Introduction to Gear Design

4 What Should They Look Like?

4.1 Mounting Characteristics

No matter how much care is taken in the design and manufacture of gears, they are sure to fail if improperly assembled or inadequately mounted. Many “gear” problems are caused by lack of attention to the accuracy required in machining the housing, in assembling the gears and bearings to the shafts, and in aligning the sub-assemblies. The author knows of gearboxes that, after giving 30 years of excellent service, have failed within hours of “field” rebuilding by inexperienced mechanics. If you are not sure how to handle a particular aspect of a design or maintenance project, ask for help or check the reference books listed in this manual. Most bearing manufacturers will be happy to review your drawings and bearing selections at little or no charge. If your gear supplier has an engineering department, they may also be available to “consult” on your design project or to train your maintenance and assembly people in proper methods of handling and adjusting gears.

4.2 Backlash

Backlash is one of the most misunderstood concepts in gearing. An individual gear cannot have backlash — it can only have a tooth thickness. Backlash occurs when gears are mated together on a given center distance and the sum of their tooth thicknesses is less than their circular pitch. The backlash of a pair of gears will vary at some points in the rotational cycle due to run-out and cutting inaccuracies. If the center distance is increased the backlash will increase; if it is reduced the backlash will decrease. Don’t confuse “low backlash” with “high quality”. Except for applications that require positioning accuracy, such as index tables or radar drives, or that are subject to frequent reversing loads, “too much” backlash seldom effects gear performance. Not having enough backlash can result in the gears “binding” under some conditions, especially at low temperatures when steel gears are used in an aluminum housing. Gears that bind are certain to fail.

When low backlash is required, the best approach is to use “anti-backlash” gears or adjustable centers (see Figure 4.1). Tight tolerances on tooth thicknesses and center distances are seldom effective and can be very expensive. Anti-backlash gears consist of two gear halves that are spring loaded to adjust the “effective” tooth thickness to fill in the space available on the mating part. These gears are not used to transmit significant amounts of power, as the required spring pressures become hard to obtain in the space available. Adjustable centers can handle slightly higher loads but are expensive to manufacture. The reference books discuss “backlash” extensively and some manufacturers include a limited range of anti-backlash gears for instrument use in their catalogs.

4.3 Blank Tolerancing

The difference between a “good” gear and a “bad” one can often be traced to how accurately the blank was machined. In a production run of gears, for example, those having bores close to the low limit (or maximum material condition) will fit the cutting arbor more snugly and usually exhibit the least “run-out”. If gears are to be cut in a “stack” the perpendicularly of the blank sides to the bore will similarly influence the results. It is important to “match” the tolerancing of those part features — which will be used for work-locating during the machining process — to the accuracy needed in the final part. Your gear supplier may have some specific requirements in this area, but the values shown in Tables 4.1 to 4.3 are a good place to start.

Table 4.1: Typical Gear-Blank Tolerances

(Courtesy of Quaker City Gear Works)

AGMA	Q6	Q7	Q8	Q9 & Q10	Q11 & up
Diameter of Bore	.002	.001	.0007	.0005	.0002
Taper of Bore (No portion to exceed tolerance)	.001/in of length Max .002	.0007/in of length Max .001	.0005/in of length Max .0007	.0003/in of length Max .0005	.0002
Concavity of Mounting & Register Surfaces	.001/in of radius for rigid blanks .0005/in of radius for flexible blanks Total .003			.0005/in of radius for rigid blanks .0003/in of radius for flexible blanks Total .0015
Convexity of Mounting & Register Surfaces	None for any class
Lateral Runout of Bevel & Face Gears	.001/in of radius Max .002	.0008/in of radius Max .0016	.0005/in of radius Max .001	.0004/in of radius Max .0008	.0003/in of radius Max .0005
Lateral Runout of Spur & Helical Gears	.002/in of radius Max .004	.0015/in of radius Max .0025	.001/in of radius Max .002	.0007/in of radius Max .0015	.0005/in of radius Max.001
Non-Parallelism	.002/in of radius Max .004	.0015/in of radius Max .0025	.001/in of radius Max .002	.0007/in of radius Max .0015	.0005/in of radius Max.001

Table 4.2: Outside-Diameter Tolerances

(Courtesy of Quaker City Gear Works)

(a) Runout of Outside Diameter with Bore or Centers

Diametral Pitch	AGMA Q5 TO Q8	AGMA Q9 & up
1 – 4	0.015	0.009
5 – 8	0.010	0.006
9 – 13	0.006	0.004
14 – 19	0.004	0.003
20 – 39	0.003	0.002
40 – 79	0.002	0.0015
80 & finer	0.001	0.001

(b) Tolerance of Outside Diameters

D.P.	+0	D.P.	+0
3	−0.020	40	−0.005
5	−0.015	48	−0.004
8	−0.010	64	−0.003
10	−0.008	72	−0.003
12	−0.007	80	−0.002
14	−0.007	96	−0.002
18	−0.007	120	−0.002
20	−0.007	124 & up	−0.001
32	−0.006

Table 4.3: Gear-Blank Standards

(Courtesy of Quaker City Gear Works)

Outside Diameter Tolerances:

Straight-Bevel Gears — All Classes

D.P.	Tol. ±.000
20 – 30	−0.005
31 – 40	−0.004
41 – 56	−0.003
57 – 94	−0.002
95 & finer	−0.001

Back-to-Corner Tolerances:

Bevel Gears

D.P.	Tol. ±.000
20 – 46	−0.002
47 & finer	−0.001

Back-Angle Tolerances — Bevel Gears:

±1°

Surface Finishes — All Types and Classes:

Machine Finish:

max. 125 Micro

Grind Finishes by Tolerances:

0.0000 – 0.0002	8 Micro
0.0002 – 0.0005	16 Micro
0.0005 – 0.0010	32 Micro

Threads:

All units to be chamfered for:

141 ⁄2° P.A.	15°
20° P.A.	20°
60° P.A.	30°

Radii:

Sharp corners to be broken to 0.005 – 0.015⁰⁰ radius.

Decimals:

0 – 6⁰⁰	±.005
6 – 12⁰⁰	±.010

Angular:

±1 ⁄2°

Thread Tolerances:

Class 2 fit

Flatness:

Mill Standard

Concentricity of Bearing Journals:

Concentricity of bearing journals, in respect to true center of part, shall be held within the total tolerance of bearing journal diameter size.

Examples:

• Bearing diameter size .125 ± .0003
• Concentricity to true centerline .0003 T.I.R.
• Bearing diameter size .500 ± .0005
• Concentricity to true centerline .0005 T.I.R.

4.4 Quality Classes

Selecting the proper quality class for a particular application is one of the most controversial areas of gear design. AGMA has provided a chart in AGMA 2000 (formerly AGMA 390.03) that can be used to select the quality level needed. Many of the texts listed in the reference section of this guide have additional information on this topic. Quality level should be a function of application, power level, and operating speed. Table 4.4 is the author’s suggestion for minimum quality level vs. maximum pinion pitch-line velocity when relatively smooth applications are considered.

\( \left (\frac {\text {Peak Load}}{\text {Nominal Load}} \, \mathbf {\leq } \, 1.25 \right ) \)

\( \text {\acro {PLV} in \si {\foot \per \minute }} = \text {pitch diameter} \times .262 \times \text {revolutions per minute} \)

It is very important to remember that increased quality levels cost money. If you want cost-effective designs you must resist the urge to “solve” your gear problems by over-specifying quality levels. Even the “best” gears will fail if they are not mounted accurately, or properly sized for the load and system dynamics. Table 4.5 shows the quality levels normally achievable for various gear elements by modern manufacturing techniques. The column on “relative cost” reflects not only the additional time and effort needed to make the gear teeth, but also the extra expense of increased blank accuracy.

Table 4.5: Achievable AGMA 2000 Quality Levels by Manufacturing Method

Manufacturing		Involute		Spacing	Relative
Method	Run-out	Profile	Lead	(Pitch)	Cost
Hobbing (Class b Hob)	8 to 10	8 to 9	8 to 9	8 to 9	1.0 to 1.25
Hobbing (Class a Hob)	9 to 11	8 to 9	9 to 11	8 to 10	1.25 to 1.5
Hobbing (Class aa Hob)	9 to 12	8 to 11	9 to 11	9 to 11	1.5 to 1.75
Shaping (Commercial Cutter)	8 to 10	8 to 10	8 to 11	8 to 10	1.25 to 1.5
Shaping (Precision Cutter)	9 to 11	9 to 10	9 to 11	9 to 11	1.5 to 1.75
Shaving	10 to 12	8 to 10	8 to 12	8 to 12	2.0 to 2.5
Grinding	9 to 14	9 to 14	8 to 14	9 to 14	3.0 to 4.0

Notes:
1: Lower quality levels are generally achievable under most conditions.
2: Upper quality levels require special controls on blanks, tooling, and machinery. This can increase costs significantly.
3: Relative costs compared to Class b hobbing for operations needed to finish gear teeth only. Material and heat-treat costs are not included in this comparison.
4: If heat treating is done after tooth finishing, quality level can drop by two levels or more.

4.5 Surface Finish

The surface finish of gear teeth is another controversial aspect of gear design. One common misconception is that specifying an AGMA quality class also specifies a tooth-surface finish. AGMA 2000 does not include surface finish in its tolerancing. Table 4.6 shows the surface finishes normally produced by common production methods. Comparing this table with the one on quality vs. production method (Table 4.5) shows that there is an indirect relationship between “quality” and “surface finish”.

Table 4.6: Achievable Tooth-Surface Finishes by Manufacturing Method

Tooth	Effort
Size	Required	Hobbing	Shaping	Shaving	Grinding
1 to 3 dp	Normal	125	80 to 125	63	32
	Extra	80	80	32	16
3 to 10 dp	Normal	80	63 to 80	63	32
	Extra	63	63	32	16
10 to 24 dp	Normal	80	63 to 80	50 to 32	32
	Extra	63	63	16	16
24 to 40 dp	Normal	80	63	50 to 32	32
	Extra	63	63 to 32	16	16
40 dp and up	Normal	80	63	not practical	32
	Extra	63	63 to 32	not practical	16

Notes:
1: Normal effort involves typical production feeds and speeds.
2: Extra effort involves special controls and procedures on tools and machines. Cycle time may increase significantly.
3: Finishes shown are for through-hardened steel of 230 – 310 bhn.
4: Finish may be poorer on steel below 230 bhn or above 310 bhn.
5: Surface finish may be slightly better in brass, bronze, aluminum, or stainless steel, provided proper feeds and speeds are selected.
6: Surface finish for surface-hardened gears that are not finished after heat treating may be slightly worse due to scale-removal operations.

When you specify a tooth surface finish (Table 4.7) you are often requiring costly gear-finishing processes (Table 4.8) that do not increase “quality” as defined by AGMA 2000. It is important to satisfy yourself, by studying whatever information is available (or through field testing), that you need a particular finish to meet your performance objectives. Surface finish has an effect on lubricant film-thickness requirements. While no consensus “standard” has been published on what lubricant viscosities are needed with what surface finishes, it is clear that heavier oil is needed when coarser finishes are present. The use of the heavier lube may or may not be possible in some applications due to cold-starting conditions, thermal considerations, or other issues.

\( \sqrt [\uproot {4}\leftroot {4}1,000]{} \)

\( \sqrt [\uproot {4}\leftroot {4}500]{} \)

4.6 Blank Design

One thing that all gear experts agree on is that you can’t make a good gear from a bad blank. “Bad” doesn’t just mean poor workmanship: it also refers to poor design or poor tolerancing. A good way to prevent these problems is to become familiar with the processes used to make gears and make provisions in the design of the part to use those processes to your advantage. Once you understand the manufacturing techniques you’ll be able to determine which parts of your gear system are likely to be problems while there is still time to make design changes. This is a good time to remember the old adage “If it looks right it probably is.” Many gear problems are really “proportion” problems. Long spindly shafts, large gears with small rim or web thicknesses, inadequate housing supports, and poor “packaging” have caused more “gear failures” than anyone cares to count. Take a careful look at the general “appearance” of your design before making the final drawings.

4.7 Tooth-Form Selection

One of the first steps in designing a gear is the selection of the tooth form to be used. To a certain extent this decision is based upon rating requirements, but the choice made will also effect the manufacturing processes used. Table 4.9 shows the “popular” tooth forms in use today. There are many other forms available, and each has its proponents. The author urges caution on the part of anyone who is thinking of using a tooth form not on Table 4.9, as the availability of cutting tools will be limited. The actual variation in tooth strength from one form to another is slight. For critical applications tooth form might make the difference between success and failure, but those instances are rare, and should be left to the “real experts.” Unless very low numbers of pinion teeth are involved, the author sees little need to use anything other than 20 full-depth teeth on new designs. If low numbers of pinion teeth (< 20) are needed, 25 full-depth is the best choice. When making modifications to existing designs, you may have to work with the other forms shown on Table 4.9, but they should be considered “obsolete” for new designs.

Maximum	Minimum-Suggested
plv in ft/min	AGMA Quality Level
250	6
500	7
1500	8
2500	9
3500	10
5000	11
7500	12
10000	13

Symbol	Description
$\sqrt [\uproot {4}\leftroot {4}1,000]{}$	Indicates that the surface is very rough and uneven within the dimensional requirements.
$\sqrt [\uproot {4}\leftroot {4}500]{}$	Indicates that the surface is rough and uneven within the dimensional requirements.
$\sqrt [\uproot {4}\leftroot {4}250]{}$	Indicates that the surface must be smooth and even to a degree obtainable by tools removing large chips or shavings. Machining marks and grooves discernible to the eye and to touch are permitted, if the surface meets dimensional requirements.
$\sqrt [\uproot {4}\leftroot {4}125]{}$	Indicates that the surface must be smooth and even to a degree obtainable by tools removing medium chips or shavings. Machining marks and grooves discernible to the eye are permitted, if the surface meets dimensional requirements.
$\sqrt [\uproot {4}\leftroot {4}63]{}$	Indicates that the surface must be smooth and even to a degree obtainable by tools removing small chips. Machining marks and grooves discernible to the eye are permitted, if the surface meets the dimensional requirements.
$\sqrt [\uproot {4}\leftroot {4}32]{}$	Indicates the surface must be smooth and even to a degree obtainable by tools removing small particles. Machining marks such as grooves must not be discernible to the eye or touch, if the surface meets the dimensional requirements.
$\sqrt [\uproot {4}\leftroot {4}16]{}$	Indicates that the surface must be very smooth and even to a degree obtainable by tools removing very small particles. Machining marks such as grooves must not be discernible to the eye or touch, if the surface meets the dimensional requirements.
$\sqrt [\uproot {4}\leftroot {4}8]{}$	Indicates that the surface must be even to a degree obtainable by tools removing minute particles, generally by grinding. Machining marks such as the fine patterns resulting from grinding must not be discernible to the eye or touch and the surface must have a polished appearance and meet dimensional requirements.
$\sqrt [\uproot {4}\leftroot {4}4]{}$	Indicates that the surface must be even to a degree obtainable by tools removing very minute particles, generally by honing, lapping, or super-finishing. Machining marks such as very fine patterns must not be discernible to the eye or touch and the surface must have a highly polished appearance and meet dimensional requirements.

Symbol	Quality class	Description	Max. rms value, micro in.	Suitable range of total tolerance	Typical fabrication methods	Approx. relative cost to produce
$\sqrt [\uproot {4}\leftroot {4}1,000]{}$	Extremely rough	Extremely crude surface produced by rapid removal of stock to nominal dimension	1,000	0.063 – 0.125	Rough sand casting, flame cutting	1
$\sqrt [\uproot {4}\leftroot {4}500]{}$	Very rough	Very rough surface unsuitable for mating surfaces	500	0.015 – 0.063	Sand casting, contour sawing	2
$\sqrt [\uproot {4}\leftroot {4}250]{}$	Rough	Heavy toolmarks	250	0.010 – 0.015	Very good sand casting, saw cutting, very rough machining	3
$\sqrt [\uproot {4}\leftroot {4}125]{}$	Fine	Machined appearance with consistent toolmarks	125	0.005 – 0.010	Average machining — turning, milling, drilling; rough hobbing and shaping; die casting, stamping, extruding	4
$\sqrt [\uproot {4}\leftroot {4}63]{}$	Fine	Semi-smooth without objectionable tool marks	63	0.002 – 0.005	Quality machining — turning, milling, reaming; hobbing, shaping; sintering, stamping, extruding, rolling	6
$\sqrt [\uproot {4}\leftroot {4}32]{}$	Smooth	Smooth, where toolmarks are barely discernible	32	0.0005 – 0.002	Careful machining; quality hobbing and shaping; shaving; grinding; sintering	10
$\sqrt [\uproot {4}\leftroot {4}16]{}$	Ground	Highly smooth finish	16	0.0002 – 0.0005	Very best hobbing and shaping; shaving; grinding, burnishing	15
$\sqrt [\uproot {4}\leftroot {4}8]{}$	Polish	Semi-mirror-like finish without any discernible scratches or marks	8	0.0001 – 0.0002	Grinding, shaving, burnishing, lapping	20
$\sqrt [\uproot {4}\leftroot {4}4]{}$	Super-finish	Mirror-like surface without tool grinding or scratch marks of any kind	4	0.00004 – 0.0001	Grinding, lapping, and polishing	25

	Normal
Tooth	Pressure	Whole			Fillet	Circular
Form	Angle	Depth	Addendum	Dedendum	Radius	Pitch
Full Depth	14.5°	2.157	1.00	1.157	0.21	3.1416
Full Depth	20°	2.157	1.00	1.157	varies	3.1416
Full Fillet	20°	2.250	1.00	1.250	0.30	3.1416
Pre-Shave or Pre-Grind	20°	2.350	1.00	1.350	0.30	3.1416
Stub	20°	1.800	0.80	1.000	0.20	3.1416
Full Depth	25°	2.250	1.00	1.250	0.25	3.1416
Full Fillet	25°	2.300	1.00	1.300	0.30	3.1416
Fellows Stub (x ⁄ y)	20°	2.25 ⁄ y	1.00 ⁄ y	1.25 ⁄ y	varies	3.1416 ⁄ x
Nutall	20°	1.728	0.79	.943	varies	3.1416