I am in the process of designing guitar tuning machines and I am looking to hire someone to design the worm and gear. I hired an engineer already, but he proved very difficult to work with and the gear set he designed did not work correctly as there was interference between the worm and gear for about 180 degrees or worm rotation. He attempted to model a double enveloping set, but I would like to change this to a cylindrical worm and globoid gear for ease and cost of manufacturing. If anyone is interested, I can send the parameters for the gear set. I have attached the design of the first gear set here to give you an idea of the basic dimensions. I only need the gear set and I can create the shaft, threads, etc. Obviously I am not an engineer so the terminology may not be 100% accurate. Thanks for any help with this.
I'm just speculating, by looking at the worm, that the interference may have been caused by the worm not being extended far enough along the length of the shaft. The type of worm and worm wheel that you show has a shape designed to more fully envelop the gear teeth compared to a straight diameter worm and gear. The design provides more contact but can make alignment more critical than a constant diameter worm. It probably costs more.
Find a gear manufacturer give them your specifications. They probably have an in house program to output the parameters you desire.