Hi everyone,
I think I have found a way to greatly reduce the stresses on the 2mm OD
shaft.
Since the stresses were so high, I decided to take a closer look at
this problem, rather than just relying on a physical test. With
variances in steel, I could have a few that would test OK, but others
that would not. Also, if I tested one and it seemed OK, I am afraid it
could yield a little more with each use, and then cause problems down
the road.
I found a beam deflection program called "beam 2d"
http://www.orandsystems.com/Bm2DShow/show0.html
This program lets you model stepped shafts. You get 30 unrestricted
uses with the demo. I found that increasing the roller from .1875"
long to .243" long so that it fits more snug inside of the .269"
support span, causes a drastic reduction in the bending stress of the
beam.
I have pasted the program printout for both the .1875" long roller and
a .243" long roller below. I will just use .010" thick delrin thrust
washers on each side of the roller instead of .03 to .04" thick thrust
washers.
The highest bending stress seems to occur right where the 2mm shaft
comes out of the 3/16" OD portion. With the .1875" long roller, the
maximum bending stress is 84,130.45 PSI, but with the .243" long roller
the maximum bending stress is reduced to 27,034.99 which surprised me.
With the .1875" long roller, the center of the roller deflected by
..0001" and the very ends of the 2mm OD end portions curled up by
..0002". With the new .243" long roller, the center of the roller
deflected by only 0.00005", and the very ends of the 2mm OD end
portions deflected up by .0001".
With the new longer roller, the first portion of the shaft is 2mm OD X
..131" long, then the second portion is .1875" OD X .243" long, and the
last portion is .2mm OD X .131" long.
The question now becomes, will the pressed on 3/16" OD center portion
act fairly close to a stepped shaft made from one solid piece as
modeled by the program ?
I do have one way to use a 1/8" OD shaft, but I must sacrifice the Igus
plastic bushings. The roller and shaft is held in a yoke, I could make
the yoke itself out of a bushing material, so the shaft turns right in
the yoke instead of the plastic bushings. This gives me room for a 1/8"
OD shaft.
However, this is a high load oscillating application, and I can only
lube the shaft once at assembly then never again. I am a Little
concerned about wear. I hear 0-6 tool steel makes good bushings, and
has a self lubricating graphitic property. The walls are so thin on the
yoke I don't think I can harden it without cracking, so I would just
have to lube the shaft at assembly, and hope for the best as far as
wear is concerned. This thing is just intermittently oscillated by
hand, so perhaps it would wear well.
Here are the printouts from the beam design program. I would appreciate
any other feedback anyone may have. If the new longer pressed on roller
acts close to a one piece stepped shaft, I think I should be OK.
NEW DESIGN WITH .243" LONG ROLLER
BEAM LENGTH = 0.5047204 in
MATERIAL PROPERTIES
steel:
Modulus of elasticity = 29000000.0 lb/inē
CROSS-SECTION PROPERTIES
#1: from 0.0 in to 0.1308602 in
Moment of inertia = 0.000001911958 in^4
Top height = 0.0395 in
Bottom height = 0.0395 in
Area = 0.00490167 inē
#2: from 0.1308602 in to 0.3738602 in
Moment of inertia = 0.00006067014 in^4
Top height = 0.09375 in
Bottom height = 0.09375 in
Area = 0.02761165 inē
#3: from 0.3738602 in to 0.5047204 in
Moment of inertia = 0.000001911958 in^4
Top height = 0.0395 in
Bottom height = 0.0395 in
Area = 0.00490167 inē
EXTERNAL CONCENTRATED FORCES
200.0 lb at 0.252 in
SUPPORT REACTIONS ***
Simple at 0.1181 in
Reaction Force =-100.4091 lb
Simple at 0.387 in
Reaction Force =-99.59093 lb
MAXIMUM DEFLECTION ***
-0.0000780247 in at 0.5047204 in
No Limit specified
MAXIMUM BENDING MOMENT ***
13.44477 lb-in at 0.252 in
MAXIMUM SHEAR FORCE ***
100.4091 lb from 0.1181 in to 0.252 in
MAXIMUM STRESS ***
Tensile = 27034.99 lb/inē No Limit specified
Compressive = 27034.99 lb/inē No Limit specified
Shear (Avg) = 20484.67 lb/inē No Limit specified
ANALYSIS AT SPECIFIED LOCATIONS ***
Location = 0.0 in
Deflection = -0.00007765793 in
Slope = 0.03767546 deg
Moment = 0.0 lb-in
Shear force = 0.0 lb
Tensile = 0.0 lb/inē
Compressive = 0.0 lb/inē
Shear stress = 0.0 lb/inē
Location = 0.07930511 in
Deflection = -0.00002550999 in
Slope = 0.03767546 deg
Moment = 0.0 lb-in
Shear force = 0.0 lb
Tensile = 0.0 lb/inē
Compressive = 0.0 lb/inē
Shear stress = 0.0 lb/inē
Location = 0.1586102 in
Deflection = 0.00002143606 in
Slope = 0.02681157 deg
Moment = 4.067595 lb-in
Shear force = 100.4091 lb
Tensile = 6285.415 lb/inē
Compressive = 6285.415 lb/inē
Shear stress = 3636.475 lb/inē
Location = 0.2523602 in
Deflection = 0.00004730955 in
Slope = 0.00002452662 deg
Moment = 13.4089 lb-in
Shear force = -99.59093 lb
Tensile = 20719.99 lb/inē
Compressive = 20719.99 lb/inē
Shear stress = 3606.844 lb/inē
Location = 0.3461102 in
Deflection = 0.00002163168 in
Slope = -0.0266601 deg
Moment = 4.07225 lb-in
Shear force = -99.59093 lb
Tensile = 6292.608 lb/inē
Compressive = 6292.608 lb/inē
Shear stress = 3606.844 lb/inē
Location = 0.4254153 in
Deflection = -0.00002546155 in
Slope = -0.03797543 deg
Moment = 0.0 lb-in
Shear force = 0.0 lb
Tensile = 0.0 lb/inē
Compressive = 0.0 lb/inē
Shear stress = 0.0 lb/inē
Location = 0.5047204 in
Deflection = -0.0000780247 in
Slope = -0.03797543 deg
Moment = 0.0 lb-in
Shear force = 0.0 lb
Tensile = 0.0 lb/inē
Compressive = 0.0 lb/inē
Shear stress = 0.0 lb/inē
OLD DESIGN WITH .1875" LONG ROLLER
BEAM LENGTH = 0.5047204 in
MATERIAL PROPERTIES
steel:
Modulus of elasticity = 29000000.0 lb/inē
CROSS-SECTION PROPERTIES
#1: from 0.0 in to 0.1586102 in
Moment of inertia = 0.000001911958 in^4
Top height = 0.0395 in
Bottom height = 0.0395 in
Area = 0.00490167 inē
#2: from 0.1586102 in to 0.3461102 in
Moment of inertia = 0.00006067014 in^4
Top height = 0.09375 in
Bottom height = 0.09375 in
Area = 0.02761165 inē
#3: from 0.3461102 in to 0.5047204 in
Moment of inertia = 0.000001911958 in^4
Top height = 0.0395 in
Bottom height = 0.0395 in
Area = 0.00490167 inē
EXTERNAL CONCENTRATED FORCES
200.0 lb at 0.252 in
SUPPORT REACTIONS ***
Simple at 0.1181 in
Reaction Force =-100.4091 lb
Simple at 0.387 in
Reaction Force =-99.59093 lb
MAXIMUM DEFLECTION ***
-0.0002312445 in at 0.5047204 in
No Limit specified
MAXIMUM BENDING MOMENT ***
13.44477 lb-in at 0.252 in
MAXIMUM SHEAR FORCE ***
100.4091 lb from 0.1181 in to 0.252 in
MAXIMUM STRESS ***
Tensile = 84130.45 lb/inē No Limit specified
Compressive = 84130.45 lb/inē No Limit specified
Shear (Avg) = 20484.67 lb/inē No Limit specified
ANALYSIS AT SPECIFIED LOCATIONS ***
Location = 0.0 in
Deflection = -0.0002310493 in
Slope = 0.1120927 deg
Moment = 0.0 lb-in
Shear force = 0.0 lb
Tensile = 0.0 lb/inē
Compressive = 0.0 lb/inē
Shear stress = 0.0 lb/inē
Location = 0.07930511 in
Deflection = -0.00007589781 in
Slope = 0.1120927 deg
Moment = 0.0 lb-in
Shear force = 0.0 lb
Tensile = 0.0 lb/inē
Compressive = 0.0 lb/inē
Shear stress = 0.0 lb/inē
Location = 0.1586102 in
Deflection = 0.00005918867 in
Slope = 0.02695565 deg
Moment = 4.067595 lb-in
Shear force = 100.4091 lb
Tensile = 84034.27 lb/inē
Compressive = 84034.27 lb/inē
Shear stress = 20484.67 lb/inē
Location = 0.2523602 in
Deflection = 0.0000852979 in
Slope = 0.0001685984 deg
Moment = 13.4089 lb-in
Shear force = -99.59093 lb
Tensile = 20719.99 lb/inē
Compressive = 20719.99 lb/inē
Shear stress = 3606.844 lb/inē
Location = 0.3461102 in
Deflection = 0.00005985576 in
Slope = -0.02651603 deg
Moment = 4.07225 lb-in
Shear force = -99.59093 lb
Tensile = 84130.45 lb/inē
Compressive = 84130.45 lb/inē
Shear stress = 20317.75 lb/inē
Location = 0.4254153 in
Deflection = -0.00007546126 in
Slope = -0.1125491 deg
Moment = 0.0 lb-in
Shear force = 0.0 lb
Tensile = 0.0 lb/inē
Compressive = 0.0 lb/inē
Shear stress = 0.0 lb/inē
Location = 0.5047204 in
Deflection = -0.0002312445 in
Slope = -0.1125491 deg
Moment = 0.0 lb-in
Shear force = 0.0 lb
Tensile = 0.0 lb/inē
Compressive = 0.0 lb/inē
Shear stress = 0.0 lb/inē