Technology of gears

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Loss of efficiency is quantified between 5% and 6%, Ref.[6]. Anyway efficiency is comparable with a drop gear solution and it’s surely higher than a drive chain configuration.

Moreover this solution is worse in terms of transmission overall mass too. By experience, It’s possible to notice that, on equal terms of tooth face width, bevel gear is weaker than cylindrical one. At the same time, bevel gears need to be installed on angular contact bearings that are usually bulky compared to radials bearing comparable loads. Angular contact bearings are installed to oppose to axial component of force generated by bevels and absent in spur gears. Moreover It’s necessary remind that gear-box cases needs to be reinforced in order to bear axial loads. By virtue of explained issues, transmissions including bevel gears are often heavier than full spur gears transmissions.

Anyway by point of view of weight distribution, longitudinal configuration ensures some advantages. First of all, It’s necessary to remember that all evaluated solutions features motors positioned on the floor of the chassis. For this reason, distribution of weights along z-axis is mainly the same. The real benefit of longitudinal solution is the installation of motors in forwarded position, closer to the centre of gravity of the vehicle. That feature allows to maintain intended value of front/rear weight distribution. Furthermore, masses of motors are closer to the mean plan of the car, y=0. That reduces significantly inertia of the vehicle around the roll axis, with important benefits by handling point of view.

About packaging issues, it’s convenient analyze Picture 4.2-7. It’s extremely clear that a transversal layout, suitable for a tubular space frame, is not adequate for the tapered shape of the monocoque. But the most significant aspect is that dimensions of motors and gear-box cause issues of integration with frame and suspensions. Furthermore affordability of electric contact boxes the maybe compromised.

By aerodynamic point of view, motors shifted forward offer more space to design a suitable diffuser. This item generates important benefits for overall performances of a formula car.

At the end of this deep evaluation it’s clear that longitudinal configuration is the best solution suitable in S.C.R. project. Issues related to mechanical efficiency and weight are widely overcame by benefits of layout, weight distribution and aerodynamic.

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4.3.1. Evolution of gears.

After a brief research performed on the web, some basic information about evolution of gears have been collected and gathered. Large majority of following information have been reported according with source “https://www.wikipedia.org/”, Ref.[8].

Starting step of this history can be surely represented by early prototypes found in China. Such artefacts can be dated around the 4th. century B.C. during the Zhang Guo times, Late East Zhou dynasty and have been preserved at the Luoyang Museum of Henan Province. Examples of mould of bronze gears dated around 2th. century B.C., during the early Han Dynasty, are displayed in the Shanghai Museum.

First European samples of gears technology can be found in the Antikythera Mechanism. It’s a complex and intricate device found in 1900 in the sea that surrounds Antikythera island in the Aegean sea, not far from Crete. Device it’s dated between the 2nd. and the 1st. century B.C.

Anyway, duties and operations aren’t been clearly understood still now. Most respected hypothesis assert that the mechanism is a sort of planetarium designed to calculate sun rising, moon phases, planet movements, equinoxes, months and days with unexpected accuracy. Parts of the bronze mechanism, fossilized on a stone, have been preserved in the National Archaeological Museum of Athens, in Greece.

Picture 4.3-1:Antikythera Mechanism (http://www.namuseum.gr).

Inside technical literature, gears can be found in some works connected with Hero from Alexandria who lived in the Roman Egypt around the A.D. 50. Anyway, other examples of gears can be traced back to the works of the Alexandrian School. That’s a collective designation used to identify literary, philosophic, medic and scientific works created in the Ptolemaic Egypt, during the 3rd. century B.C.

Many of these works can be ascribed to the well-known Greek polymath Archimedes who lived between 287th. And 212th. year B.C.

Returning to China it’s remarkable the “South Pointing Chariot”, an ancient two wheeled vehicle that mounted a movable point to indicate the south direction. The chariot, supposedly used as moving compass, is ascribed to the mythological engineer Ma Jun, who lived around the 250th.

year B.C. The relevance of this invention it’s the first example of differential gear ever installed.

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It’ necessary wait the A.D. 725 to find the first example of the most refined gear technology, clock technology. The first clock was created by Chinese engineers Yi Xing and Liang Lingzang, it’s based on a water-powered gearwheel that works as escapement mechanism.

Another step of this amazing evolution is the water lifting device invented by the Mesopotamian engineer Al-Jazari. His invention operates the first example of segmental gears of the history and it’s dated around A.D. 1206.

Gears of the type realized with the actual shape appeared in the European Middle Ages and was operated in the gigantic clock mechanism of cathedrals. Bronze and brass used to manufacture gearwheels was then replaced by the more robust steel during the industrial revolution and the cast manufacturing was replaced by more refined machining. Evolution continued in the 20th.

century, thanks to a refinement in the profile of the teeth and thanks to a well-established knowledge in the sciences of materials. Nowadays plastic or metal gears are operated in the large majority of devices employed by humans, from the little domestic electrical appliances to the colossal merchant ships.

4.3.2. Orthogonal axes.

Chapter 4.2.3 explains briefly main drawbacks about configuration based on longitudinal motors.

Orthogonal position between input and output shafts it’s clearly the most complex feature of the chosen transmission layout. With reference to Chapter 4.2.3, preliminary evaluations performed on longitudinal configuration were based on the installation of bevel gears which are widespread.

However, choice of a gear suitable to transmit power between orthogonal axes is not single.

According to Ref.[7], next chapters display some solutions which technology of gears propose to overcome the issue of orthogonal axis.

4.3.2.1. Worm Screw.

This solution is based on a endless screw featuring trapezoid profile, connected to the input, that operates a gearwheel. This solution, simple and effective, is widespread in all the industrial field. Main feature is the possibility to obtain very high gear ratios in a single reduction stage (10:1÷20:1 and more). For this reason, the solution is very convenient in terms of weight and volume. Anyway, this mechanism is not reversible and that is a strong boundary to the employ of this technology. In any case, most significant drawback is the efficiency. Very high values of friction acts in the screw-gear contact and the efficiency may fall down to 50%. A strategy operated to limit efficiency loss is shown in the Picture 4.3-2. Gear is machined by a billet of brass, a material which interfaced with steel, features a very low friction coefficient. Unfortunately, featured mechanical efficiency it’s extremely inadequate for a continuous operation transmissions. This solution is more suitable in mechanisms which operate in discontinuous way. Anyway, It’s necessary to remind that Peugeot exploited this device on transmissions installed on some models of 70’s, according with Ref.[8].

Picture 4.3-2: Example of worm-screw (http://www.altraex.com).

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4.3.2.2. Bevel Gears.

It’s the most ordinary solution to transmit power between orthogonal axes. External shape of wheels is conical, differently to the cylindrical shape used to transmit power between parallel or skew axes. This technology too allows to design a compact solution. Anyway, gear ratio that’s convenient realize by a single stage is much more lower respect to the worm screw. Range of ratios is often included between 1:1 to 4:1. However, mechanical efficiency of a single gear is greater than 90%, according with Ref.[6]. This value is considerably higher respect to that featured by worm screw solution. Anyway, as declared in advance at Chapter 4.2, it’s necessary to remember that efficiency of bevel gears is lower than efficiency of cylindrical gears which is around 98%. An important drawback of bevel gears it’s the axial touch between pinion and driven wheel. It must respect well determined values during all the operation scenarios. That fact affects manufacturing and assembly procedures which must to be very precise and accurate. It’s necessary to reiterate that, for nowadays racing gear-box too, most delicate component is the bevel set coupled on the differential, which is the output of the system. A racing bevel set installed improperly, shows serious damages in a limited number of kilometres, maybe between 2.000 [km] and 3.000 [km]. Some modern racing gear-boxes, coupled with high performance longitudinal engines, adopt a transversal layout in which shafts carrying ratios are parallel to y-axis. This solution allows to position the bevel set on the input of the gear-box, in order to improve car weight distribution. On the other hand, a longitudinal configuration gear-box houses the bevel set directly on the power output. By definition of gear ratio exploited at Chapter 4.1, it’s clear that bevel set installed on the input of the gear-box is much less stressed than bevel set installed on the output. It was explained that input torque applied to an automotive gear-box is lower than output torque.

By virtue of issues explained in advance, layout of a transmission which houses a bevel gear, become more complicated if compared to a transmission realized by cylindrical spur gears only.

Proper operation of a bevel gear inside a transmission needs angular contact bearings, preload devices, shims and well determined measure points.

Range of bevel gears is very wide, those in Picture 4.3-3 are the most basic example, straight bevels. Anyway, tooth profile of bevel gears evolved in different variants: zerol, spiral bevels, helical bevels and hypoid bevels. Benefits and drawbacks of different variants are going to be explained in next chapters, following the evolution of the design.

Picture 4.3-3: Example of bevel gears (https://dir.indiamart.com/).

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4.3.2.3. Face Gears.

According to “L. Baldassini – Vademecum per Disegntori e Tecnici 19° edizione”, Ref.[9], another option can be taken into account. That solution works substantially like the previous one, a conventional bevel gear. Main difference is represented by geometry of drive wheel which is a basic cylindrical spur pinion. On the other hand, driven wheel features a quite complicate geometry. It’s useful to image teeth of a spur gear, parallel to wheel axis, revolved of 90°. Axis of teeth which were parallel each other’s and parallel to wheel axis, are now perpendicular to wheel axis and converge on an unique point which lays on wheel axis. By virtue of that, geometry of driven wheel teeth features cuneiform shape.

Differently from what explained at previous Chapter 4.3.2.2, a face gear set doesn’t need a well determined axial touch to operate properly.

That’s due to drive wheel geometry which allows large freedom on its axial positioning. By point of view of bearings, configuration featured by face gears, looks simplified because driven gear only is loaded by axial force. For this reason, angular contact bearings are necessary on driven wheel installation only.

By virtue of previously explained benefits, face gears technology looks to be perfect applied to S.C.R. transmission design. Anyway, exhaustive information about this type of solution are difficult to find, probably because technology is quite young. Formulae and standards of calculation are very difficult to find like exhaustive data about efficiency or reliability. An additional issue is that, manufacturers skilled to produce face gears are very rare in Italy. For these reasons manufacturing looks difficult to realize in a short time.

Table 4.3-1: Gear Ratio and Efficiency exploited by main types of gears, (http://www.meadinfo.org).

Back to the topic regarding design issues, previous research material is exhaustive enough to choose one of the described options. Differently from what declared on Chapter 3.3, conventional solution represented by bevel gears is proven to be the most suitable on S.C.R. design. That’s due

Picture 4.3-4: Example of face gears (http://www.assag.ch).

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to lack of time and lack of experience which usually affect F.S.A.E. projects. Anyway, this case too, demonstrates that most experienced solution is the most suitable in motorsport oriented projects.

In order to conclude topic about face gears option, which represent the most innovative solution, It needs to be taken into account as a good starting point for an eventual design of development.