# Using Spur Gear Hobs For Trapezoidal Roughing Hobs

Many manufacturers prefer to use roughing hobs with a trapezoidal profile to rough straight side splines in part because it is less expensive to manufacture the tools.

Many manufacturers prefer to use roughing hobs with a trapezoidal profile to rough straight side splines in part because it is less expensive to manufacture the tools. Unlike hobs with two-radius sides, trapezoidal hobs require no special machines to generate the tooth forms. It does take some expertise to design the tools, however, which is why Mark Grizotsky, owner of MLG Tool Design (Willowdale, Ontario), developed a computer program to help generate hob tooth profile data.

According to Mr. Grizotsky, some kinds of splines lend themselves to clever manipulations of the data. For example, some shafts have a diametral pitch and circular pitch exactly the same as spur gears if the outside radius of the splined shaft is substituted for the pitch circle radius. This outside diameter of the splined shaft will be equal to the pitch diameter of a spur gear (in inches) with the same diametral and circular pitch. The difference will be very small—0.5 to 2 percent—and thus has no influence on the calculation of other elements of the hob teeth.

The splined shafts shown in the table can thus be roughed by hobs designed for worm and spur gears with the same diametral and circular pitch. However, the spur gear hob tooth profile will subsequently have to be ground and relieved to the profile of the trapezoidal hob tooth because in most cases the gear hob tooth is larger than that of the trapezoidal hob. Nevertheless, because spur gears are so widely manufactured, hob users will benefit from the economies of scale and have supply alternatives for emergency situations.

An example illustrates how the design process works. The spur gear and trapezoidal hob teeth will have to be drawn on separate pieces of tracing paper for comparison. Take, for example, the third splined shaft in the table below where P = 10, D = 1", N = 10, d (inside diameter) = 0.8585", W (width of splines) = 0.150" and allowances are applied for grinding the inside diameter and the widths. Once this data is entered into Mr. Grizotsky's program, it will automatically generate the hob profile tooth angle as well as the hob tooth thickness on pitch line and profile depth from pitch line to the inside radius with allowance. Then a drawing is made in a scale of 20:1.

The next step is to measure the elements of the spur gear hob tooth that are used for grinding—tooth thickness, addendum, and angle degree. These elements also can be calculated to plot a 20:1 scale drawing.

Now the trapezoidal hob tooth profile drawing is laid on the spur gear hob tooth profile to match symmetrical axes and inscribe one tooth into another. The composite drawing shows how much material will have to be ground from the spur gear profile to impart the proper size and shape of the roughing hob teeth. Note that the distance between centers of the splined shaft to the hob has to equal the OD radius of the splined shaft plus the pitch radius of the hob.

Graphical checks show that these hobs provide allowances very close to parallel with the spline's width, they have the circular pitch of a spur gear but the profile shape of a trapezoidal roughing hob.

Mr. Grizotsky also points out that the roughing of two-radius side hobs can be produced from spur gear hob profiles as well because these hobs have the same tooth thickness as trapezoidal roughing hobs. But regardless of which kind of hob is used, it is best to make graphic checks and tests by hobbing samples.

These nine pitch splined shafts are popular American standards. "N" refers to the number of splines per shaft (or teeth for spur gear) and is generated by the formula N = P x D. "P" is the diametral pitch, and "D" is the OD in inches of the splined shaft (or pitch diameter of the spur gear).

Metric versions of the group are also found in European and Japanese standards, known as module splined shafts. They are calculated by the formula
N = D/M where M is module in millimeters.

 P D N 6 1 6 4 1.5 6 10 1 10 8 1.25 10 5 2 10 4 2.5 10 16 1 16 8 2 16 4 4 16