# Shaft Design. Shaft Design. Shaft Design Procedure. Chapter 12

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Shaft Design Chapter 1 Material taken from Mott, 003, Machine Elements in Mechanical Design Shaft Design A shaft is the component of a mechanical device that transmits rotational motion and power. It is integral to any mechanical system in which power is transmitted from a prime mover, such as an electric motor or an engine, to other rotating parts of the system. Shaft Design Procedure Because of the simultaneous occurrence of torsional shear and normal stresses due to bending, the stress analysis of a shaft virtually always involves the use of a combined stress approach. The recommended approach for shaft design and analysis is the distortion energy theory of failure. 1

2 Shaft Design Procedure Vertical shear stresses and direct normal stresses due to axial loads may also occur. On very short shafts or on portions of shafts where no bending or torsion occurs, such stresses may be dominant. Procedure 1. Determine the rotational speed of the shaft.. Determine the power or the torque to be transmitted by the shaft. 3. Determine the design of the power-transmitting components or other devices that will be mounted on the shaft, and specify the required location of each device. Procedure con t 4. Specify the location of bearings to support the shaft. Normally only two bearings are used to support a shaft. The reactions on bearings supporting radial loads are assumed to act at the midpoint of the bearings. Bearings should be placed on either side of the power-transmitting elements if possible to provide stable support for the shaft and to produce reasonably well-balanced loading of the bearings.

3 Procedure con t 5. Propose the general form of the geometry for the shaft, considering how each element on the shaft will be held in position axially and how power transmission from each element to the shaft is to take place. Intermediate Shaft Mott, 003, Machine Elements in Mechanical Design Procedure con t 6. Determine the magnitude of torque that the shaft sees at all points. It is recommended that a torque diagram be prepared. 7. Determine the forces that are exerted on the shaft, both radially and axially. 3

4 Procedure con t 8. Resolve the radial forces into components in perpendicular directions, usually vertically and horizontally. 9. Solve for the reactions on all support bearings in each plane. 10. Produce the complete shearing force and bending moment diagrams to determine the distribution of bending moments in the shaft. Procedure con t 11. Select the material from which the shaft will be made, and specify its condition: cold-drawn, heat-treated, etc Plain carbon or alloy steels with medium carbon content are typical, such as AISI 1040, 4140, 4340, 4660, 5150, 6150, and Good ductility with percent elongation above about 1% is recommended. Determine the ultimate strength, yield strength, and percent elongation of the selected material. Procedure con t 1. Determine an appropriate design stress, considering the manner of loading Smooth Shock Repeated and reversed Other 4

5 Procedure con t 13. Analyze each critical region of the shaft to determine the minimum acceptable diameter of the shaft to ensure safety under the loading at that point. In general, the critical points are several and include those where a change of diameter takes place, where the higher values of torque and bending moment occur, and where stress concentrations occur. Procedure con t 14. Specify the final dimensions for each point on the shaft. Design details such as tolerances, fillet radii, shoulder heights, and keyseat dimensions must also be specified. Sometimes the size and the tolerance for a shaft diameter are dictated by the element to be mounted there. Forces Exerted on Shafts Gears, belt sheaves, chain sprockets, and other elements typically carried by shafts exert forces on the shaft that cause bending moments. 5

6 Spur Gears The force exerted on a gear tooth during power transmission acts normal (perpendicular) to the involute-tooth profile. It is convenient for the analysis of shafts to consider the rectangular components of this force acting in the radial and tangential directions. Spur Gears con t It is most convenient to compute the tangential force, W t, directly from the known torque being transmitted by the gear. T = (P)/n Forces on Teeth of Driven Gear Mott, 003, Machine Elements in Mechanical Design 6

7 Tangential Force W t = T / (D/) Where P = power being transmitted in hp n = rotational speed in rpm T = Torque on the gear in lb*in D = pitch diameter of the gear in inches Tangential Force con t The angle between the total force and the tangential component is equal to the pressure angle, φ, of the tooth form. So, if the tangential force is known, the radial force can be found from: W r = W t tan φ Tangential Force con t There is no need to compute the normal force. For gears, the pressure angle is typically 14 ½ o, 0 o, or 5 o. 7

8 Directions for Forces Representing the forces on gears in their correct directions is essential to an accurate analysis of forces and stresses in the shafts that carry the gears. The force system, shown next, represents the action of the driving gear A on the driven gear B. Mott, 003, Machine Elements in Mechanical Design Directions for Forces The tangential force, W t, pushes perpendicular to the radial line causing the driven gear to rotate. The radial force, W r, exerted by the driving gear A, acts along the radial line tending to push the driven gear B away. 8

9 Directions for Forces ACTION: Driver pushes on driven gear W t : Acts to the left W r : acts downward REACTION: Driven gear pushes back on driver W t : acts to the right W r : acts upward Directions for Forces Whenever you need to determine the direction of forces acting on a given gear, first determine whether it is a driver or driven gear. Then visualize the action forces of the driver. Mott, 003, Machine Elements in Mechanical Design 9

10 Directions for Forces If the gear of interest is the driven gear, these are the forces on it. If the gear of interest is the driver gear, the forces on it act in the opposite directions to the action forces. Shows a pair of chain sprockets transmitting power Mott, 003, Machine Elements in Mechanical Design Chain Sprockets The upper part of the chain is in tension and produces the torque on either sprocket. The lower part of the chain, or the slack side, exerts no force on either sprocket. Therefore, the total bending force on the shaft carrying the sprocket is equal to the tension in the tight side of the chain. 10

11 Chain Sprockets con t If the torque on a certain sprocket is known, F c = T / (D/) Where D = pitch diameter of that sprocket. Notice that the force, F c, acts along the direction of the tight side of the chain. Chain Sprockets con t Because of the size difference between the two sprockets, that direction is at some angle from the centerline between the shaft centers. A precise analysis would call for the force, F c, to be resolved into components parallel to the centerline and perpendicular to it. Chain Sprockets con t F cx =F c cos θ F cy =F c sin θ Where the x-direction is parallel to the centerline The y-direction is perpendicular to it The angle θ is the angle of inclination of the tight side of the chain with respect to the x- direction 11

12 Mott, 003, Machine Elements in Mechanical Design Chain Sprockets con t These two components of the force would cause bending in both the x-direction and the y- direction. Alternatively, the analysis could be carried out in the direction of the force, F c, in which single plane bending occurs. Chain Sprockets con t If the angle is small, little error will result from the assumption that the entire force, F c, acts along the x-direction. 1

13 V-Belt Sheaves The general appearance of the V-belt drive system looks similar to the chain drive system. There is one important difference: both sides of the V- belt are in tension, as shown in the next slide. Mott, 003, Machine Elements in Mechanical Design V-Belt Sheaves con t The tight side tension, F 1, is greater than the slack side tension, F, and there is a net driving force on the sheaves equal to: F N = F 1 F The magnitude of the net driving force can be computed from the torque transmitted: F N = T / (D/) 13

14 V-Belt Sheaves con t Notice that the bending force on the shaft carrying the sheave is dependent on the sum, F 1 + F = F B. To be more precise, the components of F 1 and F parallel to the line of centers of the two sprockets should be used. But unless the two sprockets are radically different in diameter, little error will result from F B = F 1 + F. V-Belt Sheaves con t To determine the bending force, F B, a second equation involving the two forces F 1 and F is needed. For V-belt drives, the ratio is: F 1 / F = 5 It is convenient to derive a relationship between F N and F B of the form: F B = CFN Where C = constant to be determined V-Belt Sheaves con t F C = F B N = F1 + F F1 F But from F 1 = 5F, F C = F F F 5F + F = 5F F = 6F 4F =

15 V-Belt Sheaves con t Then, for V-belt drives: 1.5T FB = 1.5FN = D / It is customary to consider the bending force, F B, to act as a single force in the direction along the line of centers of the two sheaves. Flat-Belt Pulleys The analysis of the bending force exerted on shafts by flat-belt pulleys is identical to that for V-belt sheaves except that the ratio of the tight side to the slack side tension is typically taken to be 3 instead of 5. Using the same logic as with V-belt sheaves, compute the constant C to be.0. Then, for flat-belt drives, F B =.0F N =.0T / (D/) Stress Concentrations In order to mount and locate the several types of machine elements on shafts properly, a final design typically contains several diameters, keyseats, ring grooves, and other geometric discontinuities that create stress concentrations. 15

16 Stress Concentrations These stress concentrations must be taken into account during the design analysis. But a problem exists because the true design values of the stress concentration factors, K t, are unknown at the start of the design process. Stress Concentrations Most of the values are dependent on the diameters of the shaft and on the fillet and groove geometries, and these are the objectives of the design. Preliminary Design Values for K t Considered here are the types of geometric discontinuities most often found in power-transmitting shafts: keyseats, shoulder fillets, and retaining ring grooves. In each case, a suggested design value is relatively high in order to produce a conservative result for the first approximation to the design. Again it is emphasized that the final design should be checked for safety. 16

17 Keyseats A keyseat is a longitudinal groove cut into a shaft for the mounting of a key, permitting the transfer of torque from the shaft to a power-transmitting element, or vice versa. Two types of keyseats are most frequently used: profile and sled runner. Mott, 003, Machine Elements in Mechanical Design Keyseats con t The profile keyseat is milled into the shaft, using an end mill having a diameter equal to the width of the key. The resulting groove is flat-bottomed and has a sharp, square corner at its end. The sled runner keyseat is produced by a circular milling cutter having a width equal to the width of the key. 17

18 Keyseats con t As the cutter begins or ends the keyseat, it produces a smooth radius. For this reason, the stress concentration factor for the sled runner keyseat is lower than that for the profile keyseat. Keyseats con t Normally used design values are: K t =.0 (profile) K t = 1.6 (sled runner) Shoulder Fillets When a change in diameter occurs in a shaft to create a shoulder against which to locate a machine element, a stress concentration dependent on the ratio of the two diameters and on the radius in the fillet is produced. 18

19 Mott, 003, Machine Elements in Mechanical Design Shoulder Fillets con t It is recommended that the fillet radius be as large as possible to minimize the stress concentration, but at times the design of the gear, bearing, or other element affects the radius that can be used. Shoulder Fillets con t The term sharp here does not mean truly sharp, without any fillet radius at all. Such a shoulder configuration would have a very high stress concentration factor and should be avoided. Instead, sharp describes a shoulder with a relatively small fillet radius. 19

20 Shoulder Fillets con t When an element with a large chamfer on its bore is located against the shoulder, or when nothing at all seats against the shoulder, the fillet radius can be much larger (well-rounded), and the corresponding stress concentration factor is smaller. K t =.5 (sharp fillet) K t = 1.5 (well-rounded fillet) Retaining Ring Grooves Retaining rings are used for many types of locating tasks in shaft applications. The rings are installed in grooves in the shaft after the element to be retained is in place. The geometry of the groove is dictated by the ring manufacturer. Retaining Ring Grooves Its usual configuration is a shallow groove with straight side walls and bottom and a small fillet at the base of the groove. The behavior of the shaft in the vicinity of the groove can be approximated by considering two sharp-filleted shoulders positioned close together. 0

21 Retaining Ring Grooves For preliminary design, apply K t = 3.0 to the bending stress at a retaining ring groove to account for the rather sharp fillet radii. Design Stresses for Shafts In a given shaft, several different stress conditions can exist at the same time. For any part of the shaft that transmits power, there will be a torsional shear stress, while bending stress is usually present on the same parts. Design Stresses for Shafts con t Only bending stresses may occur on other parts. Some points may not be subjected to either bending or torsion but will experience vertical shearing stress. Axial tensile or compressive stresses may be superimposed on the other stresses. Then there may be some points where no significant stresses at all are created. 1

22 Design Stresses for Shafts con t The decision of what design stress to use depends on the particular situation at the point of interest. In many shaft design and analysis projects, computations must be done at several points to account completely for the variety of loading and geometry conditions that exist. Design Stresses for Shafts con t The bending stresses will be assumed to be completely reversed and repeated because of the rotation of the shaft. Because ductile materials perform better under such loads, it will be assumed that the material for the shaft is ductile and that the torsional loading is relatively constant and acting in one direction. Design Shear Stress- Steady Torque The best predictor of failure in ductile materials due to a steady shear stress was the distortion energy theory in which the design shear stress is computed from: τ sy sy d = (0.577 ) N 3 = N We will use this value for steady torsional shear stress, vertical shear stress, or direct shear stress in a shaft.

23 Design Shear Stress- Reversed Vertical Shear Points on a shaft where no torque is applied and where the bending moments are zero or very low are often subjected to significant vertical shearing forces which then govern the design analysis. This typically occurs where a bearing supports an end of a shaft and where no torque is transmitted in that part of the shaft. Design Shear Stress- Reversed Vertical Shear The maximum shearing stress is at the neutral axis of the shaft. The stress decreases in a roughly parabolic manner to zero at the outer surface of the shaft. Mott, 003, Machine Elements in Mechanical Design 3

24 Design Shear Stress- Reversed Vertical Shear The maximum vertical shearing stress for the special case of a solid circular cross section can be computed from: τ max = 4V / 3A Where V = vertical shearing force A = area of cross section Design Shear Stress- Reversed Vertical Shear Where stress concentration factors are to be considered: τ max = K t (4V / 3A) Also note that the rotation of the shaft causes any point at the outer part of the cross section to experience a reversing shearing stress that varies from + τ max to zero to - τ max to zero in each revolution. Mott, 003, Machine Elements in Mechanical Design 4

25 Design Shear Stress- Reversed Vertical Shear Then the stress analysis should be completed using a safety factor: N = s sn / τ max Where s sn is the endurance limit in shear Using the distortion energy theory. Then the endurance strength is: s sn = 0.577s n Where s n is the endurance limit of the material Design Shear Stress- Reversed Vertical Shear Then the equation can be written in the form: N = 0.577s n / τ max Expressed as a design stress: τ d = 0.577s n / N Letting τ max = τ d = [K t (4V)] / 3A gives: Kt (4V) 0.577s' n = 3A N Design Shear Stress- Reversed Vertical Shear Solving for N gives: 0.577s' n(3a) 0.433s' n( A) N = = Kt(4V) Kt( V) Solving for the required area: Kt( V) N.31Kt( V) N A = = 0.433s' n s' n 5

26 Design Shear Stress- Reversed Vertical Shear By substituting: A = πd / 4 Solve for D: D =.94Kt( V) N / s' n Design Shear Stress- Reversed Vertical Shear This equation should be used to compute the required diameter for a shaft where a vertical shearing force V is the only significant loading present. In most shafts, the resulting diameter will be much smaller than that required at other parts of the shaft where significant values of torque and bending occur. Design Shear Stress- Reversed Vertical Shear Implementation of the previous equations has the complication that values for the stress concentration factor under conditions of vertical shearing stress are not well known. As an approximation, use the values for K t for torsional stress when using these equations. 6

27 Design Shear Stress- Fatigue Loading For the repeated, reversed bending in a shaft caused by transverse loads applied to the rotating shaft, the design stress is related to the endurance strength of the shaft material. Refer to the discussion in Section 5-4 in Chapter 5 for the method of computing the estimated actual endurance strength, s n, for use in shaft design. Design Shear Stress- Fatigue Loading Note that any stress concentration factor will be accounted for in the design equation developed later. Other factors, not considered here, that could have an adverse effect on the endurance strength of the shaft material are: temperatures above 400 o F variation in peak stress levels above the nominal endurance strength for some periods of time Design Shear Stress- Fatigue Loading vibration residual stresses case hardening interference fits corrosion thermal cycling plating or surface coating stresses not accounted for in the basic stress analysis. 7

28 Design Shear Stress- Fatigue Loading For parts of the shaft subjected to only reversed bending, let the design stress be: σ d = s n / N Design Factor Use N =.0 for typical shaft designs where there is average confidence in the data for material strength and loads. Higher values should be used for shock and impact loading and where uncertainty in the data exists. Design Factor con t Examples of shafts subjected to bending and torsion only are those carrying spur gears, V-belt sheaves, or chain sprockets. The power being transmitted causes the torsion, and the transverse forces on the elements cause bending. In the general case, the transverse forces do not all act in the same plane. 8

29 Design Factor con t In such cases, the bending moment diagrams for two perpendicular planes are prepared first. Then the resultant bending moment at each point of interest is determined. Design Factor con t A design equation is now developed based on the assumption that the bending stress in the shaft is repeated and reversed as the shaft rotates, but that the torsional shear stress is nearly uniform. The design equation is based on the principle shown graphically in which the vertical axis is the ratio of the reversed bending stress to the endurance strength of the material. Mott, 003, Machine Elements in Mechanical Design 9

30 Design Factor con t The horizontal axis is the ratio of the torsional shear stress to the yield strength of the material in shear. The points having value of 1.0 on these axes indicated impending failure in pure bending or pure torsion, respectively. Design Factor con t Experimental data show that failure under combinations of bending and torsion roughly follows the curve connecting these two points, which obeys the following equation: (σ / s n ) + (τ / s ys ) = 1 Design Factor con t We will use s ys = sy / 3 for the distortion energy theory. Also, a design factor can be introduced to each term on the left side of the equation to yield an expression based on design stresses: ( Nσ / s' n ) + ( Nτ 3 / sy) = 1 30

31 Design Factor con t Now we can introduce a stress concentration factor for bending in the first term only, because this stress is repeated. No factor is needed for the torsional shear stress term because it is assumed to be steady, and stress concentrations have little or no effect on the failure potential: ( K t Nσ / s' n) + ( Nτ 3 / sy) = 1 Design Factor con t For rotating, solid, circular shafts, the bending stress due to a bending moment, M, is: σ = M / S Where S = πd 3 / 3 is the rectangular section modulus. The torsional shear stress is: τ = T / Z p Where Z p = πd 3 / 16 is the polar section modulus Note that Z p = S τ = T / (S) Design Factor con t Substituting these relationships: KtNM NT 3 + = 1 Ss' n Ssy Now the terms N and S can be factored out, and the terms 3 and can be brought outside the bracket in the torsional term: N KtM 3 T + = 1 ' 4 S s n sy 31

32 3 Design Factor con t We now take the square root of the entire equation: Let S = πd 3 / 3 for a solid circular shaft: ' = + y n t s T s K M S N ' 3 3 = + π y n t s T s K M D N Design Factor con t Now we can solve for the diameter D: This is used for shaft design in this book. It is compatible with the standard ANSI B106.1M Note that it can also be used for pure bending or pure torsion. 3 1 / 4 3 ' 3 + π = y n t s T s K M N D Mott, 003, Machine Elements in Mechanical Design

33 Mott, 003, Machine Elements in Mechanical Design Mott, 003, Machine Elements in Mechanical Design Mott, 003, Machine Elements in Mechanical Design 33

34 Mott, 003, Machine Elements in Mechanical Design Mott, 003, Machine Elements in Mechanical Design Mott, 003, Machine Elements in Mechanical Design 34

35 Mott, 003, Machine Elements in Mechanical Design Mott, 003, Machine Elements in Mechanical Design Mott, 003, Machine Elements in Mechanical Design 35

36 Mott, 003, Machine Elements in Mechanical Design 36

### Belt Drives and Chain Drives. Power Train. Power Train

Belt Drives and Chain Drives Material comes for Mott, 2002 and Kurtz, 1999 Power Train A power train transmits power from an engine or motor to the load. Some of the most common power trains include: Flexible

### Stress and Deformation Analysis. Representing Stresses on a Stress Element. Representing Stresses on a Stress Element con t

Stress and Deformation Analysis Material in this lecture was taken from chapter 3 of Representing Stresses on a Stress Element One main goals of stress analysis is to determine the point within a load-carrying

### 14. Belt and Chain Drives. Objectives. Introduction. Introduction

14. Belt and Chain Drives August 15, 007 1 August 15, 007 Objectives Introduction Understand principles of operation of flexibledrive systems. Determine allowable forces and torques for flexible-drive

### POWER SCREWS (ACME THREAD) DESIGN

POWER SCREWS (ACME THREAD) DESIGN There are at least three types of power screw threads: the square thread, the Acme thread, and the buttress thread. Of these, the square and buttress threads are the most

CH 6: Fatigue Failure Resulting from Variable Loading Some machine elements are subjected to static loads and for such elements static failure theories are used to predict failure (yielding or fracture).

### Module 2 - GEARS Lecture 7 - SPUR GEAR DESIGN

Module 2 - GEARS Lecture 7 - SPUR GEAR DESIGN Contents 7.1 Spur gear tooth force analysis 7.2 Spur gear - tooth stresses 7.3 Tooth bending stress Lewis equation 7.4 Tooth bending stress AGMA procedure

### superimposing the stresses and strains cause by each load acting separately

COMBINED LOADS In many structures the members are required to resist more than one kind of loading (combined loading). These can often be analyzed by superimposing the stresses and strains cause by each

### B.TECH. (AEROSPACE ENGINEERING) PROGRAMME (BTAE) Term-End Examination December, 2011 BAS-010 : MACHINE DESIGN

No. of Printed Pages : 7 BAS-01.0 B.TECH. (AEROSPACE ENGINEERING) PROGRAMME (BTAE) CV CA CV C:) O Term-End Examination December, 2011 BAS-010 : MACHINE DESIGN Time : 3 hours Maximum Marks : 70 Note : (1)

### Torsion Testing. Objectives

Laboratory 4 Torsion Testing Objectives Students are required to understand the principles of torsion testing, practice their testing skills and interpreting the experimental results of the provided materials

### HOW BELT DRIVES IMPACT OVERHUNG LOAD

WHITE PAPER HOW BELT DRIVES IMPACT OVERHUNG LOAD Shafts and bearings on speed reducers can only take so much overhung load but how much is too much? Introduction Today s belt drive systems are capable

### Belt drives systems may be assembled to (Figure 9.1): Opened belt drive (non-reversing) Reversing crossed or twist belt drive Angled belt drive

heory of Machines / Belt Drives 9. Belt Drives 9. Geometry Specification 9.. Construction: Belt drives systems may be consist of (Figure 9.): Driving pulley Driven pulleys (multiple driven sources) Belts

### MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL 1 SIMPLE MACHINES

MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL 1 SIMPLE MACHINES Simple machines: lifting devices e.g. lever systems, inclined plane, screw jack, pulley blocks, Weston differential

### Structural Axial, Shear and Bending Moments

Structural Axial, Shear and Bending Moments Positive Internal Forces Acting Recall from mechanics of materials that the internal forces P (generic axial), V (shear) and M (moment) represent resultants

### Torsion Tests. Subjects of interest

Chapter 10 Torsion Tests Subjects of interest Introduction/Objectives Mechanical properties in torsion Torsional stresses for large plastic strains Type of torsion failures Torsion test vs.tension test

### 17. Shaft Design. Introduction. Torsion of circular shafts. Torsion of circular shafts. Standard diameters of shafts

Objetives 17. Shaft Design Compute fores ating on shafts from gears, pulleys, and sprokets. ind bending moments from gears, pulleys, or sprokets that are transmitting loads to or from other devies. Determine

### Foundation Engineering Prof. Mahendra Singh Department of Civil Engineering Indian Institute of Technology, Roorkee

Foundation Engineering Prof. Mahendra Singh Department of Civil Engineering Indian Institute of Technology, Roorkee Module - 03 Lecture - 09 Stability of Slopes Welcome back to the classes of on this Stability

### rgab.ru Берг 30 АБ Тел. (495) , факс (495) 22

rgab.ru 4. Берг Calculation АБ bergab@ya.ru of Bearing Тел. (495)-228-06-21, Load факс (495) 22 4. Calculation of Bearing Load In order to obtain the values of loads applied to a bearing, all of weight

### Solid Mechanics. Stress. What you ll learn: Motivation

Solid Mechanics Stress What you ll learn: What is stress? Why stress is important? What are normal and shear stresses? What is strain? Hooke s law (relationship between stress and strain) Stress strain

### COMPLEX STRESS TUTORIAL 3 COMPLEX STRESS AND STRAIN

COMPLX STRSS TUTORIAL COMPLX STRSS AND STRAIN This tutorial is not part of the decel unit mechanical Principles but covers elements of the following sllabi. o Parts of the ngineering Council eam subject

### GEAROLOGY 2-1 SPUR GEARS SPUR GEARS

GEAROLOGY 2-1 2 2-2 GEAROLOGY COMMON APPLICATIONS: Spur gears are used to Now that you ve been introduced to both Boston Gear and some of the basics of our Gearology course which we like to call Power

### Mechanical Principles

Unit 4: Mechanical Principles Unit code: F/60/450 QCF level: 5 Credit value: 5 OUTCOME 3 POWER TRANSMISSION TUTORIAL BELT DRIVES 3 Power Transmission Belt drives: flat and v-section belts; limiting coefficient

### Copyright 2011 Casa Software Ltd. www.casaxps.com. Centre of Mass

Centre of Mass A central theme in mathematical modelling is that of reducing complex problems to simpler, and hopefully, equivalent problems for which mathematical analysis is possible. The concept of

### MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL 2 BELT DRIVES

MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL BELT DRIVES Simple machines: lifting devices e.g. lever systems, inclined plane, screw jack, pulley blocks, Weston differential pulley

### P4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 4 Stresses on Inclined Sections

4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 4 Stresses on Inclined Sections Shear stress and shear strain. Equality of shear stresses on perpendicular planes. Hooke s law in shear. Normal and shear

### Module 2- GEARS. Lecture 8 SPUR GEAR DESIGN

Module 2- GEARS Lecture 8 SPUR GEAR DESIGN Contents 8.1 Surface durability basic concepts 8.2 Surface failures 8.3 Buckingham contact stress equation 8.4 Contact stress AGMA procedure 8.5 Surface fatigue

### Design Analysis and Review of Stresses at a Point

Design Analysis and Review of Stresses at a Point Need for Design Analysis: To verify the design for safety of the structure and the users. To understand the results obtained in FEA, it is necessary to

### MECHANICS OF SOLIDS - BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS

MECHANICS OF SOLIDS - BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS This is the second tutorial on bending of beams. You should judge your progress by completing the self assessment exercises.

### Chapter 4. Forces and Newton s Laws of Motion. continued

Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting

### Analysis of Stresses and Strains

Chapter 7 Analysis of Stresses and Strains 7.1 Introduction axial load = P / A torsional load in circular shaft = T / I p bending moment and shear force in beam = M y / I = V Q / I b in this chapter, we

### 15. Couplings and Keys. Keys. Fig Flat Key. Flat Key. Fig Other types of keys

Objectives 15. Couplings and Keys Recognize different types of keys and their standard sizes. Size keys for appropriate structural loads. Recognize many types of couplings and their advantages and disadvantages.

### Gears, Velocity Ratios and Mechanical Advantage

Gears, Velocity Ratios and Mechanical Advantage What are gears and why are they so Gears are toothed wheels which interlock to form simple machines. The tighter the joint, the less chance of slipping Gears

### ENGINEERING SCIENCE H1 OUTCOME 1 - TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P

ENGINEERING SCIENCE H1 OUTCOME 1 - TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P This material is duplicated in the Mechanical Principles module H2 and those

Fatigue Failure Due to Variable Loading Daniel Hendrickson Department of Computer Science, Physics, and Engineering University of Michigan Flint Advisor: Olanrewaju Aluko 1. Abstract Fatigue failure in

### Gear Tooth Strength Analysis by W.H.Dornfeld Tooth Strength:

Gear Tooth Strength Analysis 1 Stresses on Spur Gear Teeth The two primary failure modes for gears are: 1) Tooth Breakage - from excessive bending stress, and 2) Surface Pitting/Wear - from excessive contact

### Screw Thread Design. Rev. 3-4-09

Screw Thread Design Screw Thread Fundamentals A screw thread is defined as a ridge of uniform section in the form of a helix on either the external or internal surface of a cylinder. Internal threads refer

### Introduction: Friction Wheels:

Toothed Gearing Introduction: We have discussed in the previous chapter, that the slipping of a belt or rope is a common phenomenon, in the transmission of motion or power between two shafts. The effect

### Lecture Slides. Chapter 8. Screws, Fasteners, and the Design of Nonpermanent Joints

Lecture Slides Chapter 8 Screws, Fasteners, and the Design of Nonpermanent Joints The McGraw-Hill Companies 2012 Chapter Outline Reasons for Non-permanent Fasteners Field assembly Disassembly Maintenance

### Mechanical Analysis Belt and chain drives

Mechanical Analysis and Design ME 2104 Lecture 3 Mechanical Analysis Belt and chain drives Prof Ahmed Kovacevic School of Engineering and Mathematical Sciences Room CG25, Phone: 8780, E-Mail: a.kovacevic@city.ac.uk

Week 8 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution

### Projectile Motion. directions simultaneously. deal with is called projectile motion. ! An object may move in both the x and y

Projectile Motion! An object may move in both the x and y directions simultaneously! The form of two-dimensional motion we will deal with is called projectile motion Assumptions of Projectile Motion! The

### Newton s Third Law. object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1

Newton s Third Law! If two objects interact, the force exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1!! Note on notation: is

### Disc vs Diaphragm Couplings

A l t r a I n d u s t r i a l M o t i o n Warner Electric Boston Gear TB Wood s Formsprag Clutch Disc vs Diaphragm Couplings Wichita Clutch Marland Clutch Industrial Clutch Bauer Gear Motor Nuttall Gear

### Parts (lines) Hoist Number of lines of rope supporting the load block or hook. (ASME HST-4M-1991) Patented track Bridge Crane

Parts (lines) Number of lines of rope supporting the load block or. (ASME HST-4M-1991) Patented track A generic term referring to crane and monorail equipment built in accordance with the MMA specification

### Milling. COPYRIGHT 2008, Seco Tools AB 1/111

Milling 1/111 2/111 Milling A simple choice! Experts required? No Just follow some basic rules. 3/111 Face milling 4/111 Square shoulder milling 5/111 Disc milling 6/111 Copy milling 7/111 Plunge milling

### SOLID MECHANICS DYNAMICS TUTORIAL PULLEY DRIVE SYSTEMS. This work covers elements of the syllabus for the Edexcel module HNC/D Mechanical Principles.

SOLID MECHANICS DYNAMICS TUTORIAL PULLEY DRIVE SYSTEMS This work covers elements of the syllabus for the Edexcel module HNC/D Mechanical Principles. On completion of this tutorial you should be able to

### 9. TIME DEPENDENT BEHAVIOUR: CYCLIC FATIGUE

9. TIME DEPENDENT BEHAVIOUR: CYCLIC FATIGUE A machine part or structure will, if improperly designed and subjected to a repeated reversal or removal of an applied load, fail at a stress much lower than

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 1 NON-CONCURRENT COPLANAR FORCE SYSTEMS 1. Be able to determine the effects

### Welcome to the first lesson of third module which is on thin-walled pressure vessels part one which is on the application of stress and strain.

Strength of Materials Prof S. K. Bhattacharya Department of Civil Engineering Indian Institute of Technology, Kharagpur Lecture -15 Application of Stress by Strain Thin-walled Pressure Vessels - I Welcome

### DESIGN OF ADAPTIVE MULTI TOOL ARBOR ATTACHMENT

INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 6340(Print), ISSN 0976 6340 (Print) ISSN 0976 6359

### WEAR TESTING AND MEASUREMENT TECHNIQUES FOR POLYMER COMPOSITE GEARS

WEAR TESTING AND MEASUREMENT TECHNIQUES FOR POLYMER COMPOSITE GEARS N. A. Wright and S. N. Kukureka Wear, 250, 1567, (2001) Presented at 13 th International Wear of Materials Conference, Vancouver, 2001.

### Introduction, Method of Sections

Lecture #1 Introduction, Method of Sections Reading: 1:1-2 Mechanics of Materials is the study of the relationship between external, applied forces and internal effects (stress & deformation). An understanding

### Home"" """"> ar.cn.de.en.es.fr.id.it.ph.po.ru.sw

Home"" """"> ar.cn.de.en.es.fr.id.it.ph.po.ru.sw Milling of Grooves, Elongated Slots and Break-throughs - Course: Techniques for machining of material. Trainees' handbook of lessons (Institut fr Berufliche

### Coupling Alignment Fundamentals

Page (1 of 14) CONTENTS I. Why Align Rotating Equipment? II. Defining Shaft Misalignment III. Alignment Methods Poor, Fair, Good and Best IV. Pre-Alignment Considerations V. Alignment Methods A. Rim and

### DRAFTING MANUAL. Gears (Bevel and Hypoid) Drafting Practice

Page 1 1.0 General This section provides the basis for uniformity in engineering gears drawings and their technical data for gears with intersecting axes (bevel gears), and nonparallel, nonintersecting

### Figure 1: Typical S-N Curves

Stress-Life Diagram (S-N Diagram) The basis of the Stress-Life method is the Wohler S-N diagram, shown schematically for two materials in Figure 1. The S-N diagram plots nominal stress amplitude S versus

### SPECIFICATIONS Rev:

SPECIFICATIONS Rev: 060209 Section Helical Steel Piles 1. General 1.1. Description 1.1.1. The work of this section consists of furnishing and installing steel helical piles manufactured by MacLean-Dixie

### Dimensioning and Tolerancing

Dimensioning and Tolerancing Dimensioning Before an object can be built, complete information about both the size and shape of the object must be available. The exact shape of an object is communicated

### Survey of CVTs for Robot Joints. Simon Kalouche CMU Robotics Institute

Survey of CVTs for Robot Joints Simon Kalouche CMU Robotics Institute Types of CVTs Friction Drives Cone Drives Disk Drives Spherical Drives Pulley-Belt Drives Torodial CVT Infinitely Variable Transmission

### Machine Design II Prof. K.Gopinath & Prof. M.M.Mayuram. Module 2 - GEARS. Lecture 17 DESIGN OF GEARBOX

Module 2 - GEARS Lecture 17 DESIGN OF GEARBOX Contents 17.1 Commercial gearboxes 17.2 Gearbox design. 17.1 COMMERCIAL GEARBOXES Various commercial gearbox designs are depicted in Fig. 17.1 to 17.10. These

### Force measurement. Forces VECTORIAL ISSUES ACTION ET RÉACTION ISOSTATISM

Force measurement Forces VECTORIAL ISSUES In classical mechanics, a force is defined as "an action capable of modifying the quantity of movement of a material point". Therefore, a force has the attributes

### Common Mechanical Engineering Terms

Common Mechanical Engineering Terms Ball and Detent (n) A simple mechanical arrangement used to hold a moving part in a temporarily fixed position relative to another part. The ball slides within a bored

### The elements used in commercial codes can be classified in two basic categories:

CHAPTER 3 Truss Element 3.1 Introduction The single most important concept in understanding FEA, is the basic understanding of various finite elements that we employ in an analysis. Elements are used for

### EQUILIBRIUM AND ELASTICITY

Chapter 12: EQUILIBRIUM AND ELASTICITY 1 A net torque applied to a rigid object always tends to produce: A linear acceleration B rotational equilibrium C angular acceleration D rotational inertia E none

### Module 2- GEARS. Lecture 9 - SPUR GEAR DESIGN

Module 2- GEARS Lecture 9 - SPUR GEAR DESIGN Contents 9.1 Problem 1 Analysis 9.2 Problem 2 Spur gear 9.1 PROBLEM 1 SPUR GEAR DESIGN In a conveyor system a step-down gear drive is used. The input pinion

### INTRODUCTION TO BEAMS

CHAPTER Structural Steel Design LRFD Method INTRODUCTION TO BEAMS Third Edition A. J. Clark School of Engineering Department of Civil and Environmental Engineering Part II Structural Steel Design and Analysis

### 2. DRILLING MACHINE. 2.1 Introduction. 2.2 Construction of a drilling machine. 2.3 Types of drilling machines Portable drilling machine

2.1 Introduction 2. DRILLING MACHINE Drilling machine is one of the most important machine tools in a workshop. It was designed to produce a cylindrical hole of required diameter and depth on metal workpieces.

### ME 343: Mechanical Design-3

ME 343: Mechanical Design-3 Design of Shaft (continue) Dr. Aly Mousaad Aly Department of Mechanical Engineering Faculty of Engineering, Alexandria University Objectives At the end of this lesson, we should

### GEAROLOGY 4-1 WORMS AND WORM GEARS WORMS AND WORM GEARS

GEAROLOGY 4-1 4 4-2 GEAROLOGY COMMON APPLICATIONS: Worm and worm gear sets are used in many, everyday products including: electrical mixers, hubometers, right Now that you have an understanding of two

### Design of Bottle Filling Indexing Table with Proximity Sensor

Design of Bottle Filling Indexing Table with Proximity Sensor Waykole N.G 1, Panchal S. V 2, Rajput P. D 3 1,2,3 Student at Smt. S. S. Patil Institute of Technology (Polytechnic) Abstract: In this paper

### Stresses in Beam (Basic Topics)

Chapter 5 Stresses in Beam (Basic Topics) 5.1 Introduction Beam : loads acting transversely to the longitudinal axis the loads create shear forces and bending moments, stresses and strains due to V and

### Module 5 Couplings. Version 2 ME, IIT Kharagpur

Module 5 Couplings Lesson 1 Introduction, types and uses Instructional Objectives At the end of this lesson, the students should have the knowledge of The function of couplings in machinery. Different

### MODEL SPECIFICATIONS: Helical Pile Specifications

MODEL SPECIFICATIONS: Helical Pile Specifications March/2015 v1.1 31 66 00 HELICAL PILE/ANCHOR DEEP FOUNDATIONS PART 1 GENERAL 1.01 SCOPE OF WORK The work shall consist of the Helical Pile Contractor furnishing

### Module 13 Belt drives. Version 2 ME, IIT Kharagpur

Module 3 Belt drives Version ME, IIT Kharagpur esson Introduction to Belt drives Version ME, IIT Kharagpur Instructional Objectives: At the end of this lesson, the students should be able to understand:

### Design of Belts, Ropes and Chains -- U8

42 Design of Belts, Ropes and Chains -- U8 INTRODUCTION Power is transmitted from the prime mover to a machine by means of intermediate mechanism called drives. This intermediate mechanism known as drives

### Solving Simultaneous Equations and Matrices

Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering

### Gearing group, all types of gearing used in machine construction, gear combinations.

SECTION V \s. 65 80 Gearing group, all types of gearing used in machine construction, gear combinations. MECHANICAL MODELS 31 Section V 65. Spur gears. Gears are used to transmit power from one shaft

MET 33800 Manufacturing Processes Chapter 42 Thread and Gear Manufacturing Before you begin: Turn on the sound on your computer. There is audio to accompany this presentation. THREAD MANUFACTURING Screw

### Mechanics Lecture Notes. 1 Notes for lectures 12 and 13: Motion in a circle

Mechanics Lecture Notes Notes for lectures 2 and 3: Motion in a circle. Introduction The important result in this lecture concerns the force required to keep a particle moving on a circular path: if the

### Technical Data. 7. Bearing Fits. 7.1 Interference. 7.2 Calculation of interference F B LLLLLLLLL( A-54

Technical Data 7. Bearing Fits 7.1 Interference For rolling s the rings are fixed on the or in the housing so that slip or movement does not occur between the mated surface during operation or under. This

### LEGACY REPORT ER-5110. www.icc-es.org. ICC Evaluation Service, Inc. Reissued November 1, 2003. Legacy report on the 1997 Uniform Building Code

LEGACY REPORT Reissued November 1, 2003 ICC Evaluation Service, Inc. www.icc-es.org Business/Regional Office # 5360 Workman Mill Road, Whittier, California 90601 # (562) 699-0543 Regional Office # 900

### UNIT 6 GEAR GENERATION AND FINISHING OPERATIONS

UNIT 6 GEAR GENERATION AND FINISHING OPERATIONS Structure 6.1 Introduction Objectives 6.2 Gear Terminology 6.3 Method of Gear Manufacturing 6.4 Gear Cutting Methods 6.5 Gear Milling 6.6 Gear 6.7 Gear Shaving

### 7 Centrifugal loads and angular accelerations

7 Centrifugal loads and angular accelerations 7.1 Introduction This example will look at essentially planar objects subjected to centrifugal loads. That is, loads due to angular velocity and/or angular

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS

EDEXCEL NATIONAL CERTIICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQ LEVEL 3 OUTCOME 1 - LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS 1. Be able to determine the effects of loading in static engineering

### Forces. -using a consistent system of units, such as the metric system, we can define force as:

Forces Force: -physical property which causes masses to accelerate (change of speed or direction) -a push or pull -vector possessing both a magnitude and a direction and adds according to the Parallelogram

### A Hardware/Software Centered Approach to the Elements of Machine Design Course At a Four Year School of ET

Session #1566 A Hardware/Software Centered Approach to the Elements of Machine Design Course At a Four Year School of ET Howard A. Canistraro, Ph.D. Ward College of Technology University of Hartford Introduction:

### Physics 2305 Lab 11: Torsion Pendulum

Name ID number Date Lab CRN Lab partner Lab instructor Physics 2305 Lab 11: Torsion Pendulum Objective 1. To demonstrate that the motion of the torsion pendulum satisfies the simple harmonic form in equation

### Design of Steel Structures Dr. Damodar Maity Department of Civil Engineering Indian Institute of Technology, Guwahati

Design of Steel Structures Dr. Damodar Maity Department of Civil Engineering Indian Institute of Technology, Guwahati Module - 4 Tension Members Lecture - 2 Design of Tension Member Hello. Today, we will

### MECHANICS OF SOLIDS COMPRESSION MEMBERS TUTORIAL 1 STRUTS. On completion of this tutorial you should be able to do the following.

MECHANICS OF SOLIDS COMPRESSION MEMBERS TUTORIAL 1 STRUTS You should judge your progress by completing the self assessment exercises. On completion of this tutorial you should be able to do the following.

### Design of a Universal Robot End-effector for Straight-line Pick-up Motion

Session Design of a Universal Robot End-effector for Straight-line Pick-up Motion Gene Y. Liao Gregory J. Koshurba Wayne State University Abstract This paper describes a capstone design project in developing

### 4 Shear Forces and Bending Moments

4 Shear Forces and ending oments Shear Forces and ending oments 8 lb 16 lb roblem 4.3-1 alculate the shear force and bending moment at a cross section just to the left of the 16-lb load acting on the simple

### Basics of Mechanical Engineering CODE: ME-101-F Lecture on Power Transmission Methods and Devices

Basics of Mechanical Engineering CODE: ME-101-F Lecture on Power Transmission Methods and Devices Introduction Power is transmitted from one shaft to another shaft by means of belts, ropes, chains and

### Objective: Equilibrium Applications of Newton s Laws of Motion I

Type: Single Date: Objective: Equilibrium Applications of Newton s Laws of Motion I Homework: Assignment (1-11) Read (4.1-4.5, 4.8, 4.11); Do PROB # s (46, 47, 52, 58) Ch. 4 AP Physics B Mr. Mirro Equilibrium,

### Stack Contents. Pressure Vessels: 1. A Vertical Cut Plane. Pressure Filled Cylinder

Pressure Vessels: 1 Stack Contents Longitudinal Stress in Cylinders Hoop Stress in Cylinders Hoop Stress in Spheres Vanishingly Small Element Radial Stress End Conditions 1 2 Pressure Filled Cylinder A

### Fall 12 PHY 122 Homework Solutions #8

Fall 12 PHY 122 Homework Solutions #8 Chapter 27 Problem 22 An electron moves with velocity v= (7.0i - 6.0j)10 4 m/s in a magnetic field B= (-0.80i + 0.60j)T. Determine the magnitude and direction of the

### FOOTING DESIGN EXAMPLE

County: Any Design: BRG Date: 10/007 Hwy: Any Ck Dsn: BRG Date: 10/007 FOOTING DESIGN EXAMPLE Design: Based on AASHTO LRFD 007 Specifications, TxDOT LRFD Bridge Design Manual, and TxDOT Project 0-4371

### Physics, Chapter 3: The Equilibrium of a Particle

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Robert Katz Publications Research Papers in Physics and Astronomy 1-1-1958 Physics, Chapter 3: The Equilibrium of a Particle

### Angular Momentum Problems Challenge Problems

Angular Momentum Problems Challenge Problems Problem 1: Toy Locomotive A toy locomotive of mass m L runs on a horizontal circular track of radius R and total mass m T. The track forms the rim of an otherwise

### Direct Gear Design for Optimal Gear Performance

Direct Gear Design for Optimal Gear Performance Alex Kapelevich (AKGears, LLC), Thomas McNamara (Thermotech Company) The paper presents the Direct Gear Design an alternative method of analysis and design