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large deflection flat spring

large deflection flat spring

large deflection flat spring

(OP)
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
 

RE: large deflection flat spring

MECHANICAL SPRINGS, 1963 2nd Edition. McGraw-Hill Book Co. By A.M. Wahl page 179

RE: large deflection flat spring

Hi EngneerMech

Can you provde a sketch? the spring is supported in two positions with one end over hanging a support,where is the load applied?

regards

desertfox

RE: large deflection flat spring

(OP)
Hello israelkk-
Thank you for the information.  

 

RE: large deflection flat spring

(OP)
Hello desertfox-
I attached a pdf with the dimensions and loading you requested.  I also added information pertaing to the analysis and experimentation that I've performed.  I hope this is not too much information.  Basically, I'm trying to compare my theoretical results and ANSYS results to experimental results as shown in the pdf.

Thank you for your help,
Engineerrmech

RE: large deflection flat spring

At least one potential problem I can see - the force gauge you are using in the experimental setup probably distorts (under-reports) load readings when the force is at a severe angle to the end of the loading pin, as shown in the picture in your pdf file.

You might want to consider a loading mechanism that duplicates the installed configuration in your part, with whatever friction boundary conditions exist there (it looks like it's a plastic housing?).  If you must use the force gauge, try setting it so that the action line of the gauge is normal to the contact point on the beam at its deflected position.  Or, load the spring via a calibrated hanging weight, so that the load always remains vertical at a known value?

RE: large deflection flat spring

(OP)
Hello btrueblood-
Thank you for the insight into loading the part with a hanging weight.  I will give that a try.

RE: large deflection flat spring

I have attached a Design sheet to show you what the calculated stress are.

RE: large deflection flat spring

Hi Engneermech

I will look and post later


desertfox

RE: large deflection flat spring

(OP)
Hello ckozka-
Thank you for taking the time to simulate my problem and supplying me with a pdf.  May I ask what SW package you used for the simulation?

Thank you,
engineerrmech

RE: large deflection flat spring

ASD software made by UTS
Here is the site
www.uts.com

 

RE: large deflection flat spring

ENGINEERRMECH

In your post http://files.engineering.com/getfile.aspx?folder=1b6b6ea7-8f5f-4483-b0a1-46a0f917c731&file=engr_tips.pdf the 2D schematic shown on page one fits the formulation as appear on the top right side of page 3 (simple support over hanging case). However the way it appears on bottom left side of the last page (the solid picture) is not the same. In the 2D and the overhanging case the beam is supported on a small diameter pi which can be considered as point reaction. However in the actual solid the spring rests on a much larger radius which in practical supports the spring on a quite large area thereby reduces the actual beam length, resoling in larger stresses and less deflection than the calculated.

You didn't mention any requirement for number of operations (fatigue) and neither relaxtions with time under the constant preloaded conditions.

RE: large deflection flat spring

Ckozka's post (from a spring design calculator) has a whole bunch of warning flags on the cover page showing that the deflection is beyond the limits of "small deflections", and use of a non-linear, large-deflection formulation is warranted.

RE: large deflection flat spring

hi Engineermech

First thing that struck me was the large deflection relative to the length of beam, ie beam theory which you have used is limited to small deflections.
Also I am slightly confused by the two set ups, the first set up generates the pre-load then the second the working load but why does the load application change position and also the supports?
Changing the support and load application points will give different spring stiffness for each situation.
Also what is the yield stress for the material? with those deflections I was wondering whether you have over stressed the spring.

Regards

desertfox

RE: large deflection flat spring

(OP)
ckozka-
Could the SW you used for the simulation also simulate a  simply supported beam with a load at one end?

Thank you,
ENGINEERRMECH

RE: large deflection flat spring

(OP)
Hello israelkk-
The two 2D drawings on the first page are a simplification how the spring is loaded.  First, the spring is slipped into a channel and supported/loaded as shown in the "Preloaded Experimental" drawing.  Then when the trigger/handle is pressed the spring is supported similar to the "Trigger Experimental" drawing.  In the "Trigger Experimental" drawing the left support is a rough/frictionless contact where the spring can move.  Your observation to the size of the dowel pins vs. the actual application is true.  I used the smaller dowel pins in my experiment hoping they would more closely emulate a simply supported beam equation.  I'm currently trying to model with the correct radius to simulate when the handle/trigger is pressed.

As for the number of cycles we would like to see 20K cycles and the preload is constant.

Thanks,
ENGINEERRMECH

RE: large deflection flat spring

(OP)
Hi desertfox-

DESERTFOX:First thing that struck me was the large deflection relative to the length of beam, ie beam theory which you have used is limited to small deflections.
ENGINEERRMECH: I was worried about the large deflection, but these were the only equations I could find.  Is there a number, percentage as a rule of thumb when the deflection becomes to large for these equations?  Are there equations that can be used for large deflection applications?

DESERTFOX:Also I am slightly confused by the two set ups, the first set up generates the pre-load then the second the working load but why does the load application change position and also the supports?
ENGINEERMECH: The two 2D drawings on the first page are a simplification how the spring is loaded.  First, the spring is slipped into a channel and supported/loaded as shown in the "Preloaded Experimental" drawing.  Then when the trigger/handle is pressed the spring is supported similar to the "Trigger Experimental" drawing.  In the "Trigger Experimental" drawing the left support is a rough/frictionless contact where the spring can move.

DESERTFOX:Changing the support and load application points will give different spring stiffness for each situation.
ENGINEERRMECH: I did not know this.  Is this still true after reading the above explanation?

DESERTFOX: Also what is the yield stress for the material?
ENGINEERRMECH:  In my experiment I've been using Blue Tempered Shim Stock, 1095 high carbon spring steel.  I had to assume the temper because the vendor doesn't publish mechanical properties.  I found mechanical properties at http://www.matweb.com/search/DataSheet.aspx?MatGUID=b4a55e9a2dc7414eabcbe53f24a0c33e with a RELATIVELY close Rockwell Hardness.  

DESERTFOX: With those deflections I was wondering whether you have over stressed the spring.
ENGINEERRMECH:  In the experiment and actual use the materials are permanently deflected.  Could you suggest a material that might be better for this application?

Thank you very much,
ENGINEERRMECH

RE: large deflection flat spring

If they are permanently deflected, then the equations you are using are not valid. The equations are only valid up to the yield value. Typically, you should be using, for the maximum stress in your spring, about 40% of the yield stress for that material. At this point in time I can't suggest an alternative material that might be better as the deflections for the size and geometry of the spring are too large. I think you may need to seriously think about changing the design of the spring and the geometry.

Regards,
desertfox

RE: large deflection flat spring

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.

RE: large deflection flat spring

(OP)
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  

RE: large deflection flat spring

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.

RE: large deflection flat spring

(OP)
israelkk-
Thank you for your help.

RE: large deflection flat spring

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

RE: large deflection flat spring

(OP)
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

RE: large deflection flat spring

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

RE: large deflection flat spring

hi Again

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

desertfox

RE: large deflection flat spring

(OP)
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
 

RE: large deflection flat spring

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

RE: large deflection flat spring

(OP)
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

RE: large deflection flat spring

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

RE: large deflection flat spring

(OP)
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

RE: large deflection flat spring

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

RE: large deflection flat spring

(OP)
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

RE: large deflection flat spring

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
      
 

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