Differentiable and Self-Auditing Transient Dynamics Solver for Ball Bearings: OpenBEARD Cross-Verified Against ADORE

A transient multibody dynamics simulation of rolling-element bearings is the basis for the design of high-speed rotating machinery; however, the established solvers are proprietary, cannot be used with automatic differentiation, and offer no built-in measure of their own physical consistency. We present OpenBEARD, an open-source, fully differentiable transient dynamics solver for angular-contact ball bearings. The solver steps a 40+13Z-component state (inner ring, cage, and Z balls with quaternion attitude, plus guide-patch, lumped-thermal, and energy-audit states) forward in time under coupled Hertzian contact, Hamrock–Dowson and full-multigrid elastohydrodynamic lubrication, thermal–elastohydrodynamic traction, and centrifugal/press-fit clearance models, using nondimensionalized implicit stiff time integration. A built-in metriplectic conservation audit checks energy closure, the second law per dissipation channel, and the gyroscopic-power identity at every output step. OpenBEARD is cross-verified against two published ADORE references of Gupta. For a high-speed NASA angular-contact ball bearing, the quasi-static contact loads, angles, stresses, and centrifugal force match the published values to within 0.3%, and the ball spin and orbital velocities and the spin-axis orientation to ≤0.1%. The inner-race spin-to-roll ratio—a slip-derived secondary quantity that is the most model-sensitive metric in this class of solvers—differs from the NASA quasi-static reference by 8.8%. In the separate caged BallBearingTestCase benchmark, the corresponding quasi-static difference is 3.2%, and the transient settled value is ≈16% above the ADORE step-100 snapshot; these bounded offsets reflect different spin-moment constitutive models. The BallBearingTestCase comparison—a caged bearing under combined thrust and radial load—matches the per-ball contact angles and loads to within 0.23% RMS, and a single published dynamic snapshot (step 100) agrees with the transient contact mechanics to within a few percent. The built-in energy-closure residual stays of order 10−5 with no second-law violations. In the fully transient regime, race control emerges as a dynamical attractor of the coupled traction balance—ball-spin states perturbed by ±12% converge to a single outer-race-control solution—rather than the kinematic hypothesis assumed by quasi-static theory. OpenBEARD is released under the MIT license.