Choice of main parameters on first stage

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Eq. 6.1-24

Where:

 is “mean rotational speed on input shaft of first stage”, defined by Eq. 6.1-22, measured in [rpm].

 is “gear ratio of first stage”, a dimensionless parameter defined by Eq. 4.4-6.

In second stage too, mean value of rotational speed is intended to be common to any level of torque.

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leads to shorter face width, with increased structural strength. For this reason, a spiral gear is stronger than straight one with equal face width and similar overall dimensions.

First input parameter to be set is the gear ratio. All references about the choice of the value are deeply shown in Chapter 4.4. Anyway, Kisssoft needs a tolerance on the value of the “gear ratio”, in order to evaluate different combinations in the number of teeth.

Eq. 6.2-1

Like it was revealed at Chapter 5.1, it’s necessary to set one of the most important angular parameters:

the “pressure angle”, . That described previously, is intended to be the “axial pressure angle” which is the lonely parameter in spur gear calculation. As revealed in advance at Chapter 5.10, helix or spiral profile gears, due to their geometry, identify three different parameters: “axial pressure angle” ,

“normal pressure angle” and “transversal pressure angle” .

Normal pressure angle is the most relevant in calculation, for this reason it’s normally set up as input.

Geometrically it’s the homologous of axial pressure angle in a spur gear but it’s measured on a plan perpendicular to the helix or to the spiral profile. Technologically, normal pressure angle too depends on the geometry of tools exploited during manufacturing process. Manufacturing of tools offers a wide spectrum in which customize the pressure angle, commonly values set on Gleason’s system varies between 14.5° and 20°. Anyway reasons of time and budget made the choice focus on the most widespread value:

Eq. 6.2-2

In this way, the research of a proper gear supplier is quicker and costs of manufacturing would be logically appropriate.

Plot 6.2-1: Spiral Angle vs. Face width to module ratio and Face contact ratio (Courtesy CRF).

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By technical point of view, It’s necessary to underline that the angle of 20° is the best trade-off between stiffness of the single tooth and the transverse contact ratio. That ensures reliability and efficiency of the gear both. Due to these reasons, angle 20° is the most widespread in power transmission applications.

As revealed in advance, the main parameter which describes a spiral profile is the angle of the straight line tangent to the spiral, defined as “intermediate spiral angle” ψ. This parameter is expressed on Kisssoft as: “angolo d’elica ruota 1 (medio)” and often “ψ” is replaced by “ ”, “ ”.

Spiral angle needs to be obtained from Plot 6.2-1. Vertical axis displays the face width/module ratio, described by Eq. 5.1-1. It results that a compact gear suitable for motorsport applications needs a value between 6 and 8. Curved lines represent the overlap ratio, indicated as face contact ratio. As revealed in advance, at Chapter 5.7, a suitable value for this parameter is around 2. Thus the suitable value of spiral angle needs to be greater than 30°. Anyway, in order to maintain a good level of efficiency, the chosen value of spiral angle needs to be limited to 30°.

Eq. 6.2-3

Another parameter which is important in calculations of Kisssoft is the “quality index” which basically describes the accuracy and the surface finish on the flank of teeth. Software uses a scale parameter which it’s based on I.S.O. 17485:2006 standard.

Norm establishes a classification system that can be used to communicate geometrical accuracy specifications of unassembled bevel gears, hypoid gears, and gear pairs. It defines gear tooth accuracy terms, and specifies the structure of the gear accuracy grade system and allowable values. I.S.O.

17485:2006 provides the gear manufacturer and the customer with a mutually advantageous reference for uniform tolerances. Ten accuracy grades are defined, numbered 2 to 11 in order of decreasing precision.

Gears which features high performances , after the basic manufacturing process, need to be delivered to Lafer S.p.a., an Italian company specialized in surface finishing treatments. Components, first of all, are exposed to a “superfinish” process, then to a “coating” process. To better explain processes carried out by Lafer S.p.a. it’s necessary to exploit the notion of roughness.

.

Plot 6.2-2: Basic scheme of roughness.

Roughness of a component can be basically described by Plot 6.2-2. Zero line is the nominal dimension of the component. Around this line, actual surface of the component floats between positive values

“peaks” and negative values, “valleys”. The target of the superfinish process is to flatten all positive peaks, respecting the mechanical tolerance of the component.

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In order to have a flat and smooth surface on the component, it’s necessary to eliminate the issue of negative valleys. Therefore an additional treatment is needed, Carbonlafer which is the commercial name of a WC/C coating process. By chemical point of view, this treatment It’s based on the sediment of an amorphous multi layer of tungsten carbide, which thickness varies between 1 [μm] and 3 [µm].

According with website “http://www.lafer.eu/”, Ref.[13], this process is suitable in any application where it’s necessary to reduce the friction between mechanical components and limit the employ of lubricants. It’s normally employed for gears, hydraulic pumps, bearings, worm screws and sliding guides. Main feature of Carbonlafer is a very low coefficient of friction, C.O.F., measured around 0.15 on dry steel. Then, hardness of the surface is increased by a value included between 200HV and 300HV points which represent a surplus of 15÷20% in the total hardness of the material surface. Strong adhesion of the coating layers can be obtained at relative low temperature, 180°C and this ensures that unwanted displacements could not appear. Anyway, coating is very stable under high temperatures, that allows to treated components to work until 380°C.

Returning to focus on the software, to the setting of input parameters in particular, a value of quality set on 3 can be congruent to the treatments performed on the gear. Value of 3 instead of 2 is a preventive measure, knowing that cutting of spiral bevel gears is a very delicate process by point of view of technology. Surface finish of first manufacturing process is often a bit scratched and not all deep scratches can be sealed by coating. Parameters actually set on the software are displayed on Picture 6.2-2.

Picture 6.2-2: Detail on Kisssoft dialog window, input geometric parameters are highlighted by green squares.

A brief clarification needs to be done about profile correction factor which Kisssoft indicates with

“Fattore di spostamento del profilo”, widely described at Chapter 5.12. Software acts selecting two different options of correction: one maximizes the structural strength of the tooth, the other maximizes the efficiency of the gear.

Picture 6.2-3: Detail on Kisssoft dialog window, profile correction factor setting.

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Chosen option is symmetrical:

Eq. 6.2-4

Eq. 6.2-5

Where:

 is “profile correction factor of wheel 1” drive wheel of first stage. It’s a dimensionless parameter.

 is “profile correction factor of wheel 2” driven wheel of first stage. It’s a dimensionless parameter.

Determined value allows to maximize strength of teeth, through the strengthening of roots.

Profile of gear, on the basis of calculations, have been modelled in accordance with I.S.O. 23509:2006 Q4-7 standard.