AI 中文总结
该研究提出基于物理驱动的FPGA齿面接触计算方法，通过开源openXC7流程实现，无需训练即可在嵌入式场景下准确估计齿面接触，性能优于学习型代理模型，延迟稳定且确定性强。
AI 中文摘要
齿轮数字孪生、硬件在回路试验台和主动振动控制需围绕瞬时齿面接触状态形成闭环，这要求求解器具备实时性、确定性和可嵌入性；而加载齿面接触分析（LTCA）作为一种数据依赖型线性互补问题（LCP），采用fp64精度下每网格相位耗时数秒，在结构上不具备上述特性；学习型代理模型虽能快速推理，但每个训练样本需消耗一次完整的LTCA求解，且仅在训练范围内有保障。我们将闭式接触物理——接触点定位、主曲率提取和椭圆赫兹解——直接压缩为无分支的定点FPGA数据通路，称为物理驱动（physics-direct），该通路通过完全开源的openXC7流程实现（无需厂商工具，无浮点IP），并在退役的XC7K480T芯片上完成验证。四个片上系统（SoC）——几何、赫兹以及两个融合路径——与黄金模型的JTAG回读结果完全一致。片上预览跟踪LCP体压力的误差为-22%，加载传动误差（LTE）峰峰值误差为-19%，并保留了精确的W^(1/3)定律；无需训练的情况下，其在负载外推的准确性优于训练后的网络（18.9%对20.3%）。延迟为编译时常数（抖动σ=0），且受DSP约束的几何内核将器件逻辑资源利用率推至近63条通路。物理驱动是一种可解释、确定性的替代方案，用于嵌入式齿面接触估计，可替代神经代理模型。
英文摘要
Gear digital twins, hardware-in-the-loop rigs, and active vibration control close a loop around the instantaneous tooth-contact state, demanding a solver that is real-time, deterministic, and embeddable -- properties that loaded tooth contact analysis (LTCA), a data-dependent linear complementarity problem (LCP) costing seconds per mesh phase in fp64, structurally lacks; learned surrogates infer fast but spend one full LTCA solve per training sample and offer no guarantee beyond their training envelope. We instead compress the closed-form contact physics -- contact-point localization, principal-curvature extraction, and the elliptical Hertz solution -- directly into a branch-free fixed-point FPGA datapath, termed physics-direct, realized through the fully open-source openXC7 flow (no vendor tools, no floating-point IP) and validated on retired XC7K480T silicon. Four SoCs -- geometry, Hertz, and two fused paths -- pass bit-exact JTAG readback against a golden model. The on-chip preview tracks LCP body pressure to within -22% and loaded transmission error (LTE) peak-to-peak to -19%, preserving the exact $W^{1/3}$ law; with zero training it extrapolates in load more accurately than a trained network (18.9% versus 20.3%). Latency is a compile-time constant ($σ= 0$ jitter), and the DSP-bound geometry kernel saturates the fabric near 63 lanes. Physics-direct is an interpretable, deterministic alternative to neural surrogacy for embedded tooth-contact estimation.
