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 7 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 gear enter basic geometrical parameters in the General tab (Figure 8).

 

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 9.

The helix angle defines the slope of the tooth in lead direction against the rotational axis at the pitch diameter (Figure 10). 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 11.

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 12).

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 *.cgp property file.

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

The Profile preview >> button opens the Profile plot window for the current property file as shown in Figure 13.

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 14). 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 *.cgp 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 methods 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:

To define tooth dimensions directly, enter all parameters in the dialog box as shown on Figure 16 for external gear, and Figure 17 for internal gear according to drawing on Figure 18. 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 defined with one tool. The tooth proportions can be entered in form of diameters or coefficients of Normal Module. The Addendum Mod. Coeff is displayed on the card as informative value, the value differs from Addendum Mod. Coeff 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 19 according to drawing in Figure 21. 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 defined with one tool. The tooth proportions can be entered in form of diameters or coefficients of Normal Module. The Addendum Mod. Coeff machining is displayed on the card as informative value, the value differs from Addendum Mod. Coeff in General card as it is corrected due to specified thickness allowance.

 

The only requirement for involute gears to be conjugate is that the normal base pitch of both gears has to be the same. The normal base pitch is the distance normal to adjacent tooth flanks along a line tangent to the base circle. For hobbing tool one can specify so called Off lead tool (either short or long), in this case the pressure angle of the tool differs from the nominal pressure angle of the generating gear. To meet the requirement of identical normal base pitch the module and helix angle of the tool need to be adjusted to the tool pressure angle. This technique is extensively used for manufacturing pinion gears where the intersection between involute and root must be as low as possible. To match the module and helix angle to the tool pressure angle a calculator is available in the dialog box.

 

The final machining tool is defined with set of parameters described in next table, the meaning is also displayed on left side of Figure 21.

 

This method generates the tooth profile in two steps, after initial Pre-machining, grinding process (Final machining) treats in most cases only the involute portion of the tooth, so the thickness and the diameters are defined independently. The tool proportions can be entered in form of length or coefficients of Normal Module. The Machining Allowance defines the amount of material added on the involute profile for grinding process.

The Addendum Mod. Coeff Pre-Mach and Addendum Mod. Coeff Finishing are displayed on the cards as informative values, the values differ from Profile shift coefficient in General card as those are corrected due to specified Thickness Allowance and Machining allowance.

 

For the pre-machining hobbing tool with two step manufacturing, one can specify so called “Off lead” tool (either short or long), in this case the pressure angle of the tool differs from the nominal pressure angle of the generating gear. The only requirement for involute gears to be conjugate is that the normal base pitch of both be the same. The normal base pitch is the distance normal to adjacent tooth flanks along a line tangent to the base circle. To meet the requirement of identical normal base pitch the module and helix angle of the tool need to be adjusted to the tool pressure angle. This technique is extensively used for manufacturing pinion gears where the intersection between involute and root must be as low as possible. To match the module and helix angle to the tool pressure angle a calculator is available in the Dialog box.

 

 

The second resp. finishing often called grinding tool is defined similar with parameters defined in text table, and also displayed on Figure 21 right.

 

Activates or deactivates topping, while cutting the gear tooth profile. If activated, the gear tooth addendum height is defined by the cutter tool dedendum height. In case it is deactivated, the gear tooth height is defined by the Addendum Coefficient RefProf (h*aP), Addendum Length RefProf (h aP), resp. Tip Diameter Gear (d a); see Figure 22

The value defines the addendum height of the gear tooth relative to reference circle, resp. addendum height of the reference profile for the case topping is not activated. This entry can be specified in form of coefficient h*aP, length h aP or tip diameter d a.

 

To define a tooth manufactured by pinion cutter, enter all parameters as shown in the dialog box on the Figure 23 according to drawing in Figure 24. 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.

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

 

Activates or deactivates topping, while cutting the gear tooth profile. If activated, the gear tooth addendum height is defined by the cutter tool dedendum height. In case it’s deactivated, the gear tooth height is defined by the Addendum Coefficient RefProf (h*aP), Addendum Length RefProf (haP), resp. Tip Diameter Gear (da).

The value defines the addendum height of the gear tooth relatives to reference circle, resp. addendum height of the reference profile for the case topping is not activated. This entry can be specified in form of coefficient h*aP, length haP or tip diameter d a.

The macro geometry modifies the generated tooth profile after machining with tool or definition with reference profile. The macro geometry can not be applied if tool or reference profile already apply explicitly these modifications during the generating process. In current release only following modifications are supported:

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

In case neither of the measurement is 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 29.

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 31). 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 32).

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 30), 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 32).

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 32). The tooth thickness is evaluated from the effective base tangent length Wk (Figure 30), 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.

 

Gear 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 and reduced transmission error. The ultimate goal is to reduce gear wear and vibrations induced by the gear 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 31). 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 entered indentical for both flanks after checking Symmetric Left Right Flank toggle before opening the group dialog box. See Figure 34.

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 gear supported by Gear AT include longitudinal end relief, crowning and lead slope changes. The Figure 35 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 gear 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 36.

 

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 37.

 

 

Lead Slope defines correction of the helix angle (Figure 38), 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 38.

 

 

 

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 39 shows the lead modifications dialog box layout for the left flank.

The positions of modifications amount along tooth profile are typically expressed against roll length. User has in addition the option to enter instead of roll length also Diameter resp Roll angle value. The different input options are linked together and express the same point on involute point, see Figure 40.

 

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 41.

 

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 42.

 

 

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 43.

 

Flank modifications effects the flank topology in both the lead and profile direction. In Gear AT we support profile and lead twist modification. The Figure 44 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 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 lead slope but always with opposite sign on tooth tip and root.

 

The Profile twist modification and Lead twist modifications with the principal parameters is depicted on Figure 45 and on Figure 46., respectively.

 

 

You can preview applied modifications either individually or superimposed over the tooth flank as shown in Figure 47. The individual modifications can be switched On or Off in the Topology display container in the Microgeometry tab so only selected are displayed in the preview dialog box.

 

The distribution of the microgeometry over teeth can be defined in dedicated dialog box, user can select between harmonic or random number generated distribution or can insert self-generated distribution of value or deviation, see Figure 48

 

The distributions can be preview in dedicated preview windows as Value or Deviation, see Figure 49

You can export all applied microgeometry in form of lead, profile and flank reliefs to a text file with name cgp_name_microgeometry.txt by pressing the Export >> button on 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. The values are separated by the space character. Negative values mean material is removed.

 

 

You can define gear 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 51.

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 50).

The measurement data stored in the cylindrical measure file (CGM) can be additionally adjusted to better match the true ideal flank proportions, which are usually defined in the second step in the Shape Definition dialog box.

The Measure tab provides setting for active tip and root diameters and option to select from available measurement types stored in the Gear AT measure file (CGM) to be used in the simulation in the Apply Measurement option menu, see Figure 52. Measurement should ideally join the full tooth profile smoothly including all modifications like chamfer or undercut, so the adjustment of active tip and root diameters are available here for each tooth or averaged tooth in the table of active diameters. The relations between form and active diameters is visualized on Figure 53, the active diameters define the upper and lower boundary of measured data to be applied on the ideal contact surface, data is linearly extrapolated up to form diameters if required.

 

The complete tooth contour created with the gear generator and the measured flank surface can be previewed for the selected tooth using the “Tooth preview" button, see Figure 55. The pure measurement data can be previewed for the selected tooth using the “Preview Measure 3D” button, see Figure 55. The data resolution for preview is fixed to the resolution defined in the Gear AT measure file ( CGM ).

You can select the real surface for contact simulation with Measured Flank toggle under Options card (see Figure 56) in Gear Element dialog box. Depending on the Apply Measurement option either Simple or Detailed measurement is applied on the flank surface.