With the urgent demand of high-end equipment for high quality surfaces, the technique of ultrasonic vibration-assisted burnishing is introduced to strengthen the surface properties. To explore the influence of the ultrasonic vibration on the dynamic response of a burnishing system, the burnishing friction force generated from a multi-ball surface burnishing system was characterized by chaos theory. The system had four assisted forms: no ultrasonic vibration, one-dimensional (1D) ultrasonic in x-axis, 1D ultrasonic in z-axis, and 2D ultrasonic in xz-axis. The results showed that any burnishing system had chaotic nature. Under the 2D ultrasonic vibration-assisted burnishing, the burnishing friction force was reconstructed to be a chaotic attractor with high convergence degree. Moreover, the burnishing system has notable complexity and stability. The burnished Al7075 alloy sample has an excellent surface with a higher smoothness and hardness. The burnishing with 2D ultrasonic vibration in xz-axis is a technique to enhance surface properties.

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