Commonly found automobile differentials have a reduction ratio of 6 at max. This is because designing an automotive differential with a reduction ratio greater than 6 may lead to a bulky design which isn’t feasible to position with the limited space available. Furthermore, increasing the size of the differential may lead to excessive undesired weight. Most on-road vehicles have differentials with reductions of 3 or 4. Commercially speaking, finding a differential with a reduction greater than 6 is close to impossible. Most manufacturers would introduce an additional single speed gearbox however this would over complicate the design and increase servicing costs. The aim of this paper is to design a differential with a reduction ratio greater than 6. The paper includes all the calculations as well as a strength based analysis performed on Altair-Hypermesh, to prove the success of the design. 
Worm gear Operated Differential gearbox
Worm gear Operated Differential gearbox
We shall now design a differential using a worm gear reduction around the miter gear set. This is inspired from the “Napier Worm Gear Drive” invented by the British “Napier and Sons” before the First World War. The company was later consumed by “English Electric” however their concept of a worm drive seems very promising.  
Input Parameters 
Input power:   5.8913 kW 
Input Speed:   4100 rpm 
Input Torque:   13.7231 Nm 
Reduction Ratio Reqd.:   7:1 
Design Objective 
To design a differential offering a reduction ratio of 7 (7:1). It reduces output speed 7 times and multiplies output torque 7 times. 
Material Selection 
Alloy Steel – 15Ni4Cr1 
Sut = 1500 N/mm2 BHN = 650 
This selection is based on the design of worm gears as well. The aim is to use as few different materials so as to be able to make maximum use of recyclable metal scrap. The worm is case hardened alloy steel (15Ni4Cr1) and worm wheel (which should be always be made of a more ductile material than worm) is made of Phosphor Bronze.
• Compact. 
• Light weight. 
• Reduction ratio of even 20:1 is possible by this method. 
• Worm shaft is placed higher in this arrangement near the underbelly of the chassis  thus less prone to damage. 
• Entire structure is centralized in terms of mass & since C.G. is in the center the positioning is easier. 
• The entire differential offers rotational flexibility about the drive axle axis thus the worm shaft can be tilted at any angle without any trouble or complications. This will not affect the design calculations nor increase design complexity. 
• Limited efficiency at best up to 95%.  
• Due to poorer efficiency, temperature rise must be within permissible limits or else seals may get damaged. Also excessive temperature could lead to tooth failure due to seizure. 
• The entire system is made of two metals. The worm wheel normally has to be made of a more conformable metal (such as Phosphor Bronze). This may increase costs. 
• If the gearing size requirement is larger (for increased torque transmitting capacity), height increases. 
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