Gear Profile Tolerances

I think that one of the best ways to understand a subject is trying to build something that uses somehow materials that are part of this subject. I mean, if you want to know something about the wind, you can start building your own weather-vane, and probably you would need to read about this matter before starting to make anything until you gain the confidence to put your weather-vane at the top of the roof.
That's what have happened with this application. I am not a super gear expert but I have to deal with them, I have to decide if something has to be scrapped or not, and understand quality deviations over the tooth surface to move forward with the parts, test them, rework them (not always possible).
As many others technicians I had many doubts about how to interpret the information coming from quality, from the measurements of the gear profile, so I decided to read, and collect enough information to be sure that next time I have to review a gear report, I would have the chance to see it with a different perspective.
So, here you have some notes, links and a application created for android to define the deviation values of the profile (surface) of a gear tooth.

First of all, deviation calculations are based on the standard DIN 3691, which is similar to the ISO1328 or AGMA ISO 1328.

I will try to describe the three most important measurements (or type of measurement) that are always reported in a gear inspection:

 Profile Deviations:

If you hear the word "profile" of a gear, you should relate it to the arc that goes from the bottom of the tooth to the top of it, basically up to the tip or outside diameter of the gear.
In general, deviations in the profile, are only measured at the 92% of the active length, and it is called "profile evaluation range".
As it is defined by the ISO 1328, "Profile deviation is the amount by which an actual profile deviates from the design profile. It is in the transverse plane and normal to the involute profile."

The image describe how the profile is obtained from the roll angle of the gear tooth.

Image taken from :http://www.gearsolutions.com/article/detail/5565/an-elementary-guide-to-gear-inspection

Type of Profile Errors:

Three important types of errors are related to profile, Profile Form Deviation, Profile Slope deviation and Total profile deviation.

Profile Form Deviation (ffa):

Distance between two involutes of the actual base circle, that enclose the actual involute profile within the profile inspection range

Can also be defined as the divergence of the measured profile from a best fit line or curve.

Profile Slope Deviation (fHa):

Distance between two nominal profiles that intersect the average profile at start and end points of the profile range or Profile slope deviation is the amount of deviation from a nominal involute profile over the evaluation range.

Total Profile Deviation: (Fa):

Is the total amount of profile error, including slope and form errors or the distance between two nominal profiles enclosed within the profile test range.

Image from : http://www.geartechnology.com/articles/1114/Application_of_Statistical_Process_Capability_Indices_in_Gear_Manufacturing

Images taken from:http://www.geartechnology.com/issues/1194x/smith.pdf

Helix deviations:

AGMA’s current inspection handbook defines “helix deviation” (formerly tooth alignment variation and lead variation) as the difference between the measured helices to the design helices. In practice an appropriate measuring machine aligns the measuring probe on the test gear at the pitch circle diameter and the “lead” is traced and recorded graphically, with a correct unmodified helix being represented as a straight line on the chart. Helix measurement is used to determine correct face contact between mating gears. Incorrect helix will create uneven loading and noise.
The ISO 1328 explained in the following terms:
" Helix deviation is the amount, measured in the direction of the transverse base tangent, by which an actual helix deviates from he design helix ".

Image taken from :http://www.gearsolutions.com/article/detail/5565/an-elementary-guide-to-gear-inspection

Type of helix errors:

Helix Form Deviation (ffb):
Distance between two helical lines that enclose the actual lead within the lead inspection range. Helix form deviation is the divergence from a best fit curve along the helix

Helix Slope Deviation (fHb):
Helix slope deviation is the amount of deviation from a nominal helix over the evaluation range. Distance (in transverse plane) between two nominal leads that intersect the average lead (helix) at start and end points of the lead inspection range.

Total Helix Deviation (Fb):
Distance between the two nominal leads enclosed within the lead inspection range.The total amount of error including angle and form errors.

Source :https://www.iso.org/obp/ui/#iso:std:iso:1328:-1:ed-2:v1:en

This picture is quite helpful because it gives you an idea bout the way the tooth is measured and what is the meaning of the traces showed in the right side.

Pitch Deviations:
The notation pitch, should make you think about tooth location, and the effect that this type of deviations would have into the gear motion and torque transferring. It is related to, backlash, contact ratio variation...
It is looking at the location of a gear tooth with respect to the others, as well as the global location between all gear teeth. Measures, the difference between the actual position of the tooth and the "should be here" position.
The application calculate the values of the pitch error (fu), the single pitch deviation (fp) and total pitch deviation (Fp).

Types of pitch deviations:

Single pitch deviation (fp):
It is the difference between two adjacent teeth index values (+,-) or the algebraic difference between the actual pitch and the corresponding theoretical pitch in the transverse plane, defined on a circle concentric with the gear axis at approximately mid-depth of the tooth.

Pitch Error (fu):
It is the difference between adjacent pitches.The difference between actual dimensions of two successive right or left flank transverse pitches.

Total cumulative pitch deviation (Fp):
Maximum cumulative pitch deviation of any sector of the corresponding flanks of a gear. It is represented by the total amplitude of the cumulative pitch deviation curve.

Pitch deviations

Gear index and pitch definitions.

Transmission error deviations (tangential composite deviations):

In this case, those deviations are related to the gear motion. You need to look at the gear in touch with a master gear and how the center of the gear changes when it revolves one complete turn. That will affect load transferring, and bearing cycle load reactions.
The application gives two different values:

Two flank working deviation( f´´i):
Maximum difference between the effective and theoretical circumferential displacements at the reference circle of the gear under inspection, when meshing with a master gear, testted product gear being turned through one complete revolution.

Single flank working deviation (f´i): 
Value of the tangential composite deviation over a displacement of one pitch. It is a true tangential measurement and is indicative of the functional characteristics of the gear.The non uniform motion is called "transmission error"

As a reference, here you have also a table with the quality grades comparison between DIN and AGMA standards:

Finally, the link to the Application. You can find it at Google Play.

App Images:

Links to the different documents used to create this entry:

• Gear Charts
• Gear Inspection
• Gear troubleshooting inspection
• Gear quality inspection (II)

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

Machining Tolerances

This application help designers and engineers while designing the parts for any type of mechanical device.
The application will give you a tolerance range, equal bilateral, for a especific manufacturing process selected. Turning, Grinding, Broaching, Reaming... up to 12 different types.

  Machining Tolerances.

As a designer of mechanical components, here are a couple of recommendations I do always consider when assigning tolerances:

• It's very important to define a correct dimension composition in your drawing. Avoid having accumulation of lineal dimensions. They will only add variation in your part and in your assembly.
• Tolerance values below ±0.013 are difficult to maintain under regular conditions, even when talking about bearing bores or bearing supports, requesting values below those 0.013 mm tends to be a problem for manufacturing and quality. If you can live with something avove it, your supplier or manufacturing collegue will appreciate it.
• Face to face location in case of bearings supports (shafts or pinion gears) could be in values around ±0.05 mm. 
• Think always in those features that would need to be machined after heat treatment. In general, it is common to use a grinding operation to compensate deformation and to obtain the desired roughness. Depending on the size of the feature, values below ±0.013 can be achieved adding more cost to the part.(again, cpk requirements could be an issue for quality and for the supplier)
• Try to not assign geometric tolerance values lager than feature tolerances, so think twice about the values you define in your parts.
• Use equal bilateral tolerances in your drawings. It will help you with your stackup calculations (comming soon application) and if you are using 3D models, and your manufacturing does also, your parts will be machined centered always.
• Cost of the tolerances:

• General Tolerance values: This this the tolerance table intended to simplify drawing indications and specifies general tolerances in four tolerance classes. It applies to the dimensions of work pieces that are produced by metal removal or are formed from sheet metal. It contains three tables and an informative annex with regard to concepts behind general tolerancing of dimensions. 

         General tolerances for linear measures according to DIN ISO 2768-1

         Table one - Permissible deviations for linear dimensions except for broken    

         edges (external radius and chamfer heights) 

Designation	Description	Permissible deviations for basic size range in mm
		from 0.5# upto 3	Over 3 upto 6	over 6 upto 30	over 30 upto 120	over 120 upto 400	over 400 upto 1000	over 1000 upto 2000	over 2000 upto 4000
f	fine	±0,05	±0,05	±0,10	±0,15	±0,20	±0,30	±0,50	Nil
m	medium	±0,10	±0,10	±0,20	±0,30	±0,50	±0,80	±1.20	±2.00
c	coarse	±0,20	±0,30	±0,50	±0,80	±1.20	±2.00	±3.00	±4.00
v	very coarse	Nil	±0,50	±1.00	±1.50	±2.50	±4.00	±6.00	±8.00

Table two - Permissible deviations for broken edges (external radius and chamfer heights)

		Permissible deviations for basic size range in mm
Designation	Description	from 0.5# upto 3	over 3 upto 6		over 6
f	fine	±0,20	±0,50		±1.00
m	medium
c	coarse	±0,40	±1.00		±2.00
v	very coarse

Table three - Permissible deviations for angular dimensions

		Permissible deviations for ranges of Lengths in mm of shorter side of the angle concerned
Designation	Description	upto 10	over 10 upto 50	over 50 upto 120	over 120 upto 400	over 400
f	fine	±1.00°	±0.500°	±0.333°	±0.166°	±0.083°
m	medium
c	coarse	±1.500°	±1.000°	±0.500°	±0.250°	±0.166°
v	very coarse	±3.00°	±2.000°	±1.000°	±0.500°	±0.333

General tolerances for form and position DIN ISO 2768-2 is for simplifying drawing and fixes general tolerances in three tolerance classes for form and position. By choosing a special tolerance class exactly the precision level common in workshops should be taken into account.

General tolerances for straightness and evenness in mm

		Permissible deviations for basic size range in mm
Designation	Description	upto 10	over 10 upto 30	over 30 upto 100	over 100 upto 300	over 300 upto 1000	over 1000 upto 3000
H		0.02	0.05	0.10	0.20	0.30	0.40
K		0.05	0.10	0.20	0.40	0.60	0.80
L		0.10	0.20	0.40	0.80	1.20	1.60

General tolerances for straightness and evenness in mm

		Permissible deviations for basic size range in mm
Designation	Description	upto 100	over 100 upto 300	over 300 upto 1000	over 1000 upto 3000
H		0.20	0.30	0.40	0.50
K		0.40	0.60	0.80	1.00
L		0.60	1.00	1.50	2.00

General tolerances for symmetry

		Permissible deviations for basic size range in mm
Designation	Description	upto 100	over 100 upto 300	over 300 upto 1000	over 1000 upto 3000
H		0.50
K		0.6-		0.80	1.00
L		0.60	1.00	1.50	2.00

Source : www.huaxing.com
Links to Information:

•  Typical Tolerances
•  Machining Tolerances
•  Cost of Tolerances

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