Required Actuation Force for Drum Brakes | Self Energizing and De-Energizing Brake Shoes

Brakes, Clutches, and Frictional Elements Overview

Introduction to Braking Systems

• The lecture introduces the topic of brakes, clutches, and frictional elements, noting that it may cover more than expected due to the complexity of these systems.

• The focus will be on drum brakes as a challenging aspect of the chapter compared to disc clutches which have simpler calculations.

Understanding Drum Brakes

• Drum brakes operate using a cylindrical piece with an inner surface designed for friction; they utilize hydraulic pressure from a master cylinder to activate brake shoes.

• The primary and secondary shoes in drum brakes are identified based on their roles during braking; the primary shoe benefits from self-energization while the secondary does not.

Self-Energization Mechanism

• As the drum turns, it creates a tendency for the primary shoe to pivot and apply more force against the drum due to self-energization, enhancing braking efficiency.

• While self-energization is advantageous for stopping power, it can lead to less responsive braking feel compared to disc brakes.

Components of Drum Brakes

• A close-up view of wheel cylinders shows how fluid pressure activates pistons that push brake shoes into contact with the drum surface.

• Vehicles must have a secondary braking system (emergency brake), which operates independently from hydraulic systems.

Analyzing Brake Torque

• To achieve desired braking torque (e.g., 300 foot-pounds), calculations must determine how much force needs to be applied by wheel cylinders on each shoe.

• Each shoe contributes differently to overall torque; understanding this distribution is crucial for effective design and function.

Mathematical Modeling of Brake Forces

• Equation 16.6 describes how torque (T) relates to friction coefficient (F), radius (R), and normal force (D).

• The maximum pressure experienced at the interface between shoe and drum plays a critical role in calculating effective braking forces.

Pressure Distribution in Brake Shoes

• A sinusoidal pressure distribution occurs across brake shoes; understanding where peak pressures occur helps in designing effective brake systems.

Symmetry Assumption in Calculations

• Assuming symmetry simplifies calculations regarding angles related to both shoes despite their differing energization effects during operation.

Finalizing Force Calculations

• Two equations help calculate necessary force: one for self-energizing shoes and another for self-deenergizing ones. This distinction affects required actuation forces significantly.

By following this structured approach through timestamps linked directly back to specific parts of the lecture transcript, readers can easily navigate complex discussions about brake systems while retaining essential insights.

Understanding Rigid Molded Non-Asbestos Shoe Lining

Friction Coefficients

• The friction coefficient for rigid molded non-asbestos shoe lining ranges from 0.33 to 0.6, as referenced in Table 16-3 on page 854.

• This range indicates the variability and challenges in determining precise friction values during design processes.

Design Considerations

• When designing braking systems, it's crucial to consider worst-case scenarios, particularly the maximum force required for effective braking torque.

• For calculations, using the lowest friction coefficient (0.33) is advisable to ensure safety margins are met.

Calculating Brake Shoe Angles

Determining Radius and Angles

• The radius (R) from the center of a brake drum with a 12-inch inner diameter is calculated as 6 inches.

• The angles defining the limits of the brake shoe (theta1 and theta2) need careful calculation based on geometric relationships involving offsets and vertical axes.

Angle Calculations

• Theta P is determined using inverse tangent calculations based on known rise and run values, yielding an angle of approximately 16.7 degrees.

• Consequently, theta1 is calculated as 38.3 degrees while theta2 becomes 138.3 degrees due to their defined spacing relationship of 100 degrees between them.

Utilizing Integrals for Brake Design

Integral Calculations

• To evaluate integrals necessary for design calculations, it’s recommended to use radian mode on calculators rather than degree mode to avoid errors in results when calculating sine functions over specified angles.

• An example integral from theta1 to theta2 yields a value of approximately 1.3642 after conversion into radians for accurate computation purposes.

Torque Ratios in Self-Energizing Shoes

Torque Relationships

• The ratio between torques T1 and T2 indicates that self-energizing shoes carry more than double the amount of torque compared to self-deenergizing shoes, which has significant implications for design efficiency and effectiveness in braking systems.

Solving Torque Equations

• By establishing relationships such as T2 = T1/2.44, designers can derive specific torque values needed for effective braking performance under various conditions leading up to a total torque requirement of around 300 foot-pounds when combined with other factors like pressure area (PA).

Final Steps in Braking Force Calculation

Finding Braking Force

• With established torque values (T1 = 212.8 ft-lbs; T2 = 87.2 ft-lbs), these can be plugged into equations governing braking force calculations alongside known parameters like width and radius derived earlier in discussions about brake shoe geometry and dynamics involved in actuation forces within hydraulic systems used in brakes.

Pressure Area Calculation

• After substituting known variables into relevant equations, PA emerges at approximately 140 psi which then allows further derivation of moments induced by frictional forces acting upon brake shoes leading towards final evaluations necessary for ensuring adequate stopping power across varying load conditions encountered during operation cycles.

Enhancing Brake Efficiency

Improving Braking Force

• A suggestion made involves configuring both brake shoes as self energizing mechanisms which could significantly enhance overall braking efficiency by equalizing actuation forces across both sides thereby simplifying calculations related directly back towards achieving desired performance metrics without excessive complexity introduced through differential setups typically seen otherwise.

Example Scenario

• In practical terms this adjustment led one scenario yielding an actuation force requirement reduced downwards towards roughly around 245 pounds showcasing how minor adjustments can lead substantial improvements within system designs aimed at maximizing operational efficacy while minimizing driver effort exerted during engagement phases throughout typical usage patterns observed regularly across varied vehicle types utilized today!