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LCA Analyses

Function of the lower arm

All structures behave like a network of springs that deflects when loads are applied.  Nothing is truly rigid.  On a 4th generation F-Body, the lower arm's role in the suspension is to keep the axle in place front to back along the length of the car and to guide the axle up and down through its range of travel.  The lateral position of the axle is controlled by the panhard bar while the torque arm's job is to keep the axle sitting upright while reacting the large torque loads generated by the drive shaft through the main gears in the differential that try to flip the axle over.  Ideally, the lower control arms should only see tension and compression loads along its length.  One non-ideal behaviour is that when the car rolls to one side the arms are forced to twist and they resist this motion.  This roll stiffness adds to that of the cars springs and the sway bars.  

Some Structural Theory

Along its length, the arm assembly is really 3 springs in series.  When the car accelerates forward the axle pushes forward and the inertia of the heavy car body resists that thrust and the arm compresses.  Each bushing and the metal arm compresses simultaneously.  However, the axial stiffness of the metal arm is very high when compared to the bushings.  Overall the final stiffness of the assembly is driven by the bushings.  Making the metal arm huge and beefy accomplishes very little if the bushings are soft and mushy. 

When you compress the arm along its length it stores energy.  The arm can fail in one of 2 ways.  At a certain load, the material will fail in compression due to material yielding or the arm will buckle.  At a critical load level buckling under compression will occur when the arm can release the stored energy by deflecting to the side rather than further compressing.  The stock arm is made from stamped steel.  The flanges at the bottom of the open U shape are intended to make sure that the buckling load is much higher than the material failure load.  For an OEM part this makes a good easily produced design.  Boxing the section raises the stiffness of the arm.  More importantly it pushes the buckling load up by a huge amount.  With the flanges locked and braced to each other, buckling will not be able to occur a before the arm material yields in compression.

Material Considerations

The arm itself

Here is something to keep in mind when upgrading.  There are aluminum aftermarket arms out there and people buy them as a seemingly premium aftermarket upgrade for their car.  Most people assume they are getting a stiffer and stronger arm.  Since the Elastic Modulus of aluminum is ~ 1x107 psi versus that of steel at ~2.9x107 psi, an aluminum arm needs 2.9 times the cross section to be as stiff as any steel arm (carbon steels are all the same stiffness, only their strengths differ).  Since the ratio of the density of aluminum is ~0.100 lbm/in3 versus steel at ~0.283 lbm/in3 then the only way the aluminum arm can be stiffer than a steel arm is if it outweighs the steel version.  If your high dollar aluminum arms are also lightweight then they are also less stiff!  

The bushings

The factory uses bushings as shown below.  These ones are directional in nature, the missing rubber at the top and bottom allows the bushing sleeve to twist (about the long axis of the arm) much more easily than the core of a solid rubber bushing. 

Directional OEM Bushings

 

Most aftermarket arms use polyurethane or a variant known as polygraphite.  These plastic bushings have several drawbacks. 

They are much stiffer when the arms twist which adds to the car's roll stiffness.  This adds harshness to your car's ride.  Don't anyone try to convince you that harshness equals better handling.  This excess stiffness places additional loads on the arm mounts on the chassis and on the axle housing which may over time initiate cracking.

Since polyurethane is prone to cold flowing it changes shape over time leading to the famous squeak.  Since the arm needs to twist and the bushing eventually gives way, clunking occurs.

Risky Designs

Some of the aftermarket arms use tubular steel with ends welded on.  As good as any welder is, or can be, welding is a process with much more variability than the raw materials used in the arm.  Arm designs that use rectangular tubes with holes cut for installation of the bushings are much safer.  Improper welding can lead to the weld material properties being much stronger than the base metal of the arm but at the expense of being far more brittle.  Fatigue failure (cracks propagating through the weld) is far more likely with a weld than a crack traveling through the arm itself.  An aluminum arm will have a much much higher propensity to crack.  Its your life, choose a design that is inherently safe.  Such designs can be designed properly but how can you tell.

The OEM steel arms are made from mild steel which is very ductile (the initial yield strength of the material is very early compared to the ultimate breaking strength).  The ductility and the lack of welded joints in the main load path means that the OEM arm is very tough and abuse tolerant.  

 

Analyses

In order to do a comparison of the various arm types, an analysis model must be made.  For the following, the solid modelling was done using IDEAS, with the analysis being performed using IDEAS Model Solution and NASTRAN 2005.  The following are a way of comparing designs.

 

Solid Model of Arm

 

 

First step was to create a solid model of an arm.  This is a welded tube design where the main arm tube is welded to the bushing receiver.  The arm tube is 1.25" OD with 0.110" wall.  The bushing shell is .125" thick.  The arm is "welded" to the shell using a constant 1/4" radius fillet shown in yellow.  The fillet varies in width since the surfaces meet at varying angles.  In green the body of the bushing is shown.   In this case three variants were examined:

  1. Steel arm with OEM style solid rubber bushing

  2. Steel arm with aftermarket polyurethane bushing

  3. Aluminum arm with OEM style solid rubber bushing

Each arm was strained in two ways

A axial compression load, (as if the car was accelerating)

A torsion load, (the result of the car leaning in a turn)

 

1. Steel arm with OEM style solid rubber bushing

The arm was modeled with parabolic tetrahedron elements.  The mesh was refined more in the area of the welded area to improve the model accuracy.  In reality, the bushing is comprised of three parts, the outer shell, the rubber block and the inner sleeve, shown above.  The rubber is press fit into the shell and the sleeve is pressed into the rubber.  Because of the large amount of force required to squeeze the rubber into place, the bushing acts as if the rubber is fused to the metal even under substantial suspension loads.  For this reason the rubber is fused to the bushing receiver in the model and no discrete bushing shell was modeled.  

Material Properties

Steel

The steel is given standard Young's modulus value of 2.9E7 psi.  

Rubber

The OEM style bushings appear to use natural rubber.  There is a huge range properties for natural rubber.  After perusing many material data sheets, the stiffness of the hardest rubbers are approximately 1000x softer than steel so I just used 2.9E4 psi.  With so much rubber between the sleeve and the receiver, the sleeve was ignored and the rubber inner surface was fixed in place to anchor it. 

 

 

Axial Load

 

Stressed Bushing Shell

The above plot shows the result of applying a compressive load along the length of the arm.  The receiver shell deforms under the load and is pushed out of round.  The stress is highest where the colour is red.  This stress level is the result of a 1 pound load, it produces an overall stress in the steel of 11.2 psi.  A loaded F-Body might weigh 4000 lbs.  If your car can produce peak launch acceleration of approximately 1/2g then you might see loads of 2000 lbs shared in the 2 arms, therefore 1000 lbs each.  This load ignores short term shock loads which could be quite a bit higher.  At 1000 lbs you would have 11200 psi of stress versus a strength of 47900 psi for an typical mild steel alloy like AISI 1020.  Obviously there is a lot of margin here when looking at static strength.  We will visit this again when we look at fatigue life.

 

 

Distorted Rubber Bushing

In this plot we see that the center of the bushing has moved due to the compressive load on the arm.  Intuitively, the rubber resists getting crushed, the rubber in tension does not pull away from the shell because it was so heavily preloaded in the bushing shell.  The tensioned side of the bushing also resists the movement and adds to the overall arm stiffness.

Under a 1000 lb load the steel arm compressed by a total of .00128".  Adding the total of the steel and rubber compresion gives .0037".  Its common knowledge that the bushings deflect more than the steel arm.  The total cross section area of the rubber is many times higher than the steel arm so the 1000x difference in the materials' stiffnesses is significantly reduced.  However its still surprising that the total deflection is only 2.9 times more than the steel on its own.  

 

 

Torsion Load

 

Torsion Load Distortion

In the above figure we can see the rubber is distorted due to the arm twisting.  If during a turn one spring compresses by 2" and the other expands by 2", the car has rolled by roughly 3.25o.  From the model, this amount of roll requires 390 ft.lb to twist the arm this far.  This also generates 6000 psi stress.  This is much lower than the stress in a launch, above.

 

2. Steel arm with Polyurethane solid bushing

Now I have switched the bushing material for a polyurethane.  Like rubber, there are many grades of polyurethane.  I am not sure what exact grade is typically used but hard polyurethanes are roughly 10 times stiffer than the rubber properties used above.

Unlike a rubber bushing, polyurethane bushings are not substantially preloaded into the arm (ie not press fit).  The reason is largely due to the fact that the polyurethane will creep.  It will squeeze out of the way until the load drops down to a fairly low level.  This is why these bushing are known for squeaking, they slowly get banged out of shape until they are loose.  This also why many arms come with grease fittings to mask the ill fit of the bushings as they wear.

Since there is no preloading of the bushing, when the arm is compressed the front half of the bushing does almost nothing since its not attached to the inside of the bushing shell.  I have modified the model by removing the front half of the bushing.

 

Modified Model of Arm

 

 

The polyurethane material in reality squishes and slide out of the shell at the edges.  To mimic this I have reduced the stiffness of the polyurethane in this direction to allow it to squeeze out relatively unimpeded.  This is why the squished bushing looks at bit odd, the model doesn't strictly speaking let the bushing slide.

 

Polyurethane Bushing Deformation Magnified

 

 

In comparison to the bushing, the receiver deflects a lot less.  Displayed on its own, it takes on an egg shape as shown below.  

Steel Bushing Receiver Magnified Deformation and Stresses

 

 (Updated 060801 , Back doing analysis tasks and should have something soon!)