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Info Letter No. 46 December 1997

WL1+ Quick View

The life expectancy of roller bearings has been added to the WL1+'s Quick Output.

WL1+ Safety Margin

Until now WL1+ has calculated the safety margins in relation to alternating load due to bending, tension/pressure and torsion. In the new version you can choose whether torque is alternating, pulsating or resting.

WL1+ calculates the reference stress in relation to Sigma bw. The result is one value for the safety margin: S = Sigma bw / Sigma v.

You can select whether the load should be alternating, pulsating or static for torque and axial forces. Bending stress (from shearing force, path load and bending moments) are always alternating due to the rotating shaft, even when the load is purely static. The load frequency is equal to the rotational speed of the shaft. With the help of the reference stress, the general state of stress is converted to a plane stress. The safety margin is calculated from:
```S = sigma bw / Sigma v

Dependent on the strength theory:

Sigma v = SQRT ( sigma² + ( alpha0 * phi * tau )²)

The different stress states can be taken into account with the
correction value alpha0:

Sigma bw
alpha0= ------------
phi * tau

Whereby when tau occurs with alternating torque tau w is used;
for pulsating torque tau sch is used; and for static load tauf F
is used.  phi is dependent upon the strength theory (1, 2 or
1.73).

Example:  A shaft made of St50 is stressed by the bending moment
Mb and the torque Mt.  How great is the correction value ã0 in
accordance with the shear strain energy theory when:
a) bending occurs alternating, torsion resting;
b) both occur alternating;
c) bending occurs resting, torsion occurs alternating?

The limit stress can be taken from the WST1 material data base:
sigmabF=450N/mm² sigmabW=250N/mm²
tauF=180N/mm² tauW=150N/mm².

With phi=SQRT3

a) alpha0 = sigmabW/(phi tauF) = 250 / ( SQRT3 * 180 ) =  0.8
b) alpha0 = sigmabW/(phi tauW) = 250 / ( SQRT3 * 150 ) =  0.96 ÷ 1
c) alpha0 = sigmabW/(phi tauF) = 450 / ( SQRT3 * 150 ) =  1.7
```
The correction value ã0 is ascertained by WL1+ when a material is selected from the data base and the strength values are known.

WL1+ Tension and Bending Stress

To allow for overloading of tension stress onto the reference stress, the tension stress on the bending-alternating stress portion of the reference stress is converted as follows:
```sigmaz alternating: Sigma vb = Sigma b + Sigma z * Sigma bw / Sigma w
sigmaz pulsating: Sigma vb = Sigma b + Sigma z * Sigma bw / Sigma sch
sigmaz resting: Sigma vb = Sigma b + Sigma z * Sigma bw / Re
```

WL1+ Crit.Rotat.Speed for Triple Bearing

Now it is also possible to calculate the resonance speed for bending vibrations for triple bearing shafts. Since this drastically increases calculation time, it is possible to switch off the calculation for bending critical rotational speed, under "Edit->Calculation". The rotational speed for torsional fatigue is independent of the number of bearing positions and can therefore always be displayed.

FED8 - Spring Energy

A diagram showing the curve for spring energy is now included in the FED8 software for calculation of torsion bars. For alternatingly loaded torsion bars, the displacement angle goes from -alpha to +alpha. The maximum spring operation from -ãn to +ãn is then Mn times ãn (Index n = usable displacement angle for shearing stress tau n = tau perm).

FED2 - Index kn

For the extension spring calculation, the Index n is output as usable spring path for static load, for which the shearing stress tau n = tau zul. For dynamic load, the corrected shearing stresses (tau k = tau * k) are used for tau k1 and tau k2. The corrected shearing stresses tau k1 and tau k2 are used for positions 1 and 2 in the printout, for Positions 0 and n the values tau 0 and tau n are used. In the new version, tau kn = tau n * k are also displayed, this makes it clearer why tau k2 can be greater than tau n.
```======================================================================
Spring length   travel   mm   Spring force N      tau N/mm²       S
======================================================================
L0=  27.47ñ0.8                F0=    8.47         tau0 =   86
L1=  39.98      s1=  12.51    F1=   45.62ñ5.38    tauk1=  559     1.39
sh=  10.00    Fh=   29.69         taukh=  364     1.09
L2=  49.98      s2=  22.51    F2=   75.31ñ5.83    tauk2=  923     0.84
Lkn= 45.96      skn= 18.49    Fkn=  63.38         taukn=  777     1.00
Ln=  50.41      sn=  22.94    Fn=   76.58         taun =  777     1.00
----------------------------------------------------------------------
(S = tau zul. / tau y)

Sigma perm./ Sigma q2 = 0.68       Sigma hperm./ Sigma bh = 0.67
```

FED2 - Pre-Stress Force

When only one spring length and matching spring force is available, then F1=0, L1=L0 and sh=s2 are entered for the pressure spring calculation. In the tension spring calculation this is different because the pre-stress force with which the coils lie over one another must first be overcome. This means that during dimensioning and pre-dimensioning the pre-stress force F0, must be entered for F1 and not F1=0.

10 Year Anniversary for HEXAGON Software

Although HEXAGON GmbH wasn't founded until 1990, we had already developed our Tolerance Program TOL1 in 1987. Parallel to the Further Informatic Degree, our Engineer Office Ruoss, was already writing software for mechanical engineering designers for use on 8086-PCs with 4,77 MHz and 256 kB memory, with 360 kB disk drives without hard drives. At the time this was highly advanced compared to the previous computers such as the Sinclair ZX81 with only 1 kB of memory! The development tool Turbo Pascal 3.0 was contained in a 40 kB file (TURBO.COM) which included the compiler and program editor. This meant that a 360 kB disk included the development tool, the source code and finished program! In comparison: Borland Delphi 3.0, the successor to Turbo Pascal requires 100 MB memory on the hard drive, this is an increase by a factor 2500! After our Tolerance Program, TOL1 followed the toothing program ZAR1 and the pressure spring program FED1. The highlight in our programs was the introduction of graphic representation of the tooth form in ZAR1, and the spring drawing in FED1, later followed the feature for output to DXF or IGES files via the CAD interface. At the time, a CAD interface for calculation programs was something new, and was only available with HEXAGON software. At the time, most users stated that they rarely used the CAD interface, today, this is a standard part of any calculation program. For data bases with material values and DIN parts, the "old" DBF format from dBase 3+ is used. This means that the files can be editted and worked on with any data base or spreadsheet program (dBase, Access, FoxPro, Excel, Quattro Pro, StarOffice). After our Tolerance program, Toothing program and Pressure Spring program followed both of the graphic conversion programs, HPGL Manager and DXF Manager. Both of which were and still are useful for internal program development (generation of source code for DXF drawings). Then followed the programs for tension and spiral spring calculation, shaft calculation, bolted joints, pressed fits and shaft-hub joints. Along side this, we continually improved and updated our user interfaces.
Since 1992 we have been able to offer a UNIX version of the HPGL Manager and ZARXE, for DEC and SUN work stations. Although Unix version were sought after in 1990-92, this has now dropped off so that no further development in the Unix area is carried on. Much more successful has been the conversion to Windows. The first HEXAGON Windows version was the HPGL Manager, available in June 1993. All programs were converted after this to Windows. Today, 95% of our orders are for Windows versions. In 1997 we brought out new programs, FED8 for calculation of torsion bars, and TR1 for girder calculation. New and future oriented in all of our programs is the feature, as an alternative to printing out on a printer, the possibility for creating HTML files which can be read by Netscape or Internet Explorer.

WN2 - Dedendum

The tooth dedendum, hfP, or tool addendum haP0, wer until now set a 0.55*m. According to DIN 5480 this is the factor for broach toothing manufacture. However, a factor of 0.6*m is recommended for hobbing manufacture, and a factor of 0.65*m is recommended for wälzstossen. With the new WN2 version you can enter the dedendum factor freely. I would like to thank Mr Canovas of Moog, Böblingen, Germany for pointing this out.

FED1+ Quick View

The output for the manufacturing adjustment has been moved down one line. This avoids the text in the second column being written over.

FED3+ Clamping Angle

With twists springs, the clamping angle delta is in the opposite direction to the spring angle alpah. This is often misunderstood, and was displayed falsely in the auxiliary picture for the application example.

Analogue to pressure spring with L = L0 - s applies to the torsion spring delta = delta0 - alpha

FED3+ Clamping

The program allows you so choose between fixed clamping and supported spiral. For supported spiral, the lever arm for the center axis must also be entered. The program then calculates the deflection of the spiral and the resulting additional angle displacement ß. For fixed clamped spirals the spring is held directly on the outer diameter. When the spring ends are bent axially or inwards, you should also select "fixed clamping". A new auxiliary picture is provided for clamping.

Windows Versions for NT

All Windows version since 1996 can be installed without problem under Windows NT. The only limitation is that you can still only use the 8.3 format for file names. This means 8 characters for the file name, and three characters for the extension.

Don't use blanks in file names!

Please don't use blanks in file names. Although Windows 95/NT and old DOS versions allow this. This can result in your not being able to load files when changing to a newer version. If this has already happened, install the old DOS version again, load all your files with blanks in the file name and rename and save them under new names.

Seminar Schedule 1998

We are offering the following seminars in 1998: toothing and gearing calculation, spring calculation, working design calculation and DIN ISO 9001 certification. If you are interested in taking part in one of our seminars, please contact us to obtain our Seminar Schedule. We now offer a seminar on "Vibration Activation and Noise Behaviour in Gears". This seminar, of ever increasing importance for minimizing gear noise, is held by Dr. Müller.

Seminar: Vibration and Noise Behaviour in Gears

This seminar is a sensible follow-on, providing the newest information about noise and toothing, and noise behaviour in gears, and provides important information on preventing noise development during gearing pre-dimensioning. The topics covered are listed below:
• Basic knowledge in vibration activation and vibration behaviour
• Dynamic behaviour of toothing gears; determination of datum rotational speed N, as well as dynamic factor Kv.
• Vibration behaviour of the whole gear: Influence of the whole system "gear" including drive and work machines, also accounting for shaft bending.
• Measures for influencing the vibration and noise activation by spur gears; toothing geometry, toothing deviation and toothing adjustment, tooth flank play, etc.
• Influence parameters for bevel gears
• Special occurence of vibration: Getriebeasseln
• Relationship between noise activation and noise radiation of gears.
• Measures for influencing solid borne noise conduction and noise radiation: Housing design.
• Selected question about measuring technology
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