Gear AT Shape Definition allows you to create a file that defines the topology of a gear (both macro and micro geometry). You can define a gear tooth profile either by defining tooth proportions or by simulating manufacturing process using hobbing cutter or pinion cutter tool. Figure 360 shows how to access the tools you need to define your gear geometry.

One cannot import a profile from other gear design software in the current release.

 

The Gear AT Shape Definition has following tabs to help you design a gear

 

 

To define a spline enter basic geometrical parameters in the General tab (Figure 361).

 

 

The Normal Module and the Number of teeth are the fundamental variables in defining a gear wheel; the module is often standardized. Following variables and basic equations explain the relation between the module, pitch diameter and the number of teeth in absence of profile modifications.

 

m ... normal module

n ... number of teeth

p ... pitch

P ... diametral pitch

d ... pitch diameter

... helix_angle

The theoretical distance between two wheel centers without modification is given by

A positive integer defines number of teeth of an external gear while a negative integer a number of teeth of an internal gear.

The normal pressure angle is the angle at the pitch diameter between the line of pressure and the line tangent to the pitch circle; see Figure 362.

The helix angle defines the slope of the tooth in lead direction against the rotational axis at the pitch diameter (Figure 363). A positive sign corresponds with the right hand rule. A straight spur gear has helix angle of zero.

 

Defines whether the helix is left handed (negative) or right handed (positive)

This factor is positive, when the reference profile is moved away from a gear by the amount of module * factor. Positive factor increases tooth thickness at pitch circle while negative factor decreases.

The length of tooth flank in lead direction

If this value is set to zero, following default (see Equation  (4)) will be set

Each gear wheel has a reference marker in the middle of the gear rim of width W; the marker can be placed on any rigid or flexible body. The Z-axis of this reference marker represents the rotation axis of the gear wheel as shown on Figure 364.

 

The rim diameter for an external gear and the bore diameter for an internal gear define the boundary of the gear rim (as solid and as finite element model) with the wheel body (Figure 365).

If bore or rim diameter are left to zero, the default is defined by Equation  (5). Negative sign holds for external gear and positive sign holds for internal gear. However, the rim thickness should be in the range of . If user input is out of the range it is automatically adjusted and warning message is issued to the log file.

 

 

 

Hit the button to open info window with the content of current *.isp property file.

Hit the button to open the mesh dialog box for the current *.isp property file

The Profile preview >> button opens the Profile plot window for the current property file as shown in Figure 366.

 

The Mass card of the Shape Definition process allows you to define the mass of the gear based either on the Geometry and Material Type or by specific User Input (Figure 367). In the former case the mass, center of mass and inertia tensor is computed later on by the mesher based on FE mesh volume. In the latter case enter all required data in current model units. In either case, inertia data are written to the *.isp file.

 

 

 

The Young's modulus E is used to define Nastran MAT1 card of the flexible tooth for SOL101 and SOL103. It defines the relation between tensile strain ε and tensile stress σ by Hooke's law (Equation  (6)), thus defining flexible tooth stiffness. For detailed information: see literature about theory of elasticity.

The Poisson’s Ratio is used to define Nastran MAT1 card of the flexible tooth for SOL101 and SOL103. An extension εx of a linear elastic and isotropic material is accompanied by lateral strains εy and εz. Poisson's ratio ν defines this relation by Equation  (7) and Equation  (8)

Poisson's ratio can also be derived from the shear modulus G. see Equation  (9)

The Profile tab defines the proportions of tooth profile which can be specified by different method of profile definition. The fields and labels change according to selected definition method and input format. For two step generating process additionally the finishing stock is entered here. The one resp. two informative fields show the resulting generating profile shift upon selected method and entered input data.

 

The tooth profile can be defined by:

 

The Tooth Definition enables user to specify virtual cutting tool for resulting tooth proportions. Internal gears are generated with virtual shaping cutter and external gears with virtual hobbing cutter. Tooth proportions can be defined in form of diameters or coefficients of Normal Module.

 

 

This method generates the tooth profile in one step, without additional grinding process, so the thickness and the diameters are defines with one tool. The tooth proportions can be entered in form of diameters or coefficients of Normal Module. The Profile shift machining is displayed on the card as informative value, the value differs from Profile shift in General card as it is corrected due to specified thickness allowance.

 

 

To define a tooth manufactured by hobbing cutter, enter all dimensions of a tool in the dialog box as shown on Figure 372 according to drawing in Figure 373. Please note that unlike the Tooth definition, it expects to define cutter proportions. Here, it is important to realize the fact that addendum portion of a cutter tooth is shaping dedendum portion of a gear tooth. For hobbing one can additionally select in how many steps the profile is generated.

This method generates the tooth profile in one step, without additional grinding process, so the thickness and the diameters are defines with one tool. The tooth proportions can be entered in form of diameters or coefficients of Normal Module. The Profile shift machining is displayed on the card as informative value, the value differs from Profile shift in General card as it is corrected due to specified thickness allowance.

 

 

 

To define a tooth manufactured by pinion cutter, enter all parameters as shown in the dialog box on the Figure 374 according to drawing in Figure 375. Please note that unlike the Tooth definition, it expects to define cutter proportions. Here, it is important to realize the fact that addendum portion of a cutter tooth is shaping dedendum portion of a gear tooth.

The shaping tool can not be defined as Nonstandard tool in this release.

This method generates the tooth profile in one step, without additional grinding process, so the thickness and the diameters are defines with one tool. The tooth proportions can be entered in form of diameters or coefficients of Normal Module. The Profile shift machining is displayed on the card as informative value, the value differs from Profile shift in General card as it is corrected due to specified thickness allowance.

 

 

The Tolerances card includes definition of tooth thickness, tip and root diameter allowances. The tooth thickness allowance can be defined either direct or via normal or circular backlash, the allowance can be also defined from Dimension Over Balls and Base Tangent Length measurement.

In case either from the measurement is not known, one can initialize the measurements with Init Measurement buttons, this sets either optimal value of the Measurement ball diameter or the value of Number teeth spanned, and it derives the measurement for given thickness allowance input.

 

 

 

 

 

Extended definition:

 

The value defines the alternation of tooth thickness. Usually, the nominal tooth thickness is adjusted to ensure smooth operation of the gear pair allowing for pitch and radial deviations, gear misalignments due to assembly or system deflections to not cause unintended contact between the gear teeth, like tooth interference and/or backside contact. The relation to backlash is depicted on Figure 377.

The value represents just another way to define Thickness Allowance. The entered value represents the portion of the total backlash applied on the respective gear wheel in normal plane along line of action. It is the shortest distance between the non-working flanks of a gear pair when their working flanks are in contact.

The value represents just another way to define Thickness Allowance. The entered value represents the portion of the total backlash applied on the respective gear wheel as an arc length in radians on the reference circle in the transversal plane.

Measurement over the balls or pins enables indirect determination of the tooth Thickness Allowance. A measuring ball or pin is placed in two tooth spacing which are opposite to each other (see Figure 379). The Dimension Over Balls and Measuring Ball Diameter are the values to be entered accordingly to measurement process. The Measuring Ball Diameter is also input for gear generator which calculates Dimension Over Balls for comparison with real measurement (Figure 380).

Effective Base tangent length enables indirect determination of the tooth thickness allowance.

The tooth thickness is evaluated from the effective base tangent length W k eff (Figure 378), which is measured over a specific number of teeth. The number of teeth the instrument is placed over, depends on the total number of teeth, the pressure angle, the helix angle and width of a gear.

The number teeth spanned is also used for the computation of the effective base tangent length W k eff and the base tangent length W k (without backlash) by the profile generator and outputs resulting value for comparison with real measurement (Figure 380).

It is used for the computation of the effective base tangent length Wk and the base tangent length (without backlash) by the profile generator and outputs resulting value for comparison with real measurement (Figure 380). The tooth thickness is evaluated from the effective base tangent length Wk (Figure 378), which is measured over a specific number of teeth. The number of teeth the instrument is placed over, depends on the total number of teeth, the pressure angle and helix angle of a gear.

The value represents the alternation of Tip Diameter on respective gear wheel. The allowance is not available if tool with topping ( shaping or hobbing) generates the profile, in this case the tool adjustment due to thickness allowance defines the allowance.

The value represents the alternation of Tip Diameter on respective gear wheel. The allowance is not available if tool ( shaping or hobbing) generates the profile, in this case the tool adjustment due to thickness allowance defines the allowance.

 

 

Spline tooth flank modifications are applied to compensate for manufacturing errors, deformation of the teeth due to load and also for shafts and housing deformation thus ensure a proper meshing to achieve more favorable load distribution. The ultimate goal is to reduce spline wear and vibrations induced by the spline pair operation, thus help to design durable gearbox fulfilling specified NVH parameters.

The convention for tooth flank side used throughout the Gear AT is based on ISO standards (Figure 381). The modification amount is defined in transversal plane and perpendicular to profile curve. The principal definition is based on ISO DIN 21771 and ISO DIN 1328-1 2018.

 

 

 

The topology modifications are divided in Gear AT into 3 main groups:

 

User can enter values individually for each group on left or right flank, after opening dedicated dialog box with group button under Topology setting section. The input can be identical for both flanks after checking Symmetric Left Right Flank toggle before opening the group dialog box. See Figure 382.

Lead modifications are used to attain a low displacement sensitivity and to avoid strain peaks occurring due to displaced positions of the gear axis or helix deviations of the flank. Types of lead modifications for spline supported by Gear AT include longitudinal end relief, crowning and lead slope changes. The Figure 383 shows the lead modifications tab layout for the left flank.

 

End relief is used to avoid stress concentrations at the edges due to angular misalignment of a spline pair. This type of tooth modification is preferably used on wider gears.

 

The End Relief modifications with the principal parameters are depicted on figure Figure 384.

 

Crowning is convex shape along the width of a tooth. It is used to maintain contact in the central region of the tooth flank width allowing for spline angular and axial misalignment. This type of tooth modification is preferably used on narrow gears. The amount of crowning should not be larger than necessary as otherwise it would reduce area of contact, thus lowering load capacity of a spline pair.

 

 

The Crowning modification with the principal parameters is depicted on figure Figure 385.

 

 

Lead Slope defines correction of the helix angle (Figure 386), which is used to improve contact with mating gear teeth when system deflections would otherwise cause edge loading.

 

 

The Lead slope modification with the principal parameters is depicted on figure Figure 386.

 

Profile modifications are mostly used to decrease the engagement shock and the involved strain and noise. Types of profile modifications supported by Gear AT include tip and root relief, barreling (vertical crowning), and profile slope correction. The figure Figure 387 shows the profile modifications dialog box layout for the left flank.

 

The positions of modifications amount along tooth profile are typically expressed relative to roll length. In addition, a user has an option to enter Position at Diameter resp. Position at Roll angle instead of Position at Roll Length value. The different input options are linked together and express the same point on involute point, see Figure 388.

 

The use of tip relief will cause less noise during gear meshing. Tip relief is the most economical and most common method.

 

The Tip and Root Relief modifications with the principal parameters are depicted on figure Figure 389.

 

Profile barreling is a convex shape added to the involute curve to prevent hard contact near the tip and root.

 

The Barreling modification with the principal parameters is depicted on figure Figure 390.

 

 

Profile slope is used to compensate for tooth deflection differences between the two meshing gears and to compensate for system deflections that would otherwise result in hard contact near the root or the tip of the tooth. It effectively defines correction of pressure angle.

 

The Profile slope modification with the principal parameters is depicted on Figure 391.

 

Flank modifications affect the flank topology in both the lead and profile direction. In Gear AT we support profile and lead twist modification. The Figure 392 shows the flank modifications dialog box layout for the left flank.

 

 

The Profile Twist modification is a flank surface torsion along the tooth width. The twist is applied in correlation with the profile slope but always with opposite sign on tooth sides. The Lead Twist modification is a flank surface torsion along the tooth height. The twist is applied in correlation with the lead slope but always with opposite sign on a tooth tip and root.

 

The Profile twist modification and Lead twist modification with the principal parameters is depicted on Figure 393 and on Figure 394., respectively.

 

 

You can preview applied modifications either individually or superimposed over the tooth flank as shown in Figure 395.

The individual modifications can be switched On or Off in the Topology display container in the Microgeometry tab so only selected ones are displayed in the preview dialog box.

 

 

You can export all applied microgeometry in form of lead, profile and flank reliefs to a text file with name isp_name_microgeometry.txt by pressing the Export >> button on the Modification tab. The data for left and right flank are exported separately. Additionally, one can adjust the resolution for the underlying reference grid in the fields n_lead x n_profile. The underlying grid has the dimensions full_width x full_roll_length in model units, the topology is in micrometers.

 

You can define spline manufacturing errors to be considered in the contact simulation. Enter Runout Error for every tooth to describe deviations from ideal pitch circle or enter Cumulative Pitch Error for every tooth to describe deviations from ideal pitch, see Figure 397.

In case you don‘t have any measurement data you can also calculate harmonic distribution with cosine function by entering amplitude and phase shift, or apply generator of random numbers to get random distribution from interval of <-Amplitude, +Amplitude >. Positive value of Runout Error results in larger tooth radius and positive Pitch Error rotates tooth in counter clockwise direction according to the right hand rule. The Errors can be entered for each tooth flank individually. Both deviations represent the effect of non-uniform flank location on gear wheel, only one of their values should be applied, hence pitch error creates runout and vice versa. The Pitch Error is entered as arc length on circle with Measurement Diameter. This diameter is usually close to middle of active tooth flank height.

 

You can display plot of error distributions as well as cumulative error by Deviations Preview button (Figure 396).

 

The usage of measured flank topology is temporarily deactivated in this release for spline component.