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Nowadays, the vehicle design is highly ruled by the increasing customer demands and expectations. In addition to ride comfort and vehicle handling, the Noise, Vibration and Harshness (NVH) behavior of the powertrain is also a critical factor that has a big impact on the customer experience. To evaluate the powertrain NVH characteristics, the NVH error states should be studied. A typical NVH event could be decoupled into 3 parts: source, path, and receiver. Take-off shudder, which evaluates the NVH severity level during vehicle take-off, is one of the most important NVH error states. The main sources of Front Wheel Drive (FWD) take-off shudder are the plunging Constant Velocity Joints (CVJ) on the left and right half shafts. This is because a plunging CVJ generates a third order plunging force with half shaft Revolution Per Minute (RPM), which is along the slip of the plunging CVJ.

Drivelines used in modern pickup trucks commonly employ universal joints. This type of joint is responsible for second driveshaft order vibrations in the vehicle. Large displacements of the joint connecting the driveline and the rear axle have a detrimental effect on vehicle NVH. As leaf springs are critical energy absorbing elements that connect to the powertrain, they are used to restrain large axle windup angles. One of the most common types of leaf springs in use today is the multi-stage parabolic leaf spring. A simple SAE 3-link approximation is adequate for preliminary studies but it has been found to be inadequate to study axle windup. A vast body of literature exists on modeling leaf springs using nonlinear FEA and multibody simulations. However, these methods require significant amount of component level detail and measured data. As such, these techniques are not applicable for quick sensitivity studies at design conception stage.