Dry friction dampers are widely used to reduce vibration. The forced vibration response of a simplified turbine blade with a new kind of under-platform dry friction dampers is studied in this paper. The model consists of a clamped blade as two rigidly connected beams and two dampers in the form of masses which are allowed to slide along the blade platform in the horizontal direction and vibrate with the blade platform in the vertical direction. The horizontal and vertical vibrations of the two dampers, and the horizontal and transverse platform vibrations are coupled by friction at the contact interfaces which is assumed to follow the classical discontinuous Coulomb’s law of friction. The vertical motion of the dampers leads to time-varying contact forces and can cause horizontal stick-slip motion between the contact surfaces. Due to the relative horizontal motion between the dampers and the blade platform, the vertical contact forces and the resultant friction forces act as moving loads. The Finite Element (FE) method and Modal Superposition (MS) method are applied to solve the dynamic response, together with an algorithm that can capture nonsmooth transitions from stick to slip and slip to stick. Quasi-periodic vibration is found even under harmonic excitation.

Cutting chatter is extremely harmful to the machining process, and it is of great significance to eliminate chatter through analyzing the stability of the machining process. In this work, the stability of the milling process with multiple delays is investigated. Considering the regeneration effect, the dynamics of the milling process with variable pitch cutter is modeled as periodic coefficients delayed differential equations (DDEs) with multiple delays. An adaptive variable-step numerical integration method (AVSNIM) considering the effect of the helix angle is developed firstly, which can discretize the cutting period accurately, thereby improving the calculation accuracy of the stability limit of the milling process. The accuracy and efficiency of the AVSNIM are verified through a benchmark milling model. Subsequently, a novel spindle speed-dependent discretization algorithm is proposed, which is combined with the AVSNIM to further reduce the calculation time of the stability lobes diagram (SLD). The simulation experiment results demonstrate that the proposed algorithm can effectively reduce the calculation time.

High-cycle fatigue (HCF) failure of the turbine blades of aero-engines caused by high vibrational stresses is one of the main causes of aero-engine incidents

Chatter stability analysis is an effective way to optimize the cutting parameters and achieve chatter-free machining. This paper proposes a milling chatter stability analysis method based on the localized differential quadrature method (LDQM), which has the advantages of simple principle, easy application, and high computational efficiency. The milling process, considering the regeneration effect, is modeled using linear periodic delay differential equations (DDE), then the state transition matrix during the adjacent cutting period is constructed based on the LDQM, and finally, the stability of the milling process is obtained based on the Floquet theory. The accuracy and computation efficiency of the proposed method are verified through two benchmark milling models. The simulation results demonstrate that the proposed method in this paper can accurately and quickly obtain the chatter stability lobe diagram (SLD) of the milling process, which will provide guidance for optimizing the process parameters.