To create Gear AT Force there are number of parameters to be entered in following tabs of the dialog box shown in Figure 217 :

 

 

 

The Gear AT Force element is defined by Worm Wheel and Worm. Gear AT Elements can be selected or created by the GUI options Pick, Browse, Guess or Create; see section Gear AT Element to learn more about the creation of a Gear AT Element.

Gear AT Mesh gives you the full control about the number of contact planes and the Mesh_density; see section Gear AT Mesh. Therefore you need to select the desired *.wgs files for the worm wheel and worm

 

The icon of Figure 217 computes the clearance in the gear pair by using the solids of the gear rim. If clearance - what should be the normal case - is found, it will be shown as depicted by Figure 225. All gear pairs in the model will be checked for the minimum clearance value. Note that solids do not include the micro-geometry.

 

Contact algorithm implemented in Gear AT is based on numerical approach which makes possible to account for varying backlash and contact stiffness at arbitrary shaft positions and angular misalignments. It can calculate contact up to eleven teeth at a time to capture variation of gear mesh stiffness.

To define gear pair contact force there are 4 modeling options available. The first modeling option Gear FAST offers pre-computed contact formulation delivering high performance with good quality of results. It is based on results of number of contact simulations by Flexible Tooth modeling option. Other three modeling options Rigid Gear, Flexible Tooth and Full Flex Gear use an advanced surface-to-surface contact algorithm, which delivers accurate and smooth results. The tooth flanks are described by the extruded profile including parametric definition of micro geometry.

The contact model Full Flex Gear employs algorithm of Flexible Tooth contact taking the flexible wheel body deformation into account. Wheel body deformation is based on modal flexibility implemented by Adams Flex and employs modal force (MFORCE) statement. Other contact modeling options employ Adams GFORCE element.

 

 

 

Modeling option defines the type of contact: you have 4 options to select from. The first modeling option Gear FAST offers pre-computed contact formulation delivering high performance with good quality results; for more information see Gear AT Fast Preprocessing. It is modeled with Adams GFORCE element as well as Rigid Gear and Flexible Tooth contact options.

Other three modeling options Rigid Gear, Flexible Tooth and Full Flex Gear use an advanced surface-to-surface contact algorithm, which delivers accurate and smooth results. The algorithm considers varying shaft positions and angular misalignments. The tooth flanks are described by the extruded profile including the micro-geometry. The solids for display are not used for the contact computation. The contact is checked for the left and right flanks of 5, 7, 9, 11 tooth pairs.

For rigid body contact, the maximum penetration of each contact plane of Worm Wheel into the flank of Worm is used for the of the corresponding contact force Fcnt as shown by Equation  (28). The vector sum of all contact forces is giving the resulting contact force and torque vector per gear pair.

where:

k contact stiffness
pene maximum penetration
cexp exponent force law

 

In general, the deformation of a tooth is coming from the deformation of the wheel body, the deformation of the teeth and the 'Hertz contact'. The contribution of the 'Hertz contact' is limited compared to the two other contributions. Consequently, one has to assume, that the Stiffness Exponent is close to 1 or only slightly higher. An exponent of 1 corresponds to a linear contact stiffness.

For the Flexible Tooth contact model, the transmitted force between tooth flanks considers the flexibility of the teeth through the solution of a non-linear contact problem. The contact algorithm is of type surface-to-surface. A small relaxation by Contact Overlap is introduced for better performance; supported values are Small, Normal or High. Small overlap corresponds to stiffer contact whereas High overlap corresponds to softer contact. The effect of this additional flexibility is small compared to the flexibility of the teeth.

The contact model Full Flex Gear employs algorithm of Flexible Tooth contact taking the flexible wheel body deformation into account. Wheel body deformation is based on modal flexibility implemented by Adams Flex.

Friction of gear pair implemented in Gear AT is based on Coulomb friction model. Contribution of friction to total contact force can be turned On / Off by the Friction Model option. It is computed for each contact plane of Worm Wheel based on the relative sliding velocity at the contact point.

 

 

 

 

The static friction coefficient is usually somewhat higher than the dynamic friction coefficient. Step functions are used for smoothing the transitions; see Figure 220. Parameter of slip velocity limits the region of sign change of the sliding velocity. The combination of very small slip velocity and high friction can reduce the performance of the integrator. You are advised to validate his selection through post-processing of the sliding velocity. Transition velocity defines the start of the region, where the dynamic friction is constant. A small difference between slip velocity and transition velocity could also lead to numerical issues of the integrator.

Under Gear FAST modeling option damping and friction are computed with simplified methods. The relative velocities in contact are evaluated only in middle plane of gear wheels. This approach can lead to noisy results under dynamic simulations; therefore adjustments for damping should be made with caution. The Friction model is reduced to 2 parametric model, with one friction coefficient and one threshold velocity.

The effects of hydrodynamic damping depend on gap height and squeeze velocities. The implemented damping force defined through Damping Rate Oil approximates hydrodynamic damping in function of the gap for each contact plane between the tooth flanks and the corresponding squeeze velocity.

 

 

 

The function b defined by Equation  (1) is used to define the damping; see Figure 222.

There is no hydrodynamic damping, when b < 0; see Equation  (2)

Hydrodynamic damping increases exponentially with decreasing oil film height. The introduction of the damping exponent dexp in Equation  (3) is used for this purpose; see Figure 222.

In case of contact (penetration), the hydrodynamic damping force is set as shown by Equation  (4).

Structural damping is usually a small value. The structural damping force is made proportional to the contact force as shown by Equation  (33). A value of 0.01 means, that the structural damping force is 1.0 percent of the elastic contact force.

Parameters entered in the lubrication tab do not influence computation of contact force, they are used to compute wear results of minimum oil film thickness; see Advanced Results.

 

 

 

Min_oil_film thickness (hmin) is the key parameter to evaluate linear wear coefficient (C_lT). The coefficient can be found for different pair of materials in contact from lookup tables.

The results of Min_oil_film thickness can be found in the Wearing component of request and plotted as 2D curve or 3D plot via Advanced Results. It is calculated according to PLEWE formula. The thermal correction coefficient is also considered.

 

where:

Reqv - equivalent radius of curvature

G - elasticity coefficient

U - velocity coefficient

W - load coefficient

C - thermal correction

 

where:

αp - pressure coefficient of viscosity

αt - temperature coefficient of viscosity

λ - thermal conductivity

ν - dynamic viscosity

vΣ - sum of tangent velocities

Eeqv - equivalent module of elasticity

T - Torque

db - base diameter of pinion

αw - working pressure angle

b - width of contact