productivity is of many kinds:

Time productivity:  CNC is faster being Integrated.

Money Productivity: CNC is more automated , and hence higher Money Productivity

Tool productivity:   CNC is more technologically poised hence higher Tool productivity

Quality: : Because of  more automation CNC produces better quality

In context with smart hypoid gear having some involute properties which means robustness for the shaft misalignment. you may look for Tool productivity, quality, and consider elastic deflections

http://www.geartechnology.com/subjects/CNC&sort=date

What kind of material do you need work for obtain the hypoid gear?

good question...for Mr Park... to ensure robustness.

need help?

I consider it for the usage of automobile. So it may be steel.

I have the imaginary common rack for the generation of hypoid gear set.

So I guess some optimal tool pathing algorithm could be made. And then  it would cause productivity improvement, I think.

For mass or large size batch production it is not. In such case Hobbing or dedicated machines are more productive.

If you want to make one of (i.e one or few parts) then CNC machining is valid if you use the right tool and right machining path.

It does not depend on material type.

Best regards

As Ghassan said, the manufacturing technology depend of the size batch. For a little size you can use a 5 axis milling machine (if you want see this video: https://www.youtube.com/watch?v=KZupKP9igIs). The advantage of this technology is that  you can manufacture whatever gear geometry and reach a good quality level.

For mass production is normal to use especific machine. See this video please: https://www.youtube.com/watch?v=bojVO3KBOfg.

I totally agree with Daniel. Thanks Daniel for your exact answer.

@Nogill

 for the usage of automobile. .. may be steel.  Case carburised and heat treated? or else?

As you know current hypoid gear have been oriented a few companies such as Gleason Work and Kligenberg, etc. Then the gears are made by machine-based process.  I am developing mathematically the geometry. After finishing my first work, I will concern how to machine it effectively. But it would be too big job to me. However, first of all, I would like to know what's going on if my gear is made by 5-axis CNC machine. Hopely, if my imaginary common rack behaviors are geniously considered in developing to make tool path coding, some ecconomically reasonable productivity can be obtained.

Anyway I appriciate your kind advices.

Newly, I think that the better machine for make this part is a 5 axis milling machine. The type of 5 axis machine is RRLLL (rotating, rotating, lineal, lineal, lineal).

Dear Nogill:

I have successfully used 4-axes milling machine center (MAHO-DECKEL type) to produce high precision spiral bevel gear set.

In the case that no dedicated type machine or the manufacturing of specialized gear set is available the only option is to use CNC milling and design you tool and tool path to do the job. 

Of course we cannot offer to buy a dedicated machine if we only want to produce several sets hence the answer to your question yes if you are planning to produce few sets. 

Using 5-axis milling machine  (as Daniel said in his answer above) gives you better flexibility to work out your tool path and perhaps the use of simpler tool geometry.

Best regards