Frequency Calculations
Calculating Tire and Wheel Frequency
For a vibration concern, use the vehicle speed to determine tire/wheel frequency and rpm. Calculate tire and wheel rpm and frequency by carrying out the following:
- Measure the diameter of the tire.
- Record the speed at which the vibration occurs.
- Obtain the corresponding tire and wheel rpm and frequency from the Tire Speed and Frequency Chart.
- If the vehicle speed is not listed, calculate the tire and wheel frequency as follows:
- Divide the vehicle speed at which the vibration occurs by 16 km/h (10 mph). Multiply that number by the 16 km/h (10 mph) tire rpm listed for that tire diameter in the chart. Then divide that number by 60.
- For example, if calculating the frequency based on vehicle speed in km/h for a 64 km/h vibration with 835 mm tires, divide 64 km/h by 16 km/h = 4. Multiply 4 by 105 rpm = 420. Divide 420 by 60 seconds = 7 Hz at 64 km/h.
- If calculating the frequency based on vehicle speed in mph for a 40 mph vibration with 33 inch tires, divide 40 mph by 10 mph = 4. Multiply 4 by 105 rpm = 420. Divide 420 by 60 seconds = 7 Hz at 40 mph.
- The calculated frequency of 7 Hz is the first order tire and wheel vibration; the second order tire and wheel vibration would be twice this number at 14 Hz; the third order tire and wheel vibration would be 21 Hz; and so on.
| Tire Diameter | Tire RPM/Hz | Tire RPM/Hz | Tire RPM/Hz | Tire RPM/Hz |
|---|---|---|---|---|
| mm (in) | @ 16 km/h (10 mph) | @ 80 km/h (50 mph) | @ 97 km/h (60 mph) | @ 113 km/h (70 mph) |
| 483 (19) | 182 | 910/15 | 1092/18 | 1274/21 |
| 508 (20) | 173 | 865/14 | 1038/17 | 1211/20 |
| 533 (21) | 165 | 825/14 | 990/16 | 1155/19 |
| 560 (22) | 158 | 790/13 | 948/16 | 1106/18 |
| 585 (23) | 151 | 755/13 | 906/15 | 1057/18 |
| 610 (24) | 145 | 725/12 | 870/14 | 1015/17 |
| 635 (25) | 139 | 695/12 | 834/14 | 973/16 |
| 660 (26) | 134 | 670/11 | 804/13 | 938/16 |
| 685 (27) | 129 | 645/11 | 774/13 | 903/15 |
| 710 (28) | 124 | 620/10 | 744/12 | 868/14 |
| 735 (29) | 119 | 595/10 | 714/12 | 833/14 |
| 760 (30) | 115 | 575/10 | 690/11 | 805/13 |
| 785 (31) | 111 | 555/9 | 666/11 | 777/13 |
| 810 (32) | 108 | 540/9 | 648/11 | 756/13 |
| 835 (33) | 105 | 525/9 | 630/10 | 735/12 |
| 864 (34) | 102 | 510/8 | 612/10 | 714/12 |
Calculating Driveshaft Frequency
Knowing the tire and wheel frequency allows for easy calculation of driveshaft frequency. The driveshaft drives the tires through the rear axle. Therefore, to determine driveshaft frequency, multiply tire and wheel frequency by the ratio of the rear axle. Calculate driveshaft frequency by carrying out the following steps:
- Obtain the axle ratio of the vehicle. Suppose the vehicle you are diagnosing has a vibration problem at 64 km/h (40 mph) and a rear axle ratio of 3.08:1.
- Multiply the tire and wheel frequency of 7 Hz (calculated previously) with the rear axle ratio of 3.08:1. This results in a driveshaft frequency of 22 Hz at a vehicle speed of 64 km/h (40 mph).
The calculated frequency of 22 Hz is the first order driveshaft frequency; the second order frequency of the driveshaft is twice this number, or 44 Hz; and so on.
Calculating Engine Frequency
Use the engine rpm where the vibration symptom occurs to determine engine frequency. Calculate engine frequency by dividing the engine rpm by 60 (the number of seconds in a minute). For example, if the corresponding engine rpm of a vibration concern on a vehicle is 2,400 rpm, the resulting engine frequency is 40 Hz. Therefore, a 40 Hz vibration is a first order engine vibration. For purposes of vibration diagnosis, the engine also includes the torque converter and exhaust system.
Calculating Engine Accessory Frequency
Belt-driven engine accessories often produce vibrations at different frequencies than the engine itself. This is because the drive ratio created by the different size pulleys causes them to rotate at different speeds. Determining engine accessory frequency is comparable to calculating driveshaft frequency.
Calculate engine accessory frequency by carrying out the following steps:
- Determine the size ratio factor between the accessory pulley and the crankshaft pulley. For example, if the diameter of the crankshaft pulley is 6 inches and the accessory pulley diameter is 2 inches, the accessory pulley rotates 3 times for every crankshaft rotation (6 divided by 2).
- Multiply the engine rpm where the vibration condition occurs by the number of times the accessory pulley is rotating per crankshaft revolution. For example, if the engine rpm is 2,400 rpm, the accessory is rotating at 7,200 rpm (2,400 rpm multiplied by 3).
- Divide the accessory rpm by 60 (the number of seconds in a minute). In this example, the engine accessory frequency is 120 Hz (7,200 divided by 60).
Calculating Engine Firing Frequency
Engine firing frequency is a term used to describe the pulses an engine creates from the firing of the cylinders. Engine firing frequency depends on how many cylinders an engine has. The number of times an engine fires a cylinder with each crankshaft revolution is equal to one-half the number of cylinders. A 4-cylinder engine fires 2 cylinders with each crankshaft revolution. Two revolutions of the crankshaft fire all 4 cylinders. A 6-cylinder engine fires 3 cylinders with each crankshaft revolution. An 8-cylinder engine fires 4 cylinders for each crankshaft revolution.
Calculate engine firing frequency by carrying out the following steps:
- Multiply the engine rpm where the vibration symptom occurs by the number of cylinders fired with each crankshaft revolution. For example, a vehicle with a 6-cylinder engine experiences a vibration concern at 2,400 rpm. The engine is firing the cylinders at 7,200 times per minute (3 multiplied by 2,400).
- Divide this number by 60 (the number of seconds in a minute) to obtain the engine firing frequency. In this example, the engine firing frequency is 120 Hz (7,200 divided by 60) at 2,400 rpm.
Frequency and RPM Calculations Worksheet