🚀 Gear Ratio Calculator & Simulator
- Adjust Gear Teeth: Set the number of teeth (Z) for the driving gear (Gear 1) and driven gear (Gear 2) using the sliders or input fields.
- Adjust Input Speed (RPM) and Module: Enter the RPM of the driving gear and the gear module (m) value to determine the speed and physical dimensions.
- Observe Real-Time Gear Meshing: Watch the physics animation of the two gears perfectly meshing and rotating according to your settings, complete with real-time particle sparks on the contact surfaces.
- Analyze Output Data: Precisely analyze changes in the gear ratio, pitch circle diameter (PCD), center distance, output RPM, and torque multiplier on the real-time measurement monitor.
📚 View Detailed Mechanical Engineering Explanation and Gear Design Standards (KS/ISO) ▼
1. Basic Concept of Gear Ratio and its Significance in Mechanical Design
The gear ratio (i) is a key design factor that determines the speed ratio and torque conversion rate between the input and output shafts of two meshed gears. In power transmission system design, the gear ratio is precisely adjusted to reduce the motor's rotational speed to a level suitable for machine operation (speed reducer) or to increase the necessary operating torque.
- Speed Ratio: If the gear ratio is greater than 1, the output speed decreases, creating a reduction ratio. Conversely, if it is less than 1, the speed increases.
- Torque Conversion (Torque Multiplier): Based on the law of conservation of energy (constant power), the output torque increases in proportion to the reduction ratio.
- Mechanical Efficiency: Power transmission efficiency varies depending on the gear geometry (tooth profile), making precise tooth profile control in compliance with KS B ISO standards crucial.
2. Derivation of Gear Dimensions and Mechanical Formulas
The formulas for calculating gear geometry and meshing dynamics are derived as follows:
① Pitch Circle Diameter (PCD): The diameter of the imaginary friction circle where the two gears meet, calculated as the product of the module (m) and the number of teeth (Z).
d = m × Z [mm]
② Gear Ratio (i) and Output Speed (N2): Let the number of teeth on the driving gear be Z1 and on the driven gear be Z2. Since the meshing linear velocity is constant, the rotational speed is determined in inverse proportion to the ratio of the number of teeth.
i = Z2 / Z1 = N1 / N2
N2 = N1 × (Z1 / Z2) [RPM]
③ Center Distance (a): The distance between the rotational axes when the pitch circles of the two gears are externally tangent.
a = (d1 + d2) / 2 = m × (Z1 + Z2) / 2 [mm]
3. Transmission Efficiency and Gear Failure Design (Lewis Formula)
When designing gears, it is not enough to simply match dimensions; one must evaluate the tooth root bending strength and gear surface contact stress (surface durability) based on the power to be transmitted. Traditional bending strength calculations are based on the following Lewis Formula:
σ_b = F_t / (b × m × Y)
Where F_t is the transmitted tangential force (N), b is the tooth face width (mm), m is the module, and Y is the Lewis form factor based on the tooth geometry. Modern mechanical design standards (such as KS B ISO 6336) have advanced this Lewis formula to comprehensively incorporate load distribution factors, dynamic load factors, speed factors, etc., to evaluate fatigue failure limits.