BM Machine Shop, LLC

The Barber-Colman 6-10 through 16-56 Gear Hob Machines are specialized equipment utilized for the precise cutting of helical gears, in this case, without the need for a differential mechanism. These machines are renowned for their exceptional precision and efficiency in the gear manufacturing industry.

Symbols:

F	=	feed in inches per revolution of work
K	=	machine index constant
L	=	lead of helix (inches)
M	=	machine feed constant
N	=	number of teeth on gear
R	=	index gear ratio
T	=	number of threads on hob
C	=	C constant
pₙ	=	normal circular pitch
ψ	=	helix angle of work

The C constant is defined as the number of revolutions of the work spindle per one axial pitch of the workpiece. Its primary purpose is to establish a precise relationship between the index and feed change gears, thereby ensuring the accurate cutting of the desired helix angle. Mathematically, it can be represented through the following equation.

C =	pₙ
	F sin(ψ)

The basic formula for figuring index change gears is.

Index gear ratio =	KCT
	(CN) ± 1

Example:

To demonstrate the practical application of the fundamental formulas, the following gear, hob, and machine specifications shall be utilized as an example.

Machine – Barber-Colman No. 16-16 with single-thread index worm

Machine index constant – 30

Machine feed constant – .075

Approximate feed/revolution – .030"

Number of teeth on gear – 30

Diametral pitch – 10

Normal circular pitch – .314159

Helix angle of gear – 10° 30'

Lead of helix on gear – 51.7175

Number of threads on hob – 2

Thread angle of hob – R. H.

Hand of helical gear – Right

Direction of cut – Climb

C =	pₙ
	F sin(ψ)

=	.3142
	.03 x .18223

= 57.4

Given that the result serves as an approximation in determining the index change gears, a whole number that yields factorable numerator and denominator for the selection of appropriate change gears shall be employed. In this case, the number 57 has been chosen as it satisfies this criterion.

Choose the sign for the denominator based on the following chart.

Sign for denominator
Hob	Gear	Direction of cut	Sign
RH	RH	Conventional	-
RH	RH	Climb	+
RH	LH	Conventional	+
RH	LH	Climb	-
LH	LH	Conventional	-
LH	LH	Climb	+
LH	RH	Conventional	+
LH	RH	Climb	-

Index gear ratio =	KCT
	(CN) ± 1

=	30 x 57 x 2
	(57 x 30) + 1

=	3420
	1711

57 x 60 = 3420

59 x 29 = 1711

57/59 x 60/29

The fundamental equation for determining the feed change gears is as follows:

Feed gear ratio =	p_n
	C sin(ψ) M

=	.314159265
	57 x .1822355 x .075

= .403255881387

In order to convert the feed ratio into functional change gears, a specialized program such as Decimal to Change Gears could be employed. Upon installation, the value of .403255881387 should be entered to obtain the desired results. The outcome of this calculation will yield the change gears of 34/86 x 51/50, with a minute error of -0.0000000674. The lead error, computed over a length of 51.717566788 inches, is -0.000008648 inches.

Use this chart to select intermediate studs for Barber-Colman 6-10 through 16-56 machines.

Index and Feed intermediate studs
				Intermediate studs
Hob	Gear	Direction of cut	Sign	Index	Feed
RH	RH	Conventional	-	1	1
RH	RH	Climb	+	1	2
RH	LH	Conventional	+	1	1
RH	LH	Climb	-	1	2
LH	LH	Conventional	-	2	2
LH	LH	Climb	+	2	1
LH	RH	Conventional	+	2	2
LH	RH	Climb	-	2	1

Specialized Windows programs, designed for the purpose of determining change gears, are available for download. These programs have specific system requirements, including a minimum of 1 gigabyte of available memory and a modern CPU.

Download link -- Windows 10 and 11 -- x86, x64, arm, and arm64

Same as above from the Microsoft Store

For users running older versions of Windows, a separate download is provided.

Download link