Modelling and Dynamic Analysis of an Unbalanced and Cracked Cardan Shaft for Vehicle Propeller Shaft Systems

The vibrational behaviour of misaligned rotating machinery is described and analysed in this paper. The model, constructed based on the equations of vehicle dynamics, considered the dynamic excitation of a single Hooke’s joint. The system adopted the breathing functions from a recent publication to approximate the actual breathing mechanism of a cracked driveshaft. The study aimed to understand the transmission of a nonlinear signal from the unbalanced and cracked driveshaft to an unbalanced driven shaft via a Hooke’s joint. The governing equation of the system was established based on the energy principle and the Lagrangian approach. The instantaneous frequency (IF) identification of the cracked driveshaft was extracted based on the synchrosqueezing wavelet technique. To correlate the results, the nonlinear synchrosqueezing wavelet transforms combined with the classical waves techniques were experimentally used in various scenarios for dynamic analysis of the Cardan shaft system. The variations in the dynamic response in the form of a rising trend of higher harmonics of rotational frequency and increased level of sub-harmonic peaks in both shafts were presented as significant crack indicators. The synchrosqueezing response showed breathing crack excitation played a crucial role in the mixed faults response and caused divergence of the vibration amplitudes in the rotor’s deflections. The simulation and test results demonstrated that the driveshaft damage features impacted the transfer motion to the driven shaft and the Hooke’s joint coupling was the principal source of instability in the system. The proposed model offers new perspectives on vibration monitoring and enhancement analysis to cover complex Cardan shaft systems.

Torsional Vibration Control of a Hooke’s Joint Driven Flexible Shaft System

Torsional vibration control of a rotating mechanical system which incorporates a Hooke’s joint is investigated by pole assignment techniques. Linearized analytical models for the torsional system are established for the purposes of controller design. The resulting two-degree-of-freedom rotational system which contains time varying coefficients is parametrically excited due to an inherent non-linear velocity ratio across the Hooke’s joint. The controller is designed via full state feedback and observer based feedback in the transformed domain, using Lyapunov transformation. This transformation reduces the original time-varying system to a form suitable for controller design. A dual-system approach is employed to calculate the observer gain matrix for the time-varying system. Numerical simulation results show that the proposed control method is effective for suppressing torsional vibration of a Hooke’s joint driven system.

Geometric Constraint and Mobility Variation of Two 3SvPSv Metamorphic Parallel Mechanisms

This paper presents a unique feature of geometric constraint of adjacent axes of the variable-axis (vA) joint and analyses the effectiveness in the constructed limb, resulting in variation of mobility configuration of two 3SvPSv metamorphic parallel mechanisms. The underlying principle of the metamorphosis of this vA joint is unravelled by investigating the dependence of the corresponding screw system comprising of line vectors, leading to evolution of the vA joint from the source phase Sv to the variable Hooke’s joint phase Uv and the variable revolute-joint phase Rv. The kinematic chain installed with the vA joint forms a reconfigurable limb and is then used to construct two 3SvPSv metamorphic parallel mechanisms proposed in this paper. The phase change of the vA joints incurs the constraint change of the SvPSv limb and subsequently results in the change of mobility configuration of the metamorphic parallel mechanisms. The paper further addresses the geometrical condition for constructing 3SvPSv metamorphic parallel mechanisms following the constraints delivered by the reconfigurable limbs, leading to the analysis of mobility change of the mechanisms induced by the phase change of the limbs.

Motion Performance Analysis and Experiment Research of the Hooke’s Joint-Gear Mechanism of Differential Velocity Vane Pump

Based on the analysis of its motion performance about Hooke’s joint-gear mechanism, the Hooke’s joint-gear mechanism of differential velocity vane pump is brought forward. By analyzing its motion rule on the driving system of the differential velocity vane pump, the design parameters of the Hooke’s joint-gear mechanism of differential velocity vane pump are shown. The overall structure and its principle prototype are designed. Based on the principle prototype of the differential velocity vane pump, the experimental platform is established to testify the draining and trapping fluid. The results are shown that Hooke’s joint-gear mechanism of differential velocity vane pump can achieve the function of draining and aspirating fluid, and the design on the driving system and the pump structure are correct.

Robert Hooke's ‘universal joint’ and its application to sundials and the sundial-clock

Robert Hooke is commonly thought of as the inventor of ‘Hooke's joint’ or the ‘universal joint’. However, it is shown that this flexible coupling (based on a four-armed cross pivoted between semicircular yokes attached to two shafts) was in fact known long before Hooke's time but was always assumed to give an output exactly matching that of the input shaft. Hooke carefully measured the relative displacements of the two axes, and found that if one were inclined to the other, uniform rotation of the input produced a varying rate of rotation of the output. He also recognized that this variable rate exactly corresponded to the movement of the shadow of a gnomon across the face of a sundial, as generated by the projection of the uniform motion of the Sun around an inclined polar axis. He therefore proposed that a ‘mechanical sundial’ might be made by coupling a 24-hour clock movement (with its hour shaft at the appropriate inclination) to a pointer via a universal joint. This proposal has been investigated both practically and mathematically, and shown to be valid. Hooke's studies of the universal joint caused it to be identified with his name, and it has ultimately proved far more important as a rotary coupling than as a sundial analogue. More complex versions subsequently designed by Hooke included provision for two basic couplings to be linked by an intermediate shaft. With appropriate setting of phase and shaft angles this ‘double Hooke's joint’ could annul the variable output velocity characteristic of the single universal. It has proved invaluable for modern automotive transmissions.