In this work we describe a theoretical model that predicts the interfacial contact stiffness of fractal rough surfaces by considering the effects of elastic and plastic deformations of the fractal asperities. We also develop an original test rig that simulates dovetail joints for turbo machinery blades, which can fine tune the normal contact load existing between the contacting surfaces of the blade root. The interfacial contact stiffness is obtained through an inverse identification method in which finite element simulations are fitted to the experimental results. Excellent agreement is observed between the contact stiffness predicted by the theoretical model and by the analogous experimental results. We demonstrate that the contact stiffness is a power law function of the normal contact load with an exponent α within the whole range of fractal dimension D(1 < D < 2). We also show that for 1 < D < 1.5 the Pohrt-Popov behavior (α = 1/(3 − D)) is valid, however for 1.5 < D < 2, the exponent α is different and equal to 2(D − 1)/D. The diversity between the model developed in the work and the Pohrt-Popov one is explained in detail.

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Interfacial contact stiffness of fractal rough surfaces

Dynamic investigation of aeroengine high pressure rotor system considering assembly characteristics of bolted joints

The rod-fastened rotor is comprised of a series of discs clamped together by a central tie rod or several tie rods on the pitch circle diameter. The equivalent flexural stiffness of contact interfaces in the rod-fastened rotor is the key concern for accurate rotor dynamic performance analysis. Each contact interface was modeled as a bending spring with stiffness of Kc and a hinge in this study. The contact states of the contact interfaces which depend on the pre-tightening forces and bending moments (static) have effects on Kc. The approach to calculating Kc in two contact states is presented. The first contact state is that the whole zone of the contact interface is in contact, Kc is determined by the contact layer which consists of asperities of the contact surfaces. Hertz contact theory and the GW (Greenwood and Williamson) statistical model are used to calculate the equivalent flexural stiffness of the contact layer Kcc. The second contact state is that some zones of the contact interface are separated (when the bending moment is relative large), the equivalent flexural stiffness of the rotor segment Ksf (not include Kcc) decreases as the material in the separated zone has no contribution to the bending load carrying capacity of the rotor. The strain energy which is calculated by the finite element method (FEM) is used to determine Ksf. The stiffness Ksf is equivalent to the series stiffness of the discs of the rotor segment with flexural stiffness of Kd and a spring with bending stiffness of Kcf in the location of the contact interface, so Kc is equal to the series stiffness of Kcc and Kcf in the second contact state. The results of a simplified rod-fastened rotor indicate that for a fixed pre-tightening force, Kcc decreases with bending moments in the first contact state whereas increases with bending moments in the second contact state. In addition, Kcf and Kc decreases abruptly with the increase of bending moments in the second contact state when the rotor is subjected to a relatively large pre-tightening force. Finally, the multipoint exciting method was used to measure the modal parameters of the experimental rod-fastened rotor. It is found that the experimental modal frequencies decrease as the pre-tightening force decreases.Copyright © 2012 by ASME

Effects of Bending Moments and Pretightening Forces on the Flexural Stiffness of Contact Interfaces in Rod-Fastened Rotors

This paper presents an investigation on dynamic characteristics of a rod-fastened rotor. Based on the framework of a traditional Riccati transfer matrix method (TMM), an improved Riccati TMM considering contact effects brought by a face tooth is developed. A correction coefficient for equivalent stiffness imported from a three-dimensional (3D) finite element contact case analysis is defined to evaluate the contact effects, and then the dynamic model of the rod-fastened rotor including bearing support is established. A computer program is further developed to obtain the dynamic characteristics such as critical speeds of lateral vibration, mode shapes, and an unbalance response. The improved TMM is applied to investigate the dynamic characteristics of a real central tie rod rotor of the class-F gas turbine for verification of its effectiveness, and the calculated critical speeds are in good agreement with test measurement results, implying that the method is accurate and the dynamic model is reliable. This approach can also be applied to analyze other combined rotors with a homogeneous structure.

An Investigation on Dynamic Characteristics of a Gas Turbine Rotor Using an Improved Transfer Matrix Method

Nonlinear Dynamics of the Rod-Fastened Jeffcott Rotor

A series of simplified rod-fastened rotors, which have different surface contact roughness are manufactured and their modal parameters under different pretightening force, are measured in free-free state. The concept of surface contact stiffness is introduced to simulate the influence of pretightening force on modal parameters of these simplified rod-fastened rotors using finite element method. The experiment measured results are compared and fitted to the finite element analysis results and the relationship between contact stiffness and contact stress is established in which the contact stress is defined by the pretightening force. The relationship is then applied on the modal analysis of a real gas turbine rotor, and its modal test results and finite element analysis results are consistent with each other, proving that the relationship and the described determination method of contact stiffness based on modal test and finite element analysis are effective.

Determination of Contact Stiffness of Rod-Fastened Rotors Based on Modal Test and Finite Element Analysis

In this paper, every rotor in the shafting of an E-type gas turbine-generator set is simplified for numerical simulation. Finite element analysis on lateral critical speed, unbalance response and stability is carried out systematically. The simplified model and the conclusions would provide a reference for designing another similar type gas turbine-generator set.

Zhaogang Du

Papers

Determination of Contact Stiffness of Rod-Fastened Rotors Based on Modal Test and Finite Element Analysis

Rotor-bearing dynamic research on an E-type gas turbine-generator set