A Parallel-Type Unified Error Vector Transfer Framework for Real-Time Volumetric Error Compensation in Three-Axis CNC Machines

Geometric errors in CNC machine tools accumulate along the tool path and directly affect machining accuracy. Traditional serial-chain-based volumetric error models, such as those based on the homogeneous transformation matrix (HTM) or screw theory, often exhibit ambiguous geometric definitions, weak traceability to measurement points, and increased computational cost due to repeated coordinate transformations and inverse mappings, limiting their suitability for real-time control. To overcome these challenges, this study proposes a parallel-type unified error vector transfer (EVT) framework, based on the Abbe and Bryan principles. In this framework, axis error motions are directly expressed as vectors and transferred to the tool center point (TCP), where they are superimposed to obtain total error contributions. Building on this principle, a unified normal volumetric error model (NVEM) is formulated using survival and sign factors. The unified NVEM is applicable to various types of three-axis machining centers, including horizontal configurations. In other words, differences in coordinate system definitions can be reconciled through coordinate transformation, allowing the unified NVEM to be consistently applied. Furthermore, a real-time error compensation controller (RECC) is embedded into the CNC kernel to compute compensation values within each interpolation cycle, ensuring deterministic and low-latency operation without external computation. Experimental validations on an XYFZ-type vertical machining center demonstrate that the proposed framework improves positioning accuracy by more than 72% and machining accuracy by 60.4%. These results confirm the feasibility, efficiency, and universality of the parallel-type unified EVT framework for real-time volumetric error compensation. Here, ‘parallel-type’ denotes the parallel superposition of independent error vector contributions, rather than a parallel kinematic mechanism.