In high-precision machining of spiral bevel gears, backlash in transmission systems remains a critical challenge. This study proposes a dual-motor servo drive strategy integrated with PMAC (Programmable Multi-Axis Controller) to eliminate gear clearance nonlinearity. The methodology is experimentally validated through an IPC+PMAC motion control platform, demonstrating significant improvements in positioning accuracy and system stability.
Mechanical Principle of Dual-Motor Drive System
The anti-backlash mechanism employs two identical servo motors (Motor A and B) coupled through a torque compensator. The force equilibrium during operation can be expressed as:
$$
\begin{cases}
M_A = M_{\text{load}} + M_{\text{bias}} \\\\
M_B = M_{\text{load}} – M_{\text{bias}}
\end{cases}
$$
Where $M_{\text{bias}}$ denotes the preloaded torque eliminating gear clearance. The resultant torque acting on the spiral bevel gear transmission system becomes:
$$
M_{\text{total}} = M_A – M_B = 2M_{\text{bias}}
$$
Dynamic Modeling of Transmission System
The motion dynamics of the dual-motor system are described by:
$$
J\frac{d^2\theta}{dt^2} + B\frac{d\theta}{dt} = K_t(i_A + i_B) – T_{\text{disturbance}}
$$
Where:
$J$ = Moment of inertia (kg·m²)
$B$ = Viscous friction coefficient (N·m·s/rad)
$K_t$ = Motor torque constant (N·m/A)
$i_{A,B}$ = Motor currents (A)
| Parameter | Motor A | Motor B |
|---|---|---|
| Rated Torque | 4.8 N·m | 4.8 N·m |
| Max Speed | 3000 rpm | 3000 rpm |
| Encoder Resolution | 20-bit | 20-bit |
Control Architecture Implementation
The PMAC-based control system implements cross-coupled synchronization:
$$
G_c(s) = K_p + \frac{K_i}{s} + K_ds
$$
Velocity synchronization error is minimized through:
$$
\varepsilon_v = \frac{1}{2}\sum_{i=A,B}(\omega_{\text{ref}} – \omega_i)^2
$$
Experimental Verification
Testing under varying speeds demonstrates the anti-backlash performance:
| Speed (pulses/s) | Position Error (μm) | Torque Ripple (%) |
|---|---|---|
| 30,000 | ±2.5 | 1.8 |
| 60,000 | ±3.2 | 2.4 |
| 90,000 | ±4.7 | 3.1 |
The velocity tracking performance satisfies:
$$
\sigma_v = \sqrt{\frac{1}{N}\sum_{k=1}^N(\omega_{\text{cmd}}[k] – \omega_{\text{act}}[k])^2} \leq 0.15\%
$$
Comparative Analysis
Backlash elimination techniques comparison for spiral bevel gear machining:
| Method | Accuracy (arcmin) | Stiffness (N·m/rad) | Maintenance Cycle |
|---|---|---|---|
| Spring Preload | 3.2 | 1.5×10⁴ | 800 hrs |
| Mechanical Adjustment | 1.8 | 2.1×10⁴ | 1200 hrs |
| Dual-Motor Drive | 0.5 | 3.8×10⁴ | N/A |
Conclusion
The dual-motor anti-backlash system demonstrates superior performance in spiral bevel gear machining applications. Key advantages include:
$$
\eta = \frac{T_{\text{stable}}}{T_{\text{total}}} \times 100\% > 99.2\%
$$
where $T_{\text{stable}}$ represents vibration-free operation duration. This technology effectively eliminates transmission nonlinearities while maintaining high dynamic response characteristics essential for precision gear manufacturing.