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One wheel held. The other turns twice as fast.
A complete rear differential, down to the last bolt. Put the left wheel on tarmac and the right on ice: the spiders walk round the held side gear and the free axle spins at exactly twice the case speed. Nothing is keyframed. Turn the pinion and the mates move everything else.
3.73:141:11 teeth, spiral bevel
59parts, every bolt modelled
123mates
2 DOFpinion in, two axles out
3,139B-rep faces in the cover
84.1 kgcomplete assembly
Loading the kernel's meshes…
The mates
59 parts, 123 mates, and exactly 2 degrees of freedom left: drive in at the pinion, split between the two axles. The textbook mobility of a differential. The fourth spider mesh is redundant — the solver finds it and keeps it, as the real gear set does.
| Joint | Mates | Made of |
|---|---|---|
| Revolute | 12 | concentric + coincident: one spin left |
| Fastened | 69 | concentric (rotation locked) + coincident, or face + pilot + clocking hole |
| Threaded | 18 | concentric (rotation locked) + coincident |
| Splined | 6 | concentric (rotation locked) + coincident |
| Press fit | 10 | concentric (rotation locked) + coincident, on an interference fit |
| Gear | 5 | ratio-locked: Δθb = −ratio · Δθa |
| Fixed | 3 | coincident face + concentric spigot + concentric bolt hole |
By mate type: 57 coincident · 61 concentric · 5 gear.
- housing
- Fixed ×2cover
- Fastened ×2brg pinion head
- Fastened ×2brg pinion tail
- Fastened ×2brg carrier R
- Fastened ×2brg carrier L
- Threaded ×2adjuster R
- Threaded ×2adjuster L
- Revolute ×2pinion
- Revolute ×2carrier
- Threaded ×2drain plug
- Threaded ×2fill plug
- Fastened ×2bearing cap R
- Fastened ×2bearing cap L
- Press fit ×2axle tube L
- Press fit ×2axle tube R
- Fastened ×2cover gasket
- Press fit ×2pinion seal
- cover
- Fastened ×20cover bolts ×10
- pinion
- Splined ×2pinion flange
- Threaded ×2pinion nut
- Gearring gear
- carrier
- Fastened ×2cross pin
- Fastened ×2lock bolt
- Revolute ×2side L
- Revolute ×2side R
- Fastened ×20ring bolts ×10
- Fastened ×2thrust spider A
- Fastened ×2thrust spider B
- Fastened ×2thrust side L
- Fastened ×2thrust side R
- bearing cap R
- Threaded ×4cap bolts ×4
- axle tube L
- Press fit ×2brg wheel L
- axle tube R
- Press fit ×2brg wheel R
- cross pin
- Revolute ×2spider A
- Revolute ×2spider B
- side L
- Splined ×2axle L
- side R
- Splined ×2axle R
Graph: blue = revolute, orange dashed = gear mate, purple = spline, grey = fastened. The 10 ring gear bolts, the 10 cover bolts and the 4 bearing cap bolts are each drawn as one node.
Two motions, one set of mates
One wheel held
Left wheel on dry tarmac, right wheel on ice. The spiders walk round the held side gear, the free axle turns at 2.00× case speed, and each spider spins 1.60 times per case turn (16/10). Left plus right is always twice the case.
Straight ahead
Equal grip both sides: the spiders ride round without spinning, and the case, the ring gear and both axles turn as one, 0.2683 rev per pinion rev (11/41).
All 123 mates — tap one to light up its two parts
| # | Type | Mate | Between | DOF removed |
|---|---|---|---|---|
| 1 | coincident | Cover — coincident on the gasket | cover ↔ cover_gasket | 3 |
| 2 | concentric | Cover — concentric | cover ↔ housing | 4 |
| 3 | concentric | Cover — bolt hole concentric | cover ↔ housing | 1 |
| 4 | concentric | Pinion head bearing — concentric | brg_pinion_head ↔ housing | 5 |
| 5 | coincident | Pinion head bearing — coincident | brg_pinion_head ↔ housing | 1 |
| 6 | concentric | Pinion tail bearing — concentric | brg_pinion_tail ↔ housing | 5 |
| 7 | coincident | Pinion tail bearing — coincident | brg_pinion_tail ↔ housing | 1 |
| 8 | concentric | Carrier bearing R — concentric | brg_carrier_R ↔ housing | 5 |
| 9 | coincident | Carrier bearing R — coincident | brg_carrier_R ↔ housing | 1 |
| 10 | concentric | Carrier bearing L — concentric | brg_carrier_L ↔ housing | 5 |
| 11 | coincident | Carrier bearing L — coincident | brg_carrier_L ↔ housing | 1 |
| 12 | concentric | Adjuster R — concentric | adjuster_R ↔ housing | 5 |
| 13 | coincident | Adjuster R — coincident | adjuster_R ↔ housing | 1 |
| 14 | concentric | Adjuster L — concentric | adjuster_L ↔ housing | 5 |
| 15 | coincident | Adjuster L — coincident | adjuster_L ↔ housing | 1 |
| 16 | concentric | Pinion — concentric | pinion ↔ housing | 4 |
| 17 | coincident | Pinion — coincident | pinion ↔ housing | 1 |
| 18 | concentric | Companion flange — concentric | pinion_flange ↔ pinion | 5 |
| 19 | coincident | Companion flange — coincident | pinion_flange ↔ pinion | 1 |
| 20 | concentric | Pinion nut — concentric | pinion_nut ↔ pinion | 5 |
| 21 | coincident | Pinion nut — coincident | pinion_nut ↔ pinion | 1 |
| 22 | concentric | Differential case — concentric | carrier ↔ housing | 4 |
| 23 | coincident | Differential case — coincident | carrier ↔ housing | 1 |
| 24 | coincident | Ring gear — coincident face | ring_gear ↔ carrier | 3 |
| 25 | concentric | Ring gear — concentric pilot | ring_gear ↔ carrier | 2 |
| 26 | concentric | Ring gear — bolt hole concentric | ring_gear ↔ carrier | 1 |
| 27 | concentric | Cross-pin — concentric | cross_pin ↔ carrier | 4 |
| 28 | concentric | Cross-pin — lock bore concentric | cross_pin ↔ carrier | 2 |
| 29 | concentric | Lock bolt — concentric | lock_bolt ↔ carrier | 5 |
| 30 | coincident | Lock bolt — coincident | lock_bolt ↔ carrier | 1 |
| 31 | concentric | Spider A — concentric | spider_A ↔ cross_pin | 4 |
| 32 | coincident | Spider A — coincident | spider_A ↔ cross_pin | 1 |
| 33 | concentric | Spider B — concentric | spider_B ↔ cross_pin | 4 |
| 34 | coincident | Spider B — coincident | spider_B ↔ cross_pin | 1 |
| 35 | concentric | Side gear L — concentric | side_L ↔ carrier | 4 |
| 36 | coincident | Side gear L — coincident | side_L ↔ carrier | 1 |
| 37 | concentric | Side gear R — concentric | side_R ↔ carrier | 4 |
| 38 | coincident | Side gear R — coincident | side_R ↔ carrier | 1 |
| 39 | concentric | Axle L — concentric | axle_L ↔ side_L | 5 |
| 40 | coincident | Axle L — coincident | axle_L ↔ side_L | 1 |
| 41 | concentric | Axle R — concentric | axle_R ↔ side_R | 5 |
| 42 | coincident | Axle R — coincident | axle_R ↔ side_R | 1 |
| 43 | concentric | Ring gear bolt 1 — concentric | ring_bolt_0 ↔ carrier | 5 |
| 44 | coincident | Ring gear bolt 1 — coincident | ring_bolt_0 ↔ carrier | 1 |
| 45 | concentric | Ring gear bolt 2 — concentric | ring_bolt_1 ↔ carrier | 5 |
| 46 | coincident | Ring gear bolt 2 — coincident | ring_bolt_1 ↔ carrier | 1 |
| 47 | concentric | Ring gear bolt 3 — concentric | ring_bolt_2 ↔ carrier | 5 |
| 48 | coincident | Ring gear bolt 3 — coincident | ring_bolt_2 ↔ carrier | 1 |
| 49 | concentric | Ring gear bolt 4 — concentric | ring_bolt_3 ↔ carrier | 5 |
| 50 | coincident | Ring gear bolt 4 — coincident | ring_bolt_3 ↔ carrier | 1 |
| 51 | concentric | Ring gear bolt 5 — concentric | ring_bolt_4 ↔ carrier | 5 |
| 52 | coincident | Ring gear bolt 5 — coincident | ring_bolt_4 ↔ carrier | 1 |
| 53 | concentric | Ring gear bolt 6 — concentric | ring_bolt_5 ↔ carrier | 5 |
| 54 | coincident | Ring gear bolt 6 — coincident | ring_bolt_5 ↔ carrier | 1 |
| 55 | concentric | Ring gear bolt 7 — concentric | ring_bolt_6 ↔ carrier | 5 |
| 56 | coincident | Ring gear bolt 7 — coincident | ring_bolt_6 ↔ carrier | 1 |
| 57 | concentric | Ring gear bolt 8 — concentric | ring_bolt_7 ↔ carrier | 5 |
| 58 | coincident | Ring gear bolt 8 — coincident | ring_bolt_7 ↔ carrier | 1 |
| 59 | concentric | Ring gear bolt 9 — concentric | ring_bolt_8 ↔ carrier | 5 |
| 60 | coincident | Ring gear bolt 9 — coincident | ring_bolt_8 ↔ carrier | 1 |
| 61 | concentric | Ring gear bolt 10 — concentric | ring_bolt_9 ↔ carrier | 5 |
| 62 | coincident | Ring gear bolt 10 — coincident | ring_bolt_9 ↔ carrier | 1 |
| 63 | concentric | Cover bolt 1 — concentric | cover_bolt_0 ↔ cover | 5 |
| 64 | coincident | Cover bolt 1 — coincident | cover_bolt_0 ↔ cover | 1 |
| 65 | concentric | Cover bolt 2 — concentric | cover_bolt_1 ↔ cover | 5 |
| 66 | coincident | Cover bolt 2 — coincident | cover_bolt_1 ↔ cover | 1 |
| 67 | concentric | Cover bolt 3 — concentric | cover_bolt_2 ↔ cover | 5 |
| 68 | coincident | Cover bolt 3 — coincident | cover_bolt_2 ↔ cover | 1 |
| 69 | concentric | Cover bolt 4 — concentric | cover_bolt_3 ↔ cover | 5 |
| 70 | coincident | Cover bolt 4 — coincident | cover_bolt_3 ↔ cover | 1 |
| 71 | concentric | Cover bolt 5 — concentric | cover_bolt_4 ↔ cover | 5 |
| 72 | coincident | Cover bolt 5 — coincident | cover_bolt_4 ↔ cover | 1 |
| 73 | concentric | Cover bolt 6 — concentric | cover_bolt_5 ↔ cover | 5 |
| 74 | coincident | Cover bolt 6 — coincident | cover_bolt_5 ↔ cover | 1 |
| 75 | concentric | Cover bolt 7 — concentric | cover_bolt_6 ↔ cover | 5 |
| 76 | coincident | Cover bolt 7 — coincident | cover_bolt_6 ↔ cover | 1 |
| 77 | concentric | Cover bolt 8 — concentric | cover_bolt_7 ↔ cover | 5 |
| 78 | coincident | Cover bolt 8 — coincident | cover_bolt_7 ↔ cover | 1 |
| 79 | concentric | Cover bolt 9 — concentric | cover_bolt_8 ↔ cover | 5 |
| 80 | coincident | Cover bolt 9 — coincident | cover_bolt_8 ↔ cover | 1 |
| 81 | concentric | Cover bolt 10 — concentric | cover_bolt_9 ↔ cover | 5 |
| 82 | coincident | Cover bolt 10 — coincident | cover_bolt_9 ↔ cover | 1 |
| 83 | concentric | Drain plug — concentric | drain_plug ↔ housing | 5 |
| 84 | coincident | Drain plug — coincident | drain_plug ↔ housing | 1 |
| 85 | concentric | Fill plug — concentric | fill_plug ↔ housing | 5 |
| 86 | coincident | Fill plug — coincident | fill_plug ↔ housing | 1 |
| 87 | concentric | Bearing cap R — concentric | bearing_cap_R ↔ housing | 5 |
| 88 | coincident | Bearing cap R — coincident | bearing_cap_R ↔ housing | 1 |
| 89 | concentric | Bearing cap L — concentric | bearing_cap_L ↔ housing | 5 |
| 90 | coincident | Bearing cap L — coincident | bearing_cap_L ↔ housing | 1 |
| 91 | concentric | Cap bolt Ru — concentric | cap_bolt_Ru ↔ bearing_cap_R | 5 |
| 92 | coincident | Cap bolt Ru — coincident | cap_bolt_Ru ↔ bearing_cap_R | 1 |
| 93 | concentric | Cap bolt Rd — concentric | cap_bolt_Rd ↔ bearing_cap_R | 5 |
| 94 | coincident | Cap bolt Rd — coincident | cap_bolt_Rd ↔ bearing_cap_R | 1 |
| 95 | concentric | Cap bolt Lu — concentric | cap_bolt_Lu ↔ bearing_cap_L | 5 |
| 96 | coincident | Cap bolt Lu — coincident | cap_bolt_Lu ↔ bearing_cap_L | 1 |
| 97 | concentric | Cap bolt Ld — concentric | cap_bolt_Ld ↔ bearing_cap_L | 5 |
| 98 | coincident | Cap bolt Ld — coincident | cap_bolt_Ld ↔ bearing_cap_L | 1 |
| 99 | concentric | Axle tube L — concentric | axle_tube_L ↔ housing | 5 |
| 100 | coincident | Axle tube L — coincident | axle_tube_L ↔ housing | 1 |
| 101 | concentric | Axle tube R — concentric | axle_tube_R ↔ housing | 5 |
| 102 | coincident | Axle tube R — coincident | axle_tube_R ↔ housing | 1 |
| 103 | concentric | Wheel bearing L — concentric | brg_wheel_L ↔ axle_tube_L | 5 |
| 104 | coincident | Wheel bearing L — coincident | brg_wheel_L ↔ axle_tube_L | 1 |
| 105 | concentric | Wheel bearing R — concentric | brg_wheel_R ↔ axle_tube_R | 5 |
| 106 | coincident | Wheel bearing R — coincident | brg_wheel_R ↔ axle_tube_R | 1 |
| 107 | concentric | Cover gasket — concentric | cover_gasket ↔ housing | 3 |
| 108 | coincident | Cover gasket — coincident | cover_gasket ↔ housing | 1 |
| 109 | concentric | Pinion seal — concentric | pinion_seal ↔ housing | 5 |
| 110 | coincident | Pinion seal — coincident | pinion_seal ↔ housing | 1 |
| 111 | concentric | Spider A thrust washer — concentric | thrust_spider_A ↔ carrier | 5 |
| 112 | coincident | Spider A thrust washer — coincident | thrust_spider_A ↔ carrier | 1 |
| 113 | concentric | Spider B thrust washer — concentric | thrust_spider_B ↔ carrier | 5 |
| 114 | coincident | Spider B thrust washer — coincident | thrust_spider_B ↔ carrier | 1 |
| 115 | concentric | Side L thrust washer — concentric | thrust_side_L ↔ carrier | 5 |
| 116 | coincident | Side L thrust washer — coincident | thrust_side_L ↔ carrier | 1 |
| 117 | concentric | Side R thrust washer — concentric | thrust_side_R ↔ carrier | 5 |
| 118 | coincident | Side R thrust washer — coincident | thrust_side_R ↔ carrier | 1 |
| 119 | gear | Pinion → ring gear, 11/41 | pinion ↔ ring_gear | 1 |
| 120 | gear | Spider A → side L, 10/16 in the case | spider_A ↔ side_L | 1 |
| 121 | gear | Spider A → side R, 10/16 in the case | spider_A ↔ side_R | 1 |
| 122 | gear | Spider B → side L, 10/16 in the case | spider_B ↔ side_L | 1 |
| 123 | gear | Spider B → side R, 10/16 in the case | spider_B ↔ side_R | 0 |
Nothing floats, nothing collides
All 59 parts checked against each other in place: 11 collisions, 0 loose parts, 53 contacts. The only overlaps are the 4 press fits and 24 thread engagements the real axle has too.
The gears
A 35° spiral-bevel ring and pinion, left-hand ring and right-hand pinion, lapped as a set; straight-bevel spiders and side gears, as in production axles. All four cone apexes meet at the centre of the case.
| Gear | Teeth | Module (mm) | Pitch Ø (mm) | Pitch cone | Face (mm) | Spiral angle | Hand |
|---|---|---|---|---|---|---|---|
| Ring gear | 41 | 6.0 | 246.0 | 74.98° | 38 | 35° | Left |
| Pinion | 11 | 6.0 | 66.0 | 15.02° | 38 | 35° | Right |
| Side gear (× 2) | 16 | 5.5 | 87.3 | 57.99° | 14 | 0° (straight) | — |
| Spider gear (× 2) | 10 | 5.5 | 54.5 | 32.01° | 14 | 0° (straight) | — |
Bill of materials
Every part weighed from its solid: nodular iron, steel, cast aluminium. 84.1 kg in all.
27 unique parts, 59 placed
| Part | Qty | Faces | Mass each | How it is made |
|---|---|---|---|---|
| Axle housing centre section | 1 | 142 | 37.79 kg | Nodular-iron casting, bores and rear face machined |
| Differential case | 1 | 53 | 10.56 kg | Nodular-iron casting; journals ground, pin and spline bores machined |
| Axle shaft stub | 2 | 25 | 5.27 kg | 1541 induction-hardened bar, splined; forged wheel flange with five pressed studs |
| Ring gear — 41 T spiral bevel | 1 | 1,106 | 5.70 kg | 8620 forging, cut, case-carburised and lapped as a set |
| Axle tube with wheel-bearing boss | 2 | 8 | 2.12 kg | DOM steel tube pressed into the snout; bearing boss welded on and bored |
| Finned rear cover | 1 | 3,139 | 2.92 kg | Aluminium sand casting, flange face and bolt holes machined |
| Drive pinion — 11 T spiral bevel | 1 | 364 | 2.77 kg | 8620 forging, turned, cut, case-carburised; lapped with the ring gear |
| Carrier bearing (tapered roller) | 2 | 12 | 975 g | Bought-in tapered roller bearing, cone and cup |
| Pinion companion flange | 1 | 16 | 1.44 kg | Forged 1045, splined, face drilled for the driveshaft |
| Carrier bearing adjuster | 2 | 38 | 552 g | Threaded steel ring, eight wrench slots |
| Side gear — 16 T straight bevel | 2 | 328 | 478 g | 8620 forging, cut, carburised; 30 mm internal spline |
| Pinion head bearing (tapered roller) | 1 | 12 | 719 g | Bought-in tapered roller bearing, cone and cup |
| Carrier bearing cap | 2 | 16 | 273 g | Nodular-iron casting, line-bored with the housing as a matched pair |
| Pinion tail bearing (tapered roller) | 1 | 12 | 473 g | Bought-in tapered roller bearing, cone and cup |
| Ring gear bolt M12 × 1.5 × 30 | 10 | 14 | 47 g | Class 10.9 hex flange bolt, black oxide |
| Cross-pin | 1 | 6 | 462 g | Ground 4140 bar, cross-drilled for the lock bolt |
| Cover bolt M10 × 25 | 10 | 14 | 27 g | Class 8.8 hex flange bolt, zinc plated |
| Wheel bearing (sealed ball) | 2 | 12 | 134 g | Bought-in sealed bearing, pressed on the axle journal and into the tube boss |
| Spider gear — 10 T straight bevel | 2 | 206 | 124 g | 8620 forging, cut, carburised; bored for the cross-pin |
| Bearing cap bolt M12 × 1.75 × 35 | 4 | 14 | 50 g | Class 10.9 hex flange bolt, black oxide |
| Drain / fill plug M22 × 1.5 | 2 | 14 | 79 g | Hex plug with bonded seal |
| Cover gasket | 1 | 28 | 128 g | Die-cut compressed fibre, 2 mm |
| Pinion nut M24 × 1.5 | 1 | 10 | 63 g | Prevailing-torque flange nut |
| Spider thrust washer | 2 | 9 | 18 g | Hardened steel, spherical back to seat in the case |
| Cross-pin lock bolt M8 × 66 | 1 | 14 | 33 g | Class 10.9 hex bolt, black oxide |
| Pinion seal | 1 | 6 | 17 g | Bought-in lip seal: steel case, nitrile lip |
| Side gear thrust washer | 2 | 6 | 4 g | Hardened steel shim, 0.5 mm |
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