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Ari Holopainen / diffs

SPECIAL DIFFERENTIALS

This page contains couple of self-made differentials without normal Lego-differential housing parts. Differentials are special purpose planetary gears, which have one input and two outputs. While you build self-made differentials remember two features. When you lock input and rotate one output, other output rotates in different direction. When you lock one output and rotate input, other output rotates in same direction as input but faster.

Many differentials use two 16 teeth clutch gears connected together at their dog clutch side. If they don’t stay together in use you have two options: Minimize the gap that clutch gears make by moving axle with bushes, check this fine tuning. If this is not possible you can try non lego methods like Blu-Tack.

Table of Contents:

A. Centre Differential (to convert RWD => 4WD)
  - A.1. Version 50%-50%
  - A.2. Versions 40%-60% and 44%-56%
B. Centre Differential Ver II (50%-50%)
C. Centre Differential Ver III (33%-67%, 37%-63% or 42%-58%)
D. Centre Differential Ver IV (35%-65%)
E. Centre Differential Ver V (37,5%-62,5%)
F. Centre Differential Ver VI (36%-64%)
G. Interaxle Differential (with multiple torque allocations)
  - G.1. Alternative setup
H. Spur Gear Rear Axle Differential PARTLY NEW
I. Torque Allocation Calculations

A. Centre Differential (to convert RWD => 4WD):

A.1. Version 50%-50%:

This centre differential is useful, when you need to convert rear-wheel drive into 4WD. Input and rear axle output are coaxial so the driveline between gearbox and rear axle doesn’t need complex modifications. All you have to build is front-wheel drive.

Picture Files:	Centre Differential	Diffrential Parts	Centre Differential Modified

Brickshelf Gallery:	Diff

Modified version is useful if the previous version can’t handle enough torque. It has longer axle and extra bush to support 24 teeth crown gear, so gear won’t jump out of mesh so easy.

A.2. Versions 40%-60% and 44%-56%:

Because this centre differential converts RWD into 4WD you may want that your car still behaves a like rear-wheel drive. The solution is unequal torque allocation. In this case front axle gets only 40% (or 44%) of the torque and rear axle gets the rest 60% (56%).

Picture Files:	Centre Differential 40%-60%	Differential 40%-60% Parts	Centre Differential 44%-56%

Brickshelf Gallery:	Diff

B. Centre Differential Ver II (50%-50%):

This centre differential is actually same construction as planetary gear ver III. Basic ratio is now u=1,00, which gives 50%-50% torque allocation as differential use.

Picture Files:	Front view	Rear view	Top view	Diff parts

Brickshelf Gallery:	Diff

You can replace one or two axle pins of 8 teeth gear idlers to axle pins with friction. This way you get limited slip differential.

Building tip: move front output axle a little bit forward to prevent possible collision problems with front output and differential parts. Check picture Top view to see what I mean.

C. Centre Differential Ver III (33%-67%, 37%-63% or 42%-58%):

This centre differential is suitable for 4WD version of normally rear-wheel drive car. 67%, 63% or 58% of torque goes to rear axle so car still behaves like rear-wheel drive. Normally this type of centre differential has visco clutch to limite slip in difficult conditions. In lego world visco clutch is not possible so differential has dog clutch differential lock, which makes centre differential rigid.

Picture Files:	Differential 33%-67%	Axles	Diff housing	Differential 37%-63%	Differential 42%-58%

Brickshelf Gallery:	Diff

12 teeth gears have very weak mesh so it’s possibly that gear pair loses contact under high torque. In that case you have to use 37%-63% or 42%-58% torque allocation.

If you replace front output’s gear pairs with the same gear pairs as rear output you get 50%-50% torque allocation.

D. Centre Differential Ver IV (35%-65%):

Also this centre differential is same type as planetary gear ver III. This time basic ratio u=1,875 which gives 35% of torque to front and 65% to rear axle.

Picture Files:	Front view	Rear view	Top view	Diff housing

Brickshelf Gallery:	Diff

Also in this version you can replace one or two axle pins of 12 teeth gear idlers to axle pins with friction. This way you get limited slip differential.

Building tips: Move front output axle a little bit forward to prevent possible collision problems with front output and differential parts. Check picture Top view to see what I mean. Also check that input axle and rear axle are coaxial, it’s easy to build it misaligned.

E. Centre Differential Ver V (37,5%-62,5%):

This spur gear centre differential version V differs from others so that it has 3 axle pairs in diff housing. 12 and 20 teeth gears in differential give 37,5% torque to front output and 62,5% to rear output. Using 16 teeth gears instead of 12 and 20 teeth gears gives 50%-50% torque allocation.

Picture Files:	Front view	Rear view	Diff axles	Diff housing

Brickshelf Gallery:	Diff

You may have difficulties to fit gears in differential because there are 3 gears that mesh with output gear. If output gear won’t go into place disconnect both output gears and rotate 1 or 2 differential’s axles so that they mesh with output gear in different angle. Note that rotating all the differential’s axles while 1 output gear is in mesh won’t help to solve the problem.

Building tip: move front output axle a little bit forward so it won’t collide with differential parts.

F. Centre Differential Ver VI (36%-64%):

Also this centre differential is based on planetary gear ver III. Now basic ratio is u=1,80 so differential’s torque allocation is 36% to front output and 64% to rear output. Again you can replace one or two axle pins of 8 teeth gear idlers to axle pins with friction to get limited slip differential.

Picture Files:	Front view	Rear view	Top view	Diff housing

Brickshelf Gallery:	Diff

Building tip: move front output axle a little bit forward so it won’t collide with differential parts.

G. Interaxle Differential (with multiple torque allocations):

Here is an idea how to build interaxle spur gear planetary differential for truck that has tandem drive. You can choose from three different torque allocations. That’s handy if suspension is designed so that tandem drive has unequal axle loads. Diffrential lock is included in all versions.

Note: These torque allocations are theoretical. In practice differential has some locking effect when front axle has lower traction than back axle. This is due to bad efficiency from input to front axle.

Picture Files:

Fine tuning before use

Brickshelf Gallery:

Diff

Building tips:

Use bushes around brick parts so you can adjust front axle as rear as possible. Otherwise differential and input gear wheel will hit each other.
Make sure that front and back axle are set coaxial. It is easy to build it misaligned.

G.1. Alternative setup:

This version has an extra idler gear so you can avoid collision problems without any fine tuning.

Picture Files:

Differential 50%-50% alternative

H. Spur Gear Rear Axle Differential PARTLY NEW:

I use this spur gear differential on the rear axle of my Lego 4WD vehicle (check Vehicles). While it’s continuous 4WD it needs 3 differentials but I have only 2 new differentials. 36 teeth gear is handy part for differential housing because with 12 teeth bevel gear it gives ratio 3,00 which is needed due to 8 teeth gear and 24 teeth crown gear in front axle. Unfortunately differential lock is not available.

Picture Files:	Spur Gear Differential	Axles	Differential Housing

Picture Files:	Spur Gear Differential alter	Diff Housing alter pic1	Diff Housing alter pic2	Axles alter	Differential Itself alter

LDraw files:	spur gear diff.ldr	spur gear diff alter.ldr

Brickshelf Gallery:	Diff

Available is also alternative setup that uses 8 teeth gear wheels. There are two differential axles that transmit torque to left and right axle so this setup should handle more torque than original design. One interesting thing is that diff housing is not rigid so there can be some locking effect under torque. I haven’t built this so I can’t tell is locking effect strong enough to call this setup limited slip differential.

I. Torque Allocation Calculations:

Method 1 to calculate unequal torque allocation.

First assume that differential’s input is locked. Usually it’s differential housing.
Then think front output as input. While it’s input its ratio is 1,00.
Then calculate the rear ratio i, which means ratio from front output to rear output. Normally it’s simple calculation of gear pairs but Interaxle differential needs planetary gear equations.
Front and rear outputs rotate in different directions but forget ratio i’s minus sign in next calculations.
Allocation to front is front ratio (1,00) divided with sum of front and rear ratios. Allocation to rear is rear ratio i divided with sum of front and rear ratio.
Same in equations: Front%=1/(1+i)x100% and Rear%=i/(1+i)x100%.
Sum of Front% and Rear% should be 100%.

Example 1: Centre Differential 44%-56%. To calculate ratio i you have gear pairs S(16)-M(24) and Th(14)-Mu(20)-Su(12). Mu(20) is just idler so ratio i=24/16x12/14=9/7. Torque allocation is Front%=1/(1+9/7)x100%=43,75% and Rear%=(9/7)/(1+9/7)x100%=56,25%.

Example 2: Interaxle Differential 57%-43%. This is actually planetary gear ver II (check Planetary gears). Basic ratio u is calculated from gear pairs Su(12)-Th(14) and XS(8)-S(16) so u=14/12x16/8=7/3. Ratio i is calculated from situation where planet carrier is input, sun gear A output and sun gear B is locked, so i=1/(1-u)=1/(1-7/3)=-3/4. Now forget the minus sign. Torque allocations are Front%=1/(1+3/4)x100%=57,14% and Rear%=(3/4)/(1+3/4)x100%=42,86%. This is not the easiest way to calculate the torque allocation but it works.

Method 2 to calculate torque allocation is to use planetary gear equations. Normally differential equals to planetary gear ver III (check Planetary gears) but Interaxle differential needs equations of planetary gear ver II. First you calculate the basic ratio u. In this calculation start point equals to sun gear A and end point to sun gear B like in planetary gear’s basic ratio calculation. Then you calculate the ratio of planetary gear situation where differential’s input is input, output you calculate is output and other output is locked. Ratio gives direct the torque allocation of current output.

Example 1: Centre Differential 44%-56%. Basic ratio u is this time same as ratio i in earlier example so u=9/7. First you check planetary gear equation to situation where planet carrier is input, sun gear A is output and sun gear B is locked, so you get that allocation to front is Front%=1/(1+u)x100%=1/(1+9/7)x100%=43,75%. (Looks same as in earlier example.) Allocation to rear is situation where planet carrier is input, sun gear B is output and sun gear A is locked so Rear%=1/(1+1/u)x100%=1/(1+7/9)x100%=56,25%. (Looks different but it’s actually same equation in different form.)

Example 2: Interaxle Differential 57%-43%. Basic ratio is same as in earlier example so u=7/3. First you check planetary gear ver II equation to situation where sun gear B is input, planet carrier is output and sun gear A is locked, so you get that allocation to front is Front%=(u-1)/u x100%=(7/3-1)/(7/3)x100%=57,14%. Then you check situation where sun gear B is input, sun gear A is output and planet carrier is locked so allocation to rear is Rear%=1/u x100%=3/7x100%=42,86%.

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