Higher contact ratios for quieter gears (2023)

Gear noise can indicate a faulty design or an inferior product, and also reflects the quality and precision of your manufacturing process. The following analysis suggests solutions.

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.


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.

Higher contact ratios for quieter gears (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.

Higher contact ratios for quieter gears (2)
Higher contact ratios for quieter gears (3)

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.

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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.

Higher contact ratios for quieter gears (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.

Higher contact ratios for quieter gears (5)

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

Higher contact ratios for quieter gears (6)Higher contact ratios for quieter gears (7)Wo:

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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

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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.

Higher contact ratios for quieter gears (8)
Higher contact ratios for quieter gears (9)

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.

Higher contact ratios for quieter gears (10)
Higher contact ratios for quieter gears (11)

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:

Higher contact ratios for quieter gears (12)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.

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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:

Higher contact ratios for quieter gears (13)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:

Higher contact ratios for quieter gears (14)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.

Higher contact ratios for quieter gears (15)

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.

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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.


  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


How can I make my gears quieter? ›

Lowering rotational speed and load as far as possible will reduce gear noise. Gears which have dents on the tooth surface or the tip make cyclic, abnormal sounds. Lightened gears with a thin web thickness make high-frequency noises.

Why the contact ratio should be greater than one? ›

Contact ratio: It is defined as the average number of tooth pairs in contact during one rotation. For continuous transmission of motion, at least one tooth of one wheel must be in contact with another tooth of the second wheel therefore contact ratio must always be greater than or equal to 1.

Which gear has highest contact ratio? ›

The FEM was used to get the contact and bending stresses. The results showed that the proposed non-invlute gear has a higher contact ratio and strength than the standard LCR spur gear .

Which gear run more silently? ›

Helical gears operate more smoothly and silently when compared to spur gears. This difference is due to the oblique manner in which their teeth interact in relation to the rotational axis.

What is the cause for noisy gear shifting? ›

If the gear shifter or the shift linkage are making a hissing of buzzing noise while the car is moving, particularly while the vehicle is accelerating or decelerating, a loose bolt or worn rubber isolators in the shift linkage is the most common cause.

How can I make my exhaust quieter without losing performance? ›

Install a silencer

Essentially, silencers are small parts that narrow down the hole that releases the exhaust noise reducing the noise in the process. What's even better, these components are very easy to install so you won't need professional help.

What is the significance of contact ratio in gears? ›

The contact ratio is a measure of overlapping tooth action which is necessary to assure smooth, continuous action. For example, as one pair of teeth passes out of action, a succeeding pair of teeth must have already started action. The hunting ratio is the ratio of the number of gear and pinion teeth.

How do you increase contact ratio in gears? ›

Some ways that contact ratio is changed is through the modification of the tooth profile, i.e. addendum modification, decreasing the pressure angle for a longer line-of-action, or increase the number of teeth. Reducing backlash is one of the most effective ways to increase the contact ratio.

Can contact ratio be less than 1? ›

Transverse contact ratio less than 1 means that the length of path of contact is less than one pitch. In other words, there is a space in which teeth do not touch within the space of one pitch (Illustration 9). If this is a spur gear it will be unable to rotate at constant speed and noise will increase as a result.

Is it better to have a higher or lower gear ratio? ›

A lower (taller) gear ratio provides a higher top speed, and a higher (shorter) gear ratio provides faster acceleration. . Besides the gears in the transmission, there is also a gear in the rear differential.

Is a higher gear ratio better? ›

Gear ratios can be boiled down to a single statement: Higher ratios (with a lower numerical value) give better torque/acceleration and lower ratios allow for higher top speeds and better fuel economy. Higher ratios mean the engine has to run faster to achieve a given speed.

Is it good to have a high gear ratio? ›

Is it better to have a higher or lower gear ratio? A higher gear ratio is good when you need more acceleration to cruise your vehicle, whereas a lower gear ratio provides more torque to get the vehicle moving from a resting position.

Why is lower gear more powerful? ›

Switching to low gear reduces the amount of fuel reaching your engine, resulting in reduced engine speeds and higher torque output.

Which gear is hardest to pedal? ›

High Gear. The high gear is the "hard" gear and is primarily used when descending and sprinting. The high gear is the largest chain ring in the front and the smallest cog on the rear cassette. This achieves the most difficult pedaling position and requires the most force to push the pedals.

How do I stop my gearbox from whining? ›

This can be cured by retightening the nut on the end of the shaft or adjusting the shimming of the bearings. A whine or gnash that's only obvious when coasting in neutral or when dipping the clutch may be down to overtightened pinion bearings.

Which is the most common cause of a noisy transmission? ›

A buzzing, clicking, humming, roaring noise from inside the transmission is usually a symptom of a bad bearing, planetary gears damage, or other internal problem. A buzzing could also come from a bad internal sealing surface, a seal, or low transmission fluid due to a leak.

What does a crunchy gear mean? ›

Grinding, rumbling, buzzing, hissing and clunking are all quite easy sounds for drivers to tell apart, but this is one in particular to watch out for - a grinding or 'crunching' noise when you shift gears. If you find that's happening, it's likely to be a problem with your synchromesh cones, or synchronisers.

Are you supposed to hear your gears shifting? ›

Hi There, This is somewhat normal to an extent to hear a slight whining of gears, especially in a vehicle with a manual transmission where the exchange of gears is dependent upon the driver.

How do I make my exhaust pop? ›

“Pops and bangs” are created by unburned fuel in the exhaust system. When excess fuel enters the exhaust system it increases in temperature and ignites inside the exhaust instead of the combustion chamber. The noise can be exaggerated by fitting a decat or full decat exhaust system.

Do resonator tips make exhaust quieter? ›

Yes. Resonator exhaust tips contain specially designed cavities that cause the exhaust gases passing through to vibrate in a specific way that can alter or reduce the sound of your exhaust.

What part of the exhaust makes it quiet? ›

The purpose of the muffler is to quiet down the exhaust noise by allowing it to travel through varying chambers which smooths out the flow of the exhaust.

How do you find the contact ratio of a gear? ›

The contact ratio will be the length of this segment divided by the “length” of a single tooth. This is why the contact ratio is called a ratio–because it is calculated as the ratio of two lengths. Nevertheless, it is also the average number of teeth in engagement between meshing gears.

In which type of gearing the contact is point contact? ›

Screw Gear

While helical gears usually engage between parallel shafts, screw gears do so at 90 degrees. The teeth on a screw gear are in the form of a helix. They form a point of contact between two gears and hence are not very suitable for high load and high-speed applications.

Why are gears higher pairs? ›

A pair is said to be higher pair when the connection between two elements has only a point or line of contact. Examples of higher pairs are: A point contact takes place when spheres rest on a plane or curved surfaces (in the case of ball bearings) Contact between teeth of a skew-helical gears.

Does increasing gear ratio increase torque? ›

A Gear Ratio can increase the output torque or output speed of a mechanism, but not both. A classical example is the gears on a bicycle. One can use a low gear that allows one to pedal easily up hill, but with a lower bicycle speed.

Is a higher gear ratio easier to pedal? ›

Just remember that larger gears at the rear mean easier pedalling but more torque, and larger gears at the front mean harder pedalling but more speed. Going from “easier” gears to “harder” gears is called “upshifting”, and the reverse is called “downshifting”.

How do you get more torque with gears? ›

You can increase or decrease a gear's torque (turning force) by changing the number of rotations.

What is meant by a gear ratio of 0.8 1? ›

The gears are cutting the engine's higher speed and turning it into power. A high gear provides a high gear ratio, say 0.8:1, where the car is in overdrive and the driveshaft is spinning faster than the engine (6).

What does a ratio of 7 1 mean? ›

The ratio, being defined as a fraction, may be reduced. In this case, we can also say there is a 1:7 ratio of computers to students (or a 7:1 ratio of students to computers). We might also say "there is one computer per seven students".

What happens when gear ratio is less than 1? ›

Typically, gears 5 and sometimes even 4 have ratios less than 1, which means that engine RPM will be less than wheel RPM in those gears. For example, gear ratio for 5th gear can typically be 0.9. Such gears (with gear ratios of less than 1) are called overdrive gears.

What are 3.73 gears good for? ›

So, a truck with optional 3.73 gears will tow a heavier trailer than one with 3.55 or 3.21. But it will also use more fuel in all situations because the engine's rpm will be higher.

What does a 4.10 gear ratio mean? ›

Gear Ratio: the ratio of the ring and pinion gears in the rear axle. So, if you have a 4.10:1 (sometimes 4.10) rear axle, the pinion will turn 4.10 times for every single turn of the ring gear or in other words, for every 4.10 turns of the driveshaft, the rear wheel will spin once.

Does a lower gear ratio increase torque? ›

In short, lower gear gives higher torque at the wheel and higher acceleration and lower car speed. Higher gear gives lower torque at the wheel and lower acceleration and higher car speed.

Is a 5.2 1 gear ratio good? ›

The low gear ratios like 5.2:1 and 5.3:1 are great for fishing baits that pull hard like deep crankbaits, big swimbaits, and deep water spinnerbaits. The low gear ratio helps you reel the bait slower, keeping it in the strike zone longer when fishing moving baits in the deep water.

Is a 1 1 gear ratio good? ›

1:1 and similar ratios are considered bad in automotive gearboxes. If there is one bad tooth it will soon take others with it, if it is always meshing with the same teeth. Automotive gearboxes tend to use coprime ratios (where the 2 gears have no common multiple) to avoid this.

What does 4.88 gears mean? ›

Short (low) gears have HIGHER numerical numbers, such as 4.11, 4.30, 4.56, 4.88, 5.13, 5.36, etc. In simple terms, the numbers mean how many turns of the drive shaft to one turn of the rear wheel.

Do bigger gears go slower? ›

If the gears are of different sizes, they can be used to increase the power of a turning force. The smaller wheel turns more quickly but with less force, while the bigger one turns more slowly with more force. Cars and bicycles use gears to achieve amazing speeds our bodies could never match without help.

Should I be able to hear gears? ›

When your car shifts into another gear, it should be relatively smooth and easy – there should be no “clunking” or “thudding” noises when your transmission shifts. If you do start to hear these noises when shifting gears, they are certainly a cause for concern.

What causes gear whine on deceleration? ›

If the gears howl during deceleration only, it's possible that the pinion-bearing preload has loosened. Howling under acceleration at all speeds indicates that something in the differential — gears, pinion or carrier bearings — has worn or no longer keeps the gear alignment correct.

What causes whining noise in gearbox? ›

The intrusive noise known as gear whine is caused by vibrations generated by gears as they mesh as a result of imperfections caused by design, loading, temperature effects, and manufacturing variations.

What causes whining noise in transmission? ›

If the whining gets higher with the revere, it means that the fluid line of the transmission has been clogged. In most cases, a clogged fluid line points to a more significant issue. On an automatic transmission, if the whine gets louder when in gear, it points to a problem with the torque converter.

Why does my car grind when I shift into second gear? ›

The blocker ring is made from brass and will naturally wear out over time, exasperated by sloppy shifting techniques. As it deteriorates, it can no longer effectively slow down the shaft and gear grinding will occur when you don't wait that extra moment.

Is it normal to feel your car shift gears? ›

If your vehicle feels like it's trying to change gears on it's own and you can't stop it, that's a classic sign of a bad transmission. Shifting is rough. This common symptom of a failing transmission is easily noticed.

Why do I hear a clunk when I accelerate? ›

If you hear a clunk when accelerating, worn engine mounts are your most likely culprit. An engine mount usually lasts five to seven years and costs around $500 to replace. Your engine mounts have bolts that can loosen or rubber parts that wear out.


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