Hi everyone,

I think I have found a way to greatly reduce the stresses on the 2mm OD shaft.

The only question is whether the roller being pressed onto the center of the dowel, will basically act like a stepped shaft made from one solid piece.

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"

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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 =3D 0.5047204 in

MATERIAL PROPERTIES steel: Modulus of elasticity =3D 29000000.0 lb/in=B2

CROSS-SECTION PROPERTIES #1: from 0.0 in to 0.1308602 in Moment of inertia =3D 0.000001911958 in^4 Top height =3D 0.0395 in Bottom height =3D 0.0395 in Area =3D 0.00490167 in=B2

#2: from 0.1308602 in to 0.3738602 in Moment of inertia =3D 0.00006067014 in^4 Top height =3D 0.09375 in Bottom height =3D 0.09375 in Area =3D 0.02761165 in=B2

#3: from 0.3738602 in to 0.5047204 in Moment of inertia =3D 0.000001911958 in^4 Top height =3D 0.0395 in Bottom height =3D 0.0395 in Area =3D 0.00490167 in=B2

EXTERNAL CONCENTRATED FORCES 200.0 lb at 0.252 in

SUPPORT REACTIONS ******* Simple at 0.1181 in Reaction Force =3D-100.4091 lb

Simple at 0.387 in Reaction Force =3D-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 =3D 27034.99 lb/in=B2 No Limit specified Compressive =3D 27034.99 lb/in=B2 No Limit specified Shear (Avg) =3D 20484.67 lb/in=B2 No Limit specified

ANALYSIS AT SPECIFIED LOCATIONS ******* Location =3D 0.0 in Deflection =3D -0.00007765793 in Slope =3D 0.03767546 deg Moment =3D 0.0 lb-in Shear force =3D 0.0 lb Tensile =3D 0.0 lb/in=B2 Compressive =3D 0.0 lb/in=B2 Shear stress =3D 0.0 lb/in=B2

Location =3D 0.07930511 in Deflection =3D -0.00002550999 in Slope =3D 0.03767546 deg Moment =3D 0.0 lb-in Shear force =3D 0.0 lb Tensile =3D 0.0 lb/in=B2 Compressive =3D 0.0 lb/in=B2 Shear stress =3D 0.0 lb/in=B2

Location =3D 0.1586102 in Deflection =3D 0.00002143606 in Slope =3D 0.02681157 deg Moment =3D 4.067595 lb-in Shear force =3D 100.4091 lb Tensile =3D 6285.415 lb/in=B2 Compressive =3D 6285.415 lb/in=B2 Shear stress =3D 3636.475 lb/in=B2

Location =3D 0.2523602 in Deflection =3D 0.00004730955 in Slope =3D 0.00002452662 deg Moment =3D 13.4089 lb-in Shear force =3D -99.59093 lb Tensile =3D 20719.99 lb/in=B2 Compressive =3D 20719.99 lb/in=B2 Shear stress =3D 3606.844 lb/in=B2

Location =3D 0.3461102 in Deflection =3D 0.00002163168 in Slope =3D -0.0266601 deg Moment =3D 4.07225 lb-in Shear force =3D -99.59093 lb Tensile =3D 6292.608 lb/in=B2 Compressive =3D 6292.608 lb/in=B2 Shear stress =3D 3606.844 lb/in=B2

Location =3D 0.4254153 in Deflection =3D -0.00002546155 in Slope =3D -0.03797543 deg Moment =3D 0.0 lb-in Shear force =3D 0.0 lb Tensile =3D 0.0 lb/in=B2 Compressive =3D 0.0 lb/in=B2 Shear stress =3D 0.0 lb/in=B2

Location =3D 0.5047204 in Deflection =3D -0.0000780247 in Slope =3D -0.03797543 deg Moment =3D 0.0 lb-in Shear force =3D 0.0 lb Tensile =3D 0.0 lb/in=B2 Compressive =3D 0.0 lb/in=B2 Shear stress =3D 0.0 lb/in=B2

OLD DESIGN WITH .1875" LONG ROLLER

BEAM LENGTH =3D 0.5047204 in

MATERIAL PROPERTIES steel: Modulus of elasticity =3D 29000000.0 lb/in=B2

CROSS-SECTION PROPERTIES #1: from 0.0 in to 0.1586102 in Moment of inertia =3D 0.000001911958 in^4 Top height =3D 0.0395 in Bottom height =3D 0.0395 in Area =3D 0.00490167 in=B2

#2: from 0.1586102 in to 0.3461102 in Moment of inertia =3D 0.00006067014 in^4 Top height =3D 0.09375 in Bottom height =3D 0.09375 in Area =3D 0.02761165 in=B2

#3: from 0.3461102 in to 0.5047204 in Moment of inertia =3D 0.000001911958 in^4 Top height =3D 0.0395 in Bottom height =3D 0.0395 in Area =3D 0.00490167 in=B2

EXTERNAL CONCENTRATED FORCES 200.0 lb at 0.252 in

SUPPORT REACTIONS ******* Simple at 0.1181 in Reaction Force =3D-100.4091 lb

Simple at 0.387 in Reaction Force =3D-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 =3D 84130.45 lb/in=B2 No Limit specified Compressive =3D 84130.45 lb/in=B2 No Limit specified Shear (Avg) =3D 20484.67 lb/in=B2 No Limit specified

ANALYSIS AT SPECIFIED LOCATIONS ******* Location =3D 0.0 in Deflection =3D -0.0002310493 in Slope =3D 0.1120927 deg Moment =3D 0.0 lb-in Shear force =3D 0.0 lb Tensile =3D 0.0 lb/in=B2 Compressive =3D 0.0 lb/in=B2 Shear stress =3D 0.0 lb/in=B2

Location =3D 0.07930511 in Deflection =3D -0.00007589781 in Slope =3D 0.1120927 deg Moment =3D 0.0 lb-in Shear force =3D 0.0 lb Tensile =3D 0.0 lb/in=B2 Compressive =3D 0.0 lb/in=B2 Shear stress =3D 0.0 lb/in=B2

Location =3D 0.1586102 in Deflection =3D 0.00005918867 in Slope =3D 0.02695565 deg Moment =3D 4.067595 lb-in Shear force =3D 100.4091 lb Tensile =3D 84034.27 lb/in=B2 Compressive =3D 84034.27 lb/in=B2 Shear stress =3D 20484.67 lb/in=B2

Location =3D 0.2523602 in Deflection =3D 0.0000852979 in Slope =3D 0.0001685984 deg Moment =3D 13.4089 lb-in Shear force =3D -99.59093 lb Tensile =3D 20719.99 lb/in=B2 Compressive =3D 20719.99 lb/in=B2 Shear stress =3D 3606.844 lb/in=B2

Location =3D 0.3461102 in Deflection =3D 0.00005985576 in Slope =3D -0.02651603 deg Moment =3D 4.07225 lb-in Shear force =3D -99.59093 lb Tensile =3D 84130.45 lb/in=B2 Compressive =3D 84130.45 lb/in=B2 Shear stress =3D 20317.75 lb/in=B2

Location =3D 0.4254153 in Deflection =3D -0.00007546126 in Slope =3D -0.1125491 deg Moment =3D 0.0 lb-in Shear force =3D 0.0 lb Tensile =3D 0.0 lb/in=B2 Compressive =3D 0.0 lb/in=B2 Shear stress =3D 0.0 lb/in=B2

Location =3D 0.5047204 in Deflection =3D -0.0002312445 in Slope =3D -0.1125491 deg Moment =3D 0.0 lb-in Shear force =3D 0.0 lb Tensile =3D 0.0 lb/in=B2 Compressive =3D 0.0 lb/in=B2 Shear stress =3D 0.0 lb/in=B2