Raccolta casi Working Model, visualNastran & SimWise - Innovative progressive suspension “Unit Pro-Link”,

The Lever-Ratio (or Suspension Ratio) can be put in relation also with the fork rotation, besides the Wheel-Travel.

Fig. 3 - Force exerted by spring - Shock Absorber Group

Fig. 4 – Course of wheel vertical force versus the excursion of the wheel pivot

The force exerted by the spring depends on the endured shock travel, DeltaLi, by the spring stiffness, (k= 95 N/mm), and by the initial travel, prc = 20 mm:

Fi depends directly by the shock travel DeltaLi that is function of the rotation angle of the fork; fig. 3 shows its trend versus the shock travel.
Of course the force exerted by the spring and vertical one acting on the wheel pivot are not equal, because the work of the vertical force has to be equal to one exerted by the spring:

Fig. 5 shows the trend of the shock travel and of the Lever Ratio defined by (1). At last the wheel stiffness or “Wheel-Rate” can be obtained by the following relationship:

Fig. 5 – Shock Travel (red) and Lever Ratio (blue) versus the Wheel Travel,
in the progressive suspension Unit Pro Link

BUILDING THE CAD MODEL

Propaedeutic work.

Model construction is done by the “reverse engineering” (RE) technique, permitting the mathematical description of a physic model digitizing the surface. The RE use is rather advantageous in the memorization of existing models and objects, in the link between CAM/CAD methods and “rapid prototyping” for the design of CAD exemplar by implemented mechanism.
The preliminary phase consists in the collection of both the data furnished by the firms and obtained by object inspection, to take size and geometrical properties, but also the functional characteristics and the constructive solutions. The surfaces are successively mathematized as CAD primitives, verified and employed in the successive operations.

Fig. 6 – a) Photo of the rear suspension Unit pro link; - b) The fork assembled in Rhinoceros.

Solid model elaboration.

The new generation of parametric programs is constituted by “feature based” software, as Solid Edge (SE), based on elementary working, as an extrusion or the revolution of a profile. Rhinoceros software combines the accuracy of the traditional CAD with the modeling flexibility based on the spline, permitting the draw of objects exploiting the NURBS (Non Uniform Rational B-spline) technology. The NURBS surfaces of free – form type, can accurately define a body, also having a complex form, i.e. the bodies with cavity. Besides Boolean operations on the solids are possible, permitting the obtaining of particular penetration and/or intersections with a certain immediacy.
The synergy of both the software produces undeniable advantages in the examined case: creation of the fork solid model in Rhinoceros room, creation of the other components in SE Part and assembly of the entire body in SE Assembly. The importation of the body in SE requires the use of an interchange file; the format Parasolid was chosen, because was believed more advantageous. Fig. 6b shows the configuration obtained in Rhinoceros, and fig. 6c the final configuration obtained in SE.

Fig. 6c - CAD model of the rear suspension “UNIT Pro Link”

CINEMATIC AND DYNAMIC SIMULATION RESULTS

CAD model is imported in MSC visualNastran 4D, by means of a transfer file, putting in the model the necessary constraints and loads to execute the simulation (fig. 7). VisualNastran permits the virtual prototyping, given that the cinematic system can be studied cinematically and dynamically, after the assembly of all the elements. The software resolves the motion equations considering perfectly rigid bodies. In particular the simulation is executed applying the external load to the fork by means of a linear actuator; the applied motion law is a double ramp, with linear variation of the wheel travel versus the time, to simulate simply the motion of the wheel on the road. Initially the cinematic simulation permitted the comparison with the value calculated theoretically, obtaining very close results.
In the dynamical simulation one has to take in account:

Fig. 7 - The suspension imported by CAD software and the wheel pivot drawn in Visual Nastran room.

Table 1 – Force and acceleration decrease, corresponding to an increase of the damping coefficient.

The value of damping constant is determined in several ways. By energetic consideration one reaches to the following relationship:

Besides the value of optimum constant damping can be modified taking in account the stiffness kc of the tires:

Table 1 gives the simulations results for the maximum |FY| load and the corresponding accelerations, transmitted trough the wheel pivot to the chassis. They decrease with the increase of the damping coefficient: one can note that a decreasing trend of the transmitted force and of the acceleration corresponds to a damping coefficient increase. The minimum value of both the force on the SSAG and the maximum acceleration is obtained by the value expressed by (12. The simulations with a greater value show an increase of the maximum acceleration.

Fig. 8 –The suspension mesh (view point ¾ rear, on the left side).

Fig. 9 – Von Mises Stress distribution during the more onerous stress
on the right particular of the equalizer, that is the more stressed element

Fig. 10 – Von Mises stress in the fork (maximum stress) versus the time.

Fig. 11 – Von Mises Stress in the equalizer (maximum stress) versus the time

Fig. 12 – Von Mises stress in the connecting rod (maximum stress) versus the time.

Stress analysis

The stress analysis on the several parts of the suspension is executed by FEM module, implemented in the same multi body software visualNastran 4D. The stress evaluation on the entire rear suspension is executed trough a standard test (at double ramp), during which the excursion of the rear wheel axle achieves the end displacement position in a short time, and comes back. The purpose of the analysis is the evaluation of the highly stressed suspension elements. The worst condition is obtained achieving fast the end displacement position, when the fork reverses the motion to return to the initial position. The adopted elements for the mesh have tetrahedron shape, which size is determined by the H – Adaptivity tool of visualNastran 4D (fig. 8). All the connections, the wheel axle and the upper and lower hinges of the shock absorber are considered rigid. Fig. 9 shows the stress map in the instant of maximum load.
The more dangerous instant for the suspension is the end displacement position, and the more stressed element (fig. 10-12) is the equalizer, with a maximum Von Mises stress equal to sigmamax = 408 MPa, (against yield stress sigmas= 505 MPa of aluminum 7075-T6); it is a static resistance condition with low value of the safety coefficient.
Because the fatigue solicitation has zero cycle, it does foresee a condition of limited life strength; in effect the equalizer is frequently substituted in the competition motorcycles.

CONCLUSIONS

This work was conduced following three guide lines: the first part has the objective to explicit the progressive characteristics of the suspension trough a cinematic study, developed in plane, leaving apart from the physical characteristics of the model; the second has a double purpose: the confirm of the results obtained in the first part and the observation of the solid model behavior in dynamical conditions for several values of the damping coefficient; the third part describes the mechanical solicitation trough the FEM analysis and the effectiveness of the followed redesign method. The objectives of the three phases are reached: in fact the cinematic analysis highlights the progressive characteristic of the suspension; MSA (Multibody System Analysis) confirms the results of the previous, in lacking of damper in the two-dimensional model and shows that value of the acceleration transmitted to the chassis and to the driver is reduced increasing the damper constant, with benefits on the comfort and on the road-holding; FEM stress analysis indicates that the instant of greater stress on the suspension coincides with the end stroke, where the greatest acceleration are present, producing high inertia loads. The more stressed suspension element is the equalizer, and the more stressed zone of the fork coincides with the damper housing.
It confirms the validity of the redesign method (reverse engineering) and the potentiality of the dynamic simulation for the analysis of the suspension behavior, given that the parameters can be quickly changed to analyze the behavior, in particular the damping optimum constant value.
This analysis tool constitutes a valid aid in the design field, both in the project definition phase, helping to the constructive choice evaluation, furnishing an optimum alternative to the achievement of a prototype (rapid- prototyping), and in the design conclusive phase, simulating the indispensable road test.

REFERENCES