Worm Gear Calculation

No one that is involved in design wants to deal with Worm gears. Just the engineers or designers that are familiar with this type of applications have no problems to understand the development, working conditions, manufacturing and design of a worm gear set.
In my case, it took me a long period of time to have an idea about the minor details of this mechanical element, and I am just able now to define them geometrically, calculate the forces and evaluate the proper assembly and understand some cases of failures.
I have read some articles and gear handbooks to verify the informatoin given in this application for Android, wich is going to be available in three of four weeks.

Here you have some links to useful information:

KHK gears
Autodesk Basic Information
Research gate Worm Gears PDF

I will add more information of worm gears while I am progressing with the application.

Worm Input motion:

Worm in YouTube

Here we have the worm wheel in motion with the worm. Input and output together.

Now the final animation is ready. Time to work in the app.

It took me more time than I wanted, but the app is now available in Google Play.
The application will help you to design a worm gear according to the reccomendations found in different articles and books.
You may need to know the transmission ratio of your gearset, as well as the center distance between worm and wormgear.
After filling those two variables, the worm should be defined with a set of parameters that are neccesary to calculate the whole gearset. The app will give you some indications to fill them.

The following images explain the way to work with this new application:

The application is available in Google Play:

What have I learned during the application development and the usage of this type of mechanical ellements...
First of all, this type of gear set has the difficulties of a typical gear set design with the difficulties of the a bevel gear transmission.
The capacity of provide a huge reduction in a very small space would drive engineers to think in this transmission as a solution instead of using, maybe a planetary system. But, consider the following facts:

- Worm gear manufacturing is difficult and should be done by specific manufacturing suppliers that could provide the quality you require for your application.

- Worm wheel, may not be as difficult to machine as the worm and it will not need a quality grade as tight as the worm also, because it will tend to wear and accomodate the worm geometry to the tooth surface and part of the geometric deviations will dissapear, but it will need some work to think the way you want to attach this worm wheel (in general a piece that would be serviceable) to the ouput shaft.

- The location of the gear contact has, in worm gear design, three possible linear deviations. Compared to a typical spur gear set, the worm and worm wheel could move in X, Y and Z direction, Probably the center distance is the one that in general can not be adjusted by shims, but the axial location of the worm as well as the axial direction of the worm wheel can be adjusted slightly.
Doing that, you can reduce the transmission error and adjust the backlash of your system.

- Lubrication, Lubrication and Lubrication. It is essential to provide good lubrication to the gear mesh because the relative motion between gears is almost sliding. Therefore, oil type and oil lubrication method should be designed carefully.

Here you have some links to useful information I found about worm, and worm wheels:

• Nptel Worm Gears
• khkgears.net
• Worm Gear Design, 
• TY  - CHAP, AU  - Suleiman Khayal, Osama, PY  - 2017/07/20, SP  -, T1  - Worm GearsER  - 
• Knowledge.autodesk.com
• www.copperalloys.net
• www.machinerylubrication.com
• Lubricate-worm-gears

Shaft - Hub Press Fit Calculator

When I started to work in things related with mechanisms, materials, engineering details, transmissions...etc I was struck by the torque and resistance capacity of these type of press fit joints. 

Nobody told me, by this time, how well should be controlled the dimensions of the parts that create the joint. Even small tolerances expand considerably the difference between min and max torque capacity.

I hope the list of suggestions I am writing here help you to design your joint:

• If your joint rotates and you can add a key in your joint, just do it, It is a safety device that will help you to sleep better.
• Double check the expansion of the external part, the hub. Only in the case your surrounding parts are too close to the hub.
• Provide generous chamfer at the hub and shaft entries.In general a 20 degree angle is enough. During the assembly, try to avoid an edge contact between parts, so look at the interference sequence and verify that chamfer ends do not coincide by the time you start to press. Sometimes a difference in the chamfer angle helps.
• Tolerance ranges capable and reliable for a standard grinding are around ±0.013, Eventhough you can use a tight values like ±0.008 but probably your cpk would be far away from 1.33 unless you pay so much for the parts.
• Take care with thinner parts. On shafts, the inner diemater can end as an oval. If you press fit so much a bearing cup, the rolling ellements could find areas with less clearance than others and that would generate a speed reduction in your rolling elements, sliding, heat and infant failures. In the other hand, a thin hub, will copy so well the shaft geometry that any size imperfection will end at the outside of the hub. Also the torque capacity will be very poor and depending on the material, the elastic curve of the hub can easily be overpassed and finally yields to a permament deformation.
• Use if possible a retainer compound,
• Assemblymag.com
• Loctite Retainers
• If possible, use the same material for hub and for shaft. If not possible, at least both would have the same elasticity module. In case using a different material have a look at the part with the lowest module, this one will limit the capacity and the geometry of the joint.
• To obtain better results and to avoid excessive wear during the assembly, due to the friction between surfaces a hub preheat or a shaft temperature reduction is needed in some cases. Also that effect will help the assembly process o reduce the force needed to join the parts. Caution must be taken to avoid preheat at temperatures that could temper the parts and reduce its surface hardness. In general, I do not accept prehteats that exceeds 180 ºC.

Epicyclic Gears

This Android App is designed to perform an initial calculation of a simple epicyclic arrangement with a sun, ring, planets and carrier.

Define the motion parameters, teeth number of the different elements and the speed and torque to obtain different results as:

• Total ratio of the system.
• Relative motion to the carrier.
• Geometry verification.
• Absolute Speed of each element.
• Cycle counting, Tooth Contact per minute of each gear
• Factorization value of Sun and Ring Gear
• Torque results of each element.

Different animations are included within the app, just click at the image at the right side of the motion selection.

Also, the definition of "factorization" is described in this video (click to the link)

 App Images:

A link to a youtube video created for each motion definition is available when clicking over the gear image.

Three different types of motion were created:

Planetary:

Solar :

Star:

Many links and lectures are recommendable, I have found interesting for basic and intermediate study the following links and Standards:

• Epicyclic Gearing: A Handbook
• Agma 6123. Design Manual for Enclosed Epicyclic Gear Drives
• Efficiency of a Planetary GearBox
• Efficiency of planetary Gear Trains
• Dynamics of Planetary Gear Trains

Involute Spline Calculation App

This app calculate the shear stress, contact stress and safety factors of a involute spline shaft under a defined torque. This calculation gives a good direction on design and will help to define sizes and lengths of shafts, and therefore the parts that are assembled on it. Bearings, Seals, snap rings sizes will, in most cases, be defined by the spline torque capacity.
The calculation is based in the document released by Darle W. Dudley, and used in many different engineering books.
The geometry of the inner diameter and the outer diameter is approximated for a quality 6 spline.
This calculation can be used for splines designed under the standard ANSI B92.2M or ISO4561.
This tool is defined for giving you directions and not definitive or complete designs. For that particular purpose, It is reccomended to run more accurate analysis and of course validate your designs with physical parts.

    Involute Spline Torque Calculation

Aditional Information about Splines:

• The function of a spline can be defined as fixed or sliding. Sliding one is oftenly used in synchronizers, shift gears and other similar machine elements.Fixed ones, are designed for not allowing any axial movement, therefore a minimun clearance, side or outer diameter is desired.A good practice on fixed splines is te use of pilot diameters for centering the load distribution and avoid excesive tilting in the connection.
• Splines work better when it is lubricated. Grease or oil will avoid premature failures due to fretting.
• Fillet root splines resist better the torque load, even when the minimun diameter is smaller compared with a flat root spline.
• A minimun taper angle on the outside diameter of the spline, along the overall effective length could help when torque twist the shaft and the contact distribution runs to the front or rear area of the spline. FEA analysis can help yo to determine the amount of taper needed.
• Splines failures would happen due to:
• Wearing of the spline teeth due to high contact stress and poor lube.
• Broken shaft due to high torsional stress.
• Spline fretting due to vibration, axial movement and poor lube
• Bending failure due to a small section under the tooth. Hollow diameter to big.
• If Faiure happen due to shear stress, shock load may be the reason.
• As general rule, use quality 6, according ANSI B92.2, for general purposes splines. Quality 7 allows more geometrical deviations and can be used for low spec requirements or when the safety factors are really high. Quality 4 and 5 are choosen when the spline is grinded and the contact distribution must be controlled.
• If the teeth number is low, you will require the tooth to tooth spline locatin to have more  accuracy to asure that all teeth share a similar torque level. It is more easy for a spline with smaller module and high teeth number to share equally the load.
• It is reccomended not to have parts in contact with a different in hardness > 8.
• Splines and Shaft materials:
• SAE 1010 & SAE 1020  Low cost material, under low solicitations and where part of the shaft is heat treated (carburized)
• SAE 1045  Common steel used for shafts. Low cost material. Can be heat treated and provide high load resistance. It is not a good selection if the fatigue strength is a mayor requirement on your design.
• SAE 4340 Cr-Ni Steel, bonified (Quenched and Tempered) high toughness and tension resistance.
• SAE 4140 Cr-Mo Steel that is commonly bonified and induction hardened. This steel is used for applications under high load requirements.
• Shaft Design (Link).
• Failure modes (link)
• Load Distribution (Link)

Flange Coupling Calculation.

Quick and fast way to determine the torque capacity of a flange coupling,
Calculation is based on the combination between bolt tension and the coefficient of friction between surfaces.

This calculation do not consider, in any case, that bolts could work under shear load therefore all torque must be transfer between the surfaces.
It was observed in many cases, that once any of the bolts that belong to the pattern, starts to work under shear load, the torque distribution changes within the bolt pattern. 
Bolt will start to work also under combined bending loads which at the end will lead into a premature failure.

The tightening torque is determined using an "utilization factor" of 0.8.












































                                                                Flange Coupling Calculation

Additional Information about Flange Couplings:

Lessons Learned:

• A bolt that is not properly tightened can become loose after a short period of time
• If the fasteners are loose, they are subjected to alternating forces and may fail through fatigue.
• Few bolts could work only in tension, ans some of them work also in shear. Do not overload the flange to avoid premature failures.
• If it is possible, tight always the nut and not the bolt.
• Replace locknuts after some installations. Five or six is a good number.
• Try to keep the oil or grease out of the flange contact as well as from the bolt or nut area.
• Assembly instructions:
• Tight the bolt in pairs crosswise, looking for the opposite one each time.
  During all of the following steps, keep any gap between flanges even all around the circumference, and nuts made up approximately the same amount on each end of the bolt.
  • First time around just snug the nuts with a hand wrench.
  • Second time around tighten the nuts firmly with the same wrench.
  • Third time around apply approximately 25% recommended torque.
  • Fourth time apply approximately 75% of recommended torque.
  • Fifth time around, apply 100% of recommended torque.
  • Continue tightening nuts all around until nuts do not move under 100% recommended torque.
  • If possible, re-torque after 24 hours. Most of any bolt preload loss occurs within 24

Fastener Torque Calculation

Developed for designers and engineers that look for more information about the fastener than only the torque value.

This tool uses the concept of "Utilization Factor", that varies from 0.5 to 0.8. This factor is linked to the type of work the fastener is going to do in the joint. From just a quick clamp, no structural, no risk joint to a design where the fastener perfomance is critical.

Here are some screenshots of the application:

 

  Fastener Torque Calculation

    Additional information about joints and fasteners:

• Metric Grade
• Bolt Science
• Futek
• RoyMech
• Metric to SAE socket conversion
• MIT Open Course

   Lessons learned:

• Provide enough clearance for the wrench tools to access to the head of the bolt.
• Be sure that bolt can be assembled and dismounted, specially attention with long bolts that may be replaced without tier down all the transmission,
• Try to standarize all bolt types and sizes in the gearbox, specially in areas where the bolt is working in the same way. (housing calmping bolts for example)
• Do not mix same bolt sizes with different grades in one gearbox position.
• In castings, be sure that bolt head is not contacting an angled surface. Try to clean up always the casting surface, specially in aluminum castings.
• In aluminum, use roll form threads.
• When specifying the hole dimensions, leave at least 3 times the pitch size of gap between the tap drill depth and the thread depth. One way to specify this type of geometry can be done in this way: 
• Speficy the tap drill Max depth and specify the thread Min depth.
• A whaser under the bolt head can promote a better pressure and contact distribution. 
• Find the right location tolerances when defining the joint holes. Keep in mind always the rule of Clearance = Tolerance. An acceptable position value for threaded holes might be between 0.6 - 0.8. The MMC of the bolt is always its Outside diameter. From those values you may find the hole through diameter and its tolerance.
• If your calculations consider the bolt to be dry and without oil, make sure that you are receiveing this from your supplier.
• When the shank diameter of a bolt is less than the thread diameter thus allowing a radiused thread runout which reduces stress concentration - beneficial in fatigue applications.
• Distance between bolts to clamp the gearbox housings toghether should be around at 6.5  - 7 times the bolt diameter. (Example, M12 bolt diameter, distance between bolts should be around 78 mm and 84 mm)
• Avoid curved geometry between bolts in gearbox housings. Always think on designing for the min distace between bolts.
• If you suspect fatigue, a rule of thumb is to calculate the number of cycles a ferrous metal part has been exposed to before it failed:
• Failure at less than 10,000,000 cycles:  suspect fatigue.
• Failure at over 100,000,000 cycles: fatigue is not likely.
• It only takes 3600 rpm motor only 46 hours to produce 10,000,000 cycles.
• A 75 Rpm mixer shaft coupling bolt failing after 2 ½ years has over 100,000,000 cycles.
• From Fatigue Failure in Bolted Joint
• When joining materials with strengths lower than that of the bolt strength, a washer must be used to avoid bearing failure at the bolt/nut-material interface. In this case a washer should be used under both the nut and head of the bolt.
• The larger the washer diameter the thicker and stiffer the washer should be. It is also apparent that the strength of the washer must be at least equal to the strength of the bolt.