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The accurate characterization of the seal/groove behavior is critical to correctly modeling the drag performance. In the one-dimensional system model, the seal/groove behavior is represented by a spring and a contact pair, as shown in Fig. 5. The spring stiffness and the stick-slide behavior of the contact pair can be determined experimentally by a lab test or analytically by a finite element model [2].
3.2. Model Verification
Caliper fluid displacement test measures the compliance of the caliper system. It is also a measurement of the robustness of piston retraction. With pressure applied to different levels, the piston will retract different amount due to the stick-slide behavior between the piston and the seal. Generally, a higher preconditioning pressure results in larger piston travel and sliding distance between the piston and seal. When the brake recovers, it usually leaves more residual displacement. As a result, in a subsequent brake apply, the fluid displacement measurement will be smaller. Figure 7 shows a typical fluid displacement test results, in which fluid displacement (volume) is plotted against the pressure. The solid curve with marks is the fluid displacement up to 2000 psi pressure with a precondition of 300 psi pressure. And the dotted line curve with marks is the fluid displacement during a 2000 psi precondition. The two curves form a hand that is an indication of the retraction characteristics.
The one-dimensional system model is used to predict the fluid displacements of the caliper with different preconditioning pressures. A pressure of 300 psi is applied to the piston and then discharged. Once the response is stabilized, a 2000 psi pressure is applied to the system. The fluid volume pumped into the caliper is plotted against the pressure. For the case of 2000 psi precondition, a similar procedure is used to obtain the fluid displacement-pressure relationship. The simulation results for the two cases are plotted in Fig. 7 in comparison with the test results. The general trend in fluid displacement variation is correctly captured by the one-dimensional system model.
The simulation model is further used to predict the residual retractions of two caliper designs and the results are compared with those from experimental measurements. In Fig. 8, both the simulation results and experimental measurements are normalized for comparison. In the experimental test, Caliper B, with higher measured residual retraction, has shown higher drag performance in comparison with caliper A. The simulation results in Fig. 8 correlate well with experimental measurements and clearly indicate that caliper B results in higher residual retraction with various brake application pressure, ranging from 500 psi to 2000 psi. This correlation justifies our practice of using residual retraction as a drag performance index through our simulation study.
3.3. Parameter Study
It is known that caliper housing stiffness, lining compressibility, and seal/groove design all play important roles on drag performance. To better understand the effect of each contributing parameter as well as their interactive impact to the drag performance, a parametric study is conducted to include housing stiffness, lining stiffness, and piston slide force. In the study, the housing stiffness varies from a lower value to a higher value. The piston slide force also varies from low to high, while keeping the sliding force as a constant. The lining is assumed to be a non-linear spring with damping characteristics. We use a scale factor ranging from 0.5 to 1.5 to adjust the load-displacement curve of the baseline lining to represent the proportional lining stiffness. As discussed in the previous section, we use the term "residual retraction", which represents the un-recovered dislocation between the piston and the housing after brake release, to serves as a drag performance index throughout the study.
3.3.1. Lining Stiffness vs. Housing Stiffness