Vol.:(0123456789) 1 3 Journal of the Brazilian Society of Mechanical Sciences and Engineering (2018) 40:494 https://doi.org/10.1007/s40430-018-1411-2 TECHNICAL PAPER Experimental study of cutting force on a cutting tool during machining using inverse problem analysis Ratan A. Patil 1  · Shrinivas L. Gombi 2 Received: 11 December 2017 / Accepted: 18 September 2018 / Published online: 27 September 2018 © The Brazilian Society of Mechanical Sciences and Engineering 2018 Abstract One of the important factors when dealing with the mechanics of deformable bodies is the variation of the applied force com- ing on to the body or structure. The present study deals with the indirect measurement of impact forces acting on a shaper tool as direct measurement of these forces is very much difcult. This paper describes one of the indirect force determination methods using frequency response functions. The problem of determining the impact force acting on a body or a structure is the inverse problem. The impact force acting on a tool can be estimated by the responses measured at diferent points of the cutting tool. The estimation accuracy is improved using singular value decomposition method and Moore–Penrose pseudo-inverse method. Statistical analysis was carried out to determine the level of signifcance of the experimental method. The experimental method results in accurate identifcation of impact force which helps in better design and development of cutting tools. Keywords Impact force · Inverse problem · Frequency response function · Force identifcation 1 Introduction The life of a cutting tool is signifcantly afected by the cut- ting forces during machining as these forces are not static in nature. During the initial instance when the tool comes into contact with the workpiece greater amount of impact force comes on to the cutting tool which is an important factor while designing the cutting tools and the life of the cutting tools. The cutting parameters such as depth of cut, feed rate, speed afects the cutting forces during machining. The actual cutting forces coming on to the tool are of prior importance as these forces decide the span of the cutting tool which decides the economy of the production plant. Premature tool failure is the major concern in today’s con- ventional production plants, as the cutting tools are designed for the average cutting forces. During the starting instance of machining, a high magnitude of cutting force comes on to the tool which is enough to cause plastic deformation or chipping of tool tip which eventually causes tool failure [1]. Cutting forces afects the surface fnish and surface accuracy of the machined part. The complete tool destruction takes place because of higher magnitude of cutting forces or shock loads which occurs when tool comes in contact with the workpiece during the frst time of every machining cut [2]. The condition of cutting tool can be monitored by various methods. The direct methods such as computer vision and indirect methods such as vibration analysis can be used to monitor the essential parameters [3–5]. Direct measurement of the cutting forces during machin- ing is difcult because it is very much difcult to place the sensor at the too tip as the tool tip comes in contact with the workpiece during machining. The direct placement of the sensor [6] on the tool tip damages the sensor, so in order to measure the cutting force, inverse force identifcation technique is used to predict the cutting force coming on to the tool. The dynamics of the mechanical structures can be grouped into two types of problem: one is the forward prob- lem, and the other is the inverse problem [7]. In case of forward problem, prediction of data (output) is done based upon the estimated parameters (input) using mathematical model or physical theory, whereas in inverse problem, the parameters are predicted (input) based upon the measured data (output) using mathematical model or physical theory. Technical Editor: Márcio Bacci da Silva. * Ratan A. Patil ratan@jainbgm.in 1 Jain College of Engineering, Belgaum, India 2 KLS’ Gogte Institute of Technology, Belgaum, India