Any owner of a lathe sooner or later is faced with the task of approximate calculation of guitar gears. This may be due to the need to cut at least a few threads of inch threads, having only a metric lead screw, or to the need to manufacture a worm gear to fit the existing gears. Mathematically, the problem is very simple and boils down to sorting through all the gears available. You can find a solution to this problem online on a very interesting site for me: www.luaz967.ru. The author of the program writes that even though he has Linux: “the face of the program is made in VB because it takes a matter of seconds to develop/revise the interface.” I also have Linux, but since the program runs perfectly through wine, I considered it a waste of time to rewrite it on Gambas or QT. But making a program for a phone that you always have with you seemed quite interesting. Since the problem of calculating urgently needed gears had already been solved using the above-mentioned program, I decided to raise the fun factor to a power and write a program directly on my phone using De Re BASIC! , and even with a face, which, generally speaking, was overkill, since I was writing a program for myself and the time required to enter the required parameters into the source code would be comparable to working through the program menu. To run the program, De Re BASIC! must be installed on your phone. Then you can launch it and download the program. Or you can create a link on your desktop and launch the program by clicking on it. Submenus are called up and the program is launched by clicking on the corresponding line.
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Main menu of the program |
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Selecting the lead screw pitch. |
Selection of standard threads |
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Selecting the number of gears involved in the calculations |
Calculation results |
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Source code editor |
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The source code of the program can be downloaded. Desktop icon. The program is distributed under a license that coincides with the Russian translation of the GENERAL PUBLIC LICENSE GNU (I wrote in detail about the reasons for such licensing). Obviously, in the Eclipse development environment with the Android SDK Tools installed, it was possible to quickly write a faster and more beautiful program, but this is a task for a desktop computer, and I wanted to show that Robinson will solve the problem with one phone. As a result, HTC Desire HD with the Basic interpreter coped with the task of calculating inch threads on a machine with a metric lead screw in 19 seconds. Moreover, 5 of them were spent sorting the results by the magnitude of the deviation from the specified parameters. It's not instantaneous, but considering that changing gears takes minutes, I found the result acceptable.
To finally convince myself that 19 seconds is fast, I decided to evaluate the progress of the pocket computer technology over the past 30 years. A slide rule speeds up the task of searching through options slightly, so a Casio FX-702P calculator programmed in Basic, purchased in 1984, was taken out of the bins and the same calculation program was launched on it, although without sorting the results. The calculation took 17 minutes 45 seconds. Those. 56 times more. Moreover, I note that for such problems this is not fatal, because 30 years ago I would have written down the results of calculations, rather than running the program every time before changing gears.
Using the program quickly showed that my set of gears was by no means optimal; more were needed. The solution was again found on the same website with the program in the article: “Spindle cutting”. However, I decided that sacrificing a frying pan is overkill, given the availability of CDs, which may not last forever, but I believe that for my purposes, even one will not wear out soon, and making a new one, using the old one, when it starts to wear out can be quite quickly and accurately. Actually, I made the first disk quite roughly, marking it in inkscape, and then installing it in the device in the photo below, I made it working, clamping a drill from Proxxon instead of a cutter, while the initial errors were leveled out by the gear ratio of the splitter of 1:45.
To begin with, a gear with 42 teeth was made. In the photo it is made of white caprolon next to the original black one.
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 dry maker instructions on how to model a gear using several easily measurable parameters; on the other hand, I will not ignore the theory.
As an example, let's take a gear from a car throttle valve:
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 involute gearing.
To study the parameters of gears, we will use a 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 it. We will directly model later.
So, let's launch Gearotic
On the left in the Gears field, click Circular, we get into the gear editor:
Let's consider the proposed parameters:
First two columns Wheel and Pinion
Wheel - this will be our gear, and Pinion will be the counterpart, which will be in our in this case not interested.
Teeth- number of teeth
Mods- tooth shape modifiers. The easiest way to understand what they do is to cook them. Not all settings are applied automatically. After the change, 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 its teeth inward (ring gear).
Jackdaw Rght Hnd(Right Hand) - changes the bevel direction of 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.
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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 it to 20 degrees.
Rack fillet- smoothing the base of the tooth. Leave it at 0.
Block Tooth Form
We leave Involute - involute gearing. Epicylcoidal is a cycloid gear used in precision instrumentation, such as watch movements.
Face Width- gear thickness.
Block Type
Spur- our spur gear.
Helical- helical gear:
Let's return to our gear.
The large wheel has 47 teeth, outer diameter 44.6 mm, bore diameter 5 mm, thickness 6 mm.
The module will be equal to 44.6\(47+2)=0.91 (rounded to the second digit).
We enter this data:
On the left is a table of parameters. We look at Outside Diam (external diameter) 44.59 mm. Those. quite within the measurement error of a caliper.
This way we got the profile of our gear by taking just one simple measurement and counting the number of teeth.
Specify the thickness (Face Width) and hole diameter (Shaft Dia at the top of the screen). Click Add Wheel to Proj to get a 3D visualization:
Unfortunately, the free version does not allow you to export the result, so you will have to use other tools.
Install FreeCAD
If you don't know Frikad, don't worry, you won't need any deep knowledge. Download the FCGear plugin.
We find the folder where Frikad was installed. In the Mod folder, create a gear folder and place 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 gear that appears in the tree on the left and go to the “Data” tab at the very bottom:
In 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)
All that's left is to make a hole. Let's go to the Part tab and select Create Cylinder. In the Data we indicate a radius of 2.5 mm and a height of 20 mm
Hold down the Ctrl key, select the gears in the tree and click Create a union of several shapes on the toolbar.
Then, again holding Ctrl, select first the resulting single gear, and then the cylinder and click Trim two shapes
P.S. I wanted to talk a little more about exotic cases, but the article turned out to be long, so perhaps another time.
If you are interested in making various products from plywood, then you have probably come across/seen various moving mechanisms (consisting of various gears) on the Internet. For example, marble machines or this safe made of plywood:
You can see more details about this safe in this video:
Surely, you would like to find drawings of such a safe. Make it or use ideas for its mechanisms in your projects. Since the author of this safe sells his products, it is unlikely that he will post drawings.
But this is not a reason to be upset. You can design such mechanisms yourself. And for this you do not need special knowledge in 3D modeling programs. Enough general knowledge of how gears and programs work GEAR TEMPLATE GENERATOR
I'll tell you how to do it. But first, a little about copyrights. I found this program in free access in the Internet. The author's website has more a new version programs that cost 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.
So, after you run GEAR TEMPLATE GENERATOR, you will see a window like this
The program interface has a standard top menu, a field for visually displaying results, tabs at the bottom and fields for specifying various options and parameters.
GEAR TEMPLATE GENERATOR builds drawings of only two “elements” at a time. This can be a gear-pinion (various options), a gear-straight piece with teeth, or a sprocket-chain.
The lower part of the options screen is divided into two halves. The right side displays various options for visualizing the result. Left side– three tabs are exactly the settings for the future gear connection.
On the Spokes&more tab (spokes and more) – you can configure gear parameters, such as: the number of spokes, the diameter of the axial hole, the diameter of the gear, the gap between the teeth.
three spokes
four spokes
Chain&sprocket tab – chain and sprocket. Chain transmission parameters can be configured and obtained.
But we will be more interested in the first tab.
On the Gear properties tab – the main parameters of gears. You can set the number, size and type of teeth, the distance between them.
The cog type switch has three positions:
Involute – regular teeth, like in the first photo
Pin – sharp teeth on one gear, round teeth on the other (bearings as an option)
Protractor is simply a protractor - dividing a circle into the required number of segments.
Below in the same area, two areas Gear1 and Gear2 are highlighted with a frame. These are the parameters of the first and second gear. Here you can specify the number and size of teeth. And also choose the type of gear itself.
Spur– regular gear – teeth out
Ring– gear with teeth inside – such gears are useful for building planetary mechanisms/gearboxes.
Third option Rack– the gear turns into a rectangular piece with teeth. Ideal for building retractable safe bolts from the beginning of the post
Thus, to obtain a diagram of the functioning of the locking mechanism of a safe, you need to decide on the number of retractable bolts, estimate how many gears will be needed to transmit rotational motion to each bolt, divide the gears into pairs and draw them in this program.
I forgot to say, in this program you can select the units of measurement that suit you, which is very convenient.
GEAR TEMPLATE GENERATOR allows you to save the result in various formats. I will note only two - DXF– you can transfer it to the same AutoCAD and make a control program for CNC and PDF– Can be printed for hand cutting.
As you can see, using GEARTEMPLATEGENERATOR making a safe from plywood, which was mentioned at the beginning of the post, is quite simple. But this is not the limit of the program's use. Below is one of the more complex examples.
Planetary mechanism
| Download GEAR TEMPLATE GENERATOR |
Gear, finding the right model and selecting its exact dimensions takes quite a lot of time. Of course, the gear must also work.
Therefore, here is a small list of tools that will seriously help you in solving this task, as well as a small guide to these tools.
Gear Generator
To make sure that the project is compatible with the application, you need to see whether the customizer button is active and whether it is on the object page. If yes, just click on it and the application will open.
Now you can change the project parameters at your discretion, and then create an STL file.
Allows you to make internal gear and rack.
Inkscape
Drawing a working gear in Inkscape is not a big problem. If you don't have Inkscape, on Linux you can simply install the appropriate package from the distribution, and on Windows, run the automatic installer. The package and installer can be downloaded from the Inkscape website.
In order to create gears in this program, it is not necessary to have any knowledge of vector graphics; all the necessary steps will be performed by an extension called Gear.
Simply enter your values and click Apply to see the application in action.
When everything is ready, save the SVG, and after processing with the slicer, you can start extruding.
Blender doesn't bite! (Almost)
Yes! Blender can do all this too. It's so easy and so fast...First of all, you need to enable additional grids in the settings.
Go to the Add-ons tab and enable Mesh Extra Tools.
Now press Shift + A and select Gear option.
The tool is ready for work! Export the result of your work to STL.
Program description
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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 stress, MPa;
1.2. The adopted 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. The coefficient of the width of the crown based on the distance between axes.
2. Standard circumferential module, mm:
2.1. permissible min;
2.2. Allowable max;
2.3 Accepted according to GOST.
3. Calculation of the 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. Number of wheel teeth (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 tooth tips, mm.
5. Calculation of other parameters:
5.1. Calculation of the width of the gear and wheel, mm;
5.2. Gear peripheral speed.
6. Checking contact stresses;
6.1. Calculation of contact stresses, MPa;
6.2. Comparison with permissible contact stress.
7. Meshing forces;
7.1. Calculation of circumferential force, N;
7.2. Calculation of radial force, N;
7.3. Equivalent number of teeth;
8. Allowable bending stress:
8.1. Choice of gear and wheel material;
8.2. Calculation of permissible stress
9. Bending stress test;
9.1. Calculation of bending stress of gear and wheel;
9.2. Fulfillment of conditions.
The spur gear is the most common direct contact mechanical gear. Spur gears are less durable than other similar gears and are less durable. In such a transmission, only one tooth is loaded during operation, and vibration is also created during 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 that of 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 supports, which reduces the complexity of the gearbox supports and, accordingly, reduces the cost of the gearbox itself.
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