Some Notes on Springs - Revision history

Dnevil at 22:27, 31 December 2021

2021-12-31T22:27:33Z

← Older revision		Revision as of 17:27, 31 December 2021
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	[[Some Notes on Springs]]		[[Some Notes on Springs]]

	by Mr. H.J. Coventry		by [[Harry Coventry\|Mr. H.J. Coventry]]

	<i>[[The Modelmaker]]</i>, Volume 7, Number 4, April 1930		<i>[[The Modelmaker]]</i>, Volume 7, Number 4, April 1930

Dnevil: /* References */

2015-02-03T22:00:09Z

References

← Older revision		Revision as of 17:00, 3 February 2015
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	* [[Winton Brown Engineering Data]]		* [[Winton Brown Engineering Data]]
	* [https://www.youtube.com/watch?v=bBoqPU5nS7U "How to Select Compression Springs", <i>YouTube</i>]		* [https://www.youtube.com/watch?v=bBoqPU5nS7U "How to Select Compression Springs", <i>YouTube</i>]
			* [https://www.youtube.com/watch?v=g6h39Aun_Q0 "Fast Spring Making on a Lathe", <i>YouTube</i>]

Dnevil: /* References */

2015-02-03T21:45:46Z

References

← Older revision		Revision as of 16:45, 3 February 2015
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	* [[Winton Brown Engineering Data]]		* [[Winton Brown Engineering Data]]
			* [https://www.youtube.com/watch?v=bBoqPU5nS7U "How to Select Compression Springs", <i>YouTube</i>]

Dnevil at 20:59, 3 February 2015

2015-02-03T20:59:53Z

← Older revision		Revision as of 15:59, 3 February 2015
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	For practical purposes, these figures would perhaps have to be modified. These points will be discussed later. But if the above principles are grasped, very much work will be saved in eliminating trial and error methods.		For practical purposes, these figures would perhaps have to be modified. These points will be discussed later. But if the above principles are grasped, very much work will be saved in eliminating trial and error methods.

			== References ==

			* [[Winton Brown Engineering Data]]

Dnevil at 05:19, 5 December 2013

2013-12-05T05:19:01Z

← Older revision		Revision as of 00:19, 5 December 2013
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	Taking the capacity formula we can find the diameter of wire. Thus:		Taking the capacity formula we can find the diameter of wire. Thus:

	: [[File:~~SpringEquation12~~.gif]]		: [[File:SpringEquation11.gif]]

	: [[File:SpringEquation14.gif]]		: [[File:SpringEquation14.gif]]

Dnevil at 05:15, 5 December 2013

2013-12-05T05:15:01Z

← Older revision		Revision as of 00:15, 5 December 2013
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	: [[File:SpringEquation10.gif]]		: [[File:SpringEquation10.gif]]

	To sum up above statements, if a stiff strong spring is desired use a small number of thick leaves. If a strong flexible spring is desired use a large number of thin leaves. Having found the number and ~~thcikness~~ of leaves, it is an easy matter to so modify either or both to meet available thickness of commercial material and rework the deflection and capacity. Here is where the discussion on the relation of load deflection, width, number and thickness of leaves comes useful.		To sum up above statements, if a stiff strong spring is desired use a small number of thick leaves. If a strong flexible spring is desired use a large number of thin leaves. Having found the number and thickness of leaves, it is an easy matter to so modify either or both to meet available thickness of commercial material and rework the deflection and capacity. Here is where the discussion on the relation of load deflection, width, number and thickness of leaves comes useful.

	If we connect two leaf springs together upon one another, that is a "full elliptic", the capacity will be exactly the same as for the semi elliptic but the deflection will be doubled.		If we connect two leaf springs together upon one another, that is a "full elliptic", the capacity will be exactly the same as for the semi elliptic but the deflection will be doubled.

Dnevil at 06:21, 4 December 2013

2013-12-04T06:21:42Z

← Older revision		Revision as of 01:21, 4 December 2013
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	Now we have seven factors to deal with and perhaps it may be seen why a mere hit and miss method of spring making is likely to benefit no one but the metal merchant. All seven factors must harmonize to produce any desired spring and this harmony can be expressed as an equation. Before doing this however, let us consider a single plate or leaf cut diamond shape, Figure 2, supported at ends and loaded at center with load (W). The equation that harmonizes the load factors above mentioned is given by		Now we have seven factors to deal with and perhaps it may be seen why a mere hit and miss method of spring making is likely to benefit no one but the metal merchant. All seven factors must harmonize to produce any desired spring and this harmony can be expressed as an equation. Before doing this however, let us consider a single plate or leaf cut diamond shape, Figure 2, supported at ends and loaded at center with load (W). The equation that harmonizes the load factors above mentioned is given by

	[[File:SpringEquation1.gif]]		: [[File:SpringEquation1.gif]]

	where		where
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	We can now write our equation:		We can now write our equation:

	[[File:SpringEquation2.gif]]		: [[File:SpringEquation2.gif]]

	because instead of using one leaf of width B we will use a number of leaves (n) each of width (b). Expressed in terms this merely means that: the load W is numerically equal to twice the stress multiplied by the number of leaves, the width of leaves and the thickness squared (i.e. the thickness multiplied by itself) and divided by three times the span.		because instead of using one leaf of width B we will use a number of leaves (n) each of width (b). Expressed in terms this merely means that: the load W is numerically equal to twice the stress multiplied by the number of leaves, the width of leaves and the thickness squared (i.e. the thickness multiplied by itself) and divided by three times the span.
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	For spring steel the stress is usually taken by 80,000 lbs. per sq. in. and by placing this in our equation and eliminating the numerals we obtain		For spring steel the stress is usually taken by 80,000 lbs. per sq. in. and by placing this in our equation and eliminating the numerals we obtain

	[[File:SpringEquation3.gif]]		: [[File:SpringEquation3.gif]]

	This is the usual form and may be taken for any size semi-elliptic spring whether model or full size. If definite values are placed in and the equation worked out the amateur will very readily discovered why an actual spring, say a locomotive spring when exactly reduced to scale would be far too stiff for the model.		This is the usual form and may be taken for any size semi-elliptic spring whether model or full size. If definite values are placed in and the equation worked out the amateur will very readily discovered why an actual spring, say a locomotive spring when exactly reduced to scale would be far too stiff for the model.
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	The deflection for the load W is given by		The deflection for the load W is given by

	[[File:SpringEquation4.gif]]		: [[File:SpringEquation4.gif]]

	where (d) equals the deflection in inches and (L) and (t) as before.		where (d) equals the deflection in inches and (L) and (t) as before.
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	First find the thickness of leaf material from deflection formula		First find the thickness of leaf material from deflection formula

	[[File:SpringEquation5.gif]]		: [[File:SpringEquation5.gif]]

	or		or

	[[File:SpringEquation6.gif]]		: [[File:SpringEquation6.gif]]

	Putting in the known values, we get		Putting in the known values, we get

	[[File:SpringEquation7.gif]]		: [[File:SpringEquation7.gif]]

	Now taking the capacity formula		Now taking the capacity formula

	[[File:SpringEquation8.gif]]		: [[File:SpringEquation8.gif]]

	and putting in the known values.		and putting in the known values.

	[[File:SpringEquation9.gif]]		: [[File:SpringEquation9.gif]]

	or		or

	[[File:SpringEquation10.gif]]		: [[File:SpringEquation10.gif]]

	To sum up above statements, if a stiff strong spring is desired use a small number of thick leaves. If a strong flexible spring is desired use a large number of thin leaves. Having found the number and thcikness of leaves, it is an easy matter to so modify either or both to meet available thickness of commercial material and rework the deflection and capacity. Here is where the discussion on the relation of load deflection, width, number and thickness of leaves comes useful.		To sum up above statements, if a stiff strong spring is desired use a small number of thick leaves. If a strong flexible spring is desired use a large number of thin leaves. Having found the number and thcikness of leaves, it is an easy matter to so modify either or both to meet available thickness of commercial material and rework the deflection and capacity. Here is where the discussion on the relation of load deflection, width, number and thickness of leaves comes useful.
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	The maximum capacity of a spring is usually taken as meaning that load which would bring a leaf spring flat or a spiral spring solid and the working load is taken as sixty per cent of this.		The maximum capacity of a spring is usually taken as meaning that load which would bring a leaf spring flat or a spiral spring solid and the working load is taken as sixty per cent of this.

	If the above notes are followed, ~~nodifficulty~~ will be experienced in dealing with the fundamentals of spiral spring design.		If the above notes are followed, no difficulty will be experienced in dealing with the fundamentals of spiral spring design.

	The formula which gives us the capacity for springs of round wire is:		The formula which gives us the capacity for springs of round wire is:

	[[File:SpringEquation11.gif]]		: [[File:SpringEquation11.gif]]

	where		where
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	The deflection is given by:		The deflection is given by:

	[[File:SpringEquation12.gif]]		: [[File:SpringEquation12.gif]]

	where		where
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	* r and d being as before		* r and d being as before

	In this ~~forumula~~ it will immediately be seen that the greater the number of coils, the greater the deflection under the capacity load and also the deflection would rapidly increase with increments of mean radius, and would decrease the increments of wire diameter.		In this formula it will immediately be seen that the greater the number of coils, the greater the deflection under the capacity load and also the deflection would rapidly increase with increments of mean radius, and would decrease the increments of wire diameter.

	Now let us take an example.		Now let us take an example.

	A round wire coil spring is required to give a capacity of 10 pounds with a mean ~~readius~~ of coil of 1/4 inch and a total deflection of 1/2 inch. Find diameter of wire and number of coils.		A round wire coil spring is required to give a capacity of 10 pounds with a mean radius of coil of 1/4 inch and a total deflection of 1/2 inch. Find diameter of wire and number of coils.

	Taking the capacity formula we can find the diameter of wire. Thus:		Taking the capacity formula we can find the diameter of wire. Thus:

	[[File:SpringEquation12.gif]]		: [[File:SpringEquation12.gif]]

	[[File:SpringEquation14.gif]]		: [[File:SpringEquation14.gif]]

	[[File:SpringEquation15.gif]]		: [[File:SpringEquation15.gif]]

	: d = 0.054 inches		: d = 0.054 inches
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	The number of coils required to give the deflection called for is given by formula.		The number of coils required to give the deflection called for is given by formula.

	[[File:SpringEquation12.gif]]		: [[File:SpringEquation12.gif]]

	[[File:SpringEquation17.gif]]		: [[File:SpringEquation17.gif]]

	[[File:SpringEquation18.gif]]		: [[File:SpringEquation18.gif]]

	We now have the principal dimensions of the spring from which it is an easy matter to find the height of the spring both when closed solid and free.		We now have the principal dimensions of the spring from which it is an easy matter to find the height of the spring both when closed solid and free.
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	: Solid height = number of coils * diameter of wire		: Solid height = number of coils * diameter of wire

	[[File:SpringEquation19.gif]]		: [[File:SpringEquation19.gif]]

	: free height = solid height plus deflection = 0.22 + 0.05 = 0.72 inches		: free height = solid height plus deflection = 0.22 + 0.05 = 0.72 inches
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	So that if it is desired to make such a spring we would have to wind up 5 coils over a distance of 0.72 inches or each coil would have a pitche of		So that if it is desired to make such a spring we would have to wind up 5 coils over a distance of 0.72 inches or each coil would have a pitche of

	[[File:SpringEquation20.gif]]		: [[File:SpringEquation20.gif]]

	For practical purposes, these figures would perhaps have to be modified. These points will be discussed later. But if the above principles are grasped, very much work will be saved in eliminating trial and error methods.		For practical purposes, these figures would perhaps have to be modified. These points will be discussed later. But if the above principles are grasped, very much work will be saved in eliminating trial and error methods.

Dnevil at 06:18, 4 December 2013

2013-12-04T06:18:01Z

← Older revision		Revision as of 01:18, 4 December 2013
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	To illustrate use of above considerations, suppose we need a leaf spring of 2 inch span, to carry 10 pounds maximum load and constructional requirements limit the width of leaves to 1/4 inch, and the deflection under this is to be 3/8 inch.		To illustrate use of above considerations, suppose we need a leaf spring of 2 inch span, to carry 10 pounds maximum load and constructional requirements limit the width of leaves to 1/4 inch, and the deflection under this is to be 3/8 inch.

			First find the thickness of leaf material from deflection formula

			[[File:SpringEquation5.gif]]

			or

			[[File:SpringEquation6.gif]]

			Putting in the known values, we get

			[[File:SpringEquation7.gif]]

			Now taking the capacity formula

			[[File:SpringEquation8.gif]]

			and putting in the known values.

			[[File:SpringEquation9.gif]]

			or

			[[File:SpringEquation10.gif]]

			To sum up above statements, if a stiff strong spring is desired use a small number of thick leaves. If a strong flexible spring is desired use a large number of thin leaves. Having found the number and thcikness of leaves, it is an easy matter to so modify either or both to meet available thickness of commercial material and rework the deflection and capacity. Here is where the discussion on the relation of load deflection, width, number and thickness of leaves comes useful.

			If we connect two leaf springs together upon one another, that is a "full elliptic", the capacity will be exactly the same as for the semi elliptic but the deflection will be doubled.

			The maximum capacity of a spring is usually taken as meaning that load which would bring a leaf spring flat or a spiral spring solid and the working load is taken as sixty per cent of this.

			If the above notes are followed, nodifficulty will be experienced in dealing with the fundamentals of spiral spring design.

			The formula which gives us the capacity for springs of round wire is:

			[[File:SpringEquation11.gif]]

			where

			* W = Capacity or load to close solid in pounds
			* r = Means radius of coil in inches
			* d = Diameter of wire in inches

			Expressed in terms we would say that the Capacity varies directly as the cube of the diameter of the wire and inversely as the radius of coil.

			Now note that the number of coils do not enter into the equation at all, so that the capacity of one coil of any particular spring is exactly the same as a number of coils. In other words, it would take the same load to close solid in twenty coil spring as to flatten down only one coil of it. This is exactly opposite to the leaf spring where the capacity bears a direct proportion to the number of leaves. The formula will also show that due to the fact that the diameter of wire is cubed (ddd) the capacity rapidly increases with even small increments of wire diameter. THus if we double the diameter of the wire of a definite radius coil, we shall obtain (222) eight times the capacity where as by doubling the diameter or radius of coil, we shall have the capacity.

			The deflection is given by:

			[[File:SpringEquation12.gif]]

			where

			* D = Deflection in inches
			* n = Number of coils
			* r and d being as before

			In this forumula it will immediately be seen that the greater the number of coils, the greater the deflection under the capacity load and also the deflection would rapidly increase with increments of mean radius, and would decrease the increments of wire diameter.

			Now let us take an example.

			A round wire coil spring is required to give a capacity of 10 pounds with a mean readius of coil of 1/4 inch and a total deflection of 1/2 inch. Find diameter of wire and number of coils.

			Taking the capacity formula we can find the diameter of wire. Thus:

			[[File:SpringEquation12.gif]]

			[[File:SpringEquation14.gif]]

			[[File:SpringEquation15.gif]]

			: d = 0.054 inches

			The number of coils required to give the deflection called for is given by formula.

			[[File:SpringEquation12.gif]]

			[[File:SpringEquation17.gif]]

			[[File:SpringEquation18.gif]]

			We now have the principal dimensions of the spring from which it is an easy matter to find the height of the spring both when closed solid and free.

			Thus:

			: Solid height = number of coils * diameter of wire

			[[File:SpringEquation19.gif]]

			: free height = solid height plus deflection = 0.22 + 0.05 = 0.72 inches

			So that if it is desired to make such a spring we would have to wind up 5 coils over a distance of 0.72 inches or each coil would have a pitche of

			[[File:SpringEquation20.gif]]

			For practical purposes, these figures would perhaps have to be modified. These points will be discussed later. But if the above principles are grasped, very much work will be saved in eliminating trial and error methods.

Dnevil: /* References */

2013-11-29T15:53:55Z

References

← Older revision		Revision as of 10:53, 29 November 2013
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	To illustrate use of above considerations, suppose we need a leaf spring of 2 inch span, to carry 10 pounds maximum load and constructional requirements limit the width of leaves to 1/4 inch, and the deflection under this is to be 3/8 inch.		To illustrate use of above considerations, suppose we need a leaf spring of 2 inch span, to carry 10 pounds maximum load and constructional requirements limit the width of leaves to 1/4 inch, and the deflection under this is to be 3/8 inch.

	~~== References ==~~

	* [http://www.codecogs.com/latex/eqneditor.php "Online LaTeX Equation Editor"]

Dnevil at 07:01, 29 November 2013

2013-11-29T07:01:14Z

← Older revision		Revision as of 02:01, 29 November 2013
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	: L = Span in inches		: L = Span in inches

			[[File:HJCoventry Springs Figure2.jpg\|thumb\|center\|300px\|Figure 2]]

	Now the stress in such a plate will be uniform throughout its length and if we clip off a narrow strip each side and keep on till the middle strip is reached and then pile all the pairs of strips on one another, we will obtain a theoretical ideal spring. In other words instead of having a wide one leaf spring, we will have a multiple narrow leaf spring of exactly the same characteristics as far as load capacity and deflection is concerned. It will now be apparent why springs of this type have leaves of evenly decreasing length and also why the ends should be either pointed or tapered. It will also be seen that an ideal spring would have a very short bottom leaf. Practical considerations will, of course, modify, for we must have a buckle and also the ends of top leaf must be square to take hangers or eyes, but the nearer to the ideal form the spring is made the better.		Now the stress in such a plate will be uniform throughout its length and if we clip off a narrow strip each side and keep on till the middle strip is reached and then pile all the pairs of strips on one another, we will obtain a theoretical ideal spring. In other words instead of having a wide one leaf spring, we will have a multiple narrow leaf spring of exactly the same characteristics as far as load capacity and deflection is concerned. It will now be apparent why springs of this type have leaves of evenly decreasing length and also why the ends should be either pointed or tapered. It will also be seen that an ideal spring would have a very short bottom leaf. Practical considerations will, of course, modify, for we must have a buckle and also the ends of top leaf must be square to take hangers or eyes, but the nearer to the ideal form the spring is made the better.
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	where (d) equals the deflection in inches and (L) and (t) as before.		where (d) equals the deflection in inches and (L) and (t) as before.

			[[File:HJCoventry Springs Figure3.jpg\|thumb\|center\|300px\|Figure 3]]

	Now note that the deflection is directly proportional to the square of the span and indirectly proportional to the thickness of leaf, also note that the width and number of leaves do not influence the deflection, (L) and (t), being constant. that is to say the addition of leaves to a spring will increase the carrying capacity but the deflection under this increased load will be precisely the same as that under the capacity load before the alteration.		Now note that the deflection is directly proportional to the square of the span and indirectly proportional to the thickness of leaf, also note that the width and number of leaves do not influence the deflection, (L) and (t), being constant. that is to say the addition of leaves to a spring will increase the carrying capacity but the deflection under this increased load will be precisely the same as that under the capacity load before the alteration.