Frequency spectrum prediction model of broaching process using theoretical cutting force time history

The amplitude of tooth passing frequency in frequency spectrum is an important indicator to judge machining quality and tool wear. In comparison to the amplitude of tooth passing frequency in acceleration spectrum, broaching force more directly reflects the tool wear and machining quality, but the broaching force measurement equipment is expensive and can change the dynamic structure of the machine. Therefore, this paper establishes a frequency spectrum prediction model of the broaching process using theoretical cutting force time history. This model combines the advantages of easy acquisition of vibration data, low cost, and no change in machine structure by the acceleration sensor, with the benefits of directly reflecting tool wear and machining quality through broaching force measurement equipment. In this paper, the theoretical cutting force model is developed based on the Johnson–Cook material law. Compared to the traditional method of directly applying FFT to obtain the broaching force spectrum, this paper innovatively divides the broaching force into square waves of equal width but varying amplitudes in the time domain. The frequency domain waveform of broaching force can be regarded as the vector superposition between the harmonic series corresponding to these time-domain square waves. Through the waveform image of numerical simulation, it can be concluded that the amplitude of tooth passing frequency used for tool wear diagnosis depends on the shape of tooth passing area in cutting force time history, which is affected by factors like tool wear and lubrication conditions. Any force changes caused by tool wear and broaching quality can be reflected in the broaching force spectrum. According to the characteristics of the dynamic equation, the frequency spectrum of acceleration can be obtained by substituting the broaching force in frequency domain into the dynamic equation. Through experimental analysis, it is shown that the numerical acceleration frequency spectrum obtained by the present model is consistent with the experimental acceleration frequency spectrum.