Keywords

1 Introduction

For the all-terrain vehicles (ATV) that are configured for an automatic transmission drive using a continuously variable transmission (CVT), a gearbox has to be coupled with the CVT to get desired speed and torque output. Since the CVT is providing variable transmission ratios, a forward–neutral–reverse (FNR), two-step reduction gearbox can be used for this purpose. The work proposed here is to design a two-stage gearbox consisting of both helical and spur gears. This gearbox is designed for an ATV, made for the BAJA competitions. Here weight reduction is focused upon as the main goal to achieve maximum acceleration and also to get the centre of gravity as low as possible. Thus, factors such as weight, strength and size are optimized to achieve the best possible gearbox. The analysis operations conducted during the research were done according to Navneet et al. [1], in their study in ‘Analysis and Simulation of Gearless Transmission Mechanism’ and also by Timir Patel et al. [2], in their study ‘Design and Analysis of an Epicyclic Gearbox for an Electric Drivetrain’.

2 Vehicle Parameters

  • Engine power = 10 hp = 7.456 kW @ Max RPM = 3800 rpm

  • Engine torque = 19.2 Nm @ 2700 rpm

  • Transmission type = CVT + Gearbox drive

  • Gearbox type = forward spool two-stage helical gearbox

  • Overall reduction = 9

  • Stage 1 reduction = 3, stage 2 reduction = 3

  • Gear material = 20 MnCr5, Yield strength: 350–550 N/mm2, Tensile strength: 650–880 N/mm2.

The Table 1 shows the parameters taken into account of an ATV for which the gearbox is being designed.

Table 1 Input parameters
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3 Torque Requirements

To determine the required torque, the most important factor that turns in is the total resistance experienced by the vehicle. The driving resistance is an important variable taken into consideration while designing transmission systems. Driving resistance is made up of mainly four resistances:

  • Wheel Resistance

  • Air Resistance

  • Gear Resistance

  • Acceleration Resistance.

The Table 2 comprises of the resistance values experienced by the ATV at different RPMs. As the engine increases its RPM, the resistance value changes [3,4,5].

Table 2 Resistance calculations
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Taking reference from the Table 2, we determined what is the exact reduction required for our BAJA vehicle [4, 6, 7].

4 Design of Gearbox

Design calculations of various parts of gearbox are as follows [4, 6,7,8,9].

4.1 Design of Gears

Lewis bending equation is.

$$\sigma = \frac{{K_{v} W^{t} }}{FmY}$$
(1)

where

  • σ is the bending stress on gear teeth (not considering dynamic loading)

  • F is the face width

  • m is the module

  • Wt is the tangential load

  • Y is the Lewis form factor

  • Kv is the velocity factor

AGMA bending stress equation is

$$\sigma = \frac{{K_{v} W^{t} K_{s} K_{o} K_{H} K_{B} }}{{bm_{t} Y_{J} }}$$
(2)

where

  • σ is the bending stress-induced

  • Kv is the dynamic factor

  • Wt is the tangential transmitted load

  • b is the face width of the narrower member

  • Ko is the overload factor

  • Ks is the size factor

  • KB is the rim thickness factor

  • KH is the load distribution factor

  • YJ is the geometry factor for bending strength

  • mt is the transverse module

AGMA pitting stress equation is

$$\sigma_{c} = Z_{E} \sqrt {W^{t} K_{o} K_{v} K_{s} \frac{{K_{H} }}{{d_{wl} b}}\frac{{Z_{R} }}{{Z_{I} }}}$$
(3)

where

  • σC is the pitting stress-induced

  • ZE is the elastic coefficient

  • dwl is the pitch diameter of the pinion

  • ZI is the geometry factor of the pitting resistance

  • ZR is the surface condition factor

AGMA allowable bending stress equation is

$$\sigma_{{{\text{all}}}} = \frac{{S_{t} Y_{N} }}{{S_{F} Y_{\theta } Y_{Z} }}$$
(4)

where

  • St is the allowable bending stress

  • YN is the stress cycle factor for bending stress

  • YZ is the reliability factor

  • Yθ is the temperature factor

  • SF is the AGMA factor of safety.

AGMA allowable pitting stress equation is

$$\sigma_{{c,{\text{all}}}} = \frac{{S_{c} Z_{N} Z_{W} }}{{S_{H} Y_{\theta } Y_{Z} }}$$
(5)

where

  • σc,all is the allowable pitting stress

  • ZN is the stress cycle factor

  • Sc is the allowable contact stress

  • SH is the AGMA factor of safety

  • ZW is the hardness ratio factors for pitting resistance.

To avoid failure in gearing, the following condition must be satisfied:

σ (both of Lewis bending equation and AGMA strength equation) ≪σall, σc ≪ σc, all.

Solving the above equations by inserting the specified vehicle parameters, the above conditions are satisfied. Therefore, the design is safe.

The values obtained by solving the equations in GearTraxPRO (Camnetics Suite) are shown in Table 3 for stage 1 pinion and gear and Table 4 for stage 2 pinion and gear.

The following tables show the parameters taken as for both pinion gears for design [3] (Table 5).

Table 3 For reduction stage 1 pinion and gear
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Table 4 For reduction stage 2 pinion and gear
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Table 5 Factors for spur and helical gears
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4.2 Design of Shafts

Parameters:

  • Material: AISI/SAE 4340

  • UTS: 925 MPa

  • Yield strength: 680 MPa

  • Allowable shear stress for shaft: 462.5 MPa

Torque transmitted by pinion:

$$T = \frac{P \times 60}{{2\pi N_{P} }}$$
(6)

Equivalent no. of teeth:

$$T_{E} = \frac{{T_{P} }}{{{\text{cos}}^{3} \alpha }}$$
(7)

Tooth factor:

$$y^{\prime } = 0.154 - \frac{0.912}{{T_{E} }}$$
(8)

Tangential tooth load:

$$W_{T} = \frac{2T}{{m \times T_{P} }}$$
(9)
$$\begin{aligned} \frac{1}{n} & = \frac{16}{{\pi d^{3} }} \left\{ {\frac{1}{{S_{e} }} \left[ {4\left( {K_{f} M_{a} } \right)^{2} + 3\left( {K_{fs} T_{a} } \right)^{2} } \right]^{1/2} } \right. \\ & \quad \left. { + \frac{1}{{S_{ut} }} \left[ {4\left( {K_{f} M_{m} } \right)^{2} + 3\left( {K_{fs} T_{m} } \right)^{2} } \right]^{1/2} } \right\} \\ \end{aligned}$$
(10)

where

  • Factor of safety (FOS) = n

  • Diameter of the shaft = d

  • Endurance limit at critical location \(S_{e} = k_{a} \;k_{b} \;k_{c} \;k_{d} \;k_{e} \;k_{f} \;S_{e}^{\prime }\)

  • ka is the surface condition modification factor

  • kb is the size modification factor

  • kc is the load modification factor

  • kd is the temperature modification factor

  • ke is the reliability factor

  • kf is the miscellaneous effects modification factor

  • \(S_{e}^{\prime }\)  = rotary beam test specimen endurance limit

  • Stress concentration factor for Bending, \(K_{f} = 1 + q\left( {K_{t} - 1} \right)\).

  • Stress concentration factor for torsion, \(K_{fs} = 1 + {\text{qshear}}\left( {K_{t} - 1} \right)\).

  • q is the notch sensitivity

  • Me is the midrange bending moment

  • Ma is the maximum bending moment

  • Ta is the alternating torque

  • Te is the maximum torque

  • Sut is the tensile strength.

By drawing shear force and bending moment diagrams, we are able to find the values of Ma and Te.

Resultant bending moment: \(Ma = \sqrt {\left( {M_{1} } \right)^{2} + \left( {M_{2} } \right)^{2} }\).

Putting the values in Eq. 10, we get n = 1.37.

From the above equation, we get dP = 17 mm (standardized according to the availability of support bearing sizes and oil seals).

The value of principal shear stress is equated which is significantly less than the permissible shear stress of the shaft material. Hence, the design is safe.

Repeating the above calculations for the intermediate shaft and the output shaft, we get shaft diameters as 22 mm and 27 mm.

4.3 Design of Casing

The casing design was aimed at achieving the lowest possible volume, while constraining the shafts with gears mounted on them. The geometry is kept simple for lowering the machining cost.

5 CAD Modelling of Gears, Shafts and Casing

SolidWorks 2018–19 modelling software was used to design the various components of the gearbox. Based on the input design parameters from GearTraxPRO software, modelling was done in SolidWorks. The images of the components are shown in the figures below. Gear material was selected as 20MnCr5 [10]. Figures 1 and 2 show the gears of the first stage reduction of the gearbox. Figures 3 and 4 show the gears of the second stage reduction of the gearbox. Figures 5, 6 and 7 show the CAD model of the input shaft, intermediate shaft and output shaft, respectively. Figures 1, 2, 3, 4, 5, 6 and 7 are the gears and shafts designed as per parameters in SolidWorks [11, 12, 17].

Fig. 1
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Spur pinion

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Fig. 2
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Spur gear

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Fig. 3
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Helical pinion

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Fig. 4
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Helical gear

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Fig. 5
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Input shaft

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Fig. 6
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Intermediate shaft

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Fig. 7
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Output shaft

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The CVT is coupled with the input shaft with the help of the keyway in the input shaft. The casing design was optimized for minimum machining cost by reducing the number of contours that were made keeping in mind the weight of the gearbox. Following Figs. 8 and 9 show the final geometry including the left and right casing sides. Aluminium 6061-T6 was chosen as casing material [11].

Fig. 8
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Exploded view of complete gearbox

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Fig. 9
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Assembled view of gearbox without casing

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The final assembly was done using SolidWorks, which included all the gears, shafts, bearings and the shifter. Figures 9 and 10 show the assembled view of the gearbox.

Fig. 10
figure 10

Complete assembly of gearbox

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6 Static Analysis

6.1 Gears

Maximum loading conditions were assumed for checking the gears for maximum safety. It was assumed that the worst loading condition on the gearbox would be when the vehicle is stuck and the engine is working at full power to get out of the obstacle. At this point of time, maximum torque would fall on the intermediate shaft gear 3. In the result, maximum stress-induced under full-loading condition was less than maximum allowable stress for the selected material [1]. The following pictures are of the analysis done on gears on ANSYS software [5, 12,13,14, 16].

figure a

Gear teeth are subjected to both bending and wear. The section where it experiences the maximum stress is the root of the tooth. It is considered that there are three teeth in contact with the mating gear [12]. Tangential force (Ft) because of the torque which the gear is transmitting is applied on these three teeth. The total tangential force is distributed amongst the three teeth considering one tooth takes 50% of force and others take 25% each. The radial forces (Fr) generated on the gear are acting towards the centre of the gear [12, 13].

Magnitudes of the tangential and radial forces for the application in the analysis are taken from the GearTraxPRO output values in the design of the gears. The analysis result shows that the design is safe, even when the worst loading condition is considered. Figures 11, 12 and 13 show the dimensioning and force calculation outputs for reduction set 1 (for gear 1 and gear 2). The results were obtained by simulation in ANSYS software. Based on the results and analysis, we chose EN24 as our material for gear manufacturing [10] (Fig. 14).

Fig. 11
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Force model of gear

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Fig. 12
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Equivalent stress of gear

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Fig. 13
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Total deformation model

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Fig. 14
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Factor of safety of gear

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6.2 Shafts

Shafts are mainly subjected to bending and torsion. It is considered that the shafts are subjected to maximum torsion at the location of gear through spline. Hence, the torque is applied at that position. Bearing portion where taken as the frictionless support and the fixed support will be the output of the shaft at both ends where the drive shaft through the joints will attach [5, 14, 15] (Figs. 15, 16 and 17).

Fig. 15
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Force model of output shaft

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Fig. 16
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Equivalent stress of output shaft

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Fig. 17
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Factor of safety of output shaft

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6.3 Casing

See Figs. 18, 19, 20 and 21.

Fig. 18
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Force model of casing

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Fig. 19
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Contact region

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Fig. 20
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Equivalent stress of casing

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Fig. 21
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Factor of safety of casing

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7 Software Results for Gear Design (GearTRAXPRO)

The following pictures are screenshots of the GearTRAXPRO software while obtaining a SolidWorks part file of the gear. It also includes all parameters taken into consideration for designing the gear.

Figures 22 and 23 show the dimensioning and Figs. 24, 25, 26, 27, 28 and 29 force calculation outputs and other parameter calculations for reduction set 1 (for gear 1 and gear 2). The results were obtained by simulation in GearTraxPRO software.

Fig. 22
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Gear set 1 dimensioning

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Fig. 23
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Gear set 2 dimensioning

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Fig. 24
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Pitting resistance for gear set 1

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Fig. 25
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Force calculations for gear set 1

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Fig. 26
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Bending strength for gear set 1

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Fig. 27
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Pressure angle for first stage reduction

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Fig. 28
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Operating parameters for reduction gear 1

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Fig. 29
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Contact ratios for gear set 1

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8 Conclusion

Comparison of existing alternative options in the market and this new design of the gearbox show that there is a significant reduction in weight of the gearbox. This is achieved while keeping the performance parameters as required by the potential customers. The gearbox design was finalized in geometry and material (in accordance with AGMA standards) and was forwarded to manufacturers [3] for getting a prototype model for testing. Once manufactured, the model will be tested on a BAJA ATV, by replacing the old gearbox with this gearbox. An overall weight reduction of 9.5 kg is expected from the design, when compared with its alternative market option.