## AGMA surface endurance strength and AGMA bending strength

## AGMA surface endurance strength and AGMA bending strength

(OP)

Does anyone knows how to calculate the AGMA surface endurance strength and the AGMA bending strength?

I'm looking for a general formula (if there is, the ones i know are for steel), if there is? If not, does anyone knows these values for aluminum 2024-t4 and 303 stainless steel ( i need these values to calculate the safety factors).

For example, Sf(safety factor for bending) = (St x Yn/ Kt x Kr)/sigma (at this moment i have all values less the St).

Best regards

I'm looking for a general formula (if there is, the ones i know are for steel), if there is? If not, does anyone knows these values for aluminum 2024-t4 and 303 stainless steel ( i need these values to calculate the safety factors).

For example, Sf(safety factor for bending) = (St x Yn/ Kt x Kr)/sigma (at this moment i have all values less the St).

Best regards

## RE: AGMA surface endurance strength and AGMA bending strength

Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth.AGMA reviews materials in multiple standards, including AGMA 2004

Gear Materials and Heat Treatment Manual. Neither aluminum alloys nor austenitic stainless steels are discussed beyond a single sentence saying that they are non-standard and require special analyses.Your two specific alloys are going to be poor gear materials with respect to wear and resistance to contact stress.

Good luck with your analysis.

## RE: AGMA surface endurance strength and AGMA bending strength

About this materials being poor gear materials, they are not, it depends on your application. For example, sdp-si (www.sdp-si.com), a big gear's manufacturer, uses 303 stainless steel and aluminum 2024-t4 (i'm trying to choose which gears to use, that's why i need this values).

Hope someone knows this values.

Best regards

## RE: AGMA surface endurance strength and AGMA bending strength

## RE: AGMA surface endurance strength and AGMA bending strength

Best regards

## RE: AGMA surface endurance strength and AGMA bending strength

## RE: AGMA surface endurance strength and AGMA bending strength

Best regards

## RE: AGMA surface endurance strength and AGMA bending strength

## RE: AGMA surface endurance strength and AGMA bending strength

Hope you could reply me.

Best regards

EDIT:After reading the book again, i found that they have changed the designations of what i'm looking for, so title is wrong. What i'm looking for is the allowable stresses numbers (Sat, Sac). Does anyone know this values or a way of calculating them (sorry for confusion tbuelna, since you were always posting info about ultimate strength and yield, hope you can help me in this too :D)?

## RE: AGMA surface endurance strength and AGMA bending strength

## RE: AGMA surface endurance strength and AGMA bending strength

Best regards

EDITAfter searching around, i couldn't find the equation, could you please point it to me or post it here (this was better if forum had private messages, since you are only one helping tbuelna)

Only could find/had these ones (i think that they are not the equation for the root fillet, this are for strength/stress):

bending

1

2

contact stress

3

4

Imagine this (what will be the first stage): 8W motor, 7000 rpm pinion, 13 teeth pinion, 41 teeth gear, 80 diametral pitch (0,3175 module), 0,1 inches face width (2,5 mm), designed for 10^8 cycles, SF > 1,3, sigmalim= 42.5 :

From equation 1, i can transmite a maximum of 60500 psi, and from Ft = (1.95*10^6*P)/dg*n (dg=working pitch diameter, n= rotational speed of pinion, P=power transmitted), Ft=800psi, so Ft<<Ftlim

Now from equation 2, Ft = 9527 psi, so, what is the correct value?

Best regards

## RE: AGMA surface endurance strength and AGMA bending strength

I would recommend reading thru AGMA 917-B97 for a step-by-step approach to designing a spur gear. Sections 6.9.5 & 5.6.1 discuss methods for determining tooth bending stress other than the AGMA geometry factor method you are using. Section 6.9.6 discusses contact stress. And sections 10.2 & 10.3 briefly discuss using 300 series cres and wrought aluminum alloys for gears.

## RE: AGMA surface endurance strength and AGMA bending strength

Best regards

## RE: AGMA surface endurance strength and AGMA bending strength

## RE: AGMA surface endurance strength and AGMA bending strength

Can you be more specific for the gears are intended for?

Cycle number?

Etc.,

We have used such gears for specific application that include both for power and motion but for limited cycle numbers.

## RE: AGMA surface endurance strength and AGMA bending strength

israelkk, trying to reply to your questions, the gears are intented to use in a speed-reducer gearbox, in which the motor has 0.009 hp (approximately 7W, so this will be the transmitted power), the motor speed (pinion speed) is about 10600 rpm (no load speed - i'm using this value, but don't know if i should use another value, like max continuous speed, or even a lower value - because force will increase if speed reduces), and is intended to reduce speed to about 55 rpm (so, the ratio is about 193, for that i'm designing a 5 stage gearbox). Would you like that i post my preliminary design of the gearbox? Oh, and there is a space constraint, gears should fit in a space of 1x2 inches (25.4x50.8mm), height isn't a constraint, but should be less than 30mm.

Best regards

PS:i use SI system, but has i think this is an american forum, i'm posting the american units. If you prefer (and is better for me) i can only post in the SI system..## RE: AGMA surface endurance strength and AGMA bending strength

Is it rotate multiple rotations (continuous rotation) or just limited angular output against a torque load?

How many cycles the gearbox will see against the maximum torque?

If it is for limited angular output, how fast it needs to reach the maximum angle against the maximum torque?

## RE: AGMA surface endurance strength and AGMA bending strength

Would you like me to post the calculations that i already have with materials, etc, and each stage of the gearbox?

Thanks for your help and best regards (eng-tips doesn't have pm right?)

## RE: AGMA surface endurance strength and AGMA bending strength

## RE: AGMA surface endurance strength and AGMA bending strength

1) Carbon Steel

SC45 (1045)

40Cr

2) Alloy Steel

42CrMo (SAE 4140, SCM 440)

20CrNiMo (AISI 8620)

40CrNiMo (SAE 4340)

20CrMnTi (This is most used for spur gear and helical gear in China)

17CrNiMo6 or 18CrNiMo7 for spiral bevel gear

3) Aluminum

6061-T6 for some gears and timing pulley.

For now, my problem is really find the specific materials for each gear, so it can last all cycles

PS: This afternoon i will try to post an already made design which lasts highest torques that my gears are supposed to handle - hope this can help

EDITSo, here is the details of the other gearbox:

(13/54) -> 80dp

(15/53) -> 80dp

(15/35) -> 64dp

(13/27) -> 48dp

(14/39) -> 48dp

Ratio is, approximately, 198. In this design, the maximum torque (stall torque) is 7.3 N.m, power transmitted 8W, and maximum continuous torque is 2N.m. Which material do you think is used in this gearbox? PS: this is a tested gearbox, data was taken from internet, don't know any other specs.

Best Regards

## RE: AGMA surface endurance strength and AGMA bending strength

Are those gears use rack/profile shift or are as is?

## RE: AGMA surface endurance strength and AGMA bending strength

The knock down factor of 0.70 for fully reverse tooth bending fatigue stress is fine for vacuum melt quality steel alloys.

The allowable fatigue stress limit for a given material will vary based on the reliability rate used. For example, a material at L2 (98% reliability) will have a lower fatigue stress limit than it does at L10 (90% reliability). The statistical reliability rate required in your gear drive is something you must consider when calculating fatigue life. And it will depend on how critical your application is.

## RE: AGMA surface endurance strength and AGMA bending strength

@israelkk, modifying what i posted about the gears:

(13/54) -> 80dp, face width(F) 2.5mm (0.1inches), x1=0.34 (pinion), x2=-0.34 (gear)

(15/53) -> 80dp, F 3mm (0.12inches), x1=0.34 (pinion), x2=-0.34 (gear)

(15/35) -> 64dp, F 3.5mm (0.16inches), x1=0.34 (pinion), x2=-0.34 (gear)

(13/27) -> 48dp, F 5mm (0.2inches), x1=0.3 (pinion), x2=-0.14 (gear)

(14/39) -> 48dp, F 8mm (0.32inches), x1=0.34 (pinion), x2=-0.34 (gear)

PS: I'm not sure about the profile shift, so these values are only estimates

I'm really trying to find a suitable material (this gears that i have posted are for the dynamixel mx-64, so the design works and material will last).

@tbuelna, the 10^8 cycles are only for the first pinion. The objective is that the entire system lasts at least 20000 hours (if not possible, 10000 hours) in the max continuous torque (so, first pinion should last something like 3x10^8cyles and last stage gear only approximately 3x10^6 cycles (again, this for maximum continuous operation, not operation at stall torque).

## RE: AGMA surface endurance strength and AGMA bending strength

10000 hours at 7000 rpm at 8W is 4.2 x 10^9, it is more than 10^8. \

You need to specify the gearbox output load at continuous torque and at pick torque and the number of gearbox output RPM in both cases. From this data you go back and calculate the RPM and torque at each gearbox stage and check if the gears can live for the desired cycles 10000/20000 hours definition is not clear unless it continuously rotate at a specific rpm and torque for the whole 10000/20000 hours).

I did a quick check for the pinion made of material at 120 Brinnel hardness (2024 T4) therefore, the gears from SDP, PIC and BERG will not live more than 3000 rotations for the pinion and 22000 for the gear in bending loads. For surface loads they will fail instantly (I used 8W, 7000 rpm).

No matter what material you choose all gears must be custom designed and manufactured. You may get away with 2024-T4 for the pinion but it must have profile shift/rack shift to avoid undercut and excessive sliding velocity. From by experience the pinion is usually not the most loaded gear, generally a middle stage and/or the output stage are the most critical.

## RE: AGMA surface endurance strength and AGMA bending strength

## RE: AGMA surface endurance strength and AGMA bending strength

Best regards

## RE: AGMA surface endurance strength and AGMA bending strength

## RE: AGMA surface endurance strength and AGMA bending strength

As israelkk noted above, each tooth of your 13T pinion operating at 7000rpm for 10k hours will be subject to 10^9 load cycles. This is quite a large number of load cycles, and the stress limits used when designing for this case basically means you'll end up with unlimited fatigue life.

The most important thing to remember is to design all of your drive system components (gears, bearings, shafts, etc) so that they have balanced fatigue life. It usually does no good to have some components in the system that have much greater fatigue life than others.

## RE: AGMA surface endurance strength and AGMA bending strength

Responding first to israelkk, yeah, i know all the formulas are based in proper oiled systems.

tbuelna, that's why i'm asking here, don't know if it is asking too much, help on finding suitable materials. I already posted all the system design, i can post the calculations (need to find the proper material to resist the stall torque too, not only the maximum continuous ratings - those i already decipher - but for the stall torque i don't think the system can handle it). How do you normally choose the material for this?

Best regards

## RE: AGMA surface endurance strength and AGMA bending strength

The most difficult case to analyze accurately is the stalled condition. Since the stall torque is almost 4X the max operating torque, this is likely the case that will drive your design. You would need to go through each mesh and determine the precise point during a single tooth passing thru mesh where the surface contact stresses are highest. This would be affected by factors like contact ratio, pressure angle, profile shift, geometry errors, etc. The max static contact stress should be well below what would produce a permanent deformation in the tooth flank surface. What you'll find is that when you account for the combined worst case condition at each of your five gear meshes the result will be rather discouraging. But if this is a requirement which you must be able to demonstrate by analysis that your gear drive is capable of meeting, then that's what you must do. Also, remember to check your bearings are good at this stalled condition.

## RE: AGMA surface endurance strength and AGMA bending strength

If the system is needed to be as accurate as in optical sight systems then not only a breakage of the gear teeth is an issue but deformation of the teeth surface will be an issue. For some systems even a permanent deformation of the teeth can be allowed as the torque is transmitted without a breakage of the teeth.

## RE: AGMA surface endurance strength and AGMA bending strength

## RE: AGMA surface endurance strength and AGMA bending strength

Now in the design, for first stage pinion i have this value for bending force: 8698,649473 psi (maximum continuous), for 20000 hours, n = 3,57x10^8cycles, which gives yn pinion 0,955, temperature factor 1, reliability factor of 0,85. So, if you say safetic factor should be 4, material should be abble to withstand at least 31kpsi, is this?

Best regards

## RE: AGMA surface endurance strength and AGMA bending strength

## RE: AGMA surface endurance strength and AGMA bending strength

Remember that, no matter which technique you use, the more load stages that you can assemble into your model, the more accurate the results will be. Start with a minimum of 3.

Have a look at this page to get you started - http://www.weibull.com/hotwire/issue116/hottopics1...

## RE: AGMA surface endurance strength and AGMA bending strength

## RE: AGMA surface endurance strength and AGMA bending strength