Design Trans

8/12/2019 Design Trans

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2/6/2002 2000 Alexander Slocum5-1

Topic 5Power Transmission Elements I

Topics : Transmissions Pulleys Belts & Cables

Winches Wheels Cams Shafts Couplings Robust Design Reminder

F

W


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Transmissions

A transmission transmits power from a motor (input) to an actuator (output)that does useful work Often the transmission transducts the power:

A high speed low torque motor (voltage is cheap, current is expensive) is theinput

A low speed high torque output is desired (e.g., for a winch)

Transmission design parameters: Motion profile

Optimal transmission ratio

Velocity check

Efficiency: Sliding contact systems (screws, sliding bearings) = 0.3 Rolling contact systems (gears, ball bearings, hard wheels)

= 0.95


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Transmissions: Motion Profiles

Given it is desired to move a specified load a specified distance in a giventime:

Assume a parabolic profile is 100% efficient Triangular profile is the fastest, but only 75% efficient A trapezoidal profile with equal acceleration, slew (constant speed), and

deceleration times is 89% efficient Given the distance D that the load is required to move

Time

V e l o c

i t y

t a t dt c

D = amax2

tc3

2 + amtc

3 2tc

3 + amax

2 tc

3

2

amax = 9D2t c

2 , maximum acceleration (m/s 2 or rad/ s 2)

vmax = 3D2tc

, maximum velocity (m/s or rad/s)


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Transmissions: Lightly Loaded Systems

There is an optimal transmission ratio which maximizes system efficiency For low frictional and cutting forces, the matched inertia doctrine can be used

to find the "optimal" transmission ratio First, the mass (kg) or inertia (kg-m2) of the load and drive train components must

be known

Assume the power leaving the motor arrives at the load, and power equals the

product of torque and angular speed:

Torque also equals the product of inertia and angular acceleration, thus:

The transmission ratio n relates the motor and load velocities by wmotor = nwload Differentiating this relation once with respect to time, and substituting above:

motor load motor load = motor motor motor load load load J J =

2 2 2 _ motor transmission ratio load load load J n J =


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Transmissions: Optimal Transmission Ratios

The "optimal" transmission ratio for a pure rotational motion system dominated byinertial loads is:

For a friction or belt drive system, the optimal drive wheel radius r is:

The optimal transmission ratio to be placed between a motor and a wheel or pulley isfound by assuming the load inertia is:

For a leadscrew driven carriage, the optimal lead is:

It is a good idea to use metric (SI) units (mks)!

_ load

optimal ratiomotor

J n

J =

motor roller

load

J r

m=

2load roller transmissionroller load m J J J r = + +

2 motor load

J m

=


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Transmissions: Heavily Loaded Systems

Thermal power generated by the motor is to be minimized During a trapezoidal move, total time t c, with a constant applied external load, the motor

thermal power is:

The thermal power can be minimized with respect to the transmission ratio n from

If the load is moving linearly, J load is the mass (kg), load is the force (Newtons), load isthe maximum load speed (m/s) at the maximum force level Varying load profiles can also be modeled to find an overall optimal transmisssion ratio

for a system with complex loading patterns

Wthermal =cRmotor load2 J load2

Kt2 t c

n 2 JmotorJload

+ 1n2

2 + r

n2

c = tcta

+ tc td

r = load2 tc2

cload2 J load2

( )2/thermal W n nopt = Jload 1 + rJmotor = Jload

Jmotor @ r = 0


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Transmissions: Velocity Check

One must also check the required velocity and torque of the motor For rotational systems the motor speed in rpm is:

For linear friction (capstan) or belt drives with a linear carriage velocity inm/s, the motor speed in rpm is:

For leadscrew drives with lead and a linear carriage velocity V, the motorspeed in rpm is:

When the load inertia is very large, the transmission ratio is often very large

Select the largest ratio possible that results in a reasonable motor speed

motor optimal load n =

30 load motor

roller

V

r

=

60 load motor

V

=


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Pulleys

Pulleys (Sheaves) are a most fundamental power transmission element Mechanical advantage Capstans

Efficiency

Tracking

Mounting

F

W


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Pulleys: Mechanical Advantage For multiple strand sheave system (like seen on large cranes),

Work in = efficiency*Work out!

Atwoods machines: 2 cables, F=W/2:

Look at cranes! What do all the pulleys (sheaves) and cables do?

F

W

_ _ _

_ _ _

out number of cable strandsin

inout

number of cable strands

F N F

V V

N

=

=


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Pulleys: Capstans

A capstan is typically a fixed, or controlled rotation, body-of-revolution whicha cable wraps around A Capstan can also form the basis for a band brake, where a band is anchored to a

structure, and then wraps around a shaft

A cable wrapped around a capstan by radians with coefficient of friction mand being held with a force F hold , can resist the pull of a cable with many times

higher force F pull

hold pull e F F =

CapstanEnter numbers in BOLD

Angle of wrap (degrees, radians) 720 6.2832Coefficient of friction 0.2Holding force Fhold 1Pulling force that can be resisted Fpull 3.52

Hold

Pull


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Pulleys: Efficiency

If a belt or cable runs around a fixed shaft, then there is a lot of friction between the beltand the shaft, and the efficiency is low:

If the belt or cable rides on a pulley of diameter D with inside sliding-contact-bearing-on-shaft diameter d, then the efficiency is high:

For D = 20 mm, d = 3 mm, and = 0.1, F out/F in = 97%, vs. 85% in above example!

Cable pulling around a shaftEnter numbers in BOLDAngle of wrap (degrees, radians) 180 1.5708Coefficient of friction 0.1Pulling force 10

Net force out 8.55Efficiency 85%

( ) ( )( ) _

2 2 2

out in friction losses

out in out in

out in

work work work

d D D F F F F

D d F F

D d

= = +

= +


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Pulleys: Tracking

Pulleys can be grooved to provide a guide for a cable Two pulleys axes of rotation can never be perfectly parallel, so a flat belt will

want to drift off (tracking) Pulleys must be crowned (round profile) to keep a belt from walking off

The crown forces the belt material on either side to want to climb towards themiddle.

The crown need not be accurate, and it is easily created on the lathe

Neither side can win, so the system is stable

On a concave surface, the side with more belt in contact will cause the belt to driftfurther to that side until it falls off

A flat pulley is at best neutrally stable Great, OK, bad, & horrid pulleys:


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Pulleys: Mounting

The bore and the faces of a plastic pulley act as their own radial and thrustsliding contact bearings

Minimize axle diameter to minimize friction, but beware of bending the shaft! Do the bending stress calculations!

For a simply supported pin of length L, the maximum moment is FL/4

Beware of deflections:

Can bending induced slope cause the belt to track off the pulley despite thecrown?


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Belts & Cables

Engineering of Belts & Cables Linear motion Crawler tracks

Rotary motion

Winches

Pulley center distance

Stresses around a pulley Tensioning Manufacturing


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Belts & Cables: Linear Motion

Belts & Cables are a very effective way to convert rotary to linear motion

The force F in a belt with tension T on a pulley of diameter D that can begenerated by the torque can be conservatively estimated by:

F = 2 /D for toothed belts F = T D/2 for flat belts

A more exact model would consider the capstan effect

The speed is simply V linear =2 motor *D

Belts run on pulleys For flat belts, the pulleys must be crowned to prevent the belt from coming off the

pulley due to pulley misalignment Timing belt pulleys must also be carefully aligned to prevent premature failure

load


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Belts & Cables: Linear Motion

Cable (String) drives are often used on steering systems on outboard motorboats Foot powered lathes also used this principle!

Detailed design issues: Conservatively, the cable needs to be held in tension equal to the desired force divided by the

coefficient of friction EVOLUTION: One can also anchor one end of the string to one sideof the drum, and

anchor the other end of another string to the other side of the drum, and create a windin/wind out winch with incredible force capability!

The drum needs to be long enough so as the string winds, it has enough room to translateaccording to the helix angle

If the total travel distance is L (+/- L/2), and the drum diameter is D, then there must beSafetyFactor* LD (where SF is typically 1.2)

Otherwise there is slip caused by stretched belt accumulating on the drum and then beinglet off the other side

This is only important if linear position is to be determined with a rotary encoder on thedrum


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Belts & Cables: Linear Motion Consider the early years of industry:

Basic physics still existed, even if people did not know it! People powered tools gave rise to craftsmanship and a feel for machines and

materials which in turn gave birth to the industrial revolution

2.007 machines provide the same critical get to know your physics and materialsexperience

Ken Stone, Director of the MIT Hobby Shop,and his string-powered latheweb.mit.edu/hobbyshop


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Belts & Cables: Linear Motion Cable drives can be cascaded:

Can you change the design so that you are sure of the order of extension?(hint, anchor one stage at a time, use one to pull anotherteamwork!) Industrial lift systems often use this type of system to raise telescoping sections

h t t p : / / w w w . g e ni e l i f t . c om / ml - s e r i e s / ml -1 - 5 .h t ml


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Belts & Cables: Crawler Tracks (Treads)

Treads only help when there is loose media or a surface into which they can dig Treads DO NOT help on smooth surfaces

Smooth surfaces often are covered with a dust layer, and sharp-groove treads can help

Treads can be created by cutting angled slices from a rubber strip, and gluingthem onto the belt surface


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Belts & Cables: Rotary Motion

Synchronus Drives (timing or gear belts) can transmit torque between shaftsand also achieve a transmission ratio They combine the positive timing action of gears with the flexibility, speed and low

noise level of belts

For an in-depth discusssion on synchronus drive design, see Stock Drive Productson-line tech library: http://www.sdp-si.com/Sdptech_lib.htm

Flat belts require higher tension to transmit torque Conservatively, the belt needs to be held in tension equal to the desired torque

divided by the coefficient of friction and the small pinion radius

Vee-belts use the the principle of self help : Increased tension caused by power being transmitted, wedges the belt in a

Vee-shaped pulley groove, so it can transmit more torque

http://www.emerson-ept.com/bnames/browning/Browning.htm


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Belts & Cables: Rotary Motion

Cables can be used to couple a small motor output shaft to a large diameterwheel The capstan effect becomes an important design parameter

Roto-Lok drive from Sagebrush Technology Inc. http://www.sdp-si.com/Sdptech_lib.htm


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Belts & Cables: Pulley Center Distance

The equations for pulley center distanceas a function of pulley pitch radius and

belt length are non-linear It is best to use a spreadsheet

pulleycenterdistance.xls

A

CR 2R

1

Pulley Center Distance Calculation

Belt pitch, P 0.25 Number of teeth, N 50Start with a guess for C, and then use Goal Seek Center distance, C 3.861417Large pulley pitch radius, R2 1Small pulley pitch radius, R1 0.5

Length of belt, L 12.5Tangent segment, A 3.828908

gamma, g 0.129851Phi, f 1.440946Theta, t 1.700647error -5.6E-05


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Belts & Cables: Stress Around a Pulley

Before any belt or cable system can be conceived, the stresses in the belt orcable as it passes around a round object need to be considered The need for a reasonable diameter, can have a huge effect on the space required

for the design

A cable or belt bending around a sheave (pulley) undergoes stress For a wire rope, the ratio of pulley diameter to cable diameter depends on

the number of strands. In general the ratio should be > 30:1. 50:1 is ideal. For string and hemp rope, 10:1 is minimum. Use larger ratio for greater

life.

For a flat belt, thickness t, modulus E, Poisson ration , on a pulley ofdiameter D, the strain is all in a plane (the cross section remains rectangular) :

D

Et

=

2

1


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Belts & Cables: Tensioning Tension can be maintained by:

Stretching the belt by displacing one of the pulleys Use a spring-loaded idler pulley (which also should be crowned)

The tension T is approximately a function of the belt free-length L, belt lateraldeflection , and spring force F:

T = FL/2 One pulley is made moveable:

The bracket that holds the pulley axle has slots for the attachment bolts, and it ismoved and locked down

A screw is used to pull on a yoke that holds the pulley axle The latter two methods require tension adjustment as the belt stretches MAKE SURE TO ALWAYS REMOVE THE TENSION EVERY NIGHT.

DO NOT LEAVE THE BELTS ON YOUR MACHINE TENSIONED, AS THEYCAN CREEP

Real industrial belts do not have this problem


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2/6/2002 2000 Alexander Slocum 5-25

Belts & Cables: Manufacturing

Ideally, a belt is continuous For robotics contests:

Rubber sheet or O-Ring cord can be cut into strips

Overlap the rubber and cut through both layers with a knife

Butt-joint together the ends with Superglue

Nylon string can be cut to length

Tied (if the system can take the bump of the knot) Spliced by holding both ends to a soldering iron and then jamming them together


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Winches A winch is a motorized drum that controls cable tension (to take in or let out) and

position, see winchcable.xls A single wrap of cable on the drum requires a longer drum

Effective drum diameter and winch force capability remain constant Multiple wraps of cable on the drum allow for more cable in a smaller place

Drum diameter and winch force capability vary

A fairleader is a device to control the input/output of the cable so it winds on the drum in anorderly fashion

The simplest design just uses smooth rounded static features Vertical and horizontal roller designs reduce cable wear A powered fairleader moves back and forth ensuring that the cable winds in an orderly

fashion without randomly overlapping itself Not often used, as usually the tensioned cable causes it to wind properly

WinchCable.xlsMotor Torque (N-m) 0.4Drum Diameter (mm) 40

Drum Length (mm) 30cable diameter (mm) 1.5wrap number mm of cable/wrap Total length Maximum cable force

1 2513 2513 202 2702 5215 193 2890 8105 174 3079 11184 16


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Winches: Raising Booms Winches are often used used to raise a crane boom: WinchBoom.xls

aa

B

bb

Extended: PeRetracted: Pc

aaa

bbb

A

L Fmax

WinchBoom.xlsMotor no load speed, Wm [RPM]: 47 Wn [rad/s] 4.9Motor Stall Torque, Ts, [Nm]: 3.02Drum radius r [inches]: 0.5 r [m] 0.0127Length of boom La [inches]: 12.5 La [m]: 0.3175Angle of boom (degrees) 45Vertical load at tip of arm [N]: 6Length of cable connection along boom, Lw [inches]: 4 Lw [m]: 0.1016Vertical distance above boom pivot point of cable (inches) 1 Lc [m) 0.0254Boom moment [N-m] 1.347

Cable vectors: I jR 0 0.0254

unit vector F -0.8398 0 .5429RxF 0.0213

Cable Tension (N) 63Torque needed by motor [Nm]: 0.802Speed of Motor lifting arm, Wl [rad/s]: 3.6 Wl [RPM] 0.379Linear speed at tip [m/s] 1.1


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Winches: Design Issues

Winch design: The drum must be supported by its own bearings Torque from the motor is to be supplied via a flexible coupling or universal joint,

or a well-aligned spline

Long drums need bearingsupport at both ends, usea coupling between motorand drum, fairleader may

be needed to ensure cablewinds properly

Drum lengthFairleader

Even cable winding

Beware of increasingeffective diameter oncable force

Drum diameter,length

Large cable capacity

Small diameter needed tominimize motor torque

Motor torqueDrum diameter

High cable force,speed

PhysicsDPFR


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Wheels

System properties Traction & Controllability Overcoming obstacles Manufacturing

Mounting


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Wheels: System Properties

Bolt to flangeFlangeEasy attachment, torquetransmission

Plastic is slippery. Add rough ortacky material

Wheel surface material, normalload

Traction

One motor revolution will causeless travel

Diameter-make it smallControllability

When the motor is not torquelimited, increase diameter

Diameter-make it largeClimbing over obstacles

If motor is not torque limited,and you want speed, increase

diameter

Diameter-make it largeHigh speed

PhysicsDPFR


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Wheels: Traction & Controllability

Two-Wheel Drive vehicles are simple to build, and for zipping around, theywork fine In a pushing contest with a 4-Wheel Drive or a Tracked vehicle, they lose

Remember, motor torque is NOT infinite!

The smaller the wheel:

The greater the traction force the motors can cause The slower the vehicle per unit thumb input to the controller!

The slower the vehicle, the more controllable the vehicle

Some past robot contests feature big wheeled vehicles careeningaround

Torque-Speed for Bosch Motor (MS-L 2/98 )

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.61.8

0 10 20 30 40 50 60 70 80 90 100

Speed (RPM)

T o r q u e

( N m

)


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Wheels: Torque and Contact Pressure

The smaller the wheel diameter, the less the torque to turn the shaft Ideally, the wheel just slips when maximum torque is applied

This keeps you from stalling the motor and potentially burning it out

The smaller the diameter, the higher the contact pressure, and the greater thewear Use Hertz Contact Stress Theory to determine if the wheels are too

heavily loaded!

Turning Torque = F*(2R)

2R R

Turning Torque = F*(R)

FF

Surface pressure:F/(2R*Length)

2R R

FF

Surface pressure:F/(R*Length)


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Wheels: Traction Drives

Wheels can also be used to drive components Also known as friction drives

A traction drive is used to control the paper motion in an inkjet printer Micro roughness on the wheels imprint their own gear rack into the paper

Coordinate Measuring Machines (CMMs, which account for 10% of allmachine tool sales) often use friction drives

If a person gets in the way, they will slip before crushing The primary design challenge is that the preload force must be equal to the

desired drive force/coefficient of friction!


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Wheels: Overcoming Obstacles

How big must a wheel be to make sure it can overcome obstacles?

( ) 20 2 M d M F h dh h F = = 2

2

M dh h F F d h


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Wheels: Manufacturing

Wheels can be made from any material, or by trimming the plastic wheels provided

Modifying the wheel diameter

Cut the spokes on the bandsaw

Use a fixture for wheel diameter modification:

Mount the wheel in the fixture and turn the spoke stubs off to create asmooth round wheel

Attaching the wheel to a shaft If the wheel is to be driven by a motor, it must be securely attached to the shaft

A press-fit for plastic wheels is not reliable

An adhesive bond can work if extreme cleanliness is observed

The best method is to use a positive mechanical feature Square the end of the shaft and fit it into:

A broached square hole The molded plastic square-hole-hub


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Wheels: Mounting

Your kit contains a molded plastic part that forms an interface between awheel and the square shaft that fits through the Bosch motor gearbox

Thanks to Dean Kaman, and his company DEKA, for specially making these parts for us!

The wheel-on-shaft subassembly should overhang the gearbox as little as possible!

DO NOT drill a hole in the square shaft for a pin on the loaded side of theshaft!

Did you know that a square shaft can be threaded! A round shafts ends can be machined square to fit into a square-broached hole Beware of system deformations and the fact that they can take up all the

clearance in a system and cause it to bind!


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Cams A cam is a rotating shape whose angular motion is converted into output

motion by means of a cam follower which rides on the cam surface Rolling elements provide the highest degree of efficiency, but they take up more

space

Sliding elements are very compact, and can be efficient of the speed is high enoughto maintain oil film lubrication

A cam follower is a rolling or sliding contact machine element that follows thecontour of a surface and transmits the motion to a mechanism

A cam profile can be designed to create corresponding acceleration, velocityand dwell profiles in a mechanism (e.g., an engine valve)

Stanley Tool Works YANKEE screwdriver


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Shafts

Shafts transmit rotary and linear power via motors, leadscrews, pistons Shafts are one of the most common machine elements

The primary design issues are: Shaft support

Component mounting

Bending & Stresses

Buckling Stability

BallscrewSupport BearingsBearing Housing Ballnut

Carriage

AC Brushless Motor

Rotary Encoder

Flexible Coupling

Shafts


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Shafts: Axial Loading

Leadscrews are shafts that are axially loaded For heavy shock loads, stress concentration factor increases by a factor of 2

See R.E. Peterson, Stress Concentration Factors, 1974, John Wiley & Sons, New York

Stress concentration factor Stress

D dr

Dd

DCorner r Width bDepth t

r

Shaft loaded byaxial force F

2

4 F

d

=

0.36 0.2( / )( / )1

5 0.12/( / 1)

D d

t r d

K D d

= + +

( )0.2751 0.65/ /t d D K +20.25 F

dD D

24 F

d

=

20.25 F

bt D

1.5t K

B=D/4, t=D/8

0.511 0.34( /( 2 ) 1)

0.42( / )1

3 0.507/ ( / 2 1)

d d r

t r d K d d r

= + + D r d


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Shafts: Torsional Loading

Motors and gears torque shafts For heavy shock loads, stress concentration factor increases by a factor of 2

Stress concentration factor StressShaft loaded byTorque

D dr

Dd

Dr


r

3

16

d

=

0.3 0.2( / )( / )113 0.3/ ( / 1)

D d

t r d

K D d

= ++

3 2/16 / 6d d D

= ( )

0.1971 1.47 /t d D K

= +

316

d

=0.609 0.146( /( 2 ) 1)

0.252( / )1

5 3.73/ ( /( 2 ) 1)

d d r

t r d K d d r

= + + 1.5t K

3

16

D

= B=D/4, t=D/8

d


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Shafts: Bending

Radial loads (tangential and separation forces) from gears bend shafts For heavy shock loads, stress concentration factor increases by a factor of 2

Stress concentration factor StressShaft loaded byBending moment M

D dr

Dd


r

3

32 M

d

=

3 2/32 / 6d d D

=

332 M

d

=

3

32 M

D

=

0.66( / )111.14

t r d

K

= +B=D/4, t=D/8

0.59 0.184( /( 2 ) 1)

( / )15 0.081/( /( 2 ) 1)

d d r

t r d K d d r

= + +

0.73 0.42( / 1)

0.16( / )1

5 4.38/ ( / 1)

D d

t r d

K D d

= ++

( )0.2751 0.65/ /t d D K +

Dr, d


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Shafts: Shaft Support

Abbe and Saint-Venants Principles and Exact Constraint Design must becarefully considered when designing the mounting of shafts

The system must be designed to accommodate misalignment between bearingsor shafts Allow for clearance between bearing and shaft to accommodate misalignment

Use flexible couplings or self-aligning (spherical) bearings

Use designs that automatically accommodate misalignment Line-bore holes at the same time through mounting plates

OUCH!

EEOW!

Perpendicularity Horizontal Parallelism Vertical Parallelism


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Shafts: Component Attachment The primary functional requirements for attaching a component to a shaft (in

order of goodness) are: Prevent the component from slipping Spline: Excellent torque transmission, but can be expensive Circumferential clamp: Very good torque transmission, low stress

concentration, modest price Keyway: Very good torque transmission, modest stress concentration, low

cost

Pinned shaft: Good torque transmission, modest stress concentration, low cost Setscrew: Your worst nightmare!

Minimize stress concentration Raised diameter with radiused corner

Requires a lot of material to be removed from a long shaft Rarely required in 2.007 machines where shaft size is large compared to motor

size


44/51


Shafts: Thrust Shoulders Shafts often need a shoulder for a thrust bearing

A radiused transition between a small and a large diameter minimizes the stressconcentration

The radius will interfere with the edge of the thrust bearing

An undercut is thus often used

The net strength, Ip/Kt, is maintained

From shaft_torsion.xls :

=>+


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Shafts: Power Transmission

The higher the power, P (W), and the lower the speed, (rad/sec), the higherthe shaft torque, (N-m):

Shafts see HUGE numbers of cycles, so design for fatigue is of criticalimportance From shaft_torsion.xls :

P

=


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Shafts: Bending & Stresses

All shafts are loaded, and will thus deform and be subject to stress Bending, torsion, and shear stress for round shafts: Bending: = Mc/I where I/c = D3/32 Torsion: = r/I where I/r = D3/16; = L/GI where I = D4/32 Shear: = F/A where A = D2/4 Stress

Avoid fatigue and wear Avoid sharp transitions, even between components mounted on the shaft and

the shaft itself NEVER put a pin through a shaft on the load-side of the assembly

Deformations Minimize so as to not require inordinate bearing clearances Minimize to prevent misalignment of components mounted to the shaft (e.g.,

pulleys) Use simply supported instead of cantilevered designs whenever possible

Wheel

Shaft

Sliding bearing in

structure!!Non Optimal!!Wheel

Shaft

Sliding bearing instructure

!!Optimal!!


47/51


Shafts: Stability

Rotate a shaft at its natural frequency and it will vibrate, causing shaft whip Stable robust machines do NOT operate at the natural frequency of their

components!

The increased stress can cause rapid failure

Load a long shaft with too high a load and it will buckle

It is straightforward to predict instability caused by shaft whip or buckling : It is VERY difficult to achieve fixed-fixed design

Remember Saint-Venant!

Use the ROOT diameter for leadscrew shaft calculations!


48/51


Couplings Do not overconstrain your system!

If you overconstrain the system, then: It will wear and bind and fail! You will only harness a fraction of the potential power (force)

A coupling is stiff in the required direction, yet allows for motions along andabout other axes Essential to accommodate misalignment between power transmission components

Couplings for linear motion systems Couplings for rotary motion systems

Identifying the degrees of freedom on components is vital! Draw the actuator output Draw the thing to be moved Attach the two with a coupling element that is only stiff in the direction force is

to be transmitted!

Coupling materials in the kit: Plastic tube (between motor shaft and driven shaft) Clevis (supplied or make your own)

Look at construction equipment:


49/51


Couplings: Linear Motion

Often a linear motion actuator and the carriage it is actuating are not precisely aligned Example: A Piston must be clevis mounted at each end with enough hole-pin clearance toaccommodate lateral motions

The pin through a clevis should ideally be in shear

Super precision instruments may go to extreme measures to make sure that the forcefrom the actuator is pure Wobble pins or wire couplings are sometimes used:

If a machine element (ballnut) is located at the center of stiffness, then error motions ofone machine element will not cause pitch errors:


50/51


Couplings: Rotary Motion

To prevent over constraint from destroying bearings and fatiguing shafts, use couplings In 2.007: Plastic tube pressed over shafts with wire twisted about as a clamp Use clevis connections

Oldham couplings and universal joints can be created

Helical couplings are ideal, and can be approximated by slits in a shaft

Remember: Do shaft strength calculations if you drill through a shaft to pin a coupling!

http://www.heli-cal.com/

http://www.sdp-si.com/Sdptech_lib.htm


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Conclusion: Cables, Belts, & Wheels are SIMPLE

There are many different ways to achieve linear or rotary motion Cable or belt systems are simple to design and manufacture, but like all systems,

require careful attention to detail

Proper crowning of pulleys is the most often overlooked detail

Wheels are simple to design and manufacture, but like all systems, require carefulattention to detail

Couplings are critical elements to ensure that the motor-to-transmission connectionis not over constrained

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