitch cone is depicted with a dash-dotted line.
The bevel gear has its own specific elements and corresponding designations and dimensions that are not available in cylindrical wheel:
Φ — pitch cone angle;
Φе — angle of the cone of the protrusions;
Φi — cone angle of the depressions;
L — cone distance;
ν - angle of the external additional cone.
Basic dimensions of uncorrected bevels gear wheels can be determined using the following formulas.
Starting circle diameter:
dd = m z.
Protrusion circle diameter:
De = m (z + 2cos Φ).
Diameter of the circle of the depressions:
Di = m (z - 2.4cos Φ).
Cone distance:
L= dd/(2cos Φ)
Based on materials from the textbook “Technical Drawing” Authors: E.I. Godik, V.M. Lysyansky, V.E. Mikhailenko, A.M. Ponomarev. Kyiv. 1972
1. Making drawings of cylindrical gears
The main parameter of a cylindrical gear is the pitch circle. The diameter of the pitch circle is designated by the letter d and is called the pitch circle. (Terms, definitions and designations of cylindrical gears are established by GOST 16531-83). Along the pitch circle, the circumferential pitch of the teeth is plotted, denoted p and representing the distance along the arc of the pitch circle between adjacent teeth of the gear wheel (Fig. 1). The segments divide the pitch circle into as many parts as the number of teeth the gear has. The number of teeth is indicated by the letter z. The pitch diameter for a gear is always the same. The circumferential thickness of the tooth and the circumferential width of the cavities are measured along the pitch circle.
The dividing circle divides the tooth height h into two unequal parts - the tooth head with height h a and the stem with height h f.
The gear rim is limited by the circle of the tops of the teeth with a diameter of d a and the circle of the cavities with a diameter of d f .
The main design parameter of gears is the modulus. All other parameters are expressed through it. For spur gears, the module m is equal to the ratio of the pitch circle diameter d to the number of teeth z or the ratio of the circumferential pitch to the number.
m = d / z = p /
In other words, the module is the length of the pitch circle arc per one tooth of the wheel. To unify gears in industrial scale used for the manufacture of gears
standard values of modules that are established by GOST 9563-60. Some meanings standard module are given in the table. The values from the first row are preferred to the second; the second row of modulus values is given to expand the range of manufactured gears and is used in cases where, for technical, design or other reasons, it is impossible to produce a gear with the modulus value from the first row.
Engagement module - m, (mm) | |||||||||||||
Before drawing a gear or its solid model, it is necessary to perform calculations geometric parameters and determine the dimensions of all parts of the gear. Usually, the pitch diameter and center-to-axle value of the gear, the number of teeth are first calculated, and then the dimensions of all other parts are assigned, which are clarified when performing verification calculations.
GOST 2.403-75 establishes the rules for making working drawings of gears. As a rule, training drawings are made with acceptable simplifications relative to working drawings developed in industry. The training drawings do not include dimensional tolerances, requirements for strength and accuracy and details, etc. When making drawings of gears, you should also be guided by the requirements of GOST 2.402
In Fig. Figure 2 shows an example of an educational drawing of a gear wheel performed by students in the process of studying the discipline “Engineering Graphics”.
In accordance with these rules, in the upper right corner of the format there should be a table of parameters, the dimensions of which are shown in the figure. The parameter table consists of three parts, which must be separated from each other by solid main lines. The first part of the table contains the main parameters necessary for the manufacture of the wheel ring gear, the second - data for controlling tooth sizes and the third
- reference data.
Training drawings usually contain some data from the first and third parts of the table.
TASK OPTIONS for topic "Gears"
option | teeth - z | rim - B | hubs - l | hub-D | resp. -d |
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l - t | resp. -d | |||||||||||||
disk-s | niya-D 1 |
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option | teeth - z | rim - B | hubs - l | recesses-D | resp. -d |
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option | teeth - z | hubs - l | hub-D | |||||||||
3 – crown ( top part rims with teeth) 4 – mounting hole 5 – disk 6 – hub 7 – holes in the disk 8 – keyway Rim - outer working part pulley, gear, sprocket. May have various designs. On details gears teeth are cut on the outer surface of the rim, the outer surface of the flat belt drive pulleys is made convex, on the outer surface of the pulley for the V-belt drive, radial grooves are made for V-belts, etc. The crown is the part of the rim of gears and sprockets on which the teeth are cut. Disc - part of a gear wheel, pulley, sprocket, with the help of which the rim is connected to the hub. The disc, in parts, has a simple design and small dimensions and is made as a single unit together with the rim and hub. To lighten the weight of heavy parts, holes can be made in the disk (hole 7 in Fig. 3), the disk itself can be made in the form of spokes, such as on a bicycle wheel, in welded gears large sizes Ribs are welded to the discs to increase the rigidity of the wheel. Mounting hole- the central hole in the hub of a rotating part, through which the part is put on the shaft. Made to exact dimensions and can have various shapes. This depends on the type of connection between the wheel and the shaft. In the mounting hole can be performed various holes and grooves to prevent rotation of the mounted part relative to the shaft. Most often, a keyway is made for this purpose. The hub is the central part of a rotating part along with the mounting hole. The dimensions of the hub are selected depending on the size of the mounting hole. IN general case outside diameter hub must larger diameter mounting hole 1.5 times, the length of the hub should be approximately equal to the diameter of the hole. In some cases, for heavily loaded and critical parts, the selected hub sizes are checked by calculations. Keyway - a recess in a hole or on a shaft for placing a part called a key into this recess. Key - fastener prismatic or cylindrical in shape, inserted into the grooves of two parts and preventing their relative rotation or shift. A keyed connection is one of the types of connections between a shaft and a bushing using an additional structural element (key) designed to prevent their mutual rotation. Sequence of drawing a gear The diameter of the pitch circle d is equal to: z - number of wheel teeth m - module Diameter of lugs dvyst = m (Z + 2); Dimensions diameter dвп = m (Z – 2.5). 2. All other sizes are given in the tables 3. The drawing should be done on a scale of 1:1, 1:2 or 2:1 depending on the size of the gear image 4. On 'F. A4 draw a wheel according to the example in Fig. 2: make a cut in place of the main view, on the right along the continuation of the axis of rotation make an extended section showing the contour of the hole. along with keyway dimensions 5. Select the dimensions of the keyway from the reference tables of parallel keys, depending on the diameter of the hole. wheels from any textbook on engineering graphics. As a reference, you can take the manual “ Structural elements details", page 44, table. P1. (The author of the manual is Kitsieva V.D. Library code 74/M85. Data on keys is also available in “Technical Drawing” by Novichikhina, etc.) 6. In the main inscription write down the symbol of the material. Examples symbol The material is in the above textbook, you can also take the manual “Engineering Graphics. Drawings of parts, assembly drawings" (Author of the manual Kitsieva V.D. Library code I622. p. 49-50.) 7. On a gear drawing, a table with reference data must be placed in the upper right corner of any format. Fill out the table; do not put the table dimensions on the drawing. 8. Lines in the table “original contour, degree of accuracy and reference. leave the data free. 9. The designation of the roughness of the working lateral surfaces of the teeth is indicated in the continuation dash-dotted line showing the pitch diameter of the gear. Designation of the roughness of the depressions And The tops of the teeth are applied on lines corresponding to the circles of the cavities and the circle of the tops of the teeth. 10. The following dimensions should be indicated on the image of the gear: the diameter of the circle of the tops of the teeth, the width of the ring gear, chamfers on the end edges of the cylinder of the tops of the teeth. The remaining dimensions are applied depending on the design of the gear. Meaning pitch diameter indicated in the table, the size of the diameter of the depressions is not indicated in the drawing. The location of the pitch diameter is indicated dash-dotted line. The height of the tooth on the section is shown unshaded. 11. The dimensions of the chamfers should be from 1 to 2 mm wide, the radii of roundings from 3 to 5 mm. Make chamfers at an angle of 45 degrees. | ||||||||||||
If the size of this arc is taken as many times as there are teeth on the wheel, i.e. z times, then we also obtain the length of the initial circle; hence,
Π d = t z
from here
d = (t/Π)z
Step ratio t of a link to a number Π is called the module of the link, which is denoted by the letter m, i.e.
t / Π = m
The module is expressed in millimeters. Substituting this notation into the formula for d, we get.
d = mz
where
m = d/z
Therefore, the module can be called the length corresponding to the diameter of the initial circle per one tooth of the wheel. The diameter of the protrusions is equal to the diameter of the initial circle plus two heights of the tooth head (Fig. 517, b) i.e.
D e = d + 2h"
The height h" of the tooth head is taken equal to the module, i.e. h" = m.
Let's express the right side of the formula in terms of the modulus:
D e = mz + 2m = m (z + 2)
hence
m = D e: (z +2)
From fig. 517, b it is also clear that the diameter of the circle of the depressions is equal to the diameter of the initial circle minus two heights of the tooth stem, i.e.
D i= d - 2h"
The height h" of the tooth leg for cylindrical gears is taken equal to 1.25 modules: h" = 1.25m. Expressing the right-hand side of the formula for D in terms of the modulus i we get
D i= mz - 2 × 1.25m = mz - 2.5m
or
Di = m (z - 2.5m)
The entire tooth height h = h" + h" i.e.
h = 1m + 1.25m = 2.25m
Consequently, the height of the tooth head is related to the height of the tooth stem as 1: 1.25 or as 4: 5.
The tooth thickness s for unprocessed cast teeth is taken to be approximately equal to 1.53m, and for machined teeth (for example, milled) - equal to approximately half the pitch t engagement, i.e. 1.57m. Knowing that step t engagement is equal to the thickness s of the tooth plus the width s in the cavity (t = s + s in ) (step size t determined by the formula t/ Π = m or t = Πm), we conclude that the width of the cavity for wheels with cast raw teeth.
s in = 3.14m - 1.53m = 1.61m
A for wheels with machined teeth.
s in = 3.14m - 1.57m = 1.57m
The design of the rest of the wheel depends on the forces that the wheel experiences during operation, on the shape of the parts in contact with this wheel, etc. Detailed calculations of the dimensions of all elements of the gear wheel are given in the course “Machine Parts”. For execution graphic image gears, the following approximate relationships between their elements can be accepted:
Rim thicknesse = t/2
Shaft hole diameter D in ≈ 1 / in D e
Hub diameter D cm = 2D in
Tooth length (i.e. thickness of the wheel ring gear) b = (2 ÷ 3) t
Disc thickness K = 1/3b
Hub length L=1.5D in: 2.5D in
The dimensions t 1 and b of the keyway are taken from table No. 26. After determining the numerical values of the engagement module and the diameter of the hole for the shaft, it is necessary to coordinate the resulting dimensions with GOST 9563-60 (see table No. 42) for modules and normal linear dimensions according to GOST 6636-60 (table No. 43).