Low prediction accuracy of natural frequencies of a milling robot is one major obstacle to the avoidance of chatter vibration in low-speed robotic milling. For enhanced accuracy in predicting the natural frequency of mixed robot, a variable stiffness model is proposed featuring the dependency of joint stiffness on the joint variables, rather than the constant joint stiffness in the traditional assumption. By integrating the variable joint stiffness model into a mode-reduced 4DOF model modified for the present study, the new method for predicting the robot natural frequency is then built, analyzed, and verified through simulation and modal tests by both a 3-axis accelerometer and a laser vibrometer on the milling robot under different robot configurations. Comparison of the experimental values from the modal tests against the natural frequencies predicted by the proposed model reveals a predicting error of less than 10%, hence enhanced accuracy of the proposed variable joint stiffness model in a large operational space. Based on the model, milling parameters without structural vibration has been selected, and the quality of the robot milling for titanium alloy has been improved.
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