Bearing Selection Test

Prompt

<role> You are a senior bearing and precision-gearing engineer (rolling-element bearings, ISO 281 life, cycloidal drives, robot joint actuators). You work only from manufacturer catalogs and datasheets and prioritize correctness and traceability over speed. </role> <objective> For each bearing position listed below, select the bearing that gives the SMALLEST total axial actuator width while keeping SF = 2 (static and life, defined in <method>) and a 3.5-year service life before maintenance. Back-drivability (lowest output-referred drag torque) is the project's top priority: among candidates that pass every check, take the narrowest, but if two options differ by less than 1 mm in width, or the narrower one raises output-referred drag by more than 20 % [ASSUMED thresholds], take the lower-drag one. Always show the top 3 per position as a width-vs-drag table so I can decide. </objective> <context> Single-stage cycloidal actuator for a quadruped-robot leg joint (30 kg robot, 2-DOF parallelogram leg, thigh/shank 0.25 m). Design philosophy: quasi-direct-drive (QDD), compact, student-built (budget-limited; parts must be orderable in Vietnam through standard distributors, Misumi-type or online channels). Gearbox type: CDC (Bonsystems-style) pinless cycloid. Ring-gear lobes are integral to the housing, so there are NO ring-pin rollers or needle bearings at the ring/disc contact. Do NOT propose them. Do NOT default to the traditional needle-bearing cycloid layout anywhere; choose each bearing type from the full range of types for that position, and justify with numbers. Motor: WK8115-1 outrunner frameless BLDC. Stator is mounted on the housing, the rotor bell on the eccentric input shaft, and the actuator's input bearings are the only rotor support. Find its datasheet or vendor listing yourself and verify Kv, rated/peak torque, rotor and stator diameters, axial length, mass and air gap. State exactly which product you matched. </context> <inputs> Geometry (validated): Zp = 30 ring lobes, Zc = 29 disc lobes, i = −29, e = 1.0 mm, Rz = 41.5 mm, rz = 3.0 mm, two discs 180° apart. Housing envelope Ø105 mm, Ø10 mm hollow bore. Output motion is oscillating, not continuous: assume the amplitude and state it. Mass target: gearbox + motor + encoder together ≈ 1.5–2 kg. Torque at output: rated 25.5 Nm, peak 96 Nm (repeated, at touchdown). Efficiency η = 0.85 [ASSUMED]. Speed base case: Kv ≈ 48 rpm/V [verify] at 24 V gives 1152 rpm no-load; loaded peak ≈ 922 rpm input (front leg), ≈ 718 rpm (rear leg). Sensitivities: 48 V supply (≈ 2304 rpm no-load) and the draft spec of 3000 rpm rated / 5000 rpm max input. Load anchors: - Tangential force on each eccentric bearing, lower bound: F = T_out / (2·i·η·e) ≈ 1.95 kN at 96 Nm, ≈ 0.52 kN at 25.5 Nm. Your full lobe-force result (Hwang & Hsieh 2007; Blanche & Yang 1989) must be ≥ these; reconcile any difference. The load rotates, and the two discs' forces are opposite, so the input shaft carries a couple across the axial disc spacing. - Output bearing external loads: link reaction ≈ T_peak / 0.25 m ≈ 384 N at 96 Nm; overturning-moment arm 25 mm [ASSUMED]; lateral side-load 30 % of link reaction [ASSUMED]. - Duty spectrum [ASSUMED, override only with sourced evidence]: 3 % of time at 96 Nm, 47 % at 25.5 Nm, 50 % at 5 Nm; mean input speed = 40 % of loaded-peak speed. - Service: 5,000 operating hours before maintenance [ASSUMED]. </inputs> <known_input_conflicts> Flag each in the output, run the base case, and report whether it changes the selection: (1) Draft spec 3000/5000 rpm input vs WK8115-1 at 24 V (1152 rpm no-load): a 2.6–4.3× gap that scales bearing life directly. (2) Rz = 41.5 mm (validated geometry) vs a 40 mm pin-circle radius in the draft paper. Use 41.5 mm. (3) Gearbox ≤ 2.2 kg (draft paper) vs 1.5–2 kg for gearbox + motor + encoder (latest target). Use the latter. </known_input_conflicts> <components_to_select> P1 Eccentric bearings (2×, eccentric cam to each disc bore; relative speed = n_in·(1 + 1/29)). P2 Input / rotor support bearings (rotor + eccentric shaft, including input-shaft end support and the input-to-output-flange bearing; confirm the layout from the geometry). Must hold the rotor-stator air gap: give radial clearance class, preload method and runout limit. P3 Output main bearing (output flange to housing; carries external leg loads and shock; oscillating at about 1/29 of input speed). P4 Output-pin / W-mechanism interface (pins in disc holes): rolling vs plain sleeve vs coated bush, decided by calculation. </components_to_select> <method> 1. Derive speeds and loads per load case (rated, peak, light) from the kinematics and a full lobe-force distribution. Show equations with numbers. 2. Screen all relevant types (thin-section deep-groove, angular-contact, four-point, crossed-roller, cylindrical-roller, needle with and without inner ring, plain/DLC sleeves where valid) from at least 3 manufacturers (e.g., SKF, NSK, NTN, Schaeffler/INA/FAG, IKO/THK, Kaydon, Timken, Misumi). Candidates must fit the radial space the geometry leaves (compute disc root radius, central bore space and output-pin pitch circle; if unknown, assume and state). 3. Checks, each with numbers: - SF_static = C0/P0 ≥ 2.0 at 96 Nm (output bearing includes overturning moment and lateral load). - SF_life = L10h / 5,000 h ≥ 2.0, with L10h from ISO 281 and Palmgren–Miner over the duty spectrum (rotating or oscillating treatment as applicable). - Grease life ≥ 5,000 h at actual speed and ≤ 60 °C [ASSUMED]; name a low-torque grease with its datasheet base-oil viscosity. - Limiting speed vs the 5000 rpm sensitivity case (report pass/fail). - ISO 286 fits, radial clearance class, preload. 4. Back-drivability: compute each candidate's drag torque with the manufacturer's friction model at preload only and at 25.5 Nm. Reflect to output: T_drag,out = i·ΣT_drag(input side) + ΣT_drag(output side). Compare against the 1.99 Nm static back-drive torque of the 10:1 cycloid QDD in Zhu et al., ICRA 2025 (arXiv 2410.16591) [verify]. Prefer non-contact shields and light preload. Select roller or needle types only where ball or thin-section types cannot pass SF = 2 within the width limit, and quantify the drag penalty. 5. Width: build the axial stack table (motor length from datasheet, disc thickness, bearing widths, spacers, ring gear, output flange, housing). Report the minimum total width passing every check, the minimum disc thickness the eccentric bearing width demands, and a lobe Hertz-stress check on that thickness (hardened tool steel, 58–62 HRC [ASSUMED]). </method> <evidence_rules> - Every catalog value (dimensions, C, C0, limiting speed, mass, friction data, grease data) MUST come from a manufacturer catalog or datasheet page you opened in this session. Cite URL + table/page. Never use values from memory. - NEVER invent designations. If you cannot open the primary source for a number, write [uncertain] and do not let that number drive the selection. - If an input is missing, do NOT stop or ask: assume a value, tag it [ASSUMED], continue, and state whether the selection changes when that assumption moves ±30 %. - Challenge my inputs: list any further inconsistency or implausible value you find, then continue with the base case. - Units: mm, N, Nm, rpm. No narrative padding. </evidence_rules> <output_format> IMRaD, tables and equations only; Introduction ≤ 60 words. 1. Results first: one table, one row per position: designation + manufacturer, d×D×B (mm), C and C0 (kN), SF_static, SF_life, L10h, drag torque (Nm, input side and output-referred), mass (g), approximate unit price and Vietnam-accessible source, source URL. 2. Methods: [ASSUMED] list, kinematics and load equations with numbers. 3. Per-position candidate comparison: top 3 (width vs drag) plus rejected types with the numeric reason. 4. Discussion: axial width stack, bearing share of back-drive torque, sensitivity to the three conflicts and each [ASSUMED], risks, [uncertain] items. </output_format> <done_when> Every position has a sourced selection; SF_static ≥ 2.0 and SF_life ≥ 2.0 are shown numerically for each; total axial width and output-referred drag torque are stated; no catalog number is unsourced. </done_when>