Design a non-linear conical compression spring

[jinnkraft]

What is the method to design a Non - Telescopic, Non - Linear, conical compression spring from a Force - Deflection characteristics

 

[Tom.G]

Hmm... since a cone is a three dimensional figure, wouldn't it have to be telescopic?
Sure sounds like conflicting requirements! Can you explain?

 

[jinnkraft]

Non Telescopic is in a sense, that the coils of spring should not merge or immerse completely into each other.they should rather sit on each other.
So the solid length of such a spring will be sum of dia of all the coils.
In a telescopic spring, to my knowledge, the coils of spring will immerse into one, thus making their solid length equal to diameter of the coil

 

[Tom.G]

Ahh, OK. Then the approach would be the same as for a telescopic spring but the deflection of the individual coils stops when they hit the next-largest coil. It's not really my field, and it sounds like the math is a bit above my pay grade!

Perhaps @jrmichler can jump in and supply better insight.

 

[Baluncore]

Start here; http://www.tribology-abc.com/calculators/t14_3.htm

 

[jrmichler]

The procedure is a little too complex for a posting, but two good sources are:

1) Handbook of Spring Design, by SMI (Spring Manufacturers Institute). My 2002 edition has 100 pages of spring goodness.
2) Mechanical Springs by Wahl. An old book, but it has everything.

Any engineering library should have at least one of these, otherwise interlibrary loan. The current list price for the SMI book is $27.00. It's a bargain. The non-telescopic constraint makes the design more challenging than a telescopic design. I suspect that the design process for a non-telescopic conical compression spring will be iterative, especially if one of the constraints is solid height. The SMI book will get you started, you may need the Wahl book to finish.

 

[jinnkraft]

Start here; http://www.tribology-abc.com/calculators/t14_3.htm

Thanks for your reply.
Have already done that.
I am not sure whether the result is right or not because it assumes a boundry condition, which is not the case here

 

[jinnkraft]

The procedure is a little too complex for a posting, but two good sources are:

1) Handbook of Spring Design, by SMI (Spring Manufacturers Institute). My 2002 edition has 100 pages of spring goodness.
2) Mechanical Springs by Wahl. An old book, but it has everything.

Any engineering library should have at least one of these, otherwise interlibrary loan. The current list price for the SMI book is $27.00. It's a bargain. The non-telescopic constraint makes the design more challenging than a telescopic design. I suspect that the design process for a non-telescopic conical compression spring will be iterative, especially if one of the constraints is solid height. The SMI book will get you started, you may need the Wahl book to finish.

Hi
Thanks for your crisp reply.
If i take telescopic route, then how can i go about it.
Solid length is not an issue. It is preferable but also dispensable.
Could you please guide
Thanks again.
I surely will try to go through the guides you have mentioned

 

[jrmichler]

A conical spring is analyzed as a series of springs in series. Each spring may be one turn, or even half a turn. The spring constant at the free length is the series sum (not the algebraic sum) of the spring constants of all of the springs. As the spring is compressed, the turns are successively compressed to solid height and removed from the calculation. The spring gets stiffer. At the end, there is only one (or even half) active turn. The spring constant is then the stiffness of the last (half) turn. Now that you have spring constant as a function of compressed length, you can integrate that to get spring force as a function of length.

Remember to do the peak stress calculations for each turn. Each turn must go to solid height before exceeding maximum stress. If it goes solid at less than design stress, the spring is under designed. Under designed may be acceptable, over stressed is not.

The spring equations work for fractional turns. I once designed a spring with 2/3 of an active turn. We measured the spring constant, and it was as designed.

Hints:
Do the entire calculation numerically using a spreadsheet.
Your variables are large end diameter, small end diameter, wire diameter, and pitch.
The pitch can vary with diameter.
Free length is a result of the above variables.
Solid height is a result of the above variables.
There are multiple equations. Get the book. The SMI book, in addition to the spring equations, also has standard wire diameters, materials, and allowable stresses.

 

[Baluncore]

You have not specified any constraints on the spring you need to design. That is inefficient for us, and will not be productive for you.
You have placed yourself in the position of a story teller, who will release only the minimum information, but then only when we guess wrongly.
You need to act more like a scientist or engineer, to disclose the full spring specifications and the constraints on design.

 

[berkeman]

Non Telescopic is in a sense, that the coils of spring should not merge or immerse completely into each other.they should rather sit on each other.
So the solid length of such a spring will be sum of dia of all the coils.
In a telescopic spring, to my knowledge, the coils of spring will immerse into one, thus making their solid length equal to diameter of the coil

So put stops between each of the coils. Problem solved.

EDIT / ADD -- Or just use a conical spring with r(h) varying slowly enough so that the coils can't push inside of each other...

https://encrypted-tbn0.gstatic.com/...EJYyRl-vVZ7qAk3WN0omkxTXNaFEVZPEXSaz9YKW8w-0-

 

[jinnkraft]

You have not specified any constraints on the spring you need to design. That is inefficient for us, and will not be productive for you.
You have placed yourself in the position of a story teller, who will release only the minimum information, but then only when we guess wrongly.
You need to act more like a scientist or engineer, to disclose the full spring specifications and the constraints on design.

Thanks for your reply.
I am extremely sorry for not sharing the complete data. I did put minimal data so that the problem can be expressed in a way most can understand. Yes from here i can understand that you as an expert will appreciate the technical information i have.

I need to design a spring from its force - deflection characteristics.
From the graph that i have it is clear that
1. It is a compression spring
2. Non linear
3 conical

i prefer certain thing in the design of such a spring, though they are dispensable
1. Non telescopic
2. Constant pitch
3. Constant wire dia
4. Ends - closed & grounded

The only data that i have is force - deflection characteristics
The range of force is from 3 N - 100 N

I have no constraints on
1. Wire dia - it should be constant
2. Coil dia for both ends of the cone
3 free length of spring
4 solid length of spring

I would also like to add that jrmichler's advice is top class. A a huge load of thanks to him and to you.

I am also attaching excel sheet with force - deflection characteristics and data for your kind reference

 

[Baluncore]

Your data curve shows that turns of the conical spring will need to be progressively removed from play as the spring is compressed. That can be achieved by winding a variable pitch cylindrical spring or an equal pitch conical spring.

You have specified a conical spring so we will follow that design. If you use round piano wire, it will be difficult to land a smaller diameter turn neatly onto a larger diameter turn without a special helical seat to control the centre. Simplicity suggests the spring should progressively telescope onto a flat base. A more difficult alternative would be to wind the spring from a flat rectangular bar.

Will there be a significant difference in turn diameter from one end to the other? The gradient at the start is impossible with no change for the first 3 mm, it then rises to 15 N/mm over 30 mm. The bounds of the design are determined by that curve, but it must be realistically possible.

The spring could be wound with constant pitch, from a constant thickness wire, onto a mandrel like “unicorn's horn”. That mandrel will need to be made in a taper turning lathe with a slightly smaller diameter than the final turn diameter.

Attached is page 102 from “Spring Design and Application”, 1961, edited by Nicholas P. Chironis.

 

[Baluncore]

See also;
Optimal design of conical springs. Manuel Paredes, Emmanuel Rodriguez.
Engineering with Computers (2009) 25:147–154
DOI 10.1007/s00366-008-0112-3.

It is available here;
https://www.researchgate.net/profile/Manuel_Paredes3/publication/220677684_Optimal_design_of_conical_springs/links/562b279b08aef25a24404ff0/Optimal-design-of-conical-springs.pdf?origin=publication_detail

 

[Baluncore]

Select a prototype from this catalogue entry;
https://www.lesjoforsab.com/standard-springs/51-52_en_id965.pdf

Cat. no. = 3199 or 6702 looks like it might make a good prototype for your requirement.
N = 5 turns, of wire diameter = 1.5 mm. Inner diam = 9 mm. Outer diam = 30 mm.
Uncompressed length = 30 mm. Compressed length = 1.5 mm. Compressed force = 78 N.

 

[jinnkraft]

Select a prototype from this catalogue entry;
https://www.lesjoforsab.com/standard-springs/51-52_en_id965.pdf

Cat. no. = 3199 or 6702 looks like it might make a good prototype for your requirement.
N = 5 turns, of wire diameter = 1.5 mm. Inner diam = 9 mm. Outer diam = 30 mm.
Uncompressed length = 30 mm. Compressed length = 1.5 mm. Compressed force = 78 N.

Hi
Thanks everyone. Baluncore, jrmichler, Berkeman special thanks to all of you for sharing your valuable time on this design issue.
These information shared by you all is a tremendous source of knowledge. I am going through them. It may take a while. I am sure with these i may solve the problem and arrive at a design value.

My special thanks to all of you.