# Determination of Clamping Force Using Bolt Vibration Responses during the Tightening Process
## 1 Introduction  
Mechanically fastened joints and adhesive bonded joints are used to join structures [1; 2]. These joints affect the damping and dynamic properties of the assembled structure [3]. Fastened joints consist of bolts, rivets, and pins. Bolted joints are used widely for their reliability and cost reduction during vehicle manufacture. As the demand for lightweight structures is increasing in the automotive [4] and aerospace [5; 6] industries, advanced composite materials and alloys are being used [7]. A decrease in weight is inevitably accompanied by an increase in vibration. According to [PERSON] et al. [8], structures made of lightweight materials easily transmit sound due to small transmission losses. For systems consisting of various thin wall structures, such as automobiles, the sound transmission characteristics are determined by the mass law. Noise emission is inversely proportional to the plate thickness and material density. This results in an increase in structure-borne noise or a failure of parts during operation due to excessive vibrations. To minimize these faults, a thick bolt that can apply excessive clamping force over the designed value is required. When the clamping force is measured precisely, the reliability of the assembled parts increases with the reduction of the bolt size. The mechanism of the bolt tightening process is complex. Numerous factors affect the lifespan of an assembled bolt. The tension of the bolts induces preloading, which makes the two separate parts move in phases. By preventingslippage between parts, the force has the greatest effect on the lifecycle. Most bolt failures are caused by insufficient initial clamping force applications. When the applied preloading of the bolt is less than the design value, the bolt can be loosened by vibrations from operations. Monitoring of the bolt loosening is important to ensure the safety of structures [9; 10; 11; 12; 13; 14; 15; 16]. To minimize unexpected problems due to bolt loosening, it is important to evaluate the initial bolt clamping force during the tightening process. Torque and angle controls are used to apply uniform clamping forces to each bolt in the manufacturing process. Measurement of the tightening torque using a wrench is the least expensive and most efficient method for estimation of the clamping force [17]. When the torque is used to estimate the clamping force, the tightening is performed until the applied torque reaches the value set by the operator. Alternatively, the torque is estimated by the value measured when loosening the already tightened bolt. For the bolt assembly process, only a small portion of the fastening torque is converted to fastening force (less than 10%). Most of the applied energy is known to be used to overcome the friction generated on the bolt threads (40%) and on the bolt head or nut seat (50%). The efficiency of the conversion is affected by the bolt material, and can be changed by installing a lock washer or by lubricating the threads. Torque is converted into the product of nut factor, clamping force, and nominal diameter. Nut factor causes variation of 25-30% caused by friction, operator, geometry, tool accuracy, and relaxation factors. Consequently, it is difficult to use this for structures and joints that require precise monitoring of the clamping force [18; 19; 20]. The angle control method utilizes the linear relationship between the rotation and the clamping force in the elastic deformation of a bolt [21]. The status when the bolt head seat comes into contact with the bolted joint is called the snug point. At the snug point, the axial clamping force is zero; the fastening force increases in proportion to the angle in the rotating process [22]. Strain gauge and ultrasonic measurements were used to precisely measure the initial clamping force. The strain method measures the clamping force using Hooke's law after attaching a strain gauge to the axial direction of a bolt [18; 23]. For an axial strain gauge, the mounting should be aligned in axial directions.