modelBallScrewDrive

Model of a ball screw drive according to Gross, Hamann and Wiegärtner (2006). Can be parameterized by typical supplier data such as from A. Mannesmann
Diagram of BallScrewDriveOpen the diagram
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Parameters

TypeNameDefaultDescription
SI.Lengthone_meter1
Geometric data
SI.DiameterdNominal diameter of spindle
SI.LengthPPitch of spindle
SI.Lengthl_S1Length of spindle
SI.Conversions.NonSIunits.Angle_degrho0.2Angle of friction
Calculated › Geometric data
SI.Lengthl_S_u0.9*l_SUnsupported length of spindle
SI.Conversions.NonSIunits.Angle_degphiSI.Conversions.to_deg(atan(P/(Constants.pi*d)))Angle of lead
Physical data
SI.Densitydensity7900Density of spindle material
SI.TranslationalSpringConstantR_nu0.5*10^9Nut rigidity on nut flange
SI.TranslationalSpringConstantR_S0.09*10^9Spindle rod rigidity per m
Realmu0.006Friction coefficient of bearing
Calculated › Physical data
Modelica.SIunits.Massm(d/2)^2*Constants.pi*l_S*densityMass of Spindle
Realetatan(SI.Conversions.from_deg(phi))/tan(SI.Conversions.from_deg(phi + rho))Value of efficiency of nut
SI.MomentOfInertiaJ0.5*m*d^2/4Moment of inertia of the spindle
SI.TranslationalSpringConstantR_ax1/(1/R_nu + l_S_u/one_meter/(R_S*k))Axial rigidity
Engineering data
SI.ForceC_am50000Dynamic load rating of nut
SI.ForceC_0am80000Static load rating of nut
Realpreload_factor0.07Preload of factor for nut. preload_factor = F_pr/C_am
SI.ForceF_pr_Bearing0Preload force of bearing
BearingConfigurationbearingConfigurationBearingConfiguration.fixed_supportedBearing method of spindle
SI.Massm_ref1000Reference mass for eigenfrequency
Calculated › Engineering data
SI.Diameterd_B1.6*dDiameter of bearing
SI.ForceF_prpreload_factor*C_amPreload force of nut
SI.Frequencyf_bs1/(2*Constants.pi)*sqrt(R_ax/m_ref)Eigenfrequncy of ball screw
SI.Conversions.NonSIunits.AngularVelocity_rpmn_kritk_L*d/l_S_u^2critcial rotational speed of spindle
SI.ForceF_bk_buckling*d^4/l_S_u^2Buckling force
Limiting data
SI.Frequencyf_min50Minimum eigenfrequncy of ball screw and spindle. Constraint f_bs > f_min
SI.Conversions.NonSIunits.Time_hourL_h_min10000Minimum life expectancy of nut
RealDN_perm160000Permissible DN value of nut (diamater*max_speed)
Safety factors
RealS_n_krit1.25Safety factor for n_krit
RealS_F_b2Safety factor for buckling
RealS_C_0am3Safety factor for static load rate

Connectors

TypeNameDefaultDescription
Modelica.Mechanics.Translational.Interfaces.Flange_bflangeT(right) driven flange (flange axis directed out of cut plane)
Modelica.Mechanics.Rotational.Interfaces.Flange_aflangeRLeft flange of shaft
Modelica.Mechanics.Translational.Interfaces.SupportsupportT1Translational support/housing of component

Components

TypeNameDefaultDescription
SI.Frequencycon_fConstraint for eigenfrequncy of axis
SI.Conversions.NonSIunits.Time_hourcon_L_hConstraint for life expectancy. The value at t_end is relevant when simulation terminates.
SI.Forcecon_F_prConstraint for preload
SI.Conversions.NonSIunits.AngularVelocity_rpmcon_n_kritConstraint for critcal speed
Realcon_DN
SI.Forcecon_F_bConstraint for buckling force
SI.Forcecon_C_0amConstraint for static load rating
Realutil_f
Realutil_L_h
Realutil_F_pr
Realutil_n_krit
Realutil_DN
Realutil_F_b
Realutil_C_0am
BallScrewNutballScrewNut
Modelica.Mechanics.Rotational.Components.Inertiaspindle
RotationalComponents.BasicComponents.Bearingbearing
Modelica.Mechanics.Rotational.Components.Fixedfixed