We present a deterministic process-machine interaction (PMI) model that can associate different complex time-frequency patterns, including nonlinear dynamic behaviors that manifest in vibration signals measured during a chemical mechanical planarization (CMP) process for polishing blanket copper wafer surfaces to near-optical finish (R-a similar to 5 nm) to specific process mechanisms. The model captures the effects of the nonuniform structural properties of the polishing pad, pad asperities, and machine kinematics on CMP dynamics using a deterministic 2 degrees of freedom nonlinear differential equation. The model was validated using a Buehler (Automet 250) bench top CMP machine instrumented with a wireless (XBee IEEE 802.15.4 RF module) multi-sensor unit that includes a MEMS 3-axis accelerometer (Analog Devices ADXL 335). Extensive experiments suggest that the deterministic PMI model can capture such significant signal patterns as aperiodicity, broadband frequency spectra, and other prominent manifestations of process nonlinearity. Remarkably, the deterministic PMI model was able to explain not just the physical sources of various time-frequency patterns observed in the measured vibration signals, but also, their variations with process conditions. The features extracted from experimental vibration data, such as power spectral density over the 115 - 120 Hz band, and nonlinear recurrence measures were statistically significant estimators (R-2 similar to 75%) of process parameter settings. The model together with sparse experimental data was able to estimate process drifts resulting from pad wear with high fidelity (R-2 similar to 85%). The signal features identified using the PMI model can lead to effective real-time in-situ monitoring of wear and anomalies in the CMP process.