Introduction – Traditional Shifting
Among the motorcycle industry, the most widespread gearbox available is the sequential manual gearbox. It has got five or six speeds, single clutch with left hand control, and the left foot controls gear lever. This one has got two directions, up shift and downshift, with automatic return in neutral position after the gearshift. It’s full manual. Each couple of gears of every speed has an idle gear, either to the primary or secondary shaft.
When the rider choose to shift, he pull the clutch and the gear lever. The action on the gear lever make the gear selector shaft to rotate, and the corkscrew groove placed on this shaft move the selector fork axially. The selector fork drags a coupling gear which is rotating with one of the shafts (primary or secondary, according to the speed) and it engages the idle gear of the selected speed. So the up speed is engaged. The downshift is carried in the same way. The gearbox is called sequential because it’s not possible to jump from two non-consecutive speeds, as in cars shift.
The pros of this kind of gearbox are simplicity, efficiency, and it’s the less expensive. The cons are the time length of the gear shift, the torque drop during shifts (due to avoid collision between idle gear and coupling gear).
In order to improve shifting performance, there were introduced many complications on the traditional scheme, such as dual clutch (a clutch for odd speed, the other one for even, almost halving the shift time), quickshifter (a switch that cut the electricity, and so the power on the primary shaft, allowing to not pull the clutch in full gas upshifting), semi-automatic (the lever is a up/down electronic switch, and a hydraulic circuit handles the shifting). These innovations were mostly ignored by motorcycle industry (except for honda vfr1200 and nc700), because the performance improvement wasn’t worth the extra weight, extra design cost and complication. This technology was also banned from motorsport. The smoothest experience is available with CVT, continuously variable transmission, but it comes with a significant loose of efficiency, and it hasn’t got speeds, causing the feedback to be very different to motorcycle riders.
Seamless Shifting Concept
In 2007 Ferrari and Zeroshift developed a new idea of shifting, calling it seamless. In fact the intuition of the dual clutch remains, but the dualism is shifted to the engagement: the coupling gear is substituted by a hub, which rotate with the correspondent shaft, and two series of teeth which can move axially along the hub. The engagement is granted by these parts (in blue and red in the figure below), and the side slope of their teeth. Basically, the red ones are used for the first speed upshift and the second speed downshift, and the blue ones vice-versa. The scheme is repeated for every speed.
The seamless shifting is granted by the fact that there is no disengagement at any time. The upshift process is simple:
- the blue teeth are engaged to the lower speed gear, transmitting positive torque to the secondary axis, while reds are engaged and ready to transmit negative torque, such as engine brake.
- following the up shift command (for example when the torque spike), red teeth are moved axially by the fork towards the upper speed gear.
- the upper speed gear, which revolve at a higher speed, engages the red teeth and begins to accelerate the secondary shaft and the hub.
- the secondary shaft and the hub begin to rotate faster than lower speed gear, and the lower speed gear collide with them on the opposite side of the teeth, disengaging and moving axially the blue teeth.
- the blue teeth engages the upper speed gear, getting ready to transmit negative torque, if the throttle is released.
The downshift process follows similar steps, in reverse order.
The pro of seamless gearbox is the improvement of performance (both fuel saving, torque regularity, less shift time), and it’s gained without extra weight or less efficiency. The cons are a more thorny design, because of the immaturity of the technology, the less reliability and more costs, as collisions between teeth during engagement lead to worse fatigue life.
The aim of this project is to study the principles of this innovative mechanism, the criticalities and the strong points. Initially, the aim was to complete a quantitative performance study, comparing a real case gearbox with a seamless gearbox, in a “virtual drag race”. But for those purposes, the designing time and the available data were insufficient. Beside that, the superior performance of seamless against traditional gearbox is already known, and it’s only a matter of time to see this systems on production cars and especially hyper sport motorcycle. Real life drag race and MotoGP noise comparison give also numeric data on seamless superiority (4). This system is progressively adopted by all manufacturers, following Honda, also by Yamaha and Ducati. This can be easily identified by the presence of the neutral gear extra lever (neutral is placed below 1st gear, instead of being between 1st and 2nd as usual).
The modelling problem
The first step of the modeling process was the analysis of an existent gearbox, in this case the one of Aprilia RSV4. Gears and axle spacing were measured, and then they were modeled. The model was simplified to have only two consecutive speeds, and it can be easily choose which ones.
The seamless’s system hub (green, bracketed to secondary shaft also green) and red/blue teeth were then added, together with original gears engagement teeth. The two shafts complete the geometry. First speed secondary gear is cyan, second speed one is magenta, primary shaft and primary gears (bracketed to it) are orange. Speed gears have a gear joint between primary and secondary gear, the shafts have revolute joint with the ground, and red/blue teeth have translational joint with the green hub. Their available positions are +2,0,-2 mm from neutral (so first,neutral,second gear engagement).
The contact between red/blue teeth and speed gears is the most thorny point of the modeling. The modeling problem has been solved comparing two contact approach, “cad contact” against “sphere-to-extruded-surface”. With the first one, cad contact, the solver which tessellates the geometries and calculate forces from the relative penetration of the parts. This command is (generally) less stable compared with the other simpler contact forces, and it requires a lot more computational power, but it allows to use the actual geometry. The settings are shown in the picture below.
The other one contact model, “sphere-to-extruded-surface”, it’s based on Hertzian model (with as parameters Young modulus, Poisson ratio, restitution coefficient) or equivalent stiffness and damping. It follows my fellow experience of last years MSDSM course , in which a traditional sequential gearbox was modeled. It’s simpler, it requires less computational time, but it need an additional simplification to run the simulation without having compenetration of the bodies.
The model is simplified deleting two teeth for each colour, thus having only four contact in total (instead of all the possible combination of three dog teeth with three engagement gear teeth on two gear and two colours). Then specific spheres and bigger teeth where added. Gears and dog teeth are bracketed onto them. The last settings are shown in the picture below.
In both cases, good settings are very tricky to find, as this contact tends to swing between hooking with compenetration and bouncing. The expected behavior is an nonelastic collision, and it isn’t perfectly reached even if the restitution coefficient is set to 1, which is related to ideal anelastic collision.
Another simplification is in the input torque. In fact on the two gear is set a different costant angular speed, to set from the start the timing of the shifting. It’s very complicated (and it introduces many errors of contacts on the running) to control the axial position of the dog teeth in a automatic way, in the same way of the real components do. So that, the only option is a manual position driver.
Simulations and analysis of results
Once the simulations are done, the result achieve the expectations. The penetration length of the spheres grows fast, it reaches a max value and then it stabilizes at the equilibrium value. It’s interesting to notice that the first engagement, which takes place on the slower gear, present a much higher peak of the value of penetration than the other one. It can be due to the fact that the relative angular velocity between the driven shaft and the gear is higher on the first engagement (from 0 to w1) than on the second one (from w1 to w2).
The equilibrium value is slightly lower, on the opposite. Higher angular velocity on the second engagement is due to the lower reduction ratio of the 2nd speed. The initial peak during the collision and the following equilibrium condition is showed also in the graph of potential energy, which is correlated to the square value of the penetration distance.
Once the contact is verified with the basic model simulation, the next step would be a co-simulation with Matlab Simulink. This approach, once the setup of the programs and the data exchange between them are carried out (and this isn’t sure even strictly following the steps on ), allow the user to focus on modeling in LMS and on controlling in simulink, which permit to a more simple and faster definition of on mathematics, variables, laws.
The tricky aspect of the setup is the generation of the executable matlab function which permit the data exchange between matlab and the external environment. This procedure is very insidious and hardly repeatable, as it is subjected to different compatibility between LMS, Matlab, OS versions. As recently Siemens acquired LMS, the hope is that the internal control features or the communication with external software will be simplified and made stable.
The final objective of the simulation is to perform an acceleration test, from 1st speed 1000 rpm to 2nd speed rev limiter, and then a complete deceleration cutting off engine power, so following the up-shift scheme explained above. The torque curve has then to be qualitatively compared with traditional gearbox one, like my fellow work in  (which has spikes and evident losses of power during shifting). The idea is to verify if spikes, losses of power and speed smooth with this gearbox.
To prepare the objective simulation, many test (involving for example constant engine torque, constant resistive torque, manually controlled engagement of the dog) have been carried out, but the results are unsatisfying. In fact, the software seems to be very unstable, even after a brand new installation, and the simulation computation is badly repeatable. The annoying bugs explained above keeps on randomly occurring, frustrating the correction efforts. In fact LMS behaves correctly if a proper multibody problem is set up, such as many bodies with two-way costraints, but it lacks stability and precision with simple one-way costraints and collision contacts. This criticalities were recognized by other fellows during their works.
On the other side, the setup for co-simulation with Simulink is unfinished as there are many incompatibilities between the software at my disposal. To accomplish the task and the objectives as they’re expressed, it’s mandatory to switch back to a previous software version (like the one used in ), so being forced to redesign the analysis from scratch and from alone parts, even the newest release don’t solve the problems.
At first sight, this experience could be classified as a complete failure, not reaching the minimum foreseen objectives. However, it has been very instructive on what to do and what not to do in modeling and simulating phases, and on many LMS and Simulink instructions and controls different from the ones commonly used during courses.
The next step of this experience should be a redesign, on a different LMS release (or even better on another multibody software such as MSC ADAMS or ALTAIR Hyperworks), to fulfill the objectives, concluding the experience, and even going beyond with the study of a complete gearbox in a simulated motorcycle drag race or engine test bed.