Gear Ratio and Output Speed: Two-Stage Ratios, Service Factor Loss and Real Output RPM

Two numbers define the operating point of any gearbox application: the input rpm (from the motor) and the output rpm (required by the driven machine). The gearbox exists to map one to the other via its gear ratio, but the simple textbook formula n_out = n_in / i only tells you the nominal value. Getting the real output rpm right requires understanding what gear ratio actually means, how multi-stage units compose their ratios, and how service factor and slip losses shift the output rpm down by 1 to 5 percent from the calculated value.

Single-stage gear ratio

For a single-stage unit (one pair of gears, common on small inline reducers and on the input stage of larger units), the gear ratio i is the ratio of the driving gear teeth count to the driven gear teeth count. A unit with 20 input teeth and 60 output teeth has a ratio of 60/20 = 3.00. With a 1450 rpm four-pole motor at the input, the nominal output is 1450 / 3.00 = 483 rpm.

Two-stage and three-stage gear ratios

Multi-stage units compose the ratios of each stage multiplicatively. A two-stage unit with stage ratios of 3.0 and 5.0 has a total ratio of 3.0 × 5.0 = 15.0. At 1450 rpm input, the output is 1450 / 15.0 = 96.7 rpm. The same logic extends to three-stage units. Sample data sheets list the available total ratios per gearbox size, with the closest standard ratio being the one the factory recommends.

Why catalog ratios are nominal and not exact

Sample ratios are nominal values rounded to a small number of decimal places because gear geometry must use integer tooth counts that approximate the ratio. A unit with a nominal ratio of 15.0 may actually have a true ratio of 14.97 or 15.04 depending on the gear set fitted. For a 96.7 rpm nominal output at 1450 rpm input, the true output could be between 96.5 and 96.9 rpm. The deviation is small enough that it does not affect selection in most applications, but it is the reason sample data sheets sometimes list ratios with two or three decimals (for example, 14.93 or 15.07) when the application is sensitive to the exact output speed.

Service factor and the real output rpm

Service factor (SF) is a multiplier applied to the load to give the catalog torque capacity. As SF increases, the slip losses in the gear mesh also increase, and the output rpm drops slightly below the calculated value. For a unit running at SF 1.0 (the catalog nominal), the slip is typically 1 to 2 percent. For a unit running at SF 1.5 or SF 2.0 (heavy duty or shock load), the slip can be 3 to 5 percent. For a nominal 96.7 rpm output at SF 1.5, the real output could be 92 to 94 rpm.

What this means for the driven machine

A conveyor or mixer that requires exactly 96 rpm output from a 1450 rpm motor will not hit that target exactly. The choices are: pick a slightly different catalog ratio (for example, 14.8 instead of 15.0 for 98 rpm nominal), or specify a motor with a slightly different pole count (for example, a six-pole motor at 950 rpm for a 63 rpm output at ratio 15.0). Both adjustments are normal and supported by the factory; the data sheet lists the available ratios per gearbox size so the closest match to the target rpm can be found.

Pole count and motor speed

• 2-pole motor: 2800 to 2900 rpm at 50 Hz (depending on slip). Used for high-speed output requirements.
• 4-pole motor: 1400 to 1450 rpm at 50 Hz. The most common default and the standard reference for most sample data sheets.
• 6-pole motor: 900 to 960 rpm at 50 Hz. Used when the output target is below 100 rpm and a high gear ratio is undesirable.
• 8-pole motor: 700 to 720 rpm at 50 Hz. Used for very low output speeds and direct-coupled applications where a small gearbox is preferred over a large one.

Variable speed and ratio selection

When the application uses a variable-frequency drive (VFD), the input rpm is no longer fixed. The gearbox ratio stays the same; what changes is the operating point along the motor speed range. The ratio selection should target the most common operating point, and the VFD should be sized to deliver the full required torque at the lowest operating rpm (because motor torque is constant down to base speed and drops above base speed in the field-weakening region).

Reverse calculation: what ratio do I need?

Most selection starts from the driven machine requirement (output rpm) and works back to the motor input rpm. The formula is i = n_in / n_out. For a mixer that needs 70 rpm output from a 1450 rpm motor, the ratio is 1450 / 70 = 20.71. The closest standard ratio from the sample data sheet depends on the gearbox size; a K series or F series unit in the right frame will typically have 20.0 or 21.0 as the closest catalog ratios, giving 72.5 rpm or 69.0 rpm respectively. Pick the catalog ratio that is closer to the target rpm or that matches the driven machine's tolerance band.

Common mistakes in ratio selection

Picking the wrong ratio because the data sheet was read at 60 Hz instead of 50 Hz (motor speeds differ by 20 percent). Forgetting to account for slip losses at high SF and missing the target rpm by 3 to 5 percent. Assuming the sample ratio is exact and finding the real output rpm is off by 0.5 to 1 percent from the calculation. Ordering a special ratio that the factory does not stock when a close catalog ratio would meet the requirement.

For application-specific ratio selection or to confirm the closest catalog ratio to a target output speed, send the driven machine rpm requirement, motor nameplate rpm, service factor and any VFD operating range to sales@chinfar.com.