Dynamic Modeling and Numerical Calculation of a Hydraulic Actuated Flexible Knuckle Boom Crane

Due to its slender boom structure, the knuckle boom crane often undergoes significant elastic deformation when transporting heavy payloads in its fully extended configuration, adversely affecting operational efficiency and safety. Therefore, analyzing the crane's strong geometrical nonlinear dynamic behavior is crucial for engineering applications. This paper presents a dynamic modeling and numerical integration method for a rigid-flexible coupling knuckle boom crane, which is subjected to structural constraints and actuated by hydraulic cylinders. In terms of dynamic modeling, the dynamic equations of the crane's flexible boom are derived based on the geometrically exact Euler-Bernoulli beam theory while integrating the crane's rigid multibody dynamic equations, structural constraint equations, and hydraulic state equations. This approach results in a comprehensive dynamic model of the crane. For numerical integration, we adopt the Newmark method and the implicit single-step trapezoidal discretization scheme to establish the discrete formulation for the mechanical structure and hydraulics, and derive the Jacobian matrix required for the Newton-Raphson iteration. Numerical simulations verify the effectiveness of the integration algorithm through a comparative analysis with the results obtained from ordinary differential equation solvers, and a dynamic analysis of a representative case study was subsequently conducted. This work contributes to the optimization of crane structures and the design of control systems.