Gearsets

Abstract

A method for designing a gearset meeting one or more design targets is described. In particular, the design target is efficiency. Initially, a size and ratio of the gear set is specified. Gear friction coefficients are then calculated, and a value for a design target for the gear set is calculated. One or more of the macro-geometry parameters are modified, and the macro-geometry parameters are chosen such that the advantageous effects of one macro-geometry parameter on the design target counteract any disadvantageous effects of another macro-geometry parameter. In this way, a design for a gearset meeting the one or more design targets is produced. The efficiency calculation includes the effect of a lubricant. Further design targets can include gear noise and gear durability.

Claims

1. A computer-implemented method for designing a gearset meeting one or more design targets, in which one of the one or more design targets is efficiency, said method comprising the following steps: a. specifying a size and ratio of the gear set; b. calculating friction coefficients; c. calculating a value for the one or more design targets for the gear set; and d. modifying one or more macro-geometry parameters so that advantageous effects of one macro-geometry parameter on the one or more design targets counteract disadvantageous effects of another macro-geometry parameter; e. repeating steps b. to d. and producing a design for a gearset meeting the one or more design targets.

2. The method of claim 1, in which the step of calculating a value for a the efficiency includes the effect of the lubricant.

3. The method of claim 2, in which properties of the lubricant, including viscosity and additives and friction modifiers, are used.

4. The method of claim 3, in which the efficiency calculation is FVA 345.

5. The method of claim 3, in which the efficiency calculation includes a traction model using a combination of a boundary lubrication model and a model for elasto-hydrodynamic lubrication.

6. The method of claim 2, in which the efficiency calculation includes loaded tooth contact analysis.

7. The method of claim 2, in which the efficiency calculation includes system deflections.

8. The method of claim 2, in which the system deflections include a function of housing, shaft or non-linear bearing stiffness.

9. The method of claim 2, in which the efficiency calculation includes calculation of non-linear bearing stiffness and the use of sideband analysis for gear pairs.

10. The method of claim 1, in which the at least one design target includes gear noise, and gear durability.

11. The method of claim 1, in which said gear set comprises parallel gears, bevel gears, hypoid gears, or worm gears.

12. The method of claim 1 additionally comprising the step of modifying one or more micro-geometry parameters.

13. A computer program configured to perform the method of claim 1.

14. A computer readable product for computer aided engineering design of a driveline, the product comprising code means for implementing the steps of the method of claim 1.

15. A computer system for computer-aided engineering design of a gearset, the system comprising means designed for implementing the steps of the method of claim 1.

16. A machine including a gearset designed according to the method of claim 1.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0047] Embodiments of the present invention will now be described by way of example and with reference to the accompanying drawings, in which:

[0048] FIG. 1 illustrates a gear design process as defined by Childs (2014), with comments added in italics;

[0049] FIG. 2 shows a gear design process of the invention;

[0050] FIG. 3 illustrates the RMS (root mean square) of signal amplitude over a range of frequencies, which can be used as a noise metric;

[0051] FIG. 4 illustrates the effect of varying profile shift coefficient X (Figure taken from Stadtfeld, 2013 );

[0052] FIG. 5 illustrates the shape of gear teeth with pressure angles of 10, 20, 30, and 45 degrees (left to right);

[0053] FIG. 6 illustrates the efficiency of two lubricants with similar viscosity and different additives, calculated using ISO 14179 (left) and by using test data from a mini traction machine (right);

[0054] FIG. 7 illustrates an example of profile crowning and lead crowning;

[0055] FIG. 8 illustrates a combination of profile (barrelling)/lead crowning and an example of linear tip relief;

[0056] FIG. 9 is a schematic of tip relief;

[0057] FIG. 10 illustrates a comparison of linear and parabolic tip relief;

[0058] FIG. 11 shows the FZG test rig;

[0059] FIG. 12 shows a Stribeck curve.

DETAILED DESCRIPTION OF THE INVENTION

[0060] The invention is a multi-stage design process for gearsets, which starts with a very simple gearset definition (size and ratio) and adds detail. At each stage the trade-offs between multiple design targets (for example, efficiency, durability, and NVH) are considered. The design process can quickly generate a set of candidate designs, evaluate against a set of design targets, and identify optimal gearset designs. The efficiency calculation can include the effect of the lubricant (additives and friction modifiers, not just viscosity).

[0061] This design process has been developed by understanding how the design targets vary with the values of design variables, and does not just provide results, but also guides the designer to make design decisions which lead to the best trade-off between the targets. The design methodology has been validated via case studies and numerical modelling, and can be implemented in a software program.

[0062] The advantages of this approach may be summarised as follows:

[0063] All of the physics included in the design targets (for example, efficiency, durability, NVH) is identified at each stage of the design process, and included only if it is affecting the design decision to be made at that stage

[0064] Trade-offs identified at each stage of the design process, with guidance on how to make performance better in each case

[0065] Traceability of causality

[0066] Inclusion of the effect of lubricant on efficiency

[0067] Potential to supply data to the lubricant manufacturer to enable better lubricant design

[0068] The method for designing a gearset meeting one or more design targets comprises a number of steps.

[0069] The first step is to specify a size and ratio of the gear set. In general, the size and ratio of a gearset is defined by the application. The size (diameter, centre distance, and face width) can be limited by available packaging space.

[0070] Patent Application no. US 2013/0085722 A1 describes an approach in which simple sizing methods are used for external and planetary gear sets. Whilst these methods are not as accurate or sophisticated as rating methods (such as ISO 6336 or AGMA 2001), they are usable by engineers who are not familiar with the details of gear design and so can be used for the initial stages of transmission and gear design. Further, all the gears defined in this way have a ratio assigned to them as one of the properties. Such sizing methods require constants, related to the application and material used, which can be obtained by analysing existing transmissions using the same simple analysis methods.

[0071] When selecting tooth numbers, options are generated for tooth number combinations that satisfy the following constraints:

[0072] ratio requirement (within tolerance);

[0073] hunting tooth numbers (optional)

[0074] Table 1 lists constraints that can be applied, in terms of the tooth numbers Z.sub.1, and Z2 for the two gears.

TABLE-US-00001 TABLE 1 Constraints applied to calculate tooth numbers Constraint Mathematical formulation Ratio requirement Z.sub.1/Z.sub.2 is within a tolerance of the ratio specified by the user Hunting tooth numbers Z.sub.1 and Z.sub.2 have no common factors (optional)

[0075] A starting combination can be, for example, a large number of small teeth, which is good for efficiency. A tooth number combination with a small module/high tooth count is a good starting point. If standard tooling is required for the application, the gear tooth module can be selected from standard values.

[0076] Providing a gearset design having a predetermined number of teeth, and predetermined values of macro-geometry parameters (face width, module, pressure angle, helix angle), Table 2 below captures the main interactions between design variables and design targets in a simple format, and summarises the effect on the design targets of changing the tooth number and macro-geometry parameters.

[0077] This table is the result of sensitivity studies, in order to measure the effects of tooth number and gear macro-geometry parameters on efficiency, contact and bending strength, and transmission error.

[0078] Table 3below explains how and why the changes in tooth number and macro-geometry affect the design targets. In the table, the font type indicates whether the change is advantageous (underlined), disadvantageous (italicised), or neutral (not underlined, not italicised).

TABLE-US-00002 TABLE 3 Interactions between design variables and design targets Transmission Contact Contact error Efficiency Bending strength strength ratio Increased TE reduced Sliding loss (and Bending strength No effect Contact number due to wear on the teeth) reduces because ratio of teeth increased reduces because the teeth are increases contact ratio the contact path smaller is shorter in smaller teeth. Increased TE reduced Slightly Increased contact Increased Contact helix angle due to advantageous ratio is better for contact ratio increased bending strength; strength increases contact ratio; more pairs of teeth more pairs in contact can of teeth in share the load contact at one time give a smoother mesh Increased TE decreased Increased sliding Bending strength Increased Contact face width loss increases because contact ratio the teeth are strength increases thicker for helical gears Increased Increased Power loss Higher pressure Slightly Contact pressure TE due to decreases with angles result in increased ratio angle reduced increasing teeth that are contact increases tooth height pressure angle thicker at the strength base, with greater bending strength. However, higher pressure angles require specialist manufacturing tools.

[0079] Thus one or more macro-geometry parameters are chosen for modification such that the advantageous effects of one macro-geometry parameter on the design target counteract any disadvantageous effects of another macro-geometry parameter, and a design for a gearset meeting the one or more design targets is produced.

[0080] Sensitivity studies have shown that:

[0081] High pressure angles have the effect of increasing both durability and efficiency. There is a slight disadvantageous effect on transmission error, but if this is an issue it can be compensated for with other design changes.

[0082] High helix angles are advantageous for noise, efficiency, and bending and contact strength.

[0083] An increased face width is advantageous for noise and contact and bending strength, but disadvantageous for efficiency (and may not always be possible given packaging constraints)

[0084] Increasing the module/decreasing the number of teeth has no effect on contact strength, is beneficial for bending strength, but is detrimental for efficiency.

[0085] Non-standard modules and pressure angles will require non-standard tooling, so may not be economically feasible for low-volume cost-sensitive applications.

[0086] The following paragraphs describe how the insight into effects of tooth number and macro-geometry parameters on design targets can be leveraged in the design process, in order to balance the different targets and counteract any disadvantageous effects of design changes.

[0087] Increasing the tooth count is beneficial for efficiency, though this means that the teeth are smaller and therefore the change has a disadvantageous effect on bending strength. Increasing helix angle and pressure angle can improve the bending strength, as well as other targets. Larger face widths are mostly advantageous, if permitted by the packaging constraints. Most of the disadvantages of changing the variables in the way described above will be compensated for by other design changes, and a net efficiency benefit should result.

[0088] For example, selecting a tooth number combination with a small module/high tooth count, and then counteracting the resulting disadvantageous effect on bending strength from reducing the size of the teeth by one or more of the following:

[0089] increasing the pressure angle (if standard tooling is required, the pressure angle can be selected from standard values);

[0090] increasing the helix angle (not applicable in spur gearsets);

[0091] increasing the face width to the maximum allowed by the packaging space (in some applications this will not be possible);

[0092] and any disadvantageous effects of the above changes on other design targets are outweighed by the benefits of having smaller teeth. If the targets for bending strength are not met, a different combination of tooth numbers must be chosen, with a larger module.

[0093] A second aspect of the invention is a computer-implemented method for designing a gearset meeting one or more design targets using a combination of the efficiency methods and the sidebands methods disclosed below. The approach is for application to all types of gear pairs (including cylindrical and bevel) and planetary gearsets. Thus, the method combines the following two aspects:

[0094] a) Calculation of sidebands;

[0095] b) Calculation of non-linear bearing stiffness and system deflections.

[0096] The calculation of efficiency can be carried out using a range of different analytical methods. Standard methods have the disadvantage of not considering the lubricant frictional properties. The following standard methods for calculating gear mesh losses are commonly used:

[0097] 1. A constant friction coefficient is assumed, loaded tooth contact analysis (LTCA) is used to calculate loads and local velocities on the gear teeth, and then the power loss is calculated as the friction coefficient multiplied by the load and the sliding velocity.

[0098] 2. ISO 14179 considers only the lubricant viscosity, not the frictional characteristics of the lubricant itself (which depend on which base oil(s) and additive(s) the lubricant contains). Lubricant friction characteristics can vary significantly, so the lack of consideration for lubricant properties is a major limitation of the standard.

[0099] An alternative to these analytical methods is to use actual test data in the efficiency calculation. For example, a mini traction machine (MTM) can measure the Stribeck curve and slip curve of a lubricant. The test is easy to do, the machine is small and widely available, and can take measurements at different temperatures. The measured data (from an MTM) can be used with loads and local velocities calculated by LTCA to calculate the power loss and related gear mesh efficiency. FVA 345 is one method of including lubricant data in the efficiency calculation.

[0100] A similar approach could be achieved using a traction model using a combination of a boundary lubrication model and a model for elasto-hydrodynamic lubrication.

[0101] FIG. 6 illustrates that two lubricants with similar viscosity but different additives and different frictional properties would give the same value for efficiency according to the ISO 14179 calculation, but give different values for efficiency when calculated using test data from MTM.

[0102] FIG. 2 shows a flow chart illustrating the present invention. In current practice, the lubricant is considered only near the end of the design process. Using test data as an input to efficiency calculations not only allows the lubricant performance to be included in the design, but also opens up the potential for the oil company to improve the performance of the lubricant. Data from simulation that characterises the loading and contact conditions under all operating conditions can be made available to the oil company early in the design phase, so the choice of additives and base oils to be used in the lubricant can be decided based on real information about the operation of the gearbox.

[0103] In one embodiment the invention uses efficiency calculations including lubricant test data (for example, the FVA 345 method) combined with system deflections and loaded tooth contact analysis (LTCA). System deflections are dependent on shaft deflections, housing deflections, and non-linear bearing deflections. LTCA is a method for analysing the physics of contact between meshing gear teeth, accounting for deflection of the parts of the tooth flank that are in contact, and calculating the stress distribution on the gear tooth flank. The load is dependent on system deflections and micro-geometry, and affects the gear durability and transmission error. Thus, changing the gear tooth micro-geometry affects noise, durability and efficiency if system deflections are included, but the effects can only be fully modelled if the calculations correctly account for lubricant properties. Including lubricant properties in the efficiency calculation can be achieved by FVA 345 method. Non-linear bearing stiffness affects the system deflections and misalignments, which affect the shape of the contact patch between meshing gear teeth, and therefore affect durability/efficiency/noise. Specialist software (for example RomaxDesigner, Kisssoft, MASTA) can be used to calculate non-linear stiffness and system deflections.

[0104] Thus, in one embodiment the invention is the combination of:

[0105] a) gear efficiency, which can be calculated including the effects of loading, gear kinematics, and lubricant properties (e.g. by FVA 345 method including effects of viscosity, friction modifiers, and additives);

[0106] b) LTCA (affecting transmission error, efficiency and durability);

[0107] c) system deflections, which are a function of housing deflections, shaft deflections, and non-linear bearing stiffness.

[0108] Furthermore, the invention includes the calculation of non-linear bearing stiffness and the use of sideband analysis for gear pairs. Sidebands are formed from transmission error modulated by run-out/eccentricities in the system, which are affected by misalignment. Multibody dynamics tools can calculate sidebands for gear pairs. The combination of sideband calculation and system deflections in the same software package further enhances the production of a design for gearsets, and the process enables the system to be simultaneously optimised for noise, efficiency, and durability.

[0109] Once the macro-geometry design of the gearset is complete, the next step is to optimise the micro-geometry. Micro-geometry optimisation is the process of fine tuning the macro-geometry design in order to change the shape of the area on the gear tooth flanks that are in contact as the teeth mesh. This area is called the contact patch. It is possible to optimise the size and position of the contact patch in order to achieve optimal performance in terms of NVH, durability and efficiency. Micro-geometry modifications remove small amounts of material from the gear tooth (resulting in a gear tooth that is no longer a perfect involute). The amount of material removed can be in the order of tens of microns up to hundreds of microns depending on the size of the gear.

[0110] Fundamental flank modifications can be applied in the involute directionprofile crowning (barrelling) and profile slopeand/or in the axial directionlead crowning and lead slope. In both directions, both linear and parabolic tip and root relief are available. These are predominantly used for transmission error minimisation.

[0111] FIG. 7 illustrates the target form by applying profile and lead crowning, which have the effect of bulging the gear flank in the profile and axial directions respectively. Profile crowning has the same effect as applying tip and root relief, and can be useful for gear mesh power loss improvement. However, the bulging of the gear flank can reduce the size of the contact patch, leading to an increased contact stress .sub.H, and therefore an adverse effect on durability and NVH.

[0112] Lead crowning is commonly used by gear designers to reduce the sensitivity of the gear mesh to misalignment. This reduces the chances of edge loading (where the contact patch reaches the edge of the tooth rather than remaining in the centre of the flank), which is unfavourable for durability since the likelihood of pitting increases.

[0113] The first illustration in FIG. 8 shows a combination of barrelling and lead crowning together. Clearly it can be seen that the contact area is reduced, and thus the contact stress .sub.H may increase significantly. The second illustration in FIG. 8 is an example of linear tip relief, where some material is removed from the tip of the tooth flank. The position of the removed material is defined by the roll distance from the base tangent, illustrated schematically in FIG. 9. Tip relief has the advantage of easing the flanks into the mesh and avoiding tip contact. The variation in mesh stiffness is minimised as the contact changes between one and two teeth, and therefore there is a reduction in transmission error (TE). Tip relief can also have the effect of increasing mesh efficiency, as will be discussed later.

[0114] Tip relief can be linear or parabolic. Parabolic tip relief is not as effective as linear tip relief for improving mesh efficiency, since less material is removed from the flank. This is demonstrated in FIG. 10. Although linear tip relief is more effective for increasing mesh efficiency, the stress gradient along the flank will be greater, ultimately leading to a higher contact stress. The converse is true for parabolic relief.

[0115] Micro-geometry studies can be automated in computer implementations using the Design of Experiments method (DoE). This method allows the entry of parameters and their tolerances so as to investigate all permutations possible within the defined tolerances. Once the macro-geometry of the gears has been selected, then the optimum tip relief to be applied to the chosen macro-geometry design can be determined using DoE.

[0116] High lead crowning has the advantage of reducing the sensitivity of the gear mesh total misalignment F.sub.xby ensuring that the contact patch is in a central position on the gear tooth flank. However, this is at the expense of increased contact stress .sub.H.

[0117] It is common to apply short tip relief to gears where the emphasis is to minimise TE under light loads. This involves removing only material very close to the tip. Normally, for contact ratios <2, tip relief is applied at the point of highest single tooth contact (HPSTC), since this is where the maximum tooth deflection would occur. However, for gears with higher contact ratios, the HPSTC can be very close to the pitch point. Therefore, applying relief at this point would result in long tip relief, which is not recommended for optimal TE under light loads.

[0118] Reducing the tooth height by introducing tip relief has the advantage of easing the teeth into the mesh, thereby reducing the force f(x) in this region. A reduced force also has the benefit of running the gear mesh at a lower temperature, thus minimising the risk of pitting due to thermal stress in the lubricant. Reduced tooth height means that the contact length is reduced, leading to lower power losses due to the gear mesh and therefore higher efficiency.

[0119] There are many factors to consider when optimising the shape and size of the contact patch. A large contact patch is good for durability (the load is spread over a wider area, resulting in lower stress on the tooth surface) When more load is applied, the size of the contact patch expands. It is important to keep the contact patch away from the edges of the gear tooth if the tip of one tooth makes contact with the edge of a meshing tooth, the resulting wear can reduce the durability of the tooth. Tip contact can be prevented by barrelling and/or tip relief. Lead crowning reduces sensitivity to misalignment. All of these considerations mean that there are multiple parameters to vary, and multiple design targets (sometimes in opposition). Design of Experiments (DoE) is therefore a good method of evaluating all options and finding an optimum design.

[0120] The method for designing the gearset also includes a calculation of a sideband distribution and comparing sideband distribution with a design target for sideband distribution. This can include a sideband distribution outside the design target for sideband distribution. Furthermore, calculating the sideband distribution can include using run out/assembly errors and transmission error.

[0121] There are two possible approaches to reduce the level of vibration in gearsets: reducing the source of the noise, or changing the way in which the noise propagates through the system. The invention incorporates both of these approaches.

[0122] Reducing the source of the noise (transmission error) can be achieved via micro-geometry modifications, as will be discussed below.

[0123] In theory, involute gear teeth mesh perfectly smoothly. In practice, any system will have some slight errors, which can include tooth profile errors, misalignments, run out, or eccentricity due to manufacturing errors or deflection of shafts under load. These errors result in the mesh not being perfectly smooth and the position of the driven gear tooth flank deviating slightly from its theoretical tooth position. This deviation in position is the transmission error, and causes an excitation at the mesh frequency.

[0124] Modulations caused by errors and misalignments in a gearset can cause sidebands.

[0125] In practice, manufacturing and assembly variability can change the shape of the signals and vary the amplitude. Deviations can be caused by runout, pitch errors, mounting errors, assembly errors, and displacements or misalignments under load. Any of these errors can cause additional modulations to the gear meshing frequency.

[0126] Determining the frequency content of errors allows prediction of the sideband orders. For example, egg shaped pitch-error or out-of-position error (e.g. radial force such as gravity) causes a once-per-revolution error; ovalisation (e.g. pitch error) causes a twice-per-revolution error; triangle shaped error (e.g. three point clamping of a ring gear) causes a three-per-revolution error.

[0127] To predict the spectrum of sidebands, it is necessary for the analysis of the gearset to include deflections, misalignments, and manufacturing errors in the model. The mesh misalignment used to calculate sidebands can be calculated based on one or more of non-linear bearing stiffness, shaft deflection, gear backlash, planet carrier stiffness, and housing stiffness. Transmission error can be calculated using loaded tooth contact analysis. Run-out and assembly errors can also be included in the analysis.

[0128] The predicted magnitude of sideband excitation and the dynamic response of the system are used to calculate the extent to which an error (e.g. assembly error, tolerance, misalignment) can lead to high radiated noise. The dynamic response of the system to sidebands can be predicted using a 6 degree-of-freedom dynamic model.

[0129] The sum of the RMS (root-mean-square) response of a frequency range either side of the meshing frequency can be used as a noise metric. Reducing amplitudes of individual sidebands does not necessarily reduce the overall response if the energy is spread across more sidebands (see FIG. 3), so it is useful to consider a frequency range rather than individual sidebands.

[0130] It is well known in gear macro-geometry design that to reduce the height of the tooth for the same centre distance and same working normal pressure angle , the tooth normal module m.sub.n needs to be reduced (increased number of teeth). This has the effect of increasing the total contact ratio .sub. which is beneficial for durability and transmission error (TE). Additionally, for the same module m.sub.n, increasing the working pressure angle increases the radius of curvature which generates stubbier teeth (same number of teeth) while also reducing the tooth height. However, the consequential reduced contact ratio can have an adverse effect on durability and TE.

[0131] Tooth height has a strong influence on the gear mesh efficiency. Power losses can be described in terms of the loss factor H.sub., which is calculated as

[00001]$H_v=\frac{1}{P_{\mathrm{et}}}.Math.\frac{f\left(x\right).Math.v_{\mathrm{slip}}\left(x\right).Math.\mathrm{dx}}{f_t.Math.v_{\mathrm{tangential}}}.$

[0132] H.sub. can be minimised by reducing the f(x).sub.slip(x) term. The slip velocity .sub.slip will be maximum furthest away from the pitch point (sliding motion) and zero at the pitch point (pure rolling motion). Thus it is useful to reduce the height of the tooth, which reduces the max slip velocity .sub.slip(x).

[0133] A reduction in tooth height can be achieved by i) reducing the module, thus having a larger number of smaller teeth, or ii) introducing tip relief (as will be described later).

[0134] The pressure angle is the angle between the line of action at the pitch point and the tangent to the base circles. In FIG. 5 this is the angle between the red line and the vertical. For low the shape of the gear tooth is almost rectangular, and as increases the base of the tooth gets thicker and the tip more pointed. At the extremes, =0 would mean that the teeth would effectively be spokes with vertical sides so meshing gears would be locked together and unable to rotate. =90 would yield gears that are perfect circles with no teeth at all.

[0135] Increased pressure angles result in reduced sliding and increased rolling of the gear mesh, thus reducing the gear mesh sliding losses and improving efficiency. Bending strength is also increased due to the shape of the gear tooth becoming thicker at the base.

[0136] Increasing pressure angle has the disadvantage of increasing bearing load in gear pairs.

[0137] Increasingly, the industry is interested in designs with higher working pressure angles. The AGMA standard pressure angle was =14.5, but now pressure angles of 20 and 25 are usual for standard tooling. Hohn et al. (2007) have designed and tested gears with pressure angles of over 40.

[0138] Given the advantages of a higher pressure angle, it is useful to consider the limitations on increasing it further. The main limitations are set out below:

[0139] Power transmission. Consider the force F applied at the pitch point where two meshing gears are in contact. This force can be resolved into two components: F cos is the force transferring rotation from one gear to the other, and F sin is a separating force which tries to push the gears apart. A high pressure angle therefore reduces power transmission. In gear pairs, the separating force increases the load on the bearings.

[0140] Contact ratio. High-pressure-angle gears have a lower contact ratio, as the short stubby shape of the teeth means that fewer pairs can be in contact at any one time. The total contact ratio must be >1, otherwise there would be periods where the teeth lose contact as the gears rotate. In spur gears this limits the pressure angle to about =40. For helical gears a low transverse contact ratio can be compensated for by the axial contact ratio, so even higher pressure angles can be achieved while maintaining the mesh.

[0141] Tooling. For low-volume cost-sensitive applications, it may not be economically feasible to commission new tooling. If standard racks are to be used in manufacturing the design, the pressure angle and module must be a standard value.

[0142] Industry norms. Gear designers are conservative and unlikely to accept radical designs without proof that the gears work. Current standards reflect the state of the industry several decades ago, and current industry practice lags behind the advancement of technology.

[0143] Relationship between working pressure angle, centre distance, and profile shift coefficient

[0144] In practice it is more realistic to focus on working pressure angle .sub.w rather than the nominal pressure angle . The pressure angle is defined as the angle between the line of centres and the tangent to the contact point between meshing teeth. For gears with standard centre distance CD this point is on the pitch circle. However, if the working centre distance CD.sub.w , is increased, the point of contact will move closer to the tip of the gear tooth, resulting in a higher working pressure angle. A gear can therefore be cut with a rack with one pressure angle but operate at a different pressure angle.

CD.sub.w cos .sub.w=CD cos

[0145] The profile shift coefficient (PSC) defines how much of the involute forms the flank of the tooth above and below the pitch circle. FIG. 4 illustrates how the PSC affects the shape of the tooth when the same involute is used.

[0146] The height of the tooth above and below the pitch circle are called the addendum and dedendum respectively (h.sub.K and h.sub.F in FIG. 4). The PSC is the difference between these two (X=h.sub.Kh.sub.F). Note that the PSC, h.sub.K, and h.sub.F are all dimensionless coefficients; the actual dimension is the coefficient multiplied by the module. A tooth with zero PSC has equal addendum and dedendum (FIG. 4, left); a tooth with positive PSC has addendum greater than dedendum (FIG. 4, centre); and a tooth with negative PSC has dedendum greater than addendum (FIG. 4, right).

[0147] If a gear pair have equal and opposite PSCs, the centre distance will be the same but the working pressure angle will be different from the nominal pressure angle. Thus a gear pair can have the advantages of a higher working pressure angle but without requiring a change in centre distance, which may affect packaging. Designs with high helix angles are better for efficiency, noise, and bending and contact strength. For helical gearsets, it is therefore advantageous to increase the helix angle as far as is feasible. The only limitation on increasing helix angle is that the axial loads on the gears will be increased. The resulting higher loads on the bearings may lead to increased bearing losses and reduced bearing life. This effect can be mitigated by using double helical gears (two sets of gear teeth with helix angles in opposite directions to cancel out the axial forces), or by replacing the bearing with one with an increased load capacity. These changes incur additional cost, so may not be appropriate in all applications. It should be noted that some heavy-duty applications use spur gears; in these applications, helix angle optimisation will not be applied.

[0148] A further consideration for gearset design is in how rigidly the gearset is mounted. There is a trade-off between rigidity and flexibility: rigidity gives good alignment, low misalignment and low run out, and flexibility gives accommodation of errors. Dynamics can be included in this decision making process, by varying the rigidity of the system and simulating the system dynamic response.