ENGINEERING GUIDE · PIEZOELECTRIC CERAMICS
A torsional ultrasonic transducer produces angular rather than purely axial vibration. In a sandwich design, tangentially polarized piezoelectric rings can drive a stack clamped between metal masses. Usable resonance depends on the ceramic, ring geometry, stack, metal sections, mounting and working load. Select and test the whole assembly, not the ceramic's nominal frequency alone.
Working on an OEM design? Explore SONER's piezoelectric ceramics and ultrasonic transducer range, then send your drawing and operating conditions for an engineering review. A torsional configuration requires project confirmation; standard cleaning transducers should not be assumed to provide torsional output.
How does a piezoceramic stack create torsional motion?
In the ring-stack model described by Lin Shuyu, each thin annular piezoelectric element is polarized tangentially. Alternating electrical excitation couples to shear deformation and creates rotation about the stack axis. The elements are connected electrically in parallel and mechanically in series. When their lateral size is small relative to the torsional wavelength, the stack can be approximated as a slender torsional rod. This is a model with limits, not a substitute for testing the assembled device.
CONCEPTUAL SECTION VIEW · NOT A PRODUCTION DRAWING
Electrodes and preload are part of the real assembly; details require an engineering drawing.
For a stack of identical elements, the book derives an overall transfer matrix by cascading the single-element network. Stack count, geometry and electromechanical coupling alter wave propagation and input impedance. A ceramic ring cannot be selected from diameter or material grade alone.
Three diagrams that explain the design model
1. Tangential polarization and torsional motion
Original conceptual redraw based on Lin, Fig. 8.5. P indicates the local tangential poling direction; curved arrows indicate angular motion about the stack axis. Actual electrodes and ring segmentation require an engineering drawing.
2. From one ring to a p-ring transfer network
Mechanical port ── [ ring 1 ] ── [ ring 2 ] ── ··· ── [ ring p ] ── Mechanical port
Electrical excitation: rings connected in parallel
Matrix relation: Mstack = Mringp. For identical rings under the book's ideal two-port model, Mstack = [cosh(pγ), Z0sinh(pγ); sinh(pγ)/Z0, cosh(pγ)].
γ is the propagation constant of one ring; Z0 is its characteristic mechanical impedance. The matrix relates end torque and angular velocity with a consistent port sign convention. Based on Lin, Eqs. 8-81–8-83.
3. Equivalent T-network inside the sandwich
Rear metal mass ── Z1p ── ● ── Z1p ── Front metal mass
Z2p + electromechanical coupling
Ideal mechanical branches: Z1p = Z0 tanh(pγ/2); Z2p = Z0 / sinh(pγ).
These are frequency-dependent complex impedances, not fixed resistors. Original simplified redraw based on Lin, Fig. 8.6 and Eqs. 8-85–8-86. It omits the complete electrical branch, bolt and tool and is not a wiring diagram.
Which equation helps at the prototype stage?
For a uniform torsional rod section, the linear wave model is ∂²θ/∂x² = (ρI/K) ∂²θ/∂t², where θ is twist angle, ρ density, I the polar second moment of area and K torsional stiffness. For an isotropic circular section, K = GI with G as shear modulus. This starts the metal-section model in Lin, §8.4; the polarized ceramic stack needs its piezoelectric constitutive model.
For the thin-ring limit in Lin, §8.3, an effective torsional wave speed is approximated as cte ≈ ct√(1 − k′15²). The relation depends on the book's coupling definition, thin-ring assumption and ideal electrical boundary condition. It supports first-pass sizing; quote and release decisions still require assembled resonance, impedance and vibration measurements under representative load.
Why does the prototype resonate at a different frequency?
A common engineering problem is a frequency shift between an unloaded element, a clamped transducer and a transducer installed in its final tool or fixture. The book's sandwich model includes the piezoceramic stack and both metal sections. Its torsional frequency equation depends on density, shear stiffness, polar moment of inertia, section lengths and the vibration node. Mounting, preload, horn or tool geometry, heating and process load can move the measured response further. The model guides dimensions; impedance and vibration measurements determine whether the assembled unit meets the intended operating window.
Actual SONER component measurement. A torsional prototype requires its own mode and load validation.
Where is torsional ultrasound being investigated?
Recent research considers longitudinal–torsional motion in thermoplastic welding and vibration-assisted composite machining. Adding angular motion changes tool–workpiece interaction, but it does not guarantee better results in every process. Published research on hybrid welding transducers and 2026 composite-milling models provides context for an OEM feasibility discussion. Any performance target must be validated on the buyer's material, tooling and production cycle.
Actual SONER ceramic polarization equipment. This is a manufacturing step, not a finished torsional transducer.
What should an OEM buyer specify before requesting a quote?
- Motion and application: pure torsional or longitudinal–torsional output, tool and workpiece, target frequency, angular amplitude or torque.
- Mechanical envelope: length, diameters, horn or tool interface, mounting point, preload constraints and duty cycle.
- Electrical system: driver voltage and current limits, matching network, frequency-tracking method and acceptable impedance range.
- Validation: drawing or sample, operating temperature, process load, measurement method and sample quantity.
SONER documents custom ceramic shapes and transducer engineering on its engineering service page. Its production equipment page shows ceramic processing and testing. These capabilities are a starting point for evaluation; torsional design availability and performance should be agreed against a specific project brief.
Frequently asked questions
Is a standard ultrasonic cleaning transducer a torsional transducer?
Do not assume so. A conventional cleaning unit is specified for its intended vibration and tank load. Torsional output needs its own mode design and assembled-unit verification.
Does adding more ceramic rings always increase output?
No. Ring count changes electrical and mechanical behavior, while metal masses, preload, driver and load determine usable output. Compare measured prototypes under the intended operating condition.
What is the first step for a custom design?
Send an application description, drawing or sample, target motion and frequency, installation envelope, driver limits and process load. Contact SONER's engineering team to define a sample and test plan.
References
[1] Lin Shuyu, Principles and Design of Ultrasonic Transducers (《超声换能器的原理及设计》), Science Press, Chapter 8, §§8.3–8.4, pp. 123–126 (source pages supplied by the reader).
[2] Study of the sandwiched piezoelectric ultrasonic torsional transducer, original research.
[3] Design, Fabrication and Characterization of L&T Hybrid Mode Transducers for Thermoplastic Welding, original research.
[4] Modeling of Longitudinal–Torsional Ultrasonic Vibration-Assisted Milling of UD-CF/PPS Composites, 2026 original research. Accessed 6 November 2026.
