Background Vehicle-mounted drilling rigs (VMDRs), key devices in surface drilling for mine rescue, directly connect the ground and underground disaster-hit areas through vertical drilling, thereby creating rescue channels for trapped people. In this case, the drilling speed of VMDRs serves as an important indicator for evaluating surface drilling operations. However, directly determining the drilling speed is challenging due to the limitations of position sensors.

Methods This study developed an estimation method based on a new hybrid differentiator (NHD), allowing the drilling speed to be calculated using measurable displacement signals. First, a continuous switching function was devised, and its convergence characteristics were analyzed in combination with its derivative. Based on this function, this study designed a NHD that integrated linear and nonlinear characteristics. Then, the global asymptotic stability of the NHD was evidenced using the Lyapunov function. By designing three differentiators for comparison using the Matlab software, this study conducted simulations and analysis of the drilling speed under sinusoidal and triangular signals.

Results and Conclusions  The simulation results indicate that under the sinusoidal signals, the proposed NHD yielded average, maximum, and standard errors of the drilling speed approximately 0.1 m/s, approximately 1.02 m/s, and approximately 0.09 m/s, respectively. In contrast, under the triangular wave signals, these errors were determined approximately 0.29 m/s, approximately 2.07 m/s, and approximately 0.47 m/s, respectively. Continuous and intermittent lifting and lowering experiments were conducted on an XSL1500 rescue VMDR manufactured by XCMG. The experiment results reveal that the NHD exhibited high response speeds and denoising capacity under the two operating conditions. This indicates that the NHD is suitable for determining the drilling speed in uncertain environments. This study proposed a NHD design method based on a novel continuous switching function and developed a method that combines the NHD and position sensors to estimate the drilling speed of a drilling rig. The results of this study provide theoretical support and practical experience for determining the drilling speeds of VMDRs.