large deflection flat spring

[ENGINEERRMECH]

Hello Forum-
I am trying to design a flat spring used in an existing product. The spring is being redesigned due to fatigue failures in the field. The spring is 2.125" long x 0.340" deep x 0.025" thick and made of Blue Tempered Steel (1095), or Heat-treated SK85M. The spring is preloaded to a deflection of 0.625" and the maximum deflection will be 1.125." I have tried to model the problem in ANSYS, but the company I work for does not have the license for large deflections. When hand calculating the problem as a simply supported beam with one end overhanging one end the results, do not match experimental results. Any help modeling/calculating this large deflection problem would be great.

Thank you for reading this question.
Mike

 

[israelkk]

desertfox

The 40% of yield strength limit is normally for compression/extension spring where the wire is loaded in shear. In the flat beam case the strip is loaded in bending therefore, the limit without yielding is the yield strength. Practically fatigue requirements will probably require the maximum stress to be below the yield point. However, without actual calculations and desired safety factor it is impossible to define the maximum allowable stress.

ENGINEERRMECH

The standard formulas for simply supported beams are practically good for deflections less than 0.3 of the beam length.

By the way if you look the printout of ckozka's analysis made by the SMI/UTS Advanced Spring Design software (the file Beam_Study.pdf) you can see on page one under DESIGN STATUS the warning "Caution: Deflection/Length => 0.3". This means "large deflection" where the analysis no longer valid.

 

[ENGINEERRMECH]

Hello israelkk-
There must be equations out there that describe deflections over 30% of the beam length? I'm kind of stumped as where to go. It looks like I can't use the simple equations mentioned above and the ANSYS package we have doesn't work for large deflection? Any suggestions?

Thanks,
ENGINEERRMECH

 

[israelkk]

The equation for large deflection of cantilever beam rigidly supported on one end and loaded on the other end is given in MECHANICAL SPRINGS, 1963 2nd Edition. McGraw-Hill Book Co. By A.M. Wahl page 179 as I posted back on Oct 15.

However, your case is different. Therefore, you may follow the equation development process in Wahls book and try to develop the formulations for large deflection in your case. Another option is to (easily) modify you design such that the strip will be rigidly fixed on one end so you can use the formulation in page 179 of Wahls book.

 

[ENGINEERRMECH]

israelkk-
Thank you for your help.

 

[desertfox]

Hi Engineermech

I have had a look at the link you gave for the material properties of the SAE1095 steel and your stress values are way above the Yield stress for the material according to your calculations, even though we have already established that your equations are not valid beyond the yield value. Using the simple supported overhanging beam ie your
pre-load condition I worked backward and found using a yield stress of 116000psi from the link you provided, that a maximum load which was 3.28lbf would cause the beam to just reach yield on the upper surface with a resulting deflection of 0.26".
If you look at page 190 and 191 in the book that israelkk mentions you will find recommended allowable working corrected stresses for flat springs that may help, although they seem high to me given the yield stress we have for your material.
In "Spring Design" by WR Berry he states that for a relatively short spring life then 70% of the elastic limit for a design stress is suitable providing this includes taking account of any stress raisers, which is why I stated a 40% of yield stress as a design stress to leave a margin for any stress raisers etc.
You have not indicated whether the spring as a static or dynamic duty or whether it requires a long or short life these criteria need to be considered when you design your spring.
But looking at your spring section and deflection at present it seems pointless having the correct formula when you already know those springs take a permanent set.
In answer to your question relating to the two set ups were the load application and support points have moved, your beam support is now only 0.83" from the applied load in the trigger position as compared with 1.25" in the pre-load position and if you look at your calculations you needed 3.5lbf to deflect 0.625" but the force required to deflect to 0.7" a mere 0.075" extra is 15lbf simply because you have altered the beam stiffness by moving the supports.
Would I be correct in assuming that the pre-load on the spring is achieved when it is first assembled in the product and after that the load is always applied at the trigger point as you call it?

regards
desertfox

 

[ENGINEERRMECH]

Hi Desertfox:

DESERTFOX:I have had a look at the link you gave for the material properties of the SAE1095 steel and your stress values are way above the Yield stress for the material according to your calculations, even though we have already established that your equations are not valid beyond the yield value. Using the simple supported overhanging beam ie your pre-load condition I worked backward and found using a yield stress of 116000psi from the link you provided, that a maximum load which was 3.28lbf would cause the beam to just reach yield on the upper surface with a resulting deflection of 0.26".

DESERTFOX: If you look at page 190 and 191 in the book that israelkk mentions you will find recommended allowable working corrected stresses for flat springs that may help, although they seem high to me given the yield stress we have for your material. In "Spring Design" by WR Berry he states that for a relatively short spring life then 70% of the elastic limit for a design stress is suitable providing this includes taking account of any stress raisers, which is why I stated a 40% of yield stress as a design stress to leave a margin for any stress raisers etc.
ENGINEERRMECH: At this time I don't think the company I work for would buy either these spring books. If I were able to buy one of these books, which would you recommend?

DESERTFOX: You have not indicated whether the spring as a static or dynamic duty or whether it requires a long or short life these criteria need to be considered when you design your spring.
ENGINEERRMECH: The preload is constant, while the load intiated from the handle/trigger is approximately 25-50/day.

DESERTFOX: But looking at your spring section and deflection at present it seems pointless having the correct formula when you already know those springs take a permanent set.
ENGINEERRMECH: True.

DESERTFOX: In answer to your question relating to the two set ups were the load application and support points have moved, your beam support is now only 0.83" from the applied load in the trigger position as compared with 1.25" in the pre-load position and if you look at your calculations you needed 3.5lbf to deflect 0.625" but the force required to deflect to 0.7" a mere 0.075" extra is 15lbf simply because you have altered the beam stiffness by moving the supports.
Would I be correct in assuming that the pre-load on the spring is achieved when it is first assembled in the product and after that the load is always applied at the trigger point as you call it?
ENGINEERRMECH: Your assumption is 100% correct.

Thanks,
ENGINEERRMECH

 

[desertfox]

Hi Engineermech

Either of the books but I favour Berry.

Based on my correct assumption I will have another look at your spring.

Regards

desertfox

 

[desertfox]

hi Again

Just confirm:- the trigger end only deflects 0.075" after the preload as been applied.

desertfox

 

[ENGINEERRMECH]

Hi Desertfox-
I attached the first sheet of my pdf with a couple added notes. I made an assumption on the simply supported beam in reality the spring travels in the "-x" direction when the trigger/handle is compressed. The total deflection of the trigger end of the spring is approximately 0.700" at 15lbf. I made this assumption to simplify the analysis.

Thanks for looking at this problem.
Engineerrmech

 

[desertfox]

hi Engineermech

If the spring travels in the -x direction why does it get
further away from the pin support? ie at pre-load its 0.75"
but moves and increases its distance to 0.83" shouldn't it be less then 0.75" if moving in the -x direction?
If I understand the deflection correctly :- first the far lefthand end is deflected to 0.625" then at trigger position the righthand end needs to deflect by 0.7" so in total the whole of the spring deflects 0.7" + 0.625" am I correct?

Regards

desertfox

 

[ENGINEERRMECH]

Hi Desertfox-
DESERTFOX:If the spring travels in the -x direction why does it get further away from the pin support?
ENGINEERRMECH: Support A is part of the handle/trigger and deflects moves when compressed.

DESERTFOX: If I understand the deflection correctly :- first the far lefthand end is deflected to 0.625" then at trigger position the righthand end needs to deflect by 0.7" so in total the whole of the spring deflects 0.7" + 0.625" am I correct?
ENGINEERMECH: The maximum deflection of the spring will concave facing down, like a frown. The deflection at preload is 0.625" and the trigger deflection is 0.7"

Thanks,
Engineerrmech

 

[desertfox]

Hi Engineerrmech

Sorry I have been a bit busy of late.
Okay so the spring moves -x direction 0.25" and pin A also moves in the -x direction what makes the support pin move more in the -x direction than the spring itself.
When the trigger is pressed initially it will have a certain spring stiffness however if the support moves back during operation as you indicate the spring will have a variable stiffness, also because of the deflection of the spring being large that also alters the stiffness of the spring.
This is not a straight forward simple leaf spring and you mention your re-designing this spring due to fatigue failures in the field, how was fatigue failure of the springs determined? Also have you any stress analysis of the original leaf spring?

regards

desertfox

 

[ENGINEERRMECH]

Hi Deserfox-
Desertfox: Okay so the spring moves -x direction 0.25" and pin A also moves in the -x direction what makes the support pin move more in the -x direction than the spring itself.
Engineermech: Pin A is in the handle. There is a pivot point that allows Pin A to rotate while the handle/trigger is pressed.
Desertfox: When the trigger is pressed initially it will have a certain spring stiffness however if the support moves back during operation as you indicate the spring will have a variable stiffness, also because of the deflection of the spring being large that also alters the stiffness of the spring.
This is not a straight forward simple leaf spring and you mention your re-designing this spring due to fatigue failures in the field, how was fatigue failure of the springs determined? Also have you any stress analysis of the original leaf spring?
Engineerrmech: True, I had to make assumptions to simplify the problem. However, it looks like I may have oversimplified. If the spring fails the product will no longer operate. We don't know where the original data is.

As a side note we are currently experimenting with 3, 0.015" Blue Tempered Springs in place of a single thicker spring. Experimental results so far are promising. The minimum life so far is 30K. This is kind of a simple question, but how does multiple springs last longer? My thought is the three springs share the load equally, therefore the Mc/I stress per spring decreases. However, the geometry of each spring is much smaller therefore the moment of interia goes down causing the Mc/I to increase. Could you explain this?

Thank you,
Engineerrmech

 

[desertfox]

Hi Engineerrmech,
If you reduce the thickness of the spring, you reduce the stiffness of that spring by a cube law. So, for a given load, the deflection will be much greater. However, you are correct, if you use 3 springs, each spring will take a third share of the load, thereby reducing the bending moment on each spring. Depending on the 2nd moment of area of each spring, that will determine the final stress in each spring.
Do you know what the spring rate is of each leaf spring? ie, you say they are 0.015" thick, what about the length and depth? Has that changed or stayed the same?
Regards,
desertfox

 

[ENGINEERRMECH]

Hi Desertfox,
DESERTFOX: If you reduce the thickness of the spring, you reduce the stiffness of that spring by a cube law.
ENGINEERRMECH: I've never heard of the cube law.

DESERTFOX: So, for a given load, the deflection will be much greater. However, you are correct, if you use 3 springs, each spring will take a third share of the load, thereby reducing the bending moment on each spring. Depending on the 2nd moment of area of each spring, that will determine the final stress in each spring.
ENGINEERRMECH: Thank you for reassuring my understanding.

DESERTFOX: Do you know what the spring rate is of each leaf spring? ie, you say they are 0.015" thick, what about the length and depth? Has that changed or stayed the same?
ENGINEERRMECH: Honestly, I don't know the spring rate. I would have to do some experimenting with the deflection and load. The only change was a change to the geometry which reduced it from 0.025" to 0.015" thickness.

Regards,
Engineerrmech

 

[desertfox]

Hi Engineerrmech

What I meant by the stiffness changing by a cube law is this:-

Second moment of area = b*d^3/12

d= depth
b= width

if you alter the depth of the beam and all other dimensions stay the same then changing from 0.025" to 0.015" means

b*0.025^3/12 = 1.302*10^-6*b


b*0.015^3/12 = 2.8125*10^-7*b

Now if you the first figure by the second you will get a figure of 4.629.
This means your resistance to bending with your first spring was 4.629 times greater than with your current 0.015"
thickness spring. The stiffness increases or decreases by a cubed factor by changing the spring depth.
Now moving to three springs you share the load equally however the deflection of each spring will be the same as the single original spring because its your handle movement that determines the deflection. Further now what you have done is altered the loads that act on the handle at pre-load and final load.

regards

desertfox