Estimation of Impact Effect on the Cutting Tool of a Shaper from Measurement of Responses During Machining

Force reconstruction is a process in which response signals from a dynamic event are used to infer what the applied force must have been to produce these responses. Force reconstruction is of interest when the input force cannot be directly measured while response signals are easily obtained using transducers such as accelerometers or strain gauges. In many structural evaluation tests, the dynamic response is not sufficient information; one may really need a description of the input force. A most preferred approach to address this problem is to determine the Frequency Response Function (FRF) matrix, measure the structural responses, and calculate the dynamic forces based on Least Squares scheme. The forces obtained by this approach are prone to errors. These arise due to a combination of errors in the measurements and high condition numbers in the matrix of transfer functions to be inverted. Ill conditioning of the FRF matrix causes measurement errors to be magnified significantly. This paper demonstrates the impact effect on the force history in two cases, one on a cantilever beam and another on cutting tool of a shaper. The acceleration response is used as input for force prediction. The impact force history prediction algorithm is developed in both time and frequency domains to determine the impact force amplitude. In the time domain the beam response due to the impact load is first predicted. The sum of mean square errors between the predicted and measured response is then defined as the objective function. The optimization problem is thereby constructed and is then solved for the amplitude of the impact force. The accelerance method is used in the frequency domain. Results show that the method outlined for the identification of the magnitude of the impact force, apart from being accurate and robust to the effects of measurement noise, may be extended to solve problems of a more general nature.