2.72 Elements of Mechanical Design
Transcript of 2.72 Elements of Mechanical Design
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MIT OpenCourseWare http://ocw.mit.edu
2.72 Elements of Mechanical Design Spring 2009
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2.72 Elements of
Mechanical Design
Lecture 06: Constraints
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Schedule and reading assignment Quiz
� Quiz – HTMs
Topics � Principles of exact constraint� Bearing layout exercises
� Spindle shaft constraint/bearing layout
Reading assignment � Chapter 11 in Shigley and Mischke
• Read sections 11.1 – 11.6, 11.9 • Skim sections 11.7 – 11.8, 11.10 – 11.12
� This is 40ish pages, but most of it is pictures/graphs/examples
© Martin Culpepper, All rights reserved 2
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Principles of exact constraint
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Under, exact and over constraint Constraints are fundamental to mechanical design
� A mechanical designers goal is to control, i.e. to constrain, parts so that they are where they are supposed to be.
Exact constraint: � There should be one constraint for each degree-of-freedom that is
constrained.
Under constraint � Too few constraints, part is not held in all the directions it needs to be
Over constraint � Too many constraints, some constraints may fight each other when
trying to do the same job.
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Mechanical constraints We want to learn how to model and design each
We first need to know: � How they should be used
� What their functional requirements are
How they should be used and their FRs depend upon:� How they are laid out� Dos and don’ts
Learn to lay them out right � Use this to obtain their Functional Requirements
� Then do the detailed design of each
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Constraints and Degrees-of-freedom Rigid components have 6 degrees-of-freedom
We will represent an ideal constraint as a line
6 – C = R
C = # of Non-Redundant Constraints
R = # of Independent Degrees of Freedom
Example:
6 - 2constraints = 4DoFs
Rz
Courtesy John Hopkins, MIT
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Constraints, compliance and motion Exact constraint: Achieve desired motion
� By applying minimum number of constraints y � Arranging constraints in correct constraint topology � Adding constraints only when necessary z
For now: � Start with ideal constraints
x
Stage Ground
� Considering small motions
� Constraints = lines
Focus on rigid stage attached to ground � What do we mean by rigid?
� What do we mean by constraint? - Stiffness ratios
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The benefits of exact constraint
Penalties for over constraint © Martin Culpepper, All rights reserved
Parts of machines are now always the same strength and stiffness.
Large, stiff components have a tendency to “kill” their smaller counterparts when they are connected so that they are forced to fight.
Exact constraint design helps to prevent fights, therfore all your parts live in harmony.
8
X
Y
A
B
A
B
Loose
Binding
Figure by MIT OpenCourseWare.
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Constraint examples
1 2
More examples: y
3 z x
4 5 6
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Exact constraint practice
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Mechanical constraints: Some bearing types Sliding
� Bushings
� etc…
Radial rolling � Radial
� Shallow groove
� Deep groove (Conrad)
� Angular contact
� Tapered © Martin Culpepper, All rights reserved 11
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Examples drawn from your lathe
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Example: Carriage constraint x
z
y
Assume these are bushings as in
your lathe
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Example cont.y
x z
Misalignment& assembly
errors
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Example cont. x
z
y
Thermally Induced growth
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x
Practical embodiment y
z
Flexure that is stiff in y and z, yet compliant in x
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Group exercise – Carriage constraints Identify the motions that you desire for the carriage and
the minimum # of constraints that are needed to yield only these motions.
Identify the constraints from each bearing set and determine how they act in concert to yield the desired motions.
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Constraint layouts and
thermal stability
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Housing
Avoiding over constraint How to deal with the thermal growth issue
� The shaft typically gets hotter than the housing because the housing has better ability to carry heat away
� Whether the outer or inner race are fixed, matters…
Constraining front and rear bearings� One bearing set should be axially and radially restrained � The other bearing set should ONLY have radial restraint
19© Martin Culpepper, All rights reserved
Shaft Chuck
NutGear
Part
Tool
8.0 04.010.0
Gear
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Housing
Examples: Good or bad Outer race fixed axially, if shaft heats is this bad?
� Think about what happens to the preload…
Shaft Chuck
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Housing
Examples: Good or bad Outer race fixed axially, if shaft heats is this bad?
� Think about what happens to the preload…
Shaft Chuck
This is the back-to-back config.
It should be used when the outer race is not rotating
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Housing
Examples: Good or bad Assume the outer
race does not rotate
Shaft Chuck
Nut
Gear Gear
Sliding permitted
Spacer
1
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Housing
Examples: Good or bad Assume the outer
race does not rotate
Shaft Chuck
Nut
Gear Gear
Sliding permitted
Spacer
2
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Housing
Examples: Good or bad
Shaft Chuck
Nut
Gear Gear
Assume the outer race does not rotate
3
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Housing
Examples: Good or bad
Shaft Chuck
Nut
Gear Gear
Spring
Assume the outer race does not rotate
4
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Housing
Examples: Good or bad Assume the outer
race does not rotate
Shaft Chuck
Nut Gear Gear
5
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Housing
27 © Martin Culpepper, All rights reserved
Gear Gear
Examples: Good or bad Assume the outer
race does not rotate
Shaft Chuck
6
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Housing
Examples: Good or bad Assume the outer
race does not rotateGood � Front set constrained radially and axially � Rear set constrained only radially
Shaft Chuck
Nut
Gear Gear
Sliding permitted
Spacer
1
BUT, sliding means some gap must exist and therefore one must precision fabricate if a small gap is desired
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Housing
Examples: Good or bad Assume the outer
race does not rotateBad � Front set constrained only radially � Rear set constrained only radially
Shaft Chuck
Nut
Gear Gear
Sliding permitted
Spacer
2
This design will not work if axial loads are to be applied along both directions
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Housing
Examples: Good or bad Assume the outer
race does not rotateGood � Front set constrained radially and ½ axially � Rear set constrained radially and ½ axially
Shaft Chuck
Nut
Gear Gear
3
BUT, adding a spring increases part count/cost
Axial stiffness values (left vs. right) will be different © Martin Culpepper, All rights reserved 30
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Housing
Examples: Good or bad Assume the outer
race does not rotateBAD � Front set is constrained only ½ axially � Rear set is constrained only ½ axially
Shaft Chuck
Nut
Gear Gear
Spring
4
This design will not work if axial loads are to be applied along both directions
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Housing
Examples: Good or bad Assume the outer
race does not rotateBAD � Front set is constrained ½ axially and radially � Rear set is constrained ½ axially and radially
Shaft Chuck
Nut Gear Gear
5
At high speeds/loads, thermal growth may kill the bearing sets � Like a double face-to-face…
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Housing
Examples: Good or bad Bad
� Front set constrained radially and ½ axially
� Rear set constrained radially (if flexure is of proper stiffness)
Assume the outer race does not rotate
GearGear
Shaft Chuck
6
Left bearing set is not in the back-to-back configuration
Shaft can pop out… © Martin Culpepper, All rights reserved 33
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Group exercise
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Group exercise – Spindle constraints The spindles you have seen use tapered roller bearings.
First, sketch a layout from one of the previous lathes and diagnose its layout
Second, generate and sketch a different way to constrain the spindle shaft.
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