MECHANICAL DRIVES 1 LEARNING ACTIVITY PACKET SPUR GEAR DRIVES BB502-XD06AEN
LEARNING ACTIVITY PACKET 6 SPUR GEAR DRIVES INTRODUCTION This LAP will begin the study of the third type of adjacent shaft-to-shaft power transfer drive, the gear drive. The gear drive was the first type of drive invented. It has been in use for thousands of years and is today used in a wide variety of applications from machine tool drives to computer printers. Gear drives are preferred over belts and chains for applications that require either very high speeds, very high loads, very high gear ratios, or compact gear reduction. Gears also allow the direction of rotation to be reversed and shafts to be turned at right angles. A final advantage of gears is that they do not slip, making them ideal for synchronizing applications. Although there are many types of gear drives, the spur gear is the most common because it is low in cost and easy to maintain. It is also the fundamental gear design from which all other gears are designed. This makes it a good type to use to teach the general concepts of the operation of all types of gears; therefore, this LAP will focus on spur gears. ITEMS NEEDED Amatrol Supplied 950-ME1 Mechanical Drives 1 Learning System Amatrol or School Supplied Assorted Hand Tools FIRST EDITION, LAP 6, REV. C Amatrol, AMNET, CIMSOFT, MCL, MINI-CIM, IST, ITC, VEST, and Technovate are trademarks or registered trademarks of Amatrol, Inc. All other brand and product names are trademarks or registered trademarks of their respective companies. Copyright 2014, 2012 by AMATROL, INC. All rights Reserved. No part of this publication may be reproduced, translated, or transmitted in any form or by any means, electronic, optical, mechanical, or magnetic, including but not limited to photographing, photocopying, recording or any information storage and retrieval system, without written permission of the copyright owner. Amatrol,Inc., 2400 Centennial Blvd., Jeffersonville, IN 47130 USA, Ph 812-288-8285, FAX 812-283-1584 www.amatrol.com 2
TABLE OF CONTENTS SEGMENT 1 GEAR DRIVE CONCEPTS...................................................... 4 OBJECTIVE 1 Describe the function of the three components of a gear drive system OBJECTIVE 2 Defi ne the gear pitch, pitch circle, and pitch diameter and explain their importance OBJECTIVE 3 Describe how to calculate the gear ratio of a gear drive SKILL 1 Calculate gear ratio SEGMENT 2 GEAR DRIVE DESIGNS....................................................... 15 OBJECTIVE 4 Describe how to calculate the shaft speed and torque of a gear drive system SKILL 2 Calculate the shaft speed and torque of a gear drive system OBJECTIVE 5 Describe the functions of four types of gear drives and give an application of each OBJECTIVE 6 List four types of parallel axis gears and give an application of each SEGMENT 3 SPUR GEAR DRIVE OPERATION............................................... 29 OBJECTIVE 7 Describe eleven features of a gear OBJECTIVE 8 Identify the twelve dimensions of a gear and explain the importance of each Activity 1 Gear feature Identification OBJECTIVE 9 Identify the ten dimensions and features of a gear drive and explain the importance of each OBJECTIVE 10 Describe the operation of a spur gear drive SEGMENT 4 SPUR GEAR INSTALLATION.................................................. 46 OBJECTIVE 11 Describe how to install and align a spur gear drive system SKILL 3 Install and align a spur gear drive system OBJECTIVE 12 Describe the function of backlash OBJECTIVE 13 Describe how to determine the allowable backlash in a gear drive SKILL 4 Determine the allowable backlash in a gear drive SEGMENT 5 SPUR GEAR ANALYSIS...................................................... 63 OBJECTIVE 14 Describe two methods of measuring spur gear backlash SKILL 5 Measure gear backlash SKILL 6 Adjust gear backlash to a specifi ed amount Activity 2 Gear drive analysis 3
SEGMENT 1 GEAR DRIVE CONCEPTS OBJECTIVE 1 DESCRIBE THE FUNCTIONS OF THE THREE COMPONENTS OF A GEAR DRIVE SYSTEM A gear drive consists of three basic components, as shown in figure 1. Driver Gear Driven Gear Idler Gear DRIVER GEAR IDLER GEAR DRIVEN GEAR Figure 1. Basic Components of a Gear Drive 4
These components are described as follows: Driver Gear - The driver gear is a disk-shaped component with teeth which is attached to the shaft of the driver. It is positioned so that its teeth mesh with either the driven gear or the idler gear, as shown in figure 1. When the drive shaft turns, the driver gear rotates and one or more of its teeth apply a force to the next gear, causing it to rotate. Driven Gear - The driven gear is a disk-shaped component with teeth which is attached to the driven shaft. It rotates when the gear next to it rotates and in turn causes the driven shaft to rotate. Idler Gear - The idler gear is also a disk-shaped component with teeth of the same design as the driver and driven gears. It is positioned in between the driver and driven gears and transfers the torque and motion from the driver gear to the driven gear. Its purpose is either to change the direction of rotation of the driven gear or transfer the power to a location which is further from the driver shaft. It does not affect either the speed or the torque output of the driven gear. The relative diameters of the driver and driven gears determine the speed and torque of the driven shaft. The ratio of the sizes of the gears can be selected to either decrease or increase the speed and torque delivered to the driven shaft. A gear drive can be designed as either an open or closed unit. A closed unit has a housing which contains the gears, as shown in figure 2. This housing protects the gears and provides a way of containing the oil or grease lubrication. Open units do not have a housing but will still have a guard of some type that is used to contain the lubrication. Figure 2. Gear Drive Housing 5
OBJECTIVE 2 DEFINE THE GEAR PITCH, PITCH CIRCLE, AND PITCH DIAMETER AND EXPLAIN THEIR IMPORTANCE Like belt drives, the features of pitch circle and pitch diameter are also important concepts with gear drives. Unlike belt drives, however, pitch has a specific meaning in a gear drive. The pitch of a gear is the distance between one point on a tooth and the corresponding point on next tooth when measured along the pitch circle, as shown in figure 3. This is also called circular pitch. CIRCULAR PITCH PITCH CIRCLE Figure 3. Gear Pitch 6
The pitch circle of a gear is the location on the gear where speed and torque are transmitted. This occurs at the contact point between the gear teeth along a line that passes through the line of centers of the two gears, as shown in figure 4. The pitch diameter is simply the diameter of this pitch circle. Another dimension which is related to the pitch diameter is the pitch radius. It is equal to 1/2 the pitch diameter. PITCH DIAMETER PITCH DIAMETER PITCH RADIUS LINE OF CENTERS PITCH CIRCLE PITCH CIRCLE Figure 4. Pitch Circle and Diameter of a Gear The pitch diameter is important because it can be used to calculate the speed and torque which are transmitted to the driven shaft. The pitch circle is important only because it allows you to determine the pitch diameter. The term pitch length does not apply to the gear drive, because the gears are in direct contact with each other. 7
OBJECTIVE 3 DESCRIBE HOW TO CALCULATE THE GEAR RATIO OF A GEAR DRIVE The speed and torque which are transmitted to the driven shaft of a gear drive can be calculated using the gear ratio. This is similar to the concept of the pulley ratio in a belt drive. The gear ratio can be calculated using one of two methods: Ratio of pitch diameters Ratio of number of gear teeth Ratio of Pitch Diameters Calculating the ratio of pitch diameters is the same as calculating the pulley ratio of a belt drive, as the following formula shows: FORMULA: GEAR RATIO Pitch diameter of driven gear Gear Ratio = Pitch diameter of driver gear As an example of how to calculate the gear ratio, look at the gear drive system shown in figure 5. The pitch diameters of the driver and driven gears are 2 inches and 4 inches respectively. This means that the gear ratio is 2 (GR= 4/2). This is also stated as 2:1. 2.0 4.0 DRIVER GEAR DRIVEN GEAR Figure 5. Calculation of Gear Ratio 8
NOTE It is important to remember that the gear ratio is determined using the pitch diameter, which is not the same as the outer diameter of a gear. If you use the outer diameter, your answer will have an error. Ratio of Number of Gear Teeth Another method of calculating the gear ratio is to use the number of teeth of each gear as shown in the following formula: FORMULA: GEAR RATIO No. of Teeth of driven gear Gear Ratio = No. of Teeth of driver gear For example, if the driver and driven gears in figure 5 have 11 and 22 teeth respectively, the gear ratio is again 2:1. The particular formula you use depends on the data you have available. If you are using manufacturer s catalog data, you can probably use either one because both the number of teeth and pitch diameter are both usually listed. If you are in the plant, you will probably use the number of teeth because it is easier to count the teeth than measure the pitch diameter. 9
As with the pulley ratio of belt drives, the gear ratio determines how fast the driven gear will turn. This is because the teeth of the driver gear transfer speed to the teeth of the driven gear such that the points on the teeth of the two gears at their pitch diameters move at the same surface speed. If the gears are of different sizes, the driven shaft s rotational speed (RPM) will be different than the driver shaft s rotational speed (RPM). The shaft with the larger gear will have a slower rotational speed than the shaft with the small gear. 2.0 4.0 INPUT SPEED 1800 RPM SURFACE SPEED AT CONTACT POINT OF BOTH GEARS IS THE SAME OUPUT SPEED 900 RPM Figure 6. Effect of Relative Gear Size on the Speed of the Driven Shaft 10
In a similar manner to speed, the gear ratio also affects the torque transmitted to the driven shaft. To understand why, you should recall that the force applied to the surfaces of the two gears is the same. Since the torque radius is the pitch radius of the gear, the torque in one gear will be different than another if its radius (or pitch diameter) is different. In the case of the example in figure 7, the effective torque in the driver gear is 10 in-lbs. The effective torque in the driven gear, however, is 20 in-lbs (T = 10 x 2 = 20). The larger gear increased the torque delivered to the driven shaft. INPUT TORQUE 10.0 in-lbs PITCH RADIUS 2.0 in TORQUE OUTPUT 20.0 in-lbs PITCH RADIUS 1.0 in T e = 10 lbs Figure 7. Effect of Gear Ratio on Torque of Driven Shaft From this discussion, you can say that the larger gear turns slower but has greater torque. This is a common sense concept you can use on the job to determine in general how speed and torque are being changed by the mechanical drive system. 11
SKILL 1 CALCULATE GEAR RATIO Procedure Overview In this procedure, you will determine the gear ratio of a number of gear drive applications. To do this, you will either use the pitch diameters or the number of teeth, depending on which is given. This is a simple skill, but you will use it in the next skill in this LAP to calculate the speed and torque of gear drive shafts. 1. Calculate the gear ratio of the gear drive shown in figure 8. Gear Ratio PITCH DIA = 4 in. PITCH DIA = 2.5 in. DRIVEN GEAR DRIVER GEAR Figure 8. Gear Drive Application In this case, the pitch diameter of the driver gear is 4 inches and the pitch diameter of the driven gear is 2.5 inches. The ratio is therefore 0.625(R=2.5/4= 0.625). 12
2. Calculate the gear ratio of the gear drive given the following information. Given: Driven Gear = 65 Teeth Driver Gear = 20 Teeth Gear Ratio: The solution is 3.25 (R = 65/20). 3. Calculate the gear ratio of the gear drive given the following information. Given: Driven Gear Pitch Dia. = 6.5 inches Driver Gear Pitch Dia. = 1.8 inches Gear Ratio: The solution is 3.61 (R = 6.5/1.8). 4. Calculate the gear ratio of the gear drive given the following information. Given: Driver Gear = 80 Teeth Driven Gear = 30 Teeth Gear Ratio: The solution is 0.375 (R = 30/80). 5. Calculate the gear ratio of the gear drive given the following information Given: Driver Gear Pitch Dia. = 4 inches Driven Gear Pitch Dia. = 12 inches Gear Ratio: The solution is 3:1 (R = 12/4). 13
SEGMENT 1 SELF REVIEW 1. A gear that transfers speed and torque from a driver gear to a driven gear is called a(n) gear. 2. Idler gears the direction of rotation or transfer power to a location that is farther from the driven shaft. 3. A gear drive that has a housing which contains the gears and lubricant is called a(n) unit gear drive. 4. The ratio is determined by dividing the pitch diameter of the driven gear by that of the driver gear. 5. The same ratio can also be determined by using the ratio of the of teeth of the two gears. 6. The circle along which speed and torque are directly transferred is called the circle. 14
SEGMENT 2 GEAR DRIVE DESIGNS OBJECTIVE 4 DESCRIBE HOW TO CALCULATE THE SHAFT SPEED AND TORQUE OF A GEAR DRIVE SYSTEM The relationship between gear sizes and shaft speeds of a gear drive as described in the previous objective can be expressed in the following formulas: FORMULA: GEAR DRIVE SPEED Driver Rotational Speed (RPM) Pitch Diameter of Driven Gear = Driven Rotational Speed (RPM) Pitch Diameter of Driver Gear OR Driver Rotational Speed No. of Teeth of Driven Gear = Driven Rotational Speed No. of Teeth of Driver Gear As you can see by the formula, the shaft speeds are inversely proportional to the pitch diameters and number of teeth. This means that an increase in gear size (or teeth) causes the speed to decrease. Also, notice that the right hand side of the formula is actually the gear ratio, so the formula can also be stated as follows: FORMULA: GEAR DRIVE SPEED Driver Rotational Speed (RPM) Gear Ratio Driven Rotational Speed (RPM) = 15
The calculation of shaft torque is performed using a formula which is similar to the shaft speed formula, except that the torque is directly proportional to the pitch diameters or number of teeth. The torque formula is therefore as follows: FORMULA: GEAR DRIVE TORQUE Driven Rotational Torque = Driver Rotational Torque Driven Pitch Diameter Driver Pitch Diameter OR Driven Rotational Torque = Driver Rotational Torque No. of Teeth of Driven Gear No. of Teeth of Driver Gear As with the speed formula, the torque formula can be modified to use the gear ratio as follows: FORMULA: GEAR DRIVE TORQUE Driven Rotational Torque Gear Ratio Driver Rotational Torque = 16
SKILL 2 CALCULATE THE SHAFT SPEED AND TORQUE OF A GEAR DRIVE SYSTEM Procedure Overview In this procedure, you will use the formulas just described to determine speed and torque of either the driver or the driven shaft. On the job, you will sometimes know the driver data and will need to determine the driven data. In other cases, it will be the reverse. 1. Calculate the driven shaft speed of the gear drive system shown in figure 9. Driven Shaft Speed (RPM) 1800 RPM PITCH DIA 4.0 in 30 in-lbs PITCH DIA = 12.0 in DRIVER GEAR DRIVEN GEAR Figure 9. Gear Drive System The solution is 600 RPM. 2. Calculate the driven shaft torque of the gear drive shown in figure 9. Driven Shaft Torque(in-lbs) The solution is 90 in-lbs. 17
3. Calculate the driven shaft speed and torque of the gear drive system shown in figure 10. Driven Shaft Speed (RPM) Driven Shaft Torque (ft-lbs) The solution is 1200 RPM. The solution is 25 ft-lbs. 11 TEETH 18 TEETH 733 RPM 41 ft-lbs DRIVEN GEAR DRIVER GEAR Figure 10. Gear Drive System 18
4. Calculate the driven shaft speed and torque of the gear drive system given the following information. Driver Gear: Pitch Dia. 1.8 in Speed 1800 RPM Torque 125 in Driven Gear: Pitch Dia. 6.5 in Driven Shaft Speed (RPM) Driven Shaft Torque (in-lbs) The solutions are 498 RPM and 451 in-lbs. 5. Calculate the driven shaft speed and torque of the gear drive system given the following information. Driver Gear: No. of Teeth 80 Speed 600 RPM Torque 824 in-lbs Driven Gear: No. of Teeth 20 Driven Shaft Speed (RPM) Driven Shaft Torque (in-lbs) The solutions are 2400 RPM and 206 in-lbs. 19
OBJECTIVE 5 DESCRIBE THE FUNCTIONS OF FOUR TYPES OF GEAR DRIVES AND GIVE AN APPLICATION OF EACH Gear drives come in many designs. One way to group these designs is the direction of orientation of the driven shaft relative to the orientation of the driver shaft. There are four basic categories: Parallel Axis Intersecting Axis Non-intersecting Axis Moving axis Each of these is explained as follows: Parallel Axis Gear Drive The shafts of a parallel axis gear drive are placed side-by-side or in parallel with each other, as shown in figure 11. This is a very common configuration. It is used in applications such as machine tool drives when it is desired or where it is possible to drive a shaft which is mounted in the same direction as the driver shaft. There are several types of parallel axis gear drives. Figure 11. Parallel Axis Gear Drive 20
Intersecting Axis Gear Drive This type of gear drive gets its name because the gears are designed so that the axes of the shafts are maintained on the same plane and therefore intersect with each other. The intersecting axis gear drive is designed to transfer power to a driven shaft which is at a right angle (90 degrees) to the driver shaft, as shown in figure 12. It is commonly used in applications such as gear reducers. Figure 12. Intersecting Axis Gear Drive Non-Intersecting Axis Gear Drive The non-intersecting gear drive is also designed to transfer power at right angles to the drive shaft, but the axes of the shafts are not on the same plane, as shown in figure 13. An example of this type of gear is the worm gear or crossedaxis helical gear. Worm gears are used where there is a need for a low cost gear reducer with a very high gear ratio. WORM WORMGEAR Figure 13. Non-Intersecting Axis Gear Drive 21
Moving Axis Gear Drive The moving axis gear drive is designed to convert rotary motion to linear motion. One example of this drive is the rack and pinion drive shown in figure 14. This is used in fluid power actuators to convert linear motion into rotary motion. Figure 14. Rack and Pinion Gear Drive 22
OBJECTIVE 6 LIST FOUR TYPES OF PARALLEL AXIS GEAR DRIVES AND GIVE AN APPLICATION OF EACH There are four types of gear drives which transfer power between parallel axes: Spur Helical Herringbone Internal Each of these is described as follows: Spur Gears The spur gear is the most basic of gear drives. Its teeth are cut into the gear parallel to the axis of rotation, as shown in figure 15. This type of gear is used in mainly in low-to-medium speed applications such as machine tool drives, instrument transducers, and gear reducers because it is low cost and easy to maintain. PARALLEL AXES Figure 15. Spur Gear Drive 23
Helical Gears The helical gear is similar in design to the spur gear except that its teeth are cut into the gear at an angle to the gear s axis of rotation, as shown in figure 16. This type gear, while more expensive than the spur gear, is able to operate at higher speeds. It also operates more quietly and smoothly. One disadvantage to this gear is that it creates a side or thrust load because of its angled gear teeth. PARALLEL AXES Figure 16. Helical Gear Drive 24
Herringbone Gear Drive The herringbone gear design is composed of two helical designs, as shown in figure 17. For this reason, it is also called a double helical gear. This design eliminates the side load caused by the single helical design, because the side load of the two helical gears cancel each other out. Herringbone gears are used for applications which require quiet, high-speed, heavy-load operation. One example of an application like this is the power take-off of a gas turbine. The herringbone gear is easy to identify because it looks like the spine of a fish. PARALLEL AXES Figure 17. Herringbone Gear 25
Internal Gear Gears can be classified as either internal or external. This describes how the teeth are oriented on the gear, as shown in figure 18. EXTERNAL GEAR DRIVE INTERNAL GEAR DRIVE Figure 18. Internal and External Gears The internal gear drive uses one or more external gears to drive a larger internal gear, as shown in figure 19. This type of gear drive is used when a very large gear ratio is needed but the axes must be parallel and the gear drive must be compact. INTERNAL GEAR EXTERNAL GEAR Figure 19. Internal Gear Drive 26
One example of an internal gear drive is a planetary gear drive. This type uses small gears called planets, which revolve around a central gear called a sun gear, as shown in figure 20. PLANET GEARS PINIONS PLANET CARRIER SUN GEAR ANNULUS Figure 20. Planetary Gear Drive Another type of internal gear drive is a harmonic gear drive. This type of drive consists of a flexible external gear ring which is forced out against an internal ring gear by an elliptical shaped wave generator. As the wave generator rotates the flexible gear drives the internal ring gear. It is commonly used in precision applications such as robot axes because it has no backlash or play in the gears. ELLIPTICAL WAVE GENERATOR FLEX SPINE INTERNAL RING GEAR Figure 21. Harmonic Gear Drive 27
SEGMENT 2 SELF REVIEW 1. The speed ratio of a gear drive is proportional to the gear ratio. 2. The torque ratio of a gear drive is proportional to the gear ratio. 3. A(n) axis gear drive is one in which the driver and driven shafts lie side-by-side and point in the same direction. 4. A worm gear drive is an example of a(n) axis gear drive. 5. The shafts of an intersecting gear drive are at a(n) angle to each other. 6. A rack and pinion gear drive is an example of a(n) gear drive system. 7. The most basic type of gear, whose teeth are cut parallel to the shaft axis, is known as a(n) gear. 8. A type of gear whose teeth are cut at an angle to the axis of rotation and can be operated at higher speeds than a spur gear is known as a(n) gear. 28
SEGMENT 3 SPUR GEAR DRIVE OPERATION OBJECTIVE 7 DESCRIBE ELEVEN FEATURES OF A GEAR Because gears mesh directly with each other, the shape and dimensions of the gear teeth are very important. In order to understand the operation of meshing gear teeth you must first learn the features of a gear. The main features of a gear are shown in figure 22 and explained in the following paragraphs: TOOTH PROFILE TOOTH TOOTH SPACE TOP LAND FACE BODY FLANK BOTTOM LAND ROOT TOOTH FILLET Figure 22. Main Features of a Gear 29
Tooth - The part of the gear which makes contact with the other gear to transmit torque and speed. Tooth Space - The volume of space between two teeth of the gear. Body - The part of the gear which does not have teeth. Face - The surface area of the tooth which is above the pitch circle. Flank - The surface area of the tooth which is below the pitch circle. Tooth Profile - The shape made by the edge of the tooth. Root - The point on the profile of the tooth where the profile starts. Tooth Fillet - The line on the tooth edge which blends with the root. Top Land - The surface area which is on top of the tooth. Bottom Land - The surface area which is on the bottom of the tooth. Base Circle - The base circle is a circle from which the profile of the teeth are created. Most gears use an involute profile. It is created by the path made by unwinding a string from the base circle, as shown in figure 23. INVOLUTE CURVE CORD BEING UNWOUND FROM A CYLINDER BASE CIRCLE Figure 23. Involute Profi le Created by a String Unwound from a Base Circle 30
OBJECTIVE 8 IDENTIFY THE TWELVE DIMENSIONS OF A GEAR AND EXPLAIN THE IMPORTANCE OF EACH You have already learned the meanings of three important gear dimensions: pitch, pitch circle, and pitch diameter. Some other important dimensions of a gear are shown in figure 24 and explained in the following paragraphs: TOOTH SPACE WIDTH DEDENDUM ADDENDUM CIRCULAR TOOTH THICKNESS WHOLE DEPTH OUTER DIAMETER BASE DIAMETER PITCH DIAMETER GEAR BODY FACE WIDTH TOOTH PRESSURE ANGLE Figure 24. Gear Dimensions and Features Face Width - This is the width as measured across the face of the gear. This is an important dimension because it is used to specify gear size. A thicker gear is needed for higher loads. Circular Tooth Thickness - The circular tooth thickness is measured along the pitch circle from one side of a tooth to the other side. It can also be measured in a straight line between the two points on the pitch circle, in which case it is called the chordal thickness. The tooth thickness is important for inspection of gear wear. As gears wear, the thickness becomes smaller. Tooth Space Width - The width of a tooth space is the length between two adjacent teeth as measured along the pitch circle. It is important because it must be larger than the tooth thickness in order to allow the gears to mesh smoothly. Pressure Angle - The pressure angle can be described as the angle between a line which is tangent to the tooth profile at the pitch circle and a radial line extending from the center of the gear. 31
The pressure angle affects how the gears transmit power between each other. In general, a higher pressure angle has been found to give better operation because it does not wear as quickly, it can carry higher loads, and it allows higher speeds. Two common pressure angles are in common use today: 14.5 degree and 20 degree. The 20 degree is the type you will most often find on new machinery, while the 14.5 degree is very common on older machinery. The 14.5 degree is mainly used when replacing gears. It is important to note that two gears must have the same pressure angle in order to be used with each other. You cannot mesh gears of different pressure angles together. Outer Diameter - This is the diameter of the circle which is drawn through the top lands of the teeth. The outer diameter is not used for calculations but it is important for two reasons. One is for design of clearance of other machine elements, such as covers. The other reason is that it is easily measured and can be used to determine a dimension called the diametral pitch. The diametral pitch is used to size the gear. This is very helpful when you need to replace a gear on a machine. Base Circle Diameter - This is the diameter of the base circle. It is important because it is the basis for many other gear dimensions. However, you will not use this dimension unless you are designing gears. Another dimension which is derived from the base diameter is the base radius. It is equal to 1/2 of the base diameter. Addendum - The addendum is the distance from the pitch circle to the top land. It coincides with the tooth face. Some spur gears are made with addendums which are shorter than normal. These are called stub tooth gears. This dimension is important only if you are designing or making gears. Dedendum - The dedendum is the distance from the pitch circle to the bottom land. It coincides with the tooth flank. This dimension is important only if you are designing or making gears. Whole Depth - This is the sum of the dedendum and the addendum. This dimension is important only if you are designing or making gears. Number of Teeth - This is the number of teeth on the gear. It is used calculate the gear ratio of the two gears so that the speed and torque output of the drive can be determined. It is also used on the shop floor to calculate the diametral pitch which is used to specify replacement gears. Pitch Diameter - This is the diameter of the pitch circle. The pitch diameter is important because it defines the size of the gear and is used to calculate the speed and torque which is transmitted from one gear to another. 32
Diametral Pitch - The diametral pitch is the ratio of the number of teeth on the gear to the pitch diameter. This can be stated in mathematical form as follows. FORMULA: DIAMETRAL PITCH N DP = D Where: DP = Diametral Pitch N = Number of teeth D = Pitch Diameter The diametral pitch is a measure of the number of teeth per unit of pitch diameter. This indicates the relative size of the teeth on the gear. Diametral pitch is important because two gears must have the same size teeth in order to mesh with each other. This means they must have the same diametral pitch. The diametral pitch allows you to determine if gears of different diameters or different numbers of teeth have the same size teeth and therefore can mesh properly. In a later LAP, you will learn a simple method to determine the diametral pitch of a gear by measuring the outer diameter. This is very helpful when you need to replace a gear on the shop floor. 33
Activity 1. Gear Feature Identification Procedure Overview In this procedure, you will examine the gears supplied with the 950-ME to locate the features and some of the dimensions just described. It is very important to be able to do this in order to inspect gears for wear and to design gears. 1. Locate the Gear Drives Panel 1 on your 950-ME and place it on the overhead rack. You should see a number of gears mounted on this panel. They are all spur gears, but they are of different sizes. 2. Remove the gear from the panel which is labeled with a 1 on the panel and place it in your hand. 3. Examine the gear to see of you can identify its features. Place a letter in the table next to the feature you locate on the gear. The letters identify gear locations shown in figure 25. GEAR FEATURE Top Land Bottom Land Body Tooth Tooth Profi le Tooth Face Tooth Flank Root Tooth Space LETTER I C G E J B F D H A Figure 25. Gear Feature Locations 34
4. Use a rule or caliper to measure the sizes of the following features on the gears labeled 1, 4, and 5. Notice in the table that each gear is labeled with the number of teeth (N), diametral pitch (DP), and the pressure angle (either 14.5 or 20). This is done so that you will be able to compare the dimensions of each gear. GEAR FEATURE GEAR 1 12DP, 36N, 14.5 GEAR 2 12DP, 24N, 14.5 GEAR 3 12DP, 48N, 14.5 GEAR 4 16DP, 24N, 20 GEAR 5 16DP, 60N, 20 GEAR 6 16DP, 64N, 14.5 GEAR 7 16DP, 80N, 14.5 Whole Depth Tooth Thickness Face Width Outer Diameter You should find that gears with the same diametral pitch (DP) have the same whole depth and tooth thickness because their teeth are the same size. This means that Gears 1, 2, and 3 are the same, and that Gears 4, 5, 6, and 7 will be the same. Notice that the outer diameters of the gears are slightly different even when the diametral pitch is the same. A gear with a given diametral pitch will be larger if it has more teeth. Also, notice that the face width of the gears is the same. This is related to the load capability of the gears. You will learn more about this in a later LAP. 35
5. Now compare the shape of the tooth profiles of gear 5 and gear 6. These two gears have the same diametral pitch but different pressure angles. Gear 5 has an angle of 20 degrees and gear 6 has an angle of 14.5 degrees. What do you notice about the shapes of the two gears? You should see that the teeth of gear 6 are steeper than the teeth of gear 5. Gears with a 14.5 lower degree pressure angles have steeper teeth than those with higher degree pressure angles. 6. Perform the following substeps to test the ability of gears of various types to mesh properly. A. Pick up gears 1 and 2 with one gear in each hand. B. Mesh the two gears together and roll them, as shown in figure 26. Notice whether the gears roll easily or not. Gears Mesh and roll easily (Yes/No) You should find that they mesh and roll easily because they have the same diametral pitch (12) and the same pressure angle (14.5). However, you should notice that they do not have the same number of teeth and therefore are of different sizes. DRIVER GEAR DRIVEN GEAR Figure 26. Mesh and Roll of Gears 36
C. Mesh and roll Gears 6 and 7 as you did in the previous substep. These two gears also have the same diametral pitch and pressure angle. In this case, it is 16DP and 14.5 degrees. Record your observations. Gears Mesh and roll easily (Yes/No) You should find that they also mesh and roll easily. D. Mesh and roll Gears 4 and 5. These two gears also have the same diametral pitch and pressure angle. In this case, it is 16DP and 20 degrees. Record your observations. Gears Mesh and roll easily (Yes/No) You should find that they also mesh and roll easily. In the remaining substeps, you will mix the gear types to see how affects the mesh. E. Mesh and roll Gears 2 and 4. These two gears have the same pressure angle (14.5) but a different diametral pitch (12 vs. 16). Record your observations. Gears Mesh and roll easily (Yes/No) You should find that these gears do not mesh and roll easily. F. Mesh and roll Gears 5 and 6. These two gears have the same diametral pitch (16) but a different pressure angle (20 vs. 14.5). Record your observations. Gears Mesh and roll easily (Yes/No) You should find that these gears do not mesh and roll easily. These last two substeps show that gears must both have the same pressure angle and diametral pitch in order to mesh correctly. They do not, however, have to be of the same size or have the same number of teeth. 7. Replace the gears in the correct locations on the storage panel. 37
OBJECTIVE 9 IDENTIFY THE TEN DIMENSIONS AND FEATURES OF A GEAR DRIVE AND EXPLAIN THE IMPORTANCE OF EACH Now that you know the features and dimensions of a single gear, the next step is to learn about the key dimensions and features of two gears that mesh with each other. These are shown in figures 27 and 28 and explained in the following paragraphs: PITCH POINT PINION GEAR LINE OF CENTERS PITCH CIRCLE PITCH CIRCLE CENTER DISTANCE Figure 27. Dimensions and Features of Meshing Gears Pinion - When the gears are of different sizes, the smaller gear is called the pinion. The pinion can be attached to either the driver or the driven shafts, depending on the change in output torque and speed desired. Gear - The larger gear is called the bull gear or simply the gear. Line of Centers - The line of centers is the line that passes through the centers of the two gears. It is important because is used as a reference for a number of dimensions such as center distance and pressure angle. Center Distance - The center distance is the distance between the centers of the gears. 38
Line of Action - As shown in figure 28, the line of action is the path made by the point where the two gears make contact. For an involute profile, this path follows a line which is tangent to the two base circles. It is used to determine the pressure angle. PINION LINE OF ACTION PRESSURE ANGLE ( ) O CLEARANCE POINT OF TOOTH CONTACT PITCH POINT WORKING DEPTH BACKLASH GEAR Figure 28. Features and Dimensions of Meshing Gears Pressure Angle - The pressure angle is the angle between the line of action and a line which is perpendicular to the line of centers, as shown in figure 28. It is actually a feature of the gear tooth profile as well. The pressure angle of the gear tooth profile is generated based on this pressure angle. As you can see, the pressure angle made by the line of action depends on the distance between the gears. The actual angle is called the operating pressure angle. The angle to which the gear profile is cut is called the generating pressure angle. If the gear positions are adjusted correctly, the operating pressure angle should be the same as the generating pressure angle. 39
Pitch Point - This is the point on the line of centers where the line of action crosses it. The pitch point determines the diameters of the pitch circles of the two gears. Since the pressure angle determines where the line of action crosses the line of centers, the pitch diameter of a gear is determined by the pressure angle and the base circle. Notice that the pitch point(where the line of action crosses the line of centers) is affected by the distance between centers because this causes the pressure angle to change. This means that the actual pitch circles of the gears depend in part on the center distance of the gears. As with the pressure angle, the actual pitch circle determined by both the base circles and the center distance is called the operating pitch circle. The pitch circle which is determined by the base circle and the generating pressure angle is called the generating pitch circle. Clearance - This is the space between the top land of a tooth and the bottom land of the space between the tooth it meshes with. It is important to have some clearance in order to keep the tooth of each gear from jamming into bottom lands of each other. Working Depth - The working depth is the amount by which the meshing teeth engage each other. It is the distance between the top land of one tooth and the top land of the tooth with which it meshes. This is also equal to the whole depth minus the clearance. The working depth must be less than the whole depth or the gears will interfere with each other. Backlash - Backlash is the difference between the thickness of a tooth and the width of the tooth space. Most gears have some backlash built into them in order to allow the gears to mesh smoothly. This backlash is made by making the tooth thickness slightly smaller than the tooth width. 40
OBJECTIVE 10 DESCRIBE THE OPERATION OF A SPUR GEAR DRIVE A spur gear drive transfers the power between two parallel shafts by placing the centers of the two gears close enough together to cause the teeth to mesh, as shown in figure 29. As the driver gear rotates, one or more of its teeth will contact one or more of the teeth of the driven gear. The interaction between these teeth is a combination of rolling and sliding, causing the driven gear to rotate. Figure 29. Meshing of Spur Gear Teeth The gear teeth of a spur gear are cut parallel to the axis of rotation so that each tooth of the driver gear contacts the tooth of the driven gear across its entire face width. TOOTH FACE WIDTH Figure 30. Spur Gear Tooth Width 41
For basic transmission of force and motion, the gear teeth do not need to have any particular shape. However, for quiet and vibrationless motion, the rotational speeds of the two gears must remain constant as the gears turn. It has been proven mathematically that this will occur if a line which is normal (perpendicular) to both of the tooth profiles at the point of contact passes through a constant point on the line of centers while the two teeth remain in contact, as shown in figure 31. This proof is called the Fundamental Law of Gearing, and the point through which the normal line passes is called the pitch point. GEAR 1 CENTER NORMAL TO TANGENT PITCH RADIUS 1 PITCH POINT PITCH RADIUS 2 TANGENT TO TOOTH PROFILES = PRESSURE ANGLE GEAR 2 CENTER Figure 31. Law of Gearing 42
Any two gears which have teeth that satisfy the Law of Gearing will have constant pitch diameters and therefore a constant ratio of speed and torque. This type of motion is referred to as conjugate action. There are actually many types of tooth profiles that satisfy the Law of Gearing. Two of these are involute and cycloidal. Most spur gears use the involute tooth design, as shown in figure 32. The reason for choosing this profile is that it not only satisfies the Law of Gearing but also provides the following other advantages: Conjugate Action is Independent of Center Distance - This means that the gears do not have to be perfectly positioned with their pitch circles tangent to each other in order to maintain a constant speed ratio. In other words, the amount of backlash does not affect the speed ratio. Straight Tooth Rack - The involute tooth profile becomes straight when it is laid out on a linear rack. This makes involute tooth design easy to manufacture. One Cutter - One cutter can generate all gear tooth numbers of the same diametral pitch. INVOLUTE TOOTH PROFILE Figure 32. Involute Tooth Design Another benefit of the involute tooth shape, which is also shared by some of the other tooth shapes, is that the teeth tend roll more than they slip. This reduces friction and helps the gears to operate smoothly. Also, notice that the gear teeth have an involute design on both sides so that the gears can drive in either direction. 43
Backlash Spur gears are designed with a small amount of clearance between the backside of the driver gear tooth and the driven tooth behind it, as shown in figure 33. This clearance is called backlash. It is created by making the teeth slightly smaller than the tooth spaces. BACKLASH PITCH CIRCLES Figure 33. Spur Gear Backlash Backlash is needed in order to allow the lubricant to get to each gear tooth and to allow the teeth to mesh properly. It is important that the backlash be neither too much or too little. Spur gears are made of many different materials including cast iron, forged steel, machined steel, brass, bronze, and even plastic. Cast iron has good resistance to wear but is brittle. Unhardened low-carbon steel is sometimes used on low power applications, but it must be hardened for higher power applications like those commonly seen in industry. Spur gears are designed to be mounted with either fixed bores with keyways, as shown in figure 34, or with bushings. Figure 34. Spur Gear Construction 44
SEGMENT 3 SELF REVIEW 1. is the volume of space between two teeth of a gear. 2. The characteristic shape made by the edge of a tooth is known as the. 3. When the gears of a gear drive are of differing sizes, the smaller gear is known as the. 4. The of is the path made by the point where the two gears make contact. 5. is the difference between the thickness of a tooth and the width of the tooth space. 6. The is the distance from the pitch circle to the bottom land and coincides with the tooth flank. 45
SEGMENT 4 SPUR GEAR INSTALLATION OBJECTIVE 11 DESCRIBE HOW TO INSTALL AND ALIGN A SPUR GEAR DRIVE SYSTEM In many cases, installation of a spur gear drive is very easy because the gear drive design uses shaft bearings which have a fixed mounting. This fixes the locations of the gears, and no alignment is therefore necessary. However, some gear drives are designed so that the backlash can be adjusted. These types of drives must be aligned. In either case, the general procedure for installing a gear drive is as follows: Step 1. Mount and level the motor and the driven component The shafts must be level so that the gear teeth contact each other across their entire width. The shafts should also be checked for run-out and a soft foot. Run-out will cause the shaft to wobble making the gear teeth mesh improperly. This in turn causes the gears to wear quickly. Ideally, the shaft run-out should be no more than 0.002 inches. Step 2. Inspect the gears for cleanliness and wear. Clean or replace if necessary. If a gear has nicks, burrs, gouges, or is excessively worn, replace the gear. You will learn more about measurement of gear tooth wear in another LAP. Make sure that the gear does not have any dirt. Dirt can get mixed in with the oil that lubricates the gears and become deposited on the teeth. Use a stiff brush and to remove dirt form the gear and then wipe clean. Step 3. Mount the gears onto the shafts The gears should be attached to the shafts using either a finished bore hub and a key fastener or with a bushing. 46
Step 4. Mesh the gears Move the shafts together so that the gears mesh. The position of the gear s shafts should adjusted so that there is a little backlash in the gears. In step 6, you will adjust it precisely. If the shaft centers are fixed, this step is not necessary. Step 5. Align the gears Just as with v-belts and chain drives, it is important to align gears. Misalignment will cause the gears to either wear or fail. This misalignment can appear in several ways, as shown in figure 35. ANGULAR MISALIGNMENT TOOTH OFFSET PARALLEL MISALIGNMENT Figure 35. Types of Misalignment 47
The gears can be aligned by first leveling the two shafts using a spirit level. If this has already been done as part of mounting the motor, you can skip this step and go to the next step. The next step is to place a straight edge against the faces of the gears and check the parallelism of the shafts, as shown in figure 36. The faces of the gears should be made so that they are flush against the straight edge, as shown in figure 36. This means that the shafts are parallel and the gears are aligned. DRIVEN GEAR DRIVER GEAR 1 2 3 4 5 6 7 8 9 10 11 12 STRAIGHT EDGE Figure 36. Alignment of Gears with Straight Edge Step 6. Adjust the backlash It is important that the backlash be set to the proper amount. It cannot be too much or too little. The amount of backlash is determined using either a table or a formula. It can be measured using a dial indicator and is adjusted by moving the centers of the shafts either closer or further apart. You will learn more about backlash in the next segment. Step 7. Readjust the alignment and tighten the mounting bolts After the positions of the shafts have been set, the mounting bolts can be tightened. As you do this, use a straight edge to keep the alignment of the gears. After you have tightened the bolts, check the alignment one more time to make sure that it is still aligned. This is done because tightening the mounting hardware can often shift the alignment of the shafts. Step 8. Apply lubrication Metal gears must be lubricated. In most cases, you will use a type of oil called gear oil, which is made for gear lubrication. This oil can be applied by hand or with some type of automatic system. 48
SKILL 3 INSTALL AND ALIGN A SPUR GEAR DRIVE SYSTEM Procedure Overview In this procedure, you will perform steps 1-5 of the procedure to assemble and align a spur gear drive, which will be used to drive the prony brake. You will not, however, run the drive system in this skill. Instead, you will go to the next skill where you will continue the installation procedure by performing step 6 of the procedure, which is to adjust the backlash of the gear drive. 1. Perform the following safety checkout to prepare for working with power transmission equipment. Make sure that you are able to answer yes to each item before proceeding. YES/NO SAFETY CHECKOUT Wearing safety glasses Wearing tight fi tting clothes Ties, watches, rings, and other jewelry are removed Long hair is tied up or put in a cap or under shirt Wearing heavy duty shoes Wearing short sleeves or long sleeves are rolled up Floor is not wet 2. Perform a lockout/tagout on the Motor Control Unit s safety switch. 49
3. Place the Variable Speed Gear Motor on the work surface. It should be mounted to a small mounting plate, as shown in figure 37. Figure 37. Variable Speed Gear Motor 50
4. Perform the following substeps to mount and level the Variable Speed Gear Motor. A. Select four Gear Motor Risers from Shaft Panel 2. B. Make sure that the motor base, risers, and mounting area of the work surface shown in figure 38 are free of dirt, rust, and burrs. SHAFT 2(8 ) GEAR 5 SHAFT 1(12 ) GEAR 4 GEAR MOTOR Figure 38. Position of Components C. Position the Gear Motor over the set of holes on the 950-ME work surface, as shown in figure 38. The outlines of the other components to be mounted are also shown. D. Place one Gear Motor Riser under each of the motor feet. E. Locate four bolts with the specifications 5/16-18UNC-2A x 2-1/2 Hex Head, along with compatible flat washers, lock washers, and nuts. F. Fasten the motor base and risers to the work surface by assembling the bolts, washers, and nuts. Use a criss-cross pattern to tighten the bolts. G. Check the shaft for run-out. Record below the amount of run-out. Run-out: (in/mm) The run-out should be less than 0.002 inches. NOTE The shaft of the gear motor is significantly harder to turn than that of the constant speed motor. With strength, it will turn. 51
H. Check for motor shaft end-float. End Float (in/mm) It should be less than 0.002 inches. I. Check the level of the motor shaft. Shim the motor feet as needed. Feeler Gauge Leaf Thickness (in/mm) Effective Level Length (in/mm) Mounting Bolt Distance (in/mm) Shim Ratio Shim Thickness (in/mm) 5. Perform the following substeps to mount Shaft No. 1 and pillow block bearings. A. Select four Bearing Standoffs from Shaft Panel 1. B. Make sure that the standoffs, pillow block mounting surface, and mounting area of the work surfaces, shown in figure 38, are free of dirt, rust and burrs. C. Place the four standoffs on the 950-ME work surface. D. Remove two pillow block bearings from Shaft Panel 1. E. Place the pillow block bearings on the standoffs over the hole locations shown for Shaft 1. F. Locate four bolts with the specifications of 3/8-16UNC-2A x 4-1/2 Hex Head, along with the compatible flat washers, lock washers, and nuts. G. Fasten the pillow block bearings and the standoffs to the work surface by assembling the bolts, washers, and nuts. Hand tighten only. H. Select a 12-inch shaft from Shaft Panel 1. I. Slide the shaft through the two pillow block bearings. Position it as shown in figure 38. J. Tighten the set screws on each bearing to lock the bearing. K. Tighten the pillow block bearing mounting bolts. L. Turn the shaft by hand to make sure it turns freely. If not, loosen the bolts and adjust the positions of the bearings. M. Check the driven shaft for run-out. Run-out: (in/mm) The shaft should have no more than 0.002 inches run-out. 52
N. Level the driven shaft. Shim the bearing standoffs as needed. Place the shims between the work surface and the standoffs. Feeler Gauge Leaf Thickness (in/mm) Effective Level Length (in/mm) Mounting Bolt Distance (in/mm) Shim Ratio Shim Thickness (in/mm) 6. Repeat Step 5 in a similar manner to mount Shaft 2 (8 inch shaft) to the worksurface in the location shown in figure 38. 7. Install the prony brake on the #2 shaft and work surface in the location shown in figure 38. This brake will be used in later skills to demonstrate how the torque is affected by a gear ratio. 8. Obtain Gears 4 and 5 from Gear Drive Panel 1. Inspect the two gears for dirt. If you find any foreign material on gears, clean them. 9. Perform the following substeps to mount Gear 4 to the driver shaft. This gear is the pinion in this application. These steps are the same steps you used to install the prony brake drum. A. Locate the set screw hole which is drilled into the side of the hub of Gear 4, as shown in figure 39. SET SCREW Figure 39. Set Screw on Hub B. Use a hex key wrench to back out the set screw so that it is not extending into the shaft hole. C. Clean the shaft s key seat and the gear hub s key seat with a wire brush to make sure that no dirt or burs are in the keyseats. D. Select a 3/16 x 1 inch square key from your key stock. 53
E. Slide the key into the keyseat of Shaft 1. The key should fit into the keyseat without forcing it. If it is too tight, take it out and measure it to see which part is out of tolerance. Select another key from your stock and try it. F. Check the key for play when it is in the keyseat by wiggling it. There should be no play. If there is play, replace the key. G. Remove the key from the shaft keyseat and insert it into the pinion keyseat. It also should slide in without forcing it and have no play. H. Remove the key from the pinion hub and insert it into the shaft keyseat. Line it up flush with the end of the shaft. I. Pick up the pinion (Gear 4) in your hand and line it up in front of the shaft so that the hub s key seat is in line with the key on the shaft. J. Then slide the pinion hub onto the shaft until the end of the face of the gear is flush with the end of the shaft, as shown in figure 40. The hub should slide on without using tools. If it doesn t, pull it off and check the dimensions. Figure 40. Gear Hub Attached to Shaft 1 K. Tighten the set screw onto the key. 54
10. Repeat Step 9 in a similar manner to mount Gear 5 to Shaft 2, the driven shaft. The setup should now look like figure 41. Figure 41. Current Setup 11. Loosen the bolts on Shaft 1 and position it so that the gears mesh. 55
12. Check the gear alignment by placing a straight edge flush against the faces of the two gears, as shown in figure 42. The driver gear will be adjusted to align with the driven gear. In real world applications, it is usually easier to adjust the driver s position than it is to reposition all of the drive system components. Figure 42. Straight Edge Check for Gear Alignment If the face of the driver gear is also flush against the straight edge, the gears are aligned and the shafts are parallel. Proceed to Step 14 to tighten the bolts. If they are not all touching, proceed to Step 13. 13. Move Shaft 1 to a position where all four edges of the gears are touching the straight edge. 14. Tighten the bolts on Shaft 1 in a criss-cross pattern until the bolts are tight. NOTE You will not couple the motor to shaft 1 until later in this LAP. 15. Recheck the alignment with the straight edge after the bolts are tightened. Repeat alignment Steps 12-14 if necessary. Leave your setup in place and proceed to the next objective and skill. In a later skill, you will continue the installation process by determining the proper amount of backlash for the gear drive. 56
OBJECTIVE 12 DESCRIBE THE FUNCTION OF BACKLASH Backlash is defined as the clearance between the back of the engaged tooth of the driver gear and the front of the tooth of the driven gear immediately behind it as measured along the pitch circle. This is shown in figure 43. BACKLASH PITCH CIRCLES Figure 43. Gear Backlash A certain amount of backlash is needed in a gear drive to enable the gears to mesh smoothly and to allow lubrication to get to each tooth. If the backlash is too small, the there will be more friction between the gears, which can cause the gears to run roughly, have added load due to friction, wear out quickly, and even lock up. It is also important to not have too much backlash. This can cause the gears to make more noise and vibration, create excessive wear on the faces of the teeth, and even cause the teeth to break. Some backlash is built into gears by making the teeth slightly narrower than the spaces between the teeth. If the gears are adjusted so that their pitch circles are tangent with each other, as shown in figure 44, the gears will have the correct amount of backlash, at least when they are new. Backlash can also be changed by adjusting positions of the gears shaft centers. As the center distance is increased, the backlash becomes greater. 57
The ideal center distance is that which causes the gears pitch circles to be tangent to each other, as shown in figure 44. In this position, the gears are said to be in mesh. This applies to new gears as well as used gears. LINE OF CENTERS PITCH CIRCLE PITCH CIRCLE Figure 44. Gear Center Distance Adjusted so that Gears are in Mesh 58
OBJECTIVE 13 DESCRIBE HOW TO DETERMINE THE ALLOWABLE BACKLASH IN A GEAR DRIVE Whether gears are new or used, the backlash should remain within a certain range in order to operate smoothly with minimum wear on the teeth. This allowable range of backlash for any two gears can be determined using a table like the one shown in figure 45 if you know the diametral pitch and the center distance. This table was developed by the American Gear Manufacturers Association (AGMA) and is published in the Machinery s Handbook, as well as in other sources. COARSE - PITCH GEARS Center Distance (inches) Normal Diametral Pitches 0.5-1.99 2-3.49 3.5-5.99 6-9.99 10-19.99 Up to 5 0.005 -.015 Over 5 to 10 0.010 -.020 0.010 -.020 Over 10 to 20 0.020 -.030 0.015 -.025 0.010 -.020 Over 20 to 30 0.030 -.040 0.025 -.030 0.020 -.030 Over 30 to 40 0.040 -.060 0.035 -.045 0.030 -.040 0.025 -.040 Over 40 to 50 0.050 -.070 0.040 -.055 0.035 -.050 0.030 -.040 Over 50 to 80 0.060 -.080 0.045 -.085 0.040 -.060 Over 80 to 100 0.070 -.095 0.050 -.080 Over 100 to 120 0.080 -.10 Figure 45. AGMA Recommendations for Allowable Backlash for Coarse Pitch Gears The diametral pitch can be determined using either a table or by calculating it if you have the number of teeth and the pitch diameter. The center distance is the average of the sum of the two pitch diameters. FORMULA: DIAMETRAL PITCH DP = N P FORMULA: CENTER DISTANCE D1 + D2 C = 2 For new gears, they can be positioned correctly by measuring the backlash. If it is within the allowable range, the gears are positioned with the pitch circles tangent to each other or very close to it. This method is often easier than measuring the center distance. 59
SKILL 4 DETERMINE THE ALLOWABLE BACKLASH IN A GEAR DRIVE Procedure Overview In this procedure, you will use the AGMA table to determine the allowable backlash for various gear sets, including the set (Gears 4 and 5) now set up on your trainer. 1. Perform the following substeps to calculate the range of allowable backlash for the following gear set. GEAR FEATURE PINION GEAR No. of Teeth 12 48 Pitch Diameter (In) 0.750 3.000 A. Calculate the diametral pitch of each gear. It should be the same for both gears but it is good idea to check this. Diametral Pitch of Pinion = Diametral Pitch of Gear = The solution is as follows: N DP = P DP = 12 / 0.75 = 16 DP = 48 / 3.00 = 16 B. Calculate the center distance of the two gears. Center Distance (in/mm) The solution is as follows: D1 + D2 C = 2 = ( 0.75 + 3.00 )/ 2 = 1.875 C. Look up in the table of figure 45 the allowable backlash range for a gear set with a center distance of 1.875 inches and a diametral pitch of 16. Allowable Backlash Range (in/mm) You should find the backlash to be 0.005-0.015 inch. 60
2. Calculate the range of allowable backlash for the following gear set. Use the same procedure you used in the previous step. Fill in the data blanks in the table as part of your process. GEAR FEATURE PINION GEAR No. of Teeth 32 80 Pitch Diameter (In) 4.000 10.000 Diametral Pitch Center Distance (In/mm) Allowable Backlash Range (in/mm) Your answer should be 0.010-0.020 inch. 3. Calculate the range of allowable backlash for the following gear set. GEAR FEATURE PINION GEAR No. of Teeth 80 120 Pitch Diameter (In) 20.00 30.00 Diametral Pitch Center Distance (In/mm) Allowable Backlash Range (in/mm) Your answer should be 0.025-0.030 inch. 4. Calculate the range of allowable backlash for the following gear set. This is the gear set that is now set up on the 950-ME. GEAR FEATURE PINION (GEAR 4) GEAR (GEAR 5) No. of Teeth 24 60 Pitch Diameter (In) 1.5 3.75 Diametral Pitch Center Distance (In/mm) Allowable Backlash Range (in/mm) Your answer should be 0.005-0.015 inch. In the next segment, you will learn how to measure the backlash and then adjust the gear set (Gears 4 and 5) on the 950-ME to the backlash range you just calculated. Once done, you will complete the installation procedure and then operate the gear drive. 61
SEGMENT 4 SELF REVIEW 1. Some types of gear drives are designed so that the backlash can be. 2. The of a gear drive can be accomplished through the use of a straight edge or a length of string. 3. Metal gears must be, which is accomplished with gear oil. 4. is defined as the clearance between the back of the engaged tooth of the driver gear and the front of the engaged tooth of the driven gear. 5. A certain amount of backlash is necessary to enable the gears to mesh smoothly and to allow to get to each tooth. 6. The appropriate amount of backlash that should be used in a gear drive can be determined by locating the pitch of the gears in a table. 62
SEGMENT 5 SPUR GEAR ANALYSIS OBJECTIVE 14 DESCRIBE TWO METHODS OF MEASURING SPUR GEAR BACKLASH The actual backlash between two spur gears can be measured using one of the following two methods: Direct Dial Indicator Measurement Indirect Dial Indicator Measurement With both of these methods the basic concept used to perform the measurement is to hold one gear fixed and rotate the other gear back and forth. The amount of movement of the teeth at or near the pitch circle is the backlash, as shown in figure 46. DRIVEN GEAR FIXED DRIVER GEAR ROTATED BACK AND FORTH AMOUNT OF MOVEMENT BACKLASH Figure 46. Measurement of Backlash 63
80 70 90 60 0 50 10 20 30 40 With the direct method, the probe of a dial indicator is placed directly on a tooth and oriented perpendicular to the face of the tooth, as shown in figure 47. ROTATE BACK AND FORTH 90 0 10 80 20 70 30 60 50 40 90º DRIVEN GEAR DRIVER GEAR BEZEL OF DIAL INDICATOR Figure 47. Direct Indicator Measurement With the indirect method, a bar of some type is attached to the shaft and the indicator measures its movement, as shown in figure 48. To determine the backlash you must divide the measured value by the ratio of the distance along the bar from the shaft center to the indicator point to the pitch radius. PITCH RADIUS ARM BACKLASH RADIUS Figure 48. Indirect Measurement The direct method is most often used for larger gears where the teeth are large enough to allow the indicator probe to contact a tooth. The indirect method is used where either the gears are not easy to access or the gear teeth are very small. 64
SKILL 5 MEASURE GEAR BACKLASH Procedure Overview In this procedure, you will use the direct method with an indicator to measure the backlash in the two gears you assembled in the previous skill. This is a skill you can use either to determine if the gears are worn or to adjust the center distance. When gears become worn, the backlash increases. 1. Make sure the lockout/tagout is still in place. If not, make it so. 2. Continuing from the previous skill, perform the following substeps to see if you can feel the backlash in the gears. A. Hold the shaft of the driver gear firmly in your hand so that it cannot move. B. Use your other hand to rotate the driven gear clockwise and then counterclockwise as far as it can go in either direction. The amount the gear rotates is the backlash. In the next step, you will measure the amount of backlash. C. Release the two shafts. 3. Set up a dial indicator with a magnetic base so that its probe is touching the gear tooth of the driven gear and is oriented 90 degrees to the tooth, as shown in figure 49. You will have to position the probe at an angle to the tooth to do this. Figure 49. Orientation of Dial Indicator 65