In the development of advanced humanoid robots, the flexibility and endurance of joints critically depend on lightweight and high-precision drive systems. As a key transmission component, planetary roller screws are trending toward miniaturization (diameter ≤6 mm) and material lightweighting. TC4 titanium alloy, with a density of only 4.51 g/cm³ (58% of steel), high specific strength, and excellent corrosion resistance, has emerged as a preferred material for small-diameter roller screws in humanoid robots. However, its grinding processing presents significant technical challenges that must be addressed to meet the stringent demands of compact, dynamic, and reliable robotic joints.
From my perspective, focusing on the core needs of humanoid robots, the grinding of TC4 titanium alloy involves four major pain points: low thermal conductivity leading to heat accumulation, susceptibility to chatter in slender structures, high chemical activity causing adhesive wear, and difficulty in controlling micro-precision due to low elastic modulus. Traditional grinding methods designed for steel are inadequate, resulting in poor accuracy stability and yield rates below 60%, which hampers the industrial application of lightweight transmission systems in humanoid robots. Therefore, we have developed a comprehensive technical solution encompassing dedicated preprocessing, specialized grinding equipment and tool adaptation, segmented temperature-controlled thermal grinding processes, and full-process precision management. This approach aims to overcome these hurdles and enable the mass production of high-performance screws for humanoid robot finger joints and dexterous hands.
The importance of this work lies in its potential to enhance the manufacturing level of core components for humanoid robots. Currently, foreign techniques, such as Germany’s Junker grinding systems with high-pressure cold air cooling and Japan’s Tsugami micro-CNC grinders with air-bearing spindles, have made strides in titanium alloy precision grinding. Domestically, research has focused on ultrasonic-assisted grinding and finite element analysis of heat distribution, but a complete process system for small-diameter thread grinding is lacking. Our method fills this gap by integrating optimized preprocessing, adaptive machine tools, and dynamic thermal compensation, specifically tailored for the unique properties of TC4 titanium alloy in humanoid robot applications.
First, let’s analyze the characteristics of TC4 titanium alloy. Its chemical composition and key properties are summarized in Table 1. The alloy offers advantages like lightweight and high strength, but its low thermal conductivity (16 W/(m·K)) and high chemical activity pose grinding challenges. To balance hardness and machinability, we optimized the preprocessing to refine grains and reduce hardness.
| Core Composition | Hardness (HRC) | Density (g/cm³) | Thermal Conductivity (W/(m·K)) | Elastic Modulus (GPa) | Tensile Strength (MPa) | Advantageous Properties |
|---|---|---|---|---|---|---|
| Ti: 88–90%, Al: 5.5–6.7%, V: 3.5–4.5% | 55–58 | 4.51 | 16 | 110 | ≥950 | Lightweight, high specific strength, corrosion resistance |
Our dedicated preprocessing involves vacuum partitioned spheroidizing annealing, precision rough turning, and dual non-destructive testing. The annealing is conducted in a vacuum environment (vacuum degree ≤1×10⁻³ Pa) to prevent oxidation, with a three-stage pumping system: rough pumping (mechanical pump), intermediate pumping (Roots pump), and fine pumping (molecular pump). The process includes heating to 750°C at 5°C/min, holding for 1 hour, then raising to 780°C in the α+β phase region for 3.5 hours to transform coarse Widmanstätten structure into fine spheroidal grains, followed by slow cooling at 3°C/min to 500°C and furnace cooling. This reduces hardness to below 210 HBW and refines grain size to 10–15 μm, improving machinability by 25% in terms of wheel wear reduction.
For enhanced hardness to meet wear resistance needs in humanoid robots, we apply solution treatment (930°C, 30–40 min, water quenching) and aging treatment (530°C, 4–6 hours, air cooling). This increases hardness to 55–58 HRC without significantly compromising toughness. Precision rough turning uses PCD tools with MQL (Minimum Quantity Lubrication) at speeds of 1500–2000 r/min, feed rates of 0.03–0.08 mm/r, and cutting depths of 0.10–0.15 mm, leaving a grinding allowance of 0.10–0.15 mm. Dual testing with ultrasonic and penetrant inspection ensures defect-free blanks, crucial for reliability in humanoid robot components.
Next, we designed specialized grinding equipment and tools tailored for TC4 titanium alloy. The selection of a micro-CNC thread grinder with dynamic thermal compensation is essential. Key configurations are detailed in Table 2. The machine features a granite bed for thermal stability, air-bearing spindles with runout ≤0.0005 mm, and a high-pressure low-temperature oil mist cooling system (pressure 0.5–0.6 MPa, oil temperature ≤25°C) to mitigate heat accumulation. Vibration damping systems, including adjustable damping pads, control amplitude to ≤0.0008 mm, preventing chatter in slender screws for humanoid robots.
| Configuration Module | Technical Parameters (Titanium Alloy Specific) | Functional Role |
|---|---|---|
| CNC System | Siemens 828D-Ti, supports real-time thermal error compensation algorithms | Dynamically corrects thermal deformation errors in titanium alloy grinding |
| Spindle System | Air-bearing spindle, radial runout ≤0.0005 mm, speed 0–10000 r/min | Reduces machine vibration, suppresses chatter in titanium alloy |
| Cooling System | High-pressure low-temperature oil mist device, pressure 0.5–0.6 MPa, oil temperature ≤25°C | Enhances heat dissipation, inhibits heat accumulation |
| Vibration Damping | Damping system + titanium alloy-specific damping pads, amplitude ≤0.0008 mm | Suppresses chatter in slender screws |
| Detection Module | Built-in infrared thermometer (0–500°C, accuracy ±1°C) | Monitors workpiece temperature in real-time, triggers thermal compensation |
The dynamic thermal compensation system uses eight platinum resistance temperature sensors (accuracy ±0.1°C) to collect data at 10 Hz. A multivariate linear regression model predicts thermal error, with the core formula expressed as:
$$ \Delta L = a_0 + a_1 T_1 + a_2 T_2 + \ldots + a_8 T_8 + b_1 n_1 + b_2 n_2 $$
Here, ΔL is the thermal error in lead (μm), T₁ to T₈ are temperature readings (°C), n₁ and n₂ are spindle speeds (r/min), and a₀ to a₈, b₁ to b₂ are fitting coefficients calibrated via orthogonal experiments. The compensation algorithm updates every 100 ms, achieving accuracy ≤0.002 mm, vital for precision in humanoid robot joints.
For grinding wheels, we selected diamond (SDC) wheels optimized for TC4 titanium alloy’s high hardness and adhesiveness. Parameters are listed in Table 3. Dressing cycles are shortened: every 3 pieces for rough grinding, every 2 for semi-finishing, and every 1 for finishing. Methods include diamond pen mechanical dressing, discharge-assisted dressing, and ultrasonic-assisted mechanical dressing to maintain profile accuracy. The grinding tool, a titanium alloy-specific grinding arbor made of TC4 material with TiN coating (thickness 2 μm, hardness ≥2000 HV), increases rigidity by 40% and incorporates a mini damper (damping coefficient 0.8) to control vibration.
| Grinding Stage | Wheel Material | Grit Size | Hardness | Bond | Porosity | Rationale |
|---|---|---|---|---|---|---|
| Rough Grinding | Diamond (SDC) | 800 mesh | Medium (G-H) | Resin bond | 35% | High grinding efficiency, good heat dissipation, avoids adhesion |
| Semi-Finishing | Diamond (SDC) | 1200 mesh | Medium-Low (F-G) | Resin bond | 40% | Corrects form errors, transitions between rough and finish grinding |
| Finish Grinding | Diamond (SDC) | 2000 mesh | Low (E-F) | Ceramic bond | 45% | Ensures micro-profile accuracy, reduces surface burns |
We then optimized a segmented temperature-controlled thermal grinding process. The mechanism involves “cutting → adhesion → friction → polishing” stages. Through orthogonal experiments, we determined optimal parameters for finish grinding, focusing on wheel speed v, workpiece speed n, and radial feed f. The factor levels and results are shown in Tables 4 and 5. The most significant factor is wheel speed, and the optimal combination is v = 12 m/s, n = 80 r/min, f = 0.0015 mm/z, minimizing lead error, surface roughness, and burn rate for humanoid robot screws.
| Level | Wheel Speed v (m/s) | Workpiece Speed n (r/min) | Radial Feed f (mm/z) |
|---|---|---|---|
| 1 | 12 | 80 | 0.0015 |
| 2 | 14 | 100 | 0.0025 |
| 3 | 16 | 120 | 0.0035 |
| Experiment No. | v (m/s) | n (r/min) | f (mm/z) | Lead Error (mm/300mm) | Surface Roughness Ra (μm) | Burn Rate (%) |
|---|---|---|---|---|---|---|
| 1 | 12 | 80 | 0.0015 | 0.009 | 0.29 | 0 |
| 2 | 12 | 100 | 0.0025 | 0.010 | 0.32 | 5 |
| 3 | 12 | 120 | 0.0035 | 0.012 | 0.38 | 15 |
| 4 | 14 | 80 | 0.0025 | 0.0105 | 0.33 | 8 |
| 5 | 14 | 100 | 0.0035 | 0.0115 | 0.40 | 20 |
| 6 | 14 | 120 | 0.0015 | 0.010 | 0.31 | 6 |
| 7 | 16 | 80 | 0.0035 | 0.013 | 0.42 | 25 |
| 8 | 16 | 100 | 0.0015 | 0.011 | 0.34 | 10 |
| 9 | 16 | 120 | 0.0025 | 0.0125 | 0.39 | 18 |
The segmented grinding parameters are summarized in Table 6. Rough grinding focuses on high-efficiency material removal with controlled heat, semi-finishing corrects form errors, and finish grinding uses minimal feed with dynamic thermal compensation. For internal threads in humanoid robot components, we employ plunge grinding with adapted parameters.
| Grinding Stage | Wheel Parameters | Process Parameters | Temperature/Vibration Control | Allowance |
|---|---|---|---|---|
| Rough Grinding | Diamond, 800 mesh | v = 18–20 m/s, n = 50–60 r/min, f = 0.008–0.010 mm/z | High-pressure low-temperature oil mist (0.5–0.6 MPa, ≤25°C), temperature rise ≤10°C | 0.03–0.05 mm |
| Semi-Finishing | Diamond, 1200 mesh | v = 15–17 m/s, n = 70–90 r/min, f = 0.004–0.006 mm/z | Infrared monitoring, reduce feed by 30% if ≥80°C | 0.01–0.02 mm |
| Finish Grinding | Diamond, 2000 mesh | v = 12 m/s, n = 80 r/min, f = 0.0015 mm/z | Laser interferometer dynamic thermal compensation, amplitude ≤0.0008 mm | — |
| Internal Thread Grinding | Diamond, 1500 mesh | v = 10–12 m/s, n = 30–40 r/min, plunge speed 0.08–0.15 mm/min | Titanium alloy arbor + vibration sensor monitoring | — |
To ensure precision and performance, we implemented a full-dimensional inspection system tailored for titanium alloy. Lead accuracy is measured with a laser interferometer (e.g., Renishaw XL-80) in a controlled environment (20±1°C, humidity ≤65%), achieving error ≤0.010 mm over 300 mm. Profile and dimensions are checked with a coordinate measuring machine, ensuring thread half-angle error ≤±0.004°, pitch diameter tolerance h5 grade (≤±0.003 mm), and tooth flank straightness ≤0.002 mm/10 mm. Surface quality is verified with roughness Ra ≤0.3 μm, no burns or cracks via SEM, and hardness uniformity within ±1 HRC. A dedicated lapping process using cast iron laps and titanium alloy-specific paste (0.5–1.0 μm alumina) at 10–15 r/min for 25–30 minutes reduces pitch error to within ±2 μm and induces compressive residual stress of –180 to –220 MPa, enhancing fatigue life by 30% for humanoid robot screws.
For performance enhancement, we apply DLC (Diamond-Like Carbon) coating (thickness 1.5–2.0 μm, hardness ≥2000 HV, friction coefficient ≤0.12), providing salt spray life ≥1000 hours. Dynamic validation includes critical speed ≥8500 r/min from dynamic balancing tests and fatigue life ≥1.2×10⁷ cycles under 100 N axial load, meeting the high-duty requirements of humanoid robots.
We conducted experimental verification by processing TC4 titanium alloy screws with diameter 4 mm and lead 5 mm, typical for humanoid robot finger joints. Two groups were compared: a control group using traditional grinding (steel-based parameters, no dynamic thermal compensation) and an experimental group using our optimized titanium alloy-specific process. Each group had 10 pieces, and results are shown in Tables 7 and 8. The experimental group showed significant improvements: lead error reduced by 44.4%, surface roughness by 58.3%, burn rate eliminated, and straightness improved by 75%. Performance metrics like critical speed increased by 25%, fatigue life by 71.4%, and salt spray life by 100%. The yield rate rose from 55% to 98%, and weight reduction of 39% was achieved compared to steel screws, crucial for lightweight humanoid robots.
| Indicator | Control Group | Experimental Group | Improvement | Design Requirement |
|---|---|---|---|---|
| Lead Error (mm/300mm) | 0.018 ± 0.002 | 0.010 ± 0.001 | 44.4% | ≤0.012 |
| Thread Half-Angle Error (°) | ±0.009 ± 0.001 | ±0.004 ± 0.0005 | 55.6% | ≤±0.005 |
| Surface Roughness Ra (μm) | 0.72 ± 0.06 | 0.30 ± 0.03 | 58.3% | ≤0.4 |
| Burn Rate (%) | 35 ± 5 | 0 | 100% | 0 |
| Straightness (mm/m) | 0.008 ± 0.001 | 0.002 ± 0.0005 | 75% | ≤0.003 |
| Indicator | Control Group | Experimental Group | Improvement | Design Requirement |
|---|---|---|---|---|
| Critical Speed (r/min) | 6800 ± 300 | 8500 ± 200 | 25% | ≥8000 |
| Fatigue Life (×10⁷ cycles) | 0.7 ± 0.1 | 1.2 ± 0.1 | 71.4% | ≥1.0 |
| Salt Spray Life (h) | 500 ± 30 | 1000 ± 50 | 100% | ≥600 |
| Yield Rate (%) | 55 | 98 | 78.2% | ≥90 |
In conclusion, our optimized high-precision thread grinding method for small-diameter TC4 titanium alloy planetary roller screws effectively addresses the four major pain points: heat accumulation, chatter, adhesive wear, and micro-precision control. The dedicated preprocessing, adaptive equipment, segmented thermal grinding, and rigorous precision management collectively ensure lead error ≤0.010 mm/300 mm, surface roughness Ra ≤0.3 μm, and no burns. Experimental results confirm critical speed ≥8500 r/min, fatigue life ≥1.2×10⁷ cycles, weight reduction of 39%, and yield rate of 98%, fully meeting the demands of humanoid robots for compact, lightweight, and reliable joint drives.
Looking ahead, the integration of digital twin technology, adaptive PID control, and deep learning-based process optimization will further enhance dynamic response by 40% and control batch production errors within ±0.005 mm. At the industrial level, localization efforts will accelerate, potentially increasing domestic content of core components from 30% to 70%, supporting the growth of humanoid robot applications from industrial and medical fields to household service and education. By overcoming technical bottlenecks in material, equipment, and process, this work paves the way for humanoid robots to evolve from specialized devices to mass-market products, underpinning manufacturing upgrades and improved quality of life globally.