The objective of this project was to design a shift-fork of minimal weight to meet the given specifications of less than 1 mm axial deflection and the maximum stress exerted on it must be within
90 – 100 % of the material’s yield strength, under the given force of 1000 N. The final shift-fork that complied with the specifications was designed for aluminium; the maximum deflection was 0.97 mm and peak stress at 140 Nmm-2, 96.5% of aluminium (356.0) yield stress. The final weight was 32g, 40 times lighter than the initial steel design. The optimisation was made with the function of a shift fork and its manufacturability in mind. By using finite element analysis on Abaqus areas of high and low stress were identified and consequently altered to distribute stress evenly.
Linear and non-linear analyses were made on the initial geometry. Linear FEA was validated with the use of Solidworks and simple cantilever assumption. Non-linear model can provide more accurate results, as it takes contact non-linearity into account. Parameters of mesh were also investigated. It was concluded that linear structured hex mesh was the best option given the limitation of the software, and more nodes generally provide more accurate results.
The shift fork, also known as a gear selector fork, is fixed to a stationary rod of the gearbox via the circular hole at the top of the component. The function of the shift fork is to support the ‘collar’ with the large semi-circular groove at the base. When a vehicle changes gear, the rod translates in the axial direction and the shift fork slides forward or backward accordingly. The collar moves along with the shift fork and engages the corresponding gear; the shift fork is now static and a force is exerted on it.
The red areas on the extremities at the fixed rod connection hole in the von Mises stress plots of Figure 3.4 and Figure 3.6 represent the location of maximum stress concentration. If the stress exceeds the yield strength, the colour-contour plot allows the location of yielding to be identified. Von Mises stress in the initial shift fork design peaked at 16.7 Nmm-2, a mere 7.6 % of the yield stress of steel. This denotes an excessive amount of material for its function. The colour blue represents area under little or no stress, which can be removed or modified to distribute stress thus optimise the geometry.
The scaled-up deflection in Figure 3.6 shows the component acted like a cantilever due to the single fixed boundary condition near the top. The maximum axial deflection of 0.012 mm occurred at the
point furthest away from the constraint, i.e. the base of the shift fork.
The authenticity of the simulation and the justification of the assumptions must be validated in order for the numerical outputs to be trusted. The model can be validated by comparing the results
of independent FEA software; Figure 3.7 and Figure 3.8 shows the stress and deformation results of 24.4 Nmm-2 and 0.01458 mm, respectively for the same parameters on Solidworks Simulation.
Abaqus calculates 75 % average of von Mises stress, accordingly the equivalent stress in Solidworks is 18.3 Nmm-2. The percentage differences between the software are only 9.4 % and 0.8 % for stress
and displacement respectively. Hence, the mathematical model of Abaqus is corroborated.
Contact non-linearity will significantly affect the stress analysis and deflection of the shift-fork, thus including it in the finite element method (FEM) should provide more accurate solutions.
To include this non-linearity an analytically rigid 2-D disc will be created to model the collar, and placed in contact and concentric to the groove of the shift-fork, as shown in Figure 3.12. The new disc is restricted in all degrees of freedom (DOF) except translation in the direction of load. The interaction between the disc and one edge of the groove is assigned to be frictionless. The 1000 N force will be applied to the disc, which would then be transmitted to the shift-fork. Results of the non-linear FEA are presented in Figure 3.13 to Figure 3.15 with the analytical disc hidden.
A new monitoring output is the contact pressure from the disc to the shift-fork. The varying contact pressure and stiffness differentiate non-linear analysis from linear, where pressure is uniform and stiffness is constant. Figure 3.13 illustrates the disc transmitted most of its force at the apex of the groove, from that point the pressure distributed outwards and downwards. The relocation of pressure concentration towards the constraint effectively reduced the length of the ‘cantilever’, which in turn decreased maximum deflection, moment and stress. This is reflected in the 17 % reduction of peak von Mises stress and 48 % in deflection. The concentrated contact pressure altered the stress path from linear analysis more centrally; this is reflected in the colour stress contour plot.
The non-linear simulation set-up is not faultless, as Figure 3.16 shows; although the deflection of the disc is small, in reality both sides of the groove would restrict some movement of the disc as well as the legs of the fork consequently redistributing the contact pressure, but this was not reflected in the model. Since an analytical rigid solid cannot be defined on both sides, a deformable steel disc was used in FEM to validate this theory.
The contact pressure contour plots in Figure 3.17 and Figure 3.18 verify the redistribution as there was notable pressure on the top edge, but the peak value increased 3 fold at the corners of the leg; stress and deflection also increased 4 times at the same nodes. In practice, the rotating collar will not deflect as much as a static disc (in Figure 3.19), which would relieve stress, deflection and contact pressure at the corners of the shift fork. The non-linear analysis on the deformable disc has a stress distribution similar to that of linear, which was distributed more widely across the top and not concentrated at the apex. For the initial iterations, the simplification of the collar as an analytical rigid disc would suffice but as the design progresses the wider top stress distribution would be taken into account.
Normal low carbon steel is the original material chosen to manufacture the shift-fork. Steel is cheap, valued at around £0.40 per kg, and relatively stiff with high yield strength; the disadvantage is that steel is very dense. Titanium alloys on the other hand, have a high strength-to-weight ratio with yield strength around 800 Nmm-2, four times higher than steel and 60% of its density, 4400 kgm-3. However, titanium is less stiff with modulus of elasticity at 127 GPa consequently deflecting more and it is difficult to cast; more significantly the cost of £18 per kg renders it too expensive for the function of shift-fork, unless it is for a high performance sports car. Aluminium alloys (356.0) are also very light with density of 2780 kgm-3 and the yield strength can vary from 146 to 460 Nmm-2 depending on the heat treatment. It is also has good fatigue resistance, increasing its durability under the axial cyclic loading. The cost is about £2 per kg, which makes it ideal for manufacturing shift-forks, but their Young’s modulus is lower than titanium - at around 75 GPa.
The effects of mesh element shape and node density on the FEA results were also examined. Hex and tet elements of linear and quadratic meshes were applied to the same model. It was found that although quadratic order meshes are more accurate, the imposed 20,000 nodes limit makes linear order more suitable. Hex meshes generally provide more accurate results in a faster time than tet elements but in order to apply hex, geometry must conform to stricter conditions. For the initial geometry it was found that difference between hex and tet is minute, thus for this project the accuracy of the element shapes can be assumed the same. It was decided that linear structured hex element meshes are preferred.
Total of six iterative designs were created. The final design was modelled with the properties of aluminium and weighed 32g. The maximum axial deflection was 0.97mm and peak von Mises stress was 140 Nmm-2. The magnitude of peak stress is 96.5% of aluminium 356.0 alloys yield strength adhering to the specifications. The optimisation to the geometry was designed according to the function of a shift fork and for it to be manufactured realistically.
These images display the final design and render of the shift-fork with the technical engineering drawings.