Application considerations

The preliminary design step helped to determine the estimated values for parameters such as number of teeth, diametral pitch, pressure angle and helix angle. The detailed design step, that will be discussed in clause 6, will optimize the specific tooth geometry in order to meet the functional requirements. As mentioned previously, the three main types of gear systems are power gears,

smooth motion gears and zero backlash gears.

This clause will discuss some of the specific requirements of each of these systems. It is important to keep in mind that many applications have requirements that overlap into more than one of these classifications.

5.7.1 Design emphasis for power gear systems

As the name suggests, the primary function of power gear systems is to transmit power (speed and torque). This does not mean that the gears transmit only heavy loads, but that greater impor- tance is given to transmitting power than to transmitting uniform motion. The design process for power gears emphasizes adequate size, suit- able materials, appropriate heat treat procedures and proper lubrication to maximize gear life. Designers usually evaluate the resistance of the gears to pitting and bending fatigue. It is important to note that the designers must also recognize life--cycle costs, noise and other related parameters during the design process.

5.7.2 Design emphasis for smooth motion gears

In addition to the requirements of power gear systems, smooth motion gears are designed to have low transmission error. Transmission error is defined as the deviation of the position of the driven gear, for a given angular position of the driving gear, from the position that the driven gear would occupy if the gears were geometrically perfect and infinitely

stiff. Transmission error is usually measured as a linear error along the line of action.

Generally, transmission error in gear meshes has the following two components:

-- Once per revolution of the gear(or pinion) variation;

-- Once per tooth variation.

The once per revolution variation is due to accumu- lated pitch variation. The once per tooth variations are due to variations in profile, pitch, tooth thickness and tooth alignment. The above two components affect the positional accuracy of the drive train. In addition, the once per tooth component is related to the noise and vibration characteristics of the gear train.

The main sources of transmission error can be classified into the two following categories:

-- Variations during manufacturing and mounting;

-- Deflections of gear teeth, shafts, bearings and housing.

Parameters such as transverse contact ratio and face contact ratio influence load sharing between the gear teeth and thus affect the deflections of the gear teeth. Deflections of shafts, bearings and housings can cause an uneven load distribution across the face of the gear tooth. Calculating transmission error based on the above gear param- eters is beyond the scope of this design manual. However, this clause will discuss those variations that contribute to transmission error.

Total transmission error for a gear train can be calculated by assuming that the total transmission error is the sum of the transmission error of each mesh. However, such a technique yields very high transmission error values. Multi--mesh gear trains should be analyzed using statistical techniques to determine a more realistic value.

The sources of transmission error are discussed in 5.7.2.1 and 5.7.2.2, and techniques for minimizing transmission error are briefly discussed in 5.7.2.3.

5.7.2.1 Manufacturing variation

Some of the possible sources of these errors are: -- Eccentric mounting of the gear blank or the generating tool or both;

-- Runout in the gear blank mounting arbor or tool arbor or both;

-- Variations in the hob;

-- Tooth--spacing error in the shaper cutter; -- Position errors in the gear generator’s indexing gear train;

-- Effect of approximating the involute profile with generated straight cuts;

-- Vibration and chatter of the machine tool; -- Deflection due to the work mass and cutting forces;

-- Deformations of the gear blank;

-- Non--homogeneous gear blank material; -- Differential temperature effects;

-- Slippage of the blank on the arbor;

-- Errors in the dressing of the wheel profile for profile ground gears.

5.7.2.2 Assembly variation

Shaft misalignment causes uneven load distribution and higher tooth fillet stresses in gears. Uneven load distribution results in larger transmission error. Misalignment between shafts can cause the shaft couplings to transmit non--uniform motion. Another contributor of transmission error comes from mounting runout that causes the gear true center to be displaced from the center of rotation. Some of the sources of runout are:

-- Clearance between gear bore and shaft; -- Runout of the shaft;

-- Eccentricity of the rotating race in the ball bearing.

5.7.2.3 Minimizing transmission error

Minimizing the once per revolution component of transmission error is best achieved by minimizing accumulated pitch error. Minimizing the once per tooth component is achieved by controlling tooth form. Gear meshes with larger contact ratios exhibit lower tooth to tooth transmission error because they have more tooth pairs sharing the load. Hence it is recommended that gear designers maximize con- tact ratio when designing gears for smooth motion. Tooth modifications (tip relief and root relief) and tooth lead modifications (crowning) are techniques that have been applied successfully under certain conditions to minimize transmission error. When designed for a specific load condition, these are

suitable for only that load condition. It is recom- mended that an experienced gear designer be consulted when designing gears with profile and lead modifications.

5.7.3 Zero backlash gears

In addition to the requirements of power gear systems, zero backlash gear meshes are designed to have low backlash. Backlash is necessary to prevent tight mesh and interference due to manufacturing and assembly variations in a gear. In some applications, backlash needs to be controlled to achieve accurate angular positioning of machine components. Many techniques have been devel- oped to control backlash in a gear mesh. Clause 7 of this Design Manual deals with those techniques for controlling backlash in a gear mesh.

6 Design synthesis and analysis

6.1 Introduction

Clause 5 introduced the gear designer to basic considerations for the early conceptualization of a gear design. The selection of type of gearing and preliminary values for number of teeth, diametral pitch, helix angle and number of stages may be very simple or exceedingly complex. The function of the design and the size of the design space influence the options available to the designer. Clause 5 presented general guidelines and the most basic procedures but could not offer a complete cookbook approach because the number of options available at the preliminary stage is far too large. Therefore, it is assumed that first estimates of number of teeth, diametral pitch, pressure angle, helix angle and number of stages will be made using clause 5 as well as other sound mechanical engineering practices.

Clause 6 presents procedures by which the design- er can determine, refine and analyze the details that comprise a complete gear design. This optimization of the design may result in only minute modifications to the original concept or it may identify the need for major redesign. In either case, the proper function and life of the gear system depends upon the optimization being done with knowledge and thoroughness.

The information presented in clause 6 is rigorous mathematically and may be somewhat intimidating to the novice gear designer. It may be beneficial to remember that an involute gear tooth is a combina- tion of four geometric sections: top land, flanks, trochoid or root fillet and root circle. Within certain limits, these sections are independent of one another and each can be varied without necessarily affecting the others. For example, within certain limits, the tip diameter can be made larger or smaller without changing the tooth thickness. Standards, such as ANSI/AGMA 1003--G93, Tooth Proportions

for Fine--Pitch Spur and Helical Gearing, define

relationships between the tooth sections based upon the concept of a basic rack. However, without violating the precepts of the standard, the designer has freedom to optimize the design by specifying gear parameters.

The specifics of tip diameter, tooth thickness and root diameter are what gear optimization is all about. Clause 6 presents the procedure for accomplishing that optimization. The procedure is presented in a logical order for making the calcula- tions, i.e., the inputs needed for a given calculation have been calculated previously. Most gear practitioners use a form of spreadsheet to perform these calculations, and the sequence of clause 6 will make constructing a spreadsheet a relatively simple undertaking.

6.2 Standard gear parameters