BB installed radially in shaft --- need math help please

[archimedesCNC]

greetings,

we all have seen them . . . . . pick up a socket
extension or the ratchet. there on the hex end is
a spring loaded ball used to maintain a friction
load on the mating female hex. the ball is pressed
radially into a drilled hole usually with a compression
spring on the blind side of the hole.
what i am looking for is the math that determines
what diameter of the blind hole & the depth of the
entry chamfer. rationally, i am thinking there is
some relationship of the entry chamfer to the hole &
ultimately both relate to the diameter of the chosen
ball. i would like to find a source for the math
that will help me design this type of relationship.
TIA for the consideration,
scott

 

[desertfox]

Hi archimedes

The depth and diameter of the blind hole will depend on the spring design and the amount of compression the spring needs to reach the desired pre-load.
The spring design will be decided on by the amount of friction load to be applied between the male and female hexagons and the amount of force required to mate the two parts and the chamfer will act like a slope in a order that the spring load is applied gradually as the parts are assembled.

desertfox

 

[archimedesCNC]

hi desertfox,
thanx very much for your answer, but maybe my
question was not well put . . . . . .
disconnecting the target example from my need -
assuming the ball bearing is "pressed" into the
blind hole - how is it that it is trapped, yet still
allowed movement to provide the necessary interference
to a mating part? is there a mathematical calculation
that determines this type of circumstance?
is the hole diameter a PLUS dimension (.####)over the
BB diameter? maybe i am not understanding how the BB
becomes trapped in the blind hole??
i hope i have better elucidated my need . . . .
TIA,
scott

 

[Ron]

The hole has to have a shoulder on it to retain the ball. Squeeze it past the shoulder with much force, less force on spring to try to push back out. Elastic deformation in the first push, just retaining force by spring.

 

[desertfox]

Hi Archimedes

The ball is assemblied from the opposite side from that which it sticks through and the hole is normally smaller in diameter than the ball itself, so you end up with a spherical chord of the ball stuck through the hole but is retained from falling straight through because of the difference in diameters,however the spherical chord can be pushed back into the hole which is why its opposed by the spring, hope this helps.

desertfox

 

[archimedesCNC]

Ron & desertfox,

thanx for the replies & efforts.
i have my answer thanx to a friend who just stopped
by my garage for a visit. in most commercial apps
the ball is trapped in the blind hole (replete with
compression spring) using a swaging process. the
entry chamfer i was noticing was actually the swaged
perimeter of material compressed downward to create
a void that allows the ball to move, but keeps it from
escaping. as he explained; this is a trial & error process
that one has to determine from the material type, the hole
diameter & ball freespace (movement) which are necessary to
reach the desired objective.
with further brainstorming we determined that i could use
a drill hole diameter equaling the BB diameter thru the shaft.
index the shaft 180dg & c'bore to a desired depth
& diameter such that a portion of the ball's arc radius
is allowed to rise above the shaft surface. then use a
machined ring bored to match this calculated arc radius
& subsequently pressed into the shaft c'bore thereby
trapping the spring & ball. bottom opening would be plugged
to finish off the test. from this i could determine
how my actual process would be optimized as a blind
hole.
the 2nd test - drill 1st hole blind matching BB diameter to
certain depth. index shaft 180dg & drill a pilot hole
using its diameter to control the reach of the BB's arc radius
thru the opening & ultimately above the shaft's perimeter.
i am going to use some 3d solids application to model the
iterative process & hopefully some trig calculations will
provide a formative guideline.

thanx again for your contributions

 

[TheTick]

I designed a custom ball detent that trapped a ball and spring. The entrance to the hole was an outward cone of material. The spring and ball were pushed in and the cone flattened in a press. With nowhere else to go, the cone deformed inward and formed a ring that retained the ball.

Didn't do much math, just lucky the first or second time. It doesn't take much material. You can count on the volume of the material being conserved.

 

[MintJulep]

Actually the volume of material does not remain constant. Mr. Poison sees to that.

 

[archimedesCNC]

interesting points.
thank you for your interest & responses -- i like
mintjulep's pithy declaration. i will look at
isotropic elasticity results with a little more
interest for the next research effort.
for now, i am playing with a 3d solid model.

: )

 

[btrueblood]

"Actually the volume of material does not remain constant. Mr. Poison sees to that. "

Poisson's ratio for plastic deformation is usually right up there around 0.5, i.e. volume is conserved, less the little bit of deformation in the elastic region.

" i will look at isotropic elasticity results with a little more interest for the next research effort."

Not worth your time, IMO. Your first approach (cut & try) is more likely to work. A swage is a plastic deformation process, not a linear elastic one.

 

[waross]

Now go to Sears and buy a Craftsman ratchet wrench for a different method of using a ball to retain sockets.

Bill
--------------------
"Why not the best?"
Jimmy Carter