In my Introduction to Engineering Design Course, I worked on team of 8 student to design the transmission for a commercial-turbofan accessory-drive gearbox, beginning with the input drive shaft rotating at 8 400 rpm with 750 in·lbf of torque and finishing with four correctly-timed output accessory shafts.

Gear train rendering

The final layout packs a 16 gear transmission, 15 of which are spur gears, plus a bevel gear which drives the input drive shaft from the outside of the gearbox from the turbofan input. The gearbox has a complex u shaped geometry that is 4.75 inches in depth (see below).

Gear train rendering Gear train rendering

There are three compounded stages, mixed diametral pitches (10, 12 and 16 teeth · in⁻¹) and 20° spur teeth let every accessory hit its spec speed within ±10 rpm.

Gear train rendering

All the gears are made of Nitralloy 135M,chosen for its high nitrided hardness, but are of different grades: two drive trains are Grade 1, one is Grade 2, and one is Grade 3.

Gear train rendering

The shafts are made of 1.0 in-OD AISI 1050 steel, quenched & tempered at 400 °F, which provides the strength needed without exotic alloys. Using AGMA 2001 bending and contact formulas we verified that every gear cleared the project minimum safety factors (1.30 in bending, 1.15 in contact). The governing part is Gear 9, a 20-tooth, 1.25 in pitch-diameter pinion that accepts the full 375 in·lbf half-shaft torque, yet it still retains safety factors of 1.36 (bending) and 3.07 (pitting); a roughly 9 % torque increase would make it the first element to dip below margin. The table below shows the FoS in contact/pitting and bending stress for each gear.

Table 8: Gear Pitting (Contact) Stress Analysis Results
GearCp W t (lbf)K0 KvKs Kmdp (in) F (in)Cf IσC (psi)
22300375.15 1.251.261 1.142.001 11.0441459
32300375.15 1.251.261 1.132.331 10.9639664
42300375.15 1.251.261 1.132.331 11.0138692
52300375.15 1.251.261 1.132.581 11.0136727
62300232.71 1.251.261 1.132.501 11.0528836
72300232.71 1.251.261 1.123.001 11.1225421
82300232.71 1.251.261 1.142.171 11.1230084
92300600.24 1.251.211 1.161.251.25 11.4350060
102300600.24 1.251.211 1.161.561.25 11.4045108
112300600.24 1.251.211 1.161.881.25 11.3841551
122300600.24 1.251.211 1.161.631.25 11.4942871
132300600.24 1.251.211 1.163.001.25 11.6729905
142300370.71 1.251.221 1.163.401.25 10.8531006
152300370.71 1.251.221 1.162.301.25 10.9635515
162300370.71 1.251.221 1.161.401.25 11.0044592

We applied the DE-ASME Elliptic criterion at all shaft discontinuities. The main drive-shaft’s retaining ring groove proved critical at a 1.66 design factor, while its keyway held 1.99; the tightest accessory shaft (Shaft D) showed 2.35, all above the 1.15 / 1.10 requirements, and an S-N curve confirmed the shaft operates in the infinite-life regime. Below is the DE-ASME Elliptic criterion equation used to calculate the FoS of the shaft. The table below goes on for quiet a while, be prepared to scroll.

Gear train rendering
Drive Shaft
Bevel Gear
d_p =5
Face Width1.53
r_av2.061
W_t, bevel364.047
W_r, bevel108.54
γ = 35 degrees0.610865238
Shaft Physical Properties
Edit these properties on the Shaft Geometry Spreadsheet
Outer Diameter [in]1
φ = 20 degrees (Tooth contact Angle)0.34906585
Shaft Material
S_ut [psi]163000
S_y [psi]117000
E [psi]30000000
S'_e [psi]81500
k_a (Surface Factor)2.7
k_b (Size Factor)0.879
k_c (Loading Factor)0.59
k_d (Temperature Factor)1
k_e (Reliability Factor)0.81392
k_f (Miscellaneous Effects Factor)1
S_e (Actual Endurance Limit)92884.65662
a_b (Neuber Constant Bending)0.029520955
a_s (Neuber Constants Shear)0.023920555
Shaft Loading
T_input [lbf-in]750.3
d_1 (for Gears) [in]2
θ_1 [radians]0.139451807
T_1 [lbf-in]375.15
W_t,gear1 [lbf]375.15
W_r,gear1 [lbf]136.5434334
F_x1 [lbf]-187.3638659
F_z1 [lbf]-352.5285995
d_8 [in]1.25
θ_8 [radians]0.215024564
T_8 [lbf-in]375.15
W_t,gear8 [lbf}600.24
W_r,gear8 [lbf]218.4694934
F_x8 [lbf]85.36432788
F_z8 [lbf]633.0323125
Distance of Gears of the Shaft (measured from the front)
L_gear1 (L1) [in]0.8
L_gear8 (L2) [in]2.125
L_bevel (L3) [in]4.3125
L_end [in]5.075
Reaction Forces
R_dz,back [lbf]-301.7240462
R_dx,back [lbf]-315.5587767
R_oz,front [lbf]129.7603332
R_ox,front [lbf]781.6053147
Shaft Bending Moments
M_Ax [lbf-in]103.8082665
M_Az [lbf-in]625.2842517
M_Bx [lbf-in]-191.3596863
M_Bz [lbf-in]1412.654171
M_Cx [lbf-in]1477.249226
M_Cz [lbf-in]1696.092498
M_A [lbf-in]633.8426869
M_B [lbf-in]1425.55615
M_C [lbf-in]2249.220985
d_1 (for shaft) [in]1
σ Maximum Bending Stress [psi]14520.59571
Stress Concentrations
Groove Fatigue Stress Concentration
r (Notch Factor) [in]0.0047
K_(t) (Bending) 5
q_t (Bending)0.6990038
K_(f) (Bending)3.796015202
K_(ts) (Torsional)3
q_ts (Torsional)0.74133537
K_(fs) (Torsional)2.482670741
M_m [lbf-in]0
T_a [lbf-in]0
n (Groove Factor of Saftey)1.639825767
Keyway Fatigue Stress Concentration
r (Notch Factor) [in]0.02
K_(t) (Bending)2.14
q_t (Bending)0.827304575
K_(f) (Bending)1.943127216
K_(ts) (Torsional)3
q_ts (Torsional)0.855326729
K_(fs) (Torsional)2.710653459
M_m [lbf-in]0
T_a [lbf-in]0
A5540.073906
B3522.650631
n (Keyway Factor of Saftey)1.987233339
Yeilding FOS52.01801014

Since this gearbox is going on a plane, there is a strict weight limit of 260 lbf. All of our gears and shafts come out to 249.7 lbf, comfortably beneath the 260 lbf limit.

Total Weight of Gears and Shafts31.72
Gearbox Housing Weight85
Oil Pump Weight27
Fuel Pump Weight28
Electrical Generator Weight45
Hydraulic Pump Weight32
Total Weight of Gearbox248.72

Analysis loops were automated in Excel, and the finished SolidWorks assembly meets AGMA Quality 10, 99 % reliability, and 10⁸-cycle life targets while identifying Gear 9 and the groove as the true growth-limiters for any future power surges.

In my Introduction to Engineering Design course I completed a solo design of a torsion bar suspension shaft and all associated hardware for a theoretical heavy duty vehicle. Below is the full completed assembly of the torsion bar along with the nomenclature that will be used to reference each portion.

Gear train rendering

The side wall and base plate are made of an unspecified aluminium alloy, with the base being 0.4375 inches thick, and the side wall being 0.250 inches thick. The material and thickness of the base plate and side wall were out of the scope of this project and were intentionally vaguely defined in the project briefing.

Gear train rendering

The torsion bar is made of hollow 4130 Q&T 205°C/400°F steel with a 2.15 inch inner and 2.673 inch outer diameter. The torsion bar was dimensioned so when the bar is at the maximum operating deflection angle, (51°) it is supporting 2510 lbf, and when at its minimum operating deflection angle (47°) it is supporting 890 lbf, enough to handle bumps and hauling heavy loads. At no load, the lever arm sits at 45°.

BEING CUT OFF HERE

The torsion bar came out with a static torsional safety factor of 10.4 and a fatigue safety factor of 2.7 (Modified Goodman, 99.9 % reliability), which places the component in the infinite-life region of the S-N curve.

Gear train rendering

Both ends of the bar were keyed with a 20-tooth, 30° pressure angle 8/16 spline that transmits up to 29 k lbf-in from the lever arm to the fixed coupling without slip. ANSI-B92 checks yielded safety factors of 38.9 in compression, 1.06 in shear, and 1.73 in the spline shaft, clearing the 1.05 requirement while keeping the bar diameter in spec.

Gear train rendering

I dimensioned the aluminum bearing support lug made of 3003-H16 (0.50 in thick) with a bronze sleeve bearing that mounts the bar to the chassis. The lug records a FoS of 4.16 and the bearing interface posts 7.3 (R/D) / 31.5 (W/D)—both well above the mandated 3.75. Two SAE-Grade-2 bolts clamp the lug and the joint analysis returned safety factors of 1.21 in yield, 3.33 in overload, and 4.46 against separation.

Gear train rendering

To complete the linkage I sized a 12 in solid 1010 cold drawn steel axle to 2.5 in Ø, delivering a bending safety factor of 2.24 versus the 1.15 minimum and 0.79 in of vertical wheel travel. A minimum shaft diameter of 2.01 was required to meet the FoS, but for each of manufacturing and additional safety it was increased to a 2.5 inch diameter shaft.

All calculations (static torsion, fatigue, spline contact, bolt stiffness, lug bearing, axle bending) were automated in Excel. The result is a cost efficient and manufacturable suspension member whose weakest points, which is the spline shear and bolt yield, still hold more than 5% margin above every project criterion.

Sample 102 ImageJ Porosity Detection

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