Questions that have been plaguing me:
1) What exactly are the benefits of the M3 forged aluminum rear suspension arms vs. the 135i pressed steel arms?
2) Given that the upper, guide and toe arms function structurally as struts, which is to say they react only compression and tension loads (with some structurally insignificant bending due to torque in the rubber bushings), why are the M3 forged aluminum arms curved? This is not required for installation clearance and is structurally weaker than a straight arm. (The corresponding 135i steel parts are straight.)
Perhaps some of the answers can be found below:
Attachment 1143083
M3 Rear Suspension Arms
1 – Wheel Carrier (Upright)
4 – Camber Arm
10 – (Semi-)Trailing Arm
13 – Steering Arm (Toe Control Arm)
17 – Wishbone (Upper Arm)
18 – Guide Rod
These members provide the functional equivalent of a double A-arm suspension, with the triangles formed by the two upper arms (green) and the two lower arms (purple) forming two virtual A-arms.
Attachment 1143084
135i Rear Suspension Arms (Looking Outboard)
RUBBER BUSHINGS
The rear suspension is rubber-bushed at the following locations:
- Camber Arm inboard end (pressed into subframe, M3 and 135i)
- Trailing Arm both ends (pressed into subframe and wheel carrier, M3 and 135i)
- Toe Control Arm both ends (135i only)
- Upper Arm outboard end (M3 and 135i)
- Guide Rod (both ends on 135i, outboard end only on M3)
The rubber bushings in the Upper Arm and Guide Rod consist of a steel bushing core and two concentric metal shells, isolated by rubber. The M3 and 135i bushings are functionally identical and stiffness measurements indicate a radial stiffness of approximately 10,000 N/mm. The stiffness is linear in the (assumed) working range of ±3000 lbs (±13000 N), corresponding to a deflection of ±1.3 mm, but becomes progressively stiffer beyond that. Suspension travel causes rotation of the inner core relative to the outer shell (in the axis of the attach bolt), shearing the rubber and contributing to the total spring rate of the suspension. To minimize stress on the rubber core, it is essential that rubber bushed joints are torqued at static ride height. Rotation of the bushing in the other two axes is possible, preventing any binding in the joint.
Attachment 1143085
Bushing Compliance Test (note dial indicator)
Inspection and measurement of 2008 rear suspension arm bushings with 100,000 km service found no sign of deterioration in the rubber bushings; however, the used bushings were approximately 14% stiffer than new M3 rubber bushings, presumably due to aging of the rubber.
Attachment 1143086
Inboard Rubber Bushing / Outboard Rubber Bushing / Inboard Ball Joint
Attachment 1143087
The other rubber bushings used in the suspension at the Camber Arm (inboard end) and the Trailing Arm (both ends) are similar construction, but were not sectioned or measured for stiffness.
BALL JOINTS (Spherical Bearings)
The rear suspension is ball jointed at the following locations:
- Camber Arm outboard end (pressed into wheel carrier, M3 and 135i)
- Toe Control Arm both ends (M3 only)
- Upper Arm inboard end (M3 and 135i)
- M3 Guide Rod inboard end (pressed into arm)
The ball joints consist of a spherical steel inner race and a plastic outer race housed in a mating outer metal shell. In the 135i Upper Arm, the ball joint is a separate assembly, pressed into the arm weldment. Where ball joints are incorporated into the M3 suspension arms, the aluminum forms the housing for the plastic outer race without a separate steel shell. The bearings are permanently assembled by swaging the shell (or aluminum arm) to affix metal end plates that fix the plastic outer race in place. The bearings are permanently lubricated and sealed by rubber boots. The bearing is free to rotate in all axes, so it is not necessary to torque ball-jointed connections at ride height. This construction provides virtually no radial compliance (large radial stiffness).
Inspection and measurement of 2008 rear suspension arm ball joints with 100,000 km service found no sign of wear on the plastic outer race and no detectable radial play in the bearing assemblies.
UPPER ARM
The Upper Arm and the Camber Arm together establish the camber of the rear tire. Under static loading, the Upper Arm is in compression (less than 1000 lbs). Lateral weight transfer and bumps increase the compressive force in this member, but cornering loads on the more highly loaded outer wheel reduce the compressive force in this member.
The OE Upper Arm is pressed steel with inboard ball joint and outboard rubber bushing. LH and RH parts are identical as the pressed steel body is straight. Asymmetrical section ensures that that compressive failure will be by crippling. Ultimate compressive strength of the arm is approximately 9000 lbs, based on static testing. At this load the arm begins to cripple. The failure is progressive and benign.
Attachment 1143088
Upper Arm Test
Attachment 1143089
Upper Arm Crippling Failure
The M3 Upper Arm is forged 6082T6 aluminum with an inboard ball joint and an outboard rubber bushing. The forged bodies of the LH and RH arms are identical but installation of the bushings makes them handed. The bodies are curved (upward), not for installation clearance issues, but to ensure that the compressive failure of this member will be by progressive bending. The ball joint and bushing on this part are nominally equivalent to those in the OE Upper Arm, so installation of the M3 Upper Arm in place of the 135i Upper Arm is unlikely to have any handling benefit (e.g. reduction of compliance steer effects).
GUIDE ROD
Attachment 1143090
The Guide Rod and Trailing Arm react thrust and braking loads. A simple analysis of the in-service load levels is impractical due to the sophisticated geometry of the multi-link suspension.
The OE Guide Rod is a pair of pressed steel halves welded together with inboard and outboard rubber bushings. LH and RH parts are identical as the welded assembly is straight. The two halves of the weldment form two parallel columns that fail by buckling away from each other at a load in excess of 14,000 lbs, based on testing. The unit would be stronger if it were fully welded, but the partially welded design provides for controlled failure.
Attachment 1143091
The M3 Guide Rod is forged aluminum with inboard ball joint and outboard rubber bushing. The forged bodies of the LH and RH arms are identical but installation of the bushings makes them handed. The bodies are curved (downward), not for installation clearance issues, but to ensure that the compressive failure of this member will be by progressive bending. The ball joint used at the inboard location effectively doubles the stiffness and halves the deflection under axial loading versus the OE Guide Rod, which will alter (and presumably decrease) compliance steer effects.
Attachment 1143092
TOE CONTROL ARM
The Toe Control Arm maintains the toe angle and minimizes bump steer over the range of suspension travel. A simple analysis of the in-service load levels is impractical due to the sophisticated geometry of the multi-link suspension, however loads in this member are obviously less than those in the Upper Arm. This member is also designed for progressive crippling failure under compressive overload.
The OE Toe Control Arm is pressed steel with inboard and outboard rubber bushings. LH and RH parts are identical as the body is straight. A reduced section depth at the center of the arm ensures that that compressive failure will be by crippling at this location, and that the failure will take the arm away from conflict with the suspension spring. I have tested the OE toe arm to a compressive load of 2250 lbs without failure or permanent deformation but have not tested this member to failure. Because Toe Control Arm loads are believed to be relatively modest (in comparison to the other suspension arms), deflection in these bushings is likely small, but it will result in dynamic toe changes. The Toe Arm bushings slightly different construction to the rubber bushings in the Upper and Guide members, and they are about 30% stiffer.
Attachment 1143093
The M3 Toe Control Arm is forged aluminum with inboard and outboard ball joints. T LH and RH arms are identical. The bodies are curved (downward), not for installation clearance issues, but to ensure that the compressive failure of this member will be by progressive bending. The ball joints used at both ends of this member virtually eliminate compliance at the bolted connections. It should be noted that the M3 Toe Control Arm is not dimensionally interchangeable with the OE Toe Control Arm due to different overall pin-center lengths. To say it eliminates all compliance in this member is incorrect though, because the curved design turns the member into a spring. Provided the bending stresses are below the yield stress for the material, the compliance is elastic and reasonably linear.
I have tested an M3 Toe Control Arm to compressive failure to verify its strength and failure mode. Ultimate strength approximately 7600 lbs:
Attachment 1143094
Bending in the member is quite obvious as load increases. Beyond this load the deformation becomes permanent, but the bending is evenly distribute along the length of the member, showing that very large deflections will be tolerated before catastrophic failure. The failed arm is sitting on top of an untested arm for comparison.
Attachment 1143095
This testing was motivated by the desire to design and fabricate a ball-jointed toe arm using the same design philosophy as the M3 arm, but with the correct pin-centre geometry for the 135i. I tested a prototype article with some care to accurately measure deflections vs. load.
Attachment 1143096
Testing proceeded to ultimate then the load was removed. The load was then re-applied to produce significant permanent deformation and the load removed. The resulting load vs. deflection graph shows the classic distinction between the areas of elastic and plastic deformation.
Attachment 1143097
This test shows that the prototype toe arm is structurally equivalent to the M3 toe arm.
Aftermarket Toe Control Arms like the Rogue Engineering that use straight members will provide greater stiffness, but they do not provide the same provision for progressive failure under compressive overload and will fail suddenly if they are overloaded.
(SEMI-)TRAILING ARM
The OE and M3 Trailing Arms are identical and ride in identical rubber bushings pressed into the rear subframe and wheel carrier respectively. These parts are pressed steel and are designed to cripple under compressive overload. As BMW describes it, “the semi-trailing arm features crash beading to ensure the fuel tank is not damaged.” Under compressive overload the arm will buckle down and away from the fuel tank. Rigid, symmetrical trailing arms, like those offered by ECS Tuning do not appear to have this feature.
BUSHING WINDUP
All rubber bushing connections should be torqued at ride height so that the bushings are relaxed (unwound) at ride height. Ball joint connections can be torqued at any height as they are free to rotate and do not wind up. Rubber bushing windup contributes to the overall spring rate of the vehicle. With the OE rear suspension configuration, the wheel rate contributed by the rubber bushings is 35 lb/in. This equivalent to a spring rate of 109 lb/in or 19 N/mm (at the rear spring location), so is quite significant to the overall wheel rate of the vehicle.
Changing the Upper Arm from OE to M3 has no effect on wheel rate as both configurations use similar rubber bushings at both ends.
Changing the Guide Rod from OE to M3 removes one rubber bushing and replaces it with a ball joint, resulting in a softening of the suspension.
Installation of a ball-jointed Toe Control Arm (like the Rogue Engineering part) removes two rubber bushings, resulting in a further softening of the suspension.
Assuming the latter two changes are made, the wheel rate contributed by the rubber bushings is reduced to 23 lb/in. This is equivalent to a spring rate of 72 lb/in or 13 N/mm (at the rear spring location). A fully ball-jointed suspension would remove all this wheel rate and would need to be compensated for by a corresponding increase in spring rate.