Mount Limits

The Altair Bushing Model includes a Mount Limits feature, which lets you model the material contact that occurs between the bodies that a bushing connects. The bodies are flexible and may deflect under the load being transmitted. Given enough bushing deflection, the bodies may contact one another for negative and positive deflections in each direction.

When bushings deflect, a large amount of contact can occur between the bodies they connect limiting the deflection. However, these limits are dependent on the geometry of the bodies and are not an intrinsic bushing property. Therefore mount limits are specified in a separate Mount Limits Property File (*.gbi). In this file you can:

  • Activate mount limits for a bushing.
  • Define gap, stiffness and damping properties that are appropriate for the bodies that the bushing connects.

When the bushing deflection closes the gap between the bodies in a specific direction, the mount limit in the corresponding direction exerts a force or torque to limit the deflection. The following image shows how such a contact can occur at the connection between the A-Arm and the Strut in a suspension.

The mount limit force or torque adds to the bushing force or torque and acts to increase the normal force or torque input to the bushing friction and the local deflection of the bodies.



Figure 1.

Mount Limits depend on the geometry of the bodies that mount the bushing, and not the bushing itself. Therefore, the displacement and velocity used for computing the mount limit forces and moments, unlike the bushing, is not scaled, offset or coupled.

You can define positive and negative mount limits for any set of bushing directions: {FX, FY, FZ, TX, TY, and TZ}.

  • A positive mount limit acts to limit positive displacement in a given direction by producing a negative force or torque.
  • A negative mount limit acts to limit bushing negative displacement and produces a positive force or torque.
  • All the input parameters like stiffness, gap, and exponent for either positive or negative mount limits are always entered as positive values.

Positive Mount Limits

Let:

q k and q ˙ k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyCamaaBa aaleaacaWGRbaabeaakiaaysW7caqGHbGaaeOBaiaabsgacaaMe8Ua bmyCayaacaWaaSbaaSqaaiaadUgaaeqaaaaa@4003@
be displacement and velocity between the I body and J body less any local structural deflection as computed by the mount-stiffness CONTROL_STATEEQN.
L k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa aaleaacaWGRbaabeaaaaa@37E3@
be the gap that must be closed for material contact to occur.
K k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaWGRbaabeaaaaa@37E2@
be the stiffness of the limit.
E k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa aaleaacaWGRbaabeaaaaa@37DC@
be the exponent applied to the deflection. E k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa aaleaacaWGRbaabeaaaaa@37DC@ ≥ 1.0 to ensure a constant or rising stiffness rate with deflection.
C k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaWGRbaabeaaaaa@37DA@
be the damping coefficient.
D k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWGRbaabeaaaaa@37DB@
be the deflection at which the damping is fully active. For deflections less then D k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWGRbaabeaaaaa@37DB@ , the damping force is modified by the step function to prevent discontinuity of the contact force.

Then the force or torque in the kth direction for a positive mount limit is defined as:

if (Mount_Limits_Are_Inactive OR 
                                
                                    
                                        
                                            q
                                            k
                                        
                                        
                                        
                                            L
                                            k
                                        
                                    
                                    MathType@MTEF@5@5@+=
                                        feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                        hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                        4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                        vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                        fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyCamaaBa
                                        aaleaacaWGRbaabeaakiabgsMiJkaadYeadaWgaaWcbaGaam4Aaaqa
                                        baaaaa@3BB4@ 
                                
                            )
                
                                
                                    
                                        
                                            F
                                            k
                                        
                                    
                                    MathType@MTEF@5@5@+=
                                        feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                        hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                        4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                        vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                        fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa
                                        aaleaacaWGRbaabeaaaaa@37DD@ 
                                
                             = 0.0
else
                
                    
                        
                            
                                F
                                k
                            
                            =min(
                                
                                    0.0,
                                        K
                                        k
                                    
                                    
                                        
                                            (
                                                q
                                                k
                                            
                                            
                                                L
                                                k
                                            
                                            )
                                        
                                            
                                                E
                                                k
                                            
                                        
                                    
                                    
                                        C
                                        k
                                    
                                    
                                        
                                            q
                                            ˙
                                        
                                        
                                        k
                                    
                                    
                                        
                                            Step(q
                                        k
                                    
                                    
                                        L
                                        k
                                    
                                    ,0.0,0.0,
                                        D
                                        k
                                    
                                    ,1.0)
                                )
                        MathType@MTEF@5@5@+=
                            feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                            hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                            4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                            vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                            fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa
                            aaleaacaWGRbaabeaakiabg2da9iGac2gacaGGPbGaaiOBamaabmaa
                            baGaaGimaiaac6cacaaIWaGaaiilaiaaysW7cqGHsislcaWGlbWaaS
                            baaSqaaiaadUgaaeqaaOGaaiikaiaadghadaWgaaWcbaGaam4Aaaqa
                            baGccqGHsislcaWGmbWaaSbaaSqaaiaadUgaaeqaaOGaaiykamaaCa
                            aaleqabaGaamyramaaBaaameaacaWGRbaabeaaaaGccaaMe8UaeyOe
                            I0Iaam4qamaaBaaaleaacaWGRbaabeaakiqadghagaGaamaaBaaale
                            aacaWGRbaabeaakiaaysW7caqGtbGaaeiDaiaabwgacaqGWbGaaeik
                            aiaabghadaWgaaWcbaGaam4AaaqabaGccqGHsislcaWGmbWaaSbaaS
                            qaaiaadUgaaeqaaOGaaiilaiaaysW7caaIWaGaaiOlaiaaicdacaGG
                            SaGaaGjbVlaaicdacaGGUaGaaGimaiaacYcacaaMe8UaamiramaaBa
                            aaleaacaWGRbaabeaakiaacYcacaaMe8UaaGymaiaac6cacaaIWaGa
                            aiykaaGaayjkaiaawMcaaaaa@7073@
                        
                    
                
                

Negative Mount Limits

For a negative mount limit, the limit force is computed in the same manner as a positive mount limit, however the input displacement and velocity are negated as is the output force. Again all the input parameters are positive. The force/torque computation for a negative mount limit is:

if (Mount_Limits_Are_Inactive OR 
                                
                                    
                                        
                                            q
                                            k
                                        
                                        
                                        
                                            L
                                            k
                                        
                                    
                                    MathType@MTEF@5@5@+=
                                        feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                        hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                        4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                        vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                        fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyCamaaBa
                                        aaleaacaWGRbaabeaakiabgwMiZkaadYeadaWgaaWcbaGaam4Aaaqa
                                        baaaaa@3BC5@ 
                                
                            )
                
                                
                                    
                                        
                                            F
                                            k
                                        
                                    
                                    MathType@MTEF@5@5@+=
                                        feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                                        hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                                        4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                                        vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                                        fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa
                                        aaleaacaWGRbaabeaaaaa@37DD@ 
                                
                             = 0.0
else
                
                    
                        
                            
                                F
                                k
                            
                            =min(
                                
                                    0.0,
                                        K
                                        k
                                    
                                    
                                        
                                            (
                                                q
                                                k
                                            
                                            
                                                L
                                                k
                                            
                                            )
                                        
                                            
                                                E
                                                k
                                            
                                        
                                    
                                    
                                        C
                                        k
                                    
                                    (
                                        
                                            q
                                            ˙
                                        
                                        
                                        k
                                    
                                    )
                                        
                                            Step(-q
                                        k
                                    
                                    
                                        L
                                        k
                                    
                                    ,0.0,0.0,
                                        D
                                        k
                                    
                                    ,1.0)
                                )
                        MathType@MTEF@5@5@+=
                            feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
                            hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
                            4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
                            vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
                            fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa
                            aaleaacaWGRbaabeaakiabg2da9iabgkHiTiGac2gacaGGPbGaaiOB
                            amaabmaabaGaaGimaiaac6cacaaIWaGaaiilaiaaysW7cqGHsislca
                            WGlbWaaSbaaSqaaiaadUgaaeqaaOGaaiikaiabgkHiTiaadghadaWg
                            aaWcbaGaam4AaaqabaGccqGHsislcaWGmbWaaSbaaSqaaiaadUgaae
                            qaaOGaaiykamaaCaaaleqabaGaamyramaaBaaameaacaWGRbaabeaa
                            aaGccaaMe8UaeyOeI0Iaam4qamaaBaaaleaacaWGRbaabeaakiaacI
                            cacqGHsislceWGXbGbaiaadaWgaaWcbaGaam4AaaqabaGccaGGPaGa
                            aGjbVlaabofacaqG0bGaaeyzaiaabchacaqGOaGaaeylaiaabghada
                            WgaaWcbaGaam4AaaqabaGccqGHsislcaWGmbWaaSbaaSqaaiaadUga
                            aeqaaOGaaiilaiaaysW7caaIWaGaaiOlaiaaicdacaGGSaGaaGjbVl
                            aaicdacaGGUaGaaGimaiaacYcacaaMe8UaamiramaaBaaaleaacaWG
                            RbaabeaakiaacYcacaaMe8UaaGymaiaac6cacaaIWaGaaiykaaGaay
                            jkaiaawMcaaaaa@7543@