Validate Test Data in the SPD File

The System Performance Data file, *.spd, contains the test data used for fitting a bushing. This data should be validated to ensure that it is physically meaningful. One test for physical consistency is that the dynamic stiffness at any amplitude of vibration must always be greater than the static stiffness at the same amplitude.

Further information about how to perform such validations in the Model Identification Tool is included in the following sections:

Extract Relevant Dynamic Data from an SPD File

The following figure shows a section of the dynamic data block in an .spd file. The contents of each column are described in the header line, shown in blue.
Figure 1.


Note the following:
  • Each line specifies an individual test that was performed.
  • The first column (D_MAG) of each line of data specifies the magnitude of the sinusoidal input.
  • The third column (K_MAG) specifies the dynamic stiffness that was measured in the test.
  • The sixth column (PRELOAD) specifies the preload that was applied to the bushing before the dynamic testing was done. In the example shown, a preload of -550 N was applied to deform the bushing. Subsequently, a dynamic test was performed.

Extract Relevant Static Data from an SPD File

The figure below shows a section of the static data block. The contents of each column are described in the header line, shown in blue.
Figure 2.


Note the following:
  • The first column (DISP) of each line of data specifies the static displacement provided as input.
  • The second column (FORCE) specifies the static force that was measured for that input.

Static Curve Representation

Let the static data be represented with:
  • N displacement data points x i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaWGPbaabeaaaaa@380D@ , i=1…N.
  • N force data points, F i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaWGPbaabeaaaaa@37DB@ , at displacements x i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaWGPbaabeaaaaa@380D@ .
An AKIMA spline is used fit this curve. Symbolically, this can be represented as:
  • F ( x ) = AKIMA ( x , x i , F i ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaacI cacaWG4bGaaiykaiabg2da9iaabgeacaqGlbGaaeysaiaab2eacaqG bbGaaGjbVpaabmaabaGaamiEaiaacYcacaaMe8UaamiEamaaBaaale aacaWGPbaabeaakiaacYcacaaMe8UaamOramaaBaaaleaacaWGPbaa beaaaOGaayjkaiaawMcaaaaa@4AAC@
  • x MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaaaa@36F3@ is the displacement at which the force F ( x ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiaacI cacaWG4bGaaiykaaaa@3917@ is required.

Calculate the Average Static Stiffness in a Bushing for a Test

  1. The first step is to compute the static deflection due to preload.
    • Designate the applied preload as P (for our example, P=-550 N).
    • Solve the nonlinear problem: P = AKIMA ( x 0 , x i , F i ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiabg2 da9iaabgeacaqGlbGaaeysaiaab2eacaqGbbGaaGjbVpaabmaabaGa amiEamaaBaaaleaacaaIWaaabeaakiaacYcacaaMe8UaamiEamaaBa aaleaacaWGPbaabeaakiaacYcacaaMe8UaamOramaaBaaaleaacaWG PbaabeaaaOGaayjkaiaawMcaaaaa@4950@ and compute the required displacement x 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaaIWaaabeaaaaa@37D9@ .
  2. Compute the minimum and maximum values of the dynamic oscillation for each test, j, with an amplitude u j MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaWGQbaabeaaaaa@380B@ .
    • Maximum deformation, d j max = x 0 + u j MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGQbGaciyBaiaacggacaGG4baabeaakiabg2da9iaadIha daWgaaWcbaGaaGimaaqabaGccqGHRaWkcaWG1bWaaSbaaSqaaiaadQ gaaeqaaaaa@40C2@
    • Minimum deformation, d j min = x 0 u j MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGQbGaciyBaiaacMgacaGGUbaabeaakiabg2da9iaadIha daWgaaWcbaGaaGimaaqabaGccqGHsislcaWG1bWaaSbaaSqaaiaadQ gaaeqaaaaa@40CB@
  3. Compute the average static stiffness for the range of dynamic oscillation in test j.
    • F jmax =AKIMA( d jmax , x i , F i ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaWGQbGaciyBaiaacggacaGG4baabeaakiabg2da9iaabgea caqGlbGaaeysaiaab2eacaqGbbGaaGjbVpaabmaabaGaamizamaaBa aaleaacaWGQbGaciyBaiaacggacaGG4baabeaakiaacYcacaaMe8Ua amiEamaaBaaaleaacaWGPbaabeaakiaacYcacaaMe8UaamOramaaBa aaleaacaWGPbaabeaaaOGaayjkaiaawMcaaaaa@5034@
    • F jmin =AKIMA( d jmin , x i , F i ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaWGQbGaciyBaiaacMgacaGGUbaabeaakiabg2da9iaabgea caqGlbGaaeysaiaab2eacaqGbbGaaGjbVpaabmaabaGaamizamaaBa aaleaacaWGQbGaciyBaiaacMgacaGGUbaabeaakiaacYcacaaMe8Ua amiEamaaBaaaleaacaWGPbaabeaakiaacYcacaaMe8UaamOramaaBa aaleaacaWGPbaabeaaaOGaayjkaiaawMcaaaaa@5030@
    • F jsatic = ( F jmax F jmin )/ ( 2 u j ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaWGQbGaam4CaiaadggacaWG0bGaamyAaiaadogaaeqaaOGa eyypa0ZaaSGbaeaadaqadaqaaiaadAeadaWgaaWcbaGaamOAaiGac2 gacaGGHbGaaiiEaaqabaGccqGHsislcaWGgbWaaSbaaSqaaiaadQga ciGGTbGaaiyAaiaac6gaaeqaaaGccaGLOaGaayzkaaaabaWaaeWaae aacaaIYaGaey4fIOIaamyDamaaBaaaleaacaWGQbaabeaaaOGaayjk aiaawMcaaaaaaaa@4EFE@

Validate Bushing Dynamic Stiffness Data in an SPD File

The validation test is shown in the following plot. The test essentially consists of verifying that the average slope of the static curve in the range of operation does not exceed the dynamic stiffness measured in the test.
Figure 3.


The algorithm for performing the validation is as follows:

for each dynamic test j = 1...M

    get displacement magnitude, u j MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaWGQbaabeaaaaa@380B@ (first column of dynamic data)
    get dynamic stiffness, K j m a g MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaWGQbGaamyBaiaadggacaWGNbaabeaaaaa@3AA5@ (third column of dynamic data)
    get preload, P j MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaBa aaleaacaWGQbaabeaaaaa@37E6@ (sixth column of dynamic data)
    compute x 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaaIWaaabeaaaaa@37D9@ using algorithm (a)
    compute range of dynamic oscillations using algorithm (b)
    compute average stiffness for the range using algorithm (c)
    if K j s a t i c > K j m a g MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaWGQbGaam4CaiaadggacaWG0bGaamyAaiaadogaaeqaaOGa eyOpa4Jaam4samaaBaaaleaacaWGQbGaamyBaiaadggacaWGNbaabe aaaaa@424F@
        issue warning message