The vibration of the spindle of the worm wheel gear grinding machine has a decisive influence on the quality of gear processing. However, the periodic dressing of the grinding wheel and the continuous tool shifting during grinding will change the amplitude and frequency of the spindle vibration, making spindle vibration prediction difficult. This paper introduces the diameter parameter of the grinding wheel, converts the input grinding wheel linear speed into the grinding wheel rotational speed, and utilizes the dynamic characteristics of the grinding wheel rotational speed to characterize the influence of periodic grinding dressing; at the same time, it introduces the spindle position parameter to establish a compensation function for the grinding wheel spindle position to eliminate the influence of continuous tool shifting during grinding. Based on this, a prediction method for the spindle vibration is proposed, which predicts the spindle vibration of the worm wheel gear grinding machine through grinding process parameters. Firstly, the liquid neural network (LNN) gating mechanism is utilized to dynamically screen the process parameter features, simulate the physical conduction logic between the process parameters and the root mean square (RMS) value of vibration, discretize the process parameters through a continuoustime dynamic system, and use the activation function to capture the hidden dynamic characteristics between them. Secondly, a position compensation function is established based on LNN to capture the hidden characteristics between position information and RMS. Taking the RMS value corresponding to the standard Y-axis position as the benchmark, the RMS values corresponding to other positions are mapped and compensated. Finally, the global dependencies of the features is modeled through multiple stacked Transformer encoder blocks, and the output features of LNN are optimized using residual connections, etc. Finally, the sequence dimension is removed and combined with the compensation value to obtain the vibration prediction value. In the comparative experiments, the R2 of this prediction model reaches 99.19%, the RMSE is 0.074 1, the MAE is 0.051 1, and the MAPE is 0.05%. Compared with the traditional model, the prediction accuracy is higher. Finally, based on this prediction model, a spindle vibration suppression model for the worm wheel gear grinding machine is established. The grinding process parameters are optimized using the quantum slime mold algorithm to suppress the spindle vibration, and the suppression effect is 39.99%.