Elsevier

Tribology International

Volume 151, November 2020, 106431
Tribology International

A fretting test apparatus for measuring friction hysteresis of bolted joints

https://doi.org/10.1016/j.triboint.2020.106431Get rights and content

Highlights

  • A fretting test apparatus is developed for studying friction hysteresis of bolted joints.

  • The tangential contact force and the relative displacement are measured using a load cell and a laser vibrometer with a prism, respectively.

  • The bolt preload is recorded using a force washer.

  • A numerical analysis is conducted to evaluate the accuracy of the measurement.

Abstract

This paper focuses on an experimental investigation of the mechanical behavior of bolted joints. A new test apparatus to measure friction hysteresis was designed to provide a reliable experimental database for the calibration of contact models. This apparatus uses a piezoelectric actuator to provide the contact interfaces with stable oscillatory relative displacement. The friction force and the bolt preload were continuously measured during the test, using a load cell and a force washer, respectively. The relative motion between the interfaces was measured using a single laser vibrometer. The influence of the bolt preload and excitation amplitude on friction hysteresis was investigated. A numerical model was developed to extract the tangential contact stiffness from the measured data.

Introduction

Several mechanical assemblies use bolted joints. A significant advantage of bolted joints is that they can be easily assembled and disassembled. When a joint undergoes oscillatory loads the contact interfaces experience a relative motion. Friction forces induced by this relative motion exhibit nonlinear behavior with hysteresis. Different regimes can be observed during oscillatory motion [1]. In the stick regime, the relative displacement between the contact surfaces is very small and the tangential force depends almost linearly on the relative displacement. In the gross-slip regime, displacements are large and the tangential force is saturated to the maximum friction force. The transition between the stick and the gross-slip regime is denoted as microslip. The tangential force does not vary linearly with displacement and is lower than the maximum friction force.

Hysteresis depends on contact conditions, affects the dynamic behavior of the joint and results in energy dissipation [2]. Hysteresis loops, namely the tangential friction force as a function of the relative displacement, can be replaced with a simplified model of friction contact [[3], [4], [5], [6]]. These friction models can be combined with dynamic analysis to simulate the nonlinear dynamics of structures with bolted joints. In these models, two major issues need to be addressed: (i) the accurate reproduction of the friction nonlinear behavior, and (ii) a precise calculation of contact parameters (tangential contact stiffness and friction coefficient). A good calibration of these contact models depends on accurate measurement of the hysteresis loops using precisely controlled experiments. In this way, the development of an innovative experimental technique can advance understanding of the behavior of the bolted joint interfaces. Consequently, more reliable models can be used to simulate the nonlinear dynamics of bolted joint structures.

Previous experimental research on the nonlinear behavior of bolted joints has determined damping characteristics through the structural dynamic response [[7], [8], [9]]. Interface damping is often identified according to the experimental frequency response functions. More recently, an experimental investigation into friction damping has focused on the direct measurement of friction behavior. Gaul et al. [10,11] developed an experimental setup to measure the response functions and the damping characteristics of a bolted joint placed between two lumped masses. This setup is a resonator in which the relative motion between joint interfaces is excited by its longitudinal vibration mode. The inertia force of the free end mass is regarded as the tangential friction force transmitted over the joint interface. Sandia National Laboratories [12] utilized a similar idea and proposed a resonant apparatus. In these two experimental devices, the excitation imposed by electromagnetic shakers cannot excite any vibration modes other than the desired longitudinal mode. Abad et al. [13,14] did experiments to study the friction behavior of bolted joints with a quasi-static excitation imposed by a universal testing machine. Eriten et al. [15] developed a lap joint fretting apparatus to measure hysteresis loops and contact parameters of bolted joints and studied the influence of normal preload, maximum tangential displacement, and material on the joint parameters. This apparatus employs a piezoelectric actuator with a closed-loop control to provide oscillatory motions of the lap joint. Also, some researchers [16,17] have performed experiments on the interface friction behavior of bolted joints under torsional loading. In Ref. [16] it was found that decreasing the bolt preload the hysteresis loop changed from an elliptical shape to a distorted four-sided polygon. Increasing the angular amplitude, the hysteresis loops became shaped like parallel hexagons. This behavior was explained by the authors as being caused by the relative slippage between the contact threads [17].

In general, three variables need to be measured in fretting friction experiments, i.e. the tangential friction force, the tangential relative displacement between contact surfaces, and the normal preload. Contact stiffness, namely the slope of the hysteresis loop at the stick stage, and the friction coefficient, that is the ratio of the tangential force over the normal preload at the gross-slip stage, can both be extracted by the variables measured.

The tangential relative displacement is generally very small, less than 100 μm, and requires a very accurate measurement method. Gaul et al. [10,11] and Sandia National Laboratories [12] used frequency domain integration techniques to obtain the tangential displacement from measured acceleration data. However, the inevitable noise in measured data may introduce errors in the integration process. In Ref. [[10], [11], [12]] the tangential friction force was measured with an accelerometer located on the lumped mass at the remote end of the shaker. Kartal et al. [18] employed Digital Image Correlation (DIC) to determine the relative displacement of the contact interfaces. The accuracy of the measured displacement largely depends on the resolution and size of the selected images. Eriten et al. [15] employed a single Laser Nano Sensor and a small mirror to measure the tangential displacement of the joint specimen at the moving end. However, the motion of the specimen at the fixed end was considered negligible assuming high rigidity at that location. The tangential friction force was measured with a tri-axial load cell which allows for monitoring a possible misalignment in out-of-plane directions. Schwingshackl et al. [19] developed the “Imperial College London” first-generation friction apparatus. This apparatus utilizes a single Laser Doppler Vibrometer (LDV) to measure the displacement of the moving contact surface. Also, in this case, the displacement was considered to be the relative displacement under the assumption that the fixed contact surface has negligible movement. The first-generation was updated to a second-generation apparatus using two LDVs able to measure the true relative displacement [20]. Two LDVs were also used in test rigs described in Ref. [[21], [22], [23], [24], [25]].

The accuracy of the estimated friction coefficients heavily depends on the precision of bolt preload. In Ref. [15,27], the bolt preload was determined by a torque-preload relationship with torque-controlled measurements. The calculated preload may be inaccurate because this relationship depends on the friction coefficient [14], which is known only approximately. Li et al. [26] used a strain gauge glued to the bolt to measure the axial deformation of the bolt and therefore the corresponding preload. Abad et al. [13] used an annulus force washer to measure the bolt preload in their test device.

This paper describes a fretting test apparatus purposely developed to investigate the friction behavior of bolted joints and estimate the contact parameters. The tangential friction force is measured with a dynamic load cell, while a single LDV in combination with a prism measures the relative displacement and the bolt preload is detected by a force washer. This apparatus can also be employed to study the effect of fretting wear on the contact parameters.

The paper is organized as follows. Section 2 describes the developed test apparatus and introduces the measurement method of hysteresis loops in detail. Section 3 analyses the repeatability of test results and the effect of bolt preload, and excitation amplitude on measured hysteresis loops and contact parameters. Section 4 models the contact between the bolted joint to simulate the tangential force/relative displacement relationship. Results from the numerical simulation are validated with the measured data. Section 5 highlights the accuracy and reliability of the test apparatus.

Section snippets

Description of the test apparatus

An overall view of the rig is depicted in Fig. 1. A leaf spring (7) is clamped between two C-shaped half-frames (5) and (12) by tightening two bolts (1). The two half-frames are machined from a monolithic steel block and make up the frame of the rig. The frame forms an O-shaped closed gate so that all the internal forces are self-balanced. A piezoelectric actuator (17) is connected to the left side of the leaf spring. The actuator displaces the leaf spring with an oscillating motion that is

Experimental results and discussion

The tangential force as a function of displacement gives the hysteresis loop which represents the nonlinear characteristics of the joint interface. The area enclosed by the hysteresis loop represents dissipated energy per cycle. Fig. 8 shows a typical hysteresis loop obtained with this test apparatus. The loop shows the three fretting regimes. During the stick regime, the force varies linearly with the relative displacement and only elastic deformation occurs on the contact surface. Increasing

Extraction of contact parameters and measurement accuracy

The architecture of the fretting rig presented in this paper does not allow a direct measurement of the contact force F32 in Fig. 15 at the target interface. This architecture is common to many test rigs as those described in Ref. [[11], [12], [13], [14], [15], [16], [17]]. The force measured by the load cell depends on the contact forces at all the interfaces (between the screw head, the washer, the nut and the target interface) and on the elastic force in the bolt shank. Therefore, a

Conclusions

This paper presents a fretting apparatus to study friction hysteresis behavior in bolted joints. Compared with similar test rigs proposed in the past, this rig has some unique features. An original arrangement of the prism allows measuring the relative displacements using only one laser beam. Some rigs proposed in the past measured only the displacement of the moving surface, which was then assumed as the relative displacement. In more recent rigs the relative displacement was measured with two

CRediT authorship contribution statement

Dongwu Li: Conceptualization, Methodology, Software, Investigation, Writing - original draft. Chao Xu: Project administration, Funding acquisition, Resources, Supervision. Daniele Botto: Methodology, Software, Validation, Writing - review & editing. Zhishu Zhang: Methodology. Muzio Gola: Methodology, Writing - review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors wish to acknowledge and thank the China Science Challenge for funding their research project (TZ2018007). Dongwu Li would also like to show his gratitude to China Scholarship Council (CSC) for supporting him as a visiting Ph.D. to AERMEC lab of Politecnico di Torino within the project EXTHENdED.

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