Higher contact ratios for quieter gears (2023)

The low-noise behavior of standard industrial gearboxes is becoming an important selection criterion and an indicator of gearbox quality to customers. In several gear tests and practical investigations it has been reported that the gear contact ratio has a large influence on the noise level, especially in spur gear applications. Lower noise levels are generally associated with a gear design that results in higher contact ratios. Because of this, a high overlap gear design is an important key to reducing noise levels. This document provides guidelines for the design of high contact ratio spur gears produced using standard tools with a 20° profile angle and addendum modification with addendum modification on gears.

introduction

The main problems in gear design have changed over time. In the past, size, interchangeability, strength and efficiency were the primary concerns in gear design. Today, vibration and noise are becoming increasingly important as quieter gears are considered an indicator of product quality.

In the past, relatively high noise levels were generally accepted in transmissions. Occasionally, low noise requirements have been met through the use of soundproof hoods over the installation, resulting in higher costs while limiting accessibility for maintenance and inspection. Devices silenced by protective hoods have not found good acceptance in the market due to the additional weight and volume, even in extreme applications.

Advances in technology and increased operating speeds in current transmission applications have made it clear that noise and vibration are undesirable side effects associated with the use of gears in mechanical transmissions. Given the market pressure for higher power densities, the development of high-performance mechanical drives with reduced noise is a general problem in the power transmission market and in particular in the various gear areas.

As the noise generated is widely recognized as a measure of the overall quality of a machine, it is now expected to be reduced. This requires gear designs where gear noise reduction can be achieved. Today, gear users and customers alike demand low noise levels in their state-of-the-art industrial gears. New noise specifications, rules, regulations and standards on occupational noise exposure call for gear drives with lower noise levels. Typical noise levels for closed gears according to ANSI/AGMA 6025-D98 [1] are shown in Figure 1.

Transmission noise has multiple causes and many factors can play a role in ensuring smooth transmission engagement. In general, a good solution requires a balance between quiet running characteristics, economic concerns, ease of manufacture, and satisfactory performance. The result of numerous experiments and research projects identifies a group of factors that influence gear noise. Gear specialists have defined some of the most important factors as gear type, tooth profile, pressure angle, modulus, gear ratio, tooth load, pitch line speed and overlap ratio.

For 15 years, the author has been observing progress in reducing gear noise through higher manufacturing precision [2] or the choice of materials with special damping properties [3]. However, as shown in Figure 2 and Figure 3, improving gear quality by manufacturing or introducing special materials can increase production costs while reducing gear noise only to a certain extent. Therefore, the best time to address gear noise issues is at the design stage, as many factors come into play to ensure quiet gear engagement. Choosing and adjusting one or more factors that affect noise during design adds little to the cost, but can make a significant difference in noise floor.

In gear design, it is known that decreasing pressure angle and/or increasing tooth depth can cause internal dynamic loads to decrease by increasing the contact ratio. Since the contact ratio is reported to have a large impact on noise levels, it could be a factor to consider as an alternative design solution for quieter gears without requiring expensive manufacturing processes or drastic gear structure changes, particularly in spur gear applications. This document presents guidelines for the design of spur gears with a rational geometry, aimed at achieving higher contact ratios, which are produced with standard tools with a profile angle of 20°. Notes are based on the behavior of the contact ratio for spur gears depending on the number of teeth, module, gear ratio, working center distance and profile shift with profile shift.

Higher contact/lower noise

In general, lower noise levels are associated with helical gears than spur gears due to their higher overall contact ratio. Similarly, practical experience shows that spur gears with higher contact ratios also tend to reduce noise. Several researchers have reported that the contact ratio is the most important factor within the transmission designer's control over noise reduction.

Regarding the effect of contact ratio on the dynamic loading of spur gears, Liou et al. (1992) [4], using computer simulations established for the design of low contact ratio (less than 2.0) gears, that increasing the contact ratio reduced the dynamic loading on the gear.

In 1993, Drago et al. [5] provided details on the influence of the gear mesh on the noise level. Spur gears with high overlap (ε = 2.15) and low overlap (ε = 1.25) were tested. Although noise levels varied with both speed and torque load, the high contact ratio spur gears were generally quieter than the low contact ratio ones. Some of the results are summarized in Figure 4.

Experimental results by Kasuba (1981) [6] and Kahraman-Blankenship (1999) [7] have shown that the dynamic loads decrease with increasing overlap in face gears. Recent gear studies reported by Hedlund and Lehtovaara (2008) [8] have shown that periodic variations in gear meshing stiffness along the line of action are one of the main sources of noise and vibration excitation in gear drives.

In fact, the stiffness of each tooth varies considerably from root to tip, but when two teeth mesh, the equivalent stiffness is less variable. The highest combined stiffness for two teeth when meshing occurs when they touch at the pitch points and the stiffness decreases by about 30 percent towards the limits of motion, but the decrease is highly dependent on the contact ratio and gear details [9].

It is important to consider these and other results when designing for minimum noise, since contact ratio is one of the parameters that the transmission designer can control without drastically affecting the overall configuration of the transmission system. That is, by judicious selection of gear geometry, it is often possible to increase the contact ratio to create a quieter gear.

Spur gear geometry for high contact ratio

As FIG. 5 shows, ensuring smooth, continuous tooth movement requires at least two pairs of teeth in contact at the ends of the contact path. When a pair of teeth ends contact, a subsequent pair of teeth must already have engaged. It is desirable to have as much overlap as possible. A measure of this overlapping effect is the contact ratio.

For spur gears, the contact ratio is defined as the quotient of the active length of the contact line in meshing gears divided by the basic pitch. Based on this definition, the contact ratio can be calculated using the following formulas. Formula 1, Formula 2, Formula 3

Wo:

εα = degree of contact for spur gear

gα = contact path length

pb = fundamental pitch

m = Module

aw = Achsabstand

z1, z2 = number of teeth of pinion and gear

da1 , da2 = tip circle diameter on pinion and gear

db1 , db2 = base diameter at pinion and gear

df1 , df2 = root diameter on pinion and gear

α = pressure angle for cutting tool

αw = pressure angle on the pitch cylinder

c* = Radial air factor

Actual contact ratio values ​​are smaller than theoretical contact ratios, depending on profile deviations and tooth deformation under load. The contact ratio is also affected by shaft and bearing deflections of just a few microns as they affect the center distance between the gears. For this reason, contact ratios should be greater than 1.2, as contact between the gears must not be lost.

To illustrate the quantitative importance of the contact ratio for spur gears, Figure 6 and the formulas in Table 1 provide guidance for calculating the length of the segments for contact ratios between 1 and 2, which correspond to one or two pairs of teeth meshing on the path of contact. For example, a gear with a contact ratio of 1.6 indicates that two pairs of teeth are in contact for 3/4 of the total length of the meshing path.

Theoretical contact ratios for spur gears cut with standard tools of 20° and 15° profile angle and without profile shift without profile change were calculated for different center distances in the range from 100 mm to 500 mm, four nominal gear ratios (1.0, 1.5, 3.0 and 4.0) and modules according to ISO 54:1996. Some of the calculation results for spur gear overlaps using standard tools with a profile angle of 20° are summarized in Table 2.

Numerical results of the theoretical contact ratios for spur gears cut with standard 20° and 15° profile angle tools and without profile change were analyzed by regression techniques to estimate a statistical model relating the contact ratio as a function of the number of teeth and the modulus sets , transmission ratio and center distance. A statistical Weibull model was used to maximize the correlation coefficient (up to 0.9992). Graphical results of statistical models and contact ratio values ​​for spur gears are shown in Figure 7. The results show good results to describe the coverage behavior. The following formulas and values ​​of constants a1, a2, a3 and a4 can be used to evaluate and improve gear geometry for higher contact ratios:

Since the "k" factor appears to have an effect on the contact ratio, it would be desirable to have a gear geometry with high values ​​of the "k" factor. According to the author's experience, in order to achieve a balance between noise reduction and strength, it is advisable to carry out gearbox designs with values ​​of the factor "k" between 400 and 1,000. Better results are obtainable with a higher number of teeth.

Addendum modification for high contact ratio

Rational use of addendum modification enables gear designs with very good adaptability of the tooth profile to practical applications. In one of the author's earlier papers [10] some basic definitions and recommendations for addendum modification associated with the application of the addendum modification coefficient are given. To put it simply, it can be defined as the creation of a spur gear with addendum modification if the creation of the tooth flanks of the reference cylinder does not touch the zero line on the basic tooth profile and there is a radial offset.

The main parameter for assessing addendum modification is the addendum modification coefficient x. The addendum modification factor quantifies the ratio between the distance from the reference line on the tool to the reference diameter of the gear Δabs (radial displacement of the tool) and the module m. This coefficient is defined for pinion x1 and gear x2 as:

The coefficient of addendum modification is positive when the datum line of the tool is shifted from the reference diameter to the crest of the teeth (the tool moves away from the center of the gear), and it is negative when the datum line is shifted to the root of the teeth (the tool goes towards the center of the gear).

To account for the effect of addendum modifications for a gear pair, it is recommended to define the sum of addendum modification coefficients as follows:

Addendum modification gearing is no more complicated or expensive to manufacture than addendum modification gears because the gears are made in the same cutting machines and depend only on the relative position of the gear to be cut and the cutter. The difference can be seen in the blanks with different diameters and tooth profiles in gears.

Gears with addendum modification and addendum modifications show deviations from the standard gear geometry. The difference between the operating and standard center distance is an important indicator for the standard deviations and must be taken into account.

Increasing the degree of contact is particularly useful for gears where the operating center distance is smaller than the standard center distance. In these cases, the addendum in the pinion and gear can be negative and must be calculated to obtain the total addendum required or the sum of the addendum coefficients.

One of the topics familiar to gear specialists working with the ISO system is the use of addendum modification to design spur gears with a high contact ratio and a low noise level. Negative values ​​of the sum of the addendum modification coefficients (Σx < 0) with correct value distribution between pinion and gear enable gear pairs with high contact ratios.

When designing spur gears without addendum modification, an additional increase in contact ratio may be possible with negative shifts in the tooth profile of the pinion with addendum modification coefficient values ​​between x1 = -0.5 and x1 = -0.7. Similar results can be obtained by adding one, two or three teeth to the sum of the tooth counts in the gears and introducing appropriate negative addendum modification coefficients on gears. Table 3 shows a method for improving and calculating the spur gear geometry for higher contact ratios using values ​​of "k" and negative tip modification coefficients.

It must be considered that a negative tip shift coefficient introduced to obtain spur gears with high contact ratios can lead to a reduction in the gear's bending and scuffing resistance, mainly in gears with low accuracy. For this reason, gears with negative addendum change coefficients must be tested for bending and seizure resistance.

Conclusions

Given that the overlap ratio is reported to have a large impact on noise levels, it should be considered as an alternative design solution to produce quieter gears without expensive manufacturing processes or significant changes to the gear structure, particularly in helical gear applications. With this in mind, this document has presented some guidelines for spur gear designs with a rational geometry aimed at achieving higher contact ratios that are produced with standard tools with a 20° profile angle. Directions are based on contact ratio behavior for spur gears as a function of tooth count, module, gear ratio, work center distance and addendum modification coefficient values.

Numerical results of theoretical contact ratios for spur gears, considering cutting with standard 20° and 15° profile angle tools and without head modification, were analyzed by regression techniques to estimate a statistical model that approximates the contact ratio with a factor “k.” Based on the experience of the Author's recommendation is to aim for a balance between reducing noise levels and strength capacity values ​​of factor "k" between 400 and 1,000. Better results are obtainable with a higher number of teeth.

Values ​​of "k" and coefficients for modifying the negative addendum. according to the calculation method described in Table 3 can be used as guidelines for the design of high contact ratio spur gears when minimal noise – and quieter gears – are required.

references

1. ANSWAGMA 6025-D98, Sound for closed spur, herringbone and spiral bevel gears. American Gear Manufacturers Association, VA. 1998
2. DuWayne, P., Gearbox Noise As a Result of Nicks, Burrs, and Scale - What Can Be Done. Transmission Technology, Vol. 13, No. 4, July/August 1996, p. 26-28
3. Smith, R. E., Laskin, I., Noise Reduction in Plastic and Powdered Metal Gear Sets. Transmission Technology, Vol. 13, No. 4, July/August 1996, p. 18-23
4. Liou, Chuen-Huei; Lin, Hsiang Hsi; Oswald, Fred B.; Townsend, Dennis P. Effect of Contact Ratio on Dynamic Loading of Spur Gears. Sixth International Power Transmission and Gearing Conference, Phoenix, AZ, Sept. 1992.
5. RJ Drago, JW Lenski, RH Spencer, M Valco, and F Oswald. The relative noise levels of parallel axis gear sets with various contact ratios and gear tooth forms. AGMA paper 93FTM1. v.a. 1993
6. Kasuba, R. Dynamic loads in spur gears with normal and high contact ratio. International Symposium on Gearing and Power Transmissions, 1981, Tokyo, p. 49-55.
7. Kahraman, A., and G.W. blank ship. Influence of the involute overlap ratio on the spur gear dynamics. Transactions of ASME, 121, Journal of Mechanical Design, March 1999, p. 112-118.
8. Hedlund, Juha and Lehtovaara, Arto, Test Methods for Evaluating the Parametric Excitation of Spur Gears. Non-Destructive Testing and Evaluation, Vol. 23, No. 4, December 2008, p. 285-299.
9. Derek Smith, J. Gearbox Noise and Vibration. To edit. Marcel Dekker, New York, 2003.
10. Gonzalez Rey, G., Frechilla Fernandez and Garcia Martin, „Cylindrical Gear Conversions: ISO to AGMA.“ Gear Solutions, März 2006, p. 22-2