Geometric description: The model is a variable-diameter conical corrugated helical spring, with an overall appearance resembling an inverted truncated cone spiral cage structure, designed to provide nonlinear variable stiffness rebound force within a limited axial space. The main body is constructed based on a contracting helical trajectory, with its guide line defined in a cylindrical coordinate system. The polar angle $\theta$ ranges from $0$ to $10\pi$ (i.e., 5 full turns), and the radius of rotation $R$ decreases linearly with the angle, following the equation $R(\theta) = 40 - 1.5(\frac{\theta}{2\pi})$, causing the spring's mid-diameter to smoothly contract from 40mm at the bottom to 32.5mm at the top. On this helical conical surface, high-frequency axial sinusoidal fluctuations are superimposed, with the axial height $Z$ composed of a base helical rise component and a fluctuation component, given by the equation $Z(\theta) = 8(\frac{\theta}{2\pi}) + 2.5 \sin(6\theta)$, indicating an average pitch of 8mm per turn and including 6 full cycles of sinusoidal peaks, with a peak-to-peak amplitude of $\pm 2.5$mm. The cross-sectional feature is a rectangular solid with a width of 8mm and a thickness of 1.2mm. The long side of this rectangular section is always parallel to the global XY plane (maintaining a "flat" orientation) and perpendicular to the local radial vector, undergoing rigid sweeping only along the Z-axis. At both ends of the spring, to form stable contact surfaces, the amplitude of the fluctuations is reduced to zero over the last $\pi/2$ angular range through a linear decay factor, and the helical pitch gradually becomes 0, with the end sections perpendicular to the tangent direction of the helix. Overall, it forms a geometrically self-locking, precisely defined conical wave elastic element, strictly defined by parametric equations.

Modeling procedure: First, define the central guide line of the spring using the equation-driven curve function in a 3D modeling environment. This line is set as a contracting helical path that rotates 5 turns around the Z-axis, with its radius linearly decreasing from 40.0 mm at the bottom to 32.5 mm at the top. When defining the axial height, superimpose a uniform rise of 8.0 mm per turn with a sine wave function of 6 periods per turn, setting the amplitude to 2.5 mm. Specifically, apply decay constraints in the first and last quarter periods to smoothly reduce the amplitude and the rise angle to zero, ensuring the flatness of the end contact surfaces. Next, establish a reference plane at the start of the guide line, and draw a closed rectangular sketch with a width of 8.0 mm and a thickness of 1.2 mm. Set constraints to ensure that the long side of the rectangle remains parallel to the XY reference plane and perpendicular to the radial vector of the path in the horizontal plane. Finally, use the sweep function, with the rectangular sketch as the cross-section and the parameterized conical corrugated curve as the path, to generate the solid, ensuring that the cross-section maintains the preset horizontal orientation throughout the sweep process. This completes the modeling of the precision variable-diameter corrugated helical spring with nonlinear elastic characteristics.