DIN5480 spline, measurement over balls calculation

[Luke4b]

I've been working through the spline design example given in DIN5480-1 (120 x 3 x 38 x 9H 8f) but using the calculations given in Table 9 of 5480-15 I am struggling to match the measurement over balls values given in DIN5480-1 Fig6.

I'm assuming that values for e/s should be substituted for emin/max and smin/max to generate the upper and lower bounds.

Working through step by step for M1min:

Factor A = 1
inv a = 0.05375
Factor B = 0.054213 (external spline so s/d being smin(6.180/114))
invBETA = 0.086064
BETA = 5119.923 (V iterated to 89.3595)
M1 = 570.255

In the DIN5480-1 Fig 6, the distance should be 126.017, which makes a lot more sense on a 120mm diameter shaft!


edit:
Digging around a bit I've come across: This thread wherein the poster calculates these measurements using some different calculations in 5480-2 (which unfortunately I do not have). If there is a more simple method in 5480-2, what is the purpose in the method from 5480-15?

 

[spigor]

If your invBeta is 0.086064 then your Beta is 34.611327909590942 degrees - calculated with this:

https://keisan.casio.com/exec/system/13740457438197

In 5480-2 there are tables with over balls measurements with scale factors for each spline connection. You just take a reference measurement from the table and calculate the upper and lower limits simply by multiplying the tooth thickness deviations by a scale factor from the table.

 

[Luke4b]

Thanks, that helps highlight whereabouts in the calculation I've gone wrong.

I was calculating Beta with an implementation of the basic program in the standard written in VBA. I've actually iterated this by hand for the first 6 or so iterations to double check I'm getting the expected results too. My VBA takes 740 iterations to run.

Sub calcBETA(Bref As Range, Betaref As Range, iters As Range)

    Dim V As Double
    Dim B As Double
    Dim BETA As Double
    Dim A As Double
    Const pi = 3.14159265358979
    
    B = Bref.Value
    V = 0.5

line40:
    A = 1 / Tan(V * (pi / 180)) - 1 / (V + B)
    If Abs(A) > 0.000001 Then
        V = A + V
        GoTo line40
    End If
        
    BETA = (A + V) * 57.29577951
    
    Betaref.Value = BETA
    
End Sub

edit:
So if I remove *(pi/180) from the calculation, so I'm working in radians rather than degrees, the calculation for the external spline works.
If I do so though then the calculation for the hub internal spline breaks dramatically.

Step by step of the hub calculation:

Factor A = 1
inv a = 0.05375
Factor B = -355.628 (external spline so (pi· m -e)· d (using emin 6.305, -d because it's a hub))
invBETA = -355.545
BETA = 90.16187 (V iterated to 1.57362 in 4 iterations)
M1 = -34951.9

Definitely something fishy here. I can't help but think the problem is Factor B, but I'm blind to what I'm doing wrong here.

 

[spigor]

Is this now a math or programming problem, because if so it does not belong here?
I don't think you should work any negative values when calculating the angles from their involutes, because it violates their physical meaning. So you should use (pi*m - e)*d and it should be a positive value.

 

[Luke4b]

Not a programming problem. The program runs fine, it's just a representation of the maths (as it's an iterative problem).

Using positive values for d I get a positive value of Factor B:

Factor B = (pi*m -e)*d = (pi* 3 - 6.305) * 114 = 355.6547
invBETA = 355.7112 (or 355.8175 if I swap the sign from negative to positive for d).

this still gives me a BETA value of 89.84 which then gives me M2 of 34637.68.

 

[spigor]

89.84 degrees, huh? I see that the physical meaning is not much of a concern to you.
Looking at the equations I can see it should be Factor B = (pi*m - e)/d = -0.027366473 A factor can be negative.
z = -38
d = -114
invBeta = 0.055881513 This must be positive.
Beta = 30.36083688 degrees
M2 = 109.1682948

 

[Luke4b]

Thank you very much, that has fixed it.

I'm not sure where (pi·m -e)/d comes from though, that table 9 in DIN5480-15 definitely states (pi·m-e)·d

I'm not sure what the physical meaning of BETA is, but had imagined it was suppose to be around 30 (the pressure angle) and suspected that was the cause of my problem.

 

[spigor]

Like I commented, I took a look at the equations and saw it, because:
m*Pi = pitch
s + e = pitch
so (m*Pi -e) is really s
s/d is half angle in radians
so it should be (m*Pi -e)/d
This is a clear error in the standard.
If you invested a considerable amount of time in learning what the physical meaning of different stuff is, then you should even be able to make things like solving puzzles on this forum.