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Most centrifugal pendulum vibration absorber (CPVA) research focuses on the horizontal or vertical plane, ignoring the influence of gravity. However, with the wide application of CPVAs in the automobile industry, some gravity-related problems have been encountered in practice. In this study, employing the second kind of Lagrange equation, the differential equation of motion of a CPVA is established, and the first-order approximate analytical solution is solved using the method of multiple scales. The mathematical relations among the excitation torque amplitude and phase, gravity influence, absorber trajectory shape, absorber position, viscous damping coefficient, and mistuning level parameters are provided for study. Specifically, the second-order responses of four absorbers and two absorbers in a gravity field are studied, and the influence of the change in the torque excitation phase on the response of the absorber is thoroughly analyzed.

Centrifugal Pendulum Vibration Absorber (CPVA for short) is used to absorb torsional vibrations caused by the shifting motion of the engine. It is increasingly used in modern powertrains. In the research of the dynamic characteristics of the CPVA, it is necessary to obtain the real motion of the pendulum to compensate the fitting performance of mathematical model. The usual method is to install an angle sensor to measure the movement of the pendulum. On the one hand, the installation of the sensor will affect its movement to a certain extent, so that the measurement results do not match the actual motion. On the other hand, the motion of the pendulum is not only the rotational motion around the rotational axis of the CPVA rotor, but also has translation relative to it. As a result, it is difficult to obtain accurate motion only by the angle sensor. We proposed a non-contact centrifugal pendulum motion measurement method.