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Air Brake Design & Safety Straight Trucks

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Air Brake Design & Safety Straight Trucks SHORT PAPER PCB 2 – 2007a AIR BRAKE DESIGN & SAFETY PART ONE STRAIGHT TRUCKS Rudy Limpert, Ph.D. and Franco Gamero, BS & MS PC-BRAKE, Inc. www.pcbrakeinc.com 2007 Updated Version 12/2008 1 1.0. INTRODUCTION The update of this paper became necessary since straight truck PC-BRAKE AIR software programs discussed are now available free from our website. The changes made discuss effective use and certain limitations of the computer software. PC-BRAKE FACTOR (brake torque) and PC-BRAKE TEMPERATURE are also available free of charge. This paper presents our computer-based analysis of air brake system design and failure in accident causation. The beginning of the underlying research and computer modeling goes back to the early 1970s involving a truck/trailer braking study conducted at the University of Michigan (Re 1). The specific objectives are to show the effects of basic brake system design components on braking performance including brake lockup, friction utilization and tandem suspension dynamics, as well as to provide the computer software tools to analyze drum brake designs or brake factor, brake adjustment, defective or worn brake linings, brake temperature effects on brake adjustment and torque fade, and the inter-axle load transfer of the three commonly used tandem axle designs, namely air springs, walking beam, and leaf spring suspensions. Each brake can be analyzed individually in terms of brake components, brake factor, brake temperature fade, and tire-road friction utilization, that is, individual brake/wheel lockup. It is well known that friction utilization is a design certification requirement for manufacturers to achieve. On the other hand, it is the tool allowing prediction of individual brake lockup, that is, an accurate accident scene brake mark interpretation and brake accident causation analysis. An important element of wheel lockup is the dynamic normal load carried by each individual wheel during the braking process. Consequently, overall load transfer onto the front axle, as well as individual inter-tandem axle load-transfer as a function of vehicle deceleration has to be part of the systems analysis. The reader is reminded that a typical feature of the standard leaf spring tandem suspension is the significant decrease of dynamic axle load of the forward tandem axle during maximum decelerations. Under extreme conditions the axle may lift off the ground causing the theoretical traction coefficient to become infinite. Special provisions are made in the software to address this limiting condition, should it occur. 2.0. BASICS OF COMPUTER MODELING The fundamentals are extremely simple in terms of the algorithm (Re. 2 and 3). The brake line pressure is initialized let’s say starting at 5 psi increasing in steps of 10 psi until 115 psi. The brake line pressure at different axles may be changed by valves, such as limiting or proportioning valves in relationship to the pressure at the foot valve. The brake line pressure is used in the brake torque or braking force equation (Re. 2) under proper considerations of basic brake components, adjustments, and brake fade for each individual brake. The summation of all braking forces per braked wheel yields the 2 deceleration of the vehicle based on its weight. The deceleration computed for a particular brake line pressure is then used to compute the different dynamic axle loads for specified axle geometries and vehicle weight configurations. 2.1. COMPUTATION OF BRAKING FORCE The brake factor BF is defined by the ratio of total drum or rotor friction drag force Fd to the application force Fa of one shoe or pad. Stated differently, the brake factor is the drum or rotor friction drag force per one pound of shoe application force, that is, BF = Fd/Fa (1) Solving Equation for drum drag yields: Fd = Fa (BF); lb (2) Equation 2 is the fundamental relationship for computing the braking force of a brake, and hence, braking effectiveness of the brake system of a vehicle. The braking force produced by the brake at one wheel between one tire and roadway is computed by: Fx = (pl – p0) Ac (BF) ηm ρ fa fF (r/R); lb (3) 2 Where: Ac = Brake chamber size (area), in BF = Brake Factor of wheel brake fa = Push rod travel adjustment factor fF = Brake temperature fade adjustment factor pl = Brake line pressure at wheel brake, psi p0 = Push-out pressure, psi r = Drum or effective rotor radius, in. R = Tire radius, in. ηm = Mechanical efficiency of wheel brake ρ = Mechanical gain of brake apply mechanism The application force Fa against the tip of the brake shoe is from Equation 3: Fa = (pl – p0) Ac ηm ρ fa ; lb (4) The brake design engineer is mostly concerned with brake chamber size, brake factor (type of brake and lining or pad friction coefficient), brake line pressure (valves), and mechanical gain (cam radius and slack adjuster length). The accident reconstructionist, for a given brake system geometry, deals mostly with the adjustment factors and different lockup sequences which all are part of the software program. When brake lock occurs, the braking force at that wheel is computed by the product of dynamic normal force and tire-road friction coefficient. 3 2.1.1 PUSH ROD FORCE The push rod force of the brake chamber is computed by the product of (pl – p0) Ac. The brake chamber area is directly related to the size of the brake chamber. For example, a brake chamber Type 30 has a nominal diaphragm area of 30 in2 for a push rod travel less than the critical value Sc. Beyond the critical travel the diaphragm area decreases, and hence, the effective push rod force decreases accordingly. The following table provides guidelines for push rod travel. PUSH ROD TRAVELS and LIMITS Chamber Type Rated Travel Re-Adjust Travel Critical Travel (in2) (in) (in) (in) 9, 12 1.75 1.375 (1-3/8) 1.20 16, 20, 24 2.25 1.75 1.75 20L, 24L, 30 2.50 2.0 2.0 24L3, 30L3 3.0 2.5 2.5 36 3.0 2.25 2.25 For push rod travels less than the critical value the push rod force is approximately 90% of the average maximum force. The effective push rod travel Se for an S-cam brake is the travel that actually existed at the time of the accident or vehicle testing. For brakes, operating at an elevated temperature due to prior braking, the thermal expansion of the brake drum requires an increased push rod travel for the brake linings to contact the drum. If the brake adjustment measurements were obtained with hot brakes immediately after the accident, which is rarely the case, thermal drum expansion is included in the accident scene data collection. When push rod travel is measured for cold brakes, thermal expansion must be considered in the input data analysis. The straight-line idealization of the pushrod force, and hence, adjustment factor fa, as a function of pushrod travel is shown in Figure 1. All brake push rod travels used in the computer analysis are identified in Figure 1. The adjustment factor fa ranges between 0 for a completely ineffective brake due to excessive push rod travel (Seffective => Smax) to 1 for an effective push rod travel less than the critical one (Seffective =< Scritical). The temperature fade factor fF takes into consideration the decrease in lining-drum coefficient of friction, and hence, reduction of brake factor. It is based on published test results. The reader is reminded that in-stop fade of drum brakes may vary depending upon particular brake lining characteristics. Brake fading of truck disc brakes is generally not a significant issue in single stops from highway speeds. When designing a brake system for a truck, it may be wise to select the brake system components to match the brake factor of a wheel brake with a thoroughly “known” brake lining material exhibiting superior friction, wear, fade and noise characteristics. 4 2.1.2. BRAKE FACTOR The brake factor BF is defined by the ratio of total drum drag divided by the application force against the tip of one brake shoe. The brake factor equations for most drum brake designs are shown in Re.2. The typical S-cam brake is of the leading-trailing shoe design, however modified by the particular application force of the S-cam design (Re. 4). PC-BRAKE FACTOR software computes the brake factor of many different drum brake designs. Brake factor computer software input and out put diagrams are illustrated for a typical S-cam-brake design in Figures 2 and 3. The green line represents the total brake factor of the leading-trailing S-cam brake. For example, for a lining-drum friction coefficient of 0.35, the brake factor BF = 1.64. If a detailed inspection of the subject vehicle brake system would reveal that the leading shoe of a particular brake were excessively worn with metal rivets contacting the drum swept surface, then using 0.2 (instead of 0.35) for that shoe as illustrated in Figure 4 yields an effective brake factor of only 1.19 to be used in the braking analysis. Class 8 vehicles typically used two brake blocks per one shoe while smaller vehicles use a single brake lining per brake shoe. The nominal brake block or lining-to-drum friction coefficient is determined by SAE J661 test procedure. The specific friction class is designated by two letters where the first represents “cold” friction (200 deg F), the second “hot” friction (600 deg F). The following ranges exist: D: 0.150 to 0.250; E: 0.251 to 0.350; F: 0.351 to 0.450; G: 0.451 to 0.55o, and H > 0.550.
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