1. STABILIZER BAR WITH CONVENTIONAL BUSHING
This is the conventional bushing system. For this system, a clearance fit exists between the stabilizer bar and the bushing. The major advantage of this system is its simplicity and serviceability. However, using this bushing system, the stabilizer bar can move within the bushing thereby reducing the effectiveness of the bar. A schematic model for the bushing and the stabilizer bar is shown in Figure 2. The clearance interface between the bushing and the bar is modeled using the surface to surface contact algorithm of ABAQUS. A stress contour distribution of the bar under this load is shown in Figure 3. The maximum stress for this bar with the conventional bushing is 755 MPa and the location of the maximum stress is at the bend of the stabilizer bar. Also, the roll stiffness of the stabilizer bar with the conventional bushing is 17.7 N/ mm.

2. STABILIZER BAR WITH GRIPPY FLAT BUSHING
In this system, grippy flats (two flat faces on the bar) are introduced on the bar and the bushing matches exactly with the flat shape of the bar. As a result, the bar cannot rotate within the bushing. A disadvantage with this system is that due to the flats, a stress concentration is created thereby possibly reducing the life of the bar. Also, a secondary operation is needed to create the flats. Using the same boundary and loading conditions, the finite element analysis was carried out. A schematic cross section of the bushing is shown in Figure 4. The stress contour distribution of the bar with grippy flats is shown in Figure 5. A sharp rise in the stress magnitude can be observed near the grippy flats. The maximum stress magnitude for the bar with the grippy flat bushing is 898 MPa. The location of the maximum stress is at the grippy flat. That is, there is a 19 % increase in the stress due to the grippy flats which can significantly reduce the fatigue life of the bar. Stiffness for the bar is 18 N/mm. That is, the grippy feature does not effect the stiffness of the bar.

3. STABILIZER BAR WITH UPSET RING
For the stabilizer bar with the upset ring, the movement of the bushing is restricted at one end due to a bend while at the other end, an upset ring will prevent the movement. This feature of upset ring can be added in combination with the grippy flats. The disadvantage of this system is the expensive processing involved and the stress concentration generated near the upset ring. Stress distribution of the bar with the upset ring is shown in Figure 6. The maximum stress is 756 MPa which is same as that of the stabilizer bar with conventional bushing. For this geometry of the stabilizer bar, since the maximum stress is at the bend (not near the bushing), the stress concentration created by the upset did not increase the maximum stress. However, if the maximum stress is near the upset ring, it gets further amplified due to the stress concentration of the upset ring. The roll stiffness of the bar with the upset ring is again 18 N/mm. That is, the upset ring feature of the stabilizer bar system does not influence the roll stiffness.

4. STABILIZER BAR WITH CHEMICALLY BONDED BUSHING
In this bushing system, the bushings are bonded to the stabilizer bar using chemical adhesives. A cross section of the bushing system is shown in Figure 7. The major advantage of this system is that bushing movement can be prevented without adding any stress concentration. The major disadvantage is the cost factor involved in creating the adhesive bond between the bushing and the stabilizer bar. Also, the break-away torque or the torque that causes the bushing to slip on the stabilizer bar can be very low and once the bushing slips on the bar, the effectiveness of the bushing system is lost. This bar system was evaluated using finite elements. In this case, by assuming a perfect bond, the nodes at the interface of the bushing and the stabilizer bar are equivalenced. Stress contour is shown in Figure 8. The maximum stress for this bar is observed to be 792 MPa which is almost same as the bar with conventional bushing. That is, stress concentration did not increase much using this bushing system. The roll stiffness for this bar is 28.4 N/mm. That is, the chemically bonded bushing increased the roll stiffness by almost 58 percent.

5. STABILIZER BAR WITH COMPRESSIVELY BONDED BUSHING
A new stabilizer bar system, Vari-rate bushing system, has been developed in which the bond between the bushing and the bar is due to compressive force instead of a chemical adhesive. A schematic of the cross section is shown in Figure 9. The advantage of this system is that the bushing will be held tightly in place on the bar by the use of an externally applied compressive force. The break-away torque of this system depends on the amount of compressive force being used and can be varied. Additional advantage of this Vari-rate bushing system is that by varying the compressive force, one can vary the roll rate of the stabilizer bar. The disadvantage for this system is the additional tooling that is required in the application of the compressive force. The stress contour distribution of the stabilizer bar with a vari-rate bushing is shown in Figure 10. Maximum stress is 776 MPa which is almost the same as that of the stabilizer bar system with conventional bushings thereby indicating that there will not be any additional stress concentration. Roll stiffness of the system is 29.9 N/mm. It should be noted by varying the applied compressive force, roll rate can be varied.

CONCLUSION
Different stabilizer bar systems with bushings were evaluated using CAE tools. It was observed that the systems with grippy flats and/or the upset rings can increase the maximum stress under a given load and hence can reduce the fatigue life of the system. The systems that use chemically bonded bushings and the compressive bonded bushing do not create much additional stress concentration, but the roll stiffness rates using such bushing systems can change. Comparison of stresses and stiffness of all the systems discussed are summarized in Table 1 along with a manufacturing cost rank. Conventional bushing system is the base line and is given a rank 1 while the chemically bonded system is the most expensive one and is given rank 5.