100 Y. Champoux et al. For the proposed technique, the laboratory reproduction system requires a commercially available bike as well as a cyclist to ride it. This so-called “reproduction bike” has its own dynamic behavior. A valid question must then be asked: Is it possible, by providing adequate excitation inputs only, to accurately reproduce vibrational outputs of a different brand of bicycle? Providing the answers to this question was the motivation behind the work presented in this paper. The test environment is described in the first part of the paper. First of all, using input and output measurements on the reproduction bike only, the accuracy of reproduction was investigated. In a final step, the target output signals measured on a different commercial bike were compared to the reproduced signals in order to evaluate the quality of the reproduction. 11.2 Methods A road bike simulator that was developed for testing road bike dynamic behavior in previous studies was used in this study. Two Xcite model 1100–7 hydraulic shakers were used to impose a vertical displacement under each wheel as shown in Fig. 11.1. The bike is held vertically by using horizontal bungees attached near the seatpost clamp and to a lab fixture. The cyclist is not required to pedal. The shakers’ amplifier electric signal inputs s1.t/ and s2.t/ generate a vertical displacement under the wheels that corresponds to an existing road profile [8]. Output acceleration signals a3.t/ and a4.t/ were measured using PCB accelerometers model PCB 352C65 at the stem handlebar connection and model PCB 352C68 under the saddle at the saddle-seatpost connection. An LMS SCADA Recorder and LMS Testlab software were used to acquire and analyze data. The TestLab MIMO FRF software package was used to playback pre-recorded waveform signals. The reproduction system can be represented by a MIMO two inputs two outputs system (Fig. 11.2). The inputs S1.!/ and S2.!/ are the frequency spectrum respectively of s1.t/ and s2.t/ while A3.!/ and A4.!/ are the output Frequency spectrum for a3.t/ and a4.t/. Front wheel excitation with the stem acceleration is considered to be a direct path. Similarly, the rear wheel excitation is the direct path to the saddle acceleration response. When both excitations are provided, part of the front wheel excitation is responsible for the saddle output and part of the rear wheel excitation is responsible for the stem output. These are the coupling terms responsible for the crosstalk. Equation 11.1 represents in the frequency domain the input–output relationship. The FRF system matrix [H] contains four terms. A3 A4 D H31 H32 H41 H42 S1 S2 (11.1) The off diagonal terms H32 and H41 are the coupling terms. It is important to underline that the system matrix [H] is always measured with a cyclist riding on the bike. It should also be noted that a typical road excitation input is used to measure [H]. Fig. 11.1 Road bike simulator and the measurement points ( ) ij H ω S2(w) A3(w) A4 (w) S1(w) Fig. 11.2 MIMO representation of the system showing the direct path and the coupled transfer path
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