Spur or Helical Gear
Symbol:  
Identifier:  PowerTransmission.Transmissions.Gear  
Version:  3.9  
File:  PowerTransmission.cat  
Connectors:  Connectors for Gear 1:  
Mechanical Connector (linear)  ctrT1x  radial (tangential) support gear 1, xcomponent; connectable to elements of the Linear Mechanics library 

Mechanical Connector (linear)  ctrT1y  radial support gear 1, ycomponent; connectable to elements of the Linear Mechanics library 

Mechanical Connector (linear)  ctrT1z  axial support gear 1, zcomponent; connectable to elements of the Linear Mechanics library 

Mechanical Connector (rotational)  ctrR1  element for gear 1 can be connected here (rotation around z); connectable to elements of the Rotational Mechanics library 

Connectors for Gear 2:  
Mechanical Connector (linear)  ctrT2x  radial support gear 2, xcomponent; connectable to elements of the Linear Mechanics library 

Mechanical Connector (linear)  ctrT2y  radial support gear 2, ycomponent; connectable to elements of the Linear Mechanics library 

Mechanical Connector (linear)  ctrT2z  axial support gear 2, zcomponent; connectable to elements of the Linear Mechanics library 

Mechanical Connector (rotational)  ctrR2  element for gear 2 can be connected here (rotation around z); connectable to elements of the Rotational Mechanics library 

Parameters and Results:  see Table of Parameters and Result Quantitiesbelow 


Description:
The model Spur or Helical Gear stage can be used for the conversion of rotational speed and torque during the transmission process. It models the meshing of the gears, taking the # tooth stiffness and transverse backlash into account. It is suitable for modeling spur and helical gears. If required, the gear contact can be modeled as rigid.
The radial and axial support behavior can be modeled externally and thus can be rigid or elastic. Force, spring, and preload models are possible.
Figure 1: Coordinate systems of the Gear stage model
The gear element transforms displacements, velocities, accelerations, and forces (torques) between the red connector coordinate systems and the green inner coordinate system at the tooth contact (indicated by I). The tooth contact model is described in the chapter Tooth Contact.
Furthermore, the element is able to represent losses. The losses can be considered in the tooth contact and/or in the gear supports (at the rotational connectors).
Parameters:
Geometry
It is possible to use only constructional data for the parameterization of the gear (see Figure 1). These are in particular:
 the Normal Modulus,
 the Tooth Width ,
 the Number of Teeth z1 and z2 for the two gears,
 the Helix Angle (measured with respect to gear 1, see Figure 1),
 the Normal Pressure Angle ,
 and the Transverse Backlashj_{t}.
All the mechanical parameters (stiffness, damping, overlap) can be calculated internally, if nothing else is specified. In addition each parameter (if known) can be altered manually in further parameter groups in order to precisely adjust the model to the situation to be simulated.
Tooth Contact
The tooth contact can be modeled as rigid (see below) or elastic. If no values are given, SimulationX computes the tooth stiffness by an internal approach. Otherwise you can choose between an elastic or a rigid tooth contact model. Further information for parameterization, calculation and results of the tooth contact can be found in chapter Tooth Contact.
The principal model of the gear stage is defined by the Rigid checkbox. It can behave as
 SpringDamperBacklash: The Rigid checkbox is deselected. The behavior is defined by the given or computed stiffness, damping, and backlash parameters. Within the backlash the stiffness and damping are always zero.
 Rigid End Stop: If the Rigid checkbox is selected, the model behaves as rigid. I.e., it consists of an ideal transformation with rigid connection between all connectors (kindR=="without Backlash") or an ideal transformation combined with a rigid end stop. The kind of impact can be specified by the user via the Tooth Contact parameter  in the same way as for the rigid end stop in the Linear Mechanics library. If a backlash is present, it is set via the Rotational Backlash parameter.
 If the checkbox Rigid is selected and if the Contact enumeration kindR is switched to "without Backlash", the gear stage as a transformer (transmission). In this case, forces will only be transferred via the right tooth flanks, no matter in which direction the power is transmitted. So, the right tooth flanks transfer tensile and compressive forces (tensile forces have a negative sign). In this case, the result variables for the forces of the left tooth flanks Fbnl and Ftl are deactivated.
 If Consideration of Stiffness Change is selected (only possible if Rigid is deselected) the element computes a variable toothing stiffness by an internal approach (see chapter Tooth Contact).
Stiffness of Toothing / Damping of Toothing
 If Rigid is deselected, the properties dialog page Free Definition 1 provides parameters to define the elastic tooth contact model. Read more about the parameters and the calculation in the chapter Tooth Contact.
Modified Profile / Contact Ratio
This group provides further geometry parameters of the gear. If Consideration of Modified Profile is selected, it is possible to enter
 profile offset factors x1 and x2 for every gear. Based on this the effective radii for the force and motion quantity transformation between Tooth Contact and connector coordinate systems will be computed.
 the center distance a of the gears. Together with the tooth numbers, the effective transformation radii can be computed.
 Furthermore, the Input of an Addendum Modification is possible. The Addendum Modification kmn in the element Gear is an absolute value. If only an relative value k_{mn,rel} is given, the absolute value can be computed using the normal modulus m_{n} by:
 Finally the Total Contact Ratio can be specified. By default it is computed internally,
but it is possible to enter a constant value for epsilon (, see chapter Tooth Contact) in order to consider different kinds of modified profiles. The total contact ratio is used for the computation of the total stiffness by the specific stiffness of one pair of teeth (see also chapter Tooth Contact). Thus, this parameter is redundant if Summated Meshing Spring Stiffness is selected for kindS on page Free Definition 1. If you decide to enter a value for the total contact ratio, the addendum modification is obsolete, because this modification is always considered within the total contact ratio value.
Losses (tabs Losses 1 and Losses 2)
There are three locations for the consideration of losses:
 the tooth contact,
 the gear bearing at gear 1 (ctrR1) and ...
 the gear bearing at gear 2 (ctrR2).
Each loss location can be parametrized separately. All losses can be considered separately or in combination.
If reliable data is only available for the whole gear stage, e.g., the overall efficiency, only the parameters in the box Toothing / Gear Stage on the dialog page Losses 1 have to be entered and will determine the overall efficiency.
A detailed description of the loss models in gear stage elements can be found in the chapter Losses in Gear Stages.
Results:
 The gear model provides the normal forces, the tangential, radial, and axial forces, deformations and velocity differences of the tooth contact for the left and the right flank (see chapter Tooth Contact).
The tangential, radial, and axial forces are acting as pressure forces w.r.t. the green coordinate system in Figure 1 on gear 2. So, a negative radial force will move the gears apart.  Furthermore the Total Meshing Spring Stiffness is computed during simulation and can be observed in the result variable kbt.
 If a springdamperbacklash model (nonrigid model) of the tooth contact is selected, the Change of Potential Energy (the power flow into the spring in the contact) and the Power Loss (power dissipated in the damper) can be examined too.
 If there is a change of the contact surface, there is also a change in the place and direction where the spring stiffness, damping, and the normal force act.
 If Rigid is selected and kindR=="without Backlash", the tooth contact forces Fbnl and Ftl are inactive (see section Tooth Contact in this chapter).
 The transmission error TE is computed by: TE = r1*phi1  r2*phi2 using the operation radii of both gears r1 and r2
Periodic SteadyState Simulation:
The relative damping and Lehr's damping factor D as well as the spectral powers of the left and the right flank PSpecl and PSpecr, resp., are only taken into account in the Periodic SteadyState Simulation. These parameters are described in some detail in sections Periodic SteadyState Simulation (Parameters) and Periodic SteadyState Simulation (Results) of the chapter Tooth Contact.
Remarks:
The gear element only calculates the deformation forces in the tooth engagement. The inertia properties, i.e. the moments of rotational inertia in the gears, have to be assigned to externally connected objects.
The linear (translational) connectors ctrT1x, ctrT1y, ctrT1z, ctrT2x, ctrT2y, and ctrT2z can be used to model support properties, as well as for example a preload, which are applied to the gear stage. Some examples on how to model such situations are given in the subsection Linear connections of the Gear.
Table of Parameters and Result Quantities:
Parameters:  Geometry:  
Normal Modulus  mn  
Tooth Width  bw  
Helix Angle  beta  
Transverse Backlash  jt  not visible for Rigid model and kindR=="Without Backlash"  
No. of Teeth, Gear 1  z1  
No. of Teeth, Gear 2  z2  
Normal Pressure Angle  alphan  
Tooth Contact:  
Rigid  rigid  Selects rigid (end stop) behavior instead of elastic behavior in tooth contact 

Tooth Contact  kindR  only available, if Rigid is selected; Possible settings: "without Backlash", "Rigid Plastic", "Rigid Elastic", and "Coefficient of Restitution" 

Coefficient of Restitution  ci  only available, if kindR== "Coefficient of Restitution"  
Consideration of Stiffness Change  StiffChange  internal approach for a variable toothing stiffness; not visible, if Rigid or Preset of Stiffness is selected  
Free Definition of Elastic Toothing (Free Definition):  
Preset of Stiffness (specific, related to common face width)  stiff  not available, if Rigid is selected; switches to manual stiffness definition 

Preset of Stiffness as  kindS  only available if Preset of Stiffness is selected; Possible settings: "Function over Normalized meshing length Ln", "Characteristics over Normalized meshing length Ln", "Summated meshing spring stiffness" 

Function f(Ln)  kf  only available, if kindS== "Function over Normalized meshing length Ln"  
Characteristics  kc  Curve Parameter; only available, if kindS=="Characteristics over Normalized meshing length Ln" 

as  kindK  only available, if kindS=="Summated meshing spring stiffness"; Possible settings: "Constant Mean Value", "Function of the angle of gear 1", "Function of the angle of gear 2" 

Summated Stiffness  ksm  only available, if kindK=="Constant Mean Value"  
Summated Stiffness  ksc  only available, if kindK=="Function of the angle of gear 1" or "Function of the angle of gear 2"  
Damping of Toothing (Free Definition 1):  
Preset of Damping  damp  not available, if Rigid is selected Switches to manual damping definition 

as  kindB  only available if Preset of Damping is selected; Possible settings: "Total Damping", "Factor B for Relation to Tooth Stiffness b=B*sqrt(k)" 

Damping  b  only available, if kindB=="Total Damping"  
Damping Factor  B  only available, if kindB=="Factor B for Relation to Tooth Stiffness b=B*sqrt(k)"  
Damping in Toothing Backlash  bL  only available if Preset of Damping is selected  
Input of Stiffness/Damping  kindD  Interpretation of entered stiffness and damping values "in Meshing Direction" or "in Circumference Direction"  
Modified Profile / Contact Ratio:  
Consideration of Modified Profiles  modProf  
Input of  kindM  Possible settings: "Profile Offsets" and "Center Distance"; only available if modProf=="true" 

Profile Offset Factor (Gear 1)  x1  only available if kindM=="Profile Offsets"  
Profile Offset Factor (Gear 2)  x2  only available if kindM=="Profile Offsets"  
Center Distance  a  only available if kindM==Center Distance"  
Input of Addendum Modification  undercut  not available if kindC=="Input"  
Addendum Modification  kmn  only available if undercut=="true"  
Total Contact Ratio  kindC  not available, if Rigid is selected; Possible settings: "Internal Calculation" and "Input" 

Total Contact Ratio (input)  epsilon  only available, if kindC=="Input"  
Losses in Toothing / Gear Stage (page Losses 1 & Losses 2):  
Description  kindL  Description of the friction model used in the tooth contact or for the complete gear stage.  
Efficiency  eta  Please pay attention to direction of the value, see also chapter Losses in Gear Stages; It is possible to use this value for entering a degree of efficiency of the whole gear stage (incl. bearing losses); only available if kindL=="Constant Efficiency" 

Direction of eta from Gear 2 to Gear 1  dir  Measuring direction of eta; only available if kindL=="Constant Efficiency" 

Static Friction Coefficient  mu0  only available if kindL=="Friction Coefficients" or kindL=="Stribeck Curve"  
Sliding Friction Coefficient  mu  only available if kindL=="Friction Coefficients" or kindL=="Stribeck Curve"  
Limit Velocity  vL  only available if kindL=="Stribeck Curve"  
Consideration of Velocity Dependency  switchV  only available if kindL=="Stribeck Curve"  
Coefficient  Kv  only available if kindL=="Stribeck Curve"  
Exponent  Av  only available if kindL=="Stribeck Curve"  
Force of Static Friction  Fst  only available if kindL=="Friction Force Characteristic" or kindL=="Friction Forces"  
Force of Sliding Friction  Fsl  only available if kindL=="Friction Forces"  
Force of Sliding Friction Curve  FslCurve  only available if kindL=="Friction Force Characteristic"  
Losses in Gear Bearing 1  
Description  kindLB1  Description of the friction model used at the bearing of gear 1.  
Efficiency  etaB1  Please pay attention to direction of the value, see also chapter Losses in Gear Stages; only available if kindLB1=="Constant Efficiency" 

Direction of etaB1 from Gear 2 to Gear 1  dirB1  Measuring direction of etaB1; only available if kindLB1=="Constant Efficiency" 

Static Friction Coefficient  mu0B1  only available if kindLB1=="Friction Coefficients" or kindLB1=="Stribeck Curve"  
Sliding Friction Coefficient  muB1  only available if kindLB1=="Friction Coefficients" or kindLB1=="Stribeck Curve"  
Friction Radius  rB1  only available if kindLB1=="Friction Coefficients"; E.g., the radius of the ball bearing, measured at in the middle of the roller bearing retainer 

Limit Angular Velocity  omLB1  only available if kindLB1=="Stribeck Curve"  
Consideration of Angular Velocity Dependency  switchVB1  only available if kindLB1=="Stribeck Curve"  
Coefficient  KvB1  only available if kindLB1=="Stribeck Curve"  
Exponent  AvB1  only available if kindLB1=="Stribeck Curve"  
Static Friction Torque  TstB1  only available if kindLB1=="Friction Torque Characteristic" or kindLB1=="Friction Torques"  
Sliding Friction Torque  TslB1  only available if kindLB1=="Friction Torques"  
Sliding Friction Torque Curve  TslB1Curve  only available if kindLB1=="Friction Torque Characteristic"  
Losses in Gear Bearing 2  
Description  kindLB2  Description of the friction model used at the bearing of gear 2.  
Efficiency  etaB2  Please pay attention to direction of the value, see also chapter Losses in Gear Stages; only available if kindLB2=="Constant Efficiency" 

Direction of etaB1 from Gear 2 to Gear 1  dirB2  Measuring direction of etaB2; only available if kindLB2=="Constant Efficiency" 

Static Friction Coefficient  mu0B2  only available if kindLB2=="Friction Coefficients" or kindLB1=="Stribeck Curve"  
Sliding Friction Coefficient  muB2  only available if kindLB2=="Friction Coefficients" or kindLB1=="Stribeck Curve"  
Friction Radius  rB2  only available if kindLB2=="Friction Coefficients"; E.g., the radius of the ball bearing, measured at in the middle of the roller bearing retainer 

Limit Angular Velocity  omLB2  only available if kindLB2=="Stribeck Curve"  
Consideration of Angular Velocity Dependency  switchVB2  only available if kindLB2=="Stribeck Curve"  
Coefficient  KvB2  only available if kindLB2=="Stribeck Curve"  
Exponent  AvB2  only available if kindLB2=="Stribeck Curve"  
Static Friction Torque  TstB2  only available if kindLB2=="Friction Torque Characteristic" or kindLB2=="Friction Torques"  
Sliding Friction Torque  TslB2  only available if kindLB2=="Friction Torques"  
Sliding Friction Torque Curve  TslB2Curve  only available if kindLB2=="Friction Torque Characteristic"  
Results:  Stiffness of Toothing  
Total Meshing Spring Stiffness  kbt  not available, if Rigid is selected  
Toothing Forces  
Normal Force, Right Flank  Fbnr  
Normal Force, Left Flank  Fbnl  not available, if Rigid is selected and kindR=="without Backlash"  
Tangential Force, Right Flank  Ftr  
Tangential Force, Left Flank  Ftl  not available, if Rigid is selected and kindR=="without Backlash"  
Radial Force  Fr  
Axial Force  Fa  
Transmission Error  
Transmission Error  TE  
Deformations and Velocity Differences of the Toothing  
Displacement Difference, Left  dxbnl  
Displacement Difference, Right  dxbnr  
Velocity Difference, Left  dvbnl  
Velocity Difference, Right  dvbnr  
Powers  
Change of Potential Energy  Pp  not available, if Rigid is selected  
Power Loss  Pl  not available, if Rigid is selected  
Energy Loss  El  only available if rigid==false and backlash is taken into account  
SteadyState Simulation:  Preset of Damping  kindDamping  Only Effective in SteadyState Simulation 
Relative Damping  psi  only available if kindDamping=="Relative Damping"  
Damping Factor  D  only available if kindDamping=="Lehr's Damping Factor"  
Spectral Power of Left Flank  PSpecl  
Spectral Power of Right Flank  PSpecr 