BASICS OF VALVE SPRING DESIGN
The purpose of a mechanical spring is to exert a force, to provide
flexibility and to store or absorb energy. The primary purpose of a
valve spring in particular is to exert a force that keeps the valve
under
the control of its operating mechanism at all times. Valve springs are
typically helical round wire compression springs; hereafter RWCS.
We will deal only with compression springs but the discussion applies
equally to extension springs.
A
selection of valve springs from Ferrea, including: dual, dual with
damper and triple springs, and can be used in small and big block
applications
STATIC LOADING
When a compression spring is compressed axially, i.e. by the opening
of the valve, the spring wire itself is basically being twisted.
However, because it is coiled and end loaded it is subject to torsion
(twisting) and bending and compression. The compression factor is
minor but the bending effect is not and cannot be neglected in any
effective design analysis; see Blair et al, Paper 1 Fig.10 and related
discussion in RET035 [5].
Simplistically, imagine taking a coiled garden hose and pulling one
end of it towards you along the axis of the coil. Compression spring
calculations for stress in the wire, extension and stiffness are based
on
this principle, albeit somewhat incompletely, i.e., taking the coiled
spring wire, uncoiling it into one long straight piece of wire and then
applying an angle of twist to one end. Hence round wire will always be
a sensible starting point for a compression spring. As well as being
torsionally efficient it is highly productionised, and
spring manufacturers can stock several wire diameters, which
the
designer can select from.
Static loading ignores dynamic effects such as the inertia of the
spring. It assumes that each of the coils is subject to an identical
load
and has an identical stiffness such that when the spring is compressed
the coils approach each other equally. Static spring calculations
show us that stress in the wire is localised on the inside diameter of
the spring. This means that a RWCS will typically fail on its inside
diameter. Ideally we would design a cross section that will equalise
stress through the whole cross section; ovate and elliptical section
wire springs do this. The spring wire does not have to be round it
could have any conceivable cross sectional shape; elliptical, square
or rectangular are also possibilities and represent suitable choices in
certain applications.
DYNAMIC LOADING AND SPRING SURGE
Dynamic loading explains the phenomenon of spring surge, which is
often a cause of valve spring failure. When a valve spring is loaded
suddenly by the impulse of the camshaft on the follower, the inertia
of the spring must be considered. This is a force that tends to maintain
each particle of the spring in the position it occupied before the load
was applied.
During the initial phase of spring compression, that of valve lift,
the spring is being accelerated in the direction of compression. The
first coil (at the camshaft end) will be subject to the inertia of the
whole spring while each successive coil is subject to less inertia
for two reasons; as we progress down the spring each coil has less
mass below it, and it also undergoes less deflection, which means
lower acceleration. Hence the first coil will close up most and each
subsequent coil less.
During the latter part of the valve lift profile, as the valve
approaches maximum lift, the conditions are the exact opposite.
Rather than accelerating, the mass of the spring now decelerates,
which means that the inertia force is in the same direction as the load
from the camshaft. Under these circumstances the last coil (furthest
from the camshaft) will close up most. There is a null point, or phase,
at which there is no change in the rate of compression of the spring,
that is, the point at which valve acceleration is zero. At this stage
all of
the coils will close up uniformly.
PAC clean 1220 beehive
As the coils close up most initially at the camshaft end and then
at the platform end, the effect is that the centre of the spring
initially
approaches the camshaft end and then the platform end. Hence a
compression wave is created which travels back and forth along the
spring until it is damped out; exactly like a wave which would be
created in a slinky spring. This effect is called spring surge.
NATURAL FREQUENCY
As with any vibrating system, every valve spring has a natural,
or resonant frequency (sometimes called a fundamental critical
frequency). The force that causes (excites) vibration is the impulse
of the camshaft upon the follower and is a periodic force with
a (fundamental) frequency equal to the speed of rotation of the
camshaft. This excitation force can be mathematically broken down
(via a Fourier Analysis) into an infinite series of harmonics which
have frequencies of n times the fundamental frequency; these are called
the nth harmonics, i.e. the 3rd harmonic has a frequency of camshaft
rotational speed times 3.
If any of these harmonic frequencies coincides with the natural
frequency of the spring, then we say that resonance has occurred
and the spring may surge, i.e., the compression wave will increase in
amplitude until it reaches dangerous levels which will cause failure.
In theory the amplitude of vibration will reach infinity but in
actuality
internal damping in the spring will prevent infinity being reached.
When resonance occurs to a valve spring it can cause the spring
to jump out of contact with the platform or retainer and can induce
stresses in the spring that cause failure. Both of these consequences
are clearly potentially disastrous.
The stress in the wire that we can calculate is based on the static
case where deflection in all coils is equal. Spring surge will cause
abnormal deflections in the coils and therefore abnormal stresses,
which will cause failure.
CALCULATING NATURAL FREQUENCY
The governing equation for a spring that has its ends fixed on two flat
plates is:
f = 1/2 sqrt (k/m)
where
f Natural Frequency – Hz
k Spring Rate – N / m
m Mass Of The Active Coils of the Spring – kg
This gives us the natural frequency of the valve spring itself at the
onset of compression, assuming no coils are bound at the preload or
installed condition.
This calculation is shown in the sidebar illustration. Progressive
springs are a special case, their stiffness varies with compression, and
will be discussed later.
Performance Spring Inc. provides a range of different
valves springs to suit most requirements
DESIGNING TO COUNTERACT SPRING SURGE
In general terms lower harmonics give higher amplitudes and higher
harmonics give lower amplitudes. The designer should ensure that the
natural frequency of the spring is a minimum of 8 times the frequency
of spring operation in order to avoid resonance with the lower
harmonics, although each case should be examined individually by
comparing them with the relative strength of the harmonics of the
valve lift profile with a Foruier analysis. Some sources empirically
quote 15 to 20 times, but this should not be taken as proven fact in
all cases. The designer must allow for over revving of the engine,
indeed inducing spring surge is a primary risk of over-revving an
engine.
The basic principle then is to try to raise the natural frequency of
the spring as high as possible so as to reduce the number of
potentially influential harmonics. As we can see from the above
equation the
best way to do this is to increase its stiffness and reduce the active
mass, but there is a limit to this procedure as the valve must be
permitted to overloft at maximum lift and too light a spring implies
high stresses.
Performance
Spring’s DR1260ML drag race triple spring is used in high liftdrag
racing applications like Pro Stock, benefiting from PSI’s multi-step
Max-Life surface enhancement
In general terms a spring should be as light as possible such that
the stresses in the wire (from static calculations) remain acceptable.
By
increasing the stresses to optimally high levels we will maximise the
natural frequency and therefore reduce the risk of surge, which would
induce abnormal stresses. We can also concentrate upon reducing the
masses of the collets, retainer, valve and follower.
One common way of eliminating surge is to use more than one
spring; i.e. dual or triple valve springs which operate in parallel.
These
have a number of implications. Firstly, the stiffness of the combined
springs increases the load for a given extension within the available
space envelope.
Kdual = kinner + kouter
Secondly, they will almost always have differing natural frequencies.
Hence should one spring experience surge, the other won’t do so at
the same time. Thirdly, they provide duplication. If one fails, the
other
will continue to close the valve, albeit with the potential for delay at
high speeds.
Finally, they are generally specified with a slight interference
between them, which acts as a friction damping mechanism, reducing
the amplitude when surge does occur by removing energy from the
system via friction and heat.
Indeed it is possible that the only reason for incorporating a second
(or third) spring is to mechanically damp the main spring. Rectangular
section wire can be used for this purpose, but is rare.
One disadvantage of using friction damping is that it will with time
wear the spring, particularly on the inside diameter of an outer spring,
which is the most highly stressed area.
The designer could also re-examine the valve lift profile, as, by
reducing the peak acceleration it may be possible to use a softer
spring, which can be designed with a higher natural frequency. Springs
can also be designed so that they deliberately close up at the platform
end. This physically limits the spring’s ability to surge; although
somewhat crude, it is potentially effective.
It is also possible to fit damping devices to the valve spring, again
with the aim of absorbing energy and reducing the amplitude of
vibration, but this is really a last resort as it is somewhat
inefficient and
adds complication. It is far better to avoid surge in the first place.
The final option is to use a different type of spring altogether; we’ll
discuss that later in this article.
OVATE SPRINGS
The term ovate refers to the cross sectional shape of the spring
wire. Ovate itself means egg-shaped, but in spring design terms it
is a generic term which can be used to cover any non-circular wire
section; elliptical, egg-shaped or any arbitrary symmetrical or
nonsymmetrical multi-radiused shape.
Ovate spring wire is effectively squashed such that it is shorter along
the spring axis and wider perpendicular to it. This means the spring
has a lower stress at the inside diameter than a RWCS if everything
else remains equal. It also makes the overall spring shorter, which
helps with packaging. This reduction in stress means that a given cross
sectional area of wire can carry a higher load before failing.
BEEHIVE SPRINGS
Beehive springs have progressive characteristics which means that
their stiffness varies with lift [6-7]. We will cover the advantages of
that later. A further advantage is that the retainer is small and
light, which reduces active mass.
BUCKLING
If a compression spring has a free length which is four or more times
its mean diameter then it is at risk of failure due to buckling, but
this
situation can be overcome by efficient guidance of the spring. Valve
springs are generally well below this figure and are only guided at the
bottom by the platform and at the top by the retainer where typical
practice would be to locate just the end coil. The other effect which
guidance can have is to provide friction damping.
SPRING ENDS
The next area we should look at is the spring ends, which are
important for two reasons. Loads are fed into the spring via the end
coils, and their design will affect the spring’s mechanical properties,
as
it affects the number of active coils.
A spring with plain ends is an uninterrupted helicoid. Painful
though that sounds, it effectively means it is like a small section of a
very long spring.
Conventional valve spring practice is for squared and ground ends
at both ends. Squared means that the spring manufacturer will deform
the ends to a zero degree helix angle. Ground means that the ends
are surface ground perpendicular to the spring axis and to a tightly
toleranced overall length. Squared and ground ends are important in a
good valve spring as they help to keep the contact pressures between
spring and platform / retainer low, by increasing the contact patch and
by improving the surface finish. This also means that load from the
retainer / platform is applied over a large angular sweep which keeps
loading on the retainer / platform even, and this improves the way load
is fed into the spring. Without the squaring the load would be applied
in a cantilever.
PROGRESSIVE SPRINGS
A progressive compression spring is one in which the spring rate
(stiffness) varies with extension, and in particular does so within the
operating range of the spring. It can achieve this via variation of one
or
more of a number of design parameters, which means that the stiffness
of the spring is not consistent along its entire length. The parameters
are generally coil diameter and pitch.
The effect is that as the spring is compressed, the less stiff sections
will undergo more extension than the stiffer sections, which leads
to the less stiff sections going coil bound whilst the spring is still
in
its operating range. When this occurs the number of active coils is
reduced and therefore the stiffness of the spring increases. The
increase in stiffness will be progressive, i.e. the stiffness will
change smoothly rather than in discrete steps, as the less stiff coils
will gradually come into contact around the helix.
Progressive springs are theoretically immune to spring surge.
This is because their stiffness varies with lift, and therefore, so does
their natural frequency. For example, if an engine is at 5000 rpm,
a progressive spring may want to resonate at 8 mm lift because the
value of its natural frequency at that lift coincides with an engine
harmonic. Its lift then is instantly changed, and at the new lift, say
8.25 mm, it has a different stiffness and natural frequency, and no
longer wants to resonate. The dynamic reality is neither so simple nor
so cooperative [5]!
MATERIAL SELECTION
Three material properties are key to spring design; the torsional
modulus of rigidity, the torsional yield strength and the density.
Material properties in tension are much more easily measured than
those in torsion so we will inevitably find it harder to obtain accurate
material properties. Where we have to use estimates we must allow for
it with safety factors in mind.
In fact it is so difficult to specify material properties for use in
spring
design that it would be inaccurate to try to do so here. There are many
techniques for estimating properties based on existing data, but even
then factors such as surface finish and steel cleanliness will modify
them. There is really no substitute for experience with a given
material.
Nevertheless we present here a table that attempts to summarize
the key properties of three common race engine valve spring materials.
The reader should always conduct his or her own research before
basing calculations on this table.
Spring Material Properties
TITANIUM
Titanium valve springs are used in very high performance, short life
applications, such as top level drag racing. Titanium alloys are ideal
for use in springs due to their combination
of high strength, low density and low tensile and shear modulus. They
also have excellent resistance to corrosion and oxidation, properties
that are more applicable to their use in suspension springs. Their use
has always been limited by high cost, and in racing terms, by the fact
that high budget racing formulae solved their steel valve spring surge
problems via the use of pneumatic valve return systems (air springs),
and therefore never needed to develop titanium springs.
For suspension springs titanium is more responsive (lower inertia)
and can absorb more energy than a steel spring, but for valve springs
the advantages are a higher natural frequency due to the lower mass
and improved packaging.
Beta titanium alloys are most suitable for use in springs. Timet have
developed Timet LCB (Low Cost Beta) for automotive use. This alloy
uses iron and Molybdenum in place of Vanadium as a beta stabiliser.
LCB has a long history of automotive use, in particular in suspension
springs.
The author has completed a design example, which can be seen
in the side bar. This shows that for equivalent conditions, a titanium
spring will be 67% lighter than a Si – Cr wire spring, and would have
a,natural frequency 12% higher.
Titanium valve springs will typically cost four to five times as
much as their steel equivalents. Drag racers claim to be able to do
four to five runs on one set of springs as opposed to changing steel
springs every run, and so in this situation titanium springs can make
commercial sense.
HOW TO DESIGN A VALVE SPRING
The design of a valve spring will be dependent on the following
factors;
• Available space envelope
• Working forces and deflections
• Required component life
• Cost
It is a relatively simple task to put RWCS spring design calculations
for parallel springs [5] into a computer program such as Excel or
Mathcad, allowing an engineer to adjust the design parameters and
quickly assess their impact on spring rate and stress. It is much more
difficult to do so for a progressive or tapered spring with either round
or ovate spring and for these types the designer could use an FEA
(finite element analysis) package [4-7] or could deal directly with a
spring manufacturer.
Ferrea single beehive valve spring
a) Space Envelope
The available space envelope will be well defined for an existing
application but could be entirely open for a clean sheet of paper
design. The parameters that a designer would look at are;
Maximum available outside diameter
Minimum available inside diameter
Installed height
Height at maximum valve opening
Even in an existing application the designer should keep an open mind,
as, even if valve lift is fixed it may be possible to optimise a
spring design by adjusting the other three parameters by re-designing
the platform or retainer.
b) Working Forces
Determining the working forces will depend again on whether it is an
existing application or a fresh design. The spring must exert a force
that will overcome the inertia force of the moving parts, hence we need
to know the acceleration of the moving parts and their mass.
On an existing application for which we have no design data, the
spring designer would ideally measure the valve lift profile and from
that data reverse engineer to find the valve acceleration curve [4]. The
masses can be simply weighed; it is typical to allow for 50-66% of the
mass of the spring itself as being active.
On a clean sheet of paper design the valve lift profile designer
would take into account the requirements of the valve spring and
would either design their own spring to suit, or would issue the
acceleration and mass data to a spring manufacturer at an early stage
to ensure a satisfactory spring design was feasible.
c) Required Component Life
Valve springs are clearly subject to fatigue loading, i.e. they undergo
multiple cycles of repeated stress. Remembering that we are back to
looking at the spring in isolation, we can plot a graph which shows
how spring load varies with time.
Without going into too much detail on fatigue theory, the key loads
are the minimum, maximum, and the amplitude, which is half of the
range. From these we can calculate the stress amplitude, ta, and the
maximum stress, tmax. We then need material properties to compare
these results to
Sse Torsional Endurance Limit – MPa
Ssy Torsional Yield Strength – MPa
Ssu Torsional Ultimate Tensile Strength – MPa
For infinite life we must ensure that the following two equations are
satisfied.
ta < Sse
tmax = ( ta + tm)
< Ssy
If this is not possible then we are in the realms of designing springs
for finite life, and we need to draw an S-N diagram. This is a very
difficult area, as ever practical testing of valve springs to establish
material properties is ideal. If this is not possible then the spring
designer must either thoroughly research published data or seek
advice from a spring manufacturer who will be able to advise on safe
values of stress.
It is quite normal for racing valve springs to be lifed, but if they can
be designed for infinite life then it makes obvious commercial sense to
do so.
d) Cost
Round wire will always be cheaper than ovate, although certain spring
manufacturers do stock ovate wire. Constant pitch (parallel [5]) springs
will generally be cheaper than progressive, and so it is best to liaise
with a supplier as early as possible in a project regarding cost and
availability.
It could also be possible to use a spring from a catalogue and even
one which a manufacturer stocks, as this will generally lead to a
reduction in lead time as well as a cost saving.
ALTERNATIVES
Compression springs are not the only valve springs but they are
simple, efficient and cost effective.
Air springs, or more correctly pneumatic valve return systems
(PVRS) have been in use in Formula One for a long time now. They
effectively eliminate the issue of spring surge and therefore allow
higher operating speeds. They are more complicated and costly
to design, manufacture, build and operate but they have excellent
reliability and the cost effectiveness can be reasonable if they replace
short life coil wire springs.
Ducati’s desmodromic system eliminates valve springs entirely by
using one cam to open the valve and another to close it. Again spring
surge is eliminated leading to higher operating speeds. Again the
system is more complicated and costly to design and manufacture, but
build and operating costs are low and again lifing of coil wire springs
is eliminated. Ducati have successfully exploited this system for a long
time now and it is perhaps surprising that it has not been more widely
adopted.
It is also possible to use different types of wire spring such as
multiple leaf springs, scissors type wire springs and torsion-bar
springs,
all of which have been used in the historical past.
IMPROVING FATIGUE LIFE
Further to material selection in a highly stressed valve spring, it is
very important to specify a steel which is as clean as possible; that
is, one which is free of inclusions, which will act as stress raisers
and
cause premature failure. For spring manufacturers, this means working
closely with the steel supplier.
Surface finish is key for two reasons. A good surface finish will
remove stress raisers on the surface; there are various polishing or
abrasive cleaning processes available, and they can have a significant
impact on fatigue life. Shot peening the surface will induce a residual
compressive stress, which will increase fatigue life as any applied
tensile stress first has to counteract the residual stress.
Nitriding, whether gas or plasma, improves fatigue life by the same
principle by infusing nitrogen into the surface of the component.
Nitriding also increases surface hardness.
PAC clean 1300 dual
CONCLUSION
Valve spring design and specification is, like all things, subject to
the
laws of physics and is continually evolving. Continuous improvements
in material specification, design software and physical testing are all
combining to improve the efficiency and reliability of coil wire valve
springs.
REFERENCES
[1] J.E. Shigley, Mechanical Engineering Design, , McGraw-Hill.
[2] P.M. Heldt, High-Speed Combustion Engines, Chilton.
[3] J. Hannah & R.C. Stephens, Mechanics of Machines, Arnold.
[4] 4stHEAD Valvetrain Design & Analysis Software, www.
profblairandassociates.com.
[5] G.P. Blair, C.D. McCartan, W.M. Cahoon, “Valve Spring Design
Paper 1”, Paper 1 of 3 Papers, Race Engine Technology, Volume 7, Issue
1, January 2009.
[6] G.P. Blair, C.D. McCartan, W.M. Cahoon, “Valve Spring Design
Paper 2”, Paper 2 of 3 Papers, Race Engine Technology, Volume 7, Issue
2, February 2009.
[7] G.P. Blair, C.D. McCartan, W.M. Cahoon, “Appendix to Valve
Spring Design Paper 2”, Paper 2 Appendix, Race Engine Technology,
Volume 7, Issue 3, March 2009.
This article from Race Engine Technology
was published by permission.
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VALVE
SPRING DESIGN –
MATERIAL SELECTION ILLUSTRATION
The author has prepared the following illustration (see right) of the
influence of material properties on valve spring design. The
illustration compares Silicon – Chrome Spring Wire and Timet LCB for
use on an arbitrary single valve spring.
We start by entering the material properties (green cells). We then
input the design parameters for the Si – Cr spring; the figures used
are representative but do not describe any real engine. The load at
full extension has been arbitrarily set at 1000 N and the installed
load then works out at 360 N for a Si – Cr spring with 6.0 active coils.
Then for the Timet LCB spring we keep all of the input design
parameters constant, with the exception of the number of active
coils, and we adjust the number of active coil such that the spring
rate, and therefore the installed and maximum loads, are identical to
those for the Si – Cr spring.
The spreadsheet then calculates the solid and installed height, the
spring mass and the stress in the coil wire.
Accepting an equal stress in the wire, which is not optimal, we see the
following outcomes:
The Ti spring requires only 3.23 active coils. The installed height for
the Ti spring is then 11.1 mm shorter, which would in
actuality allow the design of a shorter engine. The mass of the spring
itself is reduced by 67%, from 37.2g to only 12.2g, and so the active
mass is reduced by 12.5g.
In a real design example we would then be able to reduce the spring
load and gain even more benefit.
If the masses of all other valve train components remain the same, this
reduction in active mass increases the natural frequency of the spring
itself by 8539 engine rpm, or 75%, and increases the natural frequency
of the system by 2136 engine rpm, or 12%.
This illustration is obviously an over simplification, but it does show
how the material properties of titanium allow a more efficient spring
design.
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