Download program for gears made of wood. Gear - construction technique for any CAD system

With the help of modern technology such as 3D modeling, developers can get the most realistic images of the parts and assemblies that they design. 3D modeling allows you to successfully visualize those objects that do not yet exist, but are still at the design stage.

Specific components such as bushings, ribs, slots, etc. have the appropriate commands to create various items within an hour or two. It contains all the tools needed to create the punch, die and any additional systems that go with them. Any sections, sections, projections, images, etc. are derived directly from the model and associated with it.

Each has a corresponding command in which additional parameters can be set, such as alphabet, scale, etc. the measurements themselves are "smart" and automatically change when editing the model. Pre-simulation of turning and milling movements in the software environment provides useful information about the manufacturing process.

Wide application 3D modeling finds in such an industry as mechanical engineering. Engineers, using specialized software packages, create three-dimensional models of the parts they develop in order to visually evaluate them and subsequently use the resulting images to draw up various technical documentation.

Once we have the design of a certain part and after it has been heavily loaded, the program is able to offer an optimal shape change that can significantly reduce the initial material resources. It reads and writes to many of the most common formats, including competing products. It can include various things such as snap to grid, view options, degrees of freedom, work view shift and more.

Thus, you can work from different parts of the world without sending large emails, and the security of your information is guaranteed. Another big advantage of this "sharing" is the ability to use resources on other computers to do, for example, heavy calculations that are typical for optimization checks. All relationships between parts can be visualized in the graphics window.

Gears are one of the most common parts of various machines and mechanisms. They are integral components of gears, and the durability and reliability of the manufactured devices largely depend on how well they are developed.

Modern technologies for the development of machines and mechanisms require mandatory three-dimensional modeling of their parts. This allows not only visualization, but also quickly and with a high degree of accuracy to determine the most diverse parameters and characteristics of products. On the basis of three-dimensional models, various types of drawings are created, which are so necessary in production. In addition, if necessary, using the prototyping method based on 3D models, can produce plastic sample gears.

A bitmap is a projection that has a lower level of detail and thus does not load the hardware. In this way, you can quickly create projections of large assembled units and only call up large parts when necessary.

This will allow you to place your geometry with fewer dimensions to get a cleaner look to your sketches. This way you will create custom models that you can easily optimize. Intuitively recognize the appropriate tool for a given case. Assemble simulated 3D bodies into assembled units by removing degrees of freedom. Being able to create visual cross sections and control the visibility of components will make your job easier. To use the parts list to easily track the weight distribution in assembled units. To create welded joints using technological processing of parts. For this purpose, you will be able to create views and sections. For dimensions with tolerances and knots. To create a BOM and place parts. A specialized set of tools is used to model sheet metal parts. With the ability to create folds of your articles and insert them into drawings. Conduct strain and strength analysis using the finite element method. This will allow you to test the strength of your parts without doing complex design calculations. For easy modeling of frame designs built from a rich set of standard profiles found in the software library. You will be able to use specialized structural analysis tools and control the stresses in the structure with automatically generated stress diagrams.

• Create 2D sketches with geometric constraints.
• Use parametrically linked dimensions.
• Create 3D geometry from 2D sketches.

Gears owe their wide popularity to the advantages they have over other designs of a similar purpose. The main ones are a fairly high efficiency, constant gear ratio, durability, compactness. In addition, gears can be used with a wide variety of speeds, ratios and transferable torques. It should also be noted that they are quite easy to maintain.

If you already have a registration on the site, just log in and start browsing the manuals. Let's look at the comparison in more detail, let's do it in order. The lack of design of sheet metal components is important - the sheet can be molded like a classic component, but the disadvantage of development.

Last but not least, libraries of standardized parts. Each project requires standard parts such as screws, screws, nuts, etc. designing these parts is a waste of time, a potential source of error, and useless because we won't manufacture them ourselves.

There are gears and disadvantages. Experts refer to them, first of all, the complexity in manufacturing. In addition, gears during operation emit quite a lot of noise when working at high speeds, and if not accurately manufactured, they cause vibrations.

Gears are used to transmit torque between intersecting, crossing and parallel axes. In the latter case, cylindrical gears are used to transmit rotation. They can have both external and internal gearing, and gears that use internal gearing have many very valuable features and properties. Among them, it should be noted that they are able to withstand quite large loads than gears with external gearing. As for the direction of the axes of rotation, it is the same for wheels with internal gearing.

To learn more about these applications, click on the logo. Using the extensive parts library, you can search for components that are available directly from the shelf. Custom is usually expensive, so if the item is already in the library then there is no reason to do so.

It is possible to produce cylindrical sprockets with straight and angled teeth. The tooth geometry is based on Polish and German standards. The wheel is based on several available hubs described in the literature. The geometric parameters of the teeth, as well as the concentrator itself, are edited. The base set of values ​​for these parameters is set by default and calculated by the program. It is possible to shift the reference profile, which mimics the implementation of gears by means of an offset.

Cylindrical wheels can have straight, helical, or chevron teeth. In the so-called helical» wheels, the teeth can be inclined either to the right or to the left, which provides an increased load capacity of the transmission, as well as greater smoothness of rotation. At the same time, during the operation of helical gears, increased axial forces occur. They are small in chevron gears, which have virtually the same advantages as "helical" gears.

You can report the need for new add-ons to our email address This email address is being protected from spambots. Each time the user gives the start and end step diameters. The user can also specify the diameter of the next shaft step and the taper angle. The client has the ability to create polyglas and splines at any level of the shaft, the parameters of which provide themselves.

Thanks to the built-in standards editor, you can optimize polyglas and spline parameters so that the values ​​​​of individual parameters comply with the norms, from the drop-down list are available as suggested values. The tools are described along with examples of use and descriptions of the functions needed to use them. Key words: gearbox, belt drive, belt One of the main functions of the roller generator implemented in the program is the gear generator, which, based on the data, forms the contour of the gear.

Rack and pinion is also classified as a spur gear is a special case of it. In it, the rack is considered as one of the sections of the gear rim. When it is required to transfer the rotation of one axis to another, which intersects it and is located with it in the same plane, gears with bevel gears are used. The teeth on them can be straight, oblique and curvilinear. To transmit rotation between intersecting axes, worm, helical and hypoid gears are used.

Built-in functions calculate wavelengths based on existing geometry. The dialog box displays the available belt and pulley graphics. The Feature Library helps you save and recall the appropriate components. By default, the module is called the ratio of the diameter in millimeters to the number of teeth. The English modulus is the ratio of the diameter in inches to the number of teeth. Standard attachment angles are fixed in combination with standard tooth pitch. Changing the vertical section or changing the height of the tooth head Changing the vertical profile will help to avoid undercutting a small number of teeth, obtain a certain distance from the center and increase the load capacity.

The main advantage of spur gears is that they are relatively easy to manufacture and quite cheap. At the same time, they are not intended for the translation of large efforts, since they have a low load capacity. Where it is necessary to achieve smooth movement of one part relative to another, worm gears are used. The main scope of hypoid gears is the main drives of transport equipment.

If the coefficient is positive, the height of the tooth head is higher; if it is negative, the height of the tooth head is smaller. In parallel gears, the circle diameter can be determined directly from the ratio of the distance to the center and the number of teeth. Then select the polyline and specify the start point: Specify the start point for the chain on the polyline and the calculation will begin. In the Size dialog box, select a standard size. Figure 5 Size selection window. In the Geometry dialog box, you need to specify the number of teeth.

Specify Cell Orientation: Specify the direction of non-symmetrical cells. Chain Opens a dialog for selecting a chain from the library. Size Specifies the size of the standard element. Number of cells to draw Specifies the number of cells to insert. Notes: The chain is dragged along the polyline. Therefore, select a polyline point. This point becomes the starting point of the chain. When you insert the first chain of links, the question arises as to the correct position of the connector.

Picture 1

The initial data for calculating the involute and gear are:
m - module (this is part of the pitch circle diameter, which falls on one tooth. The module is determined from reference books, as it is a standard value);
z is the number of teeth;
φ - profile angle of the original contour. The angle is 20° (which is the standard value).
For the calculation, we use the following data:
m = 4; z = 20; φ = 20°.
The pitch diameter is the diameter of the standard angle, modulus and profile pitch. It is determined by the formula:
D \u003d m z \u003d 4 20 \u003d 80 mm.
Let's calculate the curves that limit the involute - the diameter of the tooth troughs and the diameter of the tops of the teeth.
The diameter of the tooth cavities is calculated by the formula:
Dd \u003d D - 2 (c + m) \u003d 80 - 2 (1 + 3) \u003d 72 mm,
where c is the radial clearance of a pair of initial contours (c = 0.25 m = 0.25 4 = 1).
The diameter of the tooth tips is calculated by the formula:
Da \u003d D + 2 m \u003d 80 + (2 4) \u003d 88 mm.
The diameter of the main circle, the development of which will constitute the involute, is calculated by the formula:
Db = cos φ D = cos 20° 80 = 75.175 mm.
The involute is limited by the diameters of the tooth troughs and tooth tops. To build a complete tooth profile, you need to calculate the thickness of the tooth along the pitch circle:
S \u003d m ((π / 2) + (2 x tg φ)) \u003d 4 ((3.14 / 2) + (2 0 tg 20 °)) ≈ 6.284 mm.
where x is the displacement coefficient of the gear, which is selected from design considerations (in our case, x = 0).

Customize the toolbar. Display the Drawing toolbar. 3D sketches of the chair frame can be created using the precise coordinate tool. The sketch you created can be further modified. Determine the mechanism to be measured and defined.

View of the developed prosthesis according to the norm with characteristic dimensions. 2 3 Fig. transmission mechanisms. The idea behind creating rotational solids is simple and involves taking half of the cross section. Auxiliary materials for laboratory work with gears.

Next, we move from calculated actions to practical ones. Let's create a sketch, on which we will depict auxiliary circles with diameters calculated earlier (pitch circle, tooth tops, tooth troughs and the main one) (Figure 2).

Figure 2

Next, set a point on the auxiliary center line at a distance from the circle of the tops of the teeth equal to:
(Da - Dd) / 3 \u003d (88-72) / 3 \u003d 5.33 mm (or 41.333 from the center of the axis)
From this point to the main circle we draw a tangent. To do this, we connect the first set point with an auxiliary line with the perimeter of the main circle, select the circle and the drawn line, and establish the "Tangent" relationship. On the tangent, we set the second point at a distance from the touch point equal to the fourth part of the segment connecting the first point and the touch point (in our case, it is 17.194 / 4 ≈ 4.299 mm) (Figure 3).

For example, you might want to find a remote location on an object. Speed ​​distribution in transmission 3 4 Cycloid and involute scheme. Sizes. 1 Introduction Measuring is an important step in creating a drawing. The dimensions of the elements in the drawing are clearly defined. 2.

The thread milling tool is defined as a normal milling tool with the cutter selected. This guide is a guide to the tools for inserting and editing the available raster objects. Introduction. The design requires the construction of a geometric model in accordance with the specified dimensions, and it imposes.

Figure 3

Next, using the Arc Center tool, you need to draw a circle arc in the center of the second set point, which passes through the first set point. This will be one side of the tooth (Figure 4).

Figure 4

Now you need to draw the second side of the tooth. To begin with, let's draw an auxiliary line connecting the points of intersection of the sides of the tooth and the dividing circle, which is equal in length to the thickness of the tooth - 6.284 mm. After that, we will draw an axial line through the middle of this auxiliary line and the center of the axis, relative to which we will mirror the second side of the tooth (Figure 5).

Figure 5

Figure 6

Using the Axis tool on the Reference Geometry tab, we create an axis relative to the bottom face of the tooth (Figure 7).

Figure 7

Using the tool "circular array" ("Insert" / "Array / Mirror" / "Circular array") we multiply the teeth up to 20 pieces, according to the calculation. Next, draw a sketch of the circle on the frontal plane of the tooth and extrude to the surface. We will also make a hole for the shaft. As a result, a gear wheel with the given design parameters was obtained (Figure 8).

Figure 8

Similarly to the first one, we create the second gear wheel, but with other design parameters.
The next step is to consider how to correctly establish the relationship of two gears, using them as a gearbox. You can use the created gear models, but another way is to use the already existing Solidworks Toolbox library, where there are many widely used components in various standards. If this library has not yet been added, then it needs to be added - “Tools / Add-ons”, in the drop-down box, check the boxes next to Solidworks Toolbox and Solidworks Toolbox Browser (Figure 9).

Figure 9

Next, we create an assembly in which we add a base with two shafts and two gears from the Toolbox library. For each of the gears, we set our own parameters. To do this, call the menu by clicking on the part with the right mouse button, select "Edit Toolbox definition" and change the parameters in the editor window (module, number of teeth, shaft diameter, etc.). Let's set the number of teeth for one gear wheel to 20, and for the second - 30. Leave the rest of the parameters unchanged. In order to properly match two gears, it is necessary that their pitch diameters are tangent. The dividing diameter of the first gear is D1 = m z =4 20= 80 mm, and the second - D2 = m z =4 30= 120 mm. Accordingly, from here we find the distance between the centers - (D1 + D2) / 2 = (80 + 120) / 2 = 100 mm (Figure 10).

Figure 10

Now you need to set the position of the gears. To do this, set the middle of the top of the teeth of one wheel and the middle of the hollows of the teeth of the second wheel on the same line (Figure 11).

Figure 11

The exposed gear wheels must be paired. To do this, click on the "Mate Conditions" tool, open the "Mechanical Mates" tab, select the "Reducer" mate. We select two arbitrary faces on the gears and indicate in proportions the pitch diameters calculated above (80 mm and 120 mm) (Figure 12).

Figure 12

To create an animation of the rotation of a pair of gears, go to the "Motion Study" tab, select the "Motor" tool. In the tab open on the left, select: engine type - rotating, engine location - gear, rotation speed - for example 10 rpm. Now we click on the button "Calculate" and "Playback", having previously selected "Type of motion study" - Basic motion. Now you can watch the transmission of two gears in motion, as well as save the video file using the Save Animation tool (Figure 13).

Figure 13

All the parts created in this article, as well as the animation of the meshing of two gears, can be downloaded here >>>.

Greetings!

The issue of gear modeling has been raised many times, but the solutions either involved the use of serious paid programs, or were too simplistic and lacked engineering rigor.
In this article, on the one hand, I will try to give a dry maker's instruction on how to model a gear according to several easily measured parameters, on the other hand, I will not bypass the theory.

As an example, take a gear from a car throttle:

This is a classic spur gear with involute gearing (more precisely, these are two such gears).
The principle of involute gearing: It is important for us that the vast majority of gears found in everyday life have precisely involute gearing.
To study the parameters of the gears, we will use the program with the witty name Gearotic. The most powerful highly specialized program for modeling and animating all kinds of gears and gears.
The free version does not allow you to export the generated gears, but we don't need to. We will directly simulate later.
So let's start Gearotic

On the left in the Gears field, click Circular, we get into the gear editor:

Consider the proposed options:

First two columns Wheel and pinion

Wheel - this will be our gear, and Pinion - the counterpart, which in this case does not interest us.

Teeth- number of teeth
mods- tooth shape modifiers. The easiest way to understand what they do is to vary them. Not all settings are applied automatically. After changing, you need to press the ReGen button. In our case (as in most others), we leave these default values.
Jackdaw planetary- turns the gear with the teeth inward (crown gear).
Jackdaw Rght Hnd(Right Hand) - changes the direction of the bevel for helical gears.

Block Size Params

D.P.(Diametral Pitch) - the number of teeth divided by the diameter of the pitch circle (pitch diameter) An uninteresting parameter for us, because. measuring the diameter of the pitch circle is inconvenient.

module(module) is the most important parameter for us. It is calculated by the formula M=D/(n+2), where D is the outer diameter of the gear (easily measured with a caliper), n is the number of teeth.

pressure angle(profile angle) - an acute angle between the tangent to the profile at a given point and the radius - a vector drawn to a given point from the center of the wheel.

There are typical values ​​for this angle: 14.5 and 20 degrees. 14.5 is used much less frequently and mainly on very small gears, which will still be printed on an FDM printer with a large error, so in practice you can safely set 20 degrees.

Rack Fillet- smoothing the base of the tooth. We leave 0.

Block Tooth Form

We leave Involute - involute gearing. Epicylcoidal - A cycloid gear used in precision instrumentation such as clockwork.

Face Width- gear thickness.

Block type

Spur- our spur gear.

Helical- helical gear:

Let's go back to our gear.
The big wheel has 47 teeth, outer diameter 44.6mm, hole diameter 5mm, thickness 6mm.
The modulus will be equal to 44.6\(47+2)=0.91 (round up to the second decimal place).
We enter this data:

On the left is the parameter table. We look Outside Diam (outer diameter) 44.59 mm. Those. completely within the measurement error of the caliper.

Thus, we got the profile of our gear by doing just one simple measurement and counting the number of teeth.
Specify the thickness (Face Width) and the diameter of the hole (Shaft Dia at the top of the screen). Click Add Wheel to Proj to get 3d rendering:

Alas, the free version does not allow you to export the result, so you have to use other tools.

Install FreeCAD
If you don't own Fricade, don't worry, deep knowledge is not required. Download the FCGear plugin.
We find the folder where Frikad was installed. In the Mod folder, create a gear folder and put the contents of the archive into it.
After launching Frikad, the gear item should appear in the drop-down list:

Select it, then File - New
Click on the involute gear icon at the top of the screen, then select the appeared gear in the tree on the left and go to the "Data" tab at the very bottom:

This parameter table

teeth - number of teeth
module - module
height - thickness (or height)
alpha - profile angle
backlash - angle value for helical gears (we leave 0)

The remaining parameters are modifiers and, as a rule, are not used.
We enter our values:

Let's add another gear.
We indicate the height of 18 mm (the total height of our original gear), the number of teeth is 10, the module is 1.2083 (diameter 14.5 mm)

It remains to make a hole. Go to the Part tab and select Create Cylinder. In Data, we specify a radius of 2.5 mm and a height of 20 mm

While holding down the Ctrl key, select the gears in the tree and click Create Union of Multiple Shapes on the toolbar.
Then, again holding Ctrl, select first the resulting single gear, and then the cylinder and click Crop two shapes

P.S. I wanted to talk a little more about exotic cases, but the article turned out to be long, so maybe another time.

How to know the gear module? Online calculation of gears

Calculation of the diameter of a gear with a straight and oblique tooth.

Today we will consider how to calculate the diameter of the gear. I must say right away that the diameter of a spur gear has one formula, and the diameter of a helical gear has a different formula. Although many believe according to one formula, this is erroneous. These calculations are needed for other calculations in the manufacture of gears. So let's go directly to the formulas (without correction):

To begin with, the values ​​\u200b\u200bthat you need to know when calculating in these formulas:

• De is the diameter of the ledge circle.
• Dd is the diameter of the pitch circle (directly from the pitch of which the gear module is calculated).
• Di is the diameter of the depression circle.
• Z is the number of gear teeth.
• Z1 is the number of teeth of the small wheel gear.
• Z2 is the number of teeth of the big wheel gear.
• M (Mn) - module (module is normal, according to the dividing diameter).
• Ms - end module.
• β (βd) - the angle of inclination of the gear (meaning the angle of inclination along the pitch diameter).
• Cos βd - cosine of the angle at the pitch diameter.
• A - center distance.

The formula for calculating the diameters of a spur gear (gear):

De=(Z×M)+2M=Dd+2M=(Z+2)×M

The formula for calculating the diameters of a helical gear (gear with an oblique tooth):

It seems like on spur gears, but on helical gears we have a different dividing diameter, therefore the diameter of the circle of the protrusions will be different!

Dd=Z×Mn/Cos βd=Z×Ms

That is, we multiply the number of teeth by the module and divide by the cosine of the tooth angle by the pitch diameter, or we multiply the number of teeth by the end module.

We define the end module:

Ms=Mn/Cos βd=2A/Z1+Z2

That is, the end module is equal to - the normal module is divided by the cosine of the gear tooth angle by the pitch diameter or two times the center distance and divided by the number of teeth of the small wheel plus the number of teeth of the large wheel.

To do this, we already need to know the center-to-center distance, which can be calculated using the formula:

A=(Z1+Z2/2Cos βd)×Mn=0.5Ms(Z1+Z2)

That is, the number of teeth of the small wheel plus the number of teeth of the large wheel, divided by 2, multiplied by the cosine of the angle of the gear tooth by the dividing diameter, and all this is multiplied by the module or the number of teeth of the small wheel, plus the number of teeth of the large wheel, multiplied (0.5 multiplied by the end module).

As you can see, calculating the diameter of a spur gear is very simple, but calculating the diameter of a wheel with an oblique tooth is already more difficult here, since many different components are required. These components are not always present, which complicates the calculation. So for some calculations, you will need to know some exact parameters, such as the exact (I emphasize exact) angle of inclination of the gear teeth on the pitch diameter or the exact center distance! All calculations are interconnected, all this is necessary for other calculations of gears in the design and repair business.

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zuborez.info

Geargenerator - Online Gear Builder

If you have landed on this page, then you probably know the Gear Template Generator program (more about the program). This program allows you to calculate the parameters of gearing. Gear Template Generator is installed locally on a computer and allows you to create a drawing of a pair of gears with the necessary parameters. (Download Gear Template Generator here)

Now I will talk about an analogue of Gear Template Generator - an online gear designer Geargenerator. Actually, if you enter Geargenerator.com into the address bar of your browser, you will be taken to the constructor page.

This is what the initial window of the program looks like.

The window is divided into two parts. The left side is the program settings panel and gears. The result will be displayed on the right side.

Consider the left side

It is conditionally divided into several blocks with a set of parameters. Let's take a look at these blocks.

The topmost Animation block is the animation of the movement of the gears. Start/stop, reset. You can set the rotation speed.

Next comes the Gears block - this is a list of gears and work with their number. There are four by default. You can add, remove or clear. Moreover, the new gear will be added to the one that is currently selected.

The next block of settings is Connection properties - it is responsible for the options for docking gears

Parent gear # field: - here you can specify the number of the parent gear for the current gear (from the Gears list). By default, the very first gear is zero. Thus, you can quickly re-join the gears.

Field Axle connection: - determines how the gears are connected. If you check the box here, the gears will be joined on the same axis.

Field Connection angle: - indicates the angle to the gear center relative to the parent gear.

Explanation

Position of gear #1 at Connection angle: – 60

Gear #1 position at Connection angle: – 85

Next, Gear properties - the parameters of the gears themselves (number of teeth, tooth parameters, etc.) In the same block there is the most important button - Download SVG - clicking on it starts downloading a file with gears in SVG format

The last Display block is the display settings of the constructor itself. You can change the color scheme, turn on / off the grid and labels on the gears.

Now a small working example

Reduce the number of teeth of gear #3 to 42

Add gear #4 to gear #3 (to do this, in the Gears block, click on #3, and then on the Add New button)

Specify for #4 that it should be located on the same axis as #3

Let's add one more gear wheel to #3 and #4, specifying the Connection angle parameter (we will separate them to the sides)

Let's press the Start / Stop button - and look at the animation. Thus, you can not only assemble the desired sequence of gears, but also choose the location of the gear axes for further placement in the product body.

In this online gear builder, you can build almost the entire watch mechanism (as far as gears are concerned). You can build quite complex schemes for connecting gears. Unlike the Gear Template Generator, where you can only build one pair of gears. But the Gear Template Generator gives you a lot of freedom in setting the parameters of the gears.

GearGenerator only allows you to export to SVG.

GearGenerator is online, does not require installation, and is free.

Both programs have their own merits. Which one to choose - the choice is yours.

You can go to the GearGenerator website at this link.

mebel-sam.net.ua

Gear tooth module: calculation, standard, definition

Gear transmission was first mastered by man in ancient times. The name of the inventor remained hidden in the darkness of centuries. Initially, gears had six teeth - hence the name "gear". For many millennia of technological progress, the transmission has been improved many times, and today they are used in almost any vehicle from a bicycle to a spacecraft and a submarine. They are also used in any machine tool and mechanism, most of all gears are used in mechanical watches.

What is a gear module

Modern gears are far removed from their wooden six-tooth ancestors, made by mechanics with the help of imagination and measuring string. The design of gears has become much more complicated, the speed of rotation and the forces transmitted through such gears have increased a thousandfold. In this regard, the methods of their design have become more complicated. Each gear is characterized by several basic parameters

• diameter;
• number of teeth;
• tooth height;
• and some others.

One of the most versatile features is the gear module. There is a subspecies - the main and end.

Download GOST 9563-60

In most calculations, the main one is used. It is calculated in relation to the dividing circle and serves as one of the most important parameters.

To calculate this parameter, the following formulas are used:

where t is the step.

where h is the height of the tooth.

And finally

where De is the diameter of the circle of the protrusions, and z is the number of teeth.

What is a gear module?

this is a universal characteristic of a gear, linking together its most important parameters such as pitch, tooth height, number of teeth and diameter of the ledge circle. This characteristic is involved in all calculations related to the design of transmission systems.

The formula for calculating the parameters of a spur gear

To determine the parameters of a spur gear, you will need to perform some preliminary calculations. The length of the pitch circle is π×D, where D is its diameter.

The engagement pitch t is the distance between adjacent teeth, measured along the pitch circle. If this distance is multiplied by the number of teeth z, then we should get its length:

after transformation, we get:

If we divide the pitch by pi, we get a factor that is constant for a given gear part. It is called the module of the link m.

the dimension of the gear module is millimeters. If we substitute it into the previous expression, we get:

After performing the transformation, we find:

This implies the physical meaning of the engagement module: it is the length of the arc of the initial circle corresponding to one tooth of the wheel. The diameter of the circle of the protrusions De is equal to

where h'- head height.

The height of the head is equated to m:

Having carried out mathematical transformations with substitution, we obtain:

De=m×z+2m = m(z+2),

where it comes from:

The diameter of the circle of the cavities Di corresponds to De minus two heights of the base of the tooth:

where h“ is the height of the tooth stem.

For cylindrical wheels, h“ is equated to a value of 1.25m:

By substituting on the right side of the equality, we have:

Di = m×z-2×1.25m = m×z-2.5m;

which corresponds to the formula:

Full Height:

and if we perform the substitution, we get:

h = 1m+1.25m=2.25m.

In other words, the head and stem of the tooth are related to each other in height as 1:1.25.

The next important dimension, the thickness of the tooth s is taken approximately equal to:

• for cast teeth: 1.53m:
• for those made by milling - 1.57m, or 0.5×t

Since the step t is equal to the total thickness of the tooth s and the cavity sv, we obtain formulas for the width of the cavity

• for cast teeth: sв=πm-1.53m=1.61m:
• for those made by milling - sv \u003d πm-1.57m \u003d 1.57m

The design characteristics of the remaining part of the gear part are determined by the following factors:

• forces applied to the part during operation;
• the configuration of the parts interacting with it.

Detailed methods for calculating these parameters are given in such university courses as “Machine Parts” and others. The gear module is widely used in them as one of the main parameters.

Simplified formulas are used to display gears using engineering graphics methods. In engineering handbooks and government standards, you can find characteristic values ​​calculated for typical gear sizes.

Initial data and measurements

In practice, engineers often face the task of determining the module of a real-life gear for its repair or replacement. At the same time, it also happens that the design documentation for this part, as well as for the entire mechanism in which it is included, cannot be found.

The simplest method is the break-in method. Take a gear for which the characteristics are known. Insert it into the teeth of the part being tested and try to run it around. If the pair is engaged, then their step is the same. If not, continue selection. For a helical cutter, choose a cutter that is suitable for the step.

This empirical method works well for small gears.

For large, weighing tens or even hundreds of kilograms, this method is physically unrealizable.

Calculation results

Larger ones will require measurements and calculations.

As you know, the modulus is equal to the diameter of the circumference of the protrusions, divided by the number of teeth plus two:

The sequence of actions is as follows:

• measure the diameter with a caliper;
• count teeth;
• divide the diameter by z+2;
• round the result to the nearest whole number.

This method is suitable for both spur and helical gears.

Calculation of the parameters of the wheel and gear of the helical gear

The calculation formulas for the most important characteristics of the helical gear coincide with the formulas for the spur gear. Significant differences arise only in strength calculations.

If you find an error, please select a piece of text and press Ctrl+Enter.

stankiexpert.ru

Gear calculation in Excel

For a complete and accurate design calculation of an involute spur gear, you need to know: the gear ratio of the gear, the torque on one of the shafts, the rotational speed of one of the shafts, the total machine operating time of the gear, ...

Type of gear (spur, helical or herringbone), gear type (external or internal), load curve (mode of operation - fraction of the time of maximum loads), material and heat treatment of the gear and wheel, gear layout in the gearbox and in the overall drive scheme .

Based on the above initial data, using numerous tables, various diagrams, coefficients, formulas, the main parameters of the gear are determined: center distance, module, angle of inclination of the teeth, number of teeth of the gear and wheel, width of the gear rims of the gear and wheel.

There are about fifty semantic program steps in the detailed calculation algorithm! At the same time, when working, you often have to go back a few steps, cancel previous decisions and move forward again, realizing that you may have to go back again. The calculated values ​​​​of the center distance and module found as a result of such painstaking work must be rounded up at the end of the calculations to the nearest higher value from the standardized series ...

That is, they counted, counted, and at the end - “bang” - and simply increased the results by 15 ... 20% ...

Students in the course project on “Machine Parts” need to do such a calculation! In the real life of an engineer, I think this is not always advisable.

In the article brought to your attention, I will tell you how to quickly and with acceptable accuracy for practice perform the design calculation of a gear train. Working as a design engineer, I quite often used the algorithm described below in my work when high accuracy of strength calculations was not required. This happens with a single transmission, when it is easier, faster and cheaper to design and manufacture a gear pair with some excess safety margin. Using the proposed calculation program, you can easily and fairly quickly check the results obtained, for example, using another similar program or verify the correctness of "manual" calculations.

In fact, this article is to some extent a continuation of the topic started in the post "Calculation of the trolley drive". There, the results of the calculation were: the gear ratio of the drive, the static moment of resistance to movement, reduced to the wheel shaft and the static power of the engine. For our calculation, they will be part of the original data.

The design calculation of a spur gear will be carried out in MS Excel.

Begin. I draw your attention to the fact that we choose Steel40X or Steel45 with a hardness of HRC 30 ... 36 (for a gear - “harder”, for a wheel - “softer”, but in this range) and allowable contact stresses [σH] = 600MPa. In practice, this is the most common and affordable material and heat treatment.

The calculation in the example will be performed for a helical gear. The general scheme of the gear train is shown in the figure below.

We start Excel. In the cells with light green and turquoise filling, we write the initial data and the calculated data specified by the user (accepted). In the cells with a light yellow fill, we read the results of the calculations. The cells with a light green fill contain the initial data that is not subject to change.

Fill in the cells with the initial data:

1. The efficiency of the transmission efficiency (this is the efficiency of the involute gearing and the efficiency of two pairs of rolling bearings) is written

to cell D3: 0.931

2. The value of the integral coefficient K, depending on the type of transmission (see note to cell D4), is written

to cell D4: 11.5

3. The angle of inclination of the teeth (preliminary) bp in degrees, select from the recommended range in the note to cell D5 and enter

to cell D5: 15,000

4. Gear ratio up, determined in preliminary calculations, we write down

to cell D6: 4.020

5. Write down the power on the high-speed transmission shaft P1 in Watts

to cell D7: 250

6. The speed of rotation of the high-speed shaft n1 in revolutions per minute is entered

to cell D8: 1320

The gear calculation program outputs the first block of design parameters:

7. Torque on the high-speed shaft T1 in Newtons multiplied by a meter

in cell D9: =30*D7/(PI()*D8)=1.809

T1=30*P1/(3.14*n1)

8. Power at low-speed transmission shaft P2 in Watts

in cell D10: =D7*D3=233

9. Speed ​​of the low-speed shaft n2 in revolutions per minute

in cell D11: =D8/D6=328

10. Torque on the low-speed shaft T2 in Newtons multiplied by a meter

in cell D12: =30*D10/(PI()*D11)=6.770

T2=30*P2/(3.14*n2)

11. Estimated diameter of the pitch circle of the gear d1р in millimeters

in cell D13: =D4*(D12*(D6+1)/D6)^0.33333333=23.427

d1р=K*(T2*(up+1)/up)^0.33333333

12. Estimated diameter of the pitch circle of the wheel d2p in millimeters

in cell D14: =D13*D6=94.175

13. Maximum calculated engagement modulus m (max) p in millimeters

in cell D15: =D13/17*COS (D5/180*PI())=1.331

m(max)р=d1р/17*cos(bп)

14. Minimum calculated engagement modulus m (min) p in millimeters

in cell D16: =D15/2 =0.666

m(min)r=m(max)r/2

15. We select the engagement module m in millimeters from the range of values ​​​​calculated above and from the standardized series given in the note to cell B17 and write

16. Estimated width of the gear rim of the wheel b2p in millimeters

in cell D18: =D13*0.6=14.056

17. Round off the width of the wheel ring gear b2 in millimeters and enter

to cell D19: 14,000

18. The program determines the width of the ring gear b1 in millimeters

in cell D21: =D13*COS (D5/180*PI())/D17 =18.1

z1р=d1р*cos(bп)/m

20. We round off the value of the number of teeth of the gear z1 obtained above and write down

in cell D23: =D22*D6 =76.4

22. We write down the rounded number of teeth of the wheel z2

to cell D24: 77

23. We specify the gear ratio (final) u by calculation

in cell D25: =D24/D22=4.053

24. We calculate the deviation of the final gear ratio from the preliminary delta as a percentage and compare it with the allowable values ​​given in the note to cell D26

in cell D26: =(D25/D6-1)*100=0.81

in cell D27: =D17*(D22+D24)/(2*COS (D5/180*PI())=62.117

awр=m*(z1+z2)/(2*cos(bп))

26. Round up the calculated value of the gear center distance according to the standardized series given in the note to cell D28, and enter the final center distance aw in millimeters

to cell D28: 63,000

27. Finally, the program specifies the angle of inclination of the gear teeth b in degrees

in cell D27: =IF(D5=0;0;ACOS (D17*(D22+D24)/(2*D28))/PI()*180)=17.753

b=arccos(m*(z1+z2)/(2*aw))

So, we performed a design calculation of a spur gear according to a simplified scheme, the purpose of which was to determine the main overall parameters based on the given power ones.

REST can be downloaded just like that... - no passwords!

I will be glad to see your comments, dear readers.

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al-vo.ru

Calculation of the diameters of the belt pulleys for a V-ribbed belt. Online calculator. :: AutoMotoGarage

Works on the bulkhead of the electric motor are nearing completion. We proceed to the calculation of the belt drive pulleys of the machine. A little bit of belt drive terminology.

We will have three main input data. The first value is the speed of rotation of the rotor (shaft) of the electric motor 2790 revolutions per second. The second and third are the speeds that need to be obtained on the secondary shaft. We are interested in two denominations of 1800 and 3500 rpm. Therefore, we will make a two-stage pulley.

The note! To start a three-phase electric motor, we will use a frequency converter, so the calculated rotation speeds will be reliable. If the engine is started using capacitors, then the values ​​​​of the rotor speed will differ from the nominal one in a smaller direction. And at this stage, it is possible to minimize the error by making adjustments. But for this you have to start the engine, use the tachometer and measure the current speed of rotation of the shaft.

Our goals are defined, we proceed to the choice of the type of belt and to the main calculation. For each of the produced belts, regardless of the type (V-belt, multi-V-belt or other), there are a number of key characteristics. Which determine the rationality of the application in a particular design. The ideal option for most projects would be to use a V-ribbed belt. The polywedge-shaped got its name due to its configuration, it is a type of long closed furrows located along the entire length. The name of the belt comes from the Greek word "poly", which means many. These furrows are also called differently - ribs or streams. Their number can be from three to twenty.

A poly-V-belt has a lot of advantages over a V-belt, such as:

• due to good flexibility, work on small pulleys is possible. Depending on the belt, the minimum diameter can start from ten to twelve millimeters;
• high traction ability of the belt, therefore, the operating speed can reach up to 60 meters per second, against 20, a maximum of 35 meters per second for the V-belt;
• The grip force of a V-ribbed belt with a flat pulley at a wrap angle over 133° is approximately equal to the grip force with a grooved pulley, and as the wrap angle increases, the grip becomes higher. Therefore, for drives with a gear ratio greater than three and a small pulley wrap angle from 120° to 150°, a flat (without grooves) larger pulley can be used;
• due to the light weight of the belt, vibration levels are much lower.

Taking into account all the advantages of poly V-belts, we will use this type in our designs. Below is a table of the five main sections of the most common V-ribbed belts (PH, PJ, PK, PL, PM).

Drawing of a schematic designation of the elements of a poly-V-belt in a section.

For both the belt and the counter pulley, there is a corresponding table with the characteristics for the manufacture of pulleys.

The minimum pulley radius is set for a reason, this parameter regulates the life of the belt. It would be best if you deviate slightly from the minimum diameter to the larger side. For a specific task, we have chosen the most common "RK" type belt. The minimum radius for this type of belt is 45 millimeters. Given this, we will also start from the diameters of the available blanks. In our case, there are blanks with a diameter of 100 and 80 millimeters. Under them, we will adjust the diameters of the pulleys.

We start the calculation. Let’s revisit our initial data and set goals. The speed of rotation of the motor shaft is 2790 rpm. Poly-V-belt type "RK". The minimum diameter of the pulley, which is regulated for it, is 45 millimeters, the height of the neutral layer is 1.5 millimeters. We need to determine the optimal pulley diameters, taking into account the required speeds. The first speed of the secondary shaft is 1800 rpm, the second speed is 3500 rpm. Therefore, we get two pairs of pulleys: the first is 2790 at 1800 rpm, and the second is 2790 at 3500. First of all, we will find the gear ratio of each of the pairs.

The formula for determining the gear ratio:

, where n1 and n2 are shaft rotation speeds, D1 and D2 are pulley diameters.

First pair 2790 / 1800 = 1.55 Second pair 2790 / 3500 = 0.797

, where h0 is the neutral layer of the belt, parameter from the table above.

D2 = 45x1.55 + 2x1.5x(1.55 – 1) = 71.4 mm

For the convenience of calculations and selection of the optimal pulley diameters, you can use the online calculator.

Instructions on how to use the calculator. First, let's define the units of measurement. All parameters except speed are indicated in millimeters, speed is indicated in revolutions per minute. In the "Neutral belt layer" field, enter the parameter from the table above, the "PK" column. We enter the value h0 equal to 1.5 millimeters. In the next field, set the rotation speed of the motor shaft to 2790 rpm. In the electric motor pulley diameter field, enter the minimum value regulated for a particular type of belt, in our case it is 45 millimeters. Next, we enter the speed parameter with which we want the driven shaft to rotate. In our case, this value is 1800 rpm. Now it remains to click the "Calculate" button. We will get the corresponding diameter of the counter pulley in the field, and it is 71.4 millimeters.

Note: If it is necessary to perform an estimated calculation for a flat belt or a V-belt, then the value of the neutral layer of the belt can be neglected by setting the “ho” field to “0”.

Now we can (if necessary or required) increase the diameters of the pulleys. For example, this may be needed to increase the life of the drive belt or increase the coefficient of adhesion of the belt-pulley pair. Also, large pulleys are sometimes made intentionally to perform the function of a flywheel. But now we want to fit into the blanks as much as possible (we have blanks with a diameter of 100 and 80 millimeters) and, accordingly, we will select the optimal pulley sizes for ourselves. After several iterations of the values, we settled on the following diameters D1 - 60 millimeters and D2 - 94.5 millimeters for the first pair.

D2 = 60x1.55 + 2x1.5x(1.55 – 1) = 94.65mm

For the second pair D1 - 75 millimeters and D2 - 60 millimeters.

D2 = 75x0.797 + 2x1.5x(0.797 – 1) = 59.18 mm

Additional information on pulleys:

We have started the first experiments and have already prepared the first part of the material: Belt drive test. Poly V-belt. An educational short video was also released.

Calculation of the diameters of the belt pulleys for a V-ribbed belt. Online calculator.

Calculation of diameters of belt pulleys using a V-belt. Online calculator.

Calculation of diameters of belt drive pulleys using a flat driven pulley. Online calculator.

Calculation of the length of the V-ribbed drive belt. Online calculator.

Calculation of the length of the drive V-belt. Online calculator.

Calculation and selection of a tension roller for a V-ribbed belt

Calculation and selection of a tension roller for a V-belt

We sharpen a pulley for a V-ribbed belt

Belt drive test. Poly V-belt. First transfer.

Online calculators for all occasions, we recommend that you read:

Calculation of the amount of oil for gasoline,

Calculation of oil for the fuel mixture - container without volume marking,

Calculation of the shunt resistance of the ammeter,

Online calculator - Ohm's law (current, voltage, resistance) + Power,

Calculation of a transformer with a toroidal magnetic circuit,

Calculation of a transformer with an armored magnetic circuit.

automotogarage.ru

Program for calculating and drawing gears. GEAR TEMPLATE GENERATOR

If you are interested in the manufacture of various plywood products, then you must have met / seen various moving mechanisms (consisting of various gears) on the Internet. For example, a car marble or a plywood safe like this:

For more information about this safe, see this video:

Spur gears are the most easily visualized general gears that transmit motion between two parallel shafts. Because of their shape, they are classified as a type of spur gear. Since the tooth surfaces of the gears are parallel to the axes of the installed shafts, no axial force is generated in the axial direction. In addition, due to the ease of production, these mechanisms can be made with a high degree of accuracy. On the other hand, spurs have the disadvantage that they easily create noise.

Generally speaking, when two toothed gears are in a grid, the gear with more teeth is called "gear" and the other with fewer teeth is called "gear". In recent years, the pressure angle is usually set to 20 degrees. Commercial equipment most often uses part of the involute curve as the tooth profile.

Surely, you would like to find drawings of such a safe. Make it or use the ideas of its mechanisms in your projects. Since the author of this safe sells his products, he is unlikely to post drawings.

But this is no reason to be upset. Such mechanisms can be designed by yourself. And for this you do not need special knowledge in 3D modeling programs. Enough general knowledge of how gears work and GEAR TEMPLATE GENERATOR programs

While not limited to spur gears, shiftable gears are used when the center distance needs to be slightly adjusted or the gear teeth need to be reinforced. They are made by adjusting the distance between a toothed cutting tool, called a hob tool, and a gear during the manufacturing stage. When the shift is positive, the bending strength of the gear is increased, and when the shift is negative, the center distance slightly decreases.

Gap is a play between the teeth where the two gears are meshed and necessary to keep the gears turning smoothly. Too much play results in increased vibration and noise, while too little play results in tooth failure due to lack of lubrication.

I'll tell you how to do it. But first, a little about copyright. I found this program for free on the Internet. There is a newer version of the program on the author's website that costs money. It has more advanced functionality. I assume that the version of the program that I found was distributed free of charge. If this is not the case, please let me know and I will remove the program from my site.

In other words, they are involute gears, using part of the involute curve as the shape of their teeth. In general, the involute shape is the most common toothed belt shape due to, among other things, the ability to absorb small center distance errors, lightly made production tools make it easier to manufacture, thick tooth roots make it strong, etc. tooth shape is often described as a specification on a spur gear drawing, as indicated by the height of the teeth.

So, after you run GEAR TEMPLATE GENERATOR, you will see this window

The program interface has a standard top menu, a field for visual display of results, tabs at the bottom and fields for specifying various options and parameters.

In addition to standard full depth teeth, there are extended additions and tooth profiles. This article is reproduced with permission. Masao Kubota, Haguruma Nyumon, Tokyo: Omsha, LLC. The tooth shape of gears is usually shown as a flat curve in a cross section perpendicular to the shaft. Therefore, a pitch circle is used instead of a stepping cylinder. The contact point of the two pitch circles is called the pitch point. The pitch point is the point at which the two directions of the circles touch the rolling contact, so it is a spot that has no relative motion between the gears, or in other words, the instantaneous center of relative motion.

GEAR TEMPLATE GENERATOR builds drawings of only two "elements" at a time. It can be a gear-pinion (various options), a gear-straight part with teeth, or a sprocket-chain.

westix.ru

How to know the gear module? Calculation in Excel.

When a gear wheel or gear breaks down in the gearbox of any mechanism or machine, it becomes necessary to create a drawing for the manufacture of a new wheel and / or gear using the “old” part, and sometimes fragments of fragments. This article will be helpful for those...

Who has to restore gears in the absence of working drawings for failed parts.

Usually for a turner and miller, all the necessary dimensions can be obtained using measurements with a caliper. Requiring more attention, the so-called mating dimensions - dimensions that determine the connection with other parts of the assembly - can be specified by the diameter of the shaft on which the wheel is mounted and by the size of the key or keyway of the shaft. The situation is more complicated with the parameters for the gear milling machine. In this article, we will not only determine the module of the gear, I will try to outline the general procedure for determining all the main parameters of the gear rims based on the results of measurements of worn gear and wheel samples.

We “we arm ourselves” with a caliper, goniometer, or at least a protractor, ruler and MS Excel program, which will help you quickly perform routine and sometimes difficult calculations, and we begin work.

As usual, I will cover the topic with examples, for which we will first consider a cylindrical spur gear with external gearing, and then a helical gear.

Several articles on this site are devoted to the calculation of gears: “Calculation of a gear train”, “Calculation of the geometry of a gear train”, “Calculation of the length of the general normal of a gear wheel”. They contain figures with the designations of the parameters used in this article. This article continues the topic and is intended to reveal the algorithm of actions during repair and restoration work, that is, reverse design work.

Calculations can be performed in MS Excel or in OOo Calc from the Open Office package.

You can read about the rules for formatting Excel sheet cells that are applied in the articles of this blog on the "About the blog" page.

Calculation of the parameters of the wheel and gear of a spur gear.

Initially, we believe that the gear wheel and pinion have involute tooth profiles and were manufactured with the parameters of the original contour in accordance with GOST 13755-81. This GOST regulates three main (for our task) parameters of the initial contour for modules larger than 1 mm. (For modules less than 1 mm, the initial contour is specified in GOST 9587-81; modules less than 1 mm are recommended to be used only in kinematic, that is, not power transmissions.)

For the correct calculation of the parameters of the gear, measurements of both gears and wheels are necessary!

Initial data and measurements:

We start filling in the table in Excel with the parameters of the original contour.

1. The angle of the profile of the original contour α in degrees is written

to cell D3: 20

2. Tooth head height coefficient ha* enter

to cell D4: 1

3. The ratio of the radial clearance of the transmission c* is entered

to cell D5: 0.25

In the USSR and Russia, 90% of gears in general mechanical engineering were manufactured with precisely such parameters, which made it possible to use a unified gear-cutting tool. Of course, gears with Novikov gearing were made and special initial contours were used in the automotive industry, but nevertheless, most gears were designed and manufactured with a contour according to GOST 13755-81.

4. Type of teeth of the wheel (type of engagement) T write down

to cell D6: 1

T=1 - with external teeth at the wheel

T=-1 - with internal teeth at the wheel (transmission with internal gearing)

5. The center distance of the transmission aw in mm is measured along the gearbox housing and entered the value

to cell D7: 80.0

A number of center distances of gears is standardized. You can compare the measured value with the values ​​in the series shown in the note in cell C7. A coincidence is not necessary, but highly probable.

6-9. Gear parameters: the number of teeth z1, the diameters of the tops and bottoms of the teeth da1 and df1 in mm, the angle of inclination of the teeth on the surface of the tops βa1 in degrees are counted and measured with a caliper and protractor on the original sample and recorded accordingly

to cell D8: 16

to cell D9: 37.6

to cell D10: 28.7

to cell D11: 0.0

10-13. Wheel parameters: the number of teeth z2, the diameters of the tops and bottoms of the teeth da2 and df2 in mm, the angle of inclination of the teeth on the cylinder of tops βa2 in degrees is determined similarly - according to the original wheel sample - and written accordingly

to cell D12: 63

to cell D13: 130.3

to cell D14: 121.4

to cell D11: 0.0

I draw your attention: the angles of inclination of the teeth βa1 and βa2 are the angles measured on the cylindrical surfaces of the tops of the teeth!!!

We measure diameters as accurately as possible! For wheels with an even number of teeth, this is easier if the tops are not jammed. For wheels with an odd number of teeth, when measuring, remember that the dimensions shown by the caliper are somewhat smaller than the actual diameters of the protrusions !!! We make several measurements and write down the most reliable values ​​from our point of view in the table.

Calculation results:

14. Preliminary values ​​of the engagement module are determined by the results of measurements of the gear m1 and the gear m2 in mm, respectively

in cell D17: =D9/(D8/COS (D20/180*PI())+2*D4)=2.089

m1=da1/(z1/cos (β1)+2*(ha*))

and in cell D18: =D13/(D12/COS (D21/180*PI())+2*D4)=2.005

m2=da2/(z2/cos (β2)+2*(ha*))

The gear module plays the role of a universal scale factor that determines both the dimensions of the teeth and the overall dimensions of the wheel and gear.

We compare the obtained values ​​with the values ​​from the standard series of modules, a fragment of which is given in the note to cell C19.

The calculated values ​​obtained are usually very close to one of the values ​​of the standard series. We make the assumption that the desired module of the gear and pinion m in mm is equal to one of these values ​​and enter it

to cell D19: 2,000

15. The preliminary values ​​of the angle of inclination of the teeth are determined by the results of measurements of the gear β1 and the gear β2 in degrees, respectively

in cell D20: =ASIN (D8*D19/D9*TAN (D11/180*PI()))=0.0000

β1=arcsin(z1*m*tg(βa1)/da1)

and in cell D21: =ASIN (D12*D19/D13*TAN (D15/180*PI()))=0.0000

β2=arcsin (z2*m*tg (βa2)/da2)

We make the assumption that the desired angle of inclination of the teeth β in degrees is equal to the measured and recalculated values ​​and write down

to cell D22: 0.0000

16. Preliminary values ​​of the equalizing displacement coefficient are calculated based on the results of measurements of the gear Δy1 and the gear wheel Δy2, respectively

in cell D23: =2*D4+D5- (D9-D10)/(2*D19)=0.025

Δy1=2*(ha*)+(c*) - (da1-df1)/(2*m)

and in cell D24: =2*D4+D5- (D13-D14)/(2*D19)= 0.025

Δy2=2*(ha*)+(c*) - (da2- df2)/(2*m)

We analyze the obtained calculated values, and the decision made on the value of the equalizing displacement coefficient Δy is written down

to cell D25: 0.025

17.18. The pitch diameters of the gear d1 and the gear wheel d2 in mm are calculated accordingly

in cell D26: =D19*D8/COS(D22/180*PI())=32,000

and in cell D27: =D19*D12/COS (D22/180*PI())=126,000

19. Dividing center distance a in mm we calculate

in cell D28: =(D27+D6*D26)/2=79,000

20. Profile angle αt in degrees is calculated

in cell D29: =ATAN (TAN (D3/180*PI())/COS (D22/180*PI()))/PI()*180=20.0000

αt=arctg(tg (α)/cos(β))

21. The engagement angle αtw in degrees is calculated

in cell D30: =ACOS (D28*COS (D29/180*PI())/D7)/PI()*180=21.8831

αtw=arccos(a*cos (αt)/aw)

22.23. Coefficients of displacement of gear x1 and wheel x2 are determined accordingly

in cell D31: =(D9-D26)/(2*D19) -D4+D25=0.425

x1=(da1- d1)/(2*m) - (ha*)+Δy

and in cell D32: =(D13-D27)/(2*D19) -D4+D25 =0.100

x2=(da2- d1)/(2*m) - (ha*)+Δy

24.25. The coefficient of the sum (difference) of displacements xΣ(d) is calculated to verify the correctness of the previous calculations using two formulas, respectively

in cell D33: =D31+D6*D32=0.525

and in cell D34: =(D12+D6*D8)*((TAN (D30/180*PI()) - (D30/180*PI())) - (TAN (D29/180*PI()) - (D29/180*PI())))/(2*TAN (D3/180*PI()))=0.523

xΣ(d)=(z2+T*z1)*(inv(αtw) - inv(αt))/(2*tg(α))

The values ​​calculated by different formulas differ very slightly! We believe that the found values ​​of the modulus of the gear and pinion, as well as the displacement coefficients, are determined correctly!

Calculation of the parameters of the wheel and gear of a helical gear.

Let's move on to the helical gear example and repeat all the steps we did in the previous section.

It is practically very difficult to measure the angle of inclination of the teeth with the required accuracy using a goniometer or protractor. I used to roll the wheel and gear on a sheet of paper and then make preliminary measurements with a protractor of a drawing board dividing head with an accuracy of a degree or more ... In the example below, I measured: βa1=19° and βa2=17.5°.

Once again, I draw your attention to the fact that the angles of inclination of the teeth on the cylinder of the vertices βa1 and βa2 are not the angle β involved in all basic transmission calculations !!! The angle β is the angle of inclination of the teeth on the pitch cylinder (for transmission without offset).

Due to the smallness of the values ​​of the calculated displacement coefficients, it is appropriate to assume that the transmission was performed without displacement of the generating contours of the gear and gear.

Let's use the Excel service "Parameter Selection". I once wrote about this service in detail and with pictures here.

In the Excel main menu, select "Tools" - "Parameter selection" and in the pop-up window fill in:

Set in cell: $D$33

Value: 0

Changing cell value: $D$22

And click OK.

We get the result β=17.1462°, xΣ(d)=0, x1=0.003≈0, x2=-0.003≈0!

The transmission, most likely, was made without displacement, we determined the module of the gear and gear, as well as the angle of inclination of the teeth, you can make drawings!

Important notes.

The displacement of the initial contour when cutting the teeth is used to restore worn surfaces of the teeth of the wheel, to reduce the depth of penetration on the gear shafts, to increase the load capacity of the gear train, to perform the transmission with a given center distance not equal to the pitch distance, to eliminate trimming of the legs of the gear teeth and tooth heads wheels with internal teeth.

There are height correction (xΣ(d)=0) and angular correction (xΣ(d)≠0).

The displacement of the generating circuit is usually used in practice in the manufacture of spur gears and very rarely helical gears. This is due to the fact that in terms of bending strength, an oblique tooth is stronger than a straight one, and the required center distance can be provided with an appropriate angle of inclination of the teeth. If height correction is occasionally used for helical gears, then angular correction is almost never.

A helical gear runs smoother and quieter than a spur gear. As already mentioned, helical teeth have a higher bending strength and a given center distance can be provided by the angle of inclination of the teeth and not resort to displacement of the producing contour. However, in gears with oblique teeth, additional axial loads appear on the shaft bearings, and the wheel diameters are larger than spur gears with the same number of teeth and module. Helical gears are less manufacturable, especially those with internal teeth.

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Program description

The program is written in Excel and is very easy to use and learn. The calculation is made according to the Chernasky method.
1. Initial data:
1.1. Permissible contact voltage, MPa;
1.2. Accepted gear ratio, U;
1.3. Torque on the gear shaft t1, kN*mm;
1.4. Torque on the wheel shaft t2, kN*mm;
1.5. Coefficient;
1.6. Coefficient of crown width by center distance.

2. Standard district module, mm:
2.1. allowable min;
2.2. Permissible max;
2.3 Accepted according to GOST.

3. Calculation of number of teeth:
3.1. Accepted gear ratio, u;
3.2. Accepted center distance, mm;
3.3. Adopted engagement module;
3.4. Number of gear teeth (accepted);
3.5. The number of teeth of the wheel (accepted).

4. Calculation of wheel diameters;
4.1. Calculation of pitch diameters of gears and wheels, mm;
4.2. Calculation of the diameters of the tops of the teeth, mm.

5. Calculation of other parameters:
5.1. Calculation of the width of the gear and wheel, mm;
5.2. Peripheral speed of the gear.

6. Checking contact voltages;
6.1. Calculation of contact stresses, MPa;
6.2. Comparison with allowable contact stress.

7. Forces in engagement;
7.1. Calculation of circumferential force, N;
7.2. Calculation of radial force, N;
7.3. Equivalent number of teeth;

8. Permissible bending stress:
8.1. Choice of gear and wheel material;
8.2. Allowable stress calculation

9. Flexural stress test;
9.1. Calculation of the bending stress of the gear and wheel;
9.2. Fulfillment of conditions.

The spur gear is the most common direct contact mechanical gear. A spur gear is less durable than other similar gears and less durable. In such a transmission, only one tooth is loaded during operation, and vibration is also created during the operation of the mechanism. Due to this, it is impossible and impractical to use such a transmission at high speeds. The service life of a spur gear is much lower than other gears (helical, herringbone, curved, etc.). The main advantages of such a transmission are ease of manufacture and the absence of axial force in the bearings, which reduces the complexity of the gearbox bearings, and, accordingly, reduces the cost of the gearbox itself.